diff --git a/src/sage/libs/giac/auto-methods.pxi b/src/sage/libs/giac/auto-methods.pxi index 776900bcf4f..9af4c0023bf 100644 --- a/src/sage/libs/giac/auto-methods.pxi +++ b/src/sage/libs/giac/auto-methods.pxi @@ -14,10 +14,10 @@ cdef class GiacMethods_base: Help for Airy_Ai: Airy_Ai(Real) Returns the value of Ai the Airy function solution of w''-xw=0. Ai(x)=Ai(0)f(z)+Ai'(0)g(z)(f and g are taylor's series sol of w''-xw=0). - See also: 1/ Airy_Bi + See also: 1/ Airy_Bi Ex1:Airy_Ai(0) Ex2:Airy_Ai(1.5) - + ''' return GiacMethods['Airy_Ai'](self,*args) @@ -26,10 +26,10 @@ cdef class GiacMethods_base: Help for Airy_Bi: Airy_Bi(Real) Returns the value of Ai the Airy function solution of w''-xw=0. Bi(x)=sqrt(3)(Bi(0)f(z)-Bi'(0)g(z))(f and g are taylor's series sol of w''-xw=0). - See also: 1/ Airy_Ai + See also: 1/ Airy_Ai Ex1:Airy_Bi(1.5) Ex2:Airy_Bi(0) - + ''' return GiacMethods['Airy_Bi'](self,*args) @@ -38,9 +38,9 @@ cdef class GiacMethods_base: Help for Archive: Archive(SeqVar) Protects the variables given as argument in an archive file. - See also: 1/ Unarchiv 2/ archive 3/ unarchive + See also: 1/ Unarchiv 2/ archive 3/ unarchive Ex1:Archive(a,b) - + ''' return GiacMethods['Archive'](self,*args) @@ -49,10 +49,10 @@ cdef class GiacMethods_base: Help for BesselJ: BesselJ(Int(p),Real(x)) BesselJ(p,x) returns the Bessel function of the first kind Jp(x). - See also: 1/ besselJ 2/ BesselY 3/ besselY + See also: 1/ besselJ 2/ BesselY 3/ besselY Ex1:BesselJ(2,sqrt(2)) Ex2:BesselJ(-2,sqrt(2)) - + ''' return GiacMethods['BesselJ'](self,*args) @@ -61,10 +61,10 @@ cdef class GiacMethods_base: Help for BesselY: BesselY(Int(p),Real(x)) BesselY(p,x) returns the Bessel function of the second kind Yp(x). - See also: 1/ besselY 2/ BesselJ 3/ besselJ + See also: 1/ besselY 2/ BesselJ 3/ besselJ Ex1:BesselY(BesselJ(2,sqrt(2))) Ex2:BesselY(BesselJ(-2,sqrt(2))) - + ''' return GiacMethods['BesselY'](self,*args) @@ -73,12 +73,12 @@ cdef class GiacMethods_base: Help for Beta: Beta(Expr,Expr,[Expr],[1]) Beta(a,b)=int(t^(a-1)*(1-t)^(b-1),t=0..1), Beta(a,b,p)=int(t^(a-1)*(1-t)^(b-1),t=0..p), Beta(a,b,p,1)=Beta(a,b,p)/Beta(a,b).(Beta(x,y) returns Gamma(x)*Gamma(y)/Gamma(x+y)). - See also: 1/ Gamma 2/ igamma + See also: 1/ Gamma 2/ igamma Ex1:Beta(x,y) Ex2:Beta(3,2) Ex3:Beta(3,2,0.5) Ex4:Beta(3,2,0.5,1) - + ''' return GiacMethods['Beta'](self,*args) @@ -87,10 +87,10 @@ cdef class GiacMethods_base: Help for BlockDiagonal: BlockDiagonal(Lst(l)||Mtrx(A)) Returns either the diagonal matrix with diagonal l or the diagonal of A. - See also: 1/ identity 2/ diag + See also: 1/ identity 2/ diag Ex1:BlockDiagonal([[1,2],[3,4]]) Ex2:BlockDiagonal([1,2,3]) - + ''' return GiacMethods['BlockDiagonal'](self,*args) @@ -99,9 +99,9 @@ cdef class GiacMethods_base: Help for Ci: Ci(Expr) Cosine integral int(cos(t)/t,t=-inf..x). - See also: 1/ Ei 2/ Si 3/ Li + See also: 1/ Ei 2/ Si 3/ Li Ex1:Ci(1.0) - + ''' return GiacMethods['Ci'](self,*args) @@ -110,11 +110,11 @@ cdef class GiacMethods_base: Help for Circle: Circle(Real(xc),Real(yc),Real(r),[Intg(option)]) Draws the circle with center (xc,yc) and radius r (by default option=1 and option=0 is to remove this circle). - See also: 1/ circle + See also: 1/ circle Ex1:Circle(0,1,1) Ex2:Circle(0,1,1,0) Ex3:Circle(0,1,1,1) - + ''' return GiacMethods['Circle'](self,*args) @@ -123,9 +123,9 @@ cdef class GiacMethods_base: Help for Col: Col(NULL) Returns the index of the column of the lightened cell in the matrixwriter. - See also: 1/ Row + See also: 1/ Row Ex1:Col() - + ''' return GiacMethods['Col'](self,*args) @@ -134,9 +134,9 @@ cdef class GiacMethods_base: Help for CopyVar: CopyVar(Var(var1),Var(var2)) Copies the storage without evaluation of var1 into var2. - See also: 1/ + See also: 1/ Ex1:CopyVar(A,B) - + ''' return GiacMethods['CopyVar'](self,*args) @@ -145,11 +145,11 @@ cdef class GiacMethods_base: Help for Dirac: Dirac(Real) Function derivative of Heaviside. - See also: 1/ Heaviside + See also: 1/ Heaviside Ex1:Dirac(1) Ex2:Dirac(-1) Ex3: int(Dirac(x)*(x-1)^2,x,-1,2) - + ''' return GiacMethods['Dirac'](self,*args) @@ -158,9 +158,9 @@ cdef class GiacMethods_base: Help for Ei: Ei(Expr) Exponential integral int(exp(t)/t,t=-inf..x). - See also: 1/ Si 2/ Ci 3/ Li + See also: 1/ Si 2/ Ci 3/ Li Ex1:Ei(1.0) - + ''' return GiacMethods['Ei'](self,*args) @@ -169,10 +169,10 @@ cdef class GiacMethods_base: Help for Factor: Factor(Expr) Factors a polynomial without evaluation. - See also: 1/ factor 2/ ifactor 3/ normal + See also: 1/ factor 2/ ifactor 3/ normal Ex1:Factor(x^4-1) Ex2:Factor(x^4+12*x^3+54*x^2+108*x+81) - + ''' return GiacMethods['Factor'](self,*args) @@ -187,7 +187,7 @@ cdef class GiacMethods_base: Ex4:GF(2,w^8+w^7+w^5+w+1) Ex5:GF(2,8,['a','G']) Ex6: G:=GF(2,a^8+a^6+a^3+a^2+1,['a','G'],undef) - + ''' return GiacMethods['GF'](self,*args) @@ -196,12 +196,12 @@ cdef class GiacMethods_base: Help for Gamma: Gamma(Real(a),[Real(b)]) Calculates Gamma at a point a (Gamma(n+1)=n! for n integer) if a>0, Gamma(a)=int(e^{-t}*t^{a-1},t=0..inf)) and Gamma(a)=Gamma(a+1)/a and Gamma(a,b)=ugamma(a,b). - See also: 1/ Psi 2/ Beta 3/ ugamma 4/ igamma + See also: 1/ Psi 2/ Beta 3/ ugamma 4/ igamma Ex1:Gamma(5) Ex2:Gamma(1/2) Ex3:Gamma(gamma(-5.1)) Ex4:Gamma(-5.1,2.1) - + ''' return GiacMethods['Gamma'](self,*args) @@ -210,11 +210,11 @@ cdef class GiacMethods_base: Help for Heaviside: Heaviside(Real) Function equal to 0 if x<0 and 1 if x>=0. - See also: 1/ Dirac 2/ laplace + See also: 1/ Dirac 2/ laplace Ex1:Heaviside(1) Ex2:Heaviside(-1) Ex3:Heaviside(0) - + ''' return GiacMethods['Heaviside'](self,*args) @@ -223,9 +223,9 @@ cdef class GiacMethods_base: Help for JordanBlock: JordanBlock(Expr(a),Intg(n)) Returns an n*n matrix with a on the diagonal, 1 above and 0 everywhere else. - See also: 1/ jordan + See also: 1/ jordan Ex1:JordanBlock(7,3) - + ''' return GiacMethods['JordanBlock'](self,*args) @@ -234,10 +234,10 @@ cdef class GiacMethods_base: Help for LU: LU(Mtrx(A),Var(L),Var(U),Var(P)) For a numerical matrix A, stores in L a lower triangular matrix, in U an upper triangular matrix and in P a permutation matrix such that P*A=L*U. - See also: 1/ lu 2/ QR + See also: 1/ lu 2/ QR Ex1:LU([[1,2],[3,4]],L,U,P) Ex2:LU([[6,12,18],[5,14,31],[3,8,18]],L,U,P) - + ''' return GiacMethods['LU'](self,*args) @@ -249,7 +249,7 @@ cdef class GiacMethods_base: Ex1:LambertW(1.0) Ex2:LambertW(ln(4)) Ex3:LambertW(-0.1,-1) - + ''' return GiacMethods['LambertW'](self,*args) @@ -258,9 +258,9 @@ cdef class GiacMethods_base: Help for Li: Li(Expr) Logarithm integral Li(x)=Ei(ln(x)) primitive of 1/ln(x). - See also: 1/ Si 2/ Ci 3/ Ei + See also: 1/ Si 2/ Ci 3/ Ei Ex1:Li(2.0) - + ''' return GiacMethods['Li'](self,*args) @@ -269,9 +269,9 @@ cdef class GiacMethods_base: Help for Line: Line(Expr(a),Expr(b),Expr(c),Expr(d)) Draws the segment [a+i*b,c+i*d]. - See also: 1/ segment + See also: 1/ segment Ex1:Line(-1,-2,1,2) - + ''' return GiacMethods['Line'](self,*args) @@ -280,9 +280,9 @@ cdef class GiacMethods_base: Help for LineHorz: LineHorz(Expr(a)) Draws the horizontal line y=a. - See also: 1/ Line 2/ LineVert + See also: 1/ Line 2/ LineVert Ex1:LineHorz(-1) - + ''' return GiacMethods['LineHorz'](self,*args) @@ -291,13 +291,13 @@ cdef class GiacMethods_base: Help for LineTan: LineTan(Expr(f(x)),[Var],Expr(a)) Draws the tangent to y=f(x) at x=a. Do not use parentheses or put the parenthesis around the entire expression. - See also: 1/ tangent 2/ droite_tangente + See also: 1/ tangent 2/ droite_tangente Ex1: LineTan sin(x),pi/4 Ex2: LineTan sin(t),t=pi/4) Ex3: LineTan sin(t),t,pi/4 Ex4: LineTan x^2-x,1 Ex5: (LineTan sin(t),t,pi/4) - + ''' return GiacMethods['LineTan'](self,*args) @@ -306,9 +306,9 @@ cdef class GiacMethods_base: Help for LineVert: LineVert(Expr(a)) Draws the vertical line x=a. - See also: 1/ Line 2/ LineHorz + See also: 1/ Line 2/ LineHorz Ex1:LineVert(2) - + ''' return GiacMethods['LineVert'](self,*args) @@ -317,10 +317,10 @@ cdef class GiacMethods_base: Help for Phi: Phi(Intg(n)) Euler's function (euler(n)=card({p1 sum(1/n^a,n,1,+infinity). - See also: 1/ sum + See also: 1/ sum Ex1:Zeta(2) - + ''' return GiacMethods['Zeta'](self,*args) @@ -507,10 +507,10 @@ cdef class GiacMethods_base: Help for a2q: a2q(Mtrx,VectVar) a2q(A,X)=the quadratic form q associated to A, X=vector of variables. - See also: 1/ q2a + See also: 1/ q2a Ex1:a2q([[1,2],[4,4]],[x,y]) Ex2:a2q([[1,3],[3,4]],[x,y]) - + ''' return GiacMethods['a2q'](self,*args) @@ -519,13 +519,13 @@ cdef class GiacMethods_base: Help for abcuv: abcuv(Poly(a),Poly(b),Poly(c),[Var]) Returns [u,v] such that au+bv=c for 3 polynomials a,b,c. - See also: 1/ egcd 2/ iabcuv + See also: 1/ egcd 2/ iabcuv Ex1:abcuv(x^2+2*x+1,x^2-1,x+1) Ex2:abcuv(X^2+2*X+1,X^2-1,X+1,X) Ex3:abcuv(x^2+2*x+1,x^2-1,x^3+1) Ex4:abcuv(X^2+2*X+1,X^2-1,X^3+1,X) Ex5:abcuv([1,2,1],[1,0,-1],[1,0,0,1]) - + ''' return GiacMethods['abcuv'](self,*args) @@ -534,10 +534,10 @@ cdef class GiacMethods_base: Help for about: about(Var(a)) Returns the hypothesis made with assume on the variable a. - See also: 1/ assume 2/ purge + See also: 1/ assume 2/ purge Ex1:about(a) Ex2:about(n) - + ''' return GiacMethods['about'](self,*args) @@ -546,12 +546,12 @@ cdef class GiacMethods_base: Help for abs: abs(Cplx||LstCplx) Returns the absolute value or the norm of its argument. - See also: 1/ arg + See also: 1/ arg Ex1:abs(-4) Ex2:abs(1+2*i) Ex3:abs((1+2*i)^2) Ex4:abs([-2,1+i,-4]) - + ''' return GiacMethods['abs'](self,*args) @@ -560,12 +560,12 @@ cdef class GiacMethods_base: Help for abscissa: abscissa(Pnt or Vect) Returns the abscissa of a point or a vector. - See also: 1/ ordinate 2/ affix 3/ cote 4/ coordinates + See also: 1/ ordinate 2/ affix 3/ cote 4/ coordinates Ex1:abscissa(point(1+2*i)) Ex2:abscissa(point(i)-point(1+2*i)) Ex3:abscissa(-1-i) Ex4:abscissa(point(1,2,3)) - + ''' return GiacMethods['abscissa'](self,*args) @@ -574,9 +574,9 @@ cdef class GiacMethods_base: Help for accumulate_head_tail: accumulate_head_tail(Lst(l),Intg(p),Intg(q)) Returns the list where the first p and the last q elements of l are replaced by their sum. - See also: 1/ + See also: 1/ Ex1:accumulate_head_tail([0,1,2,3,4,5,6,7,8,9],3,2) - + ''' return GiacMethods['accumulate_head_tail'](self,*args) @@ -585,9 +585,9 @@ cdef class GiacMethods_base: Help for acos: acos(Expr) Arccosine. - See also: 1/ cos 2/ acosh + See also: 1/ cos 2/ acosh Ex1:acos(0) - + ''' return GiacMethods['acos'](self,*args) @@ -596,10 +596,10 @@ cdef class GiacMethods_base: Help for acos2asin: acos2asin(Expr) Replaces arccos(x) by pi/2-arcsin(x) in the argument. - See also: 1/ acos2atan + See also: 1/ acos2atan Ex1:acos2asin(acos(x)+asin(x)) Ex2:acos2asin(2*acos(x)) - + ''' return GiacMethods['acos2asin'](self,*args) @@ -608,10 +608,10 @@ cdef class GiacMethods_base: Help for acos2atan: acos2atan(Expr) Replaces arccos(x) by pi/2-arctan(x/sqrt(1-x^2)) in the argument. - See also: 1/ acos2asin + See also: 1/ acos2asin Ex1:acos2atan(2*acos(x)) Ex2:acos2atan(acos(sqrt(1-x^2))+acos(x)) - + ''' return GiacMethods['acos2atan'](self,*args) @@ -620,9 +620,9 @@ cdef class GiacMethods_base: Help for acosh: acosh(Expr) Hyperbolic arccosine. - See also: 1/ cosh 2/ acos + See also: 1/ cosh 2/ acos Ex1:acosh(1) - + ''' return GiacMethods['acosh'](self,*args) @@ -631,9 +631,9 @@ cdef class GiacMethods_base: Help for acot: acot(Expr) Arccotangent. - See also: 1/ atan 2/ arccos + See also: 1/ atan 2/ arccos Ex1:acot(0) - + ''' return GiacMethods['acot'](self,*args) @@ -642,10 +642,10 @@ cdef class GiacMethods_base: Help for acsc: acsc(Expr) Arccosecant: acsc(x)=asin(1/x). - See also: 1/ asin 2/ csc + See also: 1/ asin 2/ csc Ex1:acsc(1) Ex2:acsc(2) - + ''' return GiacMethods['acsc'](self,*args) @@ -654,8 +654,8 @@ cdef class GiacMethods_base: Help for acyclic: acyclic(Opt) Option for the random_network command. - See also: 1/ random_network - + See also: 1/ random_network + ''' return GiacMethods['acyclic'](self,*args) @@ -664,7 +664,7 @@ cdef class GiacMethods_base: Help for add: add(Expr,Var,VarMin(a),VarMax(b),[VarStep(p)]) Discrete sum (with 2 or 4 arguments return then sum from a to b if a<=b or of the opposite of the sum from b+1 to a-1 if a>b+1 or 0 if a=b+1) or the discrete primitive or sum of the elements of a list or a sequence. - See also: 1/ + + See also: 1/ + Ex1:add(1/n^2,n,1,17) Ex2:add(1/n^2,n=1..17) Ex3:add(1/n^2,n,17,1) @@ -675,7 +675,7 @@ cdef class GiacMethods_base: Ex8:add([[1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9]]) Ex9:add(1/(x*(x+1)),x) Ex10:add(cos(n*x),n) - + ''' return GiacMethods['add'](self,*args) @@ -684,9 +684,9 @@ cdef class GiacMethods_base: Help for add_arc: add_arc(Graph(G),Edge(e)||Trail(T)||Lst(E)) Returns a modified copy of digraph G with added arc e (or trail T or list of arcs E). - See also: 1/ add_edge 2/ delete_arc 3/ digraph 4/ edges 5/ has_arc 6/ trail + See also: 1/ add_edge 2/ delete_arc 3/ digraph 4/ edges 5/ has_arc 6/ trail Ex1:add_arc(digraph(trail(1,2,3,4,5,1)),[[1,3],[2,4]]) - + ''' return GiacMethods['add_arc'](self,*args) @@ -695,9 +695,9 @@ cdef class GiacMethods_base: Help for add_edge: add_edge(Graph(G),Edge(e)||Trail(T)||Lst(E)) Returns a modified copy of undirected graph G with added edge e (or trail T or list of edges E). - See also: 1/ add_arc 2/ delete_edge 3/ edges 4/ graph 5/ has_edge 6/ trail + See also: 1/ add_arc 2/ delete_edge 3/ edges 4/ graph 5/ has_edge 6/ trail Ex1:add_edge(graph(trail(1,2,3,4)),[4,1]) - + ''' return GiacMethods['add_edge'](self,*args) @@ -706,9 +706,9 @@ cdef class GiacMethods_base: Help for add_vertex: add_vertex(Graph(G),Vrtx(v)||Lst(V)) Returns a modified copy of G with added vertex v [or vertices from list V]. - See also: 1/ add_arc 2/ add_edge 3/ delete_vertex + See also: 1/ add_arc 2/ add_edge 3/ delete_vertex Ex1:add_vertex(cycle_graph(5),["a","b"]) - + ''' return GiacMethods['add_vertex'](self,*args) @@ -717,10 +717,10 @@ cdef class GiacMethods_base: Help for additionally: additionally(Expr) Makes an additionally assumption on a variable. - See also: 1/ purge 2/ about 3/ assume + See also: 1/ purge 2/ about 3/ assume Ex1: assume(n,integer);additionally(n>5) Ex2: assume(n,integer);assume(n>=2,additionally) - + ''' return GiacMethods['additionally'](self,*args) @@ -729,9 +729,9 @@ cdef class GiacMethods_base: Help for addtable: addtable(fourier||laplace,f(x),F(s),Var(x),Var(s)) Stores an unknown Fourier/Laplace transform pair (f,F). - See also: 1/ fourier 2/ laplace + See also: 1/ fourier 2/ laplace Ex1:addtable(fourier,y(x),Y(s),x,s) - + ''' return GiacMethods['addtable'](self,*args) @@ -740,9 +740,9 @@ cdef class GiacMethods_base: Help for adjacency_matrix: adjacency_matrix(Graph(G)) Returns the adjacency matrix of G (rows and columns are indexed by the vertices). - See also: 1/ neighbors + See also: 1/ neighbors Ex1:adjacency_matrix(graph(trail(1,2,3,4,2,5,1,3))) - + ''' return GiacMethods['adjacency_matrix'](self,*args) @@ -751,9 +751,9 @@ cdef class GiacMethods_base: Help for adjoint_matrix: adjoint_matrix(Mtrx) Returns the characteristic polynomial of A and the comatrix of A-xI. - See also: 1/ pcar + See also: 1/ pcar Ex1:adjoint_matrix([[1,i],[2,3]]) - + ''' return GiacMethods['adjoint_matrix'](self,*args) @@ -762,11 +762,11 @@ cdef class GiacMethods_base: Help for affix: affix(Pnt||Vect) Complex number equal to the affix of a point or of a vector. - See also: 1/ point 2/ vector + See also: 1/ point 2/ vector Ex1:affix(point(i)) Ex2:affix(point(i)-point(1+2*i)) Ex3:affix([1,2]) - + ''' return GiacMethods['affix'](self,*args) @@ -775,11 +775,11 @@ cdef class GiacMethods_base: Help for algsubs: algsubs(Equal(Xpr1=Xpr2),Expr(Xpr)) Substitutes in the expression Xpr, the algebraic expression Xpr1 by the algebraic expression Xpr2. - See also: 1/ subst 2/ subs + See also: 1/ subst 2/ subs Ex1:algsubs(x^2=u,1+x^2+x^4) Ex2:algsubs(a*b/c=d, 2*a*b^2/c) Ex3:algsubs(2a=p^2-q^2,algsubs(2c=p^2+q^2,c^2-a^2)) - + ''' return GiacMethods['algsubs'](self,*args) @@ -788,9 +788,9 @@ cdef class GiacMethods_base: Help for algvar: algvar(Expr) List of the variables by ascending algebraic extension order. - See also: 1/ lvar 2/ lname + See also: 1/ lvar 2/ lname Ex1:algvar(sqrt(x)+y) - + ''' return GiacMethods['algvar'](self,*args) @@ -799,10 +799,10 @@ cdef class GiacMethods_base: Help for all_trig_solutions: all_trig_solutions(:=Intg(0 or 1)) Pseudo-variable to return the general solution (all_trig_solutions:=1) or principal solution (all_trig_solutions:=0). - See also: 1/ cas_setup + See also: 1/ cas_setup Ex1: all_trig_solutions:=1 Ex2: all_trig_solutions:=0 - + ''' return GiacMethods['all_trig_solutions'](self,*args) @@ -811,9 +811,9 @@ cdef class GiacMethods_base: Help for allpairs_distance: allpairs_distance(Graph(G)) Returns a square matrix D of order equal to the number of vertices in G such that D(i,j) is the distance between i-th and j-th vertex of the (weighted) graph G. - See also: 1/ dijkstra 2/ graph_diameter 3/ vertex_distance + See also: 1/ dijkstra 2/ graph_diameter 3/ vertex_distance Ex1:allpairs_distance(graph(%{[1,2],[1,3],[1,4],[1,5],[2,3],[3,4],[4,5],[5,2]%})) - + ''' return GiacMethods['allpairs_distance'](self,*args) @@ -822,9 +822,9 @@ cdef class GiacMethods_base: Help for alog10: alog10(Expr) Function x->10^x. - See also: 1/ log10 + See also: 1/ log10 Ex1:alog10(3) - + ''' return GiacMethods['alog10'](self,*args) @@ -833,9 +833,9 @@ cdef class GiacMethods_base: Help for altitude: altitude((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) altitude(A,B,C) draws the altitude through A of the triangle ABC. - See also: 1/ perpendicular 2/ orthogonal 3/ orthocenter 4/ common_perpendicular + See also: 1/ perpendicular 2/ orthogonal 3/ orthocenter 4/ common_perpendicular Ex1:altitude(-1,1-i,i) - + ''' return GiacMethods['altitude'](self,*args) @@ -844,13 +844,13 @@ cdef class GiacMethods_base: Help for angle: angle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) angle(A,B,C) is the value of the measure of the angle (AB,AC). - See also: 1/ triangle 2/ bissector 3/ legend 4/ labels 5/ angleat 6/ angleatraw + See also: 1/ triangle 2/ bissector 3/ legend 4/ labels 5/ angleat 6/ angleatraw Ex1:angle(point(0),point(i),point(1)) Ex2:angle(0,1,i) Ex3:angle(0,1,i,"") Ex4:angle(0,1,i,"a") Ex5:angle(i,1,1+i,"b") - + ''' return GiacMethods['angle'](self,*args) @@ -859,10 +859,10 @@ cdef class GiacMethods_base: Help for angle_radian: angle_radian(:=Intg(0 or 1)) Pseudo-variable to work with radians (angle_radian:=1) or degrees (angle_radian:=0). - See also: 1/ cas_setup + See also: 1/ cas_setup Ex1: angle_radian:=1 Ex2: angle_radian:=0 - + ''' return GiacMethods['angle_radian'](self,*args) @@ -871,9 +871,9 @@ cdef class GiacMethods_base: Help for angleat: angleat(Pnt(A),Pnt(B),Pnt(C),(Pnt or Cplx(z0))) angleat(A,B,C,z0) displays at point(z0) with a legend, the value of the measure of the angle (AB,AC). - See also: 1/ angle 2/ angleatraw 3/ legend + See also: 1/ angle 2/ angleatraw 3/ legend Ex1: A:=point(0);B:=point(1);C:=point(i);angleat(A,B,C,-2-i) - + ''' return GiacMethods['angleat'](self,*args) @@ -882,9 +882,9 @@ cdef class GiacMethods_base: Help for angleatraw: angleatraw(Pnt(A)),Pnt(B),Pnt(C),(Pnt or Cplx(z0))) angleatraw(A,B,C,z0) displays at point(z0), the value of the measure of the angle (AB,AC). - See also: 1/ angle 2/ angleat + See also: 1/ angle 2/ angleat Ex1: A:=point(0);B:=point(1);C:=point(i);angleatraw(A,B,C,-2-i) - + ''' return GiacMethods['angleatraw'](self,*args) @@ -893,11 +893,11 @@ cdef class GiacMethods_base: Help for ans: ans(Intg(n)) Returns the (n+1)th answer of the command history if n>=0 or, the (-n)th previous answer if n<0 (by default n=-1 for the previous answer). - See also: 1/ quest + See also: 1/ quest Ex1:ans() Ex2:ans(2) Ex3:ans(-2) - + ''' return GiacMethods['ans'](self,*args) @@ -906,9 +906,9 @@ cdef class GiacMethods_base: Help for antiprism_graph: antiprism_graph(Intg(n)) Returns the antiprism graph of order n. - See also: 1/ prism_graph + See also: 1/ prism_graph Ex1:antiprism_graph(5) - + ''' return GiacMethods['antiprism_graph'](self,*args) @@ -917,14 +917,14 @@ cdef class GiacMethods_base: Help for append: append((Lst||Set||Str(L),Elem)) Append an element to a set or at the end of a list or of a string (L:=append(L,a) or L.append(a)). - See also: 1/ concat 2/ prepend + See also: 1/ concat 2/ prepend Ex1:append([1,2,4],6) Ex2:append(%{1,2,4%},6) Ex3: L:=[1,2,4];L:=append(L,6) Ex4: L:=[1,2,4];L.append(6) Ex5: S:=set[1,2,4];S:=append(S,6) Ex6: S:=set[1,2,4];S.append(6) - + ''' return GiacMethods['append'](self,*args) @@ -933,10 +933,10 @@ cdef class GiacMethods_base: Help for apply: apply(Fnc(f),Lst(l)) Applies the function f at the elements of the list l (option matrix for a matrix). - See also: 1/ map 2/ unapply 3/ matrix + See also: 1/ map 2/ unapply 3/ matrix Ex1:apply(x->x^3,[1,2,3]) Ex2:apply(x->x+1,[[1,2,3],[1,2,3]],matrix) - + ''' return GiacMethods['apply'](self,*args) @@ -945,14 +945,14 @@ cdef class GiacMethods_base: Help for approx: approx(Expr,[Int]) Numerical evaluation of the first argument (we can give the number of digits as second argument). - See also: 1/ evalb 2/ eval + See also: 1/ evalb 2/ eval Ex1:approx(2/3) Ex2:approx(2/3,2) Ex3:approx(2*sin(1)) Ex4:approx(2*sin(1),40) Ex5:approx(sqrt(2)+pi) Ex6:approx(sqrt(2)+pi,30) - + ''' return GiacMethods['approx'](self,*args) @@ -961,12 +961,12 @@ cdef class GiacMethods_base: Help for arc: arc(Pnt, Pnt, Real,[Var(C)],[Var(r)],[Opt(segment)]) Draws a circular arc given by 2 vertices and the central angle [Xcas will put the center in C and the radius in r]. - See also: 1/ circle 2/ segment 3/ plotparam + See also: 1/ circle 2/ segment 3/ plotparam Ex1:arc(0,1,pi/4) Ex2:arc(i,1,pi/4,C,r) Ex3:arc(i,1,pi/4,segment) Ex4:arc(i,1,pi/4,segment,affichage=1+rempli) - + ''' return GiacMethods['arc'](self,*args) @@ -975,11 +975,11 @@ cdef class GiacMethods_base: Help for arcLen: arcLen(Expr(Xpr) or Lst([Xpr1,Xpr2]),Var,Real(a),Real(b)) Returns the length of the arc of the curve defined by y=Xpr(or by x=Xpr1,y=Xpr2) when the parameter values are between a and b. - See also: 1/ int + See also: 1/ int Ex1:arcLen(t^2,t,1,2) Ex2:arcLen([t,t^2],t,1,2) Ex3:arcLen([cos(t),sin(t)],t,1,2) - + ''' return GiacMethods['arcLen'](self,*args) @@ -988,9 +988,9 @@ cdef class GiacMethods_base: Help for arccos: arccos(Expr) Arccosine. - See also: 1/ cos 2/ acosh + See also: 1/ cos 2/ acosh Ex1:arccos(0) - + ''' return GiacMethods['arccos'](self,*args) @@ -999,9 +999,9 @@ cdef class GiacMethods_base: Help for arccosh: arccosh(Expr) Hyperbolic arccosine. - See also: 1/ cosh 2/ acos + See also: 1/ cosh 2/ acos Ex1:arccosh(1) - + ''' return GiacMethods['arccosh'](self,*args) @@ -1010,11 +1010,11 @@ cdef class GiacMethods_base: Help for arclen: arclen(Expr(Xpr) or Lst([Xpr1,Xpr2]),Var,Real(a),Real(b)) Returns the length of the arc of the curve defined by y=Xpr(or by x=Xpr1,y=Xpr2) when the parameter values are between a and b. - See also: 1/ int + See also: 1/ int Ex1:arclen(t^2,t,1,2) Ex2:arclen([t,t^2],t,1,2) Ex3:arclen([cos(t),sin(t)],t,1,2) - + ''' return GiacMethods['arclen'](self,*args) @@ -1023,9 +1023,9 @@ cdef class GiacMethods_base: Help for arcsin: arcsin(Expr) Arcsine. - See also: 1/ sin + See also: 1/ sin Ex1:arcsin(0) - + ''' return GiacMethods['arcsin'](self,*args) @@ -1034,9 +1034,9 @@ cdef class GiacMethods_base: Help for arcsinh: arcsinh(Expr) Hyperbolic arcsine. - See also: 1/ sinh 2/ asin + See also: 1/ sinh 2/ asin Ex1:arcsinh(0) - + ''' return GiacMethods['arcsinh'](self,*args) @@ -1045,9 +1045,9 @@ cdef class GiacMethods_base: Help for arctan: arctan(Expr) Arctangent. - See also: 1/ tan 2/ atanh + See also: 1/ tan 2/ atanh Ex1:arctan(0) - + ''' return GiacMethods['arctan'](self,*args) @@ -1056,9 +1056,9 @@ cdef class GiacMethods_base: Help for arctanh: arctanh(Expr) Hyperbolic arctangent. - See also: 1/ atan 2/ tanh + See also: 1/ atan 2/ tanh Ex1:arctanh(0) - + ''' return GiacMethods['arctanh'](self,*args) @@ -1067,7 +1067,7 @@ cdef class GiacMethods_base: Help for area: area(Polygone || Expr,x=a..b,[n],[Method]) Algebraic area of a circle, a circular arc or of a (star) polygon (e.g. triangle, square, ...) or of the area below a curve, optionally with a quadrature method (trapezoid,left_rectangle,right_rectangle,middle_point,simpson,rombergt,rombergm). - See also: 1/ trapezoid 2/ perimeter 3/ areaatraw 4/ areaat 5/ areaplot + See also: 1/ trapezoid 2/ perimeter 3/ areaatraw 4/ areaat 5/ areaplot Ex1:area(triangle(0,1,i)) Ex2:area(square(0,2)) Ex3:area(circle(0,2)) @@ -1075,7 +1075,7 @@ cdef class GiacMethods_base: Ex5:area(x^2,x=0..1,5,trapezoid) Ex6:area(x^2,x=0..1,5,simpson) Ex7:area(x^2,x=0..1,5,rombergm) - + ''' return GiacMethods['area'](self,*args) @@ -1084,13 +1084,13 @@ cdef class GiacMethods_base: Help for areaat: areaat(Polygone, Pnt||Cplx(z0)) Displays at point(z0), with a legend, the algebraic area of a circle or of a (star) polygon (e.g. triangle, square, ...) - See also: 1/ area 2/ areaatraw 3/ polygon 4/ perimeteratraw 5/ areaplot + See also: 1/ area 2/ areaatraw 3/ polygon 4/ perimeteratraw 5/ areaplot Ex1: t:=triangle(0,1,i);areaat(t,(1+i)/2) Ex2: c:=square(0,2);areaat(c,1+i) Ex3: c2:=circle(0,2);areaat(c2,1+i) Ex4: p:=polygon(0,1,i);areaat(p,1+i) Ex5: A:=point(0);B:=point(1+i);c:=carre(A,B);areaat(c,i) - + ''' return GiacMethods['areaat'](self,*args) @@ -1099,13 +1099,13 @@ cdef class GiacMethods_base: Help for areaatraw: areaatraw(Polygone, Pnt||Cplx(z0)) Displays at point(z0), the algebraic area of a circle or of a (star-)polygon (e.g. triangle, square, ...) - See also: 1/ area 2/ areaat 3/ polygon 4/ perimeteratraw 5/ areaplot + See also: 1/ area 2/ areaat 3/ polygon 4/ perimeteratraw 5/ areaplot Ex1:areaatraw(triangle(0,1,i),(1+i)/2) Ex2:areaatraw(square(0,2),1+i) Ex3:areaatraw(circle(0,2),1+i) Ex4:areaatraw(polygon(0,1,i),1+i) Ex5: A:=point(0);B:=point(1+i);c:=carre(A,B);areaatraw(c,i) - + ''' return GiacMethods['areaatraw'](self,*args) @@ -1114,11 +1114,11 @@ cdef class GiacMethods_base: Help for areaplot: areaplot(Expr,x=a..b,[n],[Method]) Displays the area below a curve, optionally with a quadrature method (trapezoid,left_rectangle,right_rectangle,middle_point). - See also: 1/ integrate 2/ plot 3/ area 4/ areaat 5/ areaatraw + See also: 1/ integrate 2/ plot 3/ area 4/ areaat 5/ areaatraw Ex1:areaplot(sin(x),x=0..pi) Ex2:areaplot(x^2,x=0..1,5,trapezoid) Ex3:areaplot(x^2,x=0..1,5,middle_point) - + ''' return GiacMethods['areaplot'](self,*args) @@ -1127,11 +1127,11 @@ cdef class GiacMethods_base: Help for arg: arg(Expr) Returns the argument of a complex number. - See also: 1/ abs + See also: 1/ abs Ex1:arg(1+i) Ex2:arg(1+2*i) Ex3:arg((1+2*i)^2) - + ''' return GiacMethods['arg'](self,*args) @@ -1140,10 +1140,10 @@ cdef class GiacMethods_base: Help for array: array(Opt) Option for convert for definitions of sparse matrices. - See also: 1/ convert 2/ table + See also: 1/ convert 2/ table Ex1: A[0..2,0..2]:=1;A[0..1,1..2]:=2;convert(A,array) Ex2: B[0..1,1..2]:=1;B[2,2]:=2;convert(B,array) - + ''' return GiacMethods['array'](self,*args) @@ -1152,9 +1152,9 @@ cdef class GiacMethods_base: Help for arrivals: arrivals(Graph(G),[Vrtx(v)]) Returns the list of vertices in digraph G which are connected by v with arcs such that heads are in v. If v is omitted, a list of arrivals is computed for every vertex in G. - See also: 1/ in_degree + See also: 1/ in_degree Ex1:arrivals(digraph(%{[1,2],[1,3],[2,3]%}),1) - + ''' return GiacMethods['arrivals'](self,*args) @@ -1163,10 +1163,10 @@ cdef class GiacMethods_base: Help for articulation_points: articulation_points(Graph(G)) Returns the list of articulation points (cut vertices) of G. - See also: 1/ biconnected_components 2/ is_biconnected 3/ is_connected 4/ is_triconnected + See also: 1/ biconnected_components 2/ is_biconnected 3/ is_connected 4/ is_triconnected Ex1:articulation_points(path_graph(5)) Ex2:articulation_points(cycle_graph(5)) - + ''' return GiacMethods['articulation_points'](self,*args) @@ -1175,9 +1175,9 @@ cdef class GiacMethods_base: Help for asin: asin(Expr) Arcsine. - See also: 1/ sin + See also: 1/ sin Ex1:asin(0) - + ''' return GiacMethods['asin'](self,*args) @@ -1186,10 +1186,10 @@ cdef class GiacMethods_base: Help for asin2acos: asin2acos(Expr) Replaces arcsin(x) by pi/2-arccos(x) in the argument. - See also: 1/ asin2atan + See also: 1/ asin2atan Ex1:asin2acos(acos(x)+asin(x)) Ex2:asin2acos(2*asin(x)) - + ''' return GiacMethods['asin2acos'](self,*args) @@ -1198,10 +1198,10 @@ cdef class GiacMethods_base: Help for asin2atan: asin2atan(Expr) Replaces arcsin(x) by arctan(x/sqrt(1-x^2)) in the argument. - See also: 1/ asin2acos + See also: 1/ asin2acos Ex1:asin2atan(2*asin(x)) Ex2:asin2atan(asin(sqrt(1-x^2))+asin(x)) - + ''' return GiacMethods['asin2atan'](self,*args) @@ -1210,9 +1210,9 @@ cdef class GiacMethods_base: Help for asinh: asinh(Expr) Hyperbolic arcsine. - See also: 1/ sinh 2/ asin + See also: 1/ sinh 2/ asin Ex1:asinh(0) - + ''' return GiacMethods['asinh'](self,*args) @@ -1221,10 +1221,10 @@ cdef class GiacMethods_base: Help for assign_edge_weights: assign_edge_weights(Graph(G),Seq(m,n)||Intrv(a..b)) Assigns random edge weights to the edges of G and returns a modified copy of G. If integers n and m such that n>=m are specified, weights are integers randomly chosen in [m,n]. If an interval a..b is specified, weights are uniformly distributed in the interval [a,b). - See also: 1/ set_edge_weight 2/ get_edge_weight 3/ weight_matrix 4/ random_digraph 5/ random_tournament + See also: 1/ set_edge_weight 2/ get_edge_weight 3/ weight_matrix 4/ random_digraph 5/ random_tournament Ex1:assign_edge_weights(digraph(trail(1,2,3,4,1)),1,9) Ex2:assign_edge_weights(digraph(trail(1,2,3,4,1)),0..1) - + ''' return GiacMethods['assign_edge_weights'](self,*args) @@ -1233,7 +1233,7 @@ cdef class GiacMethods_base: Help for assume: assume(Expr) Makes an assumption on a variable. - See also: 1/ purge 2/ about 3/ additionally + See also: 1/ purge 2/ about 3/ additionally Ex1:assume(a>0) Ex2:assume(a=0.3) Ex3:assume(a:=[pi/4,0,pi/2]) @@ -1244,7 +1244,7 @@ cdef class GiacMethods_base: Ex8:assume((a>=2 and a<4) or a>6) Ex9:assume(a>=2);additionally(a<6) Ex10:assume(a) - + ''' return GiacMethods['assume'](self,*args) @@ -1253,10 +1253,10 @@ cdef class GiacMethods_base: Help for at: at(Lst(l)||Mtrx(m),Index(j)||Lst([j,k])) at(l,j) (or at(m,[j,k])) is the element of the list l (or matrix m) for index=j (or for index j,k). - See also: 1/ of + See also: 1/ of Ex1:at([10,11,12],1) Ex2:at([[1,2],[3,4]],[1,0]) - + ''' return GiacMethods['at'](self,*args) @@ -1265,9 +1265,9 @@ cdef class GiacMethods_base: Help for atan: atan(Expr) Arctangent. - See also: 1/ tan 2/ atanh + See also: 1/ tan 2/ atanh Ex1:atan(0) - + ''' return GiacMethods['atan'](self,*args) @@ -1276,8 +1276,8 @@ cdef class GiacMethods_base: Help for atan2acos: atan2acos(Expr) Replaces arctan(x) by pi/2-arccos(x/sqrt(1+x^2)) in the argument. - See also: 1/ atan2acos(atan(x)) - + See also: 1/ atan2acos(atan(x)) + ''' return GiacMethods['atan2acos'](self,*args) @@ -1286,8 +1286,8 @@ cdef class GiacMethods_base: Help for atan2asin: atan2asin(Expr) Replaces arctan(x) by arcsin(x/sqrt(1+x^2)) in the argument. - See also: 1/ atan2asin(atan(x)) - + See also: 1/ atan2asin(atan(x)) + ''' return GiacMethods['atan2asin'](self,*args) @@ -1296,9 +1296,9 @@ cdef class GiacMethods_base: Help for atanh: atanh(Expr) Hyperbolic arctangent. - See also: 1/ atan 2/ tanh + See also: 1/ atan 2/ tanh Ex1:atanh(0) - + ''' return GiacMethods['atanh'](self,*args) @@ -1307,11 +1307,11 @@ cdef class GiacMethods_base: Help for atrig2ln: atrig2ln(Expr) Rewrites the expression containing inverse trigonometric functions into logarithmic functions. - See also: 1/ trig2exp 2/ exp2trig + See also: 1/ trig2exp 2/ exp2trig Ex1:atrig2ln(atan(x)) Ex2:atrig2ln(asin(x)) Ex3:atrig2ln(acos(x)) - + ''' return GiacMethods['atrig2ln'](self,*args) @@ -1320,13 +1320,13 @@ cdef class GiacMethods_base: Help for augment: augment(Lst,Lst||Seq,Seq||Str,Str||Mtrx,Mtrx) Concatenates two lists or two strings or two sequences or 2 matrices; L:=concat(L,L1) or L.concat(L1). - See also: 1/ append 2/ cat 3/ semi_augment 4/ border 5/ + + See also: 1/ append 2/ cat 3/ semi_augment 4/ border 5/ + Ex1:augment([1,2],[3,4,5]) Ex2:augment("bon","jour") Ex3:augment([[1,2],[3,4]],[[4,5,6],[6,7,8]]) Ex4: L:=[1,2];L.concat([3,4,5]) Ex5: S:="abcd";S.concat("efghi") - + ''' return GiacMethods['augment'](self,*args) @@ -1335,9 +1335,9 @@ cdef class GiacMethods_base: Help for auto_correlation: auto_correlation(Lst) Returns the cross-correlation of the given signal with itself. - See also: 1/ cross_correlation 2/ correlation + See also: 1/ cross_correlation 2/ correlation Ex1:auto_correlation([1,-1,0,2,1]) - + ''' return GiacMethods['auto_correlation'](self,*args) @@ -1346,14 +1346,14 @@ cdef class GiacMethods_base: Help for autosimplify: autosimplify(Cmds) The argument is a command that Xcas will use to rewrite answers (initial value is regroup and for no simplification it is nop or 0). - See also: 1/ simplify 2/ factor 3/ regroup + See also: 1/ simplify 2/ factor 3/ regroup Ex1:autosimplify(nop) Ex2:autosimplify(0) Ex3:autosimplify(regroup) Ex4:autosimplify(1) Ex5:autosimplify(factor) Ex6:autosimplify(simplify) - + ''' return GiacMethods['autosimplify'](self,*args) @@ -1362,10 +1362,10 @@ cdef class GiacMethods_base: Help for avance: avance(NULL or Real(n)) The turtle takes n steps forward (by default n=10). - See also: 1/ recule 2/ saute + See also: 1/ recule 2/ saute Ex1: avance 30 Ex2:avance(30) - + ''' return GiacMethods['avance'](self,*args) @@ -1374,11 +1374,11 @@ cdef class GiacMethods_base: Help for avgRC: avgRC(Expr(Xpr),Var(Var),[Real(h)]) Returns (Xpr(var+h)-Xpr(Var))/h (by default h=0.001). - See also: 1/ nDeriv + See also: 1/ nDeriv Ex1:avgRC(f(x),x,h) Ex2:avgRC(x^2,x,0.1) Ex3:avgRC(x^2,x) - + ''' return GiacMethods['avgRC'](self,*args) @@ -1387,10 +1387,10 @@ cdef class GiacMethods_base: Help for axes: axes(Opt) Global option (Maple compatibility) of a graphic command to put or not the axes. - See also: 1/ line_width 2/ gl_showaxes 3/ switch_axes + See also: 1/ line_width 2/ gl_showaxes 3/ switch_axes Ex1: axes=0;segment(0,point(1,1)) Ex2: axes=1;segment(0,point(1,1),epaisseur=5) - + ''' return GiacMethods['axes'](self,*args) @@ -1400,7 +1400,7 @@ cdef class GiacMethods_base: axis(xmin,xmax,ymin,ymax,[zmin,zmaz]) Defines the graphic display Ex1:axis(-2,4,-1,6) - + ''' return GiacMethods['axis'](self,*args) @@ -1409,11 +1409,11 @@ cdef class GiacMethods_base: Help for back: back(Vect or Seq or Str) Returns the last element of a vector or a sequence or a string. - See also: 1/ inter 2/ head 3/ mid 4/ left 5/ right + See also: 1/ inter 2/ head 3/ mid 4/ left 5/ right Ex1:back(1,2,3) Ex2:back([1,2,3]) Ex3:back("bonjour") - + ''' return GiacMethods['back'](self,*args) @@ -1422,10 +1422,10 @@ cdef class GiacMethods_base: Help for backward: backward(NULL or Real(n)) The turtle takes n steps back (by default n=10). - See also: 1/ avance 2/ saute + See also: 1/ avance 2/ saute Ex1: recule 30 Ex2:backward(30) - + ''' return GiacMethods['backward'](self,*args) @@ -1434,9 +1434,9 @@ cdef class GiacMethods_base: Help for baisse_crayon: baisse_crayon(NULL) Presses the pencil down so that the turtle move with traces. - See also: 1/ leve_crayon 2/ crayon + See also: 1/ leve_crayon 2/ crayon Ex1:baisse_crayon() - + ''' return GiacMethods['baisse_crayon'](self,*args) @@ -1445,8 +1445,8 @@ cdef class GiacMethods_base: Help for bandwidth: bandwidth(Opt) Option for the kernel_density command. - See also: 1/ kernel_density 2/ bins - + See also: 1/ kernel_density 2/ bins + ''' return GiacMethods['bandwidth'](self,*args) @@ -1455,11 +1455,11 @@ cdef class GiacMethods_base: Help for bar_plot: bar_plot(Mtrx) Draws a barplot of a one variable statistical series. - See also: 1/ camembert 2/ histogram 3/ frequencies + See also: 1/ camembert 2/ histogram 3/ frequencies Ex1:bar_plot([["France",6],["Allemagne",12],["Suisse",5]]) Ex2:bar_plot([3/2,2/3,5/4,4/5,7/6,6/7,9/8,8/9,11/10]) Ex3:bar_plot([[2,"xyz","abc"],["A",2,5],["B",5,6],["C",7,7]]) - + ''' return GiacMethods['bar_plot'](self,*args) @@ -1468,11 +1468,11 @@ cdef class GiacMethods_base: Help for barplot: barplot(Mtrx) Draws a barplot of a one variable statistical series. - See also: 1/ camembert 2/ histogram 3/ frequencies + See also: 1/ camembert 2/ histogram 3/ frequencies Ex1:barplot([["France",6],["Allemagne",12],["Suisse",5]]) Ex2:barplot([3/2,2/3,5/4,4/5,7/6,6/7,9/8,8/9,11/10]) Ex3:barplot([[2,"xyz","abc"],["A",2,5],["B",5,6],["C",7,7]]) - + ''' return GiacMethods['barplot'](self,*args) @@ -1481,9 +1481,9 @@ cdef class GiacMethods_base: Help for bartlett_hann_window: bartlett_hann_window(Lst,[Interval(n1..n2)]) Applies the Bartlett-Hann windowing function to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(bartlett_hann_window(randvector(1000,0..1))) - + ''' return GiacMethods['bartlett_hann_window'](self,*args) @@ -1492,11 +1492,11 @@ cdef class GiacMethods_base: Help for barycenter: barycenter([Pnt,Real],[Pnt,Real],[Pnt,Real]) barycenter([point1,coeff1],...) draws the barycenter of point1 with weight coeff1... - See also: 1/ isobarycenter 2/ midpoint + See also: 1/ isobarycenter 2/ midpoint Ex1:barycenter([point(-1),1],[point(1+i),2],[point(1-i),1]) Ex2:barycenter([[point(-1),1],[point(1+i),2],[point(1-i),1]]) Ex3:barycenter([point(-1),point(1+i),point(1-i)],[1,2,1]) - + ''' return GiacMethods['barycenter'](self,*args) @@ -1505,11 +1505,11 @@ cdef class GiacMethods_base: Help for base: base(Opt) Option for convert : convert(p,base,b)= [a0,a1,..an] or convert([a0,a1,..an],base,b)=p with p=a0+a1*b+....an*b^(n-1). - See also: 1/ convert 2/ horner 3/ revlist + See also: 1/ convert 2/ horner 3/ revlist Ex1: convert(123,base,8) Ex2: convert([3,7,1],base,8) Ex3: horner(revlist([3,7,1]),8) - + ''' return GiacMethods['base'](self,*args) @@ -1518,9 +1518,9 @@ cdef class GiacMethods_base: Help for basis: basis(Lst(vector1,..,vectorn)) Extracts a basis from a spanning set of vectors. - See also: 1/ ker 2/ ibasis + See also: 1/ ker 2/ ibasis Ex1:basis([[1,2,3],[4,5,6],[7,8,9],[10,11,12]]) - + ''' return GiacMethods['basis'](self,*args) @@ -1529,11 +1529,11 @@ cdef class GiacMethods_base: Help for batons: batons(Mtrx) Draws for k=0..nrows, the segments (xk,0)-(xk,yk) where xk=element row k column 0 and yk=element row k column j (j=1..ncols). - See also: 1/ polygonplot 2/ scatterplot 3/ listplot + See also: 1/ polygonplot 2/ scatterplot 3/ listplot Ex1:batons([1,3],[2,5],[3,2]) Ex2:batons([[1,3],[2,5],[3,2]]) Ex3:batons([1,2,3],[3,5,2]) - + ''' return GiacMethods['batons'](self,*args) @@ -1542,9 +1542,9 @@ cdef class GiacMethods_base: Help for bellman_ford: bellman_ford(Graph(G),Vrtx(s),Vrtx(t)||Lst(T)) Returns the length of the shortest path resp. paths from s to vertex t resp. vertices in T in weighted graph G. - See also: 1/ dijkstra 2/ shortest_path + See also: 1/ dijkstra 2/ shortest_path Ex1:bellman_ford(graph(%{[[1,2],-1],[[2,3],-3],[[3,4],-7],[[4,5],-3],[[5,6],-3],[[1,6],-3]%}),1,4) - + ''' return GiacMethods['bellman_ford'](self,*args) @@ -1553,10 +1553,10 @@ cdef class GiacMethods_base: Help for bernoulli: bernoulli(Intg||(Intg,Var)) bernoulli(n) is the n-th number of Bernoulli and bernoulli(n,x) is the n-th polynomial of Bernoulli and the second argument is the variable. - See also: 1/ + See also: 1/ Ex1:bernoulli(6) Ex2:bernoulli(6,x) - + ''' return GiacMethods['bernoulli'](self,*args) @@ -1565,10 +1565,10 @@ cdef class GiacMethods_base: Help for besselJ: besselJ(Real(x),Int(p)) besselJ(x,p) returns the Bessel function of the first kind Jp(x). - See also: 1/ BesselJ 2/ BesselY 3/ besselY + See also: 1/ BesselJ 2/ BesselY 3/ besselY Ex1:besselJ(sqrt(2),2) Ex2:besselJ(sqrt(2),-2) - + ''' return GiacMethods['besselJ'](self,*args) @@ -1577,10 +1577,10 @@ cdef class GiacMethods_base: Help for besselY: besselY(Real(x),Int(p)) besselY(x,p) returns the Bessel function of the second kind Yp(x). - See also: 1/ BesselY 2/ BesselJ 3/ besselJ + See also: 1/ BesselY 2/ BesselJ 3/ besselJ Ex1:besselY(sqrt(2),2) Ex2:besselY(sqrt(2),-2) - + ''' return GiacMethods['besselY'](self,*args) @@ -1589,9 +1589,9 @@ cdef class GiacMethods_base: Help for betad: betad(Real(a>0),Real(b>0),Real(0<=x<=1)) Returns the probability density of the Beta law (=Gamma(a+b)*x^(a-1)*(1-x)^(b-1)/(Gamma(a)*Gamma(b))). - See also: 1/ betad_cdf 2/ betad_icdf + See also: 1/ betad_cdf 2/ betad_icdf Ex1:betad(2.2,1.5,0.8) - + ''' return GiacMethods['betad'](self,*args) @@ -1600,10 +1600,10 @@ cdef class GiacMethods_base: Help for betad_cdf: betad_cdf(Real(a>0),Real(b>0),Real(0<=x0<=1),[Real(0<=y0<=1)]) Returns the probability that a Beta random variable (with a and b as parameters) is less than x0 or between x0 and y0. - See also: 1/ betad 2/ betad_icdf + See also: 1/ betad 2/ betad_icdf Ex1:betad_cdf(2,1,0.2) Ex2:betad_cdf(2,1,0.1,0.3) - + ''' return GiacMethods['betad_cdf'](self,*args) @@ -1612,10 +1612,10 @@ cdef class GiacMethods_base: Help for betad_icdf: betad_icdf(Real(a>0),Real(b>0),Real(0<=p<=1)) Returns h such that the probability that a Beta random variable is less than h is p (0<=p<=1). - See also: 1/ betad_cdf 2/ betad + See also: 1/ betad_cdf 2/ betad Ex1:betad_icdf(2,1,0.95) Ex2:betad_icdf(2,1,0.5) - + ''' return GiacMethods['betad_icdf'](self,*args) @@ -1624,10 +1624,10 @@ cdef class GiacMethods_base: Help for betavariate: betavariate(Real(a),Real(b)) Returns a random real according to the Beta distribution with parameters a>0 and b>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:betavariate(1,2) Ex2:betavariate(1.5,4) - + ''' return GiacMethods['betavariate'](self,*args) @@ -1636,12 +1636,12 @@ cdef class GiacMethods_base: Help for bezier: bezier(Lst,[plot]) Bezier curve defined by control points. - See also: 1/ parameq + See also: 1/ parameq Ex1:bezier(1,1+i,2+i,3-i,plot) Ex2:bezier(point([0,0,0]),point([1,1,0]),point([0,1,1]),plot) Ex3: parameq(bezier(1,1+i,2+i,3-i)) Ex4: parameq(bezier(point([0,0,0]),point([1,1,0]),point([0,1,1]))) - + ''' return GiacMethods['bezier'](self,*args) @@ -1650,11 +1650,11 @@ cdef class GiacMethods_base: Help for bezout_entiers: bezout_entiers(Intg,Intg) Extended greatest common divisor of 2 integers. - See also: 1/ gcd 2/ iabcuv 3/ egcd + See also: 1/ gcd 2/ iabcuv 3/ egcd Ex1:bezout_entiers(45,75) Ex2:bezout_entiers(21,28) Ex3:bezout_entiers(30,49) - + ''' return GiacMethods['bezout_entiers'](self,*args) @@ -1663,9 +1663,9 @@ cdef class GiacMethods_base: Help for biconnected_components: biconnected_components(Graph(G)) Returns the biconnected components of G as a list of lists of vertices. - See also: 1/ articulation_points 2/ is_biconnected 3/ is_connected 4/ trail + See also: 1/ articulation_points 2/ is_biconnected 3/ is_connected 4/ trail Ex1:biconnected_components(graph(trail(1,2,3,4,2),trail(4,5,6,7,5))) - + ''' return GiacMethods['biconnected_components'](self,*args) @@ -1674,7 +1674,7 @@ cdef class GiacMethods_base: Help for binomial: binomial(Intg(n),Intg(k),[Real(p in 0..1)]) Returns comb(n,k)*p^k*(1-p)^(n-k) or comb(n,k) if no 3rd argument. - See also: 1/ binomial_cdf 2/ binomial_icdf 3/ multinomial 4/ randvector 5/ ranm + See also: 1/ binomial_cdf 2/ binomial_icdf 3/ multinomial 4/ randvector 5/ ranm Ex1:binomial(4,2) Ex2:binomial(4,0,0.5) Ex3:binomial(4,2,0.5) @@ -1682,7 +1682,7 @@ cdef class GiacMethods_base: Ex5: assume(p>=0 and p<=1);binomial(4,p,2) Ex6: randvector(6,binomial,4,0.2) Ex7: ranm(4,6,binomial,4,0.7) - + ''' return GiacMethods['binomial'](self,*args) @@ -1691,11 +1691,11 @@ cdef class GiacMethods_base: Help for binomial_cdf: binomial_cdf(Intg(n),Real(p),Real(x),[Real(y)]) Returns Proba(X<=x) or Proba(x<=X<=y) when X follows the B(n,p) law. - See also: 1/ binomial 2/ binomial_icdf + See also: 1/ binomial 2/ binomial_icdf Ex1:binomial_cdf(4,0.5,2) Ex2:binomial_cdf(4,0.1,2) Ex3:binomial_cdf(4,0.5,2,3) - + ''' return GiacMethods['binomial_cdf'](self,*args) @@ -1704,10 +1704,10 @@ cdef class GiacMethods_base: Help for binomial_icdf: binomial_icdf(Intg(n),Real(p),Real(t)) Returns h such as Proba(X<=h)=t when X follows the B(n,p) law. - See also: 1/ binomial 2/ binomial_cdf + See also: 1/ binomial 2/ binomial_cdf Ex1:binomial_icdf(4,0.5,0.68) Ex2:binomial_icdf(4,0.1,0.95) - + ''' return GiacMethods['binomial_icdf'](self,*args) @@ -1716,8 +1716,8 @@ cdef class GiacMethods_base: Help for bins: bins(Opt) Option for the kernel_density command. - See also: 1/ kernel_density 2/ bandwidth - + See also: 1/ kernel_density 2/ bandwidth + ''' return GiacMethods['bins'](self,*args) @@ -1726,8 +1726,8 @@ cdef class GiacMethods_base: Help for bipartite: bipartite(Opt) Option for the draw_graph command - See also: 1/ draw_graph - + See also: 1/ draw_graph + ''' return GiacMethods['bipartite'](self,*args) @@ -1736,9 +1736,9 @@ cdef class GiacMethods_base: Help for bipartite_matching: bipartite_matching(Graph(G)) Returns the list of edges in a maximum matching of the undirected unweighted bipartite graph G. - See also: 1/ is_bipartite 2/ maximum_matching + See also: 1/ is_bipartite 2/ maximum_matching Ex1:bipartite_matching(graph("desargues")) - + ''' return GiacMethods['bipartite_matching'](self,*args) @@ -1747,14 +1747,14 @@ cdef class GiacMethods_base: Help for bisection_solver: bisection_solver(Opt) Argument for fsolve giving the method for solving a numerical equation. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve(cos(x)=x,x,0..1,bisection_solver) Ex2: fsolve(cos(x)=x,x,0..1,brent_solver) Ex3: fsolve(cos(x)=x,x,0..1,falsepos_solver) Ex4: fsolve(cos(x)=x,x,0,newton_solver) Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) - + ''' return GiacMethods['bisection_solver'](self,*args) @@ -1763,9 +1763,9 @@ cdef class GiacMethods_base: Help for bisector: bisector((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Pnt(C) or Cplx)) Draws the bisector of the angle (AB,AC) given by 3 points A,B,C. - See also: 1/ angle 2/ exbisector + See also: 1/ angle 2/ exbisector Ex1:bisector(0,1,i) - + ''' return GiacMethods['bisector'](self,*args) @@ -1774,9 +1774,9 @@ cdef class GiacMethods_base: Help for bit_depth: bit_depth(Lst(clip)) Returns the bit depth of an audio clip. - See also: 1/ channels 2/ channel_data 3/ duration 4/ samplerate + See also: 1/ channels 2/ channel_data 3/ duration 4/ samplerate Ex1:bit_depth(readwav("/some/file")) - + ''' return GiacMethods['bit_depth'](self,*args) @@ -1785,9 +1785,9 @@ cdef class GiacMethods_base: Help for bitand: bitand(Intg,Intg) Logical bit and. - See also: 1/ bitxor 2/ bitor + See also: 1/ bitxor 2/ bitor Ex1:bitand(0x12,0x38) - + ''' return GiacMethods['bitand'](self,*args) @@ -1796,9 +1796,9 @@ cdef class GiacMethods_base: Help for bitor: bitor(Intg,Intg) Inclusive logical bit or. - See also: 1/ bitxor 2/ bitand + See also: 1/ bitxor 2/ bitand Ex1:bitor(0x12,0x38) - + ''' return GiacMethods['bitor'](self,*args) @@ -1807,9 +1807,9 @@ cdef class GiacMethods_base: Help for bitxor: bitxor(Intg,Intg) Exclusive logical bit or. - See also: 1/ bitor 2/ bitand + See also: 1/ bitor 2/ bitand Ex1:bitxor(0x12,0x38) - + ''' return GiacMethods['bitxor'](self,*args) @@ -1818,9 +1818,9 @@ cdef class GiacMethods_base: Help for blackman_harris_window: blackman_harris_window(Lst,[Interval(n1..n2)]) Applies the Blackman-Harris windowing function to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ bartlett_hann_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ bartlett_hann_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(blackman_harris_window(randvector(1000,0..1))) - + ''' return GiacMethods['blackman_harris_window'](self,*args) @@ -1829,9 +1829,9 @@ cdef class GiacMethods_base: Help for blackman_window: blackman_window(Lst,[Real(a)],[Interval(n1..n2)]) Applies the Blackman windowing function with parameter a (by default a=0.16) to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ bartlett_harris_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ bartlett_harris_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(blackman_window(randvector(1000,0..1))) - + ''' return GiacMethods['blackman_window'](self,*args) @@ -1840,10 +1840,10 @@ cdef class GiacMethods_base: Help for blockmatrix: blockmatrix(Intg(n),Intg(m),Lst) Returns the matrix obtained from the list divided into n lists of dimension m. - See also: 1/ list2mat + See also: 1/ list2mat Ex1:blockmatrix(2,3,[idn(2),idn(2),idn(2),idn(2),idn(2),idn(2)]) Ex2:blockmatrix(2,2,[idn(2),newMat(2,3),newMat(3,2),idn(3)]) - + ''' return GiacMethods['blockmatrix'](self,*args) @@ -1852,9 +1852,9 @@ cdef class GiacMethods_base: Help for bohman_window: bohman_window(Lst,[Interval(n1..n2)]) Applies the Bohman windowing function to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bartlett_hann_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bartlett_hann_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(bohman_window(randvector(1000,0..1))) - + ''' return GiacMethods['bohman_window'](self,*args) @@ -1863,10 +1863,10 @@ cdef class GiacMethods_base: Help for border: border(Mtrx(A),Lst(b)) Returns the matrix obtained by augmenting A with b as the last column, if nrows(A)=size(b), border(A,b)=tran(append(tran(A),b)). - See also: 1/ tran 2/ append 3/ augment + See also: 1/ tran 2/ append 3/ augment Ex1:border([[1,2,3,4],[4,5,6,8],[7,8,9,10]],[1,3,5]) Ex2:border([[1,2,3],[4,5,6],[7,8,9]],[1,0,1]) - + ''' return GiacMethods['border'](self,*args) @@ -1875,9 +1875,9 @@ cdef class GiacMethods_base: Help for boxcar: boxcar(Real(a),Real(b),Expr(x)) Returns the value at x of the boxcar function corresponding to a and b. - See also: 1/ rect 2/ Heaviside + See also: 1/ rect 2/ Heaviside Ex1:boxcar(1,2,x) - + ''' return GiacMethods['boxcar'](self,*args) @@ -1886,12 +1886,12 @@ cdef class GiacMethods_base: Help for boxwhisker: boxwhisker(Lst,[Lst],[x=a..b||y=a..b]) Box and Whisker plot for a statistical series. - See also: 1/ quartiles + See also: 1/ quartiles Ex1:boxwhisker([-1,1,2,2.2,3,4,-2,5]) Ex2:boxwhisker([1,2,3,5,10,4],x=1..2) Ex3:boxwhisker([1,2,3,5,10,4],[1,2,3,1,2,3]) Ex4:boxwhisker([[6,0,1,3,4,2,5],[0,1,3,4,2,5,6],[1,3,4,2,5,6,0],[3,4,2,5,6,0,1],[4,2,5,6,0,1,3],[2,5,6,0,1,3,4]]) - + ''' return GiacMethods['boxwhisker'](self,*args) @@ -1900,14 +1900,14 @@ cdef class GiacMethods_base: Help for brent_solver: brent_solver(Opt) Argument for fsolve giving the method for solving a numerical equation. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve(cos(x)=x,x,0..1,bisection_solver) Ex2: fsolve(cos(x)=x,x,0..1,brent_solver) Ex3: fsolve(cos(x)=x,x,0..1,falsepos_solver) Ex4: fsolve(cos(x)=x,x,0,newton_solver) Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) - + ''' return GiacMethods['brent_solver'](self,*args) @@ -1916,10 +1916,10 @@ cdef class GiacMethods_base: Help for bvpsolve: bvpsolve(Expr(f(x,y,y')),Lst(x=a..b,y),Lst(y(a),y(b),[y'(1)]),[options]) Returns an approximation of the function y (and optionally of y') on the interval a..b. - See also: 1/ odesolve + See also: 1/ odesolve Ex1:bvpsolve((32+2x^3-y*diff(y(x),x))/8,[x=1..3,y],[17,43/3],20) Ex2:bvpsolve((x^2*diff(y(x),x)^2-9y^2+4x^6)/x^5,[x=1..2,y],[0,ln(256),1],10,output=spline) - + ''' return GiacMethods['bvpsolve'](self,*args) @@ -1928,11 +1928,11 @@ cdef class GiacMethods_base: Help for cFactor: cFactor(Expr) Factorization of the expression in ℂ (on the Gaussian integers if there are more than 2 variables). - See also: 1/ factor + See also: 1/ factor Ex1:cFactor(x^2*y+y) Ex2:cFactor(x^2*y^2+y^2+4*x^2+4) Ex3:cFactor(x^2*y^2+y^2+2*x^2+2) - + ''' return GiacMethods['cFactor'](self,*args) @@ -1941,12 +1941,12 @@ cdef class GiacMethods_base: Help for cSolve: cSolve(LstEq,LstVar) Returns the list of complex solutions of an equation or a matrix where the rows are ℂ-solutions of a system of polynomial equations. - See also: 1/ cZeros 2/ solve 3/ fslove + See also: 1/ cZeros 2/ solve 3/ fslove Ex1:cSolve(x^4-1,x) Ex2:cSolve(x^4-y^4 and x+y=2,[x,y]) Ex3:cSolve(x^4-y^4 and x+y=0 and x^2=2*x,[x,y]) Ex4:cSolve(u*v-u=v and v^2=u,[u,v]) - + ''' return GiacMethods['cSolve'](self,*args) @@ -1955,10 +1955,10 @@ cdef class GiacMethods_base: Help for cZeros: cZeros(Expr(Xpr)||LstExpr, [Var||LstVar]) Returns the list of complex solutions of Xpr=0 or the matrix where the rows are the solutions of the system : Xpr1=0,Xpr2=0... - See also: 1/ solve + See also: 1/ solve Ex1:cZeros(x^2-1) Ex2:cZeros([x^2-1,x^2-y^2],[x,y]) - + ''' return GiacMethods['cZeros'](self,*args) @@ -1967,11 +1967,11 @@ cdef class GiacMethods_base: Help for camembert: camembert(Mtrx) Draws pie chart of a one variable statistical series. - See also: 1/ bar_plot + See also: 1/ bar_plot Ex1:camembert([["France",6],["Allemagne",12],["Suisse",5]]) Ex2:camembert([3/2,2/3,5/4,4/5,7/6,6/7,9/8,8/9,11/10]) Ex3:camembert([[2,"xyz","abc"],["A",2,5],["B",5,6],["C",7,7]]) - + ''' return GiacMethods['camembert'](self,*args) @@ -1980,10 +1980,10 @@ cdef class GiacMethods_base: Help for canonical_form: canonical_form(Trinom(a*x^2+b*x+c),[Var]) Canonical_form of a 2nd degree polynomial. - See also: 1/ + See also: 1/ Ex1:canonical_form(2*x^2-12*x+1) Ex2:canonical_form(2*a^2-12*a+1,a) - + ''' return GiacMethods['canonical_form'](self,*args) @@ -1992,9 +1992,9 @@ cdef class GiacMethods_base: Help for canonical_labeling: canonical_labeling(Graph(G)) Returns the permutation representing the canonical labeling of G. - See also: 1/ isomorphic_copy 2/ relabel_vertices + See also: 1/ isomorphic_copy 2/ relabel_vertices Ex1:canonical_labeling(graph("petersen")) - + ''' return GiacMethods['canonical_labeling'](self,*args) @@ -2003,9 +2003,9 @@ cdef class GiacMethods_base: Help for cartesian_product: cartesian_product(Seq(G1,G2,..)) Returns the Cartesian product of graphs G1, G2, ... with vertices labelled as "u:v:..." where u, v, ... are vertices from G1, G2, ..., respectively. - See also: 1/ tensor_product + See also: 1/ tensor_product Ex1:cartesian_product(graph(trail(1,2,3,4,5,2)),star_graph(3)) - + ''' return GiacMethods['cartesian_product'](self,*args) @@ -2014,9 +2014,9 @@ cdef class GiacMethods_base: Help for cauchy: cauchy(Real(x0),Real(a),Real(x)) Returns the density of probability at x of the Cauchy law with parameters x0 and a (by default x0=0 and a=1). - See also: 1/ cauchy_cdf 2/ cauchy_icdf + See also: 1/ cauchy_cdf 2/ cauchy_icdf Ex1:cauchy(0.0,2.0,1.0) - + ''' return GiacMethods['cauchy'](self,*args) @@ -2025,10 +2025,10 @@ cdef class GiacMethods_base: Help for cauchy_cdf: cauchy_cdf(Real(x0),Real(a),Real(x),[Real(y)]) Returns the probability that a Cauchy random variable is less than x. - See also: 1/ cauchyd 2/ cauchy_icdf + See also: 1/ cauchyd 2/ cauchy_icdf Ex1:cauchy_cdf(0.0,2.0,2.1) Ex2:cauchy_cdf(2,3,-1.9,1.4) - + ''' return GiacMethods['cauchy_cdf'](self,*args) @@ -2037,9 +2037,9 @@ cdef class GiacMethods_base: Help for cauchy_icdf: cauchy_icdf(Real(x0),Real(a),Real(p)) Returns h such that the probability that a Cauchy random variable is less than h is p (0<=p<=1). - See also: 1/ cauchy_cdf 2/ cauchy + See also: 1/ cauchy_cdf 2/ cauchy Ex1:cauchy_icdf(0.0,2.0,0.95) - + ''' return GiacMethods['cauchy_icdf'](self,*args) @@ -2048,9 +2048,9 @@ cdef class GiacMethods_base: Help for cauchyd: cauchyd(Real(x0),Real(a),Real(x)) Returns the density of probability at x of the Cauchy law with parameters x0 and a (by default x0=0 and a=1). - See also: 1/ cauchy_cdf 2/ cauchy_icdf + See also: 1/ cauchy_cdf 2/ cauchy_icdf Ex1:cauchyd(0.0,2.0,1.0) - + ''' return GiacMethods['cauchyd'](self,*args) @@ -2059,10 +2059,10 @@ cdef class GiacMethods_base: Help for cauchyd_cdf: cauchyd_cdf(Real(x0),Real(a),Real(x),[Real(y)]) Returns the probability that a Cauchy random variable is less than x. - See also: 1/ cauchyd 2/ cauchy_icdf + See also: 1/ cauchyd 2/ cauchy_icdf Ex1:cauchyd_cdf(0.0,2.0,2.1) Ex2:cauchyd_cdf(2,3,-1.9,1.4) - + ''' return GiacMethods['cauchyd_cdf'](self,*args) @@ -2071,9 +2071,9 @@ cdef class GiacMethods_base: Help for cauchyd_icdf: cauchyd_icdf(Real(x0),Real(a),Real(p)) Returns h such that the probability that a Cauchy random variable is less than h is p (0<=p<=1). - See also: 1/ cauchy_cdf 2/ cauchy + See also: 1/ cauchy_cdf 2/ cauchy Ex1:cauchyd_icdf(0.0,2.0,0.95) - + ''' return GiacMethods['cauchyd_icdf'](self,*args) @@ -2082,12 +2082,12 @@ cdef class GiacMethods_base: Help for cdf: cdf(Func,FuncParams) Cumulative distribution function. - See also: 1/ icdf 2/ binomial_cdf 3/ normald_cdf 4/ plotcdf + See also: 1/ icdf 2/ binomial_cdf 3/ normald_cdf 4/ plotcdf Ex1:cdf(binomial,10,0.5,4) Ex2:cdf(normald,0.0,1.0,2.0) Ex3:cdf([1,3,4,3,5,6],4) Ex4:cdf([1,3,4,3,5,6],plot) - + ''' return GiacMethods['cdf'](self,*args) @@ -2096,10 +2096,10 @@ cdef class GiacMethods_base: Help for ceil: ceil(Real or Cplx) Returns the smallest integer >= to the argument. - See also: 1/ floor 2/ round + See also: 1/ floor 2/ round Ex1:ceil(-4.2) Ex2:ceil(4.3+2.4*i) - + ''' return GiacMethods['ceil'](self,*args) @@ -2108,10 +2108,10 @@ cdef class GiacMethods_base: Help for ceiling: ceiling(Real or Cplx) Returns the smallest integer >= to the argument. - See also: 1/ floor 2/ round + See also: 1/ floor 2/ round Ex1:ceiling(-4.2) Ex2:ceiling(4.3+2.4*i) - + ''' return GiacMethods['ceiling'](self,*args) @@ -2120,10 +2120,10 @@ cdef class GiacMethods_base: Help for center: center(Crcle) Shows the center of a circle. - See also: 1/ circle 2/ radius + See also: 1/ circle 2/ radius Ex1:center(circle(1+i,2)) Ex2:center(circumcircle(0,1,1+i)) - + ''' return GiacMethods['center'](self,*args) @@ -2132,10 +2132,10 @@ cdef class GiacMethods_base: Help for center2interval: center2interval(LstVal(l),[Real(a0)]) Returns the list of intervals beginning with a0 and with l as centers. - See also: 1/ interval2center + See also: 1/ interval2center Ex1:center2interval([2,5,9],1) Ex2:center2interval([2,5,8]) - + ''' return GiacMethods['center2interval'](self,*args) @@ -2144,10 +2144,10 @@ cdef class GiacMethods_base: Help for centered_cube: centered_cube(Pnt(A),Pnt(B),Pnt(C)) Draws the direct cube with center A, vertex B and such that the plane ABC contains an axis of symmetry of the cube. - See also: 1/ parallelepiped 2/ cube 3/ icosahedron 4/ dodecahedron 5/ octahedron 6/ centered_tetrahedron + See also: 1/ parallelepiped 2/ cube 3/ icosahedron 4/ dodecahedron 5/ octahedron 6/ centered_tetrahedron Ex1:centered_cube([0,0,0],[3,0,0],[0,0,1]) Ex2:centered_cube(evalf([0,0,0],[3,2,4],[1,1,0])) - + ''' return GiacMethods['centered_cube'](self,*args) @@ -2156,10 +2156,10 @@ cdef class GiacMethods_base: Help for centered_tetrahedron: centered_tetrahedron(Pnt(A),Pnt(B),Pnt(C)) Draws the regular direct pyramid with center A, vertex B and a vertex in the plane (A,B,C). - See also: 1/ cube 2/ tetrahedron 3/ icosahedron 4/ dodecahedron 5/ octahedron + See also: 1/ cube 2/ tetrahedron 3/ icosahedron 4/ dodecahedron 5/ octahedron Ex1:centered_tetrahedron([0,0,0],[3,0,0],[0,1,0]) Ex2:centered_tetrahedron(evalf([0,0,0],[3,2,4],[1,1,0])) - + ''' return GiacMethods['centered_tetrahedron'](self,*args) @@ -2168,11 +2168,11 @@ cdef class GiacMethods_base: Help for cfactor: cfactor(Expr) Factorization of the expression in ℂ (on the Gaussian integers if there are more than 2 variables). - See also: 1/ factor + See also: 1/ factor Ex1:cfactor(x^2*y+y) Ex2:cfactor(x^2*y^2+y^2+4*x^2+4) Ex3:cfactor(x^2*y^2+y^2+2*x^2+2) - + ''' return GiacMethods['cfactor'](self,*args) @@ -2181,10 +2181,10 @@ cdef class GiacMethods_base: Help for cfsolve: cfsolve(Expr,Var,[Guess or Interval],[Method]) Numerical solution of an equation or a system of equations on ℂ. - See also: 1/ fsolve 2/ nSolve 3/ csolve 4/ solve + See also: 1/ fsolve 2/ nSolve 3/ csolve 4/ solve Ex1:cfsolve(cos(x)=2) Ex2:cfsolve([x^2+y+2,x+y^2+2],[x,y]) - + ''' return GiacMethods['cfsolve'](self,*args) @@ -2193,10 +2193,10 @@ cdef class GiacMethods_base: Help for changebase: changebase(Mtrx(A),Mtrx(P)) Returns the matrix B=inv(P)*A*P. - See also: 1/ + See also: 1/ Ex1:changebase([[1,2],[1,3]],[[1,1],[0,1]]) Ex2:changebase([[1,2],[1,3]],[[1,0],[1,1]]) - + ''' return GiacMethods['changebase'](self,*args) @@ -2205,12 +2205,12 @@ cdef class GiacMethods_base: Help for channel_data: channel_data(Lst(clip),[Intg(chn) or matrix],[range=a..b]) Extracts the data from an audio clip (optionally specifying the channel and range). - See also: 1/ bit_depth 2/ channels 3/ duration 4/ samplerate + See also: 1/ bit_depth 2/ channels 3/ duration 4/ samplerate Ex1:channel_data(readwav("/some/file")) Ex2:channel_data(readwav("/some/file"),matrix) Ex3:channel_data(readwav("/some/file"),2) Ex4:channel_data(readwav("/some/file"),matrix,range=1.0..2.5) - + ''' return GiacMethods['channel_data'](self,*args) @@ -2219,9 +2219,9 @@ cdef class GiacMethods_base: Help for channels: channels(Lst(clip)) Returns the number of channels in audio clip. - See also: 1/ bit_depth 2/ channel_data 3/ duration 4/ samplerate + See also: 1/ bit_depth 2/ channel_data 3/ duration 4/ samplerate Ex1:channels(readwav("/some/file")) - + ''' return GiacMethods['channels'](self,*args) @@ -2230,10 +2230,10 @@ cdef class GiacMethods_base: Help for char: char(Intg or Lst(Intg)) Returns the string corresponding to the character code of the argument. - See also: 1/ asc 2/ ord + See also: 1/ asc 2/ ord Ex1:char(65) Ex2:char([65,66,67]) - + ''' return GiacMethods['char'](self,*args) @@ -2242,12 +2242,12 @@ cdef class GiacMethods_base: Help for charpoly: charpoly(Mtrx,[Var]) List of the coefficients of the characteristic polynomial of a matrix or characteristic polynomial of a matrix with the second argument as variable. - See also: 1/ jordan 2/ egv 3/ egvl 4/ companion 5/ rat_jordan 6/ pmin 7/ adjoint_matrix + See also: 1/ jordan 2/ egv 3/ egvl 4/ companion 5/ rat_jordan 6/ pmin 7/ adjoint_matrix Ex1:charpoly([[1,2],[3,4]]) Ex2:charpoly([[1,2],[3,4]],x) Ex3:charpoly([[1,2,3],[1,3,6],[2,5,7]]) Ex4:charpoly([[1,2,3],[1,3,6],[2,5,7]],z) - + ''' return GiacMethods['charpoly'](self,*args) @@ -2256,10 +2256,10 @@ cdef class GiacMethods_base: Help for chinrem: chinrem([Lst||Expr,Lst||Expr],[Lst||Expr,Lst||Expr]) Chinese remainder for polynomials written as lists or no. - See also: 1/ ichinrem + See also: 1/ ichinrem Ex1:chinrem([x+2,x^2+1],[x+1,x^2+x+1]) Ex2:chinrem([[1,2],[1,0,1]],[[1,1],[1,1,1]]) - + ''' return GiacMethods['chinrem'](self,*args) @@ -2268,12 +2268,12 @@ cdef class GiacMethods_base: Help for chisquare: chisquare(Intg(n),Real(x0)) Returns the probability density of the Chi^2 law at x0 (n is the number of degrees of freedom). - See also: 1/ chisquare_cdf 2/ chisquare_icdf 3/ randvector 4/ ranm + See also: 1/ chisquare_cdf 2/ chisquare_icdf 3/ randvector 4/ ranm Ex1:chisquare(2,3.2) Ex2:chisquare(4,10.5) Ex3: randvector(3,chisquare,2) Ex4: ranm(4,3,chisquare,2) - + ''' return GiacMethods['chisquare'](self,*args) @@ -2282,10 +2282,10 @@ cdef class GiacMethods_base: Help for chisquare_cdf: chisquare_cdf(Intg(n),Real(x0)) Returns the probability that a Chi^2 random variable is less than x0 (n is the number of degrees of freedom). - See also: 1/ UTPC 2/ chisquare_icdf 3/ chisquared + See also: 1/ UTPC 2/ chisquare_icdf 3/ chisquared Ex1:chisquare_cdf(2,6.1) Ex2:chisquare_cdf(4,6.1) - + ''' return GiacMethods['chisquare_cdf'](self,*args) @@ -2294,10 +2294,10 @@ cdef class GiacMethods_base: Help for chisquare_icdf: chisquare_icdf(Intg(n),Real(p)) Returns h such as the probability that a Chi^2 random variable is less than h is p (n is the number of degrees of freedom and 0<=p<=1). - See also: 1/ chisquare_cdf 2/ chisquared + See also: 1/ chisquare_cdf 2/ chisquared Ex1:chisquare_icdf(2,0.95) Ex2:chisquare_icdf(4,0.05) - + ''' return GiacMethods['chisquare_icdf'](self,*args) @@ -2306,12 +2306,12 @@ cdef class GiacMethods_base: Help for chisquared: chisquared(Intg(n),Real(x0)) Returns the probability density of the Chi^2 law at x0 (n is the number of degrees of freedom). - See also: 1/ chisquare_cdf 2/ chisquare_icdf 3/ randvector 4/ ranm + See also: 1/ chisquare_cdf 2/ chisquare_icdf 3/ randvector 4/ ranm Ex1:chisquared(2,3.2) Ex2:chisquared(4,10.5) Ex3: randvector(3,chisquare,2) Ex4: ranm(4,3,chisquare,2) - + ''' return GiacMethods['chisquared'](self,*args) @@ -2320,10 +2320,10 @@ cdef class GiacMethods_base: Help for chisquared_cdf: chisquared_cdf(Intg(n),Real(x0)) Returns the probability that a Chi^2 random variable is less than x0 (n is the number of degrees of freedom). - See also: 1/ UTPC 2/ chisquare_icdf 3/ chisquared + See also: 1/ UTPC 2/ chisquare_icdf 3/ chisquared Ex1:chisquared_cdf(2,6.1) Ex2:chisquared_cdf(4,6.1) - + ''' return GiacMethods['chisquared_cdf'](self,*args) @@ -2332,10 +2332,10 @@ cdef class GiacMethods_base: Help for chisquared_icdf: chisquared_icdf(Intg(n),Real(p)) Returns h such as the probability that a Chi^2 random variable is less than h is p (n is the number of degrees of freedom and 0<=p<=1). - See also: 1/ chisquare_cdf 2/ chisquared + See also: 1/ chisquare_cdf 2/ chisquared Ex1:chisquared_icdf(2,0.95) Ex2:chisquared_icdf(4,0.05) - + ''' return GiacMethods['chisquared_icdf'](self,*args) @@ -2344,7 +2344,7 @@ cdef class GiacMethods_base: Help for chisquaret: chisquaret(Data,[Func],[FuncParams]) Chi^2 test : fitness between 2 (or n) samples or between 1 sample and a distribution law (multinomial or given by a law). - See also: 1/ normalt 2/ studentt 3/ kolmogorovt + See also: 1/ normalt 2/ studentt 3/ kolmogorovt Ex1:chisquaret([57,54]) Ex2:chisquaret([1,1,1,1,1,0,0,1,0,0,1,1,1,0,1,1,0,1,1,0,0,0,0],[.4,.6]) Ex3:chisquaret([57,30],[.6,.4]) @@ -2354,7 +2354,7 @@ cdef class GiacMethods_base: Ex7:chisquaret(ranv(1000,normald,0,.2),normald) Ex8:chisquaret([11,16,17,22,14,10],[1/6,1/6,1/6,1/6,1/6,1/6]) Ex9:chisquaret([11,16,17,22,14,10],[(1/6)$6]) - + ''' return GiacMethods['chisquaret'](self,*args) @@ -2363,12 +2363,12 @@ cdef class GiacMethods_base: Help for choice: choice(Lst(L)) choice(L)=rand(L)=one extracted element of L. - See also: 1/ rand 2/ sample + See also: 1/ rand 2/ sample Ex1:choice([1,2,3,4,5,6]) Ex2:choice(["r","r","r","b","n"]) Ex3: L:=[1,2,3,4,5,6];L:=choice(L) Ex4: L:=[1,2,3,4,5,6];L.choice() - + ''' return GiacMethods['choice'](self,*args) @@ -2377,9 +2377,9 @@ cdef class GiacMethods_base: Help for cholesky: cholesky(Mtrx) For a numerical symmetric matrix A, returns L matrix such that A=L*tran(L). - See also: 1/ lu 2/ qr 3/ gauss + See also: 1/ lu 2/ qr 3/ gauss Ex1:cholesky([[3,1],[1,4]]) - + ''' return GiacMethods['cholesky'](self,*args) @@ -2388,10 +2388,10 @@ cdef class GiacMethods_base: Help for chr: chr(Intg or Lst(Intg)) Returns the string corresponding to the character code of the argument. - See also: 1/ asc 2/ ord + See also: 1/ asc 2/ ord Ex1:chr(65) Ex2:chr([65,66,67]) - + ''' return GiacMethods['chr'](self,*args) @@ -2400,13 +2400,13 @@ cdef class GiacMethods_base: Help for chrem: chrem(LstIntg(a,b,c....),LstIntg(p,q,r,....)) Chinese remainders for integers or for polynomials. - See also: 1/ gcd 2/ fracmod 3/ chinrem 4/ ichinrem + See also: 1/ gcd 2/ fracmod 3/ chinrem 4/ ichinrem Ex1:chrem(symbolique.) Ex2:chrem([2,3],[7,5]) Ex3:chrem([2,4,6],[3,5,7]) Ex4:chrem([2,4,6,7],[3,5,7,11]) Ex5:chrem([2*x+1,4*x+2,6*x-1,x+1],[3,5,7,11]) - + ''' return GiacMethods['chrem'](self,*args) @@ -2415,10 +2415,10 @@ cdef class GiacMethods_base: Help for chromatic_index: chromatic_index(Graph(G),[Lst(cols)]) Returns the number of colors in the minimal edge coloring of G. If an unassigned identifier cols is given, the coloring is stored to it. - See also: 1/ minimal_edge_coloring 2/ chromatic_number + See also: 1/ minimal_edge_coloring 2/ chromatic_number Ex1:chromatic_index(graph("petersen")) Ex2:chromatic_index(graph("dodecahedron"),colors) - + ''' return GiacMethods['chromatic_index'](self,*args) @@ -2428,7 +2428,7 @@ cdef class GiacMethods_base: chromatic_number(Graph(G)) Returns the chromatic number of G. Ex1:chromatic_number(graph("petersen")) - + ''' return GiacMethods['chromatic_number'](self,*args) @@ -2437,10 +2437,10 @@ cdef class GiacMethods_base: Help for chromatic_polynomial: chromatic_polynomial(Graph(G),[Var(t)]) Returns the chromatic polynomial [or its value at point t] of undirected unweighted graph G. - See also: 1/ flow_polynomial 2/ reliability_polynomial 3/ tutte_polynomial + See also: 1/ flow_polynomial 2/ reliability_polynomial 3/ tutte_polynomial Ex1:chromatic_polynomial(graph("petersen")) Ex2:chromatic_polynomial(graph("petersen"),3) - + ''' return GiacMethods['chromatic_polynomial'](self,*args) @@ -2449,7 +2449,7 @@ cdef class GiacMethods_base: Help for circle: circle((Pnt(M) or Cplx(M),(Pnt(N) or Cplx(zN)),[Real(a)],[Real(b)],[Var(A)],[Var(B)]) Define for 2-d a circle with a diameter MN (arg1=M or zM,arg2=N) or with center and radius (arg1=M or zM,arg2=zN) and (center=M and radius=abs(zN)) [or the arc AB, A angle a, B angle b, (MN=angle 0) or M(M+zN)=angle 0] or by its equation and for 3-d with a diameter and a third point. - See also: 1/ circumcircle 2/ incircle 3/ excircle 4/ center 5/ radius 6/ sphere 7/ Circle + See also: 1/ circumcircle 2/ incircle 3/ excircle 4/ center 5/ radius 6/ sphere 7/ Circle Ex1:circle(0,point(2*i)) Ex2:circle(i,i) Ex3:circle(i,1) @@ -2458,7 +2458,7 @@ cdef class GiacMethods_base: Ex6:circle(x^2+y^2-x-y) Ex7:circle(cercle(point([-1,0,0]),point([1,0,0]),point([0,2,0]))) Ex8:circle(cercle([-1,0,0],point([1,0,0]),[0,2,0])) - + ''' return GiacMethods['circle'](self,*args) @@ -2467,9 +2467,9 @@ cdef class GiacMethods_base: Help for circumcircle: circumcircle((Pnt or Cplx),(Pnt or Cplx),((Pnt or Cplx)) circumcircle(A,B,C)=circumcircle of the triangle ABC. - See also: 1/ circle 2/ incircle 3/ excircle + See also: 1/ circle 2/ incircle 3/ excircle Ex1:circumcircle(0,1,1+i) - + ''' return GiacMethods['circumcircle'](self,*args) @@ -2478,13 +2478,13 @@ cdef class GiacMethods_base: Help for classes: classes(Lst(l),[ClassMin],[ClassSize||Lst(Center)]) Returns the matrix [[class,number],...] obtained with class_min and class_size: see init of geo or argument 2 and 3 or with the list of centers. - See also: 1/ histogram 2/ cumulated_frequencies 3/ bar_plot 4/ frequencies + See also: 1/ histogram 2/ cumulated_frequencies 3/ bar_plot 4/ frequencies Ex1:classes([1,1.2,1.4,1.6,1.8,2,2.5]) Ex2:classes([1,1.2,1.4,1.6,1.8,2,2.5],1.2,0.5) Ex3:classes([1,1.2,1.4,1.6,1.8,2,2.5],1,[1.2,1.6,2,2.4]) Ex4:classes([1,1.2,1.4,1.6,1.8,2,2.5],1,[1.2,1.6,2.2]) Ex5:classes([0,0.5,1,1.5,2,2.5,3,3.5,4],[0..2,2..4,4..6]) - + ''' return GiacMethods['classes'](self,*args) @@ -2493,9 +2493,9 @@ cdef class GiacMethods_base: Help for clear: clear(NULL) Clears the list of pixels. - See also: 1/ set_pixel 2/ show_pixels + See also: 1/ set_pixel 2/ show_pixels Ex1:clear() - + ''' return GiacMethods['clear'](self,*args) @@ -2504,11 +2504,11 @@ cdef class GiacMethods_base: Help for clique_cover: clique_cover(Graph(G),[Intg(k)]) Returns a clique vertex cover of G [containing at most k cliques]. - See also: 1/ clique_cover_number 2/ maximal_cliques + See also: 1/ clique_cover_number 2/ maximal_cliques Ex1:clique_cover(graph("petersen")) Ex2:clique_cover(cycle_graph(5)) Ex3:clique_cover(graph_complement(complete_graph(3,4))) - + ''' return GiacMethods['clique_cover'](self,*args) @@ -2517,11 +2517,11 @@ cdef class GiacMethods_base: Help for clique_cover_number: clique_cover_number(Graph(G)) Returns the clique cover number of G. - See also: 1/ clique_cover 3/ maximal_cliques + See also: 1/ clique_cover 3/ maximal_cliques Ex1:clique_cover_number(graph("petersen")) Ex2:clique_cover_number(cycle_graph(5)) Ex3:clique_cover_number(graph_complement(complete_graph(3,4))) - + ''' return GiacMethods['clique_cover_number'](self,*args) @@ -2530,9 +2530,9 @@ cdef class GiacMethods_base: Help for clique_number: clique_number(Graph(G)) Returns the clique number of G, which is equal to the size of a maximum clique in G. - See also: 1/ maximum_clique + See also: 1/ maximum_clique Ex1:clique_number(graph_complement(complete_graph(3,4))) - + ''' return GiacMethods['clique_number'](self,*args) @@ -2541,11 +2541,11 @@ cdef class GiacMethods_base: Help for clique_stats: clique_stats(Graph(G),[Intg(k)||Intrv(m..n)]) Returns the list of numbers of maximal cliques of size s in G for each s. If parameter k is given, the number of k-cliques is returned. If an interval m..n is given, only cliques with size between m and n (inclusive) are counted (m also may be +infinity). - See also: 1/ maximum_clique 2/ clique_cover + See also: 1/ maximum_clique 2/ clique_cover Ex1:clique_stats(random_graph(50,0.5)) Ex2:clique_stats(random_graph(50,0.5),5) Ex3:clique_stats(random_graph(50,0.5),3..5) - + ''' return GiacMethods['clique_stats'](self,*args) @@ -2554,10 +2554,10 @@ cdef class GiacMethods_base: Help for clustering_coefficient: clustering_coefficient(Graph(G),[Vrtx(v)]) Returns the average clustering coefficient of undirected graph G, or the local clustering coefficient of the vertex v in G. - See also: 1/ network_transitivity 2/ number_of_triangles + See also: 1/ network_transitivity 2/ number_of_triangles Ex1:clustering_coefficient(graph(%{[1,2],[2,3],[2,4],[3,4],[4,1]%})) Ex2:clustering_coefficient(graph(%{[1,2],[2,3],[2,4],[3,4],[4,1]%}),2) - + ''' return GiacMethods['clustering_coefficient'](self,*args) @@ -2566,11 +2566,11 @@ cdef class GiacMethods_base: Help for coeff: coeff(Expr(P),[Var]) Returns the list of coefficients of a polynomial with respect to the 2nd argument or the coefficient of degree the 3rd argument. - See also: 1/ pcoeff 2/ fcoeff + See also: 1/ pcoeff 2/ fcoeff Ex1:coeff(x*3+2) Ex2:coeff(5*y^2-3,y) Ex3:coeff(5*y^2-3,y,2) - + ''' return GiacMethods['coeff'](self,*args) @@ -2579,11 +2579,11 @@ cdef class GiacMethods_base: Help for coeffs: coeffs(Expr(P),[Var]) Returns the list of coefficients of a polynomial with respect to the 2nd argument or the coefficient of degree the 3rd argument. - See also: 1/ pcoeff 2/ fcoeff + See also: 1/ pcoeff 2/ fcoeff Ex1:coeffs(x*3+2) Ex2:coeffs(5*y^2-3,y) Ex3:coeffs(5*y^2-3,y,2) - + ''' return GiacMethods['coeffs'](self,*args) @@ -2592,11 +2592,11 @@ cdef class GiacMethods_base: Help for col: col(Mtrx(A),Intg(n)||Interval(n1..n2)) Returns column n or the sequence of the columns n1..n2 of the matrix A, or optional argument of count,count_eq,count_inf,count_sup. - See also: 1/ row 2/ count 3/ count_eq 4/ count_inf 5/ count_sup + See also: 1/ row 2/ count 3/ count_eq 4/ count_inf 5/ count_sup Ex1:col([[1,2,3],[4,5,6],[7,8,9]],1) Ex2:col([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3: count_eq(3,[[3,2,3],[4,3,2],[3,2,1]],col) - + ''' return GiacMethods['col'](self,*args) @@ -2605,10 +2605,10 @@ cdef class GiacMethods_base: Help for colDim: colDim(Mtrx) Number of columns of a matrix. - See also: 1/ rowdim + See also: 1/ rowdim Ex1:colDim([[1,2,3],[4,5,6]]) Ex2:colDim([[1,2],[3,4],[5,6]]) - + ''' return GiacMethods['colDim'](self,*args) @@ -2617,10 +2617,10 @@ cdef class GiacMethods_base: Help for colNorm: colNorm(Vect or Mtrx) Returns the max of the l1_norm of the columns of a matrix: colNorm(a_{j,k})=max_k(sum_j(|a_{j,k}|)). - See also: 1/ norm + See also: 1/ norm Ex1:colNorm([[1,2],[3,-4]]) Ex2:colNorm([[1,2,3,-4],[-5,3,2,1]]) - + ''' return GiacMethods['colNorm'](self,*args) @@ -2629,9 +2629,9 @@ cdef class GiacMethods_base: Help for colSwap: colSwap(Mtrx(A),Intg(n1),Intg(n2)) Returns the matrix obtained from A by swapping the n1-th column and the n2-th column. - See also: 1/ rowSwap + See also: 1/ rowSwap Ex1:colSwap([[1,2],[3,4],[5,6]],0,1) - + ''' return GiacMethods['colSwap'](self,*args) @@ -2640,10 +2640,10 @@ cdef class GiacMethods_base: Help for coldim: coldim(Mtrx) Number of columns of a matrix. - See also: 1/ rowdim + See also: 1/ rowdim Ex1:coldim([[1,2,3],[4,5,6]]) Ex2:coldim([[1,2],[3,4],[5,6]]) - + ''' return GiacMethods['coldim'](self,*args) @@ -2652,11 +2652,11 @@ cdef class GiacMethods_base: Help for collect: collect(Poly or LstPoly) Integer factorization of a polynomial (or of a list of poly). - See also: 1/ factor 2/ factors + See also: 1/ factor 2/ factors Ex1:collect(x^2-4) Ex2:collect(x^2-2) Ex3:collect([x^2-2,x^2-4]) - + ''' return GiacMethods['collect'](self,*args) @@ -2665,10 +2665,10 @@ cdef class GiacMethods_base: Help for colnorm: colnorm(Vect or Mtrx) Returns the max of the l1_norm of the columns of a matrix: colNorm(a_{j,k})=max_k(sum_j(|a_{j,k}|)). - See also: 1/ norm + See also: 1/ norm Ex1:colnorm([[1,2],[3,-4]]) Ex2:colnorm([[1,2,3,-4],[-5,3,2,1]]) - + ''' return GiacMethods['colnorm'](self,*args) @@ -2677,7 +2677,7 @@ cdef class GiacMethods_base: Help for color: color([GeoObj or legende],Intg) Draws a geometrical object with colors black=0 red=1 green=2 yellow=3 blue=4, filled with the color in the interior of a closed curve,line_width_n (00 (by default a=1 for sine window) to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ bartlett_hann_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ bartlett_hann_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(cosine_window(randvector(1000,0..1),1.5)) - + ''' return GiacMethods['cosine_window'](self,*args) @@ -3260,9 +3260,9 @@ cdef class GiacMethods_base: Help for cot: cot(Expr) Cotangent. - See also: 1/ acot 2/ tan + See also: 1/ acot 2/ tan Ex1:cot(pi/2) - + ''' return GiacMethods['cot'](self,*args) @@ -3271,10 +3271,10 @@ cdef class GiacMethods_base: Help for cote: cote(Vect) Third coordinate (z) of a 3-d point. - See also: 1/ abscissa 2/ ordinate 3/ coordinates + See also: 1/ abscissa 2/ ordinate 3/ coordinates Ex1:cote(point[1,2,3]) Ex2:cote(point(1,2,3)) - + ''' return GiacMethods['cote'](self,*args) @@ -3283,7 +3283,7 @@ cdef class GiacMethods_base: Help for count: count(Fnc(f)||LstIntg,(Lst||Mtrx)(l),[Opt(row||col)]) Returns f(l[0])+f(l[1])+...+f(l[size(l)-1]) or counts the number of occurrences if the argument is a vector of integers. - See also: 1/ count_eq 2/ count_inf 3/ count_sup + See also: 1/ count_eq 2/ count_inf 3/ count_sup Ex1:count(id,[-2/5,-1,0,1,2,3/5]) Ex2:count(1,[-2,-1,0,1,2,3]) Ex3:count([1,3,1,1,2,10,3]) @@ -3294,7 +3294,7 @@ cdef class GiacMethods_base: Ex8:count((x)->x>2,[[3,5/2],[4,1]],col) Ex9:count((x)->x>2 && x<4,[[3,9/2],[4,1]]) Ex10:count((x)->x<2 || x>4,[[3,9/2],[4,1]]) - + ''' return GiacMethods['count'](self,*args) @@ -3303,12 +3303,12 @@ cdef class GiacMethods_base: Help for count_eq: count_eq(Real(a),(Lst||Mtrx)(L),[Opt(row||col)]) Returns the number of elements of L equal to a. - See also: 1/ count 2/ count_inf 3/ count_sup + See also: 1/ count 2/ count_inf 3/ count_sup Ex1:count_eq(1,[-2,1,0,1,2,-3]) Ex2:count_eq(4,[[3,4],[4,1]]) Ex3:count_eq(4,[[3,4],[4,1]],row) Ex4:count_eq(4,[[3,4],[4,1]],col) - + ''' return GiacMethods['count_eq'](self,*args) @@ -3317,12 +3317,12 @@ cdef class GiacMethods_base: Help for count_inf: count_inf(Real(a),(Lst||Mtrx)(L),[Opt(row||col)]) Returns the number of elements of L strictly less than a. - See also: 1/ count 2/ count_eq 3/ count_sup + See also: 1/ count 2/ count_eq 3/ count_sup Ex1:count_inf(1,[-2,-1,0,1,2,3]) Ex2:count_inf(4,[[3,5],[4,1]]) Ex3:count_inf(4,[[3,5],[4,1]],row) Ex4:count_inf(4,[[3,5],[4,1]],col) - + ''' return GiacMethods['count_inf'](self,*args) @@ -3331,12 +3331,12 @@ cdef class GiacMethods_base: Help for count_sup: count_sup(Real(a),(Lst||Mtrx)(L),[Opt(row||col)]) Returns the number of elements of L strictly greater than a. - See also: 1/ count 2/ count_inf 3/ count_eq + See also: 1/ count 2/ count_inf 3/ count_eq Ex1:count_sup(1,[-2,-1,0,1,2,3]) Ex2:count_sup(3,[[3,5],[4,1]]) Ex3:count_sup(3,[[3,5],[4,1]],row) Ex4:count_sup(3,[[3,5],[4,1]],col) - + ''' return GiacMethods['count_sup'](self,*args) @@ -3345,7 +3345,7 @@ cdef class GiacMethods_base: Help for courbe_parametrique: courbe_parametrique(Cplx||Lst,Var||Lst(Var)) plotparam(a(x)+i*b(x),x=x0..x1) draws the curve X=a(x),Y=b(x) x=x0..x1 or plotparam([a(u,v),b(u,v),c(u,v)],[u=u0..u1,v=v0..v1]) draws the surface X=a(u,v),Y=b(u,v),Z=c(u,v) u=u0..u1 and v=v0..v1. - See also: 1/ plotfunc 2/ plotpolar 3/ arc + See also: 1/ plotfunc 2/ plotpolar 3/ arc Ex1:courbe_parametrique(sin(t)+i*cos(t),t) Ex2:courbe_parametrique(exp(i*t),t=0..pi/2,affichage=1) Ex3:courbe_parametrique(exp(i*t),t=0..pi/2,affichage=1+rempli) @@ -3354,7 +3354,7 @@ cdef class GiacMethods_base: Ex6:courbe_parametrique(sin(x)+i*cos(x),x=0..1,tstep=0.01) Ex7:courbe_parametrique([v*cos(u),v*sin(u),v],[u,v]) Ex8:courbe_parametrique([v*cos(u),v*sin(u),v],[u=0..pi,v=0..3],ustep=0.1,vstep=0.2) - + ''' return GiacMethods['courbe_parametrique'](self,*args) @@ -3363,10 +3363,10 @@ cdef class GiacMethods_base: Help for courbe_polaire: courbe_polaire(Expr,Var,VarMin,VarMax) plotpolar(f(x),x,a,b) draws the polar curve r=f(x) for x in [a,b]. - See also: 1/ plotparam 2/ plotfunc 3/ plotpolar + See also: 1/ plotparam 2/ plotfunc 3/ plotpolar Ex1:courbe_polaire(sin(2*x),x,0,pi) Ex2:courbe_polaire(sin(2*x),x,0,pi,tstep=0.1) - + ''' return GiacMethods['courbe_polaire'](self,*args) @@ -3375,9 +3375,9 @@ cdef class GiacMethods_base: Help for covariance: covariance(Lst||Mtrx,[Lst]) Returns the covariance of the elements of its argument. - See also: 1/ correlation 2/ covariance_correlation + See also: 1/ correlation 2/ covariance_correlation Ex1:covariance([[1,2],[1,1],[4,7]]) - + ''' return GiacMethods['covariance'](self,*args) @@ -3386,9 +3386,9 @@ cdef class GiacMethods_base: Help for covariance_correlation: covariance_correlation(Lst||Mtrx,[Lst]) Returns the list of the covariance and the correlation of the elements of its argument. - See also: 1/ covariance 2/ correlation + See also: 1/ covariance 2/ correlation Ex1:covariance_correlation([[1,2],[1,1],[4,7]]) - + ''' return GiacMethods['covariance_correlation'](self,*args) @@ -3397,11 +3397,11 @@ cdef class GiacMethods_base: Help for cpartfrac: cpartfrac(RatFrac) Performs partial fraction decomposition in ℂ of a fraction. - See also: 1/ factor 2/ normal + See also: 1/ factor 2/ normal Ex1:cpartfrac((x)/(4-x^2)) Ex2:cpartfrac((x^2-2*x+3)/(x^2-3*x+2)) Ex3:cpartfrac(a/(z*(z-b)),z) - + ''' return GiacMethods['cpartfrac'](self,*args) @@ -3410,9 +3410,9 @@ cdef class GiacMethods_base: Help for crationalroot: crationalroot(Poly(P)) Returns the list of complex rational roots of P without indicating the multiplicity. - See also: 1/ proot 2/ froot 3/ complexroot 4/ rationalroot 5/ realroot + See also: 1/ proot 2/ froot 3/ complexroot 4/ rationalroot 5/ realroot Ex1:crationalroot(2*x^3+(-5-7*i)*x^2+(-4+14*i)*x+8-4*i) - + ''' return GiacMethods['crationalroot'](self,*args) @@ -3421,12 +3421,12 @@ cdef class GiacMethods_base: Help for crayon: crayon(Color) Changes the color of the pencil (without parameter, returns the current color). - See also: 1/ leve_crayon 2/ baisse_crayon + See also: 1/ leve_crayon 2/ baisse_crayon Ex1: crayon vert Ex2:crayon(rouge) Ex3:crayon(5) Ex4:crayon(gomme) - + ''' return GiacMethods['crayon'](self,*args) @@ -3435,13 +3435,13 @@ cdef class GiacMethods_base: Help for createwav: createwav(Lst(data),[opts]) Returns an audio clip from data, optionally setting channel count, bit depth, sample rate, duration and normalization level. - See also: 1/ readwav 2/ writewav 3/ playsnd + See also: 1/ readwav 2/ writewav 3/ playsnd Ex1:createwav(duration=3.5) Ex2:createwav(sin(2*pi*440*soundsec(2)),samplerate=48000) Ex3:createwav(sin(2*pi*440*soundsec(2)),bit_depth=8) Ex4:createwav(10*sin(2*pi*440*soundsec(2)),normalize=-3) Ex5: t:=soundsec(3):;L,R:=sin(2*pi*440*t),sin(2*pi*445*t):;createwav([L,R]) - + ''' return GiacMethods['createwav'](self,*args) @@ -3450,10 +3450,10 @@ cdef class GiacMethods_base: Help for cross: cross(Vect(v1),Vect(v2)) Wedge product. - See also: 1/ dot + See also: 1/ dot Ex1:cross([1,2],[3,4]) Ex2:cross([1,2,3],[4,5,6]) - + ''' return GiacMethods['cross'](self,*args) @@ -3462,10 +3462,10 @@ cdef class GiacMethods_base: Help for crossP: crossP(Vect(v1),Vect(v2)) Wedge product. - See also: 1/ dot + See also: 1/ dot Ex1:crossP([1,2],[3,4]) Ex2:crossP([1,2,3],[4,5,6]) - + ''' return GiacMethods['crossP'](self,*args) @@ -3474,9 +3474,9 @@ cdef class GiacMethods_base: Help for cross_correlation: cross_correlation(cross_correlation(Lst(u),Lst(v))) Returns the cross_correlation of two signals u and v. - See also: 1/ auto_correlation 2/ correlation + See also: 1/ auto_correlation 2/ correlation Ex1:cross_correlation([1,2],[3,4,5]) - + ''' return GiacMethods['cross_correlation'](self,*args) @@ -3485,10 +3485,10 @@ cdef class GiacMethods_base: Help for cross_point: cross_point(Opt) Option of the display command for a point. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) - + ''' return GiacMethods['cross_point'](self,*args) @@ -3497,11 +3497,11 @@ cdef class GiacMethods_base: Help for cross_ratio: cross_ratio(Pnt or Cplx(a),Pnt or Cplx(b),Pnt or Cplx(c),Pnt or Cplx(d)) Returns the complex number equal to ((c-a)/(c-b))/((d-a)/(d-b)). - See also: 1/ harmonic_conjugate 2/ is_conjugate + See also: 1/ harmonic_conjugate 2/ is_conjugate Ex1:cross_ratio(i,2+i,3/2+i,3+i) Ex2:cross_ratio(0,1+i,1,i) Ex3:cross_ratio(0,1,2,3) - + ''' return GiacMethods['cross_ratio'](self,*args) @@ -3510,10 +3510,10 @@ cdef class GiacMethods_base: Help for crossproduct: crossproduct(Vect(v1),Vect(v2)) Wedge product. - See also: 1/ dot + See also: 1/ dot Ex1:crossproduct([1,2],[3,4]) Ex2:crossproduct([1,2,3],[4,5,6]) - + ''' return GiacMethods['crossproduct'](self,*args) @@ -3522,9 +3522,9 @@ cdef class GiacMethods_base: Help for csc: csc(Expr) Cosecant: csc(x)=1/sin(x). - See also: 1/ sin 2/ acsc + See also: 1/ sin 2/ acsc Ex1:csc(pi/2) - + ''' return GiacMethods['csc'](self,*args) @@ -3533,12 +3533,12 @@ cdef class GiacMethods_base: Help for csolve: csolve(LstEq,LstVar) Returns the list of complex solutions of an equation or a matrix where the rows are ℂ-solutions of a system of polynomial equations. - See also: 1/ cZeros 2/ solve 3/ fslove + See also: 1/ cZeros 2/ solve 3/ fslove Ex1:csolve(x^4-1,x) Ex2:csolve(x^4-y^4 and x+y=2,[x,y]) Ex3:csolve(x^4-y^4 and x+y=0 and x^2=2*x,[x,y]) Ex4:csolve(u*v-u=v and v^2=u,[u,v]) - + ''' return GiacMethods['csolve'](self,*args) @@ -3547,9 +3547,9 @@ cdef class GiacMethods_base: Help for csv2gen: csv2gen(Strng(filename),Strng(sep),Strng(nl),Strng(decsep),Strng(eof),[string]) Reads a file (or string) in CSV format. - See also: 1/ read + See also: 1/ read Ex1:csv2gen("mat.txt",",",char(10),".") - + ''' return GiacMethods['csv2gen'](self,*args) @@ -3558,13 +3558,13 @@ cdef class GiacMethods_base: Help for cube: cube(Pnt(A),Pnt(B),Pnt(C)) Draws the direct cube with vertices A,B with a face in the plane (A,B,C). - See also: 1/ parallelepiped 2/ cylinder 3/ icosahedron 4/ dodecahedron 5/ octahedron 6/ tetrahedron 7/ centered_cube - Ex1:cube([0,0,0],[3,0,0],[0,0,1]) - Ex2: A,B,C:=point(1,0,0),point(1,1,0),point(0,1,0);c:=cube(A,B,C);A,B,C,D,E,F,G,H:=sommets(c); - Ex3: A,B,K:=point(1,0,0),point(1,1,0),point(0,2,0);c:=cube(A,B,C);A,B,C,D,E,F,G,H:=sommets(c); - Ex4: c:=cube([0,0,0],[1,0,0],[0,1,0]);c1,c2,c4,c3,c5,c6,c7,c8:=sommets(c); - Ex5: c:=cube([0,0,0],[0,2,0],[0,0,1]);c1,c2,c4,c3,c5,c6,c7,c8:=sommets(c); - + See also: 1/ parallelepiped 2/ cylinder 3/ icosahedron 4/ dodecahedron 5/ octahedron 6/ tetrahedron 7/ centered_cube + Ex1:cube([0,0,0],[3,0,0],[0,0,1]) + Ex2: A,B,C:=point(1,0,0),point(1,1,0),point(0,1,0);c:=cube(A,B,C);A,B,C,D,E,F,G,H:=sommets(c); + Ex3: A,B,K:=point(1,0,0),point(1,1,0),point(0,2,0);c:=cube(A,B,C);A,B,C,D,E,F,G,H:=sommets(c); + Ex4: c:=cube([0,0,0],[1,0,0],[0,1,0]);c1,c2,c4,c3,c5,c6,c7,c8:=sommets(c); + Ex5: c:=cube([0,0,0],[0,2,0],[0,0,1]);c1,c2,c4,c3,c5,c6,c7,c8:=sommets(c); + ''' return GiacMethods['cube'](self,*args) @@ -3573,11 +3573,11 @@ cdef class GiacMethods_base: Help for cumSum: cumSum(Lst(l)||Seq||Str) Returns the list (or the sequence or the string) lr where the elements are the cumulative sum of the list l: lr[k]=sum(l[j],j=0..k) (or lr=sum(l[j],j=0..k)$(k=0..size(l)-1)). - See also: 1/ sum + See also: 1/ sum Ex1:cumSum([0,1,2,3,4]) Ex2:cumSum(1.2,3,4.5,6) Ex3:cumSum("a","b","c","d") - + ''' return GiacMethods['cumSum'](self,*args) @@ -3586,11 +3586,11 @@ cdef class GiacMethods_base: Help for cumsum: cumsum(Lst(l)||Seq||Str) Returns the list (or the sequence or the string) lr where the elements are the cumulative sum of the list l: lr[k]=sum(l[j],j=0..k) (or lr=sum(l[j],j=0..k)$(k=0..size(l)-1)). - See also: 1/ sum + See also: 1/ sum Ex1:cumsum([0,1,2,3,4]) Ex2:cumsum(1.2,3,4.5,6) Ex3:cumsum("a","b","c","d") - + ''' return GiacMethods['cumsum'](self,*args) @@ -3599,13 +3599,13 @@ cdef class GiacMethods_base: Help for cumulated_frequencies: cumulated_frequencies(Lst || Mtrx) Draws the diagram of the cumulated frequencies (rows=[value,frequencies]) - See also: 1/ histogram 2/ classes 3/ bar_plot + See also: 1/ histogram 2/ classes 3/ bar_plot Ex1:cumulated_frequencies([1,2,1,1,2,1,2,4,3,3]) Ex2:cumulated_frequencies([(rand(6)+1)$(k=1..100)]) Ex3:cumulated_frequencies([[1,0.3],[2,0.5],[3,0.2]]) Ex4:cumulated_frequencies([[1..2,0.3],[2..3,0.5],[3..4,0.2]]) Ex5:cumulated_frequencies([[1..2,0.3,0.5],[2..3,0.5,0.2],[3..4,0.2,0.3]]) - + ''' return GiacMethods['cumulated_frequencies'](self,*args) @@ -3614,9 +3614,9 @@ cdef class GiacMethods_base: Help for curl: curl(Lst(A,B,C),Lst(x,y,z)) curl([A,B,C],[x,y,z])=[dC/dy-dB/dz,dA/dz-dC/dx,dB/dx-dA/dy]. - See also: 1/ derive 2/ divergence + See also: 1/ derive 2/ divergence Ex1:curl([2*x*y,x*z,y*z],[x,y,z]) - + ''' return GiacMethods['curl'](self,*args) @@ -3627,7 +3627,7 @@ cdef class GiacMethods_base: Content of the matrix editor or spreadsheet. Ex1:current_sheet(1,2) Ex2:current_sheet(A1..A5,B,G) - + ''' return GiacMethods['current_sheet'](self,*args) @@ -3636,7 +3636,7 @@ cdef class GiacMethods_base: Help for curvature: curvature(Curve,Point) Curvature of curve C at point M. - See also: 1/ osculating_circle 2/ evolute + See also: 1/ osculating_circle 2/ evolute Ex1:curvature(plot(x^2),point(1,1)) Ex2:curvature([5*cos(t),5*sin(t)],t) Ex3:curvature([t,t^2],t) @@ -3644,7 +3644,7 @@ cdef class GiacMethods_base: Ex5:curvature([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t) Ex6:curvature([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t,7) Ex7: trigcos(curvature([2*cos(t),2*sin(t),3*t],t)) - + ''' return GiacMethods['curvature'](self,*args) @@ -3653,8 +3653,8 @@ cdef class GiacMethods_base: Help for curve: curve(Expr) Reserved word. - See also: 1/ - + See also: 1/ + ''' return GiacMethods['curve'](self,*args) @@ -3663,10 +3663,10 @@ cdef class GiacMethods_base: Help for cyan: cyan(Opt) Option of the display command to display with color. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),red) Ex2: F:=display(point(2+1.5*i),point_point+green) - + ''' return GiacMethods['cyan'](self,*args) @@ -3675,9 +3675,9 @@ cdef class GiacMethods_base: Help for cycle2perm: cycle2perm(Cycle) Converts the cycle c to a permutation. - See also: 1/ cycles2permu 2/ permu2cycles + See also: 1/ cycles2permu 2/ permu2cycles Ex1:cycle2perm([1,3,5]) - + ''' return GiacMethods['cycle2perm'](self,*args) @@ -3686,10 +3686,10 @@ cdef class GiacMethods_base: Help for cycle_graph: cycle_graph(Intg(n)||Lst(V)) Returns a cyclic graph with n vertices (or with vertices from list V). - See also: 1/ graph 2/ path_graph + See also: 1/ graph 2/ path_graph Ex1:cycle_graph(4) Ex2:cycle_graph(["one","two","three","four","five"]) - + ''' return GiacMethods['cycle_graph'](self,*args) @@ -3698,9 +3698,9 @@ cdef class GiacMethods_base: Help for cycleinv: cycleinv(Cycle(c)) Returns the inverse cycle of the cycle c. - See also: 1/ perminv + See also: 1/ perminv Ex1:cycleinv([1,3,5]) - + ''' return GiacMethods['cycleinv'](self,*args) @@ -3709,9 +3709,9 @@ cdef class GiacMethods_base: Help for cycles2permu: cycles2permu(Lst(Cycle)) Converts a product of cycles into a permutation. - See also: 1/ permu2cycles 2/ cycle2perm + See also: 1/ permu2cycles 2/ cycle2perm Ex1:cycles2permu([[1,3,5],[3,4]]) - + ''' return GiacMethods['cycles2permu'](self,*args) @@ -3720,9 +3720,9 @@ cdef class GiacMethods_base: Help for cyclotomic: cyclotomic(Expr) N-th cyclotomic polynomial. - See also: 1/ none + See also: 1/ none Ex1:cyclotomic(20) - + ''' return GiacMethods['cyclotomic'](self,*args) @@ -3731,10 +3731,10 @@ cdef class GiacMethods_base: Help for cylinder: cylinder(Pnt(A),Vect(v),Real(r),[Real(h)]) Draws a cylinder with axis (A,v), with radius r [and with altitude h]. - See also: 1/ half_cone 2/ cone + See also: 1/ half_cone 2/ cone Ex1:cylinder([0,0,0],[0,1,0],2) Ex2:cylinder([0,0,0],[0,1,0],2,-3) - + ''' return GiacMethods['cylinder'](self,*args) @@ -3743,10 +3743,10 @@ cdef class GiacMethods_base: Help for dash_line: dash_line(Opt) Option of the display command for a line. - See also: 1/ display + See also: 1/ display Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) - + ''' return GiacMethods['dash_line'](self,*args) @@ -3755,10 +3755,10 @@ cdef class GiacMethods_base: Help for dashdot_line: dashdot_line(Opt) Option of the display command for a line. - See also: 1/ display + See also: 1/ display Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) - + ''' return GiacMethods['dashdot_line'](self,*args) @@ -3767,10 +3767,10 @@ cdef class GiacMethods_base: Help for dashdotdot_line: dashdotdot_line(Opt) Option of the display command for a line. - See also: 1/ display + See also: 1/ display Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) - + ''' return GiacMethods['dashdotdot_line'](self,*args) @@ -3781,7 +3781,7 @@ cdef class GiacMethods_base: dayofweek(d,m,y) returns the day of the given date (day,month,year) : 0 for sunday, 1 for monday ...6 for saturday. Ex1:dayofweek(21,4,2014) Ex2:dayofweek(15,10,1582) - + ''' return GiacMethods['dayofweek'](self,*args) @@ -3790,12 +3790,12 @@ cdef class GiacMethods_base: Help for deSolve: deSolve(Eq,[TimeVar],FncVar) Solves a differential equation or a differential linear system with constant coefficients. - See also: 1/ integrate 2/ diff 3/ odesolve 4/ plotode 5/ plotfiefd + See also: 1/ integrate 2/ diff 3/ odesolve 4/ plotode 5/ plotfiefd Ex1:deSolve(y'+x*y=0) Ex2:deSolve(y'+x*y=0,y) Ex3:deSolve(y'+x*y=0,[0,1]) Ex4:deSolve([y'+x*y=0,y(0)=1],y) - Ex5:deSolve([y'=[[1,2],[2,1]]*y+[x,x+1],y(0)=[1,2]]) + Ex5:deSolve([y'=[[1,2],[2,1]]*y+[x,x+1],y(0)=[1,2]]) Ex6:deSolve(y''+y=0,y) Ex7:deSolve([y''+y=sin(x),y(0)=1,y'(0)=2],y) Ex8:deSolve([y''+y=sin(x),y(0)=1,y'(0)=2],x,y) @@ -3807,7 +3807,7 @@ cdef class GiacMethods_base: Ex14:deSolve([z''+2*z'+z,z(0)=1,z'(0)=0],z(u)) Ex15:deSolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],t,z) Ex16:deSolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],z(t)) - + ''' return GiacMethods['deSolve'](self,*args) @@ -3816,10 +3816,10 @@ cdef class GiacMethods_base: Help for debut_enregistrement: debut_enregistrement(Var(nom_du_dessin)) Begins recording the commands making up the drawing; the name of the resulting procedure is the argument. - See also: 1/ fin_enregistrement + See also: 1/ fin_enregistrement Ex1:debut_enregistrement(maison) Ex2:debut_enregistrement(arbre) - + ''' return GiacMethods['debut_enregistrement'](self,*args) @@ -3828,11 +3828,11 @@ cdef class GiacMethods_base: Help for degree: degree(Poly(P),Var(Var)) Degree of the polynomial P with respect to the second argument. - See also: 1/ valuation 2/ size 3/ total_degree + See also: 1/ valuation 2/ size 3/ total_degree Ex1:degree(x^3+x) Ex2:degree([1,0,1,0]) Ex3:degree(x^3+x*y,y) - + ''' return GiacMethods['degree'](self,*args) @@ -3841,9 +3841,9 @@ cdef class GiacMethods_base: Help for degree_sequence: degree_sequence(Graph(G)) Returns the list of degrees of vertices of G (arc directions are ignored). - See also: 1/ is_graphic_sequence 2/ is_regular 2/ sequence_graph 3/ vertex_degree + See also: 1/ is_graphic_sequence 2/ is_regular 2/ sequence_graph 3/ vertex_degree Ex1:degree_sequence(graph(trail(1,2,3,4,2))) - + ''' return GiacMethods['degree_sequence'](self,*args) @@ -3852,11 +3852,11 @@ cdef class GiacMethods_base: Help for delcols: delcols(Mtrx(A),Interval(n1..n2)||n1) Returns the matrix where the columns n1..n2 (or n1) of the matrix A are deleted. - See also: 1/ delrows + See also: 1/ delrows Ex1:delcols([[1,2,3],[4,5,6],[7,8,9]],1..1) Ex2:delcols([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3:delcols([[1,2,3],[4,5,6],[7,8,9]],1) - + ''' return GiacMethods['delcols'](self,*args) @@ -3865,9 +3865,9 @@ cdef class GiacMethods_base: Help for delete_arc: delete_arc(Graph(G),Edge(e)||Trail(T)||Lst(E)) Returns a modified copy of digraph G with arc e (or trail T or list of arcs E) removed. - See also: 1/ add_arc 2/ delete_edge 3/ digraph 4/ edges 5/ has_arc 6/ trail + See also: 1/ add_arc 2/ delete_edge 3/ digraph 4/ edges 5/ has_arc 6/ trail Ex1:delete_arc(digraph(trail(1,2,3,4,5,1)),[5,1]) - + ''' return GiacMethods['delete_arc'](self,*args) @@ -3876,9 +3876,9 @@ cdef class GiacMethods_base: Help for delete_edge: delete_edge(Graph(G),Edge(e)||Trail(T)||Lst(E)) Returns a modified copy of undirected graph G with edge e (or trail T or list of edges E) removed. - See also: 1/ add_edge 2/ delete_arc 3/ edges 4/ graph 5/ has_edge 6/ trail + See also: 1/ add_edge 2/ delete_arc 3/ edges 4/ graph 5/ has_edge 6/ trail Ex1:delete_edge(cycle_graph(4),[1,2]) - + ''' return GiacMethods['delete_edge'](self,*args) @@ -3887,9 +3887,9 @@ cdef class GiacMethods_base: Help for delete_vertex: delete_vertex(Graph(G),Vrtx(v)||Lst(V)) Returns a modified copy of G with vertex v (or vertices from V) removed. - See also: 1/ add_vertex 2/ induced_subgraph + See also: 1/ add_vertex 2/ induced_subgraph Ex1:delete_vertex(cycle_graph(5),[1,4]) - + ''' return GiacMethods['delete_vertex'](self,*args) @@ -3898,11 +3898,11 @@ cdef class GiacMethods_base: Help for delrows: delrows(Mtrx(A),Interval(n1..n2)||n1) Returns the matrix where the rows n1..n2 (or n1) of the matrix A are deleted. - See also: 1/ delcols + See also: 1/ delcols Ex1:delrows([[1,2,3],[4,5,6],[7,8,9]],1..1) Ex2:delrows([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3:delrows([[1,2,3],[4,5,6],[7,8,9]],1) - + ''' return GiacMethods['delrows'](self,*args) @@ -3911,10 +3911,10 @@ cdef class GiacMethods_base: Help for deltalist: deltalist(Lst) Returns the list of the differences of two terms in succession. - See also: 1/ + See also: 1/ Ex1:deltalist([1,4,8,9]) Ex2:deltalist([1,8,4,9]) - + ''' return GiacMethods['deltalist'](self,*args) @@ -3923,11 +3923,11 @@ cdef class GiacMethods_base: Help for denom: denom(Frac(a/b) or RatFrac) Returns the denominator of the simplified fraction. - See also: 1/ getDenom 2/ getNum 3/ numer 4/ f2nd + See also: 1/ getDenom 2/ getNum 3/ numer 4/ f2nd Ex1:denom(25/15) Ex2:denom((x^3-1)/(x^2-1)) Ex3:denom(1+(x^3-1)/x^2) - + ''' return GiacMethods['denom'](self,*args) @@ -3936,10 +3936,10 @@ cdef class GiacMethods_base: Help for densityplot: densityplot(Expr,[x=xrange,y=yrange],[z],[xstep],[ystep]) Shows in the plane with colors the graph of an expression of 2 variables. - See also: 1/ plotfunc 2/ plotcontour + See also: 1/ plotfunc 2/ plotcontour Ex1:densityplot(x^2-y^2,[x=-2..2,y=-2..2],xstep=0.1,ystep=0.1) Ex2:densityplot(x^2-y^2,[x=-2..2,y=-2..2],z=-2..2,xstep=0.1,ystep=0.1) - + ''' return GiacMethods['densityplot'](self,*args) @@ -3948,9 +3948,9 @@ cdef class GiacMethods_base: Help for departures: departures(Graph(G),[Vrtx(v)]) Returns the list of vertices of digraph G which are connected by v with arcs such that tails are in v. If v is omitted, a list of departures is computed for every vertex in G. - See also: 1/ out_degree + See also: 1/ out_degree Ex1:departures(digraph(%{[1,2],[1,3],[2,3]%}),1) - + ''' return GiacMethods['departures'](self,*args) @@ -3959,7 +3959,7 @@ cdef class GiacMethods_base: Help for derive: derive(Expr or Fnc,[SeqVar or LstVar],[n]) Returns the derivative with respect to the 2nd argument. - See also: 1/ ' 2/ function_diff 3/ integrate 4/ taux_accroissement 5/ implicitdiff + See also: 1/ ' 2/ function_diff 3/ integrate 4/ taux_accroissement 5/ implicitdiff Ex1:derive(x^3-x) Ex2:derive(x^3-x,x,3) Ex3:derive(x^3-x,quote(x)$3) @@ -3968,7 +3968,7 @@ cdef class GiacMethods_base: Ex6:derive(x*y+z*y,y,z) Ex7:derive(x*y+z*y,[y,z]) Ex8: f(x):=sin(2x);g:=diff(f);h:=diff(diff(f)) - + ''' return GiacMethods['derive'](self,*args) @@ -3977,7 +3977,7 @@ cdef class GiacMethods_base: Help for deriver: deriver(Expr or Fnc,[SeqVar or LstVar],[n]) Returns the derivative with respect to the 2nd argument. - See also: 1/ ' 2/ function_diff 3/ integrate 4/ taux_accroissement 5/ implicitdiff + See also: 1/ ' 2/ function_diff 3/ integrate 4/ taux_accroissement 5/ implicitdiff Ex1:deriver(x^3-x) Ex2:deriver(x^3-x,x,3) Ex3:deriver(x^3-x,quote(x)$3) @@ -3986,7 +3986,7 @@ cdef class GiacMethods_base: Ex6:deriver(x*y+z*y,y,z) Ex7:deriver(x*y+z*y,[y,z]) Ex8: f(x):=sin(2x);g:=diff(f);h:=diff(diff(f)) - + ''' return GiacMethods['deriver'](self,*args) @@ -3995,12 +3995,12 @@ cdef class GiacMethods_base: Help for desolve: desolve(Eq,[TimeVar],FncVar) Solves a differential equation or a differential linear system with constant coefficients. - See also: 1/ integrate 2/ diff 3/ odesolve 4/ plotode 5/ plotfiefd + See also: 1/ integrate 2/ diff 3/ odesolve 4/ plotode 5/ plotfiefd Ex1:desolve(y'+x*y=0) Ex2:desolve(y'+x*y=0,y) Ex3:desolve(y'+x*y=0,[0,1]) Ex4:desolve([y'+x*y=0,y(0)=1],y) - Ex5:desolve([y'=[[1,2],[2,1]]*y+[x,x+1],y(0)=[1,2]]) + Ex5:desolve([y'=[[1,2],[2,1]]*y+[x,x+1],y(0)=[1,2]]) Ex6:desolve(y''+y=0,y) Ex7:desolve([y''+y=sin(x),y(0)=1,y'(0)=2],y) Ex8:desolve([y''+y=sin(x),y(0)=1,y'(0)=2],x,y) @@ -4012,7 +4012,7 @@ cdef class GiacMethods_base: Ex14:desolve([z''+2*z'+z,z(0)=1,z'(0)=0],z(u)) Ex15:desolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],t,z) Ex16:desolve([z'=[[1,2],[2,1]]*z+[t,t+1],z(0)=[1,2]],z(t)) - + ''' return GiacMethods['desolve'](self,*args) @@ -4021,11 +4021,11 @@ cdef class GiacMethods_base: Help for dessine_tortue: dessine_tortue([Intg(n)]) Draws the full (or not full if n=1) triangle representing the turtle. - See also: 1/ crayon + See also: 1/ crayon Ex1:dessine_tortue() Ex2:dessine_tortue(0) Ex3:dessine_tortue(1) - + ''' return GiacMethods['dessine_tortue'](self,*args) @@ -4034,10 +4034,10 @@ cdef class GiacMethods_base: Help for det: det(Mtrx) Determinant of a square matrix M. - See also: 1/ rref 2/ det_minor 3/ Det + See also: 1/ rref 2/ det_minor 3/ Det Ex1:det([[1,2],[3,4]]) Ex2:det([[1,2,3],[1,3,6],[2,5,7]]) - + ''' return GiacMethods['det'](self,*args) @@ -4046,9 +4046,9 @@ cdef class GiacMethods_base: Help for det_minor: det_minor(Mtrx(A)) Returns the determinant calculated with the calculus of minors. - See also: 1/ det + See also: 1/ det Ex1:det_minor([[1,2],[3,4]]) - + ''' return GiacMethods['det_minor'](self,*args) @@ -4057,13 +4057,13 @@ cdef class GiacMethods_base: Help for developper: developper(Expr) Full distribution of * and / over + and -. - See also: 1/ texpand 2/ normal 3/ simplify 4/ ratnormal + See also: 1/ texpand 2/ normal 3/ simplify 4/ ratnormal Ex1:developper((x+y)*(z+1)) Ex2:developper((a+b+c)/d) Ex3:developper((y+x)*(z+y)*(x+z)) Ex4:developper((x+3)^4) Ex5:developper((2*x-2*1)*(x^2-3*x+2)+(x^2-2*x+3)*(2*x-3*1)) - + ''' return GiacMethods['developper'](self,*args) @@ -4072,11 +4072,11 @@ cdef class GiacMethods_base: Help for developper_transcendant: developper_transcendant(Expr) Expands transcendental expressions. - See also: 1/ tcollect 2/ tlin 3/ lin 4/ trigexpand + See also: 1/ tcollect 2/ tlin 3/ lin 4/ trigexpand Ex1:developper_transcendant(sin(2*x)+exp(x+y)) Ex2:developper_transcendant(cos(x+y)) Ex3:developper_transcendant(cos(3*x)) - + ''' return GiacMethods['developper_transcendant'](self,*args) @@ -4085,13 +4085,13 @@ cdef class GiacMethods_base: Help for dfc: dfc(Real(x0),Int(n)||Real(eps)) Returns the continued fraction development at x0 of order n or with precision eps. - See also: 1/ dfc2f 2/ convert + See also: 1/ dfc2f 2/ convert Ex1:dfc(sqrt(2),5) Ex2:dfc(pi,4) Ex3:dfc(evalf(pi),1e-09) Ex4: convert(sqrt(2),confrac,'dev');dev Ex5: convert(9976/6961,confrac,'l');l - + ''' return GiacMethods['dfc'](self,*args) @@ -4100,10 +4100,10 @@ cdef class GiacMethods_base: Help for dfc2f: dfc2f(LstFrac_Cont)) Converts a continued fraction into a real. - See also: 1/ dfc 2/ convert + See also: 1/ dfc 2/ convert Ex1:dfc2f([1,1,1]) Ex2:dfc2f([1,2,[2]]) - + ''' return GiacMethods['dfc2f'](self,*args) @@ -4112,14 +4112,14 @@ cdef class GiacMethods_base: Help for diag: diag(Lst(l)||(Mtrx(A),[left||right||lu])||Lst(l),Lst(d),Lst(u)) With 1 argument returns either the diagonal matrix with diagonal l or the diagonal of A, with 2 arguments returns the large left (lower) triangular part of A or the large right (upper) triangular part of A or factors A into 3 parts : strict left (lower) triangular, diagonal, strict right (upper) triangular and with 3 arguments returns the tridiagonal matrix with diagonals l,d,u. - See also: 1/ identity 2/ lu 3/ BlockDiagonal 4/ upper 5/ lower + See also: 1/ identity 2/ lu 3/ BlockDiagonal 4/ upper 5/ lower Ex1:diag([[1,2],[3,4]]) Ex2:diag([1,2,3]) Ex3:diag([[1,2],[3,4]],left) Ex4:diag([[1,2],[3,4]],right) Ex5:diag([[1,2],[3,4]],lu) Ex6:diag([1,2],[3,4,5],[6,7]) - + ''' return GiacMethods['diag'](self,*args) @@ -4128,7 +4128,7 @@ cdef class GiacMethods_base: Help for diff: diff(Expr or Fnc,[SeqVar or LstVar],[n]) Returns the derivative with respect to the 2nd argument. - See also: 1/ ' 2/ function_diff 3/ integrate 4/ taux_accroissement 5/ implicitdiff + See also: 1/ ' 2/ function_diff 3/ integrate 4/ taux_accroissement 5/ implicitdiff Ex1:diff(x^3-x) Ex2:diff(x^3-x,x,3) Ex3:diff(x^3-x,quote(x)$3) @@ -4137,7 +4137,7 @@ cdef class GiacMethods_base: Ex6:diff(x*y+z*y,y,z) Ex7:diff(x*y+z*y,[y,z]) Ex8: f(x):=sin(2x);g:=diff(f);h:=diff(diff(f)) - + ''' return GiacMethods['diff'](self,*args) @@ -4146,10 +4146,10 @@ cdef class GiacMethods_base: Help for digraph: digraph([Lst(V)],[Set(E)],[Mtrx(A)],[options]) Create a directed (un)weighted graph from vertices V, edges E and/or adjacency or weight matrix A. All parameters are optional. - See also: 1/ graph 2/ trail + See also: 1/ graph 2/ trail Ex1:digraph(%{[1,2],[2,3],[3,4],[4,1]%}) Ex2:digraph([a,b,c,d],%{[[a,b],1.0],[[a,c],2.3],[[b,d],3.1],[[c,d],4]%}) - + ''' return GiacMethods['digraph'](self,*args) @@ -4158,9 +4158,9 @@ cdef class GiacMethods_base: Help for dijkstra: dijkstra(Graph(G),Vrtx(v),[Vrtx(w)||Lst(W)]) Returns the cheapest weighted path from vertex v to w (or to vertices from W) in undirected graph G. Output is in the form [[v1,v2,...,vk],d] (or list of these) where v1,v2,...,vk are vertices along each path and d is the weight of the path. - See also: 1/ allpairs_distance 2/ shortest_path + See also: 1/ allpairs_distance 2/ shortest_path Ex1:dijkstra(graph(%{[[1,2],1],[[2,3],3],[[3,4],7],[[4,5],3],[[5,6],3],[[1,6],3]%}),1,4) - + ''' return GiacMethods['dijkstra'](self,*args) @@ -4169,9 +4169,9 @@ cdef class GiacMethods_base: Help for dim: dim(Mtrx) Returns the list which gives the dimension of the matrix specified as argument. - See also: 1/ rowdim 2/ coldim 3/ sizes 4/ size + See also: 1/ rowdim 2/ coldim 3/ sizes 4/ size Ex1:dim([[1,2,3],[4,5,6]]) - + ''' return GiacMethods['dim'](self,*args) @@ -4180,8 +4180,8 @@ cdef class GiacMethods_base: Help for directed: directed(Opt) Option for graph and digraph commands. - See also: 1/ weighted 2/ graph 3/ digraph - + See also: 1/ weighted 2/ graph 3/ digraph + ''' return GiacMethods['directed'](self,*args) @@ -4190,9 +4190,9 @@ cdef class GiacMethods_base: Help for discard_edge_attribute: discard_edge_attribute(Graph(G),Edge(e),Seq(tag1=value1,tag2=value2,..)) Discards the attributes with tags tag1, tag2, ... assigned to edge e in G and returns the modified copy of G. - See also: 1/ get_edge_attribute 2/ set_edge_attribute 3/ list_edge_attributes + See also: 1/ get_edge_attribute 2/ set_edge_attribute 3/ list_edge_attributes Ex1:discard_edge_attribute(cycle_graph(3),[1,2],"cost") - + ''' return GiacMethods['discard_edge_attribute'](self,*args) @@ -4201,9 +4201,9 @@ cdef class GiacMethods_base: Help for discard_graph_attribute: discard_graph_attribute(Graph(G),Seq(tag1=value1,tag2=value2,..)) Discards the graph attributes with tags tag1, tag2, ... and returns the modified copy of G. - See also: 1/ get_graph_attribute 2/ set_graph_attribute 3/ list_graph_attributes + See also: 1/ get_graph_attribute 2/ set_graph_attribute 3/ list_graph_attributes Ex1:discard_graph_attribute(cycle_graph(3),"name") - + ''' return GiacMethods['discard_graph_attribute'](self,*args) @@ -4212,9 +4212,9 @@ cdef class GiacMethods_base: Help for discard_vertex_attribute: discard_vertex_attribute(Graph(G),Vrtx(v),Seq(tag1=value1,tag2=value2,..)) Discards the attributes with tags tag1, tag2, ... assigned to vertex v in G and returns the modified copy of G. - See also: 1/ get_vertex_attribute 2/ set_vertex_attribute 3/ list_vertex_attributes + See also: 1/ get_vertex_attribute 2/ set_vertex_attribute 3/ list_vertex_attributes Ex1:discard_vertex_attribute(cycle_graph(3),1,"supply") - + ''' return GiacMethods['discard_vertex_attribute'](self,*args) @@ -4223,9 +4223,9 @@ cdef class GiacMethods_base: Help for disjoint_union: disjoint_union(Seq(G1,G2,...)) Returns the disjoint union of the graphs G1, G2, ... Vertices in the resulting graph are labelled with "k:v", where k is index of the corresponding k-th graph Gk and v is vertex in Gk. - See also: 1/ graph_join 2/ graph_union + See also: 1/ graph_join 2/ graph_union Ex1:disjoint_union(is_connected(disjoint_union(cycle_graph(5),path_graph(4)))) - + ''' return GiacMethods['disjoint_union'](self,*args) @@ -4234,7 +4234,7 @@ cdef class GiacMethods_base: Help for display: display([GeoObj or legende],Intg) Draws a geometrical object with colors black=0 red=1 green=2 yellow=3 blue=4, filled with the color in the interior of a closed curve,line_width_n (0=0 or, the (-n)th previous question if n<0 (by default n=-1 for the previous question). - See also: 1/ ans + See also: 1/ ans Ex1:entry() Ex2:entry(2) Ex3:entry(-2) - + ''' return GiacMethods['entry'](self,*args) @@ -4916,10 +4916,10 @@ cdef class GiacMethods_base: Help for envelope: envelope(Expr(Xpr),Var(t)||[x,y,t]) Returns the envelope of the curves with equation Xpr=0 as t varies. - See also: 1/ tangent 2/ locus + See also: 1/ tangent 2/ locus Ex1:envelope(y+x*tan(t)-2*sin(t),t) Ex2:envelope(v+u*tan(t)-3*sin(t),[u,v,t]) - + ''' return GiacMethods['envelope'](self,*args) @@ -4928,9 +4928,9 @@ cdef class GiacMethods_base: Help for epsilon: epsilon(NULL) Returns the value of epsilon of the CAS configuration. - See also: 1/ epsilon2zero + See also: 1/ epsilon2zero Ex1:epsilon() - + ''' return GiacMethods['epsilon'](self,*args) @@ -4939,9 +4939,9 @@ cdef class GiacMethods_base: Help for epsilon2zero: epsilon2zero(Expr) Values < epsilon are replaced by zero. - See also: 1/ evalf + See also: 1/ evalf Ex1:epsilon2zero(1e-13+x+5) - + ''' return GiacMethods['epsilon2zero'](self,*args) @@ -4950,11 +4950,11 @@ cdef class GiacMethods_base: Help for equal: equal(Expr,Expr) Prefixed version of =. - See also: 1/ = 2/ equal2diff 3/ equal2list 4/ left 5/ right + See also: 1/ = 2/ equal2diff 3/ equal2list 4/ left 5/ right Ex1: 2*x=4 Ex2:equal(2*x,4) Ex3:equal(x^2-3x+2,0) - + ''' return GiacMethods['equal'](self,*args) @@ -4963,10 +4963,10 @@ cdef class GiacMethods_base: Help for equal2diff: equal2diff(Equal) A=B or equal(A,B) is converted into the difference A-B. - See also: 1/ left 2/ right 3/ equal2list 4/ equal 5/ = + See also: 1/ left 2/ right 3/ equal2list 4/ equal 5/ = Ex1:equal2diff(x=2) Ex2:equal2diff(equal(x,2)) - + ''' return GiacMethods['equal2diff'](self,*args) @@ -4975,10 +4975,10 @@ cdef class GiacMethods_base: Help for equal2list: equal2list(Equal) A=B or equal(A,B) is converted into the list [A,B]. - See also: 1/ left 2/ right 3/ equal2diff 4/ equal 5/ = + See also: 1/ left 2/ right 3/ equal2diff 4/ equal 5/ = Ex1:equal2list(x=2) Ex2:equal2list(equal(x,2)) - + ''' return GiacMethods['equal2list'](self,*args) @@ -4987,9 +4987,9 @@ cdef class GiacMethods_base: Help for equation: equation(GeoObj, VectParam) equation returns the cartesian equation of a curve. - See also: 1/ parameq + See also: 1/ parameq Ex1:equation(line(1-i,i),[x,y]) - + ''' return GiacMethods['equation'](self,*args) @@ -4998,12 +4998,12 @@ cdef class GiacMethods_base: Help for equilateral_triangle: equilateral_triangle((Pnt(A) or Cplx),(Pnt(B) or Cplx),[Pnt(P)],[Var(C)]) equilateral_triangle(A,B) (resp equilateral_triangle(A,B,P)) draws the direct equilateral triangle ABC with side AB (resp in the half-plane ABP). - See also: 1/ triangle + See also: 1/ triangle Ex1:equilateral_triangle(point(1+i),0) Ex2:equilateral_triangle(0,1+i,C) Ex3:equilateral_triangle(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:equilateral_triangle(point(0,0,0),point(3,3,3),point(0,0,3),C) - + ''' return GiacMethods['equilateral_triangle'](self,*args) @@ -5012,10 +5012,10 @@ cdef class GiacMethods_base: Help for erf: erf(Real(x0)) Returns the approximate value of 2/sqrt(pi)*int(exp(-t^2),t,0,x0). - See also: 1/ erfc + See also: 1/ erfc Ex1:erf(1) Ex2:erf(1/(sqrt(2)))*1/2 - + ''' return GiacMethods['erf'](self,*args) @@ -5024,10 +5024,10 @@ cdef class GiacMethods_base: Help for erfc: erfc(Real(x0)) Returns the approximate value of 2/sqrt(pi)*int(exp(-t^2),t,x0,+infinity). - See also: 1/ erf + See also: 1/ erf Ex1:erfc(1) Ex2:erfc(1/(sqrt(2)))*1/2 - + ''' return GiacMethods['erfc'](self,*args) @@ -5036,10 +5036,10 @@ cdef class GiacMethods_base: Help for error: error(Str) Generates the display of an error in a program. - See also: 1/ try 2/ catch + See also: 1/ try 2/ catch Ex1:error("Argument should be integer") Ex2:error("je provoque une erreur") - + ''' return GiacMethods['error'](self,*args) @@ -5048,10 +5048,10 @@ cdef class GiacMethods_base: Help for est_permu: est_permu(Lst) Returns 1 if the argument is a permutation and 0 otherwise. - See also: 1/ is_cycle 2/ permu2cycles + See also: 1/ is_cycle 2/ permu2cycles Ex1:est_permu([4,2,3,1]) Ex2:est_permu([4,2,3,1,0]) - + ''' return GiacMethods['est_permu'](self,*args) @@ -5060,10 +5060,10 @@ cdef class GiacMethods_base: Help for euler: euler(Intg(n)) Euler's function (euler(n)=card({p=0):; euler_lagrange(sqrt((1+y'^2)/y),t,y) - + ''' return GiacMethods['euler_lagrange'](self,*args) @@ -5100,7 +5100,7 @@ cdef class GiacMethods_base: Ex3: purge(a,b,c);eval_level(1);a:=b+1; b:=c+1;c:=3; Ex4: purge(a,b,c);eval_level(2);a:=b+1; b:=c+1;c:=3; Ex5: purge(a,b,c);eval_level(3);a:=b+1; b:=c+1;c:=3; - + ''' return GiacMethods['eval_level'](self,*args) @@ -5109,11 +5109,11 @@ cdef class GiacMethods_base: Help for evala: evala(Expr) Simplifies the expression. - See also: 1/ simplify + See also: 1/ simplify Ex1:evala(2*x+y=1) Ex2:evala(2*x*2) Ex3:evala((2*x+1)^2) - + ''' return GiacMethods['evala'](self,*args) @@ -5122,10 +5122,10 @@ cdef class GiacMethods_base: Help for evalb: evalb(Expr) Boolean evaluation of the argument. - See also: 1/ evalf 2/ eval + See also: 1/ evalf 2/ eval Ex1:evalb(a==2) Ex2:evalb(sqrt(2)+pi>a) - + ''' return GiacMethods['evalb'](self,*args) @@ -5134,10 +5134,10 @@ cdef class GiacMethods_base: Help for evalc: evalc(Expr) Returns a complex expression simplified to the format real+i*imag. - See also: 1/ normal + See also: 1/ normal Ex1:evalc(-3+4*i+exp(i)) Ex2:evalc(1/(x+y*i)) - + ''' return GiacMethods['evalc'](self,*args) @@ -5146,14 +5146,14 @@ cdef class GiacMethods_base: Help for evalf: evalf(Expr,[Int]) Numerical evaluation of the first argument (we can give the number of digits as second argument). - See also: 1/ evalb 2/ eval + See also: 1/ evalb 2/ eval Ex1:evalf(2/3) Ex2:evalf(2/3,2) Ex3:evalf(2*sin(1)) Ex4:evalf(2*sin(1),40) Ex5:evalf(sqrt(2)+pi) Ex6:evalf(sqrt(2)+pi,30) - + ''' return GiacMethods['evalf'](self,*args) @@ -5162,9 +5162,9 @@ cdef class GiacMethods_base: Help for evalm: evalm(Expr) Evaluates its argument. - See also: 1/ evalf + See also: 1/ evalf Ex1:evalm(2*sin(pi)) - + ''' return GiacMethods['evalm'](self,*args) @@ -5173,10 +5173,10 @@ cdef class GiacMethods_base: Help for even: even(Intg(n)) Returns 1 if the integer is even, else returns 0. - See also: 1/ odd + See also: 1/ odd Ex1:even(6) Ex2:even(1251) - + ''' return GiacMethods['even'](self,*args) @@ -5185,11 +5185,11 @@ cdef class GiacMethods_base: Help for evolute: evolute(Curve) Evolute of a curve C. - See also: 1/ curvature 2/ osculating_circle + See also: 1/ curvature 2/ osculating_circle Ex1:evolute(plot(x^2)) Ex2:evolute([t,t^2],t) Ex3:evolute([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t) - + ''' return GiacMethods['evolute'](self,*args) @@ -5198,12 +5198,12 @@ cdef class GiacMethods_base: Help for exact: exact(Expr) Converts the expression to a rational or real expression. - See also: 1/ + See also: 1/ Ex1:exact(-2) Ex2:exact(1.5) Ex3:exact(1.4141) Ex4:exact(0.156381102937) - + ''' return GiacMethods['exact'](self,*args) @@ -5212,9 +5212,9 @@ cdef class GiacMethods_base: Help for exbisector: exbisector((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Pnt(C) or Cplx)) Draws the exterior bisector of the angle (AB,AC) given by 3 points A,B,C. - See also: 1/ angle 2/ bisector + See also: 1/ angle 2/ bisector Ex1:exbisector(0,1,i) - + ''' return GiacMethods['exbisector'](self,*args) @@ -5223,9 +5223,9 @@ cdef class GiacMethods_base: Help for excircle: excircle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) excircle(A,B,C) draws the A-excircle of the triangle ABC. - See also: 1/ incircle 2/ circumcircle + See also: 1/ incircle 2/ circumcircle Ex1:excircle(0,1,1+i) - + ''' return GiacMethods['excircle'](self,*args) @@ -5234,12 +5234,12 @@ cdef class GiacMethods_base: Help for execute: execute(Str) Instruction transforming a string into a command or into a number. - See also: 1/ string + See also: 1/ string Ex1:execute("ifactor(54)") Ex2:execute("123") Ex3:execute("0123") Ex4:execute(sin,x) - + ''' return GiacMethods['execute'](self,*args) @@ -5248,10 +5248,10 @@ cdef class GiacMethods_base: Help for exp: exp(Expr or Opt) Exponential or option of the convert or convertir command (id trig2exp). - See also: 1/ ln 2/ convert 3/ trig2exp + See also: 1/ ln 2/ convert 3/ trig2exp Ex1:exp(0) Ex2: convert(cos(x),exp) - + ''' return GiacMethods['exp'](self,*args) @@ -5260,10 +5260,10 @@ cdef class GiacMethods_base: Help for exp2list: exp2list(Expr) Returns the list made with the righthand member of (var=expr0 or var=expr1), to be used after solve in TI mode. - See also: 1/ list2exp + See also: 1/ list2exp Ex1:exp2list((x=2) or (x=0)) Ex2:exp2list((x=3 and y=9) or (x=-1 and y=1) ) - + ''' return GiacMethods['exp2list'](self,*args) @@ -5272,10 +5272,10 @@ cdef class GiacMethods_base: Help for exp2pow: exp2pow(Expr) Transforms exp(n*ln(x)) to x^n. - See also: 1/ pow2exp + See also: 1/ pow2exp Ex1:exp2pow(exp(3*ln(x))) Ex2:exp2pow(exp(x*ln(x))) - + ''' return GiacMethods['exp2pow'](self,*args) @@ -5284,10 +5284,10 @@ cdef class GiacMethods_base: Help for exp2trig: exp2trig(Expr) Transforms the complex exponential into sine and cosine. - See also: 1/ trig2exp 2/ atrig2ln + See also: 1/ trig2exp 2/ atrig2ln Ex1:exp2trig(exp(i*x)) Ex2:exp2trig(exp(-i*x)) - + ''' return GiacMethods['exp2trig'](self,*args) @@ -5296,13 +5296,13 @@ cdef class GiacMethods_base: Help for expand: expand(Expr) Full distribution of * and / over + and -. - See also: 1/ texpand 2/ normal 3/ simplify 4/ ratnormal + See also: 1/ texpand 2/ normal 3/ simplify 4/ ratnormal Ex1:expand((x+y)*(z+1)) Ex2:expand((a+b+c)/d) Ex3:expand((y+x)*(z+y)*(x+z)) Ex4:expand((x+3)^4) Ex5:expand((2*x-2*1)*(x^2-3*x+2)+(x^2-2*x+3)*(2*x-3*1)) - + ''' return GiacMethods['expand'](self,*args) @@ -5311,9 +5311,9 @@ cdef class GiacMethods_base: Help for expexpand: expexpand(Expr) Expands exponentials. - See also: 1/ texpand 2/ lnexpand 3/ trigexpand + See also: 1/ texpand 2/ lnexpand 3/ trigexpand Ex1:expexpand(exp(3*x)) - + ''' return GiacMethods['expexpand'](self,*args) @@ -5322,9 +5322,9 @@ cdef class GiacMethods_base: Help for expln: expln(Opt) Option of the convert or convertir command (id trig2exp). - See also: 1/ exp 2/ ln 3/ convert 4/ trig2exp + See also: 1/ exp 2/ ln 3/ convert 4/ trig2exp Ex1: convert(cos(x),expln) - + ''' return GiacMethods['expln'](self,*args) @@ -5333,12 +5333,12 @@ cdef class GiacMethods_base: Help for exponential: exponential(Real(lambda),Real(x)) Returns the probability density at x of the exponential law of parameter lambda. - See also: 1/ exponential_cdf 2/ exponential_icdf 3/ randvector 4/ ranm + See also: 1/ exponential_cdf 2/ exponential_icdf 3/ randvector 4/ ranm Ex1:exponential(2.1,3.5) Ex2:exponential(2.1,0.5) Ex3: randvector(3,exponential,1.2) Ex4: ranm(4,3,exponential,1.2) - + ''' return GiacMethods['exponential'](self,*args) @@ -5347,10 +5347,10 @@ cdef class GiacMethods_base: Help for exponential_cdf: exponential_cdf(Real(lambda),Real(x0),[Real(y0)]) Returns the probability that a exponential random variable of parameter lambda is less than x0 (or between x0 and y0). - See also: 1/ exponentiald 2/ exponential_icdf + See also: 1/ exponentiald 2/ exponential_icdf Ex1:exponential_cdf(4.2,2.1) Ex2:exponential_cdf(4.2,2.1,3.2) - + ''' return GiacMethods['exponential_cdf'](self,*args) @@ -5359,10 +5359,10 @@ cdef class GiacMethods_base: Help for exponential_icdf: exponential_icdf(Real(lambda),Real(x0),Real(p)) Returns h such that the probability that a exponential random variable of parameter lambda is less than h is p (0<=p<=1). - See also: 1/ exponential_cdf 2/ exponentiald + See also: 1/ exponential_cdf 2/ exponentiald Ex1:exponential_icdf(4.2,0.95) Ex2:exponential_icdf(4.2,0.6) - + ''' return GiacMethods['exponential_icdf'](self,*args) @@ -5371,10 +5371,10 @@ cdef class GiacMethods_base: Help for exponential_regression: exponential_regression(Lst||Mtrx(A),[Lst]) Returns the coefficients (a,b) of y=b*a^x : it is the best exponential which approx the points where the coordinates are the rows of A (or the 2 lists). - See also: 1/ logarithmic_regression + See also: 1/ logarithmic_regression Ex1:exponential_regression([[1.0,2.0],[0.0,1.0],[4.0,7.0]]) Ex2:exponential_regression([1.0,0.0,4.0],[2.0,1.0,7.0]) - + ''' return GiacMethods['exponential_regression'](self,*args) @@ -5383,10 +5383,10 @@ cdef class GiacMethods_base: Help for exponential_regression_plot: exponential_regression_plot(Lst||Mtrx(A),[Lst]) Returns the plot of y=b*a^x : it is the best exponential which approx the points where the coordinates are the rows of A (or the 2 lists). - See also: 1/ logarithmic_regression_plot + See also: 1/ logarithmic_regression_plot Ex1:exponential_regression_plot([[1.0,2.0],[0.0,1.0],[4.0,7.0]]) Ex2:exponential_regression_plot([1.0,0.0,4.0],[2.0,1.0,7.0]) - + ''' return GiacMethods['exponential_regression_plot'](self,*args) @@ -5395,12 +5395,12 @@ cdef class GiacMethods_base: Help for exponentiald: exponentiald(Real(lambda),Real(x)) Returns the probability density at x of the exponential law of parameter lambda. - See also: 1/ exponential_cdf 2/ exponential_icdf 3/ randvector 4/ ranm + See also: 1/ exponential_cdf 2/ exponential_icdf 3/ randvector 4/ ranm Ex1:exponentiald(2.1,3.5) Ex2:exponentiald(2.1,0.5) Ex3: randvector(3,exponential,1.2) Ex4: ranm(4,3,exponential,1.2) - + ''' return GiacMethods['exponentiald'](self,*args) @@ -5409,10 +5409,10 @@ cdef class GiacMethods_base: Help for exponentiald_cdf: exponentiald_cdf(Real(lambda),Real(x0),[Real(y0)]) Returns the probability that a exponential random variable of parameter lambda is less than x0 (or between x0 and y0). - See also: 1/ exponentiald 2/ exponential_icdf + See also: 1/ exponentiald 2/ exponential_icdf Ex1:exponentiald_cdf(4.2,2.1) Ex2:exponentiald_cdf(4.2,2.1,3.2) - + ''' return GiacMethods['exponentiald_cdf'](self,*args) @@ -5421,10 +5421,10 @@ cdef class GiacMethods_base: Help for exponentiald_icdf: exponentiald_icdf(Real(lambda),Real(x0),Real(p)) Returns h such that the probability that a exponential random variable of parameter lambda is less than h is p (0<=p<=1). - See also: 1/ exponential_cdf 2/ exponentiald + See also: 1/ exponential_cdf 2/ exponentiald Ex1:exponentiald_icdf(4.2,0.95) Ex2:exponentiald_icdf(4.2,0.6) - + ''' return GiacMethods['exponentiald_icdf'](self,*args) @@ -5433,9 +5433,9 @@ cdef class GiacMethods_base: Help for export_graph: export_graph(Graph(G),Str("path/to/graphname")) Writes G to the file 'graphname.dot' in directory 'path/to' in dot format, returns 1 on success and 0 on failure. - See also: 1/ import_graph + See also: 1/ import_graph Ex1:export_graph(complete_graph(5),"K5") - + ''' return GiacMethods['export_graph'](self,*args) @@ -5444,11 +5444,11 @@ cdef class GiacMethods_base: Help for export_mathml: export_mathml(Expr,[display||content]) Converts an expression to presentation or content MathML block. - See also: 1/ mathml 2/ latex + See also: 1/ mathml 2/ latex Ex1:export_mathml(a+2*b) Ex2:export_mathml(a+2*b,display) Ex3:export_mathml(a+2*b,content) - + ''' return GiacMethods['export_mathml'](self,*args) @@ -5457,10 +5457,10 @@ cdef class GiacMethods_base: Help for expovariate: expovariate(Real(a)) Returns a random real according to the exponential distribution with parameter a>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:expovariate(1) Ex2:expovariate(2) - + ''' return GiacMethods['expovariate'](self,*args) @@ -5469,12 +5469,12 @@ cdef class GiacMethods_base: Help for expr: expr(Str) Instruction transforming a string into a command or into a number. - See also: 1/ string + See also: 1/ string Ex1:expr("ifactor(54)") Ex2:expr("123") Ex3:expr("0123") Ex4:expr(sin,x) - + ''' return GiacMethods['expr'](self,*args) @@ -5483,13 +5483,13 @@ cdef class GiacMethods_base: Help for extend: extend(Lst,Lst||Seq,Seq||Str,Str||Mtrx,Mtrx) Concatenates two lists or two strings or two sequences or 2 matrices; L:=concat(L,L1) or L.concat(L1). - See also: 1/ append 2/ cat 3/ semi_augment 4/ border 5/ + + See also: 1/ append 2/ cat 3/ semi_augment 4/ border 5/ + Ex1:extend([1,2],[3,4,5]) Ex2:extend("bon","jour") Ex3:extend([[1,2],[3,4]],[[4,5,6],[6,7,8]]) Ex4: L:=[1,2];L.concat([3,4,5]) Ex5: S:="abcd";S.concat("efghi") - + ''' return GiacMethods['extend'](self,*args) @@ -5498,11 +5498,11 @@ cdef class GiacMethods_base: Help for extract_measure: extract_measure(Var) extract_measure gives as answer the value calculated by the argument. - See also: 1/ angleatraw 2/ distanceatraw 3/ angleat 4/ distanceat 5/ slopeatraw 6/ areaatraw 7/ perimeteratraw 8/ slopeat 5/ areaat 10/ perimeterat + See also: 1/ angleatraw 2/ distanceatraw 3/ angleat 4/ distanceat 5/ slopeatraw 6/ areaatraw 7/ perimeteratraw 8/ slopeat 5/ areaat 10/ perimeterat Ex1:extract_measure(distanceatraw(0,1+i,(1+i)/2)) Ex2:extract_measure(angleatraw(0,1,1+i,1)) Ex3: A:=point(0);B:=point(1+i);a:=distanceatraw(A,B,(1+i)/2);extract_measure(a) - + ''' return GiacMethods['extract_measure'](self,*args) @@ -5556,7 +5556,7 @@ cdef class GiacMethods_base: Ex43:extrema(4x*y-x^4-y^4,[x,y]) Ex44:extrema(x*sin(y),[x,y]) Ex45:extrema(x^4+y^4,[x,y]) - Ex46:extrema(x^3*y-x*y^3,[x,y]) + Ex46:extrema(x^3*y-x*y^3,[x,y]) Ex47:extrema(x^2+y^2+z^2,x^4+y^4+z^4=1,[x,y,z]) Ex48:extrema(3x+3y+8z,[x^2+z^2=1,y^2+z^2=1],[x,y,z]) Ex49:extrema(2x^2+y^2,x^4-x^2+y^2=5,[x,y]) @@ -5565,10 +5565,10 @@ cdef class GiacMethods_base: Ex52:extrema(ln(x)+2*ln(y)+3*ln(z)+4*ln(u)+5*ln(v),x+y+z+u+v=1,[x,y,z,u,v]) Ex53:extrema(x*y*z,-2x^3+15x^2*y+11y^3-24y=0,[x,y,z]) Ex54:extrema(x+y-exp(x)-exp(y)-exp(x+y),[x,y]) - Ex55:extrema(x^2*sin(y)-4*x,[x,y]) + Ex55:extrema(x^2*sin(y)-4*x,[x,y]) Ex56:extrema((1+y*sinh(x))/(1+y^2+tanh(x)^2),[x,y]) Ex57:extrema((1+y*sinh(x))/(1+y^2+tanh(x)^2),y=x^2,[x,y]) - + ''' return GiacMethods['extrema'](self,*args) @@ -5577,11 +5577,11 @@ cdef class GiacMethods_base: Help for ezgcd: ezgcd(Poly,Poly) GCD of 2 polynomials with at least 2 variables, with the ezgcd algorithm. - See also: 1/ gcd 2/ modgcd 3/ heugcd 4/ psrgcd + See also: 1/ gcd 2/ modgcd 3/ heugcd 4/ psrgcd Ex1:ezgcd(x^2-2*xy+y^2-1,x-y) Ex2:ezgcd((x+1)^4-y^4,(x+1-y)^2) Ex3:ezgcd((x+y-1)*(x+y+1),(x+y+1)^2) - + ''' return GiacMethods['ezgcd'](self,*args) @@ -5590,10 +5590,10 @@ cdef class GiacMethods_base: Help for f2nd: f2nd(Frac or RatFrac) Returns the list built with the numerator and the denominator of the simplified fraction. - See also: 1/ simp2 2/ numer 3/ denom 4/ getNum 5/ getDenom + See also: 1/ simp2 2/ numer 3/ denom 4/ getNum 5/ getDenom Ex1:f2nd(42/12) Ex2:f2nd((x^2+2*x+1)/(x^2-1)) - + ''' return GiacMethods['f2nd'](self,*args) @@ -5602,10 +5602,10 @@ cdef class GiacMethods_base: Help for fMax: fMax(Expr,[Var]) Returns the abscissa of the maximum of the expression. - See also: 1/ fMin + See also: 1/ fMin Ex1:fMax(-x^2+2*x+1,x) Ex2:fMax(-x^2+2*x+1,x=1..2) - + ''' return GiacMethods['fMax'](self,*args) @@ -5614,12 +5614,12 @@ cdef class GiacMethods_base: Help for fMin: fMin(Expr,[Var]) Returns the abscissa of the minimum of the expression. - See also: 1/ fMax + See also: 1/ fMax Ex1:fMin(x^2-2*x+1,x) Ex2:fMin(x^2-2*x+1,x=1..2) Ex3:fMin((x-3)^2+(y-5)^2+1,[],[x,y],[1,1]) Ex4:fMin((x-3)^2+(y-5)^2+1,[x+y^2=1],[x,y],[1,1]) - + ''' return GiacMethods['fMin'](self,*args) @@ -5628,13 +5628,13 @@ cdef class GiacMethods_base: Help for fPart: fPart(Real||LstReal) Returns the fractional part (if x<0 then frac(x)+floor(x)+1=x else frac(x)+floor(x)=x). - See also: 1/ floor 2/ iPart 3/ trunc + See also: 1/ floor 2/ iPart 3/ trunc Ex1:fPart(1/2) Ex2:fPart(-1/2) Ex3:fPart(1.2) Ex4:fPart(-1.2) Ex5:fPart([3.4,sqrt(2)]) - + ''' return GiacMethods['fPart'](self,*args) @@ -5643,10 +5643,10 @@ cdef class GiacMethods_base: Help for faces: faces(Polygon or Polyedr(P)) Returns the list of the faces (1 face=matrix(n,3) where the n rows are the n vertices of the face) of the polyhedron P. - See also: 1/ polyhedron + See also: 1/ polyhedron Ex1:faces(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex2:faces(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6]))[2] - + ''' return GiacMethods['faces'](self,*args) @@ -5655,10 +5655,10 @@ cdef class GiacMethods_base: Help for facteurs_premiers: facteurs_premiers(Intg(a) or LstIntg) Returns the list of prime factors of an integer (each factor is followed by its multiplicity). - See also: 1/ ifactor 2/ factors + See also: 1/ ifactor 2/ factors Ex1:facteurs_premiers(36) Ex2:facteurs_premiers([36,52]) - + ''' return GiacMethods['facteurs_premiers'](self,*args) @@ -5667,11 +5667,11 @@ cdef class GiacMethods_base: Help for factor: factor(Expr) Factors a polynomial. - See also: 1/ ifactor 2/ cfactor 3/ partfrac 4/ normal + See also: 1/ ifactor 2/ cfactor 3/ partfrac 4/ normal Ex1:factor(x^4-1) Ex2:factor(x^4-4,sqrt(2)) Ex3:factor(x^4+12*x^3+54*x^2+108*x+81) - + ''' return GiacMethods['factor'](self,*args) @@ -5680,10 +5680,10 @@ cdef class GiacMethods_base: Help for factor_xn: factor_xn(Poly(P)) Factors x^n in P (n=degree of polynomial P). - See also: 1/ ifactor 2/ partfrac 3/ normal + See also: 1/ ifactor 2/ partfrac 3/ normal Ex1:factor_xn(x^4-1) Ex2:factor_xn(x^4+12*x^3+54*x^2+108*x+81) - + ''' return GiacMethods['factor_xn'](self,*args) @@ -5692,10 +5692,10 @@ cdef class GiacMethods_base: Help for factorial: factorial(Intg(n)|| Real(a)) factorial(n)=n!. For non-integers, factorial(a)=a! = G(a + 1). This calculates the Gamma function. - See also: 1/ comb 2/ perm + See also: 1/ comb 2/ perm Ex1:factorial(4) Ex2:factorial(1.2) - + ''' return GiacMethods['factorial'](self,*args) @@ -5704,11 +5704,11 @@ cdef class GiacMethods_base: Help for factoriser: factoriser(Expr) Factors a polynomial. - See also: 1/ ifactor 2/ cfactor 3/ partfrac 4/ normal + See also: 1/ ifactor 2/ cfactor 3/ partfrac 4/ normal Ex1:factoriser(x^4-1) Ex2:factoriser(x^4-4,sqrt(2)) Ex3:factoriser(x^4+12*x^3+54*x^2+108*x+81) - + ''' return GiacMethods['factoriser'](self,*args) @@ -5717,10 +5717,10 @@ cdef class GiacMethods_base: Help for factoriser_entier: factoriser_entier(Intg(a)) Factorization of an integer into prime factors. - See also: 1/ factor 2/ ecm_factor + See also: 1/ factor 2/ ecm_factor Ex1:factoriser_entier(50) Ex2:factoriser_entier(123456789) - + ''' return GiacMethods['factoriser_entier'](self,*args) @@ -5729,11 +5729,11 @@ cdef class GiacMethods_base: Help for factoriser_sur_C: factoriser_sur_C(Expr) Factorization of the expression in ℂ (on the Gaussian integers if there are more than 2 variables). - See also: 1/ factor + See also: 1/ factor Ex1:factoriser_sur_C(x^2*y+y) Ex2:factoriser_sur_C(x^2*y^2+y^2+4*x^2+4) Ex3:factoriser_sur_C(x^2*y^2+y^2+2*x^2+2) - + ''' return GiacMethods['factoriser_sur_C'](self,*args) @@ -5742,10 +5742,10 @@ cdef class GiacMethods_base: Help for factors: factors(Poly or LstPoly) Returns the list of prime factors of a polynomial (each factor is followed by its multiplicity). - See also: 1/ factor 2/ ifactors + See also: 1/ factor 2/ ifactors Ex1:factors(x^4-1) Ex2:factors([x^2,x^2-1]) - + ''' return GiacMethods['factors'](self,*args) @@ -5754,9 +5754,9 @@ cdef class GiacMethods_base: Help for fadeev: fadeev(Opt) Option of the pcar or charpoly command to specify the algorithm. - See also: 1/ pcar + See also: 1/ pcar Ex1: pcar([[4,1,-2],[1,2,-1],[2,1,0]],fadeev) - + ''' return GiacMethods['fadeev'](self,*args) @@ -5765,9 +5765,9 @@ cdef class GiacMethods_base: Help for false: false() Boolean equal to false or 0. - See also: 1/ true + See also: 1/ true Ex1: a:=false - + ''' return GiacMethods['false'](self,*args) @@ -5776,14 +5776,14 @@ cdef class GiacMethods_base: Help for falsepos_solver: falsepos_solver(Opt) Argument for fsolve giving the method for solving a numerical equation. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve(cos(x)=x,x,0..1,bisection_solver) Ex2: fsolve(cos(x)=x,x,0..1,brent_solver) Ex3: fsolve(cos(x)=x,x,0..1,falsepos_solver) Ex4: fsolve(cos(x)=x,x,0,newton_solver) Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) - + ''' return GiacMethods['falsepos_solver'](self,*args) @@ -5792,9 +5792,9 @@ cdef class GiacMethods_base: Help for fclose: fclose(File(f)) Closes the file f. - See also: 1/ fprint 2/ fopen + See also: 1/ fprint 2/ fopen Ex1:fclose(f) - + ''' return GiacMethods['fclose'](self,*args) @@ -5803,9 +5803,9 @@ cdef class GiacMethods_base: Help for fcoeff: fcoeff(Lst(root||pole,order)) Returns the polynomial described by the list (root or pole, order). - See also: 1/ pcoeff 2/ froot 3/ proot + See also: 1/ pcoeff 2/ froot 3/ proot Ex1:fcoeff([1,2,0,1,3,-1]) - + ''' return GiacMethods['fcoeff'](self,*args) @@ -5814,13 +5814,13 @@ cdef class GiacMethods_base: Help for fdistrib: fdistrib(Expr) Full distribution of * and / over + and -. - See also: 1/ texpand 2/ normal 3/ simplify 4/ ratnormal + See also: 1/ texpand 2/ normal 3/ simplify 4/ ratnormal Ex1:fdistrib((x+y)*(z+1)) Ex2:fdistrib((a+b+c)/d) Ex3:fdistrib((y+x)*(z+y)*(x+z)) Ex4:fdistrib((x+3)^4) Ex5:fdistrib((2*x-2*1)*(x^2-3*x+2)+(x^2-2*x+3)*(2*x-3*1)) - + ''' return GiacMethods['fdistrib'](self,*args) @@ -5829,10 +5829,10 @@ cdef class GiacMethods_base: Help for fft: fft(Vect or (Vect(L),Intg(a),Intg(p)) Fast Fourier Transform in ℝ or in the field ℤ/pℤ, with a as primitive n-th root of 1 (n=size(L)). - See also: 1/ ifft + See also: 1/ ifft Ex1:fft([1,2,3,4,0,0,0,0]) Ex2:fft(ranm(128),22798,35969) - + ''' return GiacMethods['fft'](self,*args) @@ -5841,13 +5841,13 @@ cdef class GiacMethods_base: Help for fieldplot: fieldplot(Expr,VectVar,[Opt]) fieldplot(f(t,y),[t,y]) draws the plotfield of the diff equation y'=f(t,y). - See also: 1/ interactive_plotode 2/ odeplot 3/ odesolve 4/ desolve + See also: 1/ interactive_plotode 2/ odeplot 3/ odesolve 4/ desolve Ex1:fieldplot(sin(t*y),[t=-5..5,y=-3..3],xstep=0.5,ystep=0.5) Ex2:fieldplot(-t*y,[t,y]) Ex3:fieldplot(-t*y,[t,y],normalize) Ex4:fieldplot(-t*y,[t,y],normalize,xstep=0.5,ystep=0.5) Ex5:fieldplot(-t*y,[t=-6.868..6.868,y=-6.868..6.868],normalize) - + ''' return GiacMethods['fieldplot'](self,*args) @@ -5856,13 +5856,13 @@ cdef class GiacMethods_base: Help for find: find(Expr,Vect) List of positions of an object in a list, a string or a set. - See also: 1/ index 2/ member + See also: 1/ index 2/ member Ex1:find(1,[3,x,1,2,1,3]) Ex2:find(2,[0,1,3,2,4,2,5])[0] Ex3:find("a","abracadabrant") Ex4:find("ab","abracadabrant") Ex5:find(1,%{4,3,1,2%}) - + ''' return GiacMethods['find'](self,*args) @@ -5871,11 +5871,11 @@ cdef class GiacMethods_base: Help for find_cycles: find_cycles(Graph(G,[length=k||l..u])) Returns the list of elementary cycles of the digraph G. If option "length" is specified, only cycles of length k resp. of length between l and u are returned. - See also: 1/ is_acyclic + See also: 1/ is_acyclic Ex1:find_cycles(digraph(%{[1,2],[1,3],[3,1],[1,4],[2,3],[4,3],[4,5],[5,3],[5,6],[7,6],[8,6],[8,7]%})) Ex2:find_cycles(digraph(%{[1,2],[1,3],[3,1],[1,4],[2,3],[4,3],[4,5],[5,3],[5,6],[7,6],[8,6],[8,7]%}),length=3) Ex3:find_cycles(digraph(%{[1,2],[1,3],[3,1],[1,4],[2,3],[4,3],[4,5],[5,3],[5,6],[7,6],[8,6],[8,7]%}),length=3..4) - + ''' return GiacMethods['find_cycles'](self,*args) @@ -5884,9 +5884,9 @@ cdef class GiacMethods_base: Help for findhelp: findhelp(Cmd) Returns help about the command (if ? is infixed see when) . - See also: 1/ ifte 2/ when + See also: 1/ ifte 2/ when Ex1:findhelp(ifactor) - + ''' return GiacMethods['findhelp'](self,*args) @@ -5895,12 +5895,12 @@ cdef class GiacMethods_base: Help for fisher: fisher(Intg(n),Intg(m),Real(x0)) Returns the probability density of the Fisher-Snedecor law (n and m are the numbers of degrees of freedom). - See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm + See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm Ex1:fisher(4,10,2.1) Ex2:fisher(4,4,2.1) Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) - + ''' return GiacMethods['fisher'](self,*args) @@ -5909,10 +5909,10 @@ cdef class GiacMethods_base: Help for fisher_cdf: fisher_cdf(Intg(n),Intg(m),Real(x0)) Returns the probability that a Fisher-Snedecor random variable is less than x0 (n and m are the numbers of degrees of freedom). - See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd + See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd Ex1:fisher_cdf(4,4,2.1) Ex2:fisher_cdf(4,10,3.5) - + ''' return GiacMethods['fisher_cdf'](self,*args) @@ -5921,10 +5921,10 @@ cdef class GiacMethods_base: Help for fisher_icdf: fisher_icdf(Intg(n),Intg(m),Real(p)) Returns h such as the probability that a Fisher-Snedecor random variable is less than h is p (n and m are the numbers of degrees of freedom and 0<=p<=1). - See also: 1/ fisher_cdf 2/ fisherd + See also: 1/ fisher_cdf 2/ fisherd Ex1:fisher_icdf(4,10,0.95) Ex2:fisher_icdf(4,10,0.05) - + ''' return GiacMethods['fisher_icdf'](self,*args) @@ -5933,12 +5933,12 @@ cdef class GiacMethods_base: Help for fisherd: fisherd(Intg(n),Intg(m),Real(x0)) Returns the probability density of the Fisher-Snedecor law (n and m are the numbers of degrees of freedom). - See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm + See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm Ex1:fisherd(4,10,2.1) Ex2:fisherd(4,4,2.1) Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) - + ''' return GiacMethods['fisherd'](self,*args) @@ -5947,10 +5947,10 @@ cdef class GiacMethods_base: Help for fisherd_cdf: fisherd_cdf(Intg(n),Intg(m),Real(x0)) Returns the probability that a Fisher-Snedecor random variable is less than x0 (n and m are the numbers of degrees of freedom). - See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd + See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd Ex1:fisherd_cdf(4,4,2.1) Ex2:fisherd_cdf(4,10,3.5) - + ''' return GiacMethods['fisherd_cdf'](self,*args) @@ -5959,10 +5959,10 @@ cdef class GiacMethods_base: Help for fisherd_icdf: fisherd_icdf(Intg(n),Intg(m),Real(p)) Returns h such as the probability that a Fisher-Snedecor random variable is less than h is p (n and m are the numbers of degrees of freedom and 0<=p<=1). - See also: 1/ fisher_cdf 2/ fisherd + See also: 1/ fisher_cdf 2/ fisherd Ex1:fisherd_icdf(4,10,0.95) Ex2:fisherd_icdf(4,10,0.05) - + ''' return GiacMethods['fisherd_icdf'](self,*args) @@ -5971,11 +5971,11 @@ cdef class GiacMethods_base: Help for fitdistr: fitdistr(Lst(L),Fnc(D)) Returns the distribution of type D which fits most closely to the i.i.d. samples in the list L. - See also: 1/ normald 2/ poisson 3/ exponentiald 4/ geometric 5/ gammad 6/ betad 7/ cauchyd 8/ weibulld 9/ sample 10/ randvector 11/ randvar + See also: 1/ normald 2/ poisson 3/ exponentiald 4/ geometric 5/ gammad 6/ betad 7/ cauchyd 8/ weibulld 9/ sample 10/ randvector 11/ randvar Ex1:fitdistr(randvector(1000,weibulld,1/2,1),weibull) Ex2: X:=randvar(normal,stddev=9.5):;Y:=randvar(normal,stddev=1.5):;S:=sample(eval(X/Y,0),1000):;Z:=fitdistr(S,cauchy) Ex3: X:=randvar(normal,mean=5,variance=2):;S:=sample(exp(X),1000):;fitdistr(log(S),normal) - + ''' return GiacMethods['fitdistr'](self,*args) @@ -5984,9 +5984,9 @@ cdef class GiacMethods_base: Help for flatten: flatten(Lst) Recursively flatten a list containing lists. - See also: 1/ mat2list + See also: 1/ mat2list Ex1:flatten([[1,[2,3],4],[5,6]]) - + ''' return GiacMethods['flatten'](self,*args) @@ -5995,12 +5995,12 @@ cdef class GiacMethods_base: Help for float2rational: float2rational(Expr) Converts the expression to a rational or real expression. - See also: 1/ + See also: 1/ Ex1:float2rational(-2) Ex2:float2rational(1.5) Ex3:float2rational(1.4141) Ex4:float2rational(0.156381102937) - + ''' return GiacMethods['float2rational'](self,*args) @@ -6009,10 +6009,10 @@ cdef class GiacMethods_base: Help for floor: floor(Real or Cplx) Returns the greatest integer <= to the argument. - See also: 1/ round 2/ ceil 3/ iPart 4/ trunc + See also: 1/ round 2/ ceil 3/ iPart 4/ trunc Ex1:floor(-2.5) Ex2:floor(2.5-4.2*i) - + ''' return GiacMethods['floor'](self,*args) @@ -6021,10 +6021,10 @@ cdef class GiacMethods_base: Help for flow_polynomial: flow_polynomial(Graph(G),[Var(x)]) Returns the flow polynomial [or its value at point x] of undirected unweighted graph G. - See also: 1/ chromatic_polynomial 2/ reliability_polynomial 3/ tutte_polynomial + See also: 1/ chromatic_polynomial 2/ reliability_polynomial 3/ tutte_polynomial Ex1:flow_polynomial(graph("tetrahedron")) Ex2:flow_polynomial(graph("tetrahedron"),5) - + ''' return GiacMethods['flow_polynomial'](self,*args) @@ -6034,7 +6034,7 @@ cdef class GiacMethods_base: fmod(Real(a),Real(b)) Returns a mod b for a and b floats. Ex1:fmod(10.0,pi) - + ''' return GiacMethods['fmod'](self,*args) @@ -6043,9 +6043,9 @@ cdef class GiacMethods_base: Help for foldl: foldl(op,id,Seq(r1,r2,...)) Returns the composition of the binary operator or function op, with an identity or initial value id onto its arguments r1, r2, ..., associating from the left. - See also: 1/ apply 2/ foldr 3/ map + See also: 1/ apply 2/ foldr 3/ map Ex1:foldl(F,init,a,b,c) - + ''' return GiacMethods['foldl'](self,*args) @@ -6054,9 +6054,9 @@ cdef class GiacMethods_base: Help for foldr: foldr(op,id,Seq(r1,r2,...)) Returns the composition of the binary operator or function op, with an identity or initial value id onto its arguments r1, r2, ..., associating from the right. - See also: 1/ apply 2/ foldl 3/ map + See also: 1/ apply 2/ foldl 3/ map Ex1:foldr(F,init,a,b,c) - + ''' return GiacMethods['foldr'](self,*args) @@ -6065,13 +6065,13 @@ cdef class GiacMethods_base: Help for fonction_derivee: fonction_derivee(Fnc(f)) Returns the derivative function of the function f. - See also: 1/ diff 2/ ' 3/ @ + See also: 1/ diff 2/ ' 3/ @ Ex1:fonction_derivee(sin+id) Ex2:fonction_derivee(sq@sin+id) Ex3:fonction_derivee(ln)(x,y) Ex4:fonction_derivee(ln)([x,y]) - Ex5: (function_diff @@3)(ln)('x') - + Ex5: (function_diff @@3)(ln)('x') + ''' return GiacMethods['fonction_derivee'](self,*args) @@ -6080,10 +6080,10 @@ cdef class GiacMethods_base: Help for forward: forward(NULL or Real(n)) The turtle takes n steps forward (by default n=10). - See also: 1/ recule 2/ saute + See also: 1/ recule 2/ saute Ex1: avance 30 Ex2:forward(30) - + ''' return GiacMethods['forward'](self,*args) @@ -6092,7 +6092,7 @@ cdef class GiacMethods_base: Help for fourier: fourier(Expr(f(x)),[Var(x),[Var(s)]]) Returns the Fourier transform F(s) of f(x). - See also: 1/ ifourier 2/ fourier_cn 3/ fft + See also: 1/ ifourier 2/ fourier_cn 3/ fft Ex1:fourier(x/(x^3-19x+30),x,s) Ex2:fourier((x^2+1)/(x^2-1),x,s) Ex3:fourier(3x^2+2x+1,x,s) @@ -6109,7 +6109,7 @@ cdef class GiacMethods_base: Ex14:fourier(Gamma(1+i*x/3),x,s) Ex15:fourier(atan(x/4)/x,x,s) Ex16:fourier(piecewise(x<=-1,exp(x+1),x<=1,1,exp(2-2x)),x,s) - + ''' return GiacMethods['fourier'](self,*args) @@ -6118,10 +6118,10 @@ cdef class GiacMethods_base: Help for fourier_an: fourier_an(Expr(f(x)),Var(x),Period(T),Intg(n),Real(a)) Returns the n-th Fourier coefficient an=2/T*integrate(f(x)*cos(2*pi*n*x/T),a,a+T). - See also: 1/ fourier_cn 2/ fourier_bn 3/ assume + See also: 1/ fourier_cn 2/ fourier_bn 3/ assume Ex1:fourier_an(x^2,x,2,0,-1) Ex2:fourier_an(x^2,x,2,n,-1) - + ''' return GiacMethods['fourier_an'](self,*args) @@ -6130,10 +6130,10 @@ cdef class GiacMethods_base: Help for fourier_bn: fourier_bn(Expr(f(x)),Var(x),Period(T),Intg(n),Real(a)) Returns the n-th Fourier coefficient bn=2/T*integrate(f(x)*sin(2*pi*n*x/T),a,a+T). - See also: 1/ fourier_cn 2/ fourier_an 3/ assume + See also: 1/ fourier_cn 2/ fourier_an 3/ assume Ex1:fourier_bn(x^2,x,2,0,-1) Ex2:fourier_bn(x^2,x,2,n,-1) - + ''' return GiacMethods['fourier_bn'](self,*args) @@ -6142,10 +6142,10 @@ cdef class GiacMethods_base: Help for fourier_cn: fourier_cn(Expr(f(x)),Var(x),Period(T),Intg(n),Real(a)) Returns the n-th Fourier coefficient cn=1/T*integrate(f(x)*exp(-2*i*pi*n*x/T),a,a+T). - See also: 1/ fourier_an 2/ fourier_bn 3/ assume + See also: 1/ fourier_an 2/ fourier_bn 3/ assume Ex1:fourier_cn(x^2,x,2,0,-1) Ex2:fourier_cn(x^2,x,2,n,-1) - + ''' return GiacMethods['fourier_cn'](self,*args) @@ -6154,11 +6154,11 @@ cdef class GiacMethods_base: Help for fprint: fprint(File(f),Var,[Var,Var...]) Writes in the file f some data. - See also: 1/ fopen 2/ fclose + See also: 1/ fopen 2/ fclose Ex1:fprint(f,x+1,"2") Ex2:fprint(f,"blabla") Ex3:fprint(f,Unquoted,"blabla") - + ''' return GiacMethods['fprint'](self,*args) @@ -6167,13 +6167,13 @@ cdef class GiacMethods_base: Help for frac: frac(Real||LstReal) Returns the fractional part (if x<0 then frac(x)+floor(x)+1=x else frac(x)+floor(x)=x). - See also: 1/ floor 2/ iPart 3/ trunc + See also: 1/ floor 2/ iPart 3/ trunc Ex1:frac(1/2) Ex2:frac(-1/2) Ex3:frac(1.2) Ex4:frac(-1.2) Ex5:frac([3.4,sqrt(2)]) - + ''' return GiacMethods['frac'](self,*args) @@ -6182,9 +6182,9 @@ cdef class GiacMethods_base: Help for fracmod: fracmod(Expr(Xpr),Intg(n)) Returns the fraction a/b such as b*Xpr=a mod n, -sqrt(n)/20),Real(b>0),Real(x>=0)) Returns the probability density of the Gamma law (=x^(a-1)*exp(-b*x)*b^a/Gamma(a)). - See also: 1/ gammad_cdf; 2/ gammad_icdf + See also: 1/ gammad_cdf; 2/ gammad_icdf Ex1:gammad(2.2,1.5,0.8) - + ''' return GiacMethods['gammad'](self,*args) @@ -6318,10 +6318,10 @@ cdef class GiacMethods_base: Help for gammad_cdf: gammad_cdf(Real(a>0),Real(b>0),Real(x0>=0),[Real(y0>=0)]) Returns the probability that a Gamma random variable (with a and b as parameters) is less than x0 or between x0 and y0. - See also: 1/ gammad 2/ gammad_icdf + See also: 1/ gammad 2/ gammad_icdf Ex1:gammad_cdf(2,1,2.96) Ex2:gammad_cdf(2,1,1.4,2.96) - + ''' return GiacMethods['gammad_cdf'](self,*args) @@ -6330,10 +6330,10 @@ cdef class GiacMethods_base: Help for gammad_icdf: gammad_icdf(Real(a>0),Real(b>0),Real(0<=p<=1)) Returns h such that the probability that a Gamma random variable is less than h is p (0<=p<=1). - See also: 1/ gammad_cdf 2/ gammad + See also: 1/ gammad_cdf 2/ gammad Ex1:gammad_icdf(2,1,0.95) Ex2:gammad_icdf(2,1,0.5) - + ''' return GiacMethods['gammad_icdf'](self,*args) @@ -6342,10 +6342,10 @@ cdef class GiacMethods_base: Help for gammavariate: gammavariate(Real(a),Real(b)) Returns a random real according to the Gamma distribution with parameters a>0 and b>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:gammavariate(1,2) Ex2:gammavariate(1.5,4) - + ''' return GiacMethods['gammavariate'](self,*args) @@ -6354,9 +6354,9 @@ cdef class GiacMethods_base: Help for gauss: gauss(Expr,VectVar) Splits a quadratic form as a sum/difference of squares. - See also: 1/ cholesky + See also: 1/ cholesky Ex1:gauss(x^2+2*a*x*y,[x,y]) - + ''' return GiacMethods['gauss'](self,*args) @@ -6365,12 +6365,12 @@ cdef class GiacMethods_base: Help for gauss15: gauss15(Opt) Option of the area command. - See also: 1/ area + See also: 1/ area Ex1: area(x^2,x=0..1,5,simpson) Ex2: area(x^2,x=0..1,5,rombergt) Ex3: area(x^2,x=0..1,5,rombergm) Ex4:gauss15(area(x^2,x=0..1,5,gauss15)) - + ''' return GiacMethods['gauss15'](self,*args) @@ -6379,12 +6379,12 @@ cdef class GiacMethods_base: Help for gauss_seidel_linsolve: gauss_seidel_linsolve([Real(omega)],Mtrx(A),Vect(b),Real(eps),[Int(maxiter)]) Resolution of a linear system A*X=b by the iterative Gauss-Seidel method (by defaut omega=1) or by relaxation method, with eps as error margin and a number of iterations less than maxiter. - See also: 1/ jacobi_linsolve 2/ linsolve + See also: 1/ jacobi_linsolve 2/ linsolve Ex1: a:=[[100,2],[2,100]];gauss_seidel_linsolve(a,[0,1],1e-12); - Ex2: a:=[[100,2],[2,100]];gauss_seidel_linsolve(table(a),[0,1],1e-12); + Ex2: a:=[[100,2],[2,100]];gauss_seidel_linsolve(table(a),[0,1],1e-12); Ex3: a:=[[100,2],[2,100]];gauss_seidel_linsolve(1.5,a,[0,1],1e-12); - Ex4: a:=[[100,2],[2,100]];gauss_seidel_linsolve(1.5,table(a),[0,1],1e-12); - + Ex4: a:=[[100,2],[2,100]];gauss_seidel_linsolve(1.5,table(a),[0,1],1e-12); + ''' return GiacMethods['gauss_seidel_linsolve'](self,*args) @@ -6393,9 +6393,9 @@ cdef class GiacMethods_base: Help for gaussian_window: gaussian_window(Lst,[Real(a)],[Interval(n1..n2)]) Applies the Gaussian windowing function with parameter 0= b (default a=0.2 and b=1/6.) - See also: 1/ gbasis 2/ gbasis_max_pairs 3/ gbasis_reinject + See also: 1/ gbasis 2/ gbasis_max_pairs 3/ gbasis_reinject Ex1:gbasis_reinject(0.1) Ex2:gbasis_reinject(0.1,0.05) - + ''' return GiacMethods['gbasis_reinject'](self,*args) @@ -6470,9 +6470,9 @@ cdef class GiacMethods_base: Help for gbasis_simult_primes: gbasis_simult_primes(Intg) Gbasis fine-tuning: maximal number of Groebner basis modulo a prime that are computed simultaneously to rebuild a Groebner basis over Q (default 16). Set it to a smaller value if short in memory. - See also: 1/ gbasis 2/ gbasis_max_pairs 3/ gbasis_reinject + See also: 1/ gbasis 2/ gbasis_max_pairs 3/ gbasis_reinject Ex1:gbasis_simult_primes(3) - + ''' return GiacMethods['gbasis_simult_primes'](self,*args) @@ -6481,13 +6481,13 @@ cdef class GiacMethods_base: Help for gcd: gcd((Intg(a) or Poly),(Intg(b) or Poly)) Returns the greatest common divisor of 2 polynomials of several variables or of 2 integers or of 2 rationals. - See also: 1/ lcm 2/ euler 2/ modgcd 3/ ezgcd 4/ psrgcd 5/ heugcd 6/ Gcd + See also: 1/ lcm 2/ euler 2/ modgcd 3/ ezgcd 4/ psrgcd 5/ heugcd 6/ Gcd Ex1:gcd(45,75) Ex2:gcd(15/7,50/9) Ex3:gcd(x^2-2*x+1,x^3-1) Ex4:gcd(t^2-2*t+1,t^2+t-2) Ex5:gcd((x^2-1)*(y^2-1)*z^2,x^3*y^3*z+(-(y^3))*z+x^3*z-z) - + ''' return GiacMethods['gcd'](self,*args) @@ -6496,12 +6496,12 @@ cdef class GiacMethods_base: Help for gcdex: gcdex((Poly or Lst),(Poly or Lst),[Var]) Extended greatest common divisor of 2 polynomials. - See also: 1/ gcd 2/ iegcd + See also: 1/ gcd 2/ iegcd Ex1:gcdex((x-1)^2,x^3-1) Ex2:gcdex((X-1)^2,X^3-1,X) Ex3:gcdex([1,-2,1],[1,0,0,-1]) Ex4:gcdex([1,-2,1],[1,-1,2]) - + ''' return GiacMethods['gcdex'](self,*args) @@ -6510,11 +6510,11 @@ cdef class GiacMethods_base: Help for genpoly: genpoly(Poly(P),Intg(b),Var) Returns the reconstruction of a n-variables polynomial Q(-b/2<=coef<=b/2) from an (n-1)-variable polynomial P and a base b (subst(Q,var=b)=P). - See also: 1/ + See also: 1/ Ex1:genpoly(15,4,x) Ex2:genpoly(7*y+5,6,x) Ex3:genpoly(7*y-5*z,10,x) - + ''' return GiacMethods['genpoly'](self,*args) @@ -6523,12 +6523,12 @@ cdef class GiacMethods_base: Help for geometric: geometric(Real(p),Intg(k)) Returns the value at k of the geometric law with parameter p (0cos(2*x)) Ex4:getType(1.414) - + ''' return GiacMethods['getType'](self,*args) @@ -6611,9 +6611,9 @@ cdef class GiacMethods_base: Help for get_edge_attribute: get_edge_attribute(Graph(G),Edge(e),Seq(tag1=value1,tag2=value2,..)) Returns the attributes tag1, tag2, ... assigned to edge e in G as a sequence of the corresponding values. - See also: 1/ discard_edge_attribute 2/ set_edge_attribute 3/ list_edge_attributes + See also: 1/ discard_edge_attribute 2/ set_edge_attribute 3/ list_edge_attributes Ex1:get_edge_attribute(cycle_graph(3),[1,2],"cost") - + ''' return GiacMethods['get_edge_attribute'](self,*args) @@ -6622,9 +6622,9 @@ cdef class GiacMethods_base: Help for get_edge_weight: get_edge_weight(Graph(G),Edge(e)) Returns the weight of the edge e in the weighted graph G. - See also: 1/ is_weighted 2/ make_weighted 3/ set_edge_weight 4/ weight_matrix + See also: 1/ is_weighted 2/ make_weighted 3/ set_edge_weight 4/ weight_matrix Ex1:get_edge_weight(graph(%{[[1,2],5],[[2,3],6]%}),[1,2]) - + ''' return GiacMethods['get_edge_weight'](self,*args) @@ -6633,9 +6633,9 @@ cdef class GiacMethods_base: Help for get_graph_attribute: get_graph_attribute(Graph(G),Seq(tag1=value1,tag2=value2,..)) Return the graph attributes tag1, tag2, ..., as a sequence of the corresponding values. - See also: 1/ discard_graph_attribute 2/ set_graph_attribute 3/ list_graph_attributes + See also: 1/ discard_graph_attribute 2/ set_graph_attribute 3/ list_graph_attributes Ex1:get_graph_attribute(cycle_graph(3),"name") - + ''' return GiacMethods['get_graph_attribute'](self,*args) @@ -6644,9 +6644,9 @@ cdef class GiacMethods_base: Help for get_vertex_attribute: get_vertex_attribute(Graph(G),Vrtx(v),Seq(tag1=value1,tag2=value2,..)) Returns the attributes tag1, tag2, ... assigned to vertex v in G as a sequence of the corresponding values. - See also: 1/ discard_vertex_attribute 2/ set_vertex_attribute 3/ list_vertex_attributes + See also: 1/ discard_vertex_attribute 2/ set_vertex_attribute 3/ list_vertex_attributes Ex1:get_vertex_attribute(cycle_graph(3),1,"supply") - + ''' return GiacMethods['get_vertex_attribute'](self,*args) @@ -6655,10 +6655,10 @@ cdef class GiacMethods_base: Help for girth: girth(Graph(G)) Returns the length of the shortest cycle in the undirected unweighted graph G. - See also: 1/ odd_girth + See also: 1/ odd_girth Ex1:girth(graph("petersen")) Ex2:girth(hypercube_graph(3)) - + ''' return GiacMethods['girth'](self,*args) @@ -6667,10 +6667,10 @@ cdef class GiacMethods_base: Help for gl_showaxes: gl_showaxes(Opt=Boolean) Option that shows or hides axes. - See also: 1/ switch_axes 2/ axes + See also: 1/ switch_axes 2/ axes Ex1: gl_showaxes=true;plot(sin(x)) - Ex2: gl_showaxes=false;plot(sin(x)) - + Ex2: gl_showaxes=false;plot(sin(x)) + ''' return GiacMethods['gl_showaxes'](self,*args) @@ -6679,9 +6679,9 @@ cdef class GiacMethods_base: Help for grad: grad(Expr(Xpr),LstVar) Returns the gradient of the expression Xpr. - See also: 1/ hessian + See also: 1/ hessian Ex1:grad(2*x^2*y-x*z^3,[x,y,z]) - + ''' return GiacMethods['grad'](self,*args) @@ -6690,10 +6690,10 @@ cdef class GiacMethods_base: Help for gramschmidt: gramschmidt(Basis(B),ScalarProd(Sp)) Returns an orthonormal basis of E with basis B for the scalar product Sp. - See also: 1/ + See also: 1/ Ex1:gramschmidt(-2) Ex2:gramschmidt([1,1+x],(p,q)->integrate(p*q,x,-1,1)) - + ''' return GiacMethods['gramschmidt'](self,*args) @@ -6702,7 +6702,7 @@ cdef class GiacMethods_base: Help for graph: graph([Lst(V)],[Set(E)],[Mtrx(A)],[options]) Create an (un)directed (un)weighted graph from vertices V, edges E, and/or adjacency or weight matrix A. All parameters are optional. - See also: 1/ digraph 2/ trail + See also: 1/ digraph 2/ trail Ex1:graph(5) Ex2:graph([a,b,c]) Ex3:graph([1,2,3],%{[1,2],[2,3],[3,1]%}) @@ -6710,7 +6710,7 @@ cdef class GiacMethods_base: Ex5:graph([a,b,c],[[0,2,0],[2,0,3],[0,3,0]]) Ex6:graph("petersen") Ex7:graph([[0,1,1,0],[1,0,0,1],[1,0,0,0],[0,1,0,0]]) - + ''' return GiacMethods['graph'](self,*args) @@ -6719,9 +6719,9 @@ cdef class GiacMethods_base: Help for graph_automorphisms: graph_automorphisms(Graph(G)) Returns the sequence of generators of Aut(G), the automorphism group of G. Each element is a permutation in the form of list of disjoint cycles. - See also: 1/ cycles2permu 2/ isomorphic_copy 3/ permute_vertices + See also: 1/ cycles2permu 2/ isomorphic_copy 3/ permute_vertices Ex1:graph_automorphisms(graph("petersen")) - + ''' return GiacMethods['graph_automorphisms'](self,*args) @@ -6730,10 +6730,10 @@ cdef class GiacMethods_base: Help for graph_charpoly: graph_charpoly(Graph(G),[Var(x)]) Returns the value p(x) of the characteristic polynomial p of G. If x is omitted, a list of coefficients of p is returned. - See also: 1/ graph_spectrum 2/ charpoly + See also: 1/ graph_spectrum 2/ charpoly Ex1:graph_charpoly(graph(%{[1,2],[2,3]%})) Ex2:graph_charpoly(graph("shrikhande")) - + ''' return GiacMethods['graph_charpoly'](self,*args) @@ -6742,9 +6742,9 @@ cdef class GiacMethods_base: Help for graph_complement: graph_complement(Graph(G)) Return the graph with the same vertex set as G, but whose edge (arc) set consists of the edges (arcs) not present in G. - See also: 1/ edges + See also: 1/ edges Ex1:graph_complement(cycle_graph(5)) - + ''' return GiacMethods['graph_complement'](self,*args) @@ -6753,9 +6753,9 @@ cdef class GiacMethods_base: Help for graph_diameter: graph_diameter(Graph(G)) Returns the maximum distance between a pair of vertices in G or +infinity if G is disconnected. - See also: 1/ allpairs_distance 2/ dijkstra 3/ shortest_path 4/ vertex_distance + See also: 1/ allpairs_distance 2/ dijkstra 3/ shortest_path 4/ vertex_distance Ex1:graph_diameter(graph("petersen")) - + ''' return GiacMethods['graph_diameter'](self,*args) @@ -6764,9 +6764,9 @@ cdef class GiacMethods_base: Help for graph_equal: graph_equal(Graph(G1),Graph(G2)) Returns true iff the input graphs G1 and G2 are equal, that is when the sets of vertices and edges of G1 and G2, as well as the orderings of vertices in both graphs, mutually coincide. If the graphs are weighted (they must both be (un)weighted and (un)directed), weights given to the same edge in two graphs must be equal. - See also: 1/ edges 2/ graph_vertices + See also: 1/ edges 2/ graph_vertices Ex1:graph_equal(graph([1,2,3],%{[1,2],[2,3],[3,1]%}),graph(trail(1,2,3,1))) - + ''' return GiacMethods['graph_equal'](self,*args) @@ -6775,9 +6775,9 @@ cdef class GiacMethods_base: Help for graph_join: graph_join(Graph(G),Graph(H)) Returns the graph obtained by connecting every vertex from G with every vertex from H. The vertex labels in the resulting graph are strings of form "1:u" and "2:v" where u and v are vertices from G and H, respectively. - See also: 1/ disjoint_union 2/ graph_union + See also: 1/ disjoint_union 2/ graph_union Ex1:graph_join(edges(graph_join(cycle_graph(3),graph(2)))) - + ''' return GiacMethods['graph_join'](self,*args) @@ -6786,9 +6786,9 @@ cdef class GiacMethods_base: Help for graph_power: graph_power(Graph(G),Intg(k)) Returns the k-th power of G, where two vertices are connected iff there exists a path of length at most k in the original graph. - See also: 1/ adjacency matrix 2/ graph_diameter 3/ shortest_path + See also: 1/ adjacency matrix 2/ graph_diameter 3/ shortest_path Ex1:graph_power(edges(graph_power(path_graph(5),3))) - + ''' return GiacMethods['graph_power'](self,*args) @@ -6797,10 +6797,10 @@ cdef class GiacMethods_base: Help for graph_rank: graph_rank(Graph(G),[Lst(E)]) Returns the graph rank of G. If optional set E of edges is given, the rank of the spanning subgraph of G with edge set E is returned. - See also: 1/ connected_components 2/ number_of_vertices + See also: 1/ connected_components 2/ number_of_vertices Ex1:graph_rank(graph(%{[1,2],[3,4],[4,5]%})) Ex2:graph_rank(graph(%{[1,2],[3,4],[4,5]%}),[[1,2],[3,4]) - + ''' return GiacMethods['graph_rank'](self,*args) @@ -6809,9 +6809,9 @@ cdef class GiacMethods_base: Help for graph_spectrum: graph_spectrum(Graph(G)) Returns the graph spectrum of G as a list of lists with two elements, each containing an eigenvalue and its multiplicity. - See also: 1/ graph_charpoly 2/ seidel_spectrum 3/ is_integer_graph + See also: 1/ graph_charpoly 2/ seidel_spectrum 3/ is_integer_graph Ex1:graph_spectrum(cycle_graph(5)) - + ''' return GiacMethods['graph_spectrum'](self,*args) @@ -6820,9 +6820,9 @@ cdef class GiacMethods_base: Help for graph_union: graph_union(Seq(G1,G2,...)) Returns the union of the graphs G1, G2, ... The set of vertices of the resulting graph is the union of the sets of vertices of the input graphs and the set of edges of the resulting graph is the union of sets of edges of the input graphs. If the input graphs are weighted, the weight of any common edge is the sum of the weights of that edge in G1, G2, ... - See also: 1/ disjoint_union 2/ graph_join + See also: 1/ disjoint_union 2/ graph_join Ex1:graph_union(edges(graph_union(cycle_graph(4),path_graph(5)))) - + ''' return GiacMethods['graph_union'](self,*args) @@ -6831,9 +6831,9 @@ cdef class GiacMethods_base: Help for graph_vertices: graph_vertices(Graph(G)) Return the list of vertices in G. - See also: 1/ add_vertex 2/ graph 3/ neighbors 4/ permute_vertices 5/ relabel_vertices + See also: 1/ add_vertex 2/ graph 3/ neighbors 4/ permute_vertices 5/ relabel_vertices Ex1:graph_vertices(graph(%{[a,c],[b,c],[a,b]%})) - + ''' return GiacMethods['graph_vertices'](self,*args) @@ -6842,11 +6842,11 @@ cdef class GiacMethods_base: Help for greduce: greduce(Poly,LstPoly,LstVar,[order]) Returns the remainder of the division of a polynomial by a Groebner basis. - See also: 1/ gbasis + See also: 1/ gbasis Ex1:greduce(x*y-1,[x^2-y^2,2*x*y-y^2,y^3],[x,y]) Ex2:greduce(x1^2*x3^2,[x3^3-1,-x2^2-x2*x3-x3^2,x1+x2+x3],[x1,x2,x3],tdeg) Ex3:greduce(x1^2*x3^2-x2,[x3^3-1,-x2^2-x2*x3-x3^2,x1+x2+x3],[x1,x2,x3]) - + ''' return GiacMethods['greduce'](self,*args) @@ -6855,9 +6855,9 @@ cdef class GiacMethods_base: Help for greedy_color: greedy_color(Graph(G),[Permu(p)]) Returns the list of vertex colors (positive integers) obtained by coloring vertices one at a time [in the order given by permutation p], assigning to it the smallest available color. - See also: 1/ is_vertex_colorable 2/ chromatic_number + See also: 1/ is_vertex_colorable 2/ chromatic_number Ex1:greedy_color(graph("petersen")) - + ''' return GiacMethods['greedy_color'](self,*args) @@ -6866,9 +6866,9 @@ cdef class GiacMethods_base: Help for grid_graph: grid_graph(Intg(m),Intg(n),[triangle]) Returns a [triangular] grid graph on m*n vertices, where m,n>=2. - See also: 1/ torus_grid_graph + See also: 1/ torus_grid_graph Ex1:grid_graph(5,8) - + ''' return GiacMethods['grid_graph'](self,*args) @@ -6877,9 +6877,9 @@ cdef class GiacMethods_base: Help for groupermu: groupermu(Permut(a),Permut(b)) Returns the group of permutations generated by a and b. - See also: 1/ + See also: 1/ Ex1:groupermu([1,2,0],[3,1,2,0]) - + ''' return GiacMethods['groupermu'](self,*args) @@ -6888,10 +6888,10 @@ cdef class GiacMethods_base: Help for hadamard: hadamard(Mtrx,Mtrx) Hadamard bound of a matrix or element by element multiplication of 2 matrices. - See also: 1/ .* 2/ * + See also: 1/ .* 2/ * Ex1:hadamard([[1,2],[3,4]]) Ex2:hadamard([[1,2],[3,4]],[[3,4],[5,6]]) - + ''' return GiacMethods['hadamard'](self,*args) @@ -6900,10 +6900,10 @@ cdef class GiacMethods_base: Help for half_cone: half_cone(Pnt(A),Vect(v),Real(t),[Real(h)]) Draws a half-cone with vertex A, direction v and with half_angle=t [and with altitude h]. - See also: 1/ cone 2/ cylinder + See also: 1/ cone 2/ cylinder Ex1:half_cone([0,0,0],[0,0,1],pi/6) Ex2:half_cone([0,0,0],[0,1,1],pi/6,-4) - + ''' return GiacMethods['half_cone'](self,*args) @@ -6912,10 +6912,10 @@ cdef class GiacMethods_base: Help for half_line: half_line((Pnt or Cplx),(Pnt or Cplx)) half_line(A,B) draws the half-line AB with A as origin. - See also: 1/ line + See also: 1/ line Ex1:half_line(i,1+i) Ex2:half_line(point(i),point(1+i)) - + ''' return GiacMethods['half_line'](self,*args) @@ -6927,7 +6927,7 @@ cdef class GiacMethods_base: Ex1:halftan(sin(x)) Ex2:halftan(cos(x)) Ex3:halftan(tan(x)) - + ''' return GiacMethods['halftan'](self,*args) @@ -6936,9 +6936,9 @@ cdef class GiacMethods_base: Help for halftan_hyp2exp: halftan_hyp2exp(ExprTrig) Transforms the trigonometric functions in tan(x/2) and hyperbolic functions to exp. - See also: 1/ hyp2exp 2/ halftan + See also: 1/ hyp2exp 2/ halftan Ex1:halftan_hyp2exp(sin(x)+sinh(x)) - + ''' return GiacMethods['halftan_hyp2exp'](self,*args) @@ -6947,9 +6947,9 @@ cdef class GiacMethods_base: Help for halt: halt(NULL) Puts a program in step-by-step debug mode. - See also: 1/ + See also: 1/ Ex1:halt() - + ''' return GiacMethods['halt'](self,*args) @@ -6959,7 +6959,7 @@ cdef class GiacMethods_base: hamdist(Intg,Intg) Bitwise Hamming distance. Ex1:hamdist(0x12,0x38) - + ''' return GiacMethods['hamdist'](self,*args) @@ -6968,9 +6968,9 @@ cdef class GiacMethods_base: Help for hamming_window: hamming_window(Lst,[Interval(n1..n2)]) Applies the Hamming windowing function to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ bartlett_hann_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ bartlett_hann_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(hamming_window(randvector(1000,0..1))) - + ''' return GiacMethods['hamming_window'](self,*args) @@ -6979,9 +6979,9 @@ cdef class GiacMethods_base: Help for hann_poisson_window: hann_poisson_window(Lst,[Interval(n1..n2)]) Applies the Hann-Poisson windowing function with parameter a (by default a=1) to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ bartlett_hann_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ bartlett_hann_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(hann_poisson_window(randvector(1000,0..1),2)) - + ''' return GiacMethods['hann_poisson_window'](self,*args) @@ -6990,9 +6990,9 @@ cdef class GiacMethods_base: Help for hann_window: hann_window(Lst,[Interval(n1..n2)]) Applies the Hann windowing function to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ bartlett_hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ bartlett_hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(hann_window(randvector(1000,0..1))) - + ''' return GiacMethods['hann_window'](self,*args) @@ -7001,12 +7001,12 @@ cdef class GiacMethods_base: Help for harmonic_conjugate: harmonic_conjugate(Line or Pnt(A),Line or Pnt(B),Line or Pnt(C)) Returns the harmonic conjugate C with respect to A and B of 3 points or of 3 parallel or concurrent lines or the line of conjugates of a point with respect to 2 lines. - See also: 1/ is_harmonic 2/ harmonic_division + See also: 1/ is_harmonic 2/ harmonic_division Ex1:harmonic_conjugate(0,2,3/2) Ex2:harmonic_conjugate(0,1+i,2+2*i) Ex3:harmonic_conjugate(line(0,1+i),line(0,3+i),line(0,i)) Ex4:harmonic_conjugate(line(0,1+i),line(0,3+i),point(3/2+i)) - + ''' return GiacMethods['harmonic_conjugate'](self,*args) @@ -7015,12 +7015,12 @@ cdef class GiacMethods_base: Help for harmonic_division: harmonic_division(Pnt or Line,Pnt or Line,Pnt or Line,Var) Returns 4 points (resp lines) and affects the last argument, such that the 4 points (resp lines) are in a harmonic division and assigns the fourth point to the variable name. - See also: 1/ harmonic_conjugate 2/ is_harmonic + See also: 1/ harmonic_conjugate 2/ is_harmonic Ex1:harmonic_division(0,2,3/2,D) Ex2:harmonic_division(0,1+i,2+2*i,D) Ex3:harmonic_division(line(i,0),line(i,1+i),line(i,3+2*i),D) Ex4:harmonic_division(line(0,1+i),line(0,3+i),line(0,i),D) - + ''' return GiacMethods['harmonic_division'](self,*args) @@ -7029,10 +7029,10 @@ cdef class GiacMethods_base: Help for has: has(Expr,Var) Checks if a variable is in an expression. - See also: 1/ lname 2/ lvar + See also: 1/ lname 2/ lvar Ex1:has(x+y,x) Ex2:has(x+y,n) - + ''' return GiacMethods['has'](self,*args) @@ -7041,10 +7041,10 @@ cdef class GiacMethods_base: Help for has_arc: has_arc(Graph(G),Edge(e)) Returns true iff the arc e=[i,j] is contained in digraph G or, if e={i,j} is a set, iff G has both edges [i,j] and [j,i]. - See also: 1/ edges 2/ has_edge + See also: 1/ edges 2/ has_edge Ex1:has_arc(digraph(trail(1,2,3,4,1)),[4,2]) Ex2:has_arc(digraph(trail(1,2,3,4,1)),%{4,2%}) - + ''' return GiacMethods['has_arc'](self,*args) @@ -7053,9 +7053,9 @@ cdef class GiacMethods_base: Help for has_edge: has_edge(Graph(G),Edge(e)) Returns true iff the edge e=[i,j] is contained in undirected graph G. - See also: 1/ edges 2/ has_arc + See also: 1/ edges 2/ has_arc Ex1:has_edge(graph(trail(1,2,3,4,1)),[2,4]) - + ''' return GiacMethods['has_edge'](self,*args) @@ -7064,7 +7064,7 @@ cdef class GiacMethods_base: Help for hasard: hasard(Intg(n) or Interval(p..n) or NULL,[Intg(b1) or Lst(L)],[Intg(b2)]) (hasard n)=a random integer (resp (hasard p,n)=a real or hasard(p..n)=a real function) with uniform distribution in 0..n-1 (resp in [p;n])(hasard= (hasard 0,1)=a random real in [0,1[) or hasard(n,b1,b2)=n integers between b1 and b2 or hasard(n,L)=n elements of L. If hasard has only one argument, () are not necessary (compatibility with turtle language). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ srand + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ srand Ex1: hasard 4 Ex2: hasard(4) Ex3:hasard(0,2) @@ -7072,7 +7072,7 @@ cdef class GiacMethods_base: Ex5: f:=hasard 0..2 Ex6:hasard(3,1,10) Ex7:hasard(3,["r","r","r","b","n"]) - + ''' return GiacMethods['hasard'](self,*args) @@ -7081,11 +7081,11 @@ cdef class GiacMethods_base: Help for head: head(Vect or Seq or Str) Shows the first element of a vector or a sequence or a string. - See also: 1/ back 2/ tail 3/ mid 4/ left 5/ right + See also: 1/ back 2/ tail 3/ mid 4/ left 5/ right Ex1:head(1,2,3) Ex2:head([1,2,3]) Ex3:head("bonjour") - + ''' return GiacMethods['head'](self,*args) @@ -7094,11 +7094,11 @@ cdef class GiacMethods_base: Help for heading: heading(NULL or Real) Returns the turtle cap in degrees or turns the turtle in the direction given by the argument. - See also: 1/ position 2/ initialise + See also: 1/ position 2/ initialise Ex1: cap Ex2:heading() Ex3:heading(cap 90) - + ''' return GiacMethods['heading'](self,*args) @@ -7107,8 +7107,8 @@ cdef class GiacMethods_base: Help for heapify: heapify(List) Partial ordering of a list as a heap. - See also: 1/ heappush 2/ heappop - + See also: 1/ heappush 2/ heappop + ''' return GiacMethods['heapify'](self,*args) @@ -7117,8 +7117,8 @@ cdef class GiacMethods_base: Help for heappop: heappop(List) Removes and returns the root node of a heap. - See also: 1/ heapify 2/ heappush - + See also: 1/ heapify 2/ heappush + ''' return GiacMethods['heappop'](self,*args) @@ -7127,8 +7127,8 @@ cdef class GiacMethods_base: Help for heappush: heappush(List,Object) Adds an object in a heap. - See also: 1/ heapify 2/ heappop - + See also: 1/ heapify 2/ heappop + ''' return GiacMethods['heappush'](self,*args) @@ -7137,10 +7137,10 @@ cdef class GiacMethods_base: Help for hermite: hermite(Intg(n)||Matr(A)) Returns the Hermite polynomial of degree n or the Hermite normal form for a matrix with polynomial coefficients (I,U such that I*A=U). - See also: 1/ legendre 2/ laguerre 3/ smith 4/ ihermite 5/ ismith + See also: 1/ legendre 2/ laguerre 3/ smith 4/ ihermite 5/ ismith Ex1:hermite(3) Ex2: n:=5; a:=ranm(n,n) % 17; l,u:=hermite(x-a);normal(l*(x-a)-u); - + ''' return GiacMethods['hermite'](self,*args) @@ -7149,13 +7149,13 @@ cdef class GiacMethods_base: Help for hessenberg: hessenberg(Mtrx(A),[Intg(n)]) Matrix reduction to Hessenberg form. Returns [P,B] such that B=inv(P)*A*P, by default n=0 the result is exact else the result is numeric. For n=-1 B is triangular, n=-2 P is orthogonal and if n is prime the result is mod n. - See also: 1/ SCHUR + See also: 1/ SCHUR Ex1:hessenberg([[1,2,3],[4,5,6],[7,8,1]]) Ex2:hessenberg([[1,2,3,4],[4,5,6,7],[7,8,9,0],[0,1,2,3]]) Ex3:hessenberg([[1,2,3],[4,5,6],[7,8,1]],-1) Ex4:hessenberg([[1,2,3],[4,5,6],[7,8,1]],-2) Ex5:hessenberg([[1,2,3],[4,5,6],[7,8,1]],3) - + ''' return GiacMethods['hessenberg'](self,*args) @@ -7164,9 +7164,9 @@ cdef class GiacMethods_base: Help for hessian: hessian(Expr(Xpr),LstVar) Returns the hessian of the expression Xpr. - See also: 1/ grad + See also: 1/ grad Ex1:hessian(2*x^2*y-x*z,[x,y,z]) - + ''' return GiacMethods['hessian'](self,*args) @@ -7175,9 +7175,9 @@ cdef class GiacMethods_base: Help for heugcd: heugcd(Poly,Poly) GCD of 2 polynomials, with the algorithm called heuristic pgcd. - See also: 1/ gcd 2/ modgcd 3/ ezgcd 4/ psrgcd + See also: 1/ gcd 2/ modgcd 3/ ezgcd 4/ psrgcd Ex1:heugcd(x^4-1,(x-1)^2) - + ''' return GiacMethods['heugcd'](self,*args) @@ -7186,12 +7186,12 @@ cdef class GiacMethods_base: Help for hexagon: hexagon(Pnt(A)||Cplx,Pnt(B)||Cplx,[Pnt(P)],[Var(C)],[Var(D)],[Var(E)],[Var(F)]) Returns and draws the hexagon of side AB (ABCDEF is direct) (in the plane ABP). - See also: 1/ isopolygon 2/ polygon + See also: 1/ isopolygon 2/ polygon Ex1:hexagon(i,1+i) Ex2:hexagon(i,1+i,C,D,E,F) Ex3:hexagon(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:hexagon(point(0,0,0),point(3,3,3),point(0,0,3),C,D,E,F) - + ''' return GiacMethods['hexagon'](self,*args) @@ -7200,9 +7200,9 @@ cdef class GiacMethods_base: Help for highlight_edges: highlight_edges(Graph(G),Edge(e)||Lst(E),[Color(c)||Lst(C)]) Changes color of edge e resp. colors of edges in E of the input graph V to c resp C (by default red) and returns the modified copy of G. - See also: 1/ highlight_vertex 2/ highlight_subgraph 3/ highlight_trail + See also: 1/ highlight_vertex 2/ highlight_subgraph 3/ highlight_trail Ex1: draw_graph(highlight_edges(cycle_graph(3),[1,2])) - + ''' return GiacMethods['highlight_edges'](self,*args) @@ -7211,9 +7211,9 @@ cdef class GiacMethods_base: Help for highlight_subgraph: highlight_subgraph(Graph(G),Graph(S)||Lst(S1,S2,..),Seq(c1,c2)) Changes colors of edges and vertices from the sugbraph S or list of subgraphs S1, S2, ... of G to c1 and c2, respectively (red and green by default), and returns the modified copy of G. - See also: 1/ highlight_edges 2/ highlight_vertex 3/ highlight_trail + See also: 1/ highlight_edges 2/ highlight_vertex 3/ highlight_trail Ex1: draw_graph(highlight_subgraph(cycle_graph(5),path_graph(3))) - + ''' return GiacMethods['highlight_subgraph'](self,*args) @@ -7222,9 +7222,9 @@ cdef class GiacMethods_base: Help for highlight_trail: highlight_trail(Graph(G),Trail(t)||Lst(T),[Color(c)||Lst(C)]) Changes colors of edges in G which lie along the trail t resp. trails in T to c resp. C (by default red) and returns the modified copy of G. - See also: 1/ highlight_edges 2/ highlight_subgraph 3/ highlight_vertex + See also: 1/ highlight_edges 2/ highlight_subgraph 3/ highlight_vertex Ex1: draw_graph(highlight_trail(cycle_graph(5),trail(1,2,3),green) - + ''' return GiacMethods['highlight_trail'](self,*args) @@ -7233,9 +7233,9 @@ cdef class GiacMethods_base: Help for highlight_vertex: highlight_vertex(Graph(G),Vrtx(v)||Lst(V),[Color(c)||Lst(C)]) Changes the color of vertex v resp. colors of vertices from V in G to c resp. C (green by default) and returns the modified copy of G. - See also: 1/ highlight_edges 2/ highlight_subgraph 3/ highlight_trail + See also: 1/ highlight_edges 2/ highlight_subgraph 3/ highlight_trail Ex1: draw_graph(highlight_vertex(cycle_graph(3),1)) - + ''' return GiacMethods['highlight_vertex'](self,*args) @@ -7244,9 +7244,9 @@ cdef class GiacMethods_base: Help for highpass: highpass(Lst(s),Real(c),[Intg(samplerate)]) Returns the result of applying a simple first-order highpass RC filter with cutoff frequency c (the default samplerate is 44100) to the given signal s. - See also: 1/ lowpass 2/ moving_average + See also: 1/ lowpass 2/ moving_average Ex1: f:=unapply(periodic(sign(x),x,-1/880,1/880),x):;s:=createwav(apply(f,soundsec(1))):;playsnd(highpass(s,5000)) - + ''' return GiacMethods['highpass'](self,*args) @@ -7255,9 +7255,9 @@ cdef class GiacMethods_base: Help for hilbert: hilbert(Intg(n)) Returns the order n Hilbert matrix : Hjk=1/(j+k+1) j,k=1..n. - See also: 1/ + See also: 1/ Ex1:hilbert(4) - + ''' return GiacMethods['hilbert'](self,*args) @@ -7266,7 +7266,7 @@ cdef class GiacMethods_base: Help for histogram: histogram(Lst(data),[Lst(eff) || Intg(nc) || Real(classmin)],[Real(classsize)]) Draws the histogram of data, optional arguments are eff (number of data for each data element) or nc the number of classes or the classes minimum and size. - See also: 1/ cumulated_frequencies 2/ classes 3/ bar_plot 4/ frequencies + See also: 1/ cumulated_frequencies 2/ classes 3/ bar_plot 4/ frequencies Ex1:histogram([1,2,1,1,2,1,2,4,3,3]) Ex2:histogram([1,2,1,1,2,1,2,4,3,3],0.5,1) Ex3:histogram(seq(rand(1000),k,0,100),0,100) @@ -7275,7 +7275,7 @@ cdef class GiacMethods_base: Ex6:histogram([[1.5..1.65,50],[1.65..1.7,20],[1.7..1.8,30]]) Ex7:histogram(seq(rand(1000),k,0,100),0,100) Ex8:histogram(seq(rand(1000),k,0,100),10) - + ''' return GiacMethods['histogram'](self,*args) @@ -7284,11 +7284,11 @@ cdef class GiacMethods_base: Help for hold: hold(Expr) Returns its argument unevaluated (and also a:=quote(a) purges a). - See also: 1/ + See also: 1/ Ex1:hold(1+2) Ex2:hold(1/x+1/(x-1)) Ex3:hold((x+1)*(x-1)) - + ''' return GiacMethods['hold'](self,*args) @@ -7299,7 +7299,7 @@ cdef class GiacMethods_base: Make P homogeneous by adding a variable (by default t) Ex1:homogeneize(x^2-1) Ex2:homogeneize(x^2-y,z) - + ''' return GiacMethods['homogeneize'](self,*args) @@ -7308,12 +7308,12 @@ cdef class GiacMethods_base: Help for homothety: homothety(Pnt(C),Real(k),Pnt(A)) homothety(C,k,A)=point A1 such as vect(C,A1)=k*vect(C,A) i.e in 2d it is the similarity with center C, coeff abs(k) and angle arg(k). - See also: 1/ similarity 2/ inversion + See also: 1/ similarity 2/ inversion Ex1:homothety(1+i,1/3,i) Ex2:homothety(point(1,1,1),1/3,point(0,1,0)) Ex3: h:=homothety(1+i,1/3);h(i) Ex4: h:=homothety(point(1,1,1),1/3);h(point(0,1,0)) - + ''' return GiacMethods['homothety'](self,*args) @@ -7322,12 +7322,12 @@ cdef class GiacMethods_base: Help for horner: horner(Poly(P),Real(a)) Returns the value of P(a) calculated with Horner's method. With horner(list_alpha_i,list_x_i,x), evals an interpolation polynomial from the divided differences of x. - See also: 1/ convert 2/ base 3/ revlist + See also: 1/ convert 2/ base 3/ revlist Ex1:horner(x^2+1,2) Ex2:horner([1,0,1],2) Ex3:horner(x^2+y*x+y^3-1,2,y) Ex4: X:=[0.0,1.0,2.0]; A:=lagrange(X,exp,lagrange); horner(A,X,1.5); - + ''' return GiacMethods['horner'](self,*args) @@ -7336,14 +7336,14 @@ cdef class GiacMethods_base: Help for hybrid_solver: hybrid_solver(Opt) Argument for fsolve giving the method for solving a system of numerical equations. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],dnewton_solver) Ex2: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrid_solver) Ex3: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrids_solver) Ex4: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridj_solver) Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) - + ''' return GiacMethods['hybrid_solver'](self,*args) @@ -7352,14 +7352,14 @@ cdef class GiacMethods_base: Help for hybridj_solver: hybridj_solver(Opt) Argument for fsolve giving the method for solving a system of numerical equations. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],dnewton_solver) Ex2: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrid_solver) Ex3: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrids_solver) Ex4: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridj_solver) Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) - + ''' return GiacMethods['hybridj_solver'](self,*args) @@ -7368,14 +7368,14 @@ cdef class GiacMethods_base: Help for hybrids_solver: hybrids_solver(Opt) Argument for fsolve giving the method for solving a system of numerical equations. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],dnewton_solver) Ex2: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrid_solver) Ex3: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrids_solver) Ex4: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridj_solver) Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) - + ''' return GiacMethods['hybrids_solver'](self,*args) @@ -7384,14 +7384,14 @@ cdef class GiacMethods_base: Help for hybridsj_solver: hybridsj_solver(Opt) Argument for fsolve giving the method for solving a system of numerical equations. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],dnewton_solver) Ex2: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrid_solver) Ex3: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrids_solver) Ex4: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridj_solver) Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) - + ''' return GiacMethods['hybridsj_solver'](self,*args) @@ -7400,9 +7400,9 @@ cdef class GiacMethods_base: Help for hyp2exp: hyp2exp(ExprHyperb) Transforms the hyperbolic functions to the exponential function. - See also: 1/ halftan_hyp2exp + See also: 1/ halftan_hyp2exp Ex1:hyp2exp(cosh(x)) - + ''' return GiacMethods['hyp2exp'](self,*args) @@ -7411,12 +7411,12 @@ cdef class GiacMethods_base: Help for hyperbola: hyperbola(Focus(F1),Focus(F2),(Pnt(M) or Real(a))) hyperbola(F1,F2,M)=hyperbola with foci F1,F2 through M or (|MF1-MF2|=2*a geo2d) and hyperbola(p(x,y)) draws the conic if deg(p)=2. - See also: 1/ ellipse 2/ parabola + See also: 1/ ellipse 2/ parabola Ex1:hyperbola(-1,1,point(1+i)) Ex2:hyperbola(-1,1,sqrt(5)-1) Ex3:hyperbola(point(-1,0,0),point(1,0,0),point(1,1,1)) Ex4:hyperbola(x^2-y^2+y+2) - + ''' return GiacMethods['hyperbola'](self,*args) @@ -7425,9 +7425,9 @@ cdef class GiacMethods_base: Help for hypercube_graph: hypercube_graph(Intg(n)) Constructs and returns the hypercube graph in dimension n (with 2^n vertices). - See also: 1/ graph + See also: 1/ graph Ex1:hypercube_graph(3) - + ''' return GiacMethods['hypercube_graph'](self,*args) @@ -7436,11 +7436,11 @@ cdef class GiacMethods_base: Help for iPart: iPart(Real||LstReal) Returns the argument without its fractional part (type=DOM_FLOAT). - See also: 1/ fPart 2/ floor 3/ trunc + See also: 1/ fPart 2/ floor 3/ trunc Ex1:iPart(4.3) Ex2:iPart(sqrt(2)) Ex3:iPart(4.3,sqrt(2)) - + ''' return GiacMethods['iPart'](self,*args) @@ -7449,11 +7449,11 @@ cdef class GiacMethods_base: Help for iabcuv: iabcuv(Intg(a),Intg(b),Intg(c)) Returns [u,v] such that au+bv=c for 3 integers a,b,c. - See also: 1/ iegcd 2/ abcuv + See also: 1/ iegcd 2/ abcuv Ex1:iabcuv(21,28,7) Ex2:iabcuv(21,28,14) Ex3:iabcuv(21,28,1) - + ''' return GiacMethods['iabcuv'](self,*args) @@ -7462,9 +7462,9 @@ cdef class GiacMethods_base: Help for ibasis: ibasis(Lst(Vect,..,Vect),Lst(Vect,..,Vect)) Basis of the intersection of two vector spaces. - See also: 1/ basis + See also: 1/ basis Ex1:ibasis([[1,0,0],[0,1,0]],[[1,1,1],[0,0,1]]) - + ''' return GiacMethods['ibasis'](self,*args) @@ -7473,13 +7473,13 @@ cdef class GiacMethods_base: Help for ibpdv: ibpdv(Expr(f(x)),Expr(v(x)),[Var(x)],[Real(a)],[Real(b)]) Integration by parts of f(x)=u(x)*v'(x) with f(x) as 1st argument and v(x) (or 0) as 2nd argument. You can specify a variable of integration and also calculate the integral (bounds a and b). - See also: 1/ ibpu 2/ int + See also: 1/ ibpu 2/ int Ex1:ibpdv(ln(x),x) Ex2:ibpdv(ln(x),x,x,1,3) Ex3:ibpdv(x*ln(x),x^2/2) Ex4:ibpdv([x*ln(x),-1],0) Ex5:ibpdv(ibpdv(ln(x),x,x,2,3),0,x,2,3) - + ''' return GiacMethods['ibpdv'](self,*args) @@ -7488,13 +7488,13 @@ cdef class GiacMethods_base: Help for ibpu: ibpu(Expr(f(x)),Expr(u(x)),[Var(x)],[Real(a)],[Real(b)]) Integration by parts of f(x)=u(x)*v'(x) with f(x) as 1st argument and u(x) (or 0) as 2nd argument. You can specify a variable of integration and also calculate the integral (bounds a and b). - See also: 1/ ibpdv 2/ int + See also: 1/ ibpdv 2/ int Ex1:ibpu(ln(x),ln(x)) Ex2:ibpu(ln(x),ln(x),x,1,3) Ex3:ibpu(x*ln(x),ln(x)) Ex4:ibpu([x*ln(x),-1],0) Ex5:ibpu(ibpu(ln(x),ln(x),x,2,3),0,x,2,3) - + ''' return GiacMethods['ibpu'](self,*args) @@ -7503,10 +7503,10 @@ cdef class GiacMethods_base: Help for icdf: icdf(Func,FuncParams) Inverse cumulative distribution function. - See also: 1/ cdf 2/ binomial_icdf 3/ normald_icdf + See also: 1/ cdf 2/ binomial_icdf 3/ normald_icdf Ex1:icdf(binomial,10,0.5,0.6) Ex2:icdf(normald,0.0,1.0,0.975) - + ''' return GiacMethods['icdf'](self,*args) @@ -7515,12 +7515,12 @@ cdef class GiacMethods_base: Help for ichinrem: ichinrem(LstIntg(a,p),LstIntg(b,q)) Chinese remainders for integers. - See also: 1/ gcd 2/ fracmod 3/ chinrem 4/ chrem + See also: 1/ gcd 2/ fracmod 3/ chinrem 4/ chrem Ex1:ichinrem([2,7],[3,5]) Ex2:ichinrem([2%7,3%5]) Ex3:ichinrem([2%7,3%5,1%9]) Ex4:ichinrem([(x+1)%2,(x+2)%3,(3*x-1)%5]) - + ''' return GiacMethods['ichinrem'](self,*args) @@ -7529,12 +7529,12 @@ cdef class GiacMethods_base: Help for ichrem: ichrem(LstIntg(a,p),LstIntg(b,q)) Chinese remainders for integers. - See also: 1/ gcd 2/ fracmod 3/ chinrem 4/ chrem + See also: 1/ gcd 2/ fracmod 3/ chinrem 4/ chrem Ex1:ichrem([2,7],[3,5]) Ex2:ichrem([2%7,3%5]) Ex3:ichrem([2%7,3%5,1%9]) Ex4:ichrem([(x+1)%2,(x+2)%3,(3*x-1)%5]) - + ''' return GiacMethods['ichrem'](self,*args) @@ -7543,10 +7543,10 @@ cdef class GiacMethods_base: Help for icomp: icomp(Intg(n),Intg(k),[zeros=true||false]) Returns the list of compositions of n into k parts. - See also: 1/ sum + See also: 1/ sum Ex1:icomp(4,2) Ex2:icomp(6,3,zeros=false) - + ''' return GiacMethods['icomp'](self,*args) @@ -7555,10 +7555,10 @@ cdef class GiacMethods_base: Help for icontent: icontent(Poly,[Var]) GCD of the integer coefficients of a polynomial. - See also: 1/ + See also: 1/ Ex1:icontent(24x^3+6x^2-12x+18) Ex2:icontent(24t^3+6t^2-12t+18,t) - + ''' return GiacMethods['icontent'](self,*args) @@ -7567,10 +7567,10 @@ cdef class GiacMethods_base: Help for icosahedron: icosahedron(Pnt(A),Pnt(B),Pnt(C)) Draws an icosahedron with center A, vertex B and such that the plane ABC contains one vertex among the 5 nearest vertices from B. - See also: 1/ octahedron 2/ dodecahedron 3/ cube 4/ tetrahedron + See also: 1/ octahedron 2/ dodecahedron 3/ cube 4/ tetrahedron Ex1:icosahedron([0,0,0],[sqrt(5),0,0],[1,2,0]) Ex2:icosahedron(evalf([0,0,0],[3,2,4],[1,1,0])) - + ''' return GiacMethods['icosahedron'](self,*args) @@ -7579,9 +7579,9 @@ cdef class GiacMethods_base: Help for id: id(Seq) The name of the identity function (ℝ^n -> ℝ^n). - See also: 1/ sq 2/ sqrt + See also: 1/ sq 2/ sqrt Ex1:id(1,2,3) - + ''' return GiacMethods['id'](self,*args) @@ -7590,10 +7590,10 @@ cdef class GiacMethods_base: Help for identity: identity(Intg(n)) Returns the identity matrix of specified dimension n. - See also: 1/ ranm + See also: 1/ ranm Ex1:identity(3) Ex2:identity(5) - + ''' return GiacMethods['identity'](self,*args) @@ -7602,10 +7602,10 @@ cdef class GiacMethods_base: Help for idivis: idivis(Intg(a) or LstIntg) Returns the list of divisors of an integer. - See also: 1/ divis 2/ ifactors + See also: 1/ divis 2/ ifactors Ex1:idivis(36) Ex2:idivis([36,49]) - + ''' return GiacMethods['idivis'](self,*args) @@ -7614,10 +7614,10 @@ cdef class GiacMethods_base: Help for idn: idn(Intg(n)) Returns the identity matrix of specified dimension n. - See also: 1/ ranm + See also: 1/ ranm Ex1:idn(3) Ex2:idn(5) - + ''' return GiacMethods['idn'](self,*args) @@ -7626,11 +7626,11 @@ cdef class GiacMethods_base: Help for iegcd: iegcd(Intg,Intg) Extended greatest common divisor of 2 integers. - See also: 1/ gcd 2/ iabcuv 3/ egcd + See also: 1/ gcd 2/ iabcuv 3/ egcd Ex1:iegcd(45,75) Ex2:iegcd(21,28) Ex3:iegcd(30,49) - + ''' return GiacMethods['iegcd'](self,*args) @@ -7639,10 +7639,10 @@ cdef class GiacMethods_base: Help for ifactor: ifactor(Intg(a)) Factorization of an integer into prime factors. - See also: 1/ factor 2/ ecm_factor + See also: 1/ factor 2/ ecm_factor Ex1:ifactor(50) Ex2:ifactor(123456789) - + ''' return GiacMethods['ifactor'](self,*args) @@ -7651,10 +7651,10 @@ cdef class GiacMethods_base: Help for ifactors: ifactors(Intg(a) or LstIntg) Returns the list of prime factors of an integer (each factor is followed by its multiplicity). - See also: 1/ ifactor 2/ factors + See also: 1/ ifactor 2/ factors Ex1:ifactors(36) Ex2:ifactors([36,52]) - + ''' return GiacMethods['ifactors'](self,*args) @@ -7663,7 +7663,7 @@ cdef class GiacMethods_base: Help for ifourier: ifourier(Expr(F(s)),[Var(s),[Var(x)]]) Returns the inverse Fourier transform f(x) of F(s). - See also: 1/ fourier 2/ fourier_cn 3/ ifft + See also: 1/ fourier 2/ fourier_cn 3/ ifft Ex1:ifourier(2*pi*(Dirac(s)-sign(s)*sin(s)),s,x) Ex2:ifourier(-2/(s^2-1),s,x) Ex3:ifourier(pi/(exp(pi*s/4)+exp(-pi*s/4)),s,x) @@ -7671,7 +7671,7 @@ cdef class GiacMethods_base: Ex5:ifourier(pi*ugamma(0,4*abs(s)),s,x) Ex6:ifourier(fourier(exp(-abs(x)),x,s)^2,s,x) Ex7:ifourier(sinc(s),s,x) - + ''' return GiacMethods['ifourier'](self,*args) @@ -7680,11 +7680,11 @@ cdef class GiacMethods_base: Help for igamma: igamma(Real(a),Real(x),[1]) Calculates of gamma at a point (a,x). If a and x>0, igamma(a,x)=int(e^{-t}*t^{a-1},t=0..x), (igamma(a,x,1)=igamma(a,x)/Gamma(a)). - See also: 1/ Psi 2/ Beta 3/ Gamma 3/ ugamma + See also: 1/ Psi 2/ Beta 3/ Gamma 3/ ugamma Ex1:igamma(5.0,2.0) Ex2:igamma(-5.1,2.1) Ex3:igamma(5.0,2.0,1) - + ''' return GiacMethods['igamma'](self,*args) @@ -7693,13 +7693,13 @@ cdef class GiacMethods_base: Help for igcd: igcd((Intg(a) or Poly),(Intg(b) or Poly)) Returns the greatest common divisor of 2 polynomials of several variables or of 2 integers or of 2 rationals. - See also: 1/ lcm 2/ euler 2/ modgcd 3/ ezgcd 4/ psrgcd 5/ heugcd 6/ Gcd + See also: 1/ lcm 2/ euler 2/ modgcd 3/ ezgcd 4/ psrgcd 5/ heugcd 6/ Gcd Ex1:igcd(45,75) Ex2:igcd(15/7,50/9) Ex3:igcd(x^2-2*x+1,x^3-1) Ex4:igcd(t^2-2*t+1,t^2+t-2) Ex5:igcd((x^2-1)*(y^2-1)*z^2,x^3*y^3*z+(-(y^3))*z+x^3*z-z) - + ''' return GiacMethods['igcd'](self,*args) @@ -7708,11 +7708,11 @@ cdef class GiacMethods_base: Help for igcdex: igcdex(Intg,Intg) Extended greatest common divisor of 2 integers. - See also: 1/ gcd 2/ iabcuv 3/ egcd + See also: 1/ gcd 2/ iabcuv 3/ egcd Ex1:igcdex(45,75) Ex2:igcdex(21,28) Ex3:igcdex(30,49) - + ''' return GiacMethods['igcdex'](self,*args) @@ -7721,10 +7721,10 @@ cdef class GiacMethods_base: Help for ihermite: ihermite(Mtrx(A)) Hermite normal form of a matrix with coefficients in ℤ : returns L,U such that L is invertible in ℤ, U is upper triangular and U=L*A. - See also: 1/ ismith + See also: 1/ ismith Ex1:ihermite([[9,-36,30], [-36,192,-180], [30,-180,180]]) Ex2:ihermite([[1,2,3],[4,5,6],[7,8,9]]) - + ''' return GiacMethods['ihermite'](self,*args) @@ -7733,11 +7733,11 @@ cdef class GiacMethods_base: Help for ilaplace: ilaplace(Expr,[Var],[IlapVar]) Inverse Laplace transform of a rational fraction. - See also: 1/ laplace 2/ ztrans 3/ invztrans 4/ Heaviside + See also: 1/ laplace 2/ ztrans 3/ invztrans 4/ Heaviside Ex1:ilaplace(1/(x^2+1)^2) Ex2:ilaplace(s/(s^4-1),s,x) Ex3:ilaplace(exp(-s)/s,s,x) - + ''' return GiacMethods['ilaplace'](self,*args) @@ -7746,11 +7746,11 @@ cdef class GiacMethods_base: Help for im: im(Cplx) Returns the imaginary part of a complex number. - See also: 1/ re 2/ conj + See also: 1/ re 2/ conj Ex1:im(1+2*i) Ex2:im((1+2*i)^2) Ex3:im([1+2*i,(1+2*i)^2]) - + ''' return GiacMethods['im'](self,*args) @@ -7759,11 +7759,11 @@ cdef class GiacMethods_base: Help for imag: imag(Cplx) Returns the imaginary part of a complex number. - See also: 1/ re 2/ conj + See also: 1/ re 2/ conj Ex1:imag(1+2*i) Ex2:imag((1+2*i)^2) Ex3:imag([1+2*i,(1+2*i)^2]) - + ''' return GiacMethods['imag'](self,*args) @@ -7772,10 +7772,10 @@ cdef class GiacMethods_base: Help for image: image(Mtrx(M)) Image of a linear map with matrix M. - See also: 1/ ker 2/ rref + See also: 1/ ker 2/ rref Ex1:image([[1,2],[3,6]]) Ex2:image([[1,2,3],[1,3,6],[2,5,9]]) - + ''' return GiacMethods['image'](self,*args) @@ -7784,7 +7784,7 @@ cdef class GiacMethods_base: Help for implicitdiff: implicitdiff(constr,[depvars],y,diffvars) Implicit differentiation. - See also: 1/ diff + See also: 1/ diff Ex1:implicitdiff(x^2*y+y^2=1,y,x) Ex2:implicitdiff(R=P*V/T,P,T) Ex3:implicitdiff([x^2+y=z,x+y*z=1],[y(x),z(x)],y,x) @@ -7803,7 +7803,7 @@ cdef class GiacMethods_base: Ex16:implicitdiff(x*y*z,-2x^3+15x^2*y+11y^3-24y=0,[x,z,y],order=1) Ex17:implicitdiff(x*y*z,-2x^3+15x^2*y+11y^3-24y=0,[x,z,y],order=2,[1,-1,0]) Ex18: pd:=implicitdiff(x*y*z,-2x^3+15x^2*y+11y^3-24y=0,[x,z,y],order=4,[0,z,0]);pd[4,0,0] - + ''' return GiacMethods['implicitdiff'](self,*args) @@ -7812,7 +7812,7 @@ cdef class GiacMethods_base: Help for implicitplot: implicitplot(Expr,Var1,Var2) plotimplicit(f(x,y),x,y) or plotimplicit(f(x,y),[x,y]) draws graph of f(x,y)=0. - See also: 1/ plotcontour 2/ unfactored 3/ plotinequation + See also: 1/ plotcontour 2/ unfactored 3/ plotinequation Ex1:implicitplot(x^2+y^2-1,x,y) Ex2:implicitplot(x^4+y^4=x^2-y^2) Ex3:implicitplot(x^2+y^2-1,x,y,unfactored) @@ -7822,7 +7822,7 @@ cdef class GiacMethods_base: Ex7:implicitplot(y^3=x^3-x^2,[x,y],xstep=0.1,ystep=0.1) Ex8:implicitplot((x+5)^2+(y+4)^2-1,x=-6..-4,y=-5..-3) Ex9:implicitplot((x+5)^2+(y+4)^2-1,[x=-6..-4,y=-5..-3]) - + ''' return GiacMethods['implicitplot'](self,*args) @@ -7832,7 +7832,7 @@ cdef class GiacMethods_base: import_graph(Str("path/to/graphname[.dot]")) Returns the graph constructed from instructions in the file 'path/to/graphname.dot' (in dot format), or "undef" on failure. Ex1:import_graph("K5.dot") - + ''' return GiacMethods['import_graph'](self,*args) @@ -7841,10 +7841,10 @@ cdef class GiacMethods_base: Help for inString: inString(Str(l),Elem(e)) Tests if e is in the string l (returns -1 or k if l[k]=e). - See also: 1/ contains + See also: 1/ contains Ex1:inString("abcd","b") Ex2:inString("abcd","e") - + ''' return GiacMethods['inString'](self,*args) @@ -7853,10 +7853,10 @@ cdef class GiacMethods_base: Help for in_ideal: in_ideal(Poly,Lst,LstVar,[order]) Checks whether a polynomial or list of polynomials belongs to an ideal given by a Grobner basis (2nd argument) with respect to a variable list. - See also: 1/ gbasis 2/ greduce + See also: 1/ gbasis 2/ greduce Ex1:in_ideal((x+y)^2,[y^2,x^2+2*x*y],[x,y]) Ex2:in_ideal(x+y,[y^2,x^2+2*x*y],[x,y]) - + ''' return GiacMethods['in_ideal'](self,*args) @@ -7865,9 +7865,9 @@ cdef class GiacMethods_base: Help for incidence_matrix: incidence_matrix(Graph(G)) Returns the incidence matrix of G whose rows are indexed by the vertices and columns by the edges (in order defined by the command 'edges'). - See also: 1/ incident_edges + See also: 1/ incident_edges Ex1:incidence_matrix(graph("tetrahedron")) - + ''' return GiacMethods['incidence_matrix'](self,*args) @@ -7876,9 +7876,9 @@ cdef class GiacMethods_base: Help for incident_edges: incident_edges(Graph(G),Vrtx(v)) Returns the list of all edges incident to the vertex v of G (or to the vertices in the list v). - See also: 1/ adjacency_matrix 2/ vertex_degree 3/ incidence_matrix 4/ neighbors + See also: 1/ adjacency_matrix 2/ vertex_degree 3/ incidence_matrix 4/ neighbors Ex1:incident_edges(cycle_graph(8),[1,5,7]) - + ''' return GiacMethods['incident_edges'](self,*args) @@ -7887,9 +7887,9 @@ cdef class GiacMethods_base: Help for incircle: incircle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) incircle(A,B,C) draws the incircle of the triangle ABC. - See also: 1/ excircle 2/ circumcircle + See also: 1/ excircle 2/ circumcircle Ex1:incircle(0,1,1+i) - + ''' return GiacMethods['incircle'](self,*args) @@ -7898,10 +7898,10 @@ cdef class GiacMethods_base: Help for increasing_power: increasing_power(:=Intg(0 or 1)) Pseudo-variable to control the display of polynomials. - See also: 1/ cas_setup + See also: 1/ cas_setup Ex1: increasing_power:=1 Ex2: increasing_power:=0 - + ''' return GiacMethods['increasing_power'](self,*args) @@ -7910,9 +7910,9 @@ cdef class GiacMethods_base: Help for independence_number: independence_number(Graph(G)) Returns the independence number of G. - See also: 1/ clique_number 2/ graph_complement 3/ maximum_clique 4/ maximum_independent_set + See also: 1/ clique_number 2/ graph_complement 3/ maximum_clique 4/ maximum_independent_set Ex1:independence_number(complete_graph(3,4)) - + ''' return GiacMethods['independence_number'](self,*args) @@ -7921,9 +7921,9 @@ cdef class GiacMethods_base: Help for indets: indets(Expr) List of variables in the expression. - See also: 1/ has 2/ lvar + See also: 1/ has 2/ lvar Ex1:indets(exp(x)*2*sin(y)) - + ''' return GiacMethods['indets'](self,*args) @@ -7932,12 +7932,12 @@ cdef class GiacMethods_base: Help for index: index(Vect,Expr) Index of the first position of an object in a list, a string or a set or returns an error message. - See also: 1/ find 2/ member + See also: 1/ find 2/ member Ex1:index([3,x,1,2,1,3],1) Ex2:index([0,1,3,2,4,2,5],2) Ex3:index(%{4,3,1,2%},1) Ex4:index("abracadabrant","c") - + ''' return GiacMethods['index'](self,*args) @@ -7946,9 +7946,9 @@ cdef class GiacMethods_base: Help for induced_subgraph: induced_subgraph(Graph(G),Lst(V)) Returns the subgraph of G induced by the vertices in list V. - See also: 1/ subgraph + See also: 1/ subgraph Ex1:induced_subgraph(cycle_graph(6),[1,2,6]) - + ''' return GiacMethods['induced_subgraph'](self,*args) @@ -7957,12 +7957,12 @@ cdef class GiacMethods_base: Help for inequationplot: inequationplot(Expr,[x=xrange,y=yrange],[xstep],[ystep]) Shows the graph of the solutions of inequalities with 2 variables. - See also: 1/ plotfunc 2/ plotcontour 3/ plotdensity 4/ plotimplicit + See also: 1/ plotfunc 2/ plotcontour 3/ plotdensity 4/ plotimplicit Ex1:inequationplot(x^2-y^2<3) Ex2:inequationplot(x^2-y^2<3,[x=-2..2,y=-2..2],xstep=0.1,ystep=0.1) Ex3:inequationplot(3-(x^2-y^2),[x=-2..2,y=-2..2],xstep=0.1,ystep=0.1) Ex4:inequationplot([x+y>3,x^2ln(a*b^n) for integers n. - See also: 1/ texpand + See also: 1/ texpand Ex1:lncollect(ln(x)+2*ln(y)) - + ''' return GiacMethods['lncollect'](self,*args) @@ -9904,9 +9904,9 @@ cdef class GiacMethods_base: Help for lnexpand: lnexpand(Expr) Expands logarithms. - See also: 1/ texpand 2/ expexpand 3/ trigexpand + See also: 1/ texpand 2/ expexpand 3/ trigexpand Ex1:lnexpand(ln(3*x)) - + ''' return GiacMethods['lnexpand'](self,*args) @@ -9915,10 +9915,10 @@ cdef class GiacMethods_base: Help for locus: locus(Pnt,Elem) locus(M,A) draws the locus of M (or locus(d,A) draws the envelope of d) when A:=element(C) (C is a curve). The example instructions below must be written in a geometric level on different lines. - See also: 1/ envelope 2/ trace + See also: 1/ envelope 2/ trace Ex1: A:=element(circle(i,1+i));M:=homothety(0,2,A);locus(M,A) Ex2: A:=element(line(x=0));d:=perpen_bisector(1,A);locus(d,A) - + ''' return GiacMethods['locus'](self,*args) @@ -9927,11 +9927,11 @@ cdef class GiacMethods_base: Help for log: log(Expr or Opt) Natural logarithm or option of the convert or convertir command (id trig2exp). - See also: 1/ exp 2/ convert 3/ trig2exp 4/ log10 + See also: 1/ exp 2/ convert 3/ trig2exp 4/ log10 Ex1:log(1) Ex2:log(e) Ex3: convert(cos(x),ln) - + ''' return GiacMethods['log'](self,*args) @@ -9940,9 +9940,9 @@ cdef class GiacMethods_base: Help for log10: log10(Expr) Common logarithm (base 10). - See also: 1/ alog10 2/ ln + See also: 1/ alog10 2/ ln Ex1:log10(10) - + ''' return GiacMethods['log10'](self,*args) @@ -9951,10 +9951,10 @@ cdef class GiacMethods_base: Help for logarithmic_regression: logarithmic_regression(Lst||Mtrx(A),[Lst]) Returns the coefficients a and b of y=a*ln(x)+b : it is the best logarithm which approx the points where the coordinates are the rows of A (or the 2 lists). - See also: 1/ exponential_regression + See also: 1/ exponential_regression Ex1:logarithmic_regression([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) Ex2:logarithmic_regression([1.0,2.0,3.0,4.0],[1.0,4.0,9.0,16.0]) - + ''' return GiacMethods['logarithmic_regression'](self,*args) @@ -9963,10 +9963,10 @@ cdef class GiacMethods_base: Help for logarithmic_regression_plot: logarithmic_regression_plot(Lst||Mtrx(A),[Lst]) Returns the plot of y=a*ln(x)+b : it is the best logarithm which approx the points where the coordinates are the rows of A (or the 2 lists). - See also: 1/ exponential_regression_plot + See also: 1/ exponential_regression_plot Ex1:logarithmic_regression_plot([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) Ex2:logarithmic_regression_plot([1.0,2.0,3.0,4.0],[1.0,4.0,9.0,16.0]) - + ''' return GiacMethods['logarithmic_regression_plot'](self,*args) @@ -9975,10 +9975,10 @@ cdef class GiacMethods_base: Help for logb: logb(Real) Logarithm with base b. - See also: 1/ log 2/ log10 + See also: 1/ log 2/ log10 Ex1:logb(5,2) Ex2:logb(7,10) - + ''' return GiacMethods['logb'](self,*args) @@ -9987,10 +9987,10 @@ cdef class GiacMethods_base: Help for logistic_regression: logistic_regression(Lst(L),Real(x0),Real(y0)) Returns y,y',C,y'max,xmax,R : y is a logistic function (sol of y'/y=a*y+b), such that y(x0)=y0 and where [y'(x0),y'(x0+1)...] is the best approximation of L. - See also: 1/ polynomial_regression 2/ power_regression 3/ linear_regression + See also: 1/ polynomial_regression 2/ power_regression 3/ linear_regression Ex1:logistic_regression(evalf([1,2,4,6,8,7,5]),1,2) Ex2:logistic_regression([0.0,1.0,2.0,3.0,4.0],0.0,1.0) - + ''' return GiacMethods['logistic_regression'](self,*args) @@ -9999,10 +9999,10 @@ cdef class GiacMethods_base: Help for logistic_regression_plot: logistic_regression_plot(Lst(L),Real(x0),Real(y0)) Returns the plot of a logistic function y such that y(x0)=y0 and where [y'(x0),y'(x0+1)...] is the best approximation of L. - See also: 1/ polynomial_regression_plot 2/ power_regression_plot 3/ linear_regression_plot + See also: 1/ polynomial_regression_plot 2/ power_regression_plot 3/ linear_regression_plot Ex1:logistic_regression_plot(evalf([1,2,4,6,8,7,5]),1,2) Ex2:logistic_regression_plot([0.0,1.0,2.0,3.0,4.0],0.0,1.0) - + ''' return GiacMethods['logistic_regression_plot'](self,*args) @@ -10011,10 +10011,10 @@ cdef class GiacMethods_base: Help for lower: lower(Mtrx||Strng) Returns the lower triangular matrix (under the diagonal, included) or writes a string in lowercase. - See also: 1/ diag 2/ upper + See also: 1/ diag 2/ upper Ex1:lower([[1,2,3],[4,5,6],[7,8,9]]) Ex2:lower("HELLO") - + ''' return GiacMethods['lower'](self,*args) @@ -10023,10 +10023,10 @@ cdef class GiacMethods_base: Help for lowest_common_ancestor: lowest_common_ancestor(Graph(T),Vrtx(r),Seq(u,v)||Lst([u1,v1],[u2,v2],...)) Returns the lowest common ancestor of nodes u and v in the tree graph T with root r, or the list of lowest common ancestors of all pairs [uk,vk]. - See also: 1/ is_tree 2/ tree_height + See also: 1/ is_tree 2/ tree_height Ex1: T:=random_tree(30); lowest_common_ancestor(T,15,10,20) Ex2: T:=random_tree(30); lowest_common_ancestor(T,15,[[10,20],[11,19]]) - + ''' return GiacMethods['lowest_common_ancestor'](self,*args) @@ -10035,9 +10035,9 @@ cdef class GiacMethods_base: Help for lowpass: lowpass(Lst(s),Real(c),[Intg(samplerate)]) Returns the result of applying a simple first-order lowpass RC filter with cutoff frequency c (the default samplerate is 44100) to the given signal s. - See also: 1/ highpass 2/ moving_average + See also: 1/ highpass 2/ moving_average Ex1: f:=unapply(periodic(sign(x),x,-1/880,1/880),x):;s:=createwav(apply(f,soundsec(1))):;playsnd(lowpass(s,1000)) - + ''' return GiacMethods['lowpass'](self,*args) @@ -10046,8 +10046,8 @@ cdef class GiacMethods_base: Help for lp_assume: lp_assume(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_assume'](self,*args) @@ -10056,8 +10056,8 @@ cdef class GiacMethods_base: Help for lp_bestprojection: lp_bestprojection(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_bestprojection'](self,*args) @@ -10066,8 +10066,8 @@ cdef class GiacMethods_base: Help for lp_binary: lp_binary(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_binary'](self,*args) @@ -10076,8 +10076,8 @@ cdef class GiacMethods_base: Help for lp_binaryvariables: lp_binaryvariables(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_binaryvariables'](self,*args) @@ -10086,8 +10086,8 @@ cdef class GiacMethods_base: Help for lp_breadthfirst: lp_breadthfirst(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_breadthfirst'](self,*args) @@ -10096,8 +10096,8 @@ cdef class GiacMethods_base: Help for lp_depthfirst: lp_depthfirst(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_depthfirst'](self,*args) @@ -10106,8 +10106,8 @@ cdef class GiacMethods_base: Help for lp_depthlimit: lp_depthlimit(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_depthlimit'](self,*args) @@ -10116,8 +10116,8 @@ cdef class GiacMethods_base: Help for lp_firstfractional: lp_firstfractional(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_firstfractional'](self,*args) @@ -10126,8 +10126,8 @@ cdef class GiacMethods_base: Help for lp_gaptolerance: lp_gaptolerance(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_gaptolerance'](self,*args) @@ -10136,8 +10136,8 @@ cdef class GiacMethods_base: Help for lp_hybrid: lp_hybrid(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_hybrid'](self,*args) @@ -10146,8 +10146,8 @@ cdef class GiacMethods_base: Help for lp_initialpoint: lp_initialpoint(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_initialpoint'](self,*args) @@ -10156,8 +10156,8 @@ cdef class GiacMethods_base: Help for lp_integer: lp_integer(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_integer'](self,*args) @@ -10166,8 +10166,8 @@ cdef class GiacMethods_base: Help for lp_integertolerance: lp_integertolerance(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_integertolerance'](self,*args) @@ -10176,8 +10176,8 @@ cdef class GiacMethods_base: Help for lp_integervariables: lp_integervariables(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_integervariables'](self,*args) @@ -10186,8 +10186,8 @@ cdef class GiacMethods_base: Help for lp_interiorpoint: lp_interiorpoint(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_interiorpoint'](self,*args) @@ -10196,8 +10196,8 @@ cdef class GiacMethods_base: Help for lp_iterationlimit: lp_iterationlimit(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_iterationlimit'](self,*args) @@ -10206,8 +10206,8 @@ cdef class GiacMethods_base: Help for lp_lastfractional: lp_lastfractional(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_lastfractional'](self,*args) @@ -10216,8 +10216,8 @@ cdef class GiacMethods_base: Help for lp_maxcuts: lp_maxcuts(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_maxcuts'](self,*args) @@ -10226,8 +10226,8 @@ cdef class GiacMethods_base: Help for lp_maximize: lp_maximize(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_maximize'](self,*args) @@ -10236,8 +10236,8 @@ cdef class GiacMethods_base: Help for lp_method: lp_method(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_method'](self,*args) @@ -10246,8 +10246,8 @@ cdef class GiacMethods_base: Help for lp_mostfractional: lp_mostfractional(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_mostfractional'](self,*args) @@ -10256,8 +10256,8 @@ cdef class GiacMethods_base: Help for lp_nodelimit: lp_nodelimit(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_nodelimit'](self,*args) @@ -10266,8 +10266,8 @@ cdef class GiacMethods_base: Help for lp_nodeselect: lp_nodeselect(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_nodeselect'](self,*args) @@ -10276,8 +10276,8 @@ cdef class GiacMethods_base: Help for lp_nonnegative: lp_nonnegative(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_nonnegative'](self,*args) @@ -10286,8 +10286,8 @@ cdef class GiacMethods_base: Help for lp_nonnegint: lp_nonnegint(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_nonnegint'](self,*args) @@ -10296,8 +10296,8 @@ cdef class GiacMethods_base: Help for lp_pseudocost: lp_pseudocost(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_pseudocost'](self,*args) @@ -10306,8 +10306,8 @@ cdef class GiacMethods_base: Help for lp_simplex: lp_simplex(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_simplex'](self,*args) @@ -10316,8 +10316,8 @@ cdef class GiacMethods_base: Help for lp_timelimit: lp_timelimit(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_timelimit'](self,*args) @@ -10326,8 +10326,8 @@ cdef class GiacMethods_base: Help for lp_variables: lp_variables(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_variables'](self,*args) @@ -10336,8 +10336,8 @@ cdef class GiacMethods_base: Help for lp_varselect: lp_varselect(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_varselect'](self,*args) @@ -10346,8 +10346,8 @@ cdef class GiacMethods_base: Help for lp_verbose: lp_verbose(Opt) Options for lpsolve command. - See also: 1/ lpsolve - + See also: 1/ lpsolve + ''' return GiacMethods['lp_verbose'](self,*args) @@ -10356,7 +10356,7 @@ cdef class GiacMethods_base: Help for lpsolve: lpsolve(Expr(o),[List(c)],[bounds],[options]) Solves a (mixed integer/binary) LP problem in general form. - See also: 1/ nlpsolve 2/ fsolve + See also: 1/ nlpsolve 2/ fsolve Ex1:lpsolve(2x+y-z+4,[x<=1,y>=2,x+3y-z=2,2x-y+z<=8,-x+y<=5]) Ex2:lpsolve(-4x-5y,[x+2y<=6,5x+4y<=20,0<=x,0<=y]) Ex3:lpsolve(-7x+2y,[4x-12y<=20,-x+3y<=3],x=-5..5,y=0..inf,lp_maximize=true) @@ -10372,7 +10372,7 @@ cdef class GiacMethods_base: Ex13:lpsolve(x1+x2,[2x1+5x2<=16,6x1+5x2<=30],assume=nonnegint,lp_maximize) Ex14:lpsolve(8x1+11x2+6x3+4x4,[5x1+7x2+4x3+3x4<=14],assume=lp_binary,lp_maximize) Ex15:lpsolve(x1+x2,[1867x1+1913x2=3618894],assume=nonnegint,lp_verbose=true) - + ''' return GiacMethods['lpsolve'](self,*args) @@ -10381,9 +10381,9 @@ cdef class GiacMethods_base: Help for lsmod: lsmod(NULL) Displays the installed dynamic libraries. - See also: 1/ insmod 2/ rmmod + See also: 1/ insmod 2/ rmmod Ex1:lsmod() - + ''' return GiacMethods['lsmod'](self,*args) @@ -10392,10 +10392,10 @@ cdef class GiacMethods_base: Help for lsq: lsq(Mtrx(A),(Mtrx || Vect)(B)) Returns the vector (resp matrix) X which is the minimum of the euclidean (resp Frobenius) norm of A*X-B corresponding to the linear system A*X=B when B is a vector (resp matrix). - See also: 1/ lu 2/ QR + See also: 1/ lu 2/ QR Ex1:lsq([[1,2],[3,4]],[5,11]) Ex2:lsq([[1,2],[3,4]],[[5,-1],[11,-1]]) - + ''' return GiacMethods['lsq'](self,*args) @@ -10404,10 +10404,10 @@ cdef class GiacMethods_base: Help for lu: lu(Mtrx) For a numerical matrix A, returns p permutation, L and U such that PA=LU (P=permu2mat(p)). - See also: 1/ qr 2/ cholesky 3/ LU + See also: 1/ qr 2/ cholesky 3/ LU Ex1:lu([[1,2],[3,4]]) Ex2:lu([[6,12,18],[5,14,31],[3,8,18]]) - + ''' return GiacMethods['lu'](self,*args) @@ -10416,10 +10416,10 @@ cdef class GiacMethods_base: Help for lvar: lvar(Expr) List of variables of an object (with rational dependence). - See also: 1/ lname 2/ has + See also: 1/ lname 2/ has Ex1:lvar(exp(x)*2*sin(y)) Ex2:lvar(exp(x)*2*sin(y)+ln(x)) - + ''' return GiacMethods['lvar'](self,*args) @@ -10428,9 +10428,9 @@ cdef class GiacMethods_base: Help for mRow: mRow(Expr(Xpr),Mtrx(A),Intg(n1)) Multiplies row n1 of the matrix A by Xpr. - See also: 1/ rowAdd 2/ mRowAdd + See also: 1/ rowAdd 2/ mRowAdd Ex1:mRow(12,[[1,2],[3,4],[5,6]],0) - + ''' return GiacMethods['mRow'](self,*args) @@ -10439,9 +10439,9 @@ cdef class GiacMethods_base: Help for mRowAdd: mRowAdd(Expr(Xpr),Mtrx(A),Intg(n1),Intg(n2)) Multiplies row n1 of the matrix A by Xpr, then adds it to the row n2. - See also: 1/ rowAdd 2/ mRow + See also: 1/ rowAdd 2/ mRow Ex1:mRowAdd(12,[[1,2],[3,4],[5,6]],0,2) - + ''' return GiacMethods['mRowAdd'](self,*args) @@ -10450,10 +10450,10 @@ cdef class GiacMethods_base: Help for magenta: magenta(Opt) Option of the display command to display with color. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),red) Ex2: F:=display(point(2+1.5*i),point_point+green) - + ''' return GiacMethods['magenta'](self,*args) @@ -10462,9 +10462,9 @@ cdef class GiacMethods_base: Help for make_directed: make_directed(Graph(G),[Mrtx(A)]) Returns the copy of undirected graph G in which every edge is converted to a pair of arcs [and with weights specified by matrix A]. - See also: 1/ is_directed 2/ make_weighted 3/ underlying_graph + See also: 1/ is_directed 2/ make_weighted 3/ underlying_graph Ex1:make_directed(cycle_graph(4),[[0,0,0,1],[2,0,1,3],[0,1,0,4],[5,0,4,0]]) - + ''' return GiacMethods['make_directed'](self,*args) @@ -10473,9 +10473,9 @@ cdef class GiacMethods_base: Help for make_weighted: make_weighted(Graph(G),[Mrtx(M)]) Returns a copy of G with edge/arc weights set as specified by matrix M. If M is omitted, a square matrix of ones is used. If G is undirected, M is assumed to be symmetric. - See also: 1/ get_edge_weight 2/ is_weighted 3/ make_directed 4/ set_edge_weight 5/ underlying_graph 6/ weight_matrix + See also: 1/ get_edge_weight 2/ is_weighted 3/ make_directed 4/ set_edge_weight 5/ underlying_graph 6/ weight_matrix Ex1:make_weighted(cycle_graph(3),[[0,2,3],[2,0,1],[3,1,0]]) - + ''' return GiacMethods['make_weighted'](self,*args) @@ -10484,12 +10484,12 @@ cdef class GiacMethods_base: Help for makelist: makelist(Fnc,InitVal,FinalVal,StepVal) Returns a list made with a function or with a constant. - See also: 1/ seq 2/ range 3/ makemat 4/ $ + See also: 1/ seq 2/ range 3/ makemat 4/ $ Ex1:makelist(x->x^2,1,10,2) Ex2:makelist(4,1,10) Ex3:makelist(4,5,10) Ex4:makelist(x->ifte(x<5,"A","B"),1,10) - + ''' return GiacMethods['makelist'](self,*args) @@ -10498,11 +10498,11 @@ cdef class GiacMethods_base: Help for makemat: makemat(Fnct(f),RowsNumb,ColsNumb) Creates a matrix. - See also: 1/ matrix + See also: 1/ matrix Ex1:makemat((j,k)->j+k,3,2) Ex2:makemat((j,k)->1/(j+k+1),2,3) Ex3:makemat(sqrt(2),2,3) - + ''' return GiacMethods['makemat'](self,*args) @@ -10511,9 +10511,9 @@ cdef class GiacMethods_base: Help for makesuite: makesuite(Vect||Lst) Returns a sequence made with a vector. - See also: 1/ makevector 2/ op + See also: 1/ makevector 2/ op Ex1:makesuite([1,2,3]) - + ''' return GiacMethods['makesuite'](self,*args) @@ -10522,9 +10522,9 @@ cdef class GiacMethods_base: Help for makevector: makevector(Seq) Returns a vector made with a sequence. - See also: 1/ makesuite + See also: 1/ makesuite Ex1:makevector(1,2,3) - + ''' return GiacMethods['makevector'](self,*args) @@ -10533,11 +10533,11 @@ cdef class GiacMethods_base: Help for map: map(Lst(l),Fnc(f)) Applies the function f at the elements of the list l or at a polynomial of internal format. - See also: 1/ apply 2/ set 3/ unapply + See also: 1/ apply 2/ set 3/ unapply Ex1:map([1,2,3],x->x^3) Ex2:map([1,2,3],unapply(x^3,x)) Ex3:map(%%%{1,[2,0]%%%}+%%%{2,[1,1]%%%},(a,b,c)->a*(b+2*c)) - + ''' return GiacMethods['map'](self,*args) @@ -10546,8 +10546,8 @@ cdef class GiacMethods_base: Help for maple2mupad: maple2mupad(Str("Name_Maplefile"),Str("Name_Mupadfile")) maple2mupad("file1","file2") translates file1(Maple) to file2(MuPAD). - See also: 1/ maple2xcas - + See also: 1/ maple2xcas + ''' return GiacMethods['maple2mupad'](self,*args) @@ -10556,8 +10556,8 @@ cdef class GiacMethods_base: Help for maple2xcas: maple2xcas(Str("NameMapleFile"),Str("NameXcasFile")) maple2xcas("file1","file2") translates file1(Maple) to file2(Xcas). - See also: 1/ maple2mupad - + See also: 1/ maple2mupad + ''' return GiacMethods['maple2xcas'](self,*args) @@ -10566,9 +10566,9 @@ cdef class GiacMethods_base: Help for maple_ifactors: maple_ifactors(Intg(n)) Returns 1 or -1 for the sign and the prime factors with their multiplicity of n in a matrix, such as ifactors in Maple. - See also: 1/ ifactors + See also: 1/ ifactors Ex1:maple_ifactors(120) - + ''' return GiacMethods['maple_ifactors'](self,*args) @@ -10577,10 +10577,10 @@ cdef class GiacMethods_base: Help for maple_mode: maple_mode(Intg(0) or 1 or 2 or 3) Switches to mode Xcas (0), Maple (1), Mupad (2), TI89 (3). - See also: 1/ python_compat + See also: 1/ python_compat Ex1:maple_mode(1) Ex2:maple_mode(0) - + ''' return GiacMethods['maple_mode'](self,*args) @@ -10589,9 +10589,9 @@ cdef class GiacMethods_base: Help for markov: markov(Mtrx(M),[Real(eps)]) Computation of the proper elements of a Markov chain transition matrix M, returns the list of sequence of positive recurrent states, the list of corresponding invariant probabilities, the list of other strongly connected components, the list of probabilities to end up in the sequence of recurrent states. - See also: 1/ randmarkov 2/ plotproba + See also: 1/ randmarkov 2/ plotproba Ex1:markov([[0,0,1/2,0,1/2],[0,0,1,0,0],[1/4,1/4,0,1/4,1/4],[0,0,1/2,0,1/2],[0,0,0,0,1]]) - + ''' return GiacMethods['markov'](self,*args) @@ -10600,9 +10600,9 @@ cdef class GiacMethods_base: Help for mat2list: mat2list(Mtrx) Returns the list of the terms of the matrix. - See also: 1/ list2mat 2/ flatten + See also: 1/ list2mat 2/ flatten Ex1:mat2list([[1,8],[4,9]]) - + ''' return GiacMethods['mat2list'](self,*args) @@ -10611,9 +10611,9 @@ cdef class GiacMethods_base: Help for mathml: mathml(Expr) Converts the expression into a string to display maths for the web. - See also: 1/ export_mathml 2/ latex + See also: 1/ export_mathml 2/ latex Ex1:mathml(1/2) - + ''' return GiacMethods['mathml'](self,*args) @@ -10622,9 +10622,9 @@ cdef class GiacMethods_base: Help for matpow: matpow(Mtrx,Intg(n)) Calculates the nth power of a matrix by jordanization. - See also: 1/ &^ 2/ ^ + See also: 1/ &^ 2/ ^ Ex1:matpow([[1,2],[3,4]],n) - + ''' return GiacMethods['matpow'](self,*args) @@ -10633,12 +10633,12 @@ cdef class GiacMethods_base: Help for matrix: matrix(Intg(p),Intg(q),(Fnc(f) or Val(a))) Makes a matrix m(j,k) with p rows and q cols, m(j,k)=f(j,k) or m(j,k)=a : the index start at 0 or 1 according to the mode (Xcas or Maple) (or option of apply) or make a matrix with a table. - See also: 1/ makemat 2/ makelist 3/ apply + See also: 1/ makemat 2/ makelist 3/ apply Ex1:matrix(2,3,(j,k)->1/(j+k+1)) Ex2:matrix(3,2,(j,k)->j+k) Ex3:matrix(2,3,4) - Ex4: A[0..2,0..2]:=1;A[0..1,1..2]:=2;a:=matrix(A) - + Ex4: A[0..2,0..2]:=1;A[0..1,1..2]:=2;a:=matrix(A) + ''' return GiacMethods['matrix'](self,*args) @@ -10647,12 +10647,12 @@ cdef class GiacMethods_base: Help for matrix_norm: matrix_norm(Mtrx,[2]||[inf]) Matrix norm induced by l1norm or by l2norm or by linfinty norm. - See also: 1/ l1norm 2/ l2 norm 3/ linfnorm 4/ frobenius_norm + See also: 1/ l1norm 2/ l2 norm 3/ linfnorm 4/ frobenius_norm Ex1:matrix_norm([[1,2,3],[3,-9,6],[4,5,6]]) Ex2:matrix_norm([[1,2,3],[3,-9,6],[4,5,6]],1) Ex3:matrix_norm([[1,2,3],[3,-9,6],[4,5,6]],2) Ex4:matrix_norm([[1,2,3],[3,-9,6],[4,5,6]],inf) - + ''' return GiacMethods['matrix_norm'](self,*args) @@ -10661,9 +10661,9 @@ cdef class GiacMethods_base: Help for max: max(Seq||Lst) Maximum of elements of a sequence or a list of reals. - See also: 1/ min + See also: 1/ min Ex1:max(25,35) - + ''' return GiacMethods['max'](self,*args) @@ -10672,9 +10672,9 @@ cdef class GiacMethods_base: Help for maxflow: maxflow(Graph(G),Vrtx(s),Vrtx(t)) Returns the optimal value for the max flow problem for network G with the source s and sink t along with an optimal flow (as a matrix). - See also: 1/ minimum_cut + See also: 1/ minimum_cut Ex1:maxflow(digraph(%{[[1,2],2],[[2,3],4],[[3,4],3],[[1,5],3],[[5,2],1],[[5,4],2]%}),1,4) - + ''' return GiacMethods['maxflow'](self,*args) @@ -10683,9 +10683,9 @@ cdef class GiacMethods_base: Help for maximal_independent_set: maximal_independent_set(Graph(G)) Returns a maximal set of mutually independent (non-adjacent) vertices in G. - See also: 1/ maximum_independent_set + See also: 1/ maximum_independent_set Ex1:maximal_independent_set(graph("petersen")) - + ''' return GiacMethods['maximal_independent_set'](self,*args) @@ -10702,7 +10702,7 @@ cdef class GiacMethods_base: Ex6:maximize(sqrt(x^2+y^2)-z,[x^2+y^2<=16,x+y+z=10],[x,y,z]) Ex7:maximize((1+x^2+3y+5x-4*x*y)/(1+x^2+y^2),x^2/4+y^2/3=9,[x,y]) Ex8:maximize(cos(x)^2+cos(y)^2,x+y=pi/4,[x,y],locus) - + ''' return GiacMethods['maximize'](self,*args) @@ -10711,9 +10711,9 @@ cdef class GiacMethods_base: Help for maximum_clique: maximum_clique(Graph(G)) Returns the maximum clique of undirected graph G as a list of vertices. - See also: 1/ clique_number 2/ is_clique 3/ maximum_independent_set + See also: 1/ clique_number 2/ is_clique 3/ maximum_independent_set Ex1:maximum_clique(graph_complement(complete_graph(3,4))) - + ''' return GiacMethods['maximum_clique'](self,*args) @@ -10722,9 +10722,9 @@ cdef class GiacMethods_base: Help for maximum_degree: maximum_degree(Graph(G)) Returns the largest degree among the vertices of G. - See also: 1/ minimum_degree 2/ vertex_degree + See also: 1/ minimum_degree 2/ vertex_degree Ex1:maximum_degree(digraph(trail(1,2,3,4,5,6,4,7,8,2))) - + ''' return GiacMethods['maximum_degree'](self,*args) @@ -10733,9 +10733,9 @@ cdef class GiacMethods_base: Help for maximum_independent_set: maximum_independent_set(Graph(G)) Returns the maximum independent vertex set of G. - See also: 1/ clique_number 2/ graph_complement 3/ independence_number 4/ maximum_clique + See also: 1/ clique_number 2/ graph_complement 3/ independence_number 4/ maximum_clique Ex1:maximum_independent_set(complete_graph(3,4)) - + ''' return GiacMethods['maximum_independent_set'](self,*args) @@ -10744,9 +10744,9 @@ cdef class GiacMethods_base: Help for maximum_matching: maximum_matching(Graph(G)) Returns the list of edges representing maximum matching in G. - See also: 1/ maximum_independent_set + See also: 1/ maximum_independent_set Ex1: G:=graph("soccerball"); draw_graph(highlight_edges(G,maximum_matching(G))) - + ''' return GiacMethods['maximum_matching'](self,*args) @@ -10755,11 +10755,11 @@ cdef class GiacMethods_base: Help for maxnorm: maxnorm(Vect or Mtrx) Norm with the max of a vector (or of a matrix): maxnorm([x1,x2,..,xn])=max(|x1|,..,|xn|). - See also: 1/ l2norm 2/ l1norm + See also: 1/ l2norm 2/ l1norm Ex1:maxnorm([1,2]) Ex2:maxnorm([1,2,3,-4]) Ex3:maxnorm([[1,2],[3,-4]]) - + ''' return GiacMethods['maxnorm'](self,*args) @@ -10768,11 +10768,11 @@ cdef class GiacMethods_base: Help for mean: mean(Lst||Mtrx,[Lst]) Mean of a list with the second argument as weight or of the columns of a matrix. - See also: 1/ stddev + See also: 1/ stddev Ex1:mean([1,2,3]) Ex2:mean([1,2,3],[1,2,3]) Ex3:mean([[1,2,3],[1,2,3]]) - + ''' return GiacMethods['mean'](self,*args) @@ -10781,10 +10781,10 @@ cdef class GiacMethods_base: Help for median: median(Lst||Mtrx,[Lst]) Returns the median of a list with the second argument as weight or of the columns of a matrix. - See also: 1/ quartiles + See also: 1/ quartiles Ex1:median([1,2,3,5,10,4]) Ex2:median([1,2,3,5,10,4],[1,2,3,1,2,3]) - + ''' return GiacMethods['median'](self,*args) @@ -10793,9 +10793,9 @@ cdef class GiacMethods_base: Help for median_line: median_line((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) median_line(A,B,C) draws the median-line through A of the triangle ABC. - See also: 1/ midpoint 2/ perpen_bisector + See also: 1/ midpoint 2/ perpen_bisector Ex1:median_line(-1,1-i,i) - + ''' return GiacMethods['median_line'](self,*args) @@ -10804,10 +10804,10 @@ cdef class GiacMethods_base: Help for member: member(Elem(e),(Lst(l) or Set(l))) Tests if e is in the list or set l (=0, or k+1 with l[k]=e). - See also: 1/ contains 2/ est_element 3/ find 4/ index + See also: 1/ contains 2/ est_element 3/ find 4/ index Ex1:member(1,[4,3,1,2]) Ex2:member(1,%{4,3,1,2%}) - + ''' return GiacMethods['member'](self,*args) @@ -10819,7 +10819,7 @@ cdef class GiacMethods_base: Ex1:mgf(normald,1,0) Ex2:mgf(poisson,5) Ex3:mgf(binomial,n,p) - + ''' return GiacMethods['mgf'](self,*args) @@ -10828,13 +10828,13 @@ cdef class GiacMethods_base: Help for mid: mid(Lst(l) or Str(l),Intg(d),Intg(n)) Returns the extracted list of l with n elements (by default n=size(l)-d) and beginning at index d. - See also: 1/ head 2/ tail 3/ left 4/ right 5/ subMat + See also: 1/ head 2/ tail 3/ left 4/ right 5/ subMat Ex1:mid([0,1,2,3,4,5,6],2,3) Ex2:mid([0,1,2,3,4,5,6],2) Ex3:mid("azertyuiop",2,4) Ex4:mid("azertyuiop",2) Ex5:mid([[1,2],[3,4],[5,6]],1) - + ''' return GiacMethods['mid'](self,*args) @@ -10843,14 +10843,14 @@ cdef class GiacMethods_base: Help for middle_point: middle_point(Opt) Option of the plotarea command and of the area command. - See also: 1/ plotarea 2/ area + See also: 1/ plotarea 2/ area Ex1: plotarea(x^2,x=0..1,5,trapezoid) Ex2: plotarea(x^2,x=0..1,5,middle_point) Ex3: plotarea(x^2,x=0..1,5,right_rectangle) Ex4: plotarea(x^2,x=0..1,5,left_rectangle) Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) - + ''' return GiacMethods['middle_point'](self,*args) @@ -10859,9 +10859,9 @@ cdef class GiacMethods_base: Help for midpoint: midpoint((Pnt or Cplx),(Pnt or Cplx)) midpoint(A,B) draws the midpoint of the segment AB. - See also: 1/ median_line 2/ perpen_bisector + See also: 1/ median_line 2/ perpen_bisector Ex1:midpoint(-2,2i) - + ''' return GiacMethods['midpoint'](self,*args) @@ -10870,9 +10870,9 @@ cdef class GiacMethods_base: Help for min: min(Seq||Lst) Minimum of elements of a sequence or a list of reals. - See also: 1/ max + See also: 1/ max Ex1:min(25,35) - + ''' return GiacMethods['min'](self,*args) @@ -10881,10 +10881,10 @@ cdef class GiacMethods_base: Help for minimal_edge_coloring: minimal_edge_coloring(Graph(G),[sto]) Finds the minimal edge coloring of G and returns the sequence n,L where n is the class of G (1 for D colors and 2 for D+1 colors) and L is the list of colors of edges of G as returned by the edges command, or a copy of G with colored edges if the option 'sto' is specified. - See also: 1/ chromatic_index 2/ minimal_vertex_coloring 3/ edges + See also: 1/ chromatic_index 2/ minimal_vertex_coloring 3/ edges Ex1:minimal_edge_coloring(graph("petersen")) Ex2: G:=minimal_edge_coloring(graph("dodecahedron"),sto); draw_graph(G) - + ''' return GiacMethods['minimal_edge_coloring'](self,*args) @@ -10893,9 +10893,9 @@ cdef class GiacMethods_base: Help for minimal_spanning_tree: minimal_spanning_tree(Graph(G)) Returns the minimal spanning tree of undirected graph G. - See also: 1/ spanning_tree + See also: 1/ spanning_tree Ex1:minimal_spanning_tree(graph([[0,1,0,4,0,0],[1,0,1,0,4,0],[0,1,0,3,0,1],[4,0,3,0,1,0],[0,4,0,1,0,4],[0,0,1,0,4,0]])) - + ''' return GiacMethods['minimal_spanning_tree'](self,*args) @@ -10904,10 +10904,10 @@ cdef class GiacMethods_base: Help for minimal_vertex_coloring: minimal_vertex_coloring(Graph(G),[sto]) Computes the minimal vertex coloring for G and returns the colors in the order of vertices. If optional parameter "sto" is given, the colors are assigned to vertices and the modified copy of G is returned. - See also: 1/ chromatic_number 2/ is_vertex_colorable + See also: 1/ chromatic_number 2/ is_vertex_colorable Ex1:minimal_vertex_coloring(graph("petersen")) Ex2: draw_graph(minimal_vertex_coloring(graph("petersen"),sto)) - + ''' return GiacMethods['minimal_vertex_coloring'](self,*args) @@ -10926,7 +10926,7 @@ cdef class GiacMethods_base: Ex8:minimax(abs(x)*sqrt(abs(x)),x=-2..2,15) Ex9:minimax(min(1/cosh(3*sin(x)),sin(9x/10)),x=-3..4,30) Ex10:minimax(when(x==0,0,exp(-1/x^2)),x=-1..1,25) - + ''' return GiacMethods['minimax'](self,*args) @@ -10943,7 +10943,7 @@ cdef class GiacMethods_base: Ex6:minimize(sqrt(x^2+y^2)-z,[x^2+y^2<=16,x+y+z=10],[x,y,z]) Ex7:minimize((1+x^2+3y+5x-4*x*y)/(1+x^2+y^2),x^2/4+y^2/3=9,[x,y]) Ex8:minimize(cos(x)^2+cos(y)^2,x+y=pi/4,[x,y],locus) - + ''' return GiacMethods['minimize'](self,*args) @@ -10952,9 +10952,9 @@ cdef class GiacMethods_base: Help for minimum_cut: minimum_cut(Graph(G),Vrtx(s),Vrtx(t)) Returns the list of edges forming a minimum cut in a directed graph G with the source s and sink t. - See also: 1/ maxflow + See also: 1/ maxflow Ex1:minimum_cut(digraph(%{[[1,2],2],[[2,3],4],[[3,4],3],[[1,5],3],[[5,2],1],[[5,4],2]%}),1,4) - + ''' return GiacMethods['minimum_cut'](self,*args) @@ -10963,9 +10963,9 @@ cdef class GiacMethods_base: Help for minimum_degree: minimum_degree(Graph(G)) Returns the smallest degree among the vertices of G. - See also: 1/ maximum_degree 2/ vertex_degree + See also: 1/ maximum_degree 2/ vertex_degree Ex1:minimum_degree(digraph(trail(1,2,3,4,5,6,4,7,8,2))) - + ''' return GiacMethods['minimum_degree'](self,*args) @@ -10974,11 +10974,11 @@ cdef class GiacMethods_base: Help for mkisom: mkisom(Vect,(Sign(1) or -1)) Matrix of an isometry given by its proper elements. - See also: 1/ isom + See also: 1/ isom Ex1:mkisom([1,2],1) Ex2:mkisom([[1,0,0],pi/3],-1) Ex3:mkisom(pi,1) - + ''' return GiacMethods['mkisom'](self,*args) @@ -10987,9 +10987,9 @@ cdef class GiacMethods_base: Help for mksa: mksa(Unit) Converts units to the MKSA international unit system. - See also: 1/ convert 2/ ufactor + See also: 1/ convert 2/ ufactor Ex1:mksa(1_N) - + ''' return GiacMethods['mksa'](self,*args) @@ -10998,9 +10998,9 @@ cdef class GiacMethods_base: Help for modgcd: modgcd(Poly,Poly) GCD of 2 polynomials, with the modular algorithm. - See also: 1/ gcd 2/ heugcd 3/ ezgcd 4/ psrgcd + See also: 1/ gcd 2/ heugcd 3/ ezgcd 4/ psrgcd Ex1:modgcd(x^4-1,(x-1)^2) - + ''' return GiacMethods['modgcd'](self,*args) @@ -11009,11 +11009,11 @@ cdef class GiacMethods_base: Help for mods: mods(Intg,Intg) Returns the Euclidean symmetric remainder of two integers. - See also: 1/ irem 2/ iquo 3/ mod 4/ fracmod + See also: 1/ irem 2/ iquo 3/ mod 4/ fracmod Ex1:mods(8,3) Ex2:mods(10,4) Ex3:mods(11,7) - + ''' return GiacMethods['mods'](self,*args) @@ -11023,7 +11023,7 @@ cdef class GiacMethods_base: monotonic() Returns a real that increases as time passes Ex1:monotonic() - + ''' return GiacMethods['monotonic'](self,*args) @@ -11032,9 +11032,9 @@ cdef class GiacMethods_base: Help for montre_tortue: montre_tortue(NULL) Shows the turtle. - See also: 1/ cache_tortue + See also: 1/ cache_tortue Ex1:montre_tortue() - + ''' return GiacMethods['montre_tortue'](self,*args) @@ -11043,12 +11043,12 @@ cdef class GiacMethods_base: Help for moustache: moustache(Lst,[Lst],[x=a..b||y=a..b]) Box and Whisker plot for a statistical series. - See also: 1/ quartiles + See also: 1/ quartiles Ex1:moustache([-1,1,2,2.2,3,4,-2,5]) Ex2:moustache([1,2,3,5,10,4],x=1..2) Ex3:moustache([1,2,3,5,10,4],[1,2,3,1,2,3]) Ex4:moustache([[6,0,1,3,4,2,5],[0,1,3,4,2,5,6],[1,3,4,2,5,6,0],[3,4,2,5,6,0,1],[4,2,5,6,0,1,3],[2,5,6,0,1,3,4]]) - + ''' return GiacMethods['moustache'](self,*args) @@ -11057,9 +11057,9 @@ cdef class GiacMethods_base: Help for moving_average: moving_average(Lst(A),Intg(n)) Applies a moving average filter of length n to a signal sample A, and returns its result as an array of length nops(A)-n+1. - See also: 1/ lowpass + See also: 1/ lowpass Ex1: snd:=soundsec(2):;data:=0.5*threshold(3*sin(2*pi*220*snd),[-1.0,1.0])+randvector(length(snd),normald,0,0.05):;moving_average(data,25) - + ''' return GiacMethods['moving_average'](self,*args) @@ -11068,9 +11068,9 @@ cdef class GiacMethods_base: Help for moyal: moyal(Expr,Expr,VectVar) Moyal product of 2 symbols. - See also: 1/ + See also: 1/ Ex1:moyal(x^2+y^4,x^4-y^2,[x,y],5) - + ''' return GiacMethods['moyal'](self,*args) @@ -11079,11 +11079,11 @@ cdef class GiacMethods_base: Help for moyenne: moyenne(Lst||Mtrx,[Lst]) Mean of a list with the second argument as weight or of the columns of a matrix. - See also: 1/ stddev + See also: 1/ stddev Ex1:moyenne([1,2,3]) Ex2:moyenne([1,2,3],[1,2,3]) Ex3:moyenne([[1,2,3],[1,2,3]]) - + ''' return GiacMethods['moyenne'](self,*args) @@ -11092,7 +11092,7 @@ cdef class GiacMethods_base: Help for mul: mul(Expr||Lst,[Var||Lst],[Intg(a)],[Intg(b)],[Intg(p)]) Multiplies the values of the expression when the variable go from a to b with a step p (product(expression,var,begin,end,step) by default p=1) or product of the elements of a list or product element by element of 2 lists or matrices. - See also: 1/ sum + See also: 1/ sum Ex1:mul(n,n,1,10,2) Ex2:mul(1/n,n,1,10) Ex3:mul(1/n,n,11,1) @@ -11100,7 +11100,7 @@ cdef class GiacMethods_base: Ex5:mul([2,3,4,5]) Ex6:mul([2,3,4],[5,6,7]) Ex7:mul([[2,3,4],[5,6,7]],[[2,3,4],[5,6,7]]) - + ''' return GiacMethods['mul'](self,*args) @@ -11109,10 +11109,10 @@ cdef class GiacMethods_base: Help for mult_c_conjugate: mult_c_conjugate(Expr) Returns the expression after multiplication by the complex conjugate of the denominator (or of the numerator if no denominator). - See also: 1/ mult_conjugate + See also: 1/ mult_conjugate Ex1:mult_c_conjugate(1/(3+i*2)) Ex2:mult_c_conjugate(3+i*2) - + ''' return GiacMethods['mult_c_conjugate'](self,*args) @@ -11121,10 +11121,10 @@ cdef class GiacMethods_base: Help for mult_conjugate: mult_conjugate(Expr) Returns the expression after multiplication by the conjugate of the denominator (or of the numerator if no denominator). - See also: 1/ mult_c_conjugate + See also: 1/ mult_c_conjugate Ex1:mult_conjugate(sqrt(3)-sqrt(2)) Ex2:mult_conjugate(1/(sqrt(3)-sqrt(2))) - + ''' return GiacMethods['mult_conjugate'](self,*args) @@ -11133,12 +11133,12 @@ cdef class GiacMethods_base: Help for multinomial: multinomial(Intg(n),Vect(p),Vect(k)) Returns n!/(k0!*k1!*..;kj!)*(p0^k0*p1^k1..*pj^kj) (sum(p)=1 and sum(k)=n). - See also: 1/ binomial 2/ randvector 3/ ranm + See also: 1/ binomial 2/ randvector 3/ ranm Ex1:multinomial(10,[0.5,0.5],[3,7]) Ex2:multinomial(10,[0.2,0.3,0.5],[1,3,6]) Ex3: randvector(3,multinomial,[1/2,1/3,1/6]) Ex4: ranm(4,3,multinomial,[1/2,1/3,1/6]) - + ''' return GiacMethods['multinomial'](self,*args) @@ -11147,10 +11147,10 @@ cdef class GiacMethods_base: Help for multiplier_conjugue: multiplier_conjugue(Expr) Returns the expression after multiplication by the conjugate of the denominator (or of the numerator if no denominator). - See also: 1/ mult_c_conjugate + See also: 1/ mult_c_conjugate Ex1:multiplier_conjugue(sqrt(3)-sqrt(2)) Ex2:multiplier_conjugue(1/(sqrt(3)-sqrt(2))) - + ''' return GiacMethods['multiplier_conjugue'](self,*args) @@ -11159,10 +11159,10 @@ cdef class GiacMethods_base: Help for multiplier_conjugue_complexe: multiplier_conjugue_complexe(Expr) Returns the expression after multiplication by the complex conjugate of the denominator (or of the numerator if no denominator). - See also: 1/ mult_conjugate + See also: 1/ mult_conjugate Ex1:multiplier_conjugue_complexe(1/(3+i*2)) Ex2:multiplier_conjugue_complexe(3+i*2) - + ''' return GiacMethods['multiplier_conjugue_complexe'](self,*args) @@ -11171,11 +11171,11 @@ cdef class GiacMethods_base: Help for multiply: multiply(Intg or Lst, Intg or Lst) Returns the product of the 2 arguments. - See also: 1/ * + See also: 1/ * Ex1:multiply(41,-4) Ex2:multiply([4,1],[-4,2]) Ex3:multiply([[4,1],[-4,1]],[[4,1],[-4,1]]) - + ''' return GiacMethods['multiply'](self,*args) @@ -11184,8 +11184,8 @@ cdef class GiacMethods_base: Help for mupad2maple: mupad2maple(Str("NameMupadFile"),Str("NameMapleFile")) mupad2maple("file1","file2") translates file1(MuPAD) to file2(Maple). - See also: 1/ mupad2xcas - + See also: 1/ mupad2xcas + ''' return GiacMethods['mupad2maple'](self,*args) @@ -11194,8 +11194,8 @@ cdef class GiacMethods_base: Help for mupad2xcas: mupad2xcas(Str("NameMupadFile"),Str("NameXcasFile")) mupad2xcas("file1","file2") translates file1(MuPAD) to file2(Xcas). - See also: 1/ mupad2maple - + See also: 1/ mupad2maple + ''' return GiacMethods['mupad2xcas'](self,*args) @@ -11204,10 +11204,10 @@ cdef class GiacMethods_base: Help for mycielski: mycielski(Graph(G)) Returns the Mycielskian of undirected graph G. - See also: 1/ chromatic_number 2/ number_of_triangles + See also: 1/ chromatic_number 2/ number_of_triangles Ex1:mycielski(graph("petersen")) Ex2: is_isomorphic(mycielski(mycielski(path_graph(2))),graph("grotzsch")) - + ''' return GiacMethods['mycielski'](self,*args) @@ -11216,9 +11216,9 @@ cdef class GiacMethods_base: Help for nCr: nCr(Intg(n),Intg(r)) comb(n,r)=number of combinations of r objects taken among n : n!/(r!(n-r)!) (If n<0 comb(n,r)=n(n-1)..(n-r+1)/r!). - See also: 1/ factorial 2/ perm + See also: 1/ factorial 2/ perm Ex1:nCr(4,2) - + ''' return GiacMethods['nCr'](self,*args) @@ -11227,11 +11227,11 @@ cdef class GiacMethods_base: Help for nDeriv: nDeriv(Expr(Xpr),Var(Var),[Real(h)]) Returns an approximation of the derivative number at a point: (Xpr(var+h)-Xpr(var-h))/(2*h) (by default h=0.001). - See also: 1/ avgRC + See also: 1/ avgRC Ex1:nDeriv(f(x),x,h) Ex2:nDeriv(x^2,x,0.1) Ex3:nDeriv(x^2,x) - + ''' return GiacMethods['nDeriv'](self,*args) @@ -11240,11 +11240,11 @@ cdef class GiacMethods_base: Help for nInt: nInt(Expr(f(x)),Var(x),Real(a),Real(b)) Returns the approximate value of integrate(f(x),x,a,b) by Romberg's method. - See also: 1/ integrate 2/ gaussquad + See also: 1/ integrate 2/ gaussquad Ex1:nInt(exp(x^2),x,0,1) Ex2:nInt(x^2,x,0,1) Ex3:nInt(exp(-x^2),x,-1,1) - + ''' return GiacMethods['nInt'](self,*args) @@ -11253,9 +11253,9 @@ cdef class GiacMethods_base: Help for nPr: nPr(Intg(n),Intg(p)) perm(n,p)=number of arrangements of p objects taken among n : n!/(n-p)! - See also: 1/ comb 2/ factorial + See also: 1/ comb 2/ factorial Ex1:nPr(4,2) - + ''' return GiacMethods['nPr'](self,*args) @@ -11264,10 +11264,10 @@ cdef class GiacMethods_base: Help for nSolve: nSolve(Expr,Var,[Guess or Interval],[Method]) Numerical solution of an equation or a system of equations. - See also: 1/ solve 2/ fsolve 3/ csolve + See also: 1/ solve 2/ fsolve 3/ csolve Ex1:nSolve(cos(x)=x,x) Ex2:nSolve(cos(x)=x,x=1.3) - + ''' return GiacMethods['nSolve'](self,*args) @@ -11276,10 +11276,10 @@ cdef class GiacMethods_base: Help for ncols: ncols(Mtrx) Number of columns of a matrix. - See also: 1/ rowdim + See also: 1/ rowdim Ex1:ncols([[1,2,3],[4,5,6]]) Ex2:ncols([[1,2],[3,4],[5,6]]) - + ''' return GiacMethods['ncols'](self,*args) @@ -11288,11 +11288,11 @@ cdef class GiacMethods_base: Help for negbinomial: negbinomial(Intg(n),Intg(k),Real(p in 0..1)) Returns comb(n+k-1,k)*p^k*(1-p)^n. - See also: 1/ negbinomial_cdf 2/ negbinomial_icdf 3/ binomial + See also: 1/ negbinomial_cdf 2/ negbinomial_icdf 3/ binomial Ex1:negbinomial(4,0,0.5) Ex2:negbinomial(4,2,0.6) Ex3:negbinomial(4,6,0.3) - + ''' return GiacMethods['negbinomial'](self,*args) @@ -11301,11 +11301,11 @@ cdef class GiacMethods_base: Help for negbinomial_cdf: negbinomial_cdf(Intg(n),Real(p),Real(x),[Real(y)]) Returns Proba(X<=x) or Proba(x<=X<=y) when X follows the negbinomial(n,p) law. - See also: 1/ negbinomial 2/ negbinomial_icdf + See also: 1/ negbinomial 2/ negbinomial_icdf Ex1:negbinomial_cdf(4,0.5,2) Ex2:negbinomial_cdf(4,0.1,2) Ex3:negbinomial_cdf(4,0.5,2,3) - + ''' return GiacMethods['negbinomial_cdf'](self,*args) @@ -11314,10 +11314,10 @@ cdef class GiacMethods_base: Help for negbinomial_icdf: negbinomial_icdf(Intg(n),Real(p),Real(t)) Returns h such as Proba(X<=h)=t when X follows the negbinomial(n,p) law. - See also: 1/ negbinomial 2/ negbinomial_cdf + See also: 1/ negbinomial 2/ negbinomial_cdf Ex1:negbinomial_icdf(4,0.5,0.68) Ex2:negbinomial_icdf(4,0.1,0.95) - + ''' return GiacMethods['negbinomial_icdf'](self,*args) @@ -11326,9 +11326,9 @@ cdef class GiacMethods_base: Help for neighbors: neighbors(Graph(G),[Vrtx(v)]) Returns the list of vertices adjacent to vertex v of G. If v is omitted, a list of adjacency lists of all vertices in G is returned. - See also: 1/ adjacency_matrix 2/ vertex_degree 3/ in_degree 3/ out_degree + See also: 1/ adjacency_matrix 2/ vertex_degree 3/ in_degree 3/ out_degree Ex1:neighbors(digraph(trail(1,2,3,4,5,6,4,7,8,2)),4) - + ''' return GiacMethods['neighbors'](self,*args) @@ -11337,9 +11337,9 @@ cdef class GiacMethods_base: Help for network_transitivity: network_transitivity(Graph(G)) Returns the transitivity (also called triangle density or global clustering coefficient) of G. - See also: 1/ clustering_coefficient 2/ number_of_triangles + See also: 1/ clustering_coefficient 2/ number_of_triangles Ex1:network_transitivity(graph(%{[1,2],[2,3],[2,4],[3,4],[4,1]%})) - + ''' return GiacMethods['network_transitivity'](self,*args) @@ -11348,9 +11348,9 @@ cdef class GiacMethods_base: Help for newList: newList(Intg(n)) Returns the list made with n zeros. - See also: 1/ newMat 2/ makelist + See also: 1/ newMat 2/ makelist Ex1:newList(4) - + ''' return GiacMethods['newList'](self,*args) @@ -11359,9 +11359,9 @@ cdef class GiacMethods_base: Help for newMat: newMat(Intg(n),Intg(p)) Returns the list with n rows and p columns, made with zeros. - See also: 1/ newList 2/ makemat + See also: 1/ newList 2/ makemat Ex1:newMat(2,3) - + ''' return GiacMethods['newMat'](self,*args) @@ -11370,12 +11370,12 @@ cdef class GiacMethods_base: Help for newton: newton(Expr(f(x)),Var(x),[ApproxVal(a),NumIter(p)]) newton(f(x),x,a,p)=one root of f(x) by Newton method beginning with a and p iterations (by default p=20). - See also: 1/ rootof + See also: 1/ rootof Ex1:newton(x^2-2,x) Ex2:newton(x^2-2,x,2) Ex3:newton(x^2-2,x,-2) Ex4:newton(x^2-2,x,2,5,1e-7) - + ''' return GiacMethods['newton'](self,*args) @@ -11384,14 +11384,14 @@ cdef class GiacMethods_base: Help for newton_solver: newton_solver(Opt) Argument for fsolve giving the method for solving a numerical equation. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve(cos(x)=x,x,0..1,bisection_solver) Ex2: fsolve(cos(x)=x,x,0..1,brent_solver) Ex3: fsolve(cos(x)=x,x,0..1,falsepos_solver) Ex4: fsolve(cos(x)=x,x,0,newton_solver) Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) - + ''' return GiacMethods['newton_solver'](self,*args) @@ -11400,14 +11400,14 @@ cdef class GiacMethods_base: Help for newtonj_solver: newtonj_solver(Opt) Argument for fsolve giving the method for solving a system of numerical equations. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],dnewton_solver) Ex2: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrid_solver) Ex3: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybrids_solver) Ex4: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridj_solver) Ex5: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],hybridsj_solver) Ex6: fsolve([x^2+y-2,x+y^2-2],[x,y],[2,2],newtonj_solver) - + ''' return GiacMethods['newtonj_solver'](self,*args) @@ -11416,10 +11416,10 @@ cdef class GiacMethods_base: Help for nextperm: nextperm(Intg(n)) Returns the next permutation with the lexicographic order. - See also: 1/ prevperm 2/ is_permu + See also: 1/ prevperm 2/ is_permu Ex1:nextperm([0,2,1,3]) Ex2:nextperm([0,3,2,1]) - + ''' return GiacMethods['nextperm'](self,*args) @@ -11428,10 +11428,10 @@ cdef class GiacMethods_base: Help for nextprime: nextprime(Intg(a)) Next prime or pseudo-prime after a given integer. - See also: 1/ prevprime 2/ is_prime 3/ ithprime + See also: 1/ prevprime 2/ is_prime 3/ ithprime Ex1:nextprime(9856989898990) Ex2:nextprime(97160249868928888261606009) - + ''' return GiacMethods['nextprime'](self,*args) @@ -11440,7 +11440,7 @@ cdef class GiacMethods_base: Help for nlpsolve: nlpsolve(objective, [constr], [bd], [opts]) Solves a nonlinear programming problem of optimizing the objective obj under constraints constr (list of equations and/or inequations) and within bounds bd (sequence of x=a..b) with optional options (for example setting an initial point). - See also: 1/ lpsolve 2/ fsolve 3/ fMin 4/ fMax + See also: 1/ lpsolve 2/ fsolve 3/ fMin 4/ fMax Ex1:nlpsolve((x1-10)^3+(x2-20)^3,[(x1-5)^2+(x2-5)^2>=100,(x2-5)^2+(x1-6)^2<=82.81],nlp_initialpoint=[x1=20.1,x2=5.84]) Ex2:nlpsolve(sin(x1+x2)+(x1-x2)^2-1.5x1+2.5x2+1,x1=-1.5..4,x2=-3..3) Ex3:nlpsolve(ln(1+x1^2)-x2,[(1+x1^2)^2+x2^2=4]) @@ -11448,10 +11448,10 @@ cdef class GiacMethods_base: Ex5:nlpsolve(-x1*x2*x3,[72-x1-2x2-2x3>=0],x1=0..20,x2=0..11,x3=0..42) Ex6:nlpsolve(2-1/120*x1*x2*x3*x4*x5,[x1<=1,x2<=2,x3<=3,x4<=4,x5<=5],assume=nlp_nonnegative) Ex7:nlpsolve(sin(x)/x,x=1..30) - Ex8:nlpsolve(x^3+2x*y-2y^2,x=-10..10,y=-10..10,nlp_initialpoint=[x=3,y=4],maximize) + Ex8:nlpsolve(x^3+2x*y-2y^2,x=-10..10,y=-10..10,nlp_initialpoint=[x=3,y=4],maximize) Ex9:nlpsolve(w^3*(v-w)^2+(w-x-1)^2+(x-y-2)^2+(y-z-3)^2,[w+x+y+z<=5,3z+2v=3],assume=nlp_nonnegative) Ex10:nlpsolve(sin(x)*Psi(x),x=1..20,nlp_initialpoint=[x=16]) - + ''' return GiacMethods['nlpsolve'](self,*args) @@ -11461,7 +11461,7 @@ cdef class GiacMethods_base: nodisp(Expr) Displays Done in place of a value. Ex1:nodisp(A:=ranm(50,50)) - + ''' return GiacMethods['nodisp'](self,*args) @@ -11470,10 +11470,10 @@ cdef class GiacMethods_base: Help for non_recursive_normal: non_recursive_normal(Expr) Simplifies the expressions, but without simplification inside of non-rational expressions. - See also: 1/ normal + See also: 1/ normal Ex1:non_recursive_normal(sin(x+x)+sin(2*x)+x+x) Ex2:non_recursive_normal(sin(2*x)+sin(2*x)+x+x) - + ''' return GiacMethods['non_recursive_normal'](self,*args) @@ -11482,9 +11482,9 @@ cdef class GiacMethods_base: Help for nop: nop(NULL) No OPeration instruction. - See also: 1/ + See also: 1/ Ex1:nop() - + ''' return GiacMethods['nop'](self,*args) @@ -11493,11 +11493,11 @@ cdef class GiacMethods_base: Help for nops: nops(Lst or Str or Seq) Returns the size of a list, a string or a sequence. - See also: 1/ sizes 2/ dim 3/ degree + See also: 1/ sizes 2/ dim 3/ degree Ex1:nops([1,2,3]) Ex2:nops("bonjour") Ex3:nops(1,2,3) - + ''' return GiacMethods['nops'](self,*args) @@ -11506,12 +11506,12 @@ cdef class GiacMethods_base: Help for norm: norm(Vect or Mtrx) Returns the l2 norm of a vector = sqrt(x1^2+x2^2+...xn^2) or matrix norm induced by l2 norm. - See also: 1/ maxnorm 2/ l1norm + See also: 1/ maxnorm 2/ l1norm Ex1:norm([1,2]) Ex2:norm([1,2,3,-4]) Ex3:norm([[1,2],[3,-4]]) Ex4:norm([[1,2,3],[3,-9,6],[4,5,6]]) - + ''' return GiacMethods['norm'](self,*args) @@ -11520,11 +11520,11 @@ cdef class GiacMethods_base: Help for normal: normal(Expr) Simplifies the expression. - See also: 1/ simplify + See also: 1/ simplify Ex1:normal(2*x+y=1) Ex2:normal(2*x*2) Ex3:normal((2*x+1)^2) - + ''' return GiacMethods['normal'](self,*args) @@ -11533,11 +11533,11 @@ cdef class GiacMethods_base: Help for normal_cdf: normal_cdf(Real(mu),Real(sigma),Real(x0),[Real(y0)]) Returns the probability that a Normal random variable is less than x0 or between x0 and y0 (mu is the mean and sigma the standard deviation). - See also: 1/ UTPN 2/ normal_icdf 3/ normald + See also: 1/ UTPN 2/ normal_icdf 3/ normald Ex1:normal_cdf(1.96) Ex2:normal_cdf(1,2,2.96*sqrt(2)) Ex3:normal_cdf(1,2,1.4*sqrt(2),2.96*sqrt(2)) - + ''' return GiacMethods['normal_cdf'](self,*args) @@ -11546,10 +11546,10 @@ cdef class GiacMethods_base: Help for normal_icdf: normal_icdf(Real(mu),Real(sigma),Real(p)) Returns h such as the probability that a Normal random variable is less than h is p (mu is the mean and sigma the standard deviation and 0<=p<=1). - See also: 1/ normal_cdf 2/ normald + See also: 1/ normal_cdf 2/ normald Ex1:normal_icdf(0.95) Ex2:normal_icdf(1,2,0.95) - + ''' return GiacMethods['normal_icdf'](self,*args) @@ -11558,12 +11558,12 @@ cdef class GiacMethods_base: Help for normald: normald(Real(mu),Real(sigma),Real(x0)) Returns the probability density of the Normal law (mu is the mean and sigma the standard deviation). - See also: 1/ normal_cdf 2/ normal_icdf 3/ randvector 4/ ranm + See also: 1/ normal_cdf 2/ normal_icdf 3/ randvector 4/ ranm Ex1:normald(1) Ex2:normald(1,2,3.5) Ex3: randvector(3,normald,1,0.5) Ex4: ranm(4,3,normald,1,0.5) - + ''' return GiacMethods['normald'](self,*args) @@ -11572,11 +11572,11 @@ cdef class GiacMethods_base: Help for normald_cdf: normald_cdf(Real(mu),Real(sigma),Real(x0),[Real(y0)]) Returns the probability that a Normal random variable is less than x0 or between x0 and y0 (mu is the mean and sigma the standard deviation). - See also: 1/ UTPN 2/ normal_icdf 3/ normald + See also: 1/ UTPN 2/ normal_icdf 3/ normald Ex1:normald_cdf(1.96) Ex2:normald_cdf(1,2,2.96*sqrt(2)) Ex3:normald_cdf(1,2,1.4*sqrt(2),2.96*sqrt(2)) - + ''' return GiacMethods['normald_cdf'](self,*args) @@ -11585,10 +11585,10 @@ cdef class GiacMethods_base: Help for normald_icdf: normald_icdf(Real(mu),Real(sigma),Real(p)) Returns h such as the probability that a Normal random variable is less than h is p (mu is the mean and sigma the standard deviation and 0<=p<=1). - See also: 1/ normal_cdf 2/ normald + See also: 1/ normal_cdf 2/ normald Ex1:normald_icdf(0.95) Ex2:normald_icdf(1,2,0.95) - + ''' return GiacMethods['normald_icdf'](self,*args) @@ -11597,12 +11597,12 @@ cdef class GiacMethods_base: Help for normalize: normalize(Lst||Cplx) Returns the vector divided by its l2norm. It is also an option for plotfield. - See also: 1/ l2norm + See also: 1/ l2norm Ex1:normalize(3+4*i) Ex2:normalize([3,4]) Ex3: fieldplot(-t*y,[t,y],normalize) Ex4: fieldplot(-t*y,[t,y],normalize,xstep=0.5,ystep=0.5) - + ''' return GiacMethods['normalize'](self,*args) @@ -11611,10 +11611,10 @@ cdef class GiacMethods_base: Help for normalt: normalt(Lst,Real,[Real],Fnc,[Real]) Z-Test/normal law: arg1=[success,trial] or [mean,sample size] or data, arg2=proportion or data, arg3 optional if data=sigma, arg4 alternative '!=' or '>' or '<', arg5 optional alpha confidence level. - See also: 1/ studentt 2/ chisquaret 3/ kolmogorovt + See also: 1/ studentt 2/ chisquaret 3/ kolmogorovt Ex1:normalt([10,30],.5,.02,'!=',0.1) Ex2:normalt([0.48,50],0.5,0.1,'<') - + ''' return GiacMethods['normalt'](self,*args) @@ -11623,10 +11623,10 @@ cdef class GiacMethods_base: Help for normalvariate: normalvariate(Real(mu),Real(sigma)) Returns a random real with normal distribution N(mu,sigma). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randpoisson 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randpoisson 8/ randgeometric 9/ randmultinomial Ex1:normalvariate(0,1) Ex2:normalvariate(2,1) - + ''' return GiacMethods['normalvariate'](self,*args) @@ -11635,9 +11635,9 @@ cdef class GiacMethods_base: Help for nprimes: nprimes(Intg(n)) Counts the number of primes less than n. - See also: 1/ ithprime 2/ prevprime 3/ nextprime 4/ isprime + See also: 1/ ithprime 2/ prevprime 3/ nextprime 4/ isprime Ex1:nprimes(20) - + ''' return GiacMethods['nprimes'](self,*args) @@ -11646,10 +11646,10 @@ cdef class GiacMethods_base: Help for nrows: nrows(Mtrx) Number of rows of a matrix. - See also: 1/ ncols + See also: 1/ ncols Ex1:nrows([[1,2,3],[4,5,6]]) Ex2:nrows([[1,2],[3,4],[5,6]]) - + ''' return GiacMethods['nrows'](self,*args) @@ -11658,9 +11658,9 @@ cdef class GiacMethods_base: Help for nuage_points: nuage_points(Mtrx) Draws for k=0..nrows, the points (xk,yk) where xk=element row k column 0 and yk=element row k column j (j=1..ncols). - See also: 1/ polygonplot 2/ polygonscatterplot 3/ listplot + See also: 1/ polygonplot 2/ polygonscatterplot 3/ listplot Ex1:nuage_points([[1,2,3],[2,0,1],[-1,2,3]]) - + ''' return GiacMethods['nuage_points'](self,*args) @@ -11669,10 +11669,10 @@ cdef class GiacMethods_base: Help for nullspace: nullspace(Mtrx) Kernel of a linear map with matrix M. - See also: 1/ image 2/ rref 3/ Nullspace + See also: 1/ image 2/ rref 3/ Nullspace Ex1:nullspace([[1,2],[3,6]]) Ex2:nullspace([[1,2,3],[1,3,6],[2,5,9]]) - + ''' return GiacMethods['nullspace'](self,*args) @@ -11681,9 +11681,9 @@ cdef class GiacMethods_base: Help for number_of_edges: number_of_edges(Graph(G)) Returns the number of edges/arcs of G. - See also: 1/ edges 2/ number_of_vertices + See also: 1/ edges 2/ number_of_vertices Ex1:number_of_edges(complete_graph(5)) - + ''' return GiacMethods['number_of_edges'](self,*args) @@ -11692,10 +11692,10 @@ cdef class GiacMethods_base: Help for number_of_spanning_trees: number_of_spanning_trees(Graph(G)) Returns the number of spanning trees in undirected graph G. - See also: 1/ spanning_tree + See also: 1/ spanning_tree Ex1:number_of_spanning_trees(complete_graph(4)) Ex2:number_of_spanning_trees(graph(trail(1,2,3,4,1,3))) - + ''' return GiacMethods['number_of_spanning_trees'](self,*args) @@ -11704,9 +11704,9 @@ cdef class GiacMethods_base: Help for number_of_triangles: number_of_triangles(Graph(G)) Returns the number of 3-cliques if G is undirected resp. the number of directed cycles on 3 vertices if G is directed. - See also: 1/ is_clique 2/ maximal_clique + See also: 1/ is_clique 2/ maximal_clique Ex1:number_of_triangles(graph("tetrahedron")) - + ''' return GiacMethods['number_of_triangles'](self,*args) @@ -11715,9 +11715,9 @@ cdef class GiacMethods_base: Help for number_of_vertices: number_of_vertices(Graph(G)) Returns the number of vertices of G. - See also: 1/ graph_vertices 2/ number_of_edges + See also: 1/ graph_vertices 2/ number_of_edges Ex1:number_of_vertices(graph("petersen")) - + ''' return GiacMethods['number_of_vertices'](self,*args) @@ -11726,11 +11726,11 @@ cdef class GiacMethods_base: Help for numer: numer(Frac(a/b) or RatFrac) Returns the numerator of the simplified fraction. - See also: 1/ getNum 2/ getDenom 3/ denom 4/ f2nd + See also: 1/ getNum 2/ getDenom 3/ denom 4/ f2nd Ex1:numer(25/15) Ex2:numer((x^3-1)/(x^2-1)) Ex3:numer(1+(x^3-1)/x^2) - + ''' return GiacMethods['numer'](self,*args) @@ -11739,10 +11739,10 @@ cdef class GiacMethods_base: Help for octahedron: octahedron(Pnt(A),Pnt(B),Pnt(C)) Draws an octahedron with center A, vertex B and such that the plane ABC contains 4 vertices. - See also: 1/ icosahedron 2/ dodecahedron 3/ cube 4/ tetrahedron + See also: 1/ icosahedron 2/ dodecahedron 3/ cube 4/ tetrahedron Ex1:octahedron([0,0,0],[0,0,5],[0,5,0]) Ex2:octahedron(evalf([0,0,0],[3,2,4],[1,1,0])) - + ''' return GiacMethods['octahedron'](self,*args) @@ -11751,10 +11751,10 @@ cdef class GiacMethods_base: Help for odd: odd(Intg(n)) Returns 1 if the integer is odd, else returns 0. - See also: 1/ even + See also: 1/ even Ex1:odd(6) Ex2:odd(1251) - + ''' return GiacMethods['odd'](self,*args) @@ -11763,10 +11763,10 @@ cdef class GiacMethods_base: Help for odd_girth: odd_girth(Graph(G)) Returns the length of the shortest odd cycle in the undirected unweighted graph G. - See also: 1/ girth + See also: 1/ girth Ex1:odd_girth(graph("petersen")) Ex2:odd_girth(hypercube_graph(3)) - + ''' return GiacMethods['odd_girth'](self,*args) @@ -11775,9 +11775,9 @@ cdef class GiacMethods_base: Help for odd_graph: odd_graph(Intg(n)) Returns the odd graph of order n as Kneser graph K(2n-1,n-1), where n<=8. - See also: 1/ kneser_graph + See also: 1/ kneser_graph Ex1:odd_graph(3) - + ''' return GiacMethods['odd_graph'](self,*args) @@ -11786,7 +11786,7 @@ cdef class GiacMethods_base: Help for odeplot: odeplot(Expr,VectVar,VectInitCond) odeplot(f(t,y),[t,y],[t0,y0]) draws the solution of y'=f(t,y) and y(t0)=y0 or of the system [x'=g(t,x,y),y'=h(t,x,y)] with x(t0)=x0 and y(t0)=y0. - See also: 1/ interactive_plotode 2/ fieldplot 3/ odesolve 4/ desolve + See also: 1/ interactive_plotode 2/ fieldplot 3/ odesolve 4/ desolve Ex1:odeplot(sin(t*y),[t,y],[0,1]) Ex2:odeplot(sin(t*y),[t=-10..10,y],[0,1]) Ex3:odeplot(sin(t*y),[t=-3..3,y],[0,1],tstep=0.1,color=vert) @@ -11794,7 +11794,7 @@ cdef class GiacMethods_base: Ex5:odeplot([x-0.3*x*y, 0.3*x*y-y], [t,x,y],[0,0.3,0.7],plan) Ex6:odeplot([-y+b,-1+(x-a)^2+(y-b)^2],[t=-3..3,x,y],[0,a+1,b+0.5],plan) Ex7:odeplot(5*[-y,x],[t=0..1,x,y],[0,0.3,0.7],tstep=0.05,plan) - + ''' return GiacMethods['odeplot'](self,*args) @@ -11803,13 +11803,13 @@ cdef class GiacMethods_base: Help for odesolve: odesolve(Expr,VectVar,VectInitCond,FinalVal,[tstep=Val,curve]) odesolve(f(t,y),[t,y],[t0,y0],t1)=odesolve(t0..t1,f,y0)=y(t1) for y approx sol of y'=f(t,y) and y(t0)=y0 with y=vector for systems. - See also: 1/ plotode 2/ plotfield 3/ interactive_plotode 4/ desolve + See also: 1/ plotode 2/ plotfield 3/ interactive_plotode 4/ desolve Ex1:odesolve(sin(t*y),[t,y],[0,1],2) Ex2:odesolve(0..2,(t,y)->sin(t*y),1) Ex3:odesolve(0..pi,(t,v)->{[-v[1],v[0]]},[0,1]) Ex4:odesolve(sin(t*y),t=0..2,y,1,tstep=0.5) Ex5:odesolve(sin(t*y),t=0..2,y,1,tstep=0.5,curve) - + ''' return GiacMethods['odesolve'](self,*args) @@ -11818,13 +11818,13 @@ cdef class GiacMethods_base: Help for op: op(Op or Fnc) Returns the arguments of an operator as a sequence. - See also: 1/ sommet 2/ quote 3/ makesuite + See also: 1/ sommet 2/ quote 3/ makesuite Ex1:op(quote(gcd(45,126))) Ex2:op('gcd(45,126)') Ex3:op('1+2')[1] Ex4:op([1,2,3]) Ex5:op(set[1,2,3]) - + ''' return GiacMethods['op'](self,*args) @@ -11833,10 +11833,10 @@ cdef class GiacMethods_base: Help for open_polygon: open_polygon(LstPnt||LstCplx) Returns and draws the polygonal line where its vertices are the element of l. - See also: 1/ isopolygon 2/ quadrilateral + See also: 1/ isopolygon 2/ quadrilateral Ex1:open_polygon(i,1+i,2-i,-1,-1+i/2) Ex2:open_polygon(point(0,0,0),point(3,3,3),point(0,0,3),point(3,0,0)) - + ''' return GiacMethods['open_polygon'](self,*args) @@ -11845,11 +11845,11 @@ cdef class GiacMethods_base: Help for ord: ord(Char||LstChar) Returns the ASCII code of a character or of the first character of a string. - See also: 1/ asc 2/ char + See also: 1/ asc 2/ char Ex1:ord("A") Ex2:ord("ABC") Ex3:ord(["a","b","c"]) - + ''' return GiacMethods['ord'](self,*args) @@ -11860,7 +11860,7 @@ cdef class GiacMethods_base: Returns element order of g in (Z/nZ)^* or in a finite field. Ex1:order(3 % 7) Ex2: GF(3,5,g); order(g^2+g+1); - + ''' return GiacMethods['order'](self,*args) @@ -11869,10 +11869,10 @@ cdef class GiacMethods_base: Help for order_size: order_size(Expr) Remainder (O term) of a series expansion: limit(x^a*order_size(x),x=0)=0 if a>0. - See also: 1/ series + See also: 1/ series Ex1:order_size(x) Ex2: limit(sqrt(x)*order_size(x),x=0) - + ''' return GiacMethods['order_size'](self,*args) @@ -11881,12 +11881,12 @@ cdef class GiacMethods_base: Help for ordinate: ordinate(Pnt or Vect) Returns the ordinate of a point or a vector. - See also: 1/ abscissa 2/ affix 3/ cote 4/ coordinates + See also: 1/ abscissa 2/ affix 3/ cote 4/ coordinates Ex1:ordinate(point(1+2*i)) Ex2:ordinate(point(i)-point(1+2*i)) Ex3:ordinate(-1-i) Ex4:ordinate(point(1,2,3)) - + ''' return GiacMethods['ordinate'](self,*args) @@ -11895,11 +11895,11 @@ cdef class GiacMethods_base: Help for orthocenter: orthocenter((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) Shows the orthocenter of a triangle or of the triangle made with 3 points. - See also: 1/ altitude 2/ triangle + See also: 1/ altitude 2/ triangle Ex1:orthocenter(1+i,2,i) Ex2:orthocenter(point(1+i),point(2),point(i)) Ex3:orthocenter(triangle(0,1,1+i)) - + ''' return GiacMethods['orthocenter'](self,*args) @@ -11908,10 +11908,10 @@ cdef class GiacMethods_base: Help for orthogonal: orthogonal((Pnt),(Line or Plan)) orthogonal(A,line(B,C)) draws the orthogonal plane of line BC through A and orthogonal(A,plane(B,C,D)) draws the orthogonal line of plane(B,C,D) through A. - See also: 1/ altitude 2/ perpendicular + See also: 1/ altitude 2/ perpendicular Ex1:orthogonal(point(0,0,0),line(point(1,0,0),point(0,1,0))) Ex2:orthogonal(point(0,0,0),plane(point(1,0,0),point(0,1,0),point(0,0,1))) - + ''' return GiacMethods['orthogonal'](self,*args) @@ -11920,14 +11920,14 @@ cdef class GiacMethods_base: Help for osculating_circle: osculating_circle(Curve,Point) Osculating circle at point M to the curve C. - See also: 1/ curvature 2/ evolute + See also: 1/ curvature 2/ evolute Ex1:osculating_circle(plot(x^2),point(1,1)) Ex2:osculating_circle([5*cos(t),5*sin(t)],t,0) Ex3:osculating_circle([t,t^2],t) Ex4:osculating_circle([t,t^2],t,1) Ex5:osculating_circle([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t) Ex6:osculating_circle([3*exp(t/2)*cos(t),3*exp(t/2)*sin(t)],t,7) - + ''' return GiacMethods['osculating_circle'](self,*args) @@ -11936,9 +11936,9 @@ cdef class GiacMethods_base: Help for p1oc2: p1oc2(Permut,Cycle) Returns the permutation product of p1 and c2. - See also: 1/ c1op2 2/ p1op2 + See also: 1/ c1op2 2/ p1op2 Ex1:p1oc2([0,2,1],[2,1,3]) - + ''' return GiacMethods['p1oc2'](self,*args) @@ -11947,9 +11947,9 @@ cdef class GiacMethods_base: Help for p1op2: p1op2(Permut,Permut) Returns the permutation product of p1 and p2. - See also: 1/ c1op2 2/ p1oc2 + See also: 1/ c1op2 2/ p1oc2 Ex1:p1op2([0,2,1],[1,0,3,2]) - + ''' return GiacMethods['p1op2'](self,*args) @@ -11961,7 +11961,7 @@ cdef class GiacMethods_base: Ex1:pa2b2(17) Ex2:pa2b2(209) Ex3:pa2b2(229) - + ''' return GiacMethods['pa2b2'](self,*args) @@ -11970,9 +11970,9 @@ cdef class GiacMethods_base: Help for pade: pade(Expr(Xpr), Var(x), (Intg(n) || Poly(N)), Intg(p)) Pade approximation P/Q=Xpr mod x^(n+1) or mod N with degree(P)3,x^20 (by default a=1) to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ bartlett_hann_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ bartlett_hann_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(poisson_window(randvector(1000,0..1),0.5)) - + ''' return GiacMethods['poisson_window'](self,*args) @@ -12932,10 +12932,10 @@ cdef class GiacMethods_base: Help for polar: polar(Crcle,Pnt or Cplxe(A)) Returns the line of the conjugated points of A with respect to the circle. - See also: 1/ pole 2/ is_conjugate + See also: 1/ pole 2/ is_conjugate Ex1:polar(circle(0,1),point(1+i)/2) Ex2:polar(circle(0,1),point(1+i)) - + ''' return GiacMethods['polar'](self,*args) @@ -12944,12 +12944,12 @@ cdef class GiacMethods_base: Help for polar_coordinates: polar_coordinates(Pnt or Cplx or LstRectCoord) Returns the list of the norm and of the argument of the affix of a point (for 2D) or of a complex number or of the list of rectangular coordinates. - See also: 1/ abscissapoint 2/ ordinate 3/ rectangular_coordinates 4/ polar_point + See also: 1/ abscissapoint 2/ ordinate 3/ rectangular_coordinates 4/ polar_point Ex1:polar_coordinates(point(1+2*i)) Ex2:polar_coordinates(-1-i) Ex3:polar_coordinates([-1,2]) Ex4:polar_coordinates(point(1+2*i)-point(-1+i)) - + ''' return GiacMethods['polar_coordinates'](self,*args) @@ -12958,10 +12958,10 @@ cdef class GiacMethods_base: Help for polar_point: polar_point(Real(r),Real(t)) Returns the point (for 2D) with the arguments r and t as polar coordinates (i.e. with r*exp(i*t) as affix). - See also: 1/ abscissa 2/ ordinate 3/ polar_coordinates 4/ rectangular_coordinates 5/ point + See also: 1/ abscissa 2/ ordinate 3/ polar_coordinates 4/ rectangular_coordinates 5/ point Ex1:polar_point(1,pi/4) Ex2:polar_point(2,-pi/3) - + ''' return GiacMethods['polar_point'](self,*args) @@ -12970,10 +12970,10 @@ cdef class GiacMethods_base: Help for polarplot: polarplot(Expr,Var,VarMin,VarMax) plotpolar(f(x),x,a,b) draws the polar curve r=f(x) for x in [a,b]. - See also: 1/ plotparam 2/ plotfunc 3/ plotpolar + See also: 1/ plotparam 2/ plotfunc 3/ plotpolar Ex1:polarplot(sin(2*x),x,0,pi) Ex2:polarplot(sin(2*x),x,0,pi,tstep=0.1) - + ''' return GiacMethods['polarplot'](self,*args) @@ -12982,10 +12982,10 @@ cdef class GiacMethods_base: Help for pole: pole(Crcle,Line) Returns the point having the line as polar with respect to the circle . - See also: 1/ polar 2/ is_conjugate + See also: 1/ polar 2/ is_conjugate Ex1:pole(circle(0,1),line(i,1)) Ex2:pole(circle(0,1),line((1+i),2)) - + ''' return GiacMethods['pole'](self,*args) @@ -12994,12 +12994,12 @@ cdef class GiacMethods_base: Help for poly2symb: poly2symb(Lst,Var) Gives the polynomial (or its value) : the first argument is the vector of coefficients and the second argument is the variable (by default x). - See also: 1/ e2r 2/ symb2poly + See also: 1/ e2r 2/ symb2poly Ex1:poly2symb([1,2,3]) Ex2:poly2symb([1,2,3],x) Ex3:poly2symb([1,2,3],-1) Ex4:poly2symb([1,2,-1],y) - + ''' return GiacMethods['poly2symb'](self,*args) @@ -13008,10 +13008,10 @@ cdef class GiacMethods_base: Help for polyEval: polyEval(Vect,Real(x0)) Evaluates at a point x0, a polynomial given by its coefficients. - See also: 1/ proot 2/ pcoeff + See also: 1/ proot 2/ pcoeff Ex1:polyEval([1,0,-2],1) Ex2:polyEval([1,2,-25,-26,120],8) - + ''' return GiacMethods['polyEval'](self,*args) @@ -13020,10 +13020,10 @@ cdef class GiacMethods_base: Help for polygon: polygon(LstPnt||LstCplx) Returns and draws the polygon where its vertices are the elements of l. - See also: 1/ isopolygon 2/ quadrilateral 3/ convexhull 4/ hexagon + See also: 1/ isopolygon 2/ quadrilateral 3/ convexhull 4/ hexagon Ex1:polygon(i,1+i,2-i,-1,-1+i/2) Ex2:polygon(point(0,0,0),point(3,3,3),point(0,0,3),point(3,0,0)) - + ''' return GiacMethods['polygon'](self,*args) @@ -13032,11 +13032,11 @@ cdef class GiacMethods_base: Help for polygone_rempli: polygone_rempli(Intg(n)) The argument is an integer <-1 which gives the number of previous turtle positions drawing a polygon and created this full polygon. - See also: 1/ + See also: 1/ Ex1: repete(4,avance 40,tourne_droite);polygone_rempli -8 Ex2: repete(3,avance 40,tourne_droite 120);polygone_rempli -6 Ex3: repete(3,avance 40,avance 40,tourne_droite 120);polygone_rempli -9 - + ''' return GiacMethods['polygone_rempli'](self,*args) @@ -13045,9 +13045,9 @@ cdef class GiacMethods_base: Help for polygonplot: polygonplot(Mtrx) Draws the polygons joining for j fixed and for k=0..nrows, the points (xk,yk) where xk=element row k column 0 and yk=element row k column j, after the xk are sorted (we obtain ncols-1 polygons). - See also: 1/ scatterplot 2/ listplot 3/ polygonscatterplot + See also: 1/ scatterplot 2/ listplot 3/ polygonscatterplot Ex1:polygonplot([[1,2,3],[2,0,1],[-1,2,3]]) - + ''' return GiacMethods['polygonplot'](self,*args) @@ -13056,9 +13056,9 @@ cdef class GiacMethods_base: Help for polygonscatterplot: polygonscatterplot(Mtrx) Draws the points (xk,yk) and the polygons joining for j fixed and for k=0..nrows, the points (xk,yk) where xk=element row k column 0 et yk=element row k column j, after the xk are sorted (we obtain ncols-1 polygons). - See also: 1/ scatterplot 2/ polygonplot 3/ listplot + See also: 1/ scatterplot 2/ polygonplot 3/ listplot Ex1:polygonscatterplot([[1,2,3],[2,0,1],[-1,2,3]]) - + ''' return GiacMethods['polygonscatterplot'](self,*args) @@ -13067,9 +13067,9 @@ cdef class GiacMethods_base: Help for polyhedron: polyhedron(SeqPnt(A,B,C...)) Draws a convex polyhedron with vertices among the arguments. - See also: 1/ cube 2/ parallelepiped + See also: 1/ cube 2/ parallelepiped Ex1:polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6]) - + ''' return GiacMethods['polyhedron'](self,*args) @@ -13078,13 +13078,13 @@ cdef class GiacMethods_base: Help for polynom: polynom(Opt) Option of the convert or convertir command and of the taylor and series commands (list=>n-poly or series=>poly). - See also: 1/ poly2symb 2/ taylor 3/ series 4/ convert + See also: 1/ poly2symb 2/ taylor 3/ series 4/ convert Ex1: convert([[10,[3,1]],[12,[2,2]]],polynom) Ex2: convert(taylor(sin(x)),polynom) Ex3: convert(series(sin(x),x=0,6),polynom) Ex4: taylor(sin(x),x=0,5,polynom) Ex5: series(sin(x),x=0,6,,polynom) - + ''' return GiacMethods['polynom'](self,*args) @@ -13093,11 +13093,11 @@ cdef class GiacMethods_base: Help for polynomial_regression: polynomial_regression(Lst||Mtrx(A),[Lst],Intg(n)) Returns the coefficients (an,...a1,a0) of y=an*x^n+..a1x+a0 : it is the best polynomial which approx the points where the coordinates are the rows of A (or the 2 lists) (n is the 2nd argument). - See also: 1/ linear_regression 2/ power_regression + See also: 1/ linear_regression 2/ power_regression Ex1:polynomial_regression([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]],3) Ex2:polynomial_regression([[0.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]],3) Ex3:polynomial_regression([0.0,2.0,3.0,4.0],[1.0,4.0,9.0,16.0],3) - + ''' return GiacMethods['polynomial_regression'](self,*args) @@ -13106,11 +13106,11 @@ cdef class GiacMethods_base: Help for polynomial_regression_plot: polynomial_regression_plot(Lst||Mtrx(A),[Lst],Intg(n)) Returns the plot of y=an*x^n+..a1x+a0 : it is the best polynomial which approx the points where the coordinates are the rows of A (or the 2 lists) (n is the 2nd argument). - See also: 1/ linear_regression_plot 2/ power_regression_plot + See also: 1/ linear_regression_plot 2/ power_regression_plot Ex1:polynomial_regression_plot([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]],3) Ex2:polynomial_regression_plot([[0.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]],3) Ex3:polynomial_regression_plot([0.0,2.0,3.0,4.0],[1.0,4.0,9.0,16.0],3) - + ''' return GiacMethods['polynomial_regression_plot'](self,*args) @@ -13119,11 +13119,11 @@ cdef class GiacMethods_base: Help for position: position(NULL or LstCoord) Returns the turtle position in pixels or puts the turtle at the position given by the argument with the same direction. - See also: 1/ cap 2/ initialise + See also: 1/ cap 2/ initialise Ex1:position() Ex2:position(50,70) Ex3:position([50,70]) - + ''' return GiacMethods['position'](self,*args) @@ -13132,9 +13132,9 @@ cdef class GiacMethods_base: Help for poslbdLMQ: poslbdLMQ(Poly(P)) Returns a lower bound on the values of the positive roots of P. Akritas-Strzebonski-Vigklas' Local Max Quadratic (LMQ) method is used. - See also: 1/ posubLMQ 2/ VAS_positive 3/ realroot + See also: 1/ posubLMQ 2/ VAS_positive 3/ realroot Ex1:poslbdLMQ(x^3-7*x+7) - + ''' return GiacMethods['poslbdLMQ'](self,*args) @@ -13143,9 +13143,9 @@ cdef class GiacMethods_base: Help for posubLMQ: posubLMQ(Poly(P)) Returns an upper bound on the values of the positive roots of P. Akritas-Strzebonski-Vigklas' Local Max Quadratic (LMQ) method is used. - See also: 1/ poslbdLMQ 2/ VAS_positive 3/ realroot + See also: 1/ poslbdLMQ 2/ VAS_positive 3/ realroot Ex1:posubLMQ(x^3-7*x+7) - + ''' return GiacMethods['posubLMQ'](self,*args) @@ -13154,9 +13154,9 @@ cdef class GiacMethods_base: Help for potential: potential(Vect(V),VectVar) Returns U such that derive(U,Vector_of_variable)=V. - See also: 1/ derive 2/ vpotential + See also: 1/ derive 2/ vpotential Ex1:potential([2*x*y+3,x^2-4*z,-4*y],[x,y,z]) - + ''' return GiacMethods['potential'](self,*args) @@ -13165,9 +13165,9 @@ cdef class GiacMethods_base: Help for pow2exp: pow2exp(Expr) Converts powers to exponentials. - See also: 1/ exp2pow + See also: 1/ exp2pow Ex1:pow2exp(a^b) - + ''' return GiacMethods['pow2exp'](self,*args) @@ -13176,11 +13176,11 @@ cdef class GiacMethods_base: Help for power_regression: power_regression(Lst|Mtrx(A),[Lst]) Returns the coefficients (m,b) of y=b*x^m : it is the best monomial which approx the points where the coordinates are the rows of A (or the 2 lists). - See also: 1/ polynomial_regression 2/ linear_regressiont + See also: 1/ polynomial_regression 2/ linear_regressiont Ex1:power_regression([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) Ex2:power_regression([[1.0,2.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) Ex3:power_regression([1.0,2.0,3.0,4.0],[2.0,4.0,9.0,16.0]) - + ''' return GiacMethods['power_regression'](self,*args) @@ -13189,11 +13189,11 @@ cdef class GiacMethods_base: Help for power_regression_plot: power_regression_plot(Lst||Mtrx(A),[Lst]) Returns the plot of y=b*x^m : it is the best monomial which approx the points where the coordinates are the rows of A (or the 2 lists). - See also: 1/ polynomial_regression_plot 2/ linear_regression_plot + See also: 1/ polynomial_regression_plot 2/ linear_regression_plot Ex1:power_regression_plot([[1.0,1.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) Ex2:power_regression_plot([[1.0,2.0],[2.0,4.0],[3.0,9.0],[4.0,16.0]]) Ex3:power_regression_plot([1.0,2.0,3.0,4.0],[2.0,4.0,9.0,16.0]) - + ''' return GiacMethods['power_regression_plot'](self,*args) @@ -13202,10 +13202,10 @@ cdef class GiacMethods_base: Help for powermod: powermod(Intg(a),Intg(n),Intg(p),[Expr(P(x))],[Var]) Computes a^n modulo p or modulo p,P(x) (fast algorithm). - See also: 1/ pow 2/ ^ + See also: 1/ pow 2/ ^ Ex1:powermod(17,452,19) Ex2:powermod(x+1,452,19,x^4+x+1,x) - + ''' return GiacMethods['powermod'](self,*args) @@ -13214,10 +13214,10 @@ cdef class GiacMethods_base: Help for powerpc: powerpc(Cercle,Pnt or Cplx) Returns the real number d^2-R^2 (d=distance between point and center, R=radius). - See also: 1/ radical_axis + See also: 1/ radical_axis Ex1:powerpc(circle(0,1+i),3+i) Ex2:powerpc(circle(0,point(1+i)),3+i) - + ''' return GiacMethods['powerpc'](self,*args) @@ -13226,10 +13226,10 @@ cdef class GiacMethods_base: Help for powexpand: powexpand(Expr) Expands the expression as a function of the exponent. - See also: 1/ + See also: 1/ Ex1:powexpand(2^(x+y)) Ex2:powexpand(3^(2*x)) - + ''' return GiacMethods['powexpand'](self,*args) @@ -13238,10 +13238,10 @@ cdef class GiacMethods_base: Help for powmod: powmod(Intg(a),Intg(n),Intg(p),[Expr(P(x))],[Var]) Computes a^n modulo p or modulo p,P(x) (fast algorithm). - See also: 1/ pow 2/ ^ + See also: 1/ pow 2/ ^ Ex1:powmod(17,452,19) Ex2:powmod(x+1,452,19,x^4+x+1,x) - + ''' return GiacMethods['powmod'](self,*args) @@ -13250,14 +13250,14 @@ cdef class GiacMethods_base: Help for prepend: prepend(Lst||Set||Str(L),Elem(n)) Adds an element to a set or at the beginning of a list or of a string (L:=prepend(L,a) or L.prepend(a)). - See also: 1/ append 2/ concat + See also: 1/ append 2/ concat Ex1:prepend([1,2],3) Ex2:prepend(set[1,2],3) Ex3: L:=[1,2];L:=prepend(L,3) - Ex4: L:=[1,2];L.prepend(L,3) + Ex4: L:=[1,2];L.prepend(L,3) Ex5: S:=set[1,2];S:=prepend(L,3) Ex6: S:=set[1,2];S.prepend(L,3) - + ''' return GiacMethods['prepend'](self,*args) @@ -13266,12 +13266,12 @@ cdef class GiacMethods_base: Help for preval: preval(Expr(F(Var)),Real(a),Real(b),[Var]) Returns F(b)-F(a). - See also: 1/ subst 2/ int + See also: 1/ subst 2/ int Ex1:preval(x^2-2,2,3) Ex2:preval(y^2-2,2,3,y) Ex3:preval(int(x),0,1) Ex4:preval(int(y,y),0,1,y) - + ''' return GiacMethods['preval'](self,*args) @@ -13280,10 +13280,10 @@ cdef class GiacMethods_base: Help for prevperm: prevperm(Intg(n)) Returns the previous permutation with the lexicographic order. - See also: 1/ nextperm 2/ is_permu + See also: 1/ nextperm 2/ is_permu Ex1:prevperm([0,1,3,2]) Ex2:prevperm([0,1,2,3]) - + ''' return GiacMethods['prevperm'](self,*args) @@ -13292,10 +13292,10 @@ cdef class GiacMethods_base: Help for prevprime: prevprime(Intg(a)) Previous prime or pseudo-prime before a given integer a. - See also: 1/ nextprime 2/ is_prime 3/ ithprime + See also: 1/ nextprime 2/ is_prime 3/ ithprime Ex1:prevprime(9856989898999) Ex2:prevprime(97160249868928888261606009) - + ''' return GiacMethods['prevprime'](self,*args) @@ -13304,10 +13304,10 @@ cdef class GiacMethods_base: Help for primpart: primpart(Poly(P),[Var]) Returns the polynomial P divided by the gcd of its coefficients. - See also: 1/ content + See also: 1/ content Ex1:primpart(2x^2+10x+6) Ex2:primpart(2t^2+10t+6,t) - + ''' return GiacMethods['primpart'](self,*args) @@ -13316,10 +13316,10 @@ cdef class GiacMethods_base: Help for printf: printf(Expr) 2d printing. - See also: 1/ print + See also: 1/ print Ex1:printf(sqrt(2)) Ex2:printf("%gen+%gen=%gen",a,b,a+b) - + ''' return GiacMethods['printf'](self,*args) @@ -13328,9 +13328,9 @@ cdef class GiacMethods_base: Help for prism: prism(LstPnt([A,B,C,D]),Pnt(A1)) Draws a prism with plane base ABCD...and with edges parallel to AA1 (the faces are parallelograms). - See also: 1/ cube 2/ polyhedron + See also: 1/ cube 2/ polyhedron Ex1:prism([[0,0,0],[5,0,0],[0,5,0],[-5,5,0]],[0,0,5]) - + ''' return GiacMethods['prism'](self,*args) @@ -13339,9 +13339,9 @@ cdef class GiacMethods_base: Help for prism_graph: prism_graph(Intg(n)) Returns the generalized Petersen graph GP(n,1). - See also: 1/ antiprism_graph 2/ web_graph + See also: 1/ antiprism_graph 2/ web_graph Ex1:prism_graph(5) - + ''' return GiacMethods['prism_graph'](self,*args) @@ -13350,7 +13350,7 @@ cdef class GiacMethods_base: Help for product: product(Expr||Lst,[Var||Lst],[Intg(a)],[Intg(b)],[Intg(p)]) Multiplies the values of the expression when the variable go from a to b with a step p (product(expression,var,begin,end,step) by default p=1) or product of the elements of a list or product element by element of 2 lists or matrices. - See also: 1/ sum + See also: 1/ sum Ex1:product(n,n,1,10,2) Ex2:product(1/n,n,1,10) Ex3:product(1/n,n,11,1) @@ -13358,7 +13358,7 @@ cdef class GiacMethods_base: Ex5:product([2,3,4,5]) Ex6:product([2,3,4],[5,6,7]) Ex7:product([[2,3,4],[5,6,7]],[[2,3,4],[5,6,7]]) - + ''' return GiacMethods['product'](self,*args) @@ -13367,11 +13367,11 @@ cdef class GiacMethods_base: Help for projection: projection(Curve,Pnt) projection(C,A) is the orthogonal projection of A on the curve C. - See also: 1/ perpendicular + See also: 1/ perpendicular Ex1: H:=projection(line(i,1-i),1+i) Ex2: K:=projection(circle(0,1),1+i) Ex3: J:=projection(circle(0,1),point(1+2*i)) - + ''' return GiacMethods['projection'](self,*args) @@ -13380,12 +13380,12 @@ cdef class GiacMethods_base: Help for proot: proot(Vect||Poly,[Intg(n)]) Returns all computed roots of a polynomial given by its coefficients (may not work if roots are not simple). - See also: 1/ pcoeff 2/ peval 3/ realroot 4/ complexroot 5/ rationalroot 6/ crationalroot + See also: 1/ pcoeff 2/ peval 3/ realroot 4/ complexroot 5/ rationalroot 6/ crationalroot Ex1:proot([1,0,-2]) Ex2:proot(x^2-2) Ex3:proot([1,2,-25,-26,120]) Ex4:proot(x^4+5x-3,30) - + ''' return GiacMethods['proot'](self,*args) @@ -13394,10 +13394,10 @@ cdef class GiacMethods_base: Help for propFrac: propFrac(Frac or RatFrac) Simplifies and writes the fraction (or rational fraction) A/B as Q+R/B with R=0 or, the (-n)th previous question if n<0 (by default n=-1 for the previous question). - See also: 1/ ans + See also: 1/ ans Ex1:quest() Ex2:quest(2) Ex3:quest(-2) - + ''' return GiacMethods['quest'](self,*args) @@ -13604,11 +13604,11 @@ cdef class GiacMethods_base: Help for quo: quo((Vect or Poly),(Vect or Poly),[Var]) Euclidean quotient of 2 polynomials. - See also: 1/ rem 2/ quorem 3/ Quo 4/ iquo + See also: 1/ rem 2/ quorem 3/ Quo 4/ iquo Ex1:quo([1,2,3,4],[-1,2]) Ex2:quo(x^3+2x^2+3x+4,-x+2) Ex3:quo(t^3+2t^2+3t+4,-t+2,t) - + ''' return GiacMethods['quo'](self,*args) @@ -13617,12 +13617,12 @@ cdef class GiacMethods_base: Help for quorem: quorem((Vect or Poly),(Vect or Poly),[Var]) Euclidean quotient and remainder of 2 polynomials. - See also: 1/ rem 2/ quo 3/ iquorem + See also: 1/ rem 2/ quo 3/ iquorem Ex1:quorem([1,2,3,4],[-1,2]) Ex2:quorem(x^3+2x^2+3x+4,-x+2) Ex3:quorem(t^3+2t^2+3t+4,-t+2,t) Ex4:quorem(t^4-1,(t+1)^2,t) - + ''' return GiacMethods['quorem'](self,*args) @@ -13631,11 +13631,11 @@ cdef class GiacMethods_base: Help for quote: quote(Expr) Returns its argument unevaluated (and also a:=quote(a) purges a). - See also: 1/ + See also: 1/ Ex1:quote(1+2) Ex2:quote(1/x+1/(x-1)) Ex3:quote((x+1)*(x-1)) - + ''' return GiacMethods['quote'](self,*args) @@ -13644,12 +13644,12 @@ cdef class GiacMethods_base: Help for r2e: r2e(Lst,Var) Gives the polynomial (or its value) : the first argument is the vector of coefficients and the second argument is the variable (by default x). - See also: 1/ e2r 2/ symb2poly + See also: 1/ e2r 2/ symb2poly Ex1:r2e([1,2,3]) Ex2:r2e([1,2,3],x) Ex3:r2e([1,2,3],-1) Ex4:r2e([1,2,-1],y) - + ''' return GiacMethods['r2e'](self,*args) @@ -13658,10 +13658,10 @@ cdef class GiacMethods_base: Help for radical_axis: radical_axis(Crcle,Crcle) Returns the line of points with same powerpc with respect to the 2 circles. - See also: 1/ powerpc + See also: 1/ powerpc Ex1:radical_axis(circle(0,1+i),circle(1,1+i)) Ex2:radical_axis(circle(0,point(1+i)),circle(1,point(1+i))) - + ''' return GiacMethods['radical_axis'](self,*args) @@ -13670,9 +13670,9 @@ cdef class GiacMethods_base: Help for radius: radius(Crcle) radius(C) gives the radius of the circle C. - See also: 1/ center 2/ circle + See also: 1/ center 2/ circle Ex1:radius(incircle(-1,1-i,i)) - + ''' return GiacMethods['radius'](self,*args) @@ -13681,9 +13681,9 @@ cdef class GiacMethods_base: Help for ramene: ramene(Str(fich_name)) Reads variables and their values from the file fich_name. - See also: 1/ write 2/ readrgb 3/ readwav 4/ csv2gen + See also: 1/ write 2/ readrgb 3/ readwav 4/ csv2gen Ex1:ramene("toto") - + ''' return GiacMethods['ramene'](self,*args) @@ -13692,7 +13692,7 @@ cdef class GiacMethods_base: Help for rand: rand(Intg(n) or Interval(p..n) or NULL,[Intg(b1) or Lst(L)],[Intg(b2)]) rand(n)=a random integer (resp rand(p,n)=a real or rand(p..n)=a real function) with uniform distribution in 0..n-1 (resp in [p;n])(rand()=rand(0,1)=a real in [0,1[) or rand(n,b1,b2)=n integers between b1 and b2 or rand(n,L)=list of n elements of L. - See also: 1/ srand 2/ randpoly 3/ ranm 4/ randvector 5/ hasard + See also: 1/ srand 2/ randpoly 3/ ranm 4/ randvector 5/ hasard Ex1:rand(4) Ex2:rand() Ex3:rand(0,2) @@ -13704,7 +13704,7 @@ cdef class GiacMethods_base: Ex9: L:=["r","r","r","b","n"];L3:=L.rand(3) Ex10: L:=["r","r","r","b","n"];a:=rand(L) Ex11: L:=["r","r","r","b","n"];a:=L.rand() - + ''' return GiacMethods['rand'](self,*args) @@ -13713,7 +13713,7 @@ cdef class GiacMethods_base: Help for randMat: randMat(Intg(n), [Intg(m)],[Interval or quote(DistribLaw)]) Returns a list of size n or an n*m matrix that contains random integers in the range -99 through 99 with uniform distribution or contains random numbers according to the law put between quotes. - See also: 1/ idn 2/ randPoly 3/ rand 4/ randvector + See also: 1/ idn 2/ randPoly 3/ rand 4/ randvector Ex1:randMat(3) Ex2:randMat(3,2) Ex3:randMat(3,2,6) @@ -13727,7 +13727,7 @@ cdef class GiacMethods_base: Ex11:randMat(3,2,1..2) Ex12:randMat(3,5,multinomial,[1/2,1/3,1/6],["R","V","B"]) Ex13: GF(2,8,g);ranm(3,3,g) - + ''' return GiacMethods['randMat'](self,*args) @@ -13736,10 +13736,10 @@ cdef class GiacMethods_base: Help for randNorm: randNorm(Real(mu),Real(sigma)) Returns a random real with normal distribution N(mu,sigma). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randpoisson 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randpoisson 8/ randgeometric 9/ randmultinomial Ex1:randNorm(0,1) Ex2:randNorm(2,1) - + ''' return GiacMethods['randNorm'](self,*args) @@ -13748,14 +13748,14 @@ cdef class GiacMethods_base: Help for randPoly: randPoly([Var(Var)],Intg(n),[law]) Returns a polynomial with variable var (or x), of degree n and where the coefficients are random integers in the range -99 through 99 with uniform distribution or according to a law. - See also: 1/ ranm 2/ randvector + See also: 1/ ranm 2/ randvector Ex1:randPoly(5) Ex2:randPoly(t,8) Ex3:randPoly(t,8,-1..1) Ex4:randPoly([x,y],[10,3]) Ex5:randPoly([x,y],[10,3],1 mod 7) Ex6: GF(2,8,g);randpoly(t,8,g);randpoly([x,y],[2,3],g) - + ''' return GiacMethods['randPoly'](self,*args) @@ -13764,10 +13764,10 @@ cdef class GiacMethods_base: Help for randbetad: randbetad(Real(a),Real(b)) Returns a random real according to the Beta distribution with parameters a>0 and b>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:randbetad(1,2) Ex2:randbetad(1.5,4) - + ''' return GiacMethods['randbetad'](self,*args) @@ -13776,10 +13776,10 @@ cdef class GiacMethods_base: Help for randbinomial: randbinomial(Intg(n),Real(p)) Returns a random integer with binomial distribution B(n,p) i.e. the number of successes in n independant tests where for each test, the success of probability is p. - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randnorm 7/ randpoisson 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randnorm 7/ randpoisson 8/ randgeometric 9/ randmultinomial Ex1:randbinomial(10,0.4) Ex2:randbinomial(100,0.8) - + ''' return GiacMethods['randbinomial'](self,*args) @@ -13788,10 +13788,10 @@ cdef class GiacMethods_base: Help for randchisquare: randchisquare(Intg(n)) Returns a random integer with chi^2 distribution, χ^2(n). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial Ex1:randchisquare(5) Ex2:randchisquare(2) - + ''' return GiacMethods['randchisquare'](self,*args) @@ -13800,10 +13800,10 @@ cdef class GiacMethods_base: Help for randexp: randexp(Real(a)) Returns a random real according to the exponential distribution with parameter a>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:randexp(1) Ex2:randexp(2) - + ''' return GiacMethods['randexp'](self,*args) @@ -13812,10 +13812,10 @@ cdef class GiacMethods_base: Help for randfisher: randfisher(Intg(n),Intg(m)) Returns a random integer with Fisher-Snedecor distribution F(n,m). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial Ex1:randfisher(5,2) Ex2:randfisher(2,4) - + ''' return GiacMethods['randfisher'](self,*args) @@ -13824,10 +13824,10 @@ cdef class GiacMethods_base: Help for randgammad: randgammad(Real(a),Real(b)) Returns a random real according to the Gamma distribution with parameters a>0 and b>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:randgammad(1,2) Ex2:randgammad(1.5,4) - + ''' return GiacMethods['randgammad'](self,*args) @@ -13836,9 +13836,9 @@ cdef class GiacMethods_base: Help for randgeometric: randgeometric(Real(p)) Returns a random integer following the geometric distribution with parameter p. - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randnorm 7/ randpoisson 8/ randbinomial 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randnorm 7/ randpoisson 8/ randbinomial 9/ randmultinomial Ex1:randgeometric(0.4) - + ''' return GiacMethods['randgeometric'](self,*args) @@ -13847,10 +13847,10 @@ cdef class GiacMethods_base: Help for randint: randint(Intg(n1),Intg(n2)) randint(n1,n2)=an integer in [n1, n2] or [n2,n1]. - See also: 1/ rand + See also: 1/ rand Ex1:randint(1,10) Ex2:randint(-1,-10) - + ''' return GiacMethods['randint'](self,*args) @@ -13859,10 +13859,10 @@ cdef class GiacMethods_base: Help for randmarkov: randmarkov(Mtrx(M) || Vctr(v),Intg(i0),[Intg(n)]) Returns a random sequence of n states (Markov chain) starting from i0, with probability transition matrix M, or returns a stochastic matrix with p recurrent loops v=[n1,..,np] and i0 transient states. - See also: 1/ markov 2/ plotproba + See also: 1/ markov 2/ plotproba Ex1:randmarkov([[0,0,1/2,0,1/2],[0,0,1,0,0],[1/4,1/4,0,1/4,1/4],[0,0,1/2,0,1/2],[0,0,0,0,1]],2,20) Ex2:randmarkov([1,2,1,3],4) - + ''' return GiacMethods['randmarkov'](self,*args) @@ -13871,7 +13871,7 @@ cdef class GiacMethods_base: Help for randmatrix: randmatrix(Intg(n), [Intg(m)],[Interval or quote(DistribLaw)]) Returns a list of size n or an n*m matrix that contains random integers in the range -99 through 99 with uniform distribution or contains random numbers according to the law put between quotes. - See also: 1/ idn 2/ randPoly 3/ rand 4/ randvector + See also: 1/ idn 2/ randPoly 3/ rand 4/ randvector Ex1:randmatrix(3) Ex2:randmatrix(3,2) Ex3:randmatrix(3,2,6) @@ -13885,7 +13885,7 @@ cdef class GiacMethods_base: Ex11:randmatrix(3,2,1..2) Ex12:randmatrix(3,5,multinomial,[1/2,1/3,1/6],["R","V","B"]) Ex13: GF(2,8,g);ranm(3,3,g) - + ''' return GiacMethods['randmatrix'](self,*args) @@ -13894,10 +13894,10 @@ cdef class GiacMethods_base: Help for randmultinomial: randmultinomial(List(P),[List(K)]) Returns a random index or list element according to a multinomial distribution probability list P. - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randnorm 7/ randpoisson 8/ randgeometric 9/ randbinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randnorm 7/ randpoisson 8/ randgeometric 9/ randbinomial Ex1:randmultinomial([1/2,1/3,1/6]) Ex2:randmultinomial([1/2,1/3,1/6],["R","V","B"]) - + ''' return GiacMethods['randmultinomial'](self,*args) @@ -13906,10 +13906,10 @@ cdef class GiacMethods_base: Help for randnorm: randnorm(Real(mu),Real(sigma)) Returns a random real with normal distribution N(mu,sigma). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randpoisson 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randpoisson 8/ randgeometric 9/ randmultinomial Ex1:randnorm(0,1) Ex2:randnorm(2,1) - + ''' return GiacMethods['randnorm'](self,*args) @@ -13918,7 +13918,7 @@ cdef class GiacMethods_base: Help for random: random(Intg(n) or Interval(p..n) or NULL,[Intg(b1) or Lst(L)],[Intg(b2)]) rand(n)=a random integer (resp rand(p,n)=a real or rand(p..n)=a real function) with uniform distribution in 0..n-1 (resp in [p;n])(rand()=rand(0,1)=a real in [0,1[) or rand(n,b1,b2)=n integers between b1 and b2 or rand(n,L)=list of n elements of L. - See also: 1/ srand 2/ randpoly 3/ ranm 4/ randvector 5/ hasard + See also: 1/ srand 2/ randpoly 3/ ranm 4/ randvector 5/ hasard Ex1:random(4) Ex2:random() Ex3:random(0,2) @@ -13930,7 +13930,7 @@ cdef class GiacMethods_base: Ex9: L:=["r","r","r","b","n"];L3:=L.rand(3) Ex10: L:=["r","r","r","b","n"];a:=rand(L) Ex11: L:=["r","r","r","b","n"];a:=L.rand() - + ''' return GiacMethods['random'](self,*args) @@ -13939,10 +13939,10 @@ cdef class GiacMethods_base: Help for random_bipartite_graph: random_bipartite_graph(Intg(n)||Lst(a,b),Real(p)||Intg(m)) Returns a random undirected unweighted bipartite graph with n vertices where each possible edge is present with probability p or where m edges are created at random. When the first argument is list [a,b] of integers, two groups of vertices with sizes a and b are created. - See also: 1/ random_digraph 2/ random_graph 3/ random_planar_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree + See also: 1/ random_digraph 2/ random_graph 3/ random_planar_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree Ex1:random_bipartite_graph(10,0.5) Ex2:random_bipartite_graph([2,3],1.0) - + ''' return GiacMethods['random_bipartite_graph'](self,*args) @@ -13951,10 +13951,10 @@ cdef class GiacMethods_base: Help for random_digraph: random_digraph(Intg(n)||Lst(V),Real(p)||Intg(m)) Returns a random directed unweighted graph with n vertices (list V of labels may me specified) where two vertices are connected with probability p or where m edges are created at random. - See also: 1/ random_bipartite_graph 2/ random_graph 3/ random_planar_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree + See also: 1/ random_bipartite_graph 2/ random_graph 3/ random_planar_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree Ex1:random_digraph(8,0.5) Ex2:random_digraph(8,10) - + ''' return GiacMethods['random_digraph'](self,*args) @@ -13963,10 +13963,10 @@ cdef class GiacMethods_base: Help for random_graph: random_graph(Intg(n)||Lst(V),Real(p)||Intg(m)) Returns a random undirected unweighted graph with n vertices (list V of labels may be specified) where two vertices are connected with probability p or where m edges are created at random. - See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_planar_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree + See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_planar_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree Ex1:random_graph(8,0.5) Ex2:random_graph(8,10) - + ''' return GiacMethods['random_graph'](self,*args) @@ -13975,11 +13975,11 @@ cdef class GiacMethods_base: Help for random_network: random_network(Intg(a),Intg(b),[Real(p)],[opts]) Returns a random network with b grid frames of size a*a in which every edge appears with the probability p (by default 0.5). - See also: 1/ is_network 2/ maxflow + See also: 1/ is_network 2/ maxflow Ex1:random_network(3,3) Ex2:random_network(3,3,acyclic) Ex3:random_network(3,4,0.75) - + ''' return GiacMethods['random_network'](self,*args) @@ -13988,8 +13988,8 @@ cdef class GiacMethods_base: Help for random_planar_graph: random_planar_graph(Intg(n)||Lst(V),Real(p),[Intg(c)]) Returns a random planar graph with n vertices, which can also be specified as a list V of their labels, obtained by trying to remove each edge of a random triangulated graph with probability 0<=p<1 [c is connectivity level : 0 - any, 1 - connected, 2 - biconnected, 3 - triconnected (by default, c=1)]. - See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree - + See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_regular_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree + ''' return GiacMethods['random_planar_graph'](self,*args) @@ -13998,9 +13998,9 @@ cdef class GiacMethods_base: Help for random_regular_graph: random_regular_graph(Intg(n)||Lst(V),Intg(d),[connected]) Returns a random d-regular graph with n vertices, which may be specified as list V of their labels. - See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree + See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree Ex1:random_regular_graph(100,80,connected) - + ''' return GiacMethods['random_regular_graph'](self,*args) @@ -14009,9 +14009,9 @@ cdef class GiacMethods_base: Help for random_sequence_graph: random_sequence_graph(Lst(L)) Returns a random undirected graph with degree sequence L. - See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree + See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_sequence_graph 6/ random_tournament 7/ random_tree Ex1:random_sequence_graph([1,3,3,2,1,2,2,2,3,3]) - + ''' return GiacMethods['random_sequence_graph'](self,*args) @@ -14020,9 +14020,9 @@ cdef class GiacMethods_base: Help for random_tournament: random_tournament(Intg(n)||Lst(V)) Returns a random tournament graph with n vertices, which may be specified as list V of their labels. - See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_regular_graph 6/ random_sequence_graph 7/ random_tree + See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_regular_graph 6/ random_sequence_graph 7/ random_tree Ex1:random_tournament(5) - + ''' return GiacMethods['random_tournament'](self,*args) @@ -14031,8 +14031,8 @@ cdef class GiacMethods_base: Help for random_tree: random_tree(Intg(n)||Lst(V),[Intg(d)||root[=Vrtx(v)]]) Returns a random tree graph with n vertices, which may be specified as list V of their labels [with the upper bound d (positive integer) for the degree of graph or 'root' for rooted trees]. - See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_regular_graph 6/ random_sequence_graph 7/ random_tournament - + See also: 1/ random_bipartite_graph 2/ random_digraph 3/ random_graph 4/ random_planar_graph 5/ random_regular_graph 6/ random_sequence_graph 7/ random_tournament + ''' return GiacMethods['random_tree'](self,*args) @@ -14041,7 +14041,7 @@ cdef class GiacMethods_base: Help for random_variable: random_variable(Lst(W)||Mtrx(M)||Fnc(f),[params]) Returns a random variable from a probability density function f or from list of weights (discrete variable). - See also: 1/ randvector 2/ randmatrix 3/ rand + See also: 1/ randvector 2/ randmatrix 3/ rand Ex1:random_variable(fisher,2,3) Ex2:random_variable([["apple",1/3],["orange",1/4],["pear",1/5],["plum",13/60]]) Ex3:random_variable(k->1-(k/10)^2,range=-10..10) @@ -14052,7 +14052,7 @@ cdef class GiacMethods_base: Ex8:random_variable(weibull,mean=12.5,variance=1) Ex9:random_variable(uniform,mean=10,stddev=2) Ex10:random_variable(uniform,e..pi) - + ''' return GiacMethods['random_variable'](self,*args) @@ -14061,13 +14061,13 @@ cdef class GiacMethods_base: Help for randperm: randperm(Intg(n)||Lst(L)) Returns a random permutation of [0,1,2,..,n-1] or of the list L. - See also: 1/ permu2cycles 2/ is_permu 3/ permu2mat + See also: 1/ permu2cycles 2/ is_permu 3/ permu2mat Ex1:randperm(4) Ex2:randperm(7) Ex3:randperm([1,3,5,7,9]) Ex4: L:=[1,3,5,7,9];L:=randperm(L) Ex5: L:=[1,3,5,7,9];L.randperm() - + ''' return GiacMethods['randperm'](self,*args) @@ -14076,10 +14076,10 @@ cdef class GiacMethods_base: Help for randpoisson: randpoisson(Real(λ)) Returns a random integer with poisson distribution P(λ). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial Ex1:randpoisson(5.4) Ex2:randpoisson(2.8) - + ''' return GiacMethods['randpoisson'](self,*args) @@ -14088,14 +14088,14 @@ cdef class GiacMethods_base: Help for randpoly: randpoly([Var(Var)],Intg(n),[law]) Returns a polynomial with variable var (or x), of degree n and where the coefficients are random integers in the range -99 through 99 with uniform distribution or according to a law. - See also: 1/ ranm 2/ randvector + See also: 1/ ranm 2/ randvector Ex1:randpoly(5) Ex2:randpoly(t,8) Ex3:randpoly(t,8,-1..1) Ex4:randpoly([x,y],[10,3]) Ex5:randpoly([x,y],[10,3],1 mod 7) Ex6: GF(2,8,g);randpoly(t,8,g);randpoly([x,y],[2,3],g) - + ''' return GiacMethods['randpoly'](self,*args) @@ -14104,10 +14104,10 @@ cdef class GiacMethods_base: Help for randseed: randseed() srand returns an integer and initializes the sequence of random numbers. - See also: 1/ RandSeed + See also: 1/ RandSeed Ex1:randseed(12) Ex2: srand - + ''' return GiacMethods['randseed'](self,*args) @@ -14116,10 +14116,10 @@ cdef class GiacMethods_base: Help for randstudent: randstudent(Intg(n)) Returns a random integer with Student distribution S(n). - See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial + See also: 1/ rand 2/ randpoly 3/ ranm 4/ randvector 5/ randexp 6/ randbinomial 7/ randnorm 8/ randgeometric 9/ randmultinomial Ex1:randstudent(5) Ex2:randstudent(2) - + ''' return GiacMethods['randstudent'](self,*args) @@ -14128,7 +14128,7 @@ cdef class GiacMethods_base: Help for randvar: randvar(Lst(W)||Mtrx(M)||Fnc(f),[params]) Returns a random variable from a probability density function f or from list of weights (discrete variable). - See also: 1/ randvector 2/ randmatrix 3/ rand + See also: 1/ randvector 2/ randmatrix 3/ rand Ex1:randvar(fisher,2,3) Ex2:randvar([["apple",1/3],["orange",1/4],["pear",1/5],["plum",13/60]]) Ex3:randvar(k->1-(k/10)^2,range=-10..10) @@ -14139,7 +14139,7 @@ cdef class GiacMethods_base: Ex8:randvar(weibull,mean=12.5,variance=1) Ex9:randvar(uniform,mean=10,stddev=2) Ex10:randvar(uniform,e..pi) - + ''' return GiacMethods['randvar'](self,*args) @@ -14148,7 +14148,7 @@ cdef class GiacMethods_base: Help for randvector: randvector(Intg(n), [Intg(m)],[Interval or quote(DistribLaw)]) Returns a list of size n that contains random integers in the range -99 through 99 (or in 0..m-1) with uniform distribution or contains random numbers according to the law put between quotes. - See also: 1/ idn 2/ randPoly 3/ rand 4/ ranm + See also: 1/ idn 2/ randPoly 3/ rand 4/ ranm Ex1:randvector(3) Ex2:randvector(3,6) Ex3:randvector(3,normald,0,1) @@ -14159,7 +14159,7 @@ cdef class GiacMethods_base: Ex8:randvector(3,'rand(3)') Ex9:randvector(3,1..2) Ex10: GF(2,8,g);randvector(3,g) - + ''' return GiacMethods['randvector'](self,*args) @@ -14168,10 +14168,10 @@ cdef class GiacMethods_base: Help for randweibulld: randweibulld(Real(a),Real(b)) Returns a random real according to the Weibull distribution with parameters a>0 and b>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:randweibulld(1,2) Ex2:randweibulld(1.5,4) - + ''' return GiacMethods['randweibulld'](self,*args) @@ -14180,10 +14180,10 @@ cdef class GiacMethods_base: Help for rank: rank(Mtrx) Returns the rank of the matrix. - See also: 1/ det 2/ image + See also: 1/ det 2/ image Ex1:rank([[1,1,2],[2,1,3],[3,1,4]]) Ex2:rank([[1,1,2],[2,1,3],[3,1,5]]) - + ''' return GiacMethods['rank'](self,*args) @@ -14192,7 +14192,7 @@ cdef class GiacMethods_base: Help for ranm: ranm(Intg(n), [Intg(m)],[Interval or quote(DistribLaw)]) Returns a list of size n or an n*m matrix that contains random integers in the range -99 through 99 with uniform distribution or contains random numbers according to the law put between quotes. - See also: 1/ idn 2/ randPoly 3/ rand 4/ randvector + See also: 1/ idn 2/ randPoly 3/ rand 4/ randvector Ex1:ranm(3) Ex2:ranm(3,2) Ex3:ranm(3,2,6) @@ -14206,7 +14206,7 @@ cdef class GiacMethods_base: Ex11:ranm(3,2,1..2) Ex12:ranm(3,5,multinomial,[1/2,1/3,1/6],["R","V","B"]) Ex13: GF(2,8,g);ranm(3,3,g) - + ''' return GiacMethods['ranm'](self,*args) @@ -14215,7 +14215,7 @@ cdef class GiacMethods_base: Help for ranv: ranv(Intg(n), [Intg(m)],[Interval or quote(DistribLaw)]) Returns a list of size n that contains random integers in the range -99 through 99 (or in 0..m-1) with uniform distribution or contains random numbers according to the law put between quotes. - See also: 1/ idn 2/ randPoly 3/ rand 4/ ranm + See also: 1/ idn 2/ randPoly 3/ rand 4/ ranm Ex1:ranv(3) Ex2:ranv(3,6) Ex3:ranv(3,normald,0,1) @@ -14226,7 +14226,7 @@ cdef class GiacMethods_base: Ex8:ranv(3,'rand(3)') Ex9:ranv(3,1..2) Ex10: GF(2,8,g);randvector(3,g) - + ''' return GiacMethods['ranv'](self,*args) @@ -14235,9 +14235,9 @@ cdef class GiacMethods_base: Help for rassembler_trigo: rassembler_trigo(Expr) Collects trigonometric expressions. - See also: 1/ texpand 2/ tlin + See also: 1/ texpand 2/ tlin Ex1:rassembler_trigo(sin(x)+cos(x)) - + ''' return GiacMethods['rassembler_trigo'](self,*args) @@ -14246,11 +14246,11 @@ cdef class GiacMethods_base: Help for rat_jordan: rat_jordan(Mtrx) Returns the list made by the transition matrix and the rational Jordan form of a matrix. - See also: 1/ egv 2/ egvl 3/ jordan 4/ companion + See also: 1/ egv 2/ egvl 3/ jordan 4/ companion Ex1:rat_jordan([[0,2],[1,0]]) Ex2:rat_jordan([[-2,-2,1],[-2,1,-2],[1,-2,-2]]) Ex3:rat_jordan([[1,1,-1,2,-1],[2,0,1,-4,-1],[0,1,1,1,1],[0,1,2,0,1],[0,0,-3,3,-1]]) - + ''' return GiacMethods['rat_jordan'](self,*args) @@ -14259,11 +14259,11 @@ cdef class GiacMethods_base: Help for rational: rational(Opt) DOM_RAT or rational is the type of a rational, as returned by the type command. It is also an option of the assume command. - See also: 1/ type 2/ assume 3/ DOM_INT 4/ DOM_FLOAT + See also: 1/ type 2/ assume 3/ DOM_INT 4/ DOM_FLOAT Ex1: assume(a,rational) Ex2: assume(a,DOM_RAT) Ex3: a:=1/2;type(a) - + ''' return GiacMethods['rational'](self,*args) @@ -14272,9 +14272,9 @@ cdef class GiacMethods_base: Help for rationalroot: rationalroot(Poly(P)) Returns the list of rational roots of P without indicating the multiplicity. - See also: 1/ proot 2/ froot 3/ complexroot 4/ realroot 5/ crationalroot + See also: 1/ proot 2/ froot 3/ complexroot 4/ realroot 5/ crationalroot Ex1:rationalroot(2*x^3-9*x^2+13*x-6) - + ''' return GiacMethods['rationalroot'](self,*args) @@ -14283,11 +14283,11 @@ cdef class GiacMethods_base: Help for ratnormal: ratnormal(Expr) Rewrites as an irreducible rational fraction. - See also: 1/ normal 2/ simplify 3/ factor 4/ expand + See also: 1/ normal 2/ simplify 3/ factor 4/ expand Ex1:ratnormal((x^2-1)/(x^3-1)) Ex2:ratnormal(c/d+b/d+a/d) Ex3:ratnormal((x^2-1)/(x^3-1)+(x-1)/(x^3-1)+1) - + ''' return GiacMethods['ratnormal'](self,*args) @@ -14296,10 +14296,10 @@ cdef class GiacMethods_base: Help for rdiv: rdiv(Expr(a),Expr(b)) Division of a by b (prefixed version of /). - See also: 1/ / + See also: 1/ / Ex1:rdiv(3,5) Ex2:rdiv(3.2,5.4) - + ''' return GiacMethods['rdiv'](self,*args) @@ -14308,11 +14308,11 @@ cdef class GiacMethods_base: Help for re: re(Cplx or LstCplx) Returns the real part of a complex number. - See also: 1/ im 2/ conj + See also: 1/ im 2/ conj Ex1:re(1+2*i) Ex2:re((1+2*i)^2) Ex3:re([1+2*i,(1+2*i)^2]) - + ''' return GiacMethods['re'](self,*args) @@ -14321,9 +14321,9 @@ cdef class GiacMethods_base: Help for read: read(Str(fich_name)) Reads variables and their values from the file fich_name. - See also: 1/ write 2/ readrgb 3/ readwav 4/ csv2gen + See also: 1/ write 2/ readrgb 3/ readwav 4/ csv2gen Ex1:read("toto") - + ''' return GiacMethods['read'](self,*args) @@ -14332,10 +14332,10 @@ cdef class GiacMethods_base: Help for readrgb: readrgb(Str(s),[Intg(w)],[Intg(h)]) Reads a picture file, using it's natural dimensions, or using specified dimensions. - See also: 1/ writergb 2/ readwav + See also: 1/ writergb 2/ readwav Ex1:readrgb("image.png") Ex2:readrgb("image.png",50,50) - + ''' return GiacMethods['readrgb'](self,*args) @@ -14344,9 +14344,9 @@ cdef class GiacMethods_base: Help for readwav: readwav(Str(s)) Reads a WAV sound file. - See also: 1/ writewav 2/ readrgb + See also: 1/ writewav 2/ readrgb Ex1:readwav("pop.wav") - + ''' return GiacMethods['readwav'](self,*args) @@ -14355,11 +14355,11 @@ cdef class GiacMethods_base: Help for real: real(Cplx or LstCplx) Returns the real part of a complex number. - See also: 1/ im 2/ conj + See also: 1/ im 2/ conj Ex1:real(1+2*i) Ex2:real((1+2*i)^2) Ex3:real([1+2*i,(1+2*i)^2]) - + ''' return GiacMethods['real'](self,*args) @@ -14368,14 +14368,14 @@ cdef class GiacMethods_base: Help for realroot: realroot([sturm],Poly(P),[Real(l)],[Cplx(a)],[Cplx(b)]) Returns the list of intervals of length <=l containing the real roots of P inside a..b with their multiplicity. By default the Vincent-Akritas-Strzebonski (VAS) method is used. realroot(sturm,P) uses Sturm's method. - See also: 1/ proot 2/ froot 3/ complexroot 4/ rationalroot 5/ crationalroot 6/ sturmab 7/ VAS + See also: 1/ proot 2/ froot 3/ complexroot 4/ rationalroot 5/ crationalroot 6/ sturmab 7/ VAS Ex1:realroot(x^3+7,0.1) Ex2:realroot(x^3-7*x+7) Ex3:realroot(sturm,x^3-7*x+7) Ex4:realroot(x^5-2*x^4+x^3+1) Ex5:realroot(x^5-2*x^4+x^3+1,0.1) Ex6:realroot(x^3+x+8,1e-5,-4,4) - + ''' return GiacMethods['realroot'](self,*args) @@ -14384,10 +14384,10 @@ cdef class GiacMethods_base: Help for reciprocation: reciprocation(Crcle,Lst(Pnt,Line)) Returns the list where the points (resp lines) are replaced with their polars (resp poles) with respect to the circle C. - See also: 1/ pole 2/ polar + See also: 1/ pole 2/ polar Ex1:reciprocation(circle(0,1),[point((1+i)/2), line(1,-1+i)]) Ex2:reciprocation(circle(0,1),[line(1+i,2),point(1+i*2)]) - + ''' return GiacMethods['reciprocation'](self,*args) @@ -14396,9 +14396,9 @@ cdef class GiacMethods_base: Help for rect: rect(Expr(x)) Returns the value of the rectangle function at x. - See also: 1/ boxcar 2/ tri 3/ Heaviside + See also: 1/ boxcar 2/ tri 3/ Heaviside Ex1:rect(x/2) - + ''' return GiacMethods['rect'](self,*args) @@ -14407,12 +14407,12 @@ cdef class GiacMethods_base: Help for rectangle: rectangle(Pnt(A)||Cplx,Pnt(B)||Cplx,Real(k)||Pnt(P)||Lst(P,k),[Var(D)],[Var(C)]) Returns and draws the rectangle ABCD, AD=k*AB; if k>0 ABCD is direct else indirect (in the plane ABP AD=AP or AD=k*AB). - See also: 1/ quadrilateral 2/ square + See also: 1/ quadrilateral 2/ square Ex1:rectangle(-i,1,2) Ex2:rectangle(-i,1,-2,D,C) Ex3:rectangle(point(0,0,0),point(3,3,3),point(0,0,3),D,C) Ex4:rectangle(point(0,0,0),point(3,3,3),2,D,C) - + ''' return GiacMethods['rectangle'](self,*args) @@ -14421,14 +14421,14 @@ cdef class GiacMethods_base: Help for rectangle_droit: rectangle_droit(Opt) Option of the plotarea command and of the area command. - See also: 1/ plotarea 2/ area + See also: 1/ plotarea 2/ area Ex1: plotarea(x^2,x=0..1,5,trapezoid) Ex2: plotarea(x^2,x=0..1,5,middle_point) Ex3: plotarea(x^2,x=0..1,5,right_rectangle) Ex4: plotarea(x^2,x=0..1,5,left_rectangle) Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) - + ''' return GiacMethods['rectangle_droit'](self,*args) @@ -14437,14 +14437,14 @@ cdef class GiacMethods_base: Help for rectangle_gauche: rectangle_gauche(Opt) Option of the plotarea command and of the area command. - See also: 1/ plotarea 2/ area + See also: 1/ plotarea 2/ area Ex1: plotarea(x^2,x=0..1,5,trapezoid) Ex2: plotarea(x^2,x=0..1,5,middle_point) Ex3: plotarea(x^2,x=0..1,5,right_rectangle) Ex4: plotarea(x^2,x=0..1,5,left_rectangle) Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) - + ''' return GiacMethods['rectangle_gauche'](self,*args) @@ -14453,11 +14453,11 @@ cdef class GiacMethods_base: Help for rectangle_plein: rectangle_plein(Real(a),[Real(b)]) Draws a full direct rectangle (resp square) with sides a,b (resp a) from the turtle position and on the left (by default b=a). - See also: 1/ triangle_plein + See also: 1/ triangle_plein Ex1: rectangle_plein 20 Ex2:rectangle_plein(20) Ex3:rectangle_plein(20,40) - + ''' return GiacMethods['rectangle_plein'](self,*args) @@ -14466,10 +14466,10 @@ cdef class GiacMethods_base: Help for rectangular_coordinates: rectangular_coordinates(LstPolCoord) Returns the list of the abscissa and of the ordinate of a point given by the list of its polar coordinates. - See also: 1/ abscissa 2/ ordinate 3/ rectangular_coordinates 4/ polar_point + See also: 1/ abscissa 2/ ordinate 3/ rectangular_coordinates 4/ polar_point Ex1:rectangular_coordinates([1,pi/4]) Ex2:rectangular_coordinates(polar_point(1,pi/4)) - + ''' return GiacMethods['rectangular_coordinates'](self,*args) @@ -14478,10 +14478,10 @@ cdef class GiacMethods_base: Help for recule: recule(NULL or Real(n)) The turtle takes n steps back (by default n=10). - See also: 1/ avance 2/ saute + See also: 1/ avance 2/ saute Ex1: recule 30 Ex2:recule(30) - + ''' return GiacMethods['recule'](self,*args) @@ -14490,10 +14490,10 @@ cdef class GiacMethods_base: Help for red: red(Opt) Option of the display command to display with color. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),red) Ex2: F:=display(point(2+1.5*i),point_point+green) - + ''' return GiacMethods['red'](self,*args) @@ -14502,12 +14502,12 @@ cdef class GiacMethods_base: Help for reduced_conic: reduced_conic(Expr,[LstVar]) Returns the origin and the matrix of a base in which the conic given by its equation is reduced, 0 or 1 (0 if the conic is degenerate) and the equation of the conic in this base and also its parametric equation. - See also: 1/ gauss 2/ conic + See also: 1/ gauss 2/ conic Ex1:reduced_conic(x^2+2*x-2*y+1) Ex2:reduced_conic(a*x^2-2*x*y+a*y^2-2*x+2*y+3,[x,y]) Ex3:reduced_conic(2*u^2+2*u*v+2*v^2+5*u+3,[u,v]) Ex4:reduced_conic((x+y)^2-2*x+1,x,y) - + ''' return GiacMethods['reduced_conic'](self,*args) @@ -14516,12 +14516,12 @@ cdef class GiacMethods_base: Help for reduced_quadric: reduced_quadric(Expr, [LstVar]) Returns the origin and the matrix of a basis in which the quadric (given by its equation) is reduced, the list of its eigenvalues, the equation of the quadric in this basis and its parametric equation. - See also: 1/ gauss 2/ quadric + See also: 1/ gauss 2/ quadric Ex1:reduced_quadric(4*x^2+y^2+z^2-4*x*y+4*x*z-2*y*z+8*x-4*y+4*z+2) Ex2:reduced_quadric(x^2+3*y^2-3*z^2-8*y*z+2*z*x-4*x*y-1,x,y,z) Ex3:reduced_quadric((u+v)*(v-w)+3*u-5*v,[u,v,w]) Ex4:reduced_quadric(7*x^2+4*y^2+4*z^2+4*x*y-4*x*z-2*y*z-4*x+5*y+4*z-18,[x,y,z]) - + ''' return GiacMethods['reduced_quadric'](self,*args) @@ -14530,10 +14530,10 @@ cdef class GiacMethods_base: Help for ref: ref(Mtrx(M)) Gaussian reduction of AX=b (M=A|(-b)). - See also: 1/ rref 2/ det + See also: 1/ rref 2/ det Ex1:ref([[3,1,-2],[3,2,2]]) Ex2:ref([[2,1,1,-1],[1,1,2,-1],[1,2,1,-4]]) - + ''' return GiacMethods['ref'](self,*args) @@ -14542,11 +14542,11 @@ cdef class GiacMethods_base: Help for reflection: reflection((Pnt(A) or Line(D)),(Pnt(C) or Curve(C))) reflection(D,C) (or reflection(A,C))=symmetry of C with the symmetry-line D (or sym-point A). - See also: 1/ rotation 2/ translation + See also: 1/ rotation 2/ translation Ex1:reflection(line(0,1+i),A) Ex2:reflection(B,A) Ex3:reflection(line(0,1+i),circle(i,1+i)) - + ''' return GiacMethods['reflection'](self,*args) @@ -14555,9 +14555,9 @@ cdef class GiacMethods_base: Help for regroup: regroup(Expr) Collects terms in an expression. - See also: 1/ simplify 2/ normal + See also: 1/ simplify 2/ normal Ex1:regroup(x+3*x+5*4/x) - + ''' return GiacMethods['regroup'](self,*args) @@ -14566,9 +14566,9 @@ cdef class GiacMethods_base: Help for relabel_vertices: relabel_vertices(Graph(G),Lst(L)) Returns a copy of G with vertex labels changed to those in the list L. - See also: 1/ graph_vertices 2/ isomorphic_copy 3/ permute_vertices + See also: 1/ graph_vertices 2/ isomorphic_copy 3/ permute_vertices Ex1:relabel_vertices(graph([a,b,c]),["first","second","third"]) - + ''' return GiacMethods['relabel_vertices'](self,*args) @@ -14577,10 +14577,10 @@ cdef class GiacMethods_base: Help for reliability_polynomial: reliability_polynomial(Graph(G),[Var(p)]) Returns the reliability polynomial [or its value at point p] of undirected graph G. If G is weighted, all weights must be positive integers and are interpreted as edge multiplicities. - See also: 1/ chromatic_polynomial 2/ flow_polynomial 3/ tutte_polynomial + See also: 1/ chromatic_polynomial 2/ flow_polynomial 3/ tutte_polynomial Ex1:reliability_polynomial(graph("petersen")) Ex2:reliability_polynomial(graph("petersen"),0.5) - + ''' return GiacMethods['reliability_polynomial'](self,*args) @@ -14589,11 +14589,11 @@ cdef class GiacMethods_base: Help for rem: rem((Vect or Poly),(Vect or Poly),[Var]) Euclidean remainder of 2 polynomials. - See also: 1/ quo 2/ quorem 3/ Rem 4/ irem + See also: 1/ quo 2/ quorem 3/ Rem 4/ irem Ex1:rem([1,2,3,4],[-1,2]) Ex2:rem(x^3+2x^2+3x+4,-x+2) Ex3:rem(t^3+2t^2+3t+4,-t+2,t) - + ''' return GiacMethods['rem'](self,*args) @@ -14602,12 +14602,12 @@ cdef class GiacMethods_base: Help for remain: remain(Intg(a),Intg(b)) Euclidean remainder of 2 integers. - See also: 1/ iquo 2/ smod 3/ rem 4/ mod + See also: 1/ iquo 2/ smod 3/ rem 4/ mod Ex1:remain(125,15) Ex2:remain(125,41) Ex3:remain(-7,3) Ex4:remain(25+12*i,5+7*i) - + ''' return GiacMethods['remain'](self,*args) @@ -14616,10 +14616,10 @@ cdef class GiacMethods_base: Help for remove: remove(FncBool(f)||a,Lst(l)) Remove the occurrences a of l or the elements a such that f(a)=true. - See also: 1/ select 2/ suppress + See also: 1/ select 2/ suppress Ex1:remove(x->x>=5,[1,2,6,7]) Ex2:remove(5,[1,2,5,6,7,5]) - + ''' return GiacMethods['remove'](self,*args) @@ -14628,10 +14628,10 @@ cdef class GiacMethods_base: Help for reorder: reorder(Expr, LstVar) Reorders the variables in E according to the order of the 2nd argument. - See also: 1/ + See also: 1/ Ex1:reorder(-2) Ex2:reorder(x^2+2*x+y^2,[y,x]) - + ''' return GiacMethods['reorder'](self,*args) @@ -14640,10 +14640,10 @@ cdef class GiacMethods_base: Help for resample: resample(Lst(clip),[Intg(s),[Intg(q)]]) Returns a copy of the input audio clip resampled to the rate s (by default 44100), optionally with quality level q (from 0 to 4, by default 2). - See also: 1/ samplerate 2/ playsnd 3/ readwav 4/ writewav + See also: 1/ samplerate 2/ playsnd 3/ readwav 4/ writewav Ex1:resample(readwav("/some/file"),48000) Ex2:resample(readwav("/some/file"),48000,3) - + ''' return GiacMethods['resample'](self,*args) @@ -14652,12 +14652,12 @@ cdef class GiacMethods_base: Help for residue: residue(Expr,Var(v),Cplx(a)) Returns the residue in a of the expression with v as variable. - See also: 1/ series + See also: 1/ series Ex1:residue(1/z,z,0) Ex2:residue(5/z,z=0) Ex3:residue(cos(z)/(z*(z-b)),z,0) Ex4:residue(c/(z*(z-b)),z=b) - + ''' return GiacMethods['residue'](self,*args) @@ -14666,12 +14666,12 @@ cdef class GiacMethods_base: Help for resoudre: resoudre(Expr,[Var]) Solves a (or a set of) polynomial equation. - See also: 1/ linsolve 2/ proot 3/ fsolve 4/ csolve 5/ nSolve + See also: 1/ linsolve 2/ proot 3/ fsolve 4/ csolve 5/ nSolve Ex1:resoudre(x^2-3=1) Ex2:resoudre(x^3-3*y,y) Ex3:resoudre([y-z=0,z-x=0,x-y=0,x-1+y+z=0],[x,y,z]) Ex4:resoudre([x^2-y^2=0,x^2-z^2=0],[x,y,z]) - + ''' return GiacMethods['resoudre'](self,*args) @@ -14680,12 +14680,12 @@ cdef class GiacMethods_base: Help for resoudre_dans_C: resoudre_dans_C(LstEq,LstVar) Returns the list of complex solutions of an equation or a matrix where the rows are ℂ-solutions of a system of polynomial equations. - See also: 1/ cZeros 2/ solve 3/ fslove + See also: 1/ cZeros 2/ solve 3/ fslove Ex1:resoudre_dans_C(x^4-1,x) Ex2:resoudre_dans_C(x^4-y^4 and x+y=2,[x,y]) Ex3:resoudre_dans_C(x^4-y^4 and x+y=0 and x^2=2*x,[x,y]) Ex4:resoudre_dans_C(u*v-u=v and v^2=u,[u,v]) - + ''' return GiacMethods['resoudre_dans_C'](self,*args) @@ -14694,17 +14694,17 @@ cdef class GiacMethods_base: Help for resoudre_systeme_lineaire: resoudre_systeme_lineaire(LstLinEq,LstVar) Linear equations system solver. - See also: 1/ solve 2/ proot 3/ simult 4/ gaussjord 5/ pivot 6/ ref 7/ conjugate_gradient + See also: 1/ solve 2/ proot 3/ simult 4/ gaussjord 5/ pivot 6/ ref 7/ conjugate_gradient Ex1:resoudre_systeme_lineaire([x+y+z=1,x-y=2,2*x-z=3],[x,y,z]) Ex2:resoudre_systeme_lineaire([m*x+y=a,x+m*y=b],[x,y]) Ex3:resoudre_systeme_lineaire([x+y-z-1,x-y+1,x-y-z-1]%2,[x,y,z]) Ex4:resoudre_systeme_lineaire([[3,4],[1,2]],[0,1]) - Ex5: p,l,u:=lu([[3,4],[1,2]]); linsolve(p,l,u,[0,1]) + Ex5: p,l,u:=lu([[3,4],[1,2]]); linsolve(p,l,u,[0,1]) Ex6:resoudre_systeme_lineaire([2*x+y+z=1,x+y+2*z=1,x+2*y+z=4],[x,y,z]) Ex7:resoudre_systeme_lineaire([[2,1,1],[1,1,2],[1,2,1]],[1,1,4]) Ex8: p,l,u:=lu([[2,1,1],[1,1,2],[1,2,1]]);linsolve(p,l,u,[1,1,4]) Ex9: a:=[[100,2],[2,100]];linsolve(evalf(a),[0,1]); - + ''' return GiacMethods['resoudre_systeme_lineaire'](self,*args) @@ -14713,10 +14713,10 @@ cdef class GiacMethods_base: Help for resultant: resultant(Poly,Poly,Var) Resultant of two polynomials. - See also: 1/ sylvester 2/ gcd + See also: 1/ sylvester 2/ gcd Ex1:resultant(x^2-1,x^3-1,x) Ex2:resultant(x^3-p*x+q,3*x^2-p,x) - + ''' return GiacMethods['resultant'](self,*args) @@ -14729,7 +14729,7 @@ cdef class GiacMethods_base: Ex2: L:=[1,2,3,4];L:=revlist(L) Ex3: L:=[1,2,3,4];L.revlist() Ex4: L:=[1,2,3,4];L.reverse() - + ''' return GiacMethods['reverse'](self,*args) @@ -14738,9 +14738,9 @@ cdef class GiacMethods_base: Help for reverse_graph: reverse_graph(Graph(G)) Returns the copy of G with the directions of all edges reversed. - See also: 1/ digraph + See also: 1/ digraph Ex1:reverse_graph(digraph(%{[1,2],[1,3],[2,3]%})) - + ''' return GiacMethods['reverse_graph'](self,*args) @@ -14749,9 +14749,9 @@ cdef class GiacMethods_base: Help for reverse_rsolve: reverse_rsolve(Vect(v)) If v=[v_0 ... v_(2n-1)], returns [b_n,...,b_0] such that b_n*v_{n+k}+...+b_0*v_k=0 for k=0..n-1. - See also: 1/ rsolve + See also: 1/ rsolve Ex1:reverse_rsolve([1,-1,3,3]) - + ''' return GiacMethods['reverse_rsolve'](self,*args) @@ -14760,9 +14760,9 @@ cdef class GiacMethods_base: Help for revert: revert(Expr) Returns the inverse expansion of a series expansion at 0. - See also: 1/ series + See also: 1/ series Ex1:revert(x+x^2+x^4) - + ''' return GiacMethods['revert'](self,*args) @@ -14771,8 +14771,8 @@ cdef class GiacMethods_base: Help for revlex: revlex(Opt) Option of the gbasis or greduce command to specify an order for monomials (complete degree then inverse lexicographic order). - See also: 1/ gbasis 2/ greduce - + See also: 1/ gbasis 2/ greduce + ''' return GiacMethods['revlex'](self,*args) @@ -14785,7 +14785,7 @@ cdef class GiacMethods_base: Ex2: L:=[1,2,3,4];L:=revlist(L) Ex3: L:=[1,2,3,4];L.revlist() Ex4: L:=[1,2,3,4];L.reverse() - + ''' return GiacMethods['revlist'](self,*args) @@ -14794,14 +14794,14 @@ cdef class GiacMethods_base: Help for rgb: rgb(Opt) Option of the display (or affichage) command to defined colors RGB. - See also: 1/ display 2/ filled + See also: 1/ display 2/ filled Ex1: redcolor:=rgb(0.99,0,0);display(square(0,2+i),filled+redcolor) Ex2: greencolor:=rgb(0,0.99,0);display(square(0,2+i),filled+greencolor) Ex3: bluecolor:=rgb(0,0,0.99);display(square(0,2+i),filled+bluecolor) Ex4: greycolor:=rgb(0.5,0.5,0.5);display(square(0,2+i),filled+greycolor) Ex5: F:=display(square(0,2+i),filled+rgb(rand(),rand(),rand())) Ex6: L:=rand(),rand(),rand();affichage(square(0,2+i),rgb(L)+rempli);legend(0.2,[L]) - + ''' return GiacMethods['rgb'](self,*args) @@ -14810,13 +14810,13 @@ cdef class GiacMethods_base: Help for rhombus: rhombus(Pnt(A)||Cplx,Pnt(B)||Cplx,Angle(a)||Pnt(P)||Lst(P,a)),[Var(C)],[Var(D)]) Returns and draws the rhombus ABCD such that the angle (AB,AD)=a (or in the plane ABP angle(AB,AD)=angle(AB,AP) or such that angle(AB,AD)=a). - See also: 1/ square 2/ quadrilateral + See also: 1/ square 2/ quadrilateral Ex1:rhombus(i,1+i,pi/4) Ex2:rhombus(i,1+i,pi/4,C,D) Ex3:rhombus(point(0,0,0),point(3,3,3),[point(0,0,3),pi/4]) Ex4:rhombus(point(0,0,0),point(3,3,3),point(0,0,3),C,D) Ex5:rhombus(point(0,0,0),point(3,3,3),[point(0,0,3),pi/4],C,D) - + ''' return GiacMethods['rhombus'](self,*args) @@ -14825,10 +14825,10 @@ cdef class GiacMethods_base: Help for rhombus_point: rhombus_point(Opt) Option of the display command for a point. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) - + ''' return GiacMethods['rhombus_point'](self,*args) @@ -14837,12 +14837,12 @@ cdef class GiacMethods_base: Help for rhs: rhs(Equal(a=b) or Interval(a..b) or Str,Intg) Returns the right part of an equality, of an interval, of a list or of a string. - See also: 1/ left 2/ mid 3/ tail 4/ head + See also: 1/ left 2/ mid 3/ tail 4/ head Ex1:rhs(a=b) Ex2:rhs(x^2+1=5) Ex3:rhs(1..5) Ex4:rhs("abcdefg",3) - + ''' return GiacMethods['rhs'](self,*args) @@ -14851,9 +14851,9 @@ cdef class GiacMethods_base: Help for riemann_window: riemann_window(Lst,[Interval(n1..n2)]) Applies the Riemann windowing function to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ bartlett_hann_window 12/ triangle_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ bartlett_hann_window 12/ triangle_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(riemann_window(randvector(1000,0..1))) - + ''' return GiacMethods['riemann_window'](self,*args) @@ -14862,12 +14862,12 @@ cdef class GiacMethods_base: Help for right: right(Equal(a=b) or Interval(a..b) or Str,Intg) Returns the right part of an equality, of an interval, of a list or of a string. - See also: 1/ left 2/ mid 3/ tail 4/ head + See also: 1/ left 2/ mid 3/ tail 4/ head Ex1:right(a=b) Ex2:right(x^2+1=5) Ex3:right(1..5) Ex4:right("abcdefg",3) - + ''' return GiacMethods['right'](self,*args) @@ -14876,14 +14876,14 @@ cdef class GiacMethods_base: Help for right_rectangle: right_rectangle(Opt) Option of the plotarea command and of the area command. - See also: 1/ plotarea 2/ area + See also: 1/ plotarea 2/ area Ex1: plotarea(x^2,x=0..1,5,trapezoid) Ex2: plotarea(x^2,x=0..1,5,middle_point) Ex3: plotarea(x^2,x=0..1,5,right_rectangle) Ex4: plotarea(x^2,x=0..1,5,left_rectangle) Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) - + ''' return GiacMethods['right_rectangle'](self,*args) @@ -14892,13 +14892,13 @@ cdef class GiacMethods_base: Help for right_triangle: right_triangle((Pnt(A) or Cplx),(Pnt(B) or Cplx),(Real(k) or Pnt(P) or Lst(P,k)),[Var(C)]) Draws the A_rectangular triangle ABC with AC=k*AB (or in the plane ABP AC=AP or AC=k*AB). - See also: 1/ triangle + See also: 1/ triangle Ex1:right_triangle(1,i,tan(pi/3)) Ex2:right_triangle(1,i,1/2,C) Ex3:right_triangle(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:right_triangle(point(0,0,0),point(3,3,3),[point(0,0,3),1/2],C) Ex5:right_triangle(point(0,0,0),point(3,3,3),[point(0,0,3),1/2],C) - + ''' return GiacMethods['right_triangle'](self,*args) @@ -14907,11 +14907,11 @@ cdef class GiacMethods_base: Help for risch: risch(Expr,[Var]) Returns a primitive of the expression calculated with the Risch algorithm. - See also: 1/ int + See also: 1/ int Ex1:risch(ln(x),x) Ex2:risch(ln(x)) Ex3:risch(exp(x^2),x) - + ''' return GiacMethods['risch'](self,*args) @@ -14920,9 +14920,9 @@ cdef class GiacMethods_base: Help for rm_a_z: rm_a_z(NULL) Erases all the variable name made up of only one lowercase a..z character. - See also: 1/ rm_all_vars + See also: 1/ rm_all_vars Ex1:rm_a_z() - + ''' return GiacMethods['rm_a_z'](self,*args) @@ -14931,9 +14931,9 @@ cdef class GiacMethods_base: Help for rm_all_vars: rm_all_vars(NULL) Erases all the variable names. - See also: 1/ rm_a_z + See also: 1/ rm_a_z Ex1:rm_all_vars() - + ''' return GiacMethods['rm_all_vars'](self,*args) @@ -14942,9 +14942,9 @@ cdef class GiacMethods_base: Help for rmbreakpoint: rmbreakpoint(Intg) Removes a breakpoint. - See also: 1/ breakpoint + See also: 1/ breakpoint Ex1:rmbreakpoint(1) - + ''' return GiacMethods['rmbreakpoint'](self,*args) @@ -14953,9 +14953,9 @@ cdef class GiacMethods_base: Help for rmmod: rmmod(Str(pwd)) Removes the installed dynamic libraries. - See also: 1/ lsmod 2/ insmod + See also: 1/ lsmod 2/ insmod Ex1:rmmod("/home/parisse/giac/src/libprogfr.so") - + ''' return GiacMethods['rmmod'](self,*args) @@ -14964,9 +14964,9 @@ cdef class GiacMethods_base: Help for rmwatch: rmwatch(Var) Clears a variables from the table of displayed variables in step/step. - See also: 1/ watch + See also: 1/ watch Ex1:rmwatch(a) - + ''' return GiacMethods['rmwatch'](self,*args) @@ -14975,11 +14975,11 @@ cdef class GiacMethods_base: Help for romberg: romberg(Expr(f(x)),Var(x),Real(a),Real(b)) Returns the approximate value of integrate(f(x),x,a,b) by Romberg's method. - See also: 1/ integrate 2/ gaussquad + See also: 1/ integrate 2/ gaussquad Ex1:romberg(exp(x^2),x,0,1) Ex2:romberg(x^2,x,0,1) Ex3:romberg(exp(-x^2),x,-1,1) - + ''' return GiacMethods['romberg'](self,*args) @@ -14988,12 +14988,12 @@ cdef class GiacMethods_base: Help for rombergm: rombergm(Opt) Option of the area command. - See also: 1/ area + See also: 1/ area Ex1: area(x^2,x=0..1,5,simpson) Ex2: area(x^2,x=0..1,5,rombergt) Ex3: area(x^2,x=0..1,5,rombergm) Ex4:rombergm(area(x^2,x=0..1,5,gauss15)) - + ''' return GiacMethods['rombergm'](self,*args) @@ -15002,12 +15002,12 @@ cdef class GiacMethods_base: Help for rombergt: rombergt(Opt) Option of the area command. - See also: 1/ area + See also: 1/ area Ex1: area(x^2,x=0..1,5,simpson) Ex2: area(x^2,x=0..1,5,rombergt) Ex3: area(x^2,x=0..1,5,rombergm) Ex4:rombergt(area(x^2,x=0..1,5,gauss15)) - + ''' return GiacMethods['rombergt'](self,*args) @@ -15016,12 +15016,12 @@ cdef class GiacMethods_base: Help for rond: rond(Real(r),[Real(a)],[Real(b)]) Draws a circle (resp a arc) with radius r (resp and with angle (0,a) or (a,b)), tangent at the turtle position. - See also: 1/ disque + See also: 1/ disque Ex1: rond 30 Ex2:rond(40) Ex3:rond(40,90) Ex4:rond(40,10,100) - + ''' return GiacMethods['rond'](self,*args) @@ -15030,12 +15030,12 @@ cdef class GiacMethods_base: Help for root: root(Expr(a),Expr(b)) Returns b^(1/a) (root(2,3)=sqrt(3)). - See also: 1/ + See also: 1/ Ex1:root(3,2) Ex2:root(1/3,2) Ex3:root(3,1.2) Ex4:root(3.2,1.2) - + ''' return GiacMethods['root'](self,*args) @@ -15044,11 +15044,11 @@ cdef class GiacMethods_base: Help for rootof: rootof(LstPoly(P),LstPoly(Q)) Polynomial in terms of a root of an irreducible polynomial on Q. Returns P(a) with a the greatest root of Q. - See also: 1/ + See also: 1/ Ex1: normal(1/rootof([1,0],[1,0,10,0,1])) Ex2: normal(1/rootof([1,0,0],[1,1,0,-1])) - Ex3: rootof(x^4+x+1):='j'; normal(j^5); - + Ex3: rootof(x^4+x+1):='j'; normal(j^5); + ''' return GiacMethods['rootof'](self,*args) @@ -15057,10 +15057,10 @@ cdef class GiacMethods_base: Help for roots: roots(Poly,[Var]) Returns a matrix having 2 columns and where the rows are the roots of the polynomial with their multiplicity (for 1 variable). - See also: 1/ proot 2/ cZeros + See also: 1/ proot 2/ cZeros Ex1:roots(t^3-1,t) Ex2:roots(x^5-2*x^4+x^3) - + ''' return GiacMethods['roots'](self,*args) @@ -15069,7 +15069,7 @@ cdef class GiacMethods_base: Help for rotate: rotate(Lst||Str(L),[Intg(n)]) Returns the list where the last element [or the tail beginning with the n-th element] is moved to the first element (by default n=-1);L:=rotate(L,n) or L.rotate(n). - See also: 1/ tail 2/ mid 3/ shift + See also: 1/ tail 2/ mid 3/ shift Ex1:rotate([0,1,2,3],2) Ex2:rotate([[1,2,3],[4,5,6],[7,8,9]]) Ex3:rotate([0,1,2,3,4]) @@ -15078,7 +15078,7 @@ cdef class GiacMethods_base: Ex6: L:=[0,1,2,3,4];L.rotate() Ex7: L:=[0,1,2,3];L:=rotate([0,1,2,3],2) Ex8: L:=[0,1,2,3];L.rotate(2) - + ''' return GiacMethods['rotate'](self,*args) @@ -15087,13 +15087,13 @@ cdef class GiacMethods_base: Help for rotation: rotation((Pnt(B) or Cplx or Dr3),Angle(a1),(Pnt(A) or Curve)) rotation(B,a1,A) (resp rotation(d,a1,A)) is the transformation of A by rotation with center B (resp of axis d) and angle a1. - See also: 1/ translation 2/ reflection + See also: 1/ translation 2/ reflection Ex1:rotation(point(1+i),pi/2,point(i)) Ex2:rotation(1+i,pi/3,line(i,1)) Ex3:rotation(line(x=y,y=z),pi/2,point(1,-1,2)) Ex4: r:=rotation(1+i,pi/2);r(i) Ex5: r:=rotation(line(x=y,y=z),pi/2);r(point(1,-1,2)) - + ''' return GiacMethods['rotation'](self,*args) @@ -15102,13 +15102,13 @@ cdef class GiacMethods_base: Help for round: round(Real or Cplx,[Intg(n)]) Rounds the real or complex to the nearest integer (resp the nearest decimal number) or to the nearest element of ℤ[i], (resp with n decimals). - See also: 1/ floor 2/ ceil + See also: 1/ floor 2/ ceil Ex1:round(2.5) Ex2:round(-2.4) Ex3:round(-2.5+i*2.4) Ex4:round(1.237,2) Ex5:round(sqrt(2)+i*sqrt(5),4) - + ''' return GiacMethods['round'](self,*args) @@ -15117,11 +15117,11 @@ cdef class GiacMethods_base: Help for row: row(Mtrx(A),Intg(n)||Interval(n1..n2)) Returns row n or the sequence of the rows n1..n2 of the matrix A, or optional argument of count,count_eq,count_inf,count_sup. - See also: 1/ col 2/ count 3/ count_eq 4/ count_inf 5/ count_sup + See also: 1/ col 2/ count 3/ count_eq 4/ count_inf 5/ count_sup Ex1:row([[1,2,3],[4,5,6],[7,8,9]],1) Ex2:row([[1,2,3],[4,5,6],[7,8,9]],0..1) Ex3: count_eq(3,[[1,2,3],[4,3,2],[3,2,1]],row) - + ''' return GiacMethods['row'](self,*args) @@ -15130,9 +15130,9 @@ cdef class GiacMethods_base: Help for rowAdd: rowAdd(Mtrx(A),Intg(n1),Intg(n2)) Returns the matrix obtained from A by replacing the n2-th row by the sum of the n1-th and n2-th rows. - See also: 1/ rowSwap + See also: 1/ rowSwap Ex1:rowAdd([[1,2],[3,4],[5,6]],1,2) - + ''' return GiacMethods['rowAdd'](self,*args) @@ -15141,10 +15141,10 @@ cdef class GiacMethods_base: Help for rowDim: rowDim(Mtrx) Number of rows of a matrix. - See also: 1/ ncols + See also: 1/ ncols Ex1:rowDim([[1,2,3],[4,5,6]]) Ex2:rowDim([[1,2],[3,4],[5,6]]) - + ''' return GiacMethods['rowDim'](self,*args) @@ -15153,10 +15153,10 @@ cdef class GiacMethods_base: Help for rowNorm: rowNorm(Vect or Mtrx) Returns the max of the l1_norm of the rows of a matrix: rowNorm(a_{j,k})=max_j(sum_k(|a_{j,k}|)). - See also: 1/ norm + See also: 1/ norm Ex1:rowNorm([[1,2],[3,-4]]) Ex2:rowNorm([[1,2,3,-4],[-5,3,2,1]]) - + ''' return GiacMethods['rowNorm'](self,*args) @@ -15165,9 +15165,9 @@ cdef class GiacMethods_base: Help for rowSwap: rowSwap(Mtrx(A),Intg(n1),Intg(n2)) Returns the matrix obtained from A by swapping the n1-th row and the n2-th row. - See also: 1/ rowAdd 2/ colSwap + See also: 1/ rowAdd 2/ colSwap Ex1:rowSwap([[1,2],[3,4],[5,6]],1,2) - + ''' return GiacMethods['rowSwap'](self,*args) @@ -15176,10 +15176,10 @@ cdef class GiacMethods_base: Help for rowdim: rowdim(Mtrx) Number of rows of a matrix. - See also: 1/ ncols + See also: 1/ ncols Ex1:rowdim([[1,2,3],[4,5,6]]) Ex2:rowdim([[1,2],[3,4],[5,6]]) - + ''' return GiacMethods['rowdim'](self,*args) @@ -15188,10 +15188,10 @@ cdef class GiacMethods_base: Help for rownorm: rownorm(Vect or Mtrx) Returns the max of the l1_norm of the rows of a matrix: rowNorm(a_{j,k})=max_j(sum_k(|a_{j,k}|)). - See also: 1/ norm + See also: 1/ norm Ex1:rownorm([[1,2],[3,-4]]) Ex2:rownorm([[1,2,3,-4],[-5,3,2,1]]) - + ''' return GiacMethods['rownorm'](self,*args) @@ -15200,10 +15200,10 @@ cdef class GiacMethods_base: Help for rowspace: rowspace(Mtrx(A), [Var(d)]) Returns a matrix where the rows are a basis of the vector space generated by the rows of the matrix A [d is the dimension of this space]. - See also: 1/ colspace + See also: 1/ colspace Ex1:rowspace([[1,2,3],[1,2,3],[1,2,4],[1,2,5]]) Ex2:rowspace([[1,2,3],[1,3,6],[2,5,9]],d) - + ''' return GiacMethods['rowspace'](self,*args) @@ -15212,9 +15212,9 @@ cdef class GiacMethods_base: Help for rowswap: rowswap(Mtrx(A),Intg(n1),Intg(n2)) Returns the matrix obtained from A by swapping the n1-th row and the n2-th row. - See also: 1/ rowAdd 2/ colSwap + See also: 1/ rowAdd 2/ colSwap Ex1:rowswap([[1,2],[3,4],[5,6]],1,2) - + ''' return GiacMethods['rowswap'](self,*args) @@ -15223,12 +15223,12 @@ cdef class GiacMethods_base: Help for rref: rref(Mtrx(M),[Intg(k)]||Opt) Row reduction to echelon form of AX=b (M=A|(-b)) [Reduction on columns 0..k-1]. - See also: 1/ ker 2/ image 3/ det 4/ Rref 5/ pivot 6/ ref 7/ keep_pivot + See also: 1/ ker 2/ image 3/ det 4/ Rref 5/ pivot 6/ ref 7/ keep_pivot Ex1:rref([[3,1,-2],[3,2,2]]) Ex2:rref([[2,1,1,-1],[1,1,2,-1],[1,2,1,-4]]) Ex3:rref([[2,1,1,-1],[1,1,2,-1],[1,2,1,-4]],2) Ex4:rref([[1,1,0,0,-a1],[0,1,1,0,-a2],[0,0,1,1,-a3],[1,0,0,1,-a4]],keep_pivot) - + ''' return GiacMethods['rref'](self,*args) @@ -15237,13 +15237,13 @@ cdef class GiacMethods_base: Help for rsolve: rsolve((Expr or LstExpr),(Var or LstVar),(InitVal or LstInitVal)) Gives the value of a recurrent sequence or of a system of recurrent sequences. - See also: 1/ seqsolve 2/ plotseq 3/ tableseq 4/ reverse_rsolve + See also: 1/ seqsolve 2/ plotseq 3/ tableseq 4/ reverse_rsolve Ex1:rsolve(u(n+1)=2*u(n)+n,u(n),u(0)=1) Ex2:rsolve(u(n+1)=2*u(n)+n,u(n),u(1)^2=1) Ex3:rsolve(u(n+1)=(u(n)-1)/(u(n)-2),u(n),u(0)=4) Ex4:rsolve(u(n+2)=u(n)+2*u(n+1)+n+1,u(n),[u(0)=0,u(1)=1]) Ex5:rsolve([u(n+1)=3*v(n)+u(n),v(n+1)=v(n)+u(n)],[u(n),v(n)],[u(0)=1,v(0)=2]) - + ''' return GiacMethods['rsolve'](self,*args) @@ -15252,10 +15252,10 @@ cdef class GiacMethods_base: Help for same: same(Expr,Expr) Equality test. - See also: 1/ + See also: 1/ Ex1:same(a,b) Ex2:same((2-1)^2,2^2-2*2+1) - + ''' return GiacMethods['same'](self,*args) @@ -15264,14 +15264,14 @@ cdef class GiacMethods_base: Help for sample: sample(Lst(L),Intg(n)) sample(L,n)= rand(n,L)=list of the n extracted elements of L without replacement. - See also: 1/ rand + See also: 1/ rand Ex1:sample([1,2,3,4,5,6],6) Ex2:sample([1,2,3,4,5,6],3) Ex3:sample(["r","r","r","b","n"],3) Ex4: L:=[1,2,3,4,5,6];L:=sample(L,3) Ex5: L:=[1,2,3,4,5,6];L.sample(3) - Ex6: - + Ex6: + ''' return GiacMethods['sample'](self,*args) @@ -15280,9 +15280,9 @@ cdef class GiacMethods_base: Help for samplerate: samplerate(Lst(clip)) Returns the sampling rate of an audio clip, in Hertz. - See also: 1/ bit_depth 2/ channels 3/ channel_data 4/ duration + See also: 1/ bit_depth 2/ channels 3/ channel_data 4/ duration Ex1:samplerate(readwav("/some/file")) - + ''' return GiacMethods['samplerate'](self,*args) @@ -15291,13 +15291,13 @@ cdef class GiacMethods_base: Help for sans_factoriser: sans_factoriser(Opt.) Option of the plotimplicit command. - See also: 1/ plotimplicit + See also: 1/ plotimplicit Ex1: plotimplicit(x^2+y^2-1,x,y,unfactored) Ex2: plotimplicit(x^2+y^2-1,[x,y],unfactored) Ex3: plotimplicit(x^2+y^2+z^2-1,x,y,z,xstep=0.2,ystep=0.2,zstep=0.2,unfactored) Ex4: plotimplicit(x^2+y^2+z^2-1,[x,y,z],xstep=0.2,ystep=0.2,zstep=0.2,unfactored) Ex5: plotimplicit(x^2+y^2+z^2-1,x=0..1,y=0..1,z=0..1,xstep=0.2,ystep=0.2,zstep=0.2,unfactored) - + ''' return GiacMethods['sans_factoriser'](self,*args) @@ -15306,10 +15306,10 @@ cdef class GiacMethods_base: Help for saute: saute(NULL or Real(n)) The turtle takes n steps forward without traces (by default n=10). - See also: 1/ avance 2/ recule + See also: 1/ avance 2/ recule Ex1: saute 30 Ex2:saute(30) - + ''' return GiacMethods['saute'](self,*args) @@ -15318,11 +15318,11 @@ cdef class GiacMethods_base: Help for scalarProduct: scalarProduct(Vect(v1),Vect(v2)) Scalar product. - See also: 1/ * 2/ cross 3/ .* 4/ hadamard + See also: 1/ * 2/ cross 3/ .* 4/ hadamard Ex1:scalarProduct([1,2],[3,4]) Ex2:scalarProduct([3,2,4],[3,2,4]) Ex3:scalarProduct([[1,2],[3,4]],[[3,2],[4,5]]) - + ''' return GiacMethods['scalarProduct'](self,*args) @@ -15331,11 +15331,11 @@ cdef class GiacMethods_base: Help for scalar_product: scalar_product(Vect(v1),Vect(v2)) Scalar product. - See also: 1/ * 2/ cross 3/ .* 4/ hadamard + See also: 1/ * 2/ cross 3/ .* 4/ hadamard Ex1:scalar_product([1,2],[3,4]) Ex2:scalar_product([3,2,4],[3,2,4]) Ex3:scalar_product([[1,2],[3,4]],[[3,2],[4,5]]) - + ''' return GiacMethods['scalar_product'](self,*args) @@ -15344,9 +15344,9 @@ cdef class GiacMethods_base: Help for scatterplot: scatterplot(Mtrx) Draws for k=0..nrows, the points (xk,yk) where xk=element row k column 0 and yk=element row k column j (j=1..ncols). - See also: 1/ polygonplot 2/ polygonscatterplot 3/ listplot + See also: 1/ polygonplot 2/ polygonscatterplot 3/ listplot Ex1:scatterplot([[1,2,3],[2,0,1],[-1,2,3]]) - + ''' return GiacMethods['scatterplot'](self,*args) @@ -15355,10 +15355,10 @@ cdef class GiacMethods_base: Help for schur: schur(Mtrx(A)) Matrix reduction to Hessenberg form. Returns [P,B] such that B=inv(P)*A*P:SCHUR(A)=hessenberg(A,-1). - See also: 1/ hessenberg + See also: 1/ hessenberg Ex1:schur([[1,2,3],[4,5,6],[7,8,1]]) Ex2:schur([[1,2,3,4],[4,5,6,7],[7,8,9,0],[0,1,2,3]]) - + ''' return GiacMethods['schur'](self,*args) @@ -15367,9 +15367,9 @@ cdef class GiacMethods_base: Help for sec: sec(Expr) Secant: sec(x)=1/cos(x). - See also: 1/ cos 2/ asec + See also: 1/ cos 2/ asec Ex1:sec(pi/3) - + ''' return GiacMethods['sec'](self,*args) @@ -15378,14 +15378,14 @@ cdef class GiacMethods_base: Help for secant_solver: secant_solver(Opt) Argument for fsolve giving the method for solving a numerical equation. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve(cos(x)=x,x,0..1,bisection_solver) Ex2: fsolve(cos(x)=x,x,0..1,brent_solver) Ex3: fsolve(cos(x)=x,x,0..1,falsepos_solver) Ex4: fsolve(cos(x)=x,x,0,newton_solver) Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) - + ''' return GiacMethods['secant_solver'](self,*args) @@ -15394,7 +15394,7 @@ cdef class GiacMethods_base: Help for segment: segment((Pnt or Cplx or Lst([xM,yM])),(Pnt or Cplx or Lst([xN,yN]),[Var],[Var] or Opt) segment(A,B) draws the segment AB and segment([xM,yM],[xN,yN]) draws the vector as origin [xM,yM], of coordinates [xN,yN] (i.e draws segment(M,point(M+N)) or Option of the arc command. - See also: 1/ line 2/ arc + See also: 1/ line 2/ arc Ex1:segment(i,1+i) Ex2:segment(point(i),point(1+i)) Ex3:segment(point(i),point(1+i),A,B) @@ -15402,7 +15402,7 @@ cdef class GiacMethods_base: Ex5:segment([-1,0],point([-1,0]+[2,1])) Ex6: arc(i,1,pi/4,segment) Ex7: affichage( arc(i,1,pi/4,segment),1+rempli) - + ''' return GiacMethods['segment'](self,*args) @@ -15411,9 +15411,9 @@ cdef class GiacMethods_base: Help for seidel_spectrum: seidel_spectrum(Graph(G)) Returns the Seidel spectrum of G as a list of lists with two elements, each containing an eigenvalue and its multiplicity. - See also: 1/ graph_spectrum + See also: 1/ graph_spectrum Ex1:seidel_spectrum(graph("clebsch")) - + ''' return GiacMethods['seidel_spectrum'](self,*args) @@ -15422,9 +15422,9 @@ cdef class GiacMethods_base: Help for seidel_switch: seidel_switch(Graph(G),Lst(V)) Returns a copy of G in which the edges between vertices in list V and vertices not in V are inverted (replaced with a set of edges from V to other vertices which are not present in G). - See also: 1/ neighbors 2/ graph_complement + See also: 1/ neighbors 2/ graph_complement Ex1:seidel_switch(cycle_graph(5),[1,2]) - + ''' return GiacMethods['seidel_switch'](self,*args) @@ -15433,10 +15433,10 @@ cdef class GiacMethods_base: Help for select: select(FncBool(f),Lst(l)) Selects the elements e of l such that f(e)=true. - See also: 1/ remove 2/ range + See also: 1/ remove 2/ range Ex1:select(x->x>=5,[1,2,6,7]) Ex2:select(x->isprime(x),range(20)).^2 - + ''' return GiacMethods['select'](self,*args) @@ -15445,9 +15445,9 @@ cdef class GiacMethods_base: Help for semi_augment: semi_augment(Mtrx(A),Mtrx(B)) Returns a matrix made with A and B, with n1+n2 rows and p columns if dim(A)=[n1,p] and dim(B)=[n2,p]. - See also: 1/ augment + See also: 1/ augment Ex1:semi_augment([[68,-21],[56,59],[1,2]],[[68,-21],[56,59]]) - + ''' return GiacMethods['semi_augment'](self,*args) @@ -15455,8 +15455,8 @@ cdef class GiacMethods_base: r'''From Giac's documentation: Help for seq: seq(Expr(Xpr),Var(Var)=Int(a..b),[Real(p)]||Expr(Xpr),Var(Var),Real(a),Real(b),[Real(p)]) - Returns the sequence (2 or 3 arg) or the list (4 or 5 arg) obtained when var goes from a to b (step p) in Xpr (or the Xpr is repeated n times or returns the sequence of reals from a to b (step p)). And also seq(expression,variable,list) is equivalent to map(list,unapply(expression,variable)) - See also: 1/ $ 2/ makelist 3/ range 4/ map 5/ unapply + Returns the sequence (2 or 3 arg) or the list (4 or 5 arg) obtained when var goes from a to b (step p) in Xpr (or the Xpr is repeated n times or returns the sequence of reals from a to b (step p)). And also seq(expression,variable,list) is equivalent to map(list,unapply(expression,variable)) + See also: 1/ $ 2/ makelist 3/ range 4/ map 5/ unapply Ex1:seq(0.3,4) Ex2:seq(t,4) Ex3:seq(0,0) @@ -15466,9 +15466,9 @@ cdef class GiacMethods_base: Ex7:seq(2^k,k,0,8) Ex8:seq(2^k,k,0,8,2) Ex9:seq(x^3,x,[1,2,3]) - Ex10: [seq(0.3..2,0.2)] + Ex10: [seq(0.3..2,0.2)] Ex11: a:=(1,2,3);eval(seq(a,4)) - + ''' return GiacMethods['seq'](self,*args) @@ -15477,11 +15477,11 @@ cdef class GiacMethods_base: Help for seqplot: seqplot(Expr(f(Var)),Var=[a,xm,xM],Intg(p)) For seeing the pth terms of the sequence u(0)=a,u(n)=f(u(n-1)). - See also: 1/ seqsolve 2/ rsolve + See also: 1/ seqsolve 2/ rsolve Ex1:seqplot(sqrt(2+x),6,5) Ex2:seqplot(sqrt(2+t),t=6,5) Ex3:seqplot(sqrt(2+x),x=[6,1,7],5,affichage=epaisseur_ligne_2) - + ''' return GiacMethods['seqplot'](self,*args) @@ -15490,14 +15490,14 @@ cdef class GiacMethods_base: Help for seqsolve: seqsolve((Expr or LstExpr),(Var or LstVar),(InitVal or LstInitVal)) Gives the value of a recurrent sequence (u_{n+1}=f(u_n) or u_{n+k}=f(u_n,u_{n+1}...u_{n+k-1})) or of a system of recurrent sequences. - See also: 1/ rsolve 2/ plotseq 3/ tableseq + See also: 1/ rsolve 2/ plotseq 3/ tableseq Ex1:seqsolve(2x+n,[x,n],1) Ex2:seqsolve(2x+n*3^n,[x,n],1) Ex3:seqsolve(x+y,[x,y,n],[1,1]) Ex4:seqsolve(x+2*y+n+1,[x,y,n],[0,1]) Ex5:seqsolve([x+2*y,n+1+x],[x,y,n],[0,1]) Ex6:seqsolve([x+2*y+n+1,x],[x,y,n],[0,1]) - + ''' return GiacMethods['seqsolve'](self,*args) @@ -15506,9 +15506,9 @@ cdef class GiacMethods_base: Help for sequence_graph: sequence_graph(Lst(L)) Returns an undirected graph with the degree sequence equal to the list L. - See also: 1/ degree_sequence 2/ is_graphic_sequence + See also: 1/ degree_sequence 2/ is_graphic_sequence Ex1:sequence_graph(degree_sequence(sequence_graph([3,2,4,2,3,4,5,7]))) - + ''' return GiacMethods['sequence_graph'](self,*args) @@ -15517,13 +15517,13 @@ cdef class GiacMethods_base: Help for series: series(Expr,Equal(var=limit_point),[Order],[Dir(1,0,-1)]) Series expansion at finite or infinite points. - See also: 1/ limit 2/ taylor 3/ pad 4/ polynom 5/ truncate + See also: 1/ limit 2/ taylor 3/ pad 4/ polynom 5/ truncate Ex1:series(sin(x)/x,x=0) Ex2:series(sin(x),x=0,6,polynom) Ex3:series(ln(x+x^2)-ln(x),x=0,1) Ex4:series((x^4+x+2)/(x^2+1),x=0,5) Ex5: series("h",8); ln(1+h); - Ex6:series(1/(1+x+y),[x,y],[0,0],5) + Ex6:series(1/(1+x+y),[x,y],[0,0],5) Ex7:series(sin(x*y),[x,y],[1,pi/2],3) Ex8:series(sin((1+h*t)*(pi/2+k*t)),t=0,3,polynom)(t=1) Ex9:series(y^2/x^3,[x,y],[1,-1],3) @@ -15531,7 +15531,7 @@ cdef class GiacMethods_base: Ex11:series(subst(sin(x+y)+cos(y*x),[x,y],h*[x,y]),h=0,6,polynom) Ex12:series(subst(sin(x+y)+cos(y*x),[x,y],h*[x,y]),h=0,6,polynom)(h=1) Ex13: truncate(series(sin(x),x=0,6),6) - + ''' return GiacMethods['series'](self,*args) @@ -15540,9 +15540,9 @@ cdef class GiacMethods_base: Help for set_edge_attribute: set_edge_attribute(Graph(G),Edge(e),Seq(tag1=value1,tag2=value2,..)) Stores the attributes to edge e and returns the modified copy of G. - See also: 1/ discard_edge_attribute 2/ get_edge_attribute 3/ list_edge_attributes + See also: 1/ discard_edge_attribute 2/ get_edge_attribute 3/ list_edge_attributes Ex1:set_edge_attribute(cycle_graph(3),[1,2],"cost"=12.4) - + ''' return GiacMethods['set_edge_attribute'](self,*args) @@ -15551,9 +15551,9 @@ cdef class GiacMethods_base: Help for set_edge_weight: set_edge_weight(Graph(G),Edge(e),Real(w)) Sets the weight of the edge e in the weighted graph G to w and returns the modified copy of G. - See also: 1/ is_weighted 2/ get_edge_weight 3/ make_weighted 4/ weight_matrix + See also: 1/ is_weighted 2/ get_edge_weight 3/ make_weighted 4/ weight_matrix Ex1:set_edge_weight(graph(%{[1,2],[2,3]%}),[1,2],5) - + ''' return GiacMethods['set_edge_weight'](self,*args) @@ -15562,9 +15562,9 @@ cdef class GiacMethods_base: Help for set_graph_attribute: set_graph_attribute(Graph(G),Seq(tag1=value1,tag2=value2,..)) Stores the attributes where each tag is a string, and returns the modified copy of G. - See also: 1/ discard_graph_attribute 2/ get_graph_attribute 3/ list_graph_attributes + See also: 1/ discard_graph_attribute 2/ get_graph_attribute 3/ list_graph_attributes Ex1:set_graph_attribute(cycle_graph(3),"name"="cycle graph") - + ''' return GiacMethods['set_graph_attribute'](self,*args) @@ -15573,9 +15573,9 @@ cdef class GiacMethods_base: Help for set_pixel: set_pixel(Intg(x),Intg(y),Intg(col)) Pixel on and adds to the list of pixels. Run show_pixels() to display - See also: 1/ clear 2/ show_pixels 3/ draw_line 4/ draw_rectangle 5/ draw_polygon + See also: 1/ clear 2/ show_pixels 3/ draw_line 4/ draw_rectangle 5/ draw_polygon Ex1: clear(); set_pixel(4); draw_pixel(1,2,red); show_pixels(); - + ''' return GiacMethods['set_pixel'](self,*args) @@ -15584,9 +15584,9 @@ cdef class GiacMethods_base: Help for set_vertex_attribute: set_vertex_attribute(Graph(G),Vrtx(v),Seq(tag1=value1,tag2=value2,..)) Stores the attributes to vertex v and returns the modified copy of G. - See also: 1/ discard_vertex_attribute 2/ get_vertex_attribute 3/ list_vertex_attributes + See also: 1/ discard_vertex_attribute 2/ get_vertex_attribute 3/ list_vertex_attributes Ex1:set_vertex_attribute(cycle_graph(3),1,"supply"=27) - + ''' return GiacMethods['set_vertex_attribute'](self,*args) @@ -15595,9 +15595,9 @@ cdef class GiacMethods_base: Help for set_vertex_positions: set_vertex_positions(Graph(G),Lst(vp)) Sets the coordinates, given in the list vp, to the vertices of G and returns the modified copy of G. - See also: 1/ draw_graph + See also: 1/ draw_graph Ex1: G:=graph([1,2,3,4,5,6],%{[1,2],[1,4],[4,5],[2,5],[2,3],[3,6],[5,6]%}); G:=set_vertex_positions(G,[[0,0],[0.5,0],[1,0],[0,0.5],[0.5,0.5],[1,0.5]]) - + ''' return GiacMethods['set_vertex_positions'](self,*args) @@ -15606,13 +15606,13 @@ cdef class GiacMethods_base: Help for shift: shift(Lst,[Intg(n)]) Returns the list where the last element [or the tail beginning with the n-th element] is moved to the first element and then completed with 0s (by default n=-1);L:=shift(L,2) o L.shift(2). - See also: 1/ rotate 2/ tail + See also: 1/ rotate 2/ tail Ex1:shift([0,1,2,3],2) Ex2:shift([0,1,2,3]) Ex3:shift([0,1,2,3,4]) Ex4: L:=[0,1,2,3];L:=shift(L,2) Ex5: L:=[0,1,2,3];L.shift(2) - + ''' return GiacMethods['shift'](self,*args) @@ -15621,14 +15621,14 @@ cdef class GiacMethods_base: Help for shift_phase: shift_phase(Expr) shift_phase returns the expressions where the phase of the evaluated trigonometric expressions is increased by pi/2. - See also: 1/ series + See also: 1/ series Ex1:shift_phase(sin(x)) Ex2:shift_phase('sin(x+pi/2)') Ex3:shift_phase(x+sin(x)) Ex4:shift_phase(x+sin(x)) Ex5:shift_phase(cos(t)) Ex6:shift_phase(tan(u)) - + ''' return GiacMethods['shift_phase'](self,*args) @@ -15637,9 +15637,9 @@ cdef class GiacMethods_base: Help for shortest_path: shortest_path(Graph(G),Vrtx(s),Vrtx(t)||Lst(T)) Returns the shortest path from vertex s to vertex t in G. If such path does not exist, returns an empty list. If vector T of vertices from G is given, the list of shortest paths from s to each t int T is returned. - See also: 1/ dijkstra 2/ vertex_distance + See also: 1/ dijkstra 2/ vertex_distance Ex1:shortest_path(cycle_graph(6),1,5) - + ''' return GiacMethods['shortest_path'](self,*args) @@ -15648,9 +15648,9 @@ cdef class GiacMethods_base: Help for show_pixels: show_pixels(NULL) Displays the list of pixels. - See also: 1/ set_pixel 2/ clear + See also: 1/ set_pixel 2/ clear Ex1:show_pixels() - + ''' return GiacMethods['show_pixels'](self,*args) @@ -15659,13 +15659,13 @@ cdef class GiacMethods_base: Help for shuffle: shuffle(Intg(n)||Lst(L)) Returns a random permutation of [0,1,2,..,n-1] or of the list L. - See also: 1/ permu2cycles 2/ is_permu 3/ permu2mat + See also: 1/ permu2cycles 2/ is_permu 3/ permu2mat Ex1:shuffle(4) Ex2:shuffle(7) Ex3:shuffle([1,3,5,7,9]) Ex4: L:=[1,3,5,7,9];L:=randperm(L) Ex5: L:=[1,3,5,7,9];L.randperm() - + ''' return GiacMethods['shuffle'](self,*args) @@ -15674,13 +15674,13 @@ cdef class GiacMethods_base: Help for sierpinski_graph: sierpinski_graph(Intg(n),Intg(k),[triangle]) Returns Sierpiński (triangle) graph S(n,k) (resp. ST(n,k)). - See also: 1/ graph + See also: 1/ graph Ex1:sierpinski_graph(2,4) Ex2:sierpinski_graph(4,3) Ex3:sierpinski_graph(3,4) Ex4:sierpinski_graph(3,2) Ex5:sierpinski_graph(3,3,at_triangle) - + ''' return GiacMethods['sierpinski_graph'](self,*args) @@ -15689,10 +15689,10 @@ cdef class GiacMethods_base: Help for sign: sign(Expr) Returns the sign (-1,0,+1) of its argument. - See also: 1/ abs + See also: 1/ abs Ex1:sign(-4) Ex2:sign(4-5) - + ''' return GiacMethods['sign'](self,*args) @@ -15701,9 +15701,9 @@ cdef class GiacMethods_base: Help for signature: signature(Permut) Returns the signature of a permutation. - See also: 1/ permu2cycles 2/ is_permu + See also: 1/ permu2cycles 2/ is_permu Ex1:signature([1,0,3,4,2]) - + ''' return GiacMethods['signature'](self,*args) @@ -15712,10 +15712,10 @@ cdef class GiacMethods_base: Help for signe: signe(Str(s)) Writes the string s with the font 20 at the point [10,10]. - See also: 1/ ecris + See also: 1/ ecris Ex1:signe("Thomas") Ex2:signe(Thomas) - + ''' return GiacMethods['signe'](self,*args) @@ -15724,12 +15724,12 @@ cdef class GiacMethods_base: Help for similarity: similarity(Pnt or Dr3,Real,Angle,Pnt) similarity(B,k,a1,A)=transformation of A in the similarity (center B or axis d, coeff k,angle a1) (or also homothety(B,k*exp(i*a1),A)). - See also: 1/ homothety + See also: 1/ homothety Ex1:similarity(1+i,2,pi/3,i) Ex2:similarity(line(x=y,y=z),2,pi/3,point(-1,2,1)) Ex3: s:=similarity(1+i,2,pi/3);s(i) Ex4: s:=similarity(line(x=y,y=z),2,pi/3),s(point(-1,2,1)) - + ''' return GiacMethods['similarity'](self,*args) @@ -15738,10 +15738,10 @@ cdef class GiacMethods_base: Help for simp2: simp2(Intg(A) or Poly(A),Intg(B) or Poly(B)) Returns the list [A/gcd(A,B),B/gcd(A,B)]. - See also: 1/ gcd + See also: 1/ gcd Ex1:simp2(12,18) Ex2:simp2(x^3-1,x^2-1) - + ''' return GiacMethods['simp2'](self,*args) @@ -15755,7 +15755,7 @@ cdef class GiacMethods_base: Ex3:simplex_reduce([[-3,2],[1,1]],[3,4],[1,2]) Ex4:simplex_reduce([[-3,2,1,0,3],[1,1,0,1,4],[-1,-2,0,0,0]]) Ex5:simplex_reduce([[2,1,1,1,0,0,2],[1,2,3,0,1,0,5],[2,2,1,0,0,1,6],[-3,-1,-3,1,-1,2,0]]) - + ''' return GiacMethods['simplex_reduce'](self,*args) @@ -15764,11 +15764,11 @@ cdef class GiacMethods_base: Help for simplifier: simplifier(Expr) Simplifies an expression. - See also: 1/ normal + See also: 1/ normal Ex1:simplifier(4*atan(1/5)-atan(1/239)) Ex2:simplifier(texpand((sin(3*x)+sin(7*x))/sin(5*x))) Ex3:simplifier(texpand((cos(3*x)+cos(7*x))/cos(5*x))) - + ''' return GiacMethods['simplifier'](self,*args) @@ -15777,11 +15777,11 @@ cdef class GiacMethods_base: Help for simplify: simplify(Expr) Simplifies an expression. - See also: 1/ normal + See also: 1/ normal Ex1:simplify(4*atan(1/5)-atan(1/239)) Ex2:simplify(texpand((sin(3*x)+sin(7*x))/sin(5*x))) Ex3:simplify(texpand((cos(3*x)+cos(7*x))/cos(5*x))) - + ''' return GiacMethods['simplify'](self,*args) @@ -15790,12 +15790,12 @@ cdef class GiacMethods_base: Help for simpson: simpson(Opt) Option of the area command. - See also: 1/ area + See also: 1/ area Ex1: area(x^2,x=0..1,5,simpson) Ex2: area(x^2,x=0..1,5,rombergt) Ex3: area(x^2,x=0..1,5,rombergm) Ex4:simpson(area(x^2,x=0..1,5,gauss15)) - + ''' return GiacMethods['simpson'](self,*args) @@ -15804,10 +15804,10 @@ cdef class GiacMethods_base: Help for simult: simult(Mtrx(A),Mtrx(B)) Returns the matrix where the column of index k is solution of A*X=column of index k of B (=B[0..nr-1,k..k] with nr=number of rows of B). - See also: 1/ rref 2/ linsolve + See also: 1/ rref 2/ linsolve Ex1:simult([[3,1],[3,2]],[[-2],[2]]) Ex2:simult([[3,1],[3,2]],[[-2,1],[2,-1]]) - + ''' return GiacMethods['simult'](self,*args) @@ -15816,10 +15816,10 @@ cdef class GiacMethods_base: Help for sin: sin(Expr or Opt) Sine or option of the convert or convertir command (id trigsin). - See also: 1/ asin 2/ convert 3/ trigsin + See also: 1/ asin 2/ convert 3/ trigsin Ex1:sin(0) Ex2: convert(cos(x)^4+sin(x)^2,sin) - + ''' return GiacMethods['sin'](self,*args) @@ -15828,9 +15828,9 @@ cdef class GiacMethods_base: Help for sin2costan: sin2costan(Expr) Replaces sin(x) by cos(x)*tan(x) in the argument. - See also: 1/ tan2sincos 2/ cos2sintan 3/ tan2sincos2 4/ tan2cossin2 + See also: 1/ tan2sincos 2/ cos2sintan 3/ tan2sincos2 4/ tan2cossin2 Ex1:sin2costan(sin(x)) - + ''' return GiacMethods['sin2costan'](self,*args) @@ -15839,9 +15839,9 @@ cdef class GiacMethods_base: Help for sinc: sinc(Expr(x)) Returns the value of the cardinal sine function at x. - See also: 1/ sin + See also: 1/ sin Ex1:sinc(pi*x) - + ''' return GiacMethods['sinc'](self,*args) @@ -15850,11 +15850,11 @@ cdef class GiacMethods_base: Help for sincos: sincos(Expr or Opt) Transforms the complex exponential into sine and cosine (id exp2trig) or option of the convert or convertir command (id sincos). - See also: 1/ trig2trig 2/ trig2exp 3/ atrig2ln 4/ convert + See also: 1/ trig2trig 2/ trig2exp 3/ atrig2ln 4/ convert Ex1:sincos(exp(i*x)) Ex2:sincos(exp(-i*x)) Ex3: convert(exp(i*x),sincos) - + ''' return GiacMethods['sincos'](self,*args) @@ -15863,7 +15863,7 @@ cdef class GiacMethods_base: Help for single_inter: single_inter(Curve,Curve,[Pnt(A)||LstPnt(L)]) Gives one of the points of intersection of 2 curves or surfaces (or the intersection near A or not in L). - See also: 1/ intersect 2/ head + See also: 1/ intersect 2/ head Ex1:single_inter(line(i,1-i),line(0,1)) Ex2:single_inter(line(i,1-i),circle(0,1)) Ex3:single_inter(line(i,1+2*i),circle(0,1),[point(i)]) @@ -15871,7 +15871,7 @@ cdef class GiacMethods_base: Ex5:single_inter(circle(1,sqrt(2)),circle(0,1)) Ex6:single_inter(plane(x=y),plane(y=z)) Ex7:single_inter(line(x=y+1,y=2*z),plane(y=z)) - + ''' return GiacMethods['single_inter'](self,*args) @@ -15880,9 +15880,9 @@ cdef class GiacMethods_base: Help for sinh: sinh(Expr) Hyperbolic sine. - See also: 1/ asinh + See also: 1/ asinh Ex1:sinh(0) - + ''' return GiacMethods['sinh'](self,*args) @@ -15891,9 +15891,9 @@ cdef class GiacMethods_base: Help for sizes: sizes(Lst or Str or Seq) Returns the list of sizes of a list of lists. - See also: 1/ size 2/ dim + See also: 1/ size 2/ dim Ex1:sizes([[1,2,3],[1,2],[1]]) - + ''' return GiacMethods['sizes'](self,*args) @@ -15902,7 +15902,7 @@ cdef class GiacMethods_base: Help for slope: slope(Line||Pnt||Cplx,[Pnt||Cplx]) Returns the slope of the line defined in the argument or is an attribute of line. - See also: 1/ line 2/ tangent 3/ LinTan 4/ slopeatraw 5/ slopeat + See also: 1/ line 2/ tangent 3/ LinTan 4/ slopeatraw 5/ slopeat Ex1:slope(line(1,2i)) Ex2:slope(segment(1,2i)) Ex3:slope(1,2i) @@ -15911,7 +15911,7 @@ cdef class GiacMethods_base: Ex6:slope(tangent(plotfunc(sin(x)),pi/4)) Ex7:slope(LineTan(sin(x),pi/4)) Ex8: line(point(1,2),slope=-1) - + ''' return GiacMethods['slope'](self,*args) @@ -15920,11 +15920,11 @@ cdef class GiacMethods_base: Help for slopeat: slopeat(Line, Pnt||Cplx(z0)) slopeat(d,z0) displays at the point(z0), with a legend, the value of the slope of the line or segment d. - See also: 1/ slope 2/ slopeatraw + See also: 1/ slope 2/ slopeatraw Ex1: A:=point(0);B:=point(1+i);slopeat(droite(A,B),(1+i)/2) Ex2: s:=segment(1-i,i);slopeat(s,point(0.4)) Ex3: t:=tangent(plotfunc(sin(x)),pi/4);slopeat(t,0) - + ''' return GiacMethods['slopeat'](self,*args) @@ -15933,12 +15933,12 @@ cdef class GiacMethods_base: Help for slopeatraw: slopeatraw(Line, Pnt||Cplx(z0)) slopeatraw(d,z0) displays at point(z0), the value of the slope of the line or segment d. - See also: 1/ slope 2/ slopeat + See also: 1/ slope 2/ slopeat Ex1: A:=point(0);B:=point(1+i);slopeatraw(droite(A,B),(1+i)/2) Ex2: s:=segment(1-i,i);slopeatraw(s,point(0.4)) Ex3:slopeatraw(tangent(plotfunc(sin(x)),pi/4),0) Ex4:slopeatraw((LineTan sin(x),pi/4),i) - + ''' return GiacMethods['slopeatraw'](self,*args) @@ -15947,10 +15947,10 @@ cdef class GiacMethods_base: Help for smith: smith(Mtrx(A)) Smith normal form of a matrix with polynomial coefficients : returns U,D,V such that U and V are invertible, D is diagonal, and U*A*V=D. - See also: 1/ hermite 2/ ismith 3/ ihermite + See also: 1/ hermite 2/ ismith 3/ ihermite Ex1: n:=10; A:=ranm(n,n) % 17; U,D,V:=smith(x*idn(n)-A);normal(U*(x*idn(n)-A)*V-D); diag(D); Ex2: GF(3,5,g); n:=3; A:=ranm(n,n,g); U,D,V:=smith(x*idn(n)-A);normal(U*(x*idn(n)-A)*V-D); diag(D); - + ''' return GiacMethods['smith'](self,*args) @@ -15959,11 +15959,11 @@ cdef class GiacMethods_base: Help for smod: smod(Intg,Intg) Returns the Euclidean symmetric remainder of two integers. - See also: 1/ irem 2/ iquo 3/ mod 4/ fracmod + See also: 1/ irem 2/ iquo 3/ mod 4/ fracmod Ex1:smod(8,3) Ex2:smod(10,4) Ex3:smod(11,7) - + ''' return GiacMethods['smod'](self,*args) @@ -15972,12 +15972,12 @@ cdef class GiacMethods_base: Help for snedecor: snedecor(Intg(n),Intg(m),Real(x0)) Returns the probability density of the Fisher-Snedecor law (n and m are the numbers of degrees of freedom). - See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm + See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm Ex1:snedecor(4,10,2.1) Ex2:snedecor(4,4,2.1) Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) - + ''' return GiacMethods['snedecor'](self,*args) @@ -15986,10 +15986,10 @@ cdef class GiacMethods_base: Help for snedecor_cdf: snedecor_cdf(Intg(n),Intg(m),Real(x0)) Returns the probability that a Fisher-Snedecor random variable is less than x0 (n and m are the numbers of degrees of freedom). - See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd + See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd Ex1:snedecor_cdf(4,4,2.1) Ex2:snedecor_cdf(4,10,3.5) - + ''' return GiacMethods['snedecor_cdf'](self,*args) @@ -15998,10 +15998,10 @@ cdef class GiacMethods_base: Help for snedecor_icdf: snedecor_icdf(Intg(n),Intg(m),Real(p)) Returns h such as the probability that a Fisher-Snedecor random variable is less than h is p (n and m are the numbers of degrees of freedom and 0<=p<=1). - See also: 1/ fisher_cdf 2/ fisherd + See also: 1/ fisher_cdf 2/ fisherd Ex1:snedecor_icdf(4,10,0.95) Ex2:snedecor_icdf(4,10,0.05) - + ''' return GiacMethods['snedecor_icdf'](self,*args) @@ -16010,12 +16010,12 @@ cdef class GiacMethods_base: Help for snedecord: snedecord(Intg(n),Intg(m),Real(x0)) Returns the probability density of the Fisher-Snedecor law (n and m are the numbers of degrees of freedom). - See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm + See also: 1/ fisher_cdf 2/ fisher_icdf 3/ randvector 4/ ranm Ex1:snedecord(4,10,2.1) Ex2:snedecord(4,4,2.1) Ex3: randvector(5,fisher,4,6) Ex4: ranm(2,3,fisher,4,6) - + ''' return GiacMethods['snedecord'](self,*args) @@ -16024,10 +16024,10 @@ cdef class GiacMethods_base: Help for snedecord_cdf: snedecord_cdf(Intg(n),Intg(m),Real(x0)) Returns the probability that a Fisher-Snedecor random variable is less than x0 (n and m are the numbers of degrees of freedom). - See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd + See also: 1/ UTPF 2/ fisher_icdf 3/ fisherd Ex1:snedecord_cdf(4,4,2.1) Ex2:snedecord_cdf(4,10,3.5) - + ''' return GiacMethods['snedecord_cdf'](self,*args) @@ -16036,10 +16036,10 @@ cdef class GiacMethods_base: Help for snedecord_icdf: snedecord_icdf(Intg(n),Intg(m),Real(p)) Returns h such as the probability that a Fisher-Snedecor random variable is less than h is p (n and m are the numbers of degrees of freedom and 0<=p<=1). - See also: 1/ fisher_cdf 2/ fisherd + See also: 1/ fisher_cdf 2/ fisherd Ex1:snedecord_icdf(4,10,0.95) Ex2:snedecord_icdf(4,10,0.05) - + ''' return GiacMethods['snedecord_icdf'](self,*args) @@ -16048,10 +16048,10 @@ cdef class GiacMethods_base: Help for solid_line: solid_line(Opt) Option of the display command for a line. - See also: 1/ display + See also: 1/ display Ex1: display(line(y=x),green+dash_line+line_width_2) Ex2: d:=display(line(2+i,1),cap_round_line) - + ''' return GiacMethods['solid_line'](self,*args) @@ -16060,12 +16060,12 @@ cdef class GiacMethods_base: Help for solve: solve(Expr,[Var]) Solves a (or a set of) polynomial equation. - See also: 1/ linsolve 2/ proot 3/ fsolve 4/ csolve 5/ nSolve + See also: 1/ linsolve 2/ proot 3/ fsolve 4/ csolve 5/ nSolve Ex1:solve(x^2-3=1) Ex2:solve(x^3-3*y,y) Ex3:solve([y-z=0,z-x=0,x-y=0,x-1+y+z=0],[x,y,z]) Ex4:solve([x^2-y^2=0,x^2-z^2=0],[x,y,z]) - + ''' return GiacMethods['solve'](self,*args) @@ -16074,7 +16074,7 @@ cdef class GiacMethods_base: Help for somme: somme(Expr,Var,VarMin(a),VarMax(b),[VarStep(p)]) Discrete sum (with 2 or 4 arguments return then sum from a to b if a<=b or of the opposite of the sum from b+1 to a-1 if a>b+1 or 0 if a=b+1) or the discrete primitive or sum of the elements of a list or a sequence. - See also: 1/ + + See also: 1/ + Ex1:somme(1/n^2,n,1,17) Ex2:somme(1/n^2,n=1..17) Ex3:somme(1/n^2,n,17,1) @@ -16085,7 +16085,7 @@ cdef class GiacMethods_base: Ex8:somme([[1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9]]) Ex9:somme(1/(x*(x+1)),x) Ex10:somme(cos(n*x),n) - + ''' return GiacMethods['somme'](self,*args) @@ -16094,10 +16094,10 @@ cdef class GiacMethods_base: Help for sommet: sommet(Op or Fnct) Returns the top of an operator. - See also: 1/ feuille 2/ quote + See also: 1/ feuille 2/ quote Ex1:sommet(quote(gcd(45,123))) Ex2:sommet('gcd(45,123)') - + ''' return GiacMethods['sommet'](self,*args) @@ -16106,13 +16106,13 @@ cdef class GiacMethods_base: Help for sort: sort(LstReal or Seq [Fnc]) Returns the sorted list (or sequence) with increasing order according to the second argument which defines a weak strict ordering or sorts and collects equal terms in sums and products. - See also: 1/ SortA 2/ SortD + See also: 1/ SortA 2/ SortD Ex1:sort([3,2,2,4,1,0]) Ex2:sort(3,2.1,2,4,1,0) Ex3:sort([3,4,2],(x,y)->x>y) Ex4:sort([[1,2],[2,3],[4,3]],(x,y)->when(x[1]==y[1],x[0]>y[0],x[1]>y[1])) Ex5:sort(y*x*2+x*y) - + ''' return GiacMethods['sort'](self,*args) @@ -16121,11 +16121,11 @@ cdef class GiacMethods_base: Help for sorta: sorta(LstReal||Seq×||Mtrx) Sorts the list in increasing order or sorts the columns of the matrix so the first row is in increasing order. - See also: 1/ SortA 2/ sortd 3/ sort + See also: 1/ SortA 2/ sortd 3/ sort Ex1:sorta(3,4,2) Ex2:sorta([3,4,2]) Ex3:sorta([[3,4,2],[6,4,5]]) - + ''' return GiacMethods['sorta'](self,*args) @@ -16134,11 +16134,11 @@ cdef class GiacMethods_base: Help for sortd: sortd(LstReal||Seq||Mtrx) Sorts the list in decreasing order or sorts the columns of the matrix so the first row is in decreasing order. - See also: 1/ SortD 2/ sorta 3/ sort + See also: 1/ SortD 2/ sorta 3/ sort Ex1:sortd(3,4,2) Ex2:sortd([3,4,2]) Ex3:sortd([[3,4,2],[6,4,5]]) - + ''' return GiacMethods['sortd'](self,*args) @@ -16147,13 +16147,13 @@ cdef class GiacMethods_base: Help for sorted: sorted(LstReal or Seq [Fnc]) Returns the sorted list (or sequence) with increasing order according to the second argument which defines a weak strict ordering or sorts and collects equal terms in sums and products. - See also: 1/ SortA 2/ SortD + See also: 1/ SortA 2/ SortD Ex1:sorted([3,2,2,4,1,0]) Ex2:sorted(3,2.1,2,4,1,0) Ex3:sorted([3,4,2],(x,y)->x>y) Ex4:sorted([[1,2],[2,3],[4,3]],(x,y)->when(x[1]==y[1],x[0]>y[0],x[1]>y[1])) Ex5:sorted(y*x*2+x*y) - + ''' return GiacMethods['sorted'](self,*args) @@ -16162,10 +16162,10 @@ cdef class GiacMethods_base: Help for soundsec: soundsec(Intg(n),[Intg(N)]) Generates a vector coding n seconds of time/N (default N=44100). - See also: 1/ readwav 2/ writewav 3/ playsnd + See also: 1/ readwav 2/ writewav 3/ playsnd Ex1:soundsec(1) Ex2:soundsec(1,22100) - + ''' return GiacMethods['soundsec'](self,*args) @@ -16174,10 +16174,10 @@ cdef class GiacMethods_base: Help for spanning_tree: spanning_tree(Graph(G),[Vrtx(r)]) Returns a spanning tree of undirected graph G [with the vertex r as the root node]. - See also: 1/ number_of_spanning_trees 2/ minimal_spanning_tree + See also: 1/ number_of_spanning_trees 2/ minimal_spanning_tree Ex1:spanning_tree(graph("petersen")) Ex2:spanning_tree(graph("petersen"),5) - + ''' return GiacMethods['spanning_tree'](self,*args) @@ -16186,10 +16186,10 @@ cdef class GiacMethods_base: Help for sphere: sphere((Pnt or Vect),(Pnt or Real)) sphere(A,B) (resp sphere(A,r)) draws the sphere with diameter AB (resp center A and radius r) in 3D space. - See also: 1/ circle + See also: 1/ circle Ex1:sphere([0,0,0],[2,2,2]) Ex2:sphere([1,1,1],1) - + ''' return GiacMethods['sphere'](self,*args) @@ -16198,9 +16198,9 @@ cdef class GiacMethods_base: Help for spline: spline(Lst(lx),Lst(ly),Var(x),Intg(d)) Natural spline through the points given by the lx and ly lists, variable x, degree d. - See also: 1/ lagrange + See also: 1/ lagrange Ex1:spline([0,1,2],[1,3,0],x,3) - + ''' return GiacMethods['spline'](self,*args) @@ -16209,10 +16209,10 @@ cdef class GiacMethods_base: Help for split: split(Expr(Xpr),Lst(var1,var2)) Splits the two variables var1,var2 of the expression Xpr (without denominator) or returns [0]. - See also: 1/ factor + See also: 1/ factor Ex1:split(x^3*y^2-y^2+x^3-1,[x,y]) Ex2:split(x^3*y^2-y^2+x^3+1,[x,y]) - + ''' return GiacMethods['split'](self,*args) @@ -16221,8 +16221,8 @@ cdef class GiacMethods_base: Help for spring: spring(Opt) Option for the draw_graph command. - See also: 1/ planar 2/ tree 3/ draw_graph - + See also: 1/ planar 2/ tree 3/ draw_graph + ''' return GiacMethods['spring'](self,*args) @@ -16231,10 +16231,10 @@ cdef class GiacMethods_base: Help for sq: sq(Seq) Is the name of the function (ℝ^n -> ℝ)=sum of the squares of the arguments. - See also: 1/ sqrt + See also: 1/ sqrt Ex1:sq(5) Ex2:sq(1,2,3) - + ''' return GiacMethods['sq'](self,*args) @@ -16243,10 +16243,10 @@ cdef class GiacMethods_base: Help for sqrfree: sqrfree(Expr) Factorization of the its argument gathering the terms with the same exponent. - See also: 1/ factor + See also: 1/ factor Ex1:sqrfree(x^4-2*x^2+1) Ex2:sqrfree((x-2)^7*(x+2)^7*(x^4-2*x^2+1)) - + ''' return GiacMethods['sqrfree'](self,*args) @@ -16255,10 +16255,10 @@ cdef class GiacMethods_base: Help for sqrt: sqrt(Expr) Square root. - See also: 1/ surd 2/ ^ + See also: 1/ surd 2/ ^ Ex1:sqrt(50) Ex2:sqrt(x^2) - + ''' return GiacMethods['sqrt'](self,*args) @@ -16267,12 +16267,12 @@ cdef class GiacMethods_base: Help for square: square((Pnt(A) or Cplx),(Pnt(B) or Cplx),[Pnt(P),Var(C),Var(D)]) Returns and draws the square of side AB (ABCD is direct) (in the plane ABP). - See also: 1/ rhombus 2/ quadrilateral + See also: 1/ rhombus 2/ quadrilateral Ex1:square(i,1+i) Ex2:square(i,1+i,C,D) Ex3:square(point(0,0,0),point(3,3,3),point(0,0,3)) Ex4:square(point(0,0,0),point(3,3,3),point(0,0,3),C,D) - + ''' return GiacMethods['square'](self,*args) @@ -16281,10 +16281,10 @@ cdef class GiacMethods_base: Help for square_point: square_point(Opt) Option of the display command for a point. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) - + ''' return GiacMethods['square_point'](self,*args) @@ -16293,10 +16293,10 @@ cdef class GiacMethods_base: Help for srand: srand() srand returns an integer and initializes the sequence of random numbers. - See also: 1/ RandSeed + See also: 1/ RandSeed Ex1:srand(12) Ex2: srand - + ''' return GiacMethods['srand'](self,*args) @@ -16305,9 +16305,9 @@ cdef class GiacMethods_base: Help for sst: sst(NULL) Steps 1 instruction. - See also: 1/ + See also: 1/ Ex1:sst() - + ''' return GiacMethods['sst'](self,*args) @@ -16316,9 +16316,9 @@ cdef class GiacMethods_base: Help for sst_in: sst_in(NULL) Enters into a function in step-by-step mode. - See also: 1/ + See also: 1/ Ex1:sst_in() - + ''' return GiacMethods['sst_in'](self,*args) @@ -16327,9 +16327,9 @@ cdef class GiacMethods_base: Help for st_ordering: st_ordering(Graph(G),Vrtx(s),Vrtx(t)) Returns ST numbering for the biconnected graph G with source s and sink (target) t. - See also: 1/ is_biconnected + See also: 1/ is_biconnected Ex1:st_ordering(graph("petersen"),1,2) - + ''' return GiacMethods['st_ordering'](self,*args) @@ -16338,9 +16338,9 @@ cdef class GiacMethods_base: Help for star_graph: star_graph(Intg(n)) Returns the complete bipartite graph complete_graph(1,n). - See also: 1/ complete_graph 2/ wheel_graph + See also: 1/ complete_graph 2/ wheel_graph Ex1:star_graph(5) - + ''' return GiacMethods['star_graph'](self,*args) @@ -16349,10 +16349,10 @@ cdef class GiacMethods_base: Help for star_point: star_point(Opt) Option of the display command for a point. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) - + ''' return GiacMethods['star_point'](self,*args) @@ -16361,11 +16361,11 @@ cdef class GiacMethods_base: Help for stdDev: stdDev(Lst||Mtrx,[Lst]) Returns an unbiased estimate of the population standard deviation of the sample (first argument) with an optional list of weight as second argument. - See also: 1/ mean 2/ stddev + See also: 1/ mean 2/ stddev Ex1:stdDev([1,2,3]) Ex2:stdDev([1,2,3],[1,2,1]) Ex3:stdDev([[1,2,3],[5,6,7]]) - + ''' return GiacMethods['stdDev'](self,*args) @@ -16374,11 +16374,11 @@ cdef class GiacMethods_base: Help for stddev: stddev(Lst||Mtrx,[Lst]) Returns the standard deviation of the elements of its argument with an optional second argument as weight or the list of standard deviations of the columns of a matrix. - See also: 1/ mean 2/ variance 3/ stddevp + See also: 1/ mean 2/ variance 3/ stddevp Ex1:stddev([1,2,3]) Ex2:stddev([1,2,3],[1,2,1]) Ex3:stddev([[1,2,3],[5,6,7]]) - + ''' return GiacMethods['stddev'](self,*args) @@ -16387,11 +16387,11 @@ cdef class GiacMethods_base: Help for stddevp: stddevp(Lst||Mtrx,[Lst]) Returns an unbiased estimate of the population standard deviation of the sample (first argument) with an optional list of weight as second argument. - See also: 1/ mean 2/ stddev + See also: 1/ mean 2/ stddev Ex1:stddevp([1,2,3]) Ex2:stddevp([1,2,3],[1,2,1]) Ex3:stddevp([[1,2,3],[5,6,7]]) - + ''' return GiacMethods['stddevp'](self,*args) @@ -16400,14 +16400,14 @@ cdef class GiacMethods_base: Help for steffenson_solver: steffenson_solver(Opt) Argument for fsolve giving the method for solving a numerical equation. - See also: 1/ fsolve + See also: 1/ fsolve Ex1: fsolve(cos(x)=x,x,0..1,bisection_solver) Ex2: fsolve(cos(x)=x,x,0..1,brent_solver) Ex3: fsolve(cos(x)=x,x,0..1,falsepos_solver) Ex4: fsolve(cos(x)=x,x,0,newton_solver) Ex5: fsolve(cos(x)=x,x,0,secant_solver) Ex6: fsolve(cos(x)=x,x,0,steffenson_solver) - + ''' return GiacMethods['steffenson_solver'](self,*args) @@ -16416,9 +16416,9 @@ cdef class GiacMethods_base: Help for stereo2mono: stereo2mono(Lst(clip)) Returns an audio clip with all channels in the input clip downmixed to a single one. - See also: 1/ channel_data 2/ mean 3/ createwav + See also: 1/ channel_data 2/ mean 3/ createwav Ex1:stereo2mono(readwav("/some/file")) - + ''' return GiacMethods['stereo2mono'](self,*args) @@ -16427,12 +16427,12 @@ cdef class GiacMethods_base: Help for str: str(Expr or Opt) Returns the evaluated expression as a string or is an option of the convert or convertir command (id string). - See also: 1/ expr 2/ format 3/ convert + See also: 1/ expr 2/ format 3/ convert Ex1:str(1.23) Ex2:str(a:=12) Ex3:str(quote(a:=12)) Ex4: convert(quote(a:=12),string) - + ''' return GiacMethods['str'](self,*args) @@ -16441,9 +16441,9 @@ cdef class GiacMethods_base: Help for strongly_connected_components: strongly_connected_components(Graph(G)) Returns the list of strongly connected components in digraph G. - See also: 1/ connected_components 2/ is_connected 3/ is_strongly_connected + See also: 1/ connected_components 2/ is_connected 3/ is_strongly_connected Ex1:strongly_connected_components(digraph([1,2,3],%{[1,2],[1,3],[2,3],[3,2]%})) - + ''' return GiacMethods['strongly_connected_components'](self,*args) @@ -16452,10 +16452,10 @@ cdef class GiacMethods_base: Help for student: student(Intg(n),Real(x0)) Returns the probability density of the Student law (n is the number of degrees of freedom). - See also: 1/ student_cdf 2/ student_icdf + See also: 1/ student_cdf 2/ student_icdf Ex1:student(3,5.2) Ex2:student(1,5.2) - + ''' return GiacMethods['student'](self,*args) @@ -16464,10 +16464,10 @@ cdef class GiacMethods_base: Help for student_cdf: student_cdf(Intg(n),Real(x0)) Returns the probability that a Student random variable is less than x0 (n is the number of degrees of freedom). - See also: 1/ UTPT 2/ student_icdf 3/ studentd + See also: 1/ UTPT 2/ student_icdf 3/ studentd Ex1:student_cdf(3,2.35) Ex2:student_cdf(3,-3.2) - + ''' return GiacMethods['student_cdf'](self,*args) @@ -16476,10 +16476,10 @@ cdef class GiacMethods_base: Help for student_icdf: student_icdf(Intg(n),Real(p)) Returns h such as the probability that a Student random variable is less than h is p (n is the number of degrees of freedom and 0<=p<=1). - See also: 1/ student_cdf 2/ studentd + See also: 1/ student_cdf 2/ studentd Ex1:student_icdf(3,0.95) Ex2:student_icdf(3,0.05) - + ''' return GiacMethods['student_icdf'](self,*args) @@ -16488,10 +16488,10 @@ cdef class GiacMethods_base: Help for studentd: studentd(Intg(n),Real(x0)) Returns the probability density of the Student law (n is the number of degrees of freedom). - See also: 1/ student_cdf 2/ student_icdf + See also: 1/ student_cdf 2/ student_icdf Ex1:studentd(3,5.2) Ex2:studentd(1,5.2) - + ''' return GiacMethods['studentd'](self,*args) @@ -16500,10 +16500,10 @@ cdef class GiacMethods_base: Help for studentt: studentt(Lst,Real,[Real],Fnc,[Real]) T-Test/Student law: arg1=[success,trial] or [mean,sample size] or data, arg2=proportion or data, arg3 optional if data=sigma, arg4 alternative '!=' or '>' or '<', arg5 optional alpha confidence level. - See also: 1/ normalt 2/ chisquaret 3/ kolmogorovt + See also: 1/ normalt 2/ chisquaret 3/ kolmogorovt Ex1:studentt([10,20],.5,.02,'!=',0.1) Ex2:studentt([0.48,20],0.5,0.1,'<') - + ''' return GiacMethods['studentt'](self,*args) @@ -16512,13 +16512,13 @@ cdef class GiacMethods_base: Help for sturm: sturm(Poly,[Var],[Cplx(a)],[Cplx(b)]) Sturm sequence corresponding to a polynomial or number of sign changes of this polynomial in ]a;b]. - See also: 1/ sturmseq 2/ sturmab + See also: 1/ sturmseq 2/ sturmab Ex1:sturm(x^3-1,x) Ex2:sturm(x^5-x^3,x) Ex3:sturm((x^5-x^3)/(x+2),x) Ex4:sturm(x^5-x^3,x,-2,5) Ex5:sturm(x^3-1,x,-2-i,5+3i) - + ''' return GiacMethods['sturm'](self,*args) @@ -16527,10 +16527,10 @@ cdef class GiacMethods_base: Help for sturmab: sturmab(Poly,Var,Cplx(a),Cplx(b)) Number of sign changes of a polynomial in ]a;b] or of complex roots in a..b if a or b is non-real. - See also: 1/ sturm 2/ sturmseq 3/ realroot + See also: 1/ sturm 2/ sturmseq 3/ realroot Ex1:sturmab(x^3-1,x,-2,5) Ex2:sturmab(x^3-1,x,-2-i,5+3i) - + ''' return GiacMethods['sturmab'](self,*args) @@ -16539,11 +16539,11 @@ cdef class GiacMethods_base: Help for sturmseq: sturmseq(Poly,[Var]) Sturm sequence corresponding to a polynomial or to a rational fraction. - See also: 1/ sturm 2/ sturmab + See also: 1/ sturm 2/ sturmab Ex1:sturmseq(x^3-1,x) Ex2:sturmseq(x^5-x^3,x) Ex3:sturmseq((x^5-x^3)/(x+2),x) - + ''' return GiacMethods['sturmseq'](self,*args) @@ -16552,10 +16552,10 @@ cdef class GiacMethods_base: Help for style: style(Opt) Local option (Maple compatibility) of a graphic command to plot a line with dots with style=point. - See also: 1/ line_width + See also: 1/ line_width Ex1: segment(0,point(1,1),style=point) Ex2: line(y=x,style=point,display=green+line_width_2) - + ''' return GiacMethods['style'](self,*args) @@ -16564,9 +16564,9 @@ cdef class GiacMethods_base: Help for subMat: subMat(Mtrx(A),Intg(n1),Intg(n2),Intg(n3),Intg(n4).) Extracts a sub matrix with first element=A[n1,n2] and last element=A[n3,n4]. - See also: 1/ mid + See also: 1/ mid Ex1:subMat([[1,2],[3,4],[5,6]],1,0,2,1) - + ''' return GiacMethods['subMat'](self,*args) @@ -16575,9 +16575,9 @@ cdef class GiacMethods_base: Help for subdivide_edges: subdivide_edges(Graph(G),Lst(E),[Intg(r)]) Inserts r (by default 1) new vertices to each edge/arc in G contained in the list E (which may be a single edge/arc) and returns the modified copy of G. New vertices are labelled with smallest available integers. - See also: 1/ edges + See also: 1/ edges Ex1:subdivide_edges(complete_graph(2,3),[[1,3],[1,4]],2) - + ''' return GiacMethods['subdivide_edges'](self,*args) @@ -16586,9 +16586,9 @@ cdef class GiacMethods_base: Help for subgraph: subgraph(Graph(G),Lst(E)) Returns the subgraph of G defined by the edges in list E. - See also: 1/ induced_subgraph 2/ highlight_subgraph + See also: 1/ induced_subgraph 2/ highlight_subgraph Ex1:subgraph(complete_graph(5),[[1,2],[2,3],[3,4],[4,1]]) - + ''' return GiacMethods['subgraph'](self,*args) @@ -16597,11 +16597,11 @@ cdef class GiacMethods_base: Help for subs: subs(Expr or Var=value,Var=value or Expr) Equivalent of subst except in maple_mode where the arguments are switched over, in maple_mode choose the second example. - See also: 1/ subst 2/ maple_mode 3/ algsubs 4/ () + See also: 1/ subst 2/ maple_mode 3/ algsubs 4/ () Ex1:subs(1/(4+x^2),x=2) Ex2:subs(x=2,1/(4+x^2)) Ex3: f:=1/(4+x^2);f(x=2) - + ''' return GiacMethods['subs'](self,*args) @@ -16614,7 +16614,7 @@ cdef class GiacMethods_base: Ex2:subsop([[1,2],[3,4]],[1,1]=5) Ex3:subsop([[1,2],[3,4]],1=[10,8]) Ex4:subsop([0,1,2,3],'1=NULL') - + ''' return GiacMethods['subsop'](self,*args) @@ -16623,7 +16623,7 @@ cdef class GiacMethods_base: Help for subst: subst(Expr,Var(v)=value(a)) Substitutes a value for a variable in an expression. - See also: 1/ eval 2/ algsubs 3/ subs 4/ () + See also: 1/ eval 2/ algsubs 3/ subs 4/ () Ex1:subst(1/(4+x^2),x=2) Ex2:subst(1/(x^2+y^2),x=2,y=3) Ex3:subst(1/(x^2+y^2+z^2),[x=2,y=3,z=1]) @@ -16631,7 +16631,7 @@ cdef class GiacMethods_base: Ex5:subst('integrate(sin(x^2)*x,x)',x=sqrt(t)) Ex6:subst('sum(x^(n+1)/((n+p+1)*(n+1)),n,0,inf)',n=k-1) Ex7: f:=1/(x^2+y^2;f(x=2,y=3) - + ''' return GiacMethods['subst'](self,*args) @@ -16640,7 +16640,7 @@ cdef class GiacMethods_base: Help for substituer: substituer(Expr,Var(v)=value(a)) Substitutes a value for a variable in an expression. - See also: 1/ eval 2/ algsubs 3/ subs 4/ () + See also: 1/ eval 2/ algsubs 3/ subs 4/ () Ex1:substituer(1/(4+x^2),x=2) Ex2:substituer(1/(x^2+y^2),x=2,y=3) Ex3:substituer(1/(x^2+y^2+z^2),[x=2,y=3,z=1]) @@ -16648,7 +16648,7 @@ cdef class GiacMethods_base: Ex5:substituer('integrate(sin(x^2)*x,x)',x=sqrt(t)) Ex6:substituer('sum(x^(n+1)/((n+p+1)*(n+1)),n,0,inf)',n=k-1) Ex7: f:=1/(x^2+y^2;f(x=2,y=3) - + ''' return GiacMethods['substituer'](self,*args) @@ -16657,12 +16657,12 @@ cdef class GiacMethods_base: Help for subtype: subtype(Expr) Returns 1 for a sequence,2 for a set, 10 for a polynomial and 0 otherwise. - See also: 1/ DOM_LIST 2/ type + See also: 1/ DOM_LIST 2/ type Ex1:subtype(1,2,3) Ex2:subtype(set[1,2,3]) Ex3:subtype(poly1[1,2,3]) Ex4:subtype([1,2,3]) - + ''' return GiacMethods['subtype'](self,*args) @@ -16671,7 +16671,7 @@ cdef class GiacMethods_base: Help for sum: sum(Expr,Var,VarMin(a),VarMax(b),[VarStep(p)]) Discrete sum (with 2 or 4 arguments return then sum from a to b if a<=b or of the opposite of the sum from b+1 to a-1 if a>b+1 or 0 if a=b+1) or the discrete primitive or sum of the elements of a list or a sequence. - See also: 1/ + + See also: 1/ + Ex1:sum(1/n^2,n,1,17) Ex2:sum(1/n^2,n=1..17) Ex3:sum(1/n^2,n,17,1) @@ -16682,7 +16682,7 @@ cdef class GiacMethods_base: Ex8:sum([[1,2,3,4,5,6,7,8,9],[1,2,3,4,5,6,7,8,9]]) Ex9:sum(1/(x*(x+1)),x) Ex10:sum(cos(n*x),n) - + ''' return GiacMethods['sum'](self,*args) @@ -16691,11 +16691,11 @@ cdef class GiacMethods_base: Help for sum_riemann: sum_riemann(Expr(Xpr),Lst(var1,var2)) Returns an equivalent when var1=+infinity of the sum of Xpr(var1,var2) for var2 from 1 to var1 when the sum is a Riemann sum. - See also: 1/ + See also: 1/ Ex1:sum_riemann(1/(n+k),[n,k]) Ex2:sum_riemann(n/(n^2+k),[n,k]) Ex3:sum_riemann(n/(n^2+k^2),[n,k]) - + ''' return GiacMethods['sum_riemann'](self,*args) @@ -16704,12 +16704,12 @@ cdef class GiacMethods_base: Help for suppress: suppress(Vect(L)||Str(l),Intg(n)) Returns L without the element of index n; L:=suppress(L,n) or L.suppress(n). - See also: 1/ tail 2/ mid 3/ remove 4/ insert + See also: 1/ tail 2/ mid 3/ remove 4/ insert Ex1:suppress([0,1,2,3],2) Ex2:suppress("0123",2) Ex3: L:=[0,1,2,3];L:=suppress(L,2) Ex4: L:=[0,1,2,3];L.suppress(2) - + ''' return GiacMethods['suppress'](self,*args) @@ -16718,10 +16718,10 @@ cdef class GiacMethods_base: Help for surd: surd(Expr,Intg(n)) Power 1/n. - See also: 1/ sqrt 2/ ^ + See also: 1/ sqrt 2/ ^ Ex1:surd(8,3) Ex2:surd(-8,3) - + ''' return GiacMethods['surd'](self,*args) @@ -16731,7 +16731,7 @@ cdef class GiacMethods_base: svd(Mtrx(A)) For a square numerical real matrix A, returns U orthogonal, S vector of singular values, Q orthogonal such that A=U*diag(S)*tran(Q). Ex1:svd([[1,2],[3,4]]) - + ''' return GiacMethods['svd'](self,*args) @@ -16740,9 +16740,9 @@ cdef class GiacMethods_base: Help for swapcol: swapcol(Mtrx(A),Intg(n1),Intg(n2)) Returns the matrix obtained from A by swapping the n1-th column and the n2-th column. - See also: 1/ rowSwap + See also: 1/ rowSwap Ex1:swapcol([[1,2],[3,4],[5,6]],0,1) - + ''' return GiacMethods['swapcol'](self,*args) @@ -16751,9 +16751,9 @@ cdef class GiacMethods_base: Help for swaprow: swaprow(Mtrx(A),Intg(n1),Intg(n2)) Returns the matrix obtained from A by swapping the n1-th row and the n2-th row. - See also: 1/ rowAdd 2/ colSwap + See also: 1/ rowAdd 2/ colSwap Ex1:swaprow([[1,2],[3,4],[5,6]],1,2) - + ''' return GiacMethods['swaprow'](self,*args) @@ -16762,11 +16762,11 @@ cdef class GiacMethods_base: Help for switch_axes: switch_axes([Intg(0 or 1)]) switch_axes() puts or erases the axes of the graphic-screen. - See also: 1/ gl_showaxes 2/ axes + See also: 1/ gl_showaxes 2/ axes Ex1:switch_axes() Ex2:switch_axes(0) Ex3:switch_axes(1) - + ''' return GiacMethods['switch_axes'](self,*args) @@ -16775,10 +16775,10 @@ cdef class GiacMethods_base: Help for sylvester: sylvester(Poly,Poly,Var) Sylvester matrix of two polynomials. - See also: 1/ resultant + See also: 1/ resultant Ex1:sylvester(x^2-1,x^3-1,x) Ex2:sylvester(x^3-p*x+q,3*x^2-p,x) - + ''' return GiacMethods['sylvester'](self,*args) @@ -16787,14 +16787,14 @@ cdef class GiacMethods_base: Help for symb2poly: symb2poly(Expr, LstVar or [Var]) Returns the coefficients of a polynomial with respect to the 2nd argument or if the second argument is a list the internal format of the polynomial. - See also: 1/ poly2symb 2/ r2e + See also: 1/ poly2symb 2/ r2e Ex1:symb2poly(x*3+2.1) Ex2:symb2poly(3*x*y+2*y+1,y) Ex3:symb2poly(3*x*y+2*y+1,x,y) Ex4:symb2poly(3*x*y+2*y+1,[x,y]) Ex5:symb2poly(-x^4+x*3*y+2+y^2*z,[x,y,z]) Ex6:symb2poly(-x^4+x*3*y+2+y^2*z,[x,y,z]) - + ''' return GiacMethods['symb2poly'](self,*args) @@ -16803,12 +16803,12 @@ cdef class GiacMethods_base: Help for symbol: symbol(Opt) DOM_SYMBOLIC or symbol is the type of a symbolic variable, as returned by the type command. It is also an option of the assume command. - See also: 1/ type 2/ assume 3/ DOM_INT 4/ DOM_FLOAT + See also: 1/ type 2/ assume 3/ DOM_INT 4/ DOM_FLOAT Ex1: assume(a,symbol) Ex2: assume(a,DOM_SYMBOLIC) Ex3: a:=sqrt(2);type(a) Ex4: type(2x+1) - + ''' return GiacMethods['symbol'](self,*args) @@ -16817,9 +16817,9 @@ cdef class GiacMethods_base: Help for syst2mat: syst2mat(LstLinEq,LstVar) Returns the matrix M=A|(-b) associate to the system Y=AX+b. - See also: 1/ linsolve 2/ rref + See also: 1/ linsolve 2/ rref Ex1:syst2mat([x-y=1,x+2*y],[x,y]) - + ''' return GiacMethods['syst2mat'](self,*args) @@ -16828,9 +16828,9 @@ cdef class GiacMethods_base: Help for tCollect: tCollect(Expr) Collects trigonometric expressions. - See also: 1/ texpand 2/ tlin + See also: 1/ texpand 2/ tlin Ex1:tCollect(sin(x)+cos(x)) - + ''' return GiacMethods['tCollect'](self,*args) @@ -16839,11 +16839,11 @@ cdef class GiacMethods_base: Help for tExpand: tExpand(Expr) Expands transcendental expressions. - See also: 1/ tcollect 2/ tlin 3/ lin 4/ trigexpand + See also: 1/ tcollect 2/ tlin 3/ lin 4/ trigexpand Ex1:tExpand(sin(2*x)+exp(x+y)) Ex2:tExpand(cos(x+y)) Ex3:tExpand(cos(3*x)) - + ''' return GiacMethods['tExpand'](self,*args) @@ -16852,11 +16852,11 @@ cdef class GiacMethods_base: Help for table: table(SeqEqual(index=value)) Defines an array where the indices are strings or real numbers or defines a table with a matrix. - See also: 1/ matrix 2/ convert 3/ array + See also: 1/ matrix 2/ convert 3/ array Ex1:table(3=-10,"a"=10,"b"=20,"c"=30,"d"=40) - Ex2: A:=[[0,1],[2,3]];table(A) + Ex2: A:=[[0,1],[2,3]];table(A) Ex3: B:=table([1,2]=12,[2,5]=25);matrix(B) - + ''' return GiacMethods['table'](self,*args) @@ -16865,10 +16865,10 @@ cdef class GiacMethods_base: Help for tablefunc: tablefunc(Expr,Var) Table of values of a function : you must be in a spreadsheet. - See also: 1/ tabvar 2/ tableseq + See also: 1/ tabvar 2/ tableseq Ex1:tablefunc(sin(x),x) Ex2:tablefunc(x^2-x-2,x) - + ''' return GiacMethods['tablefunc'](self,*args) @@ -16877,10 +16877,10 @@ cdef class GiacMethods_base: Help for tableseq: tableseq(Expr,(Var or LstVar),(InitVal or LstInitVal)) Table of values of a sequence (in a spreadsheet.) - See also: 1/ tablefunc + See also: 1/ tablefunc Ex1:tableseq(cos(x),x,0.0) Ex2:tableseq(x+y,[x,y],[1,1]) - + ''' return GiacMethods['tableseq'](self,*args) @@ -16889,11 +16889,11 @@ cdef class GiacMethods_base: Help for tabsign: tabsign(Expr,Var) Table of signs of a function. - See also: 1/ tablefunc 2/ tabvar + See also: 1/ tablefunc 2/ tabvar Ex1:tabsign(x^2-x,x) Ex2:tabsign(x^2,x,-3,5) Ex3:tabsign(sin(x),x) - + ''' return GiacMethods['tabsign'](self,*args) @@ -16902,13 +16902,13 @@ cdef class GiacMethods_base: Help for tabvar: tabvar(Expr,Var) Table of variations of a function with its graph on DispG. - See also: 1/ tablefunc 2/ tabsign + See also: 1/ tablefunc 2/ tabsign Ex1:tabvar(sin(x),x) Ex2:tabvar(1/ln(x^2-1),x,diff=1) Ex3:tabvar(x^2+x+1,x) Ex4:tabvar(x^2,x,-3,5) Ex5:tabvar([sin(2t),cos(3t)]) - + ''' return GiacMethods['tabvar'](self,*args) @@ -16917,11 +16917,11 @@ cdef class GiacMethods_base: Help for tail: tail(Lst or Seq or Str) Returns the list (or sequence or string) without its first element. - See also: 1/ head 2/ mid 3/ left 4/ right 5/ back + See also: 1/ head 2/ mid 3/ left 4/ right 5/ back Ex1:tail([3,2,4,1,0]) Ex2:tail(3,2,4,1,0) Ex3:tail("bonjour") - + ''' return GiacMethods['tail'](self,*args) @@ -16930,11 +16930,11 @@ cdef class GiacMethods_base: Help for tan: tan(Expr) Tangent or option of the convert or convertir command (id halftan). - See also: 1/ atan or Opt 2/ convert 3/ halftan + See also: 1/ atan or Opt 2/ convert 3/ halftan Ex1:tan(0) Ex2:tan(pi/4) Ex3: convert(tan(x),tan) - + ''' return GiacMethods['tan'](self,*args) @@ -16943,9 +16943,9 @@ cdef class GiacMethods_base: Help for tan2cossin2: tan2cossin2(Expr) Replaces tan(x) by (1-cos(2*x))/sin(2*x) in the argument. - See also: 1/ tan2sincos2 2/ tan2sincos 3/ sin2costan 4/ cos2sintan + See also: 1/ tan2sincos2 2/ tan2sincos 3/ sin2costan 4/ cos2sintan Ex1:tan2cossin2(tan(x)) - + ''' return GiacMethods['tan2cossin2'](self,*args) @@ -16954,9 +16954,9 @@ cdef class GiacMethods_base: Help for tan2sincos: tan2sincos(Expr) Replaces tan(x) by sin(x)/cos(x) in the argument. - See also: 1/ sin2costan 2/ cos2sintan 3/ tan2sincos2 4/ tan2cossin2 + See also: 1/ sin2costan 2/ cos2sintan 3/ tan2sincos2 4/ tan2cossin2 Ex1:tan2sincos(tan(x)) - + ''' return GiacMethods['tan2sincos'](self,*args) @@ -16965,9 +16965,9 @@ cdef class GiacMethods_base: Help for tan2sincos2: tan2sincos2(Expr) Replaces tan(x) by sin(2*x)/(1+cos(2*x)) in the argument. - See also: 1/ tan2cossin2 2/ tan2sincos 3/ sin2costan 4/ cos2sintan + See also: 1/ tan2cossin2 2/ tan2sincos 3/ sin2costan 4/ cos2sintan Ex1:tan2sincos2(tan(x)) - + ''' return GiacMethods['tan2sincos2'](self,*args) @@ -16976,7 +16976,7 @@ cdef class GiacMethods_base: Help for tangent: tangent(Curve(C),Pnt(A)) tangent(C,A) draws the tangents (line or plane) to C through A. - See also: 1/ LineTan 2/ droite_tangente + See also: 1/ LineTan 2/ droite_tangente Ex1:tangent(circle(i,1+i),A) Ex2:tangent(plotfunc(sin(x)),3*pi/4) Ex3:tangent(plotfunc(sin(x)),point(3*pi/4+i*sqrt(2)/2)) @@ -16985,7 +16985,7 @@ cdef class GiacMethods_base: Ex6:tangent(plotparam(3*exp(t/2)*exp(i*t),t),7) Ex7:tangent(plotpolar(3*exp(t/2),t),7) Ex8: equation(tangente([2*cos(t),2*sin(t),3*t],t)) - + ''' return GiacMethods['tangent'](self,*args) @@ -16994,7 +16994,7 @@ cdef class GiacMethods_base: Help for tangente: tangente(Curve(C),Pnt(A)) tangent(C,A) draws the tangents (line or plane) to C through A. - See also: 1/ LineTan 2/ droite_tangente + See also: 1/ LineTan 2/ droite_tangente Ex1:tangente(circle(i,1+i),A) Ex2:tangente(plotfunc(sin(x)),3*pi/4) Ex3:tangente(plotfunc(sin(x)),point(3*pi/4+i*sqrt(2)/2)) @@ -17003,7 +17003,7 @@ cdef class GiacMethods_base: Ex6:tangente(plotparam(3*exp(t/2)*exp(i*t),t),7) Ex7:tangente(plotpolar(3*exp(t/2),t),7) Ex8: equation(tangente([2*cos(t),2*sin(t),3*t],t)) - + ''' return GiacMethods['tangente'](self,*args) @@ -17012,10 +17012,10 @@ cdef class GiacMethods_base: Help for tanh: tanh(Expr) Hyperbolic tangent. - See also: 1/ atanh 2/ hyp2exp + See also: 1/ atanh 2/ hyp2exp Ex1:tanh(0) Ex2:tanh(hyp2exp(tanh(1))) - + ''' return GiacMethods['tanh'](self,*args) @@ -17024,11 +17024,11 @@ cdef class GiacMethods_base: Help for taux_accroissement: taux_accroissement(Expr,Var,Val1,(Val1+Var or Val2)) Returns the rate of change of an expression when the variable goes from Val1 to Val2 (by default Var=x). - See also: 1/ diff 2/ limit + See also: 1/ diff 2/ limit Ex1:taux_accroissement(x^2,1,1+h) Ex2:taux_accroissement(x^2,1,2) Ex3:taux_accroissement(a^2,a,1,1+h) - + ''' return GiacMethods['taux_accroissement'](self,*args) @@ -17037,7 +17037,7 @@ cdef class GiacMethods_base: Help for taylor: taylor(Expr,[Var=limit_point],[Order]) Series expansion at finite or infinite points (by default x=0, and relative order=5). - See also: 1/ series 2/ limit 3/ pade 4/ polynom + See also: 1/ series 2/ limit 3/ pade 4/ polynom Ex1:taylor(sin(x)/x,x,0) Ex2:taylor(sin(x),x=0,5,polynom) Ex3:taylor(ln(y+y^2)-ln(y),y) @@ -17045,10 +17045,10 @@ cdef class GiacMethods_base: Ex5:taylor(ln(x+x^2)-ln(x),x=0,2) Ex6:taylor(ln(x+x^2)-ln(x),x=1,2) Ex7:taylor((x^4+x+2)/(x^2+1),x,5) - Ex8:taylor(sin(t*x+t*y)+cos(t*x*t*y),t=0,6,polynom)(h=1) + Ex8:taylor(sin(t*x+t*y)+cos(t*x*t*y),t=0,6,polynom)(h=1) Ex9:taylor(sin((1+h*t)*(pi/2+k*t)),t=0,3,polynom)(t=1) Ex10:taylor((-1+k*t)^2/(1+h*t)^3,t=0,3,polynom)(t=1) - + ''' return GiacMethods['taylor'](self,*args) @@ -17057,9 +17057,9 @@ cdef class GiacMethods_base: Help for tchebyshev1: tchebyshev1(Intg(n)) Returns the n-th Tchebyshev polynomial of first kind. - See also: 1/ tchebyshev2 2/ hermite + See also: 1/ tchebyshev2 2/ hermite Ex1:tchebyshev1(3) - + ''' return GiacMethods['tchebyshev1'](self,*args) @@ -17068,9 +17068,9 @@ cdef class GiacMethods_base: Help for tchebyshev2: tchebyshev2(Intg(n)) Returns the nt-h Tchebyshev polynomial of second kind. - See also: 1/ tchebyshev1 2/ hermite + See also: 1/ tchebyshev1 2/ hermite Ex1:tchebyshev2(3) - + ''' return GiacMethods['tchebyshev2'](self,*args) @@ -17079,10 +17079,10 @@ cdef class GiacMethods_base: Help for tcoeff: tcoeff(Poly||Lst) Returns the coefficient of the term of lowest degree of a polynomial (t=trailing). - See also: 1/ lcoeff + See also: 1/ lcoeff Ex1:tcoeff(-2*x^3+x^2+7*x) Ex2:tcoeff([-2,1,7,0]) - + ''' return GiacMethods['tcoeff'](self,*args) @@ -17091,9 +17091,9 @@ cdef class GiacMethods_base: Help for tcollect: tcollect(Expr) Collects trigonometric expressions. - See also: 1/ texpand 2/ tlin + See also: 1/ texpand 2/ tlin Ex1:tcollect(sin(x)+cos(x)) - + ''' return GiacMethods['tcollect'](self,*args) @@ -17102,8 +17102,8 @@ cdef class GiacMethods_base: Help for tdeg: tdeg(Opt) Option of the gbasis or greduce command to specify an order for monomials (complete degree then lexicographic order). - See also: 1/ gbasis 2/ greduce - + See also: 1/ gbasis 2/ greduce + ''' return GiacMethods['tdeg'](self,*args) @@ -17112,9 +17112,9 @@ cdef class GiacMethods_base: Help for tensor_product: tensor_product(Seq(G1,G2,..)) Returns the tensor product of the input graphs G1, G2, ... with vertices labelled as "u:v:..." where u, v, ... are vertices from G1, G2, ..., respectively. - See also: 1/ cartesian_product + See also: 1/ cartesian_product Ex1:tensor_product(graph(trail(1,2,3,4,5,2)),star_graph(3)) - + ''' return GiacMethods['tensor_product'](self,*args) @@ -17123,10 +17123,10 @@ cdef class GiacMethods_base: Help for tetrahedron: tetrahedron(Pnt(A),Pnt(B),Pnt(C),[Pnt(D)]) Draws the regular direct pyramid ABCD with vertices A,B and a face in the plane (A,B,C) when there is 3 arguments and the pyramid ABCD when there are 4 arguments. - See also: 1/ cube 2/ cylinder 3/ icosahedron 4/ dodecahedron 5/ octahedron + See also: 1/ cube 2/ cylinder 3/ icosahedron 4/ dodecahedron 5/ octahedron Ex1:tetrahedron([0,0,0],[3,0,0],[0,1,0]) Ex2:tetrahedron([0,0,0],[3,0,0],[0,3,0],[0,0,4]) - + ''' return GiacMethods['tetrahedron'](self,*args) @@ -17135,11 +17135,11 @@ cdef class GiacMethods_base: Help for texpand: texpand(Expr) Expands transcendental expressions. - See also: 1/ tcollect 2/ tlin 3/ lin 4/ trigexpand + See also: 1/ tcollect 2/ tlin 3/ lin 4/ trigexpand Ex1:texpand(sin(2*x)+exp(x+y)) Ex2:texpand(cos(x+y)) Ex3:texpand(cos(3*x)) - + ''' return GiacMethods['texpand'](self,*args) @@ -17148,10 +17148,10 @@ cdef class GiacMethods_base: Help for thickness: thickness(Opt) Option (Maple compatibility) of a graphic command to define the thickness of lines. - See also: 1/ line_width + See also: 1/ line_width Ex1: segment(0,point(1,1),thickness=5) Ex2: segment(0,point(1,1),epaisseur=5) - + ''' return GiacMethods['thickness'](self,*args) @@ -17160,10 +17160,10 @@ cdef class GiacMethods_base: Help for threshold: threshold(Lst,Real(bound)[=Expr(repl)] or Lst[Real(lower)[=Expr(rl)],Real(upper)[=Expr(ru)]],[Fnc(compare)],[abs[=true or false]]) Performs thresholding operations on a list of real or complex numbers. - See also: 1/ max 2/ min + See also: 1/ max 2/ min Ex1:threshold([1,3,2,4,5,4,3,2,3,1],3,'>=') Ex2:threshold([-10,-5,0,5,10],7=a,abs=true) - + ''' return GiacMethods['threshold'](self,*args) @@ -17172,10 +17172,10 @@ cdef class GiacMethods_base: Help for throw: throw(Str) Generates the display of an error in a program. - See also: 1/ try 2/ catch + See also: 1/ try 2/ catch Ex1:throw("Argument should be integer") Ex2:throw("je provoque une erreur") - + ''' return GiacMethods['throw'](self,*args) @@ -17184,10 +17184,10 @@ cdef class GiacMethods_base: Help for title: title(Opt) Global option of a graphic command to put a title in a graphic. - See also: 1/ line_width + See also: 1/ line_width Ex1: title="segment";segment(0,point(1,1),epaisseur=5) Ex2: titre="segment";segment(0,point(1,1),epaisseur=5) - + ''' return GiacMethods['title'](self,*args) @@ -17196,10 +17196,10 @@ cdef class GiacMethods_base: Help for titre: titre(Opt) Global option of a graphic command to put a title in a graphic. - See also: 1/ line_width + See also: 1/ line_width Ex1: title="segment";segment(0,point(1,1),epaisseur=5) Ex2: titre="segment";segment(0,point(1,1),epaisseur=5) - + ''' return GiacMethods['titre'](self,*args) @@ -17208,10 +17208,10 @@ cdef class GiacMethods_base: Help for tlin: tlin(ExprTrig) Trigonometric linearization. - See also: 1/ texpand 2/ lin + See also: 1/ texpand 2/ lin Ex1:tlin(sin(x)^3) Ex2:tlin(cos(x)*cos(y)) - + ''' return GiacMethods['tlin'](self,*args) @@ -17220,10 +17220,10 @@ cdef class GiacMethods_base: Help for tonnetz: tonnetz(Intg(a),Intg(b),Intg(c),[Intg(d)]) Returns the graph corresponding to the [a,b,c] resp. [a,b,c,d] tone network (tonnetz) used in neo-Riemannian music theory. - See also: 1/ is_regular 2/ clique_stats + See also: 1/ is_regular 2/ clique_stats Ex1:tonnetz(3,4,5) Ex2:tonnetz(2,3,3,4) - + ''' return GiacMethods['tonnetz'](self,*args) @@ -17232,9 +17232,9 @@ cdef class GiacMethods_base: Help for topologic_sort: topologic_sort(Graph(G)) Returns the list of vertices sorted according to the topological ordering in the directed acyclic graph G. - See also: 1/ digraph 2/ is_acyclic + See also: 1/ digraph 2/ is_acyclic Ex1:topologic_sort(digraph(%{[c,a],[c,b],[c,d],[a,d],[b,d],[a,b]%})) - + ''' return GiacMethods['topologic_sort'](self,*args) @@ -17243,9 +17243,9 @@ cdef class GiacMethods_base: Help for topological_sort: topological_sort(Graph(G)) Returns the list of vertices sorted according to the topological ordering in the directed acyclic graph G. - See also: 1/ digraph 2/ is_acyclic + See also: 1/ digraph 2/ is_acyclic Ex1:topological_sort(digraph(%{[c,a],[c,b],[c,d],[a,d],[b,d],[a,b]%})) - + ''' return GiacMethods['topological_sort'](self,*args) @@ -17254,9 +17254,9 @@ cdef class GiacMethods_base: Help for torus_grid_graph: torus_grid_graph(Intg(m),Intg(n)) Returns a torus grid graph on m*n vertices, where m,n>=3. - See also: 1/ grid_graph + See also: 1/ grid_graph Ex1:torus_grid_graph(6,12) - + ''' return GiacMethods['torus_grid_graph'](self,*args) @@ -17265,9 +17265,9 @@ cdef class GiacMethods_base: Help for total_degree: total_degree(Poly(P),Lst(Vars)) Total degree of the polynomial P with respect to the second argument. - See also: 1/ valuation 2/ size 3/ degree + See also: 1/ valuation 2/ size 3/ degree Ex1:total_degree(x^3*y+x*y,[x,y]) - + ''' return GiacMethods['total_degree'](self,*args) @@ -17276,10 +17276,10 @@ cdef class GiacMethods_base: Help for tourne_droite: tourne_droite(NULL or Real(n)) The turtle turns right by n degrees (by default n=90). - See also: 1/ tourne_gauche 2/ pas_de_cote + See also: 1/ tourne_gauche 2/ pas_de_cote Ex1: tourne_droite 60 Ex2:tourne_droite(60) - + ''' return GiacMethods['tourne_droite'](self,*args) @@ -17288,10 +17288,10 @@ cdef class GiacMethods_base: Help for tourne_gauche: tourne_gauche(NULL or Real(n)) The turtle turns left by n degrees (by defaults n=90). - See also: 1/ tourne_droite + See also: 1/ tourne_droite Ex1: tourne_gauche 60 Ex2:tourne_gauche(60) - + ''' return GiacMethods['tourne_gauche'](self,*args) @@ -17304,7 +17304,7 @@ cdef class GiacMethods_base: Ex2:tpsolve([7,10,8,8,9,6],[9,6,12,8,10],[[36,40,32,43,29],[28,27,29,40,38],[34,35,41,29,31],[41,42,35,27,36],[25,28,40,34,38],[31,30,43,38,40]]) Ex3:tpsolve([95,70,165,165],[195,150,30,45,75],[[15,M,45,M,0],[12,40,M,M,0],[0,15,25,25,0],[M,0,M,12,0]]) Ex4:tpsolve([1,1,1,1],[1,1,1,1],[[10,12,9,11],[5,10,7,8],[12,14,13,11],[8,15,11,9]]) - + ''' return GiacMethods['tpsolve'](self,*args) @@ -17313,12 +17313,12 @@ cdef class GiacMethods_base: Help for trace: trace(Mtrx or GeoObj) Returns the trace of a square matrix or draws the trace of a geometric object when the parameter changes (see Trace in Menu button of a geometric level and write only one instruction on each line). - See also: 1/ det 2/ lieu + See also: 1/ det 2/ lieu Ex1:trace([[1,2,3],[1,3,6],[2,5,7]]) Ex2:trace([[1+i,2,3],[1,3,6],[2,5,9-i]]) Ex3: assume(a=[0.7,-5,5,0.1]);trace(point(a-i*a)) Ex4: assume(a=[0.7,-5,5,0.1]);trace(inter_unique(droite(y=a*x+a),droite(y=2*a*x+1))) - + ''' return GiacMethods['trace'](self,*args) @@ -17327,9 +17327,9 @@ cdef class GiacMethods_base: Help for trail: trail(Seq(V)) Returns a trail of vertices from V (inert command). - See also: 1/ graph 2/ digraph + See also: 1/ graph 2/ digraph Ex1:trail(1,2,3,4,1) - + ''' return GiacMethods['trail'](self,*args) @@ -17338,10 +17338,10 @@ cdef class GiacMethods_base: Help for trail2edges: trail2edges(Trail(T)) Converts a trail T to the list of its edges. - See also: 1/ subgraph 2/ trail + See also: 1/ subgraph 2/ trail Ex1:trail2edges(trail(1,2,3,4,1,3)) Ex2:trail2edges([1,2,3,4,1,3]) - + ''' return GiacMethods['trail2edges'](self,*args) @@ -17350,10 +17350,10 @@ cdef class GiacMethods_base: Help for trames: trames(Opt) Option of animate and animate3d commands to give the number of pictures. - See also: 1/ animate 2/ animate3d + See also: 1/ animate 2/ animate3d Ex1: animate(sin(x*t),x=-pi..pi,t=-3..3,frames=30) Ex2: animate3d(x^2+t*y^2,[x=-2..2,y=-2..2],t=-3..3,frames=10) - + ''' return GiacMethods['trames'](self,*args) @@ -17362,11 +17362,11 @@ cdef class GiacMethods_base: Help for tran: tran(Mtrx) Transposes a matrix (without conjugation). - See also: 1/ conj 2/ trn + See also: 1/ conj 2/ trn Ex1:tran([[1,2,3],[1,3,6],[2,5,7]]) Ex2:tran([[1+i,2,3],[1,3,6],[2,5,9-i]]) Ex3:tran(conj([[1+i,2,3],[1,3,6],[2,5,9-i]])) - + ''' return GiacMethods['tran'](self,*args) @@ -17375,9 +17375,9 @@ cdef class GiacMethods_base: Help for transitive_closure: transitive_closure(Graph(G),[weighted[=true||false]]) Returns the [weighted, by default false] transitive closure of G. - See also: 1/ allpairs_distance 2/ is_connected 3/ shortest_path 4/ vertex_distance + See also: 1/ allpairs_distance 2/ is_connected 3/ shortest_path 4/ vertex_distance Ex1:transitive_closure(digraph([1,2,3,4,5,6],%{[1,2],[2,3],[2,4],[4,5],[3,5]%}),weighted) - + ''' return GiacMethods['transitive_closure'](self,*args) @@ -17386,12 +17386,12 @@ cdef class GiacMethods_base: Help for translation: translation(Vect, Pnt(C)) translation(B-A,C) (resp translation([a,b,c],C)) is the translation of C in the translation of vector AB (resp [a,b,c]). - See also: 1/ rotation 2/ reflection + See also: 1/ rotation 2/ reflection Ex1:translation(1+i,i) Ex2:translation([1,1,1],point([1,2,3])) Ex3: t:=translation(1+i);t(i) Ex4: t:=translation([1,1,1]);t(point([1,2,3])) - + ''' return GiacMethods['translation'](self,*args) @@ -17400,11 +17400,11 @@ cdef class GiacMethods_base: Help for transpose: transpose(Mtrx) Transposes a matrix (without conjugation). - See also: 1/ conj 2/ trn + See also: 1/ conj 2/ trn Ex1:transpose([[1,2,3],[1,3,6],[2,5,7]]) Ex2:transpose([[1+i,2,3],[1,3,6],[2,5,9-i]]) Ex3:transpose(conj([[1+i,2,3],[1,3,6],[2,5,9-i]])) - + ''' return GiacMethods['transpose'](self,*args) @@ -17413,14 +17413,14 @@ cdef class GiacMethods_base: Help for trapeze: trapeze(Opt) Option of the plotarea command and of the area command. - See also: 1/ plotarea 2/ area + See also: 1/ plotarea 2/ area Ex1: plotarea(x^2,x=0..1,5,trapezoid) Ex2: plotarea(x^2,x=0..1,5,middle_point) Ex3: plotarea(x^2,x=0..1,5,right_rectangle) Ex4: plotarea(x^2,x=0..1,5,left_rectangle) Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) - + ''' return GiacMethods['trapeze'](self,*args) @@ -17429,14 +17429,14 @@ cdef class GiacMethods_base: Help for trapezoid: trapezoid(Opt) Option of the plotarea command and of the area command. - See also: 1/ plotarea 2/ area + See also: 1/ plotarea 2/ area Ex1: plotarea(x^2,x=0..1,5,trapezoid) Ex2: plotarea(x^2,x=0..1,5,middle_point) Ex3: plotarea(x^2,x=0..1,5,right_rectangle) Ex4: plotarea(x^2,x=0..1,5,left_rectangle) Ex5: area(x^2,x=0..1,5,middle_point) Ex6: area(x^2,x=0..1,5,trapezoid) - + ''' return GiacMethods['trapezoid'](self,*args) @@ -17445,13 +17445,13 @@ cdef class GiacMethods_base: Help for traveling_salesman: traveling_salesman(Graph(G),[Mtrx(M)],[opts]) Returns a Hamiltonian cycle in an unweighted graph G or solves traveling salesman problem if G is weighted (matrix M can be used for edge weights), returning a sequence containing the minimal cost and the corresponding Hamiltonian cycle. - See also: 1/ is_hamiltonian + See also: 1/ is_hamiltonian Ex1:traveling_salesman(hypercube_graph(5)) Ex2:traveling_salesman(digraph(%{[[1,2],1],[[1,3],2],[[2,3],2],[[2,4],3],[[3,2],3],[[3,4],2],[[4,1],1]%})) Ex3: M:=randmatrix(4,4,99); traveling_salesman(graph("tetrahedron"),M) Ex4: G:=set_vertex_positions(complete_graph(42),[randvector(2,1000)$(k=1..42)]); traveling_salesman(G,vertex_distance) Ex5: G:=set_vertex_positions(complete_graph(120),[randvector(2,1000)$(k=1..120)]); c,T:=traveling_salesman(G,vertex_distance,approx) - + ''' return GiacMethods['traveling_salesman'](self,*args) @@ -17460,8 +17460,8 @@ cdef class GiacMethods_base: Help for tree: tree(Opt) Option for the draw_graph command. - See also: 1/ planar 2/ spring 3/ draw_graph - + See also: 1/ planar 2/ spring 3/ draw_graph + ''' return GiacMethods['tree'](self,*args) @@ -17470,9 +17470,9 @@ cdef class GiacMethods_base: Help for tree_height: tree_height(Graph(T),Vrtx(r)) Returns the height of the tree graph T with r as the root node. - See also: 1/ is_tree 2/ random_tree + See also: 1/ is_tree 2/ random_tree Ex1:tree_height(graph(%{[1,2],[2,3],[2,4],[4,5]%}),1) - + ''' return GiacMethods['tree_height'](self,*args) @@ -17481,9 +17481,9 @@ cdef class GiacMethods_base: Help for tri: tri(Expr(x)) Returns the value of the triangle function at x. - See also: 1/ rect 2/ Heaviside + See also: 1/ rect 2/ Heaviside Ex1:tri(x-1) - + ''' return GiacMethods['tri'](self,*args) @@ -17492,11 +17492,11 @@ cdef class GiacMethods_base: Help for triangle: triangle((Pnt or Cplx),(Pnt or Cplx),(Pnt or Cplx)) triangle(A,B,C) draws the triangle ABC. - See also: 1/ equilateral_triangle 2/ isosceles_triangle 3/ right_triangle + See also: 1/ equilateral_triangle 2/ isosceles_triangle 3/ right_triangle Ex1:triangle(point(1+i),1,0) Ex2:triangle(0,1,1+i) Ex3:triangle(point(0,0,0),point(3,3,3),point(0,3,3)) - + ''' return GiacMethods['triangle'](self,*args) @@ -17509,7 +17509,7 @@ cdef class GiacMethods_base: Ex2:triangle_paper(1,pi/3,sqrt(3)/2,x=-1..4,y=-2..2) Ex3:triangle_paper(papier_triangule(1,pi/3,sqrt(3)/2,x=-2..6,y=-4*sqrt(3)..4*sqrt(3))) Ex4:triangle_paper(0.5,3*pi/4,0.5) - + ''' return GiacMethods['triangle_paper'](self,*args) @@ -17518,12 +17518,12 @@ cdef class GiacMethods_base: Help for triangle_plein: triangle_plein(Real(a),[Real(b)],[Real(t)]) Draws a full direct triangle with sides a,b and with angle t, from the turtle position (by default t=90 or (b=a and t=60)). - See also: 1/ rectangle_plein + See also: 1/ rectangle_plein Ex1: triangle_plein 30 Ex2:triangle_plein(30) Ex3:triangle_plein(30,40) Ex4:triangle_plein(30,40,60) - + ''' return GiacMethods['triangle_plein'](self,*args) @@ -17532,10 +17532,10 @@ cdef class GiacMethods_base: Help for triangle_point: triangle_point(Opt) Option of the display command for a point. - See also: 1/ display + See also: 1/ display Ex1: F:=display(point(2+1.5*i),point_point) Ex2: F:=display(point(2+1.5*i),rhombus_point) - + ''' return GiacMethods['triangle_point'](self,*args) @@ -17544,9 +17544,9 @@ cdef class GiacMethods_base: Help for triangle_window: triangle_window(Lst,[Intg(d)],[Interval(n1..n2)]) Applies the triangular windowing function with parameter d in {-1,0,1} (by default L=0) to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ bartlett_hann_window 13/ tukey_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ bartlett_hann_window 13/ tukey_window 14/ welch_window Ex1: scatterplot(triangle_window(randvector(1000,0..1),1)) - + ''' return GiacMethods['triangle_window'](self,*args) @@ -17555,9 +17555,9 @@ cdef class GiacMethods_base: Help for trig2exp: trig2exp(Expr) Replaces in the argument the trigonometric functions by complex exponentials without linearisation. - See also: 1/ exp2trig 2/ atrig2ln + See also: 1/ exp2trig 2/ atrig2ln Ex1:trig2exp(sin(x)) - + ''' return GiacMethods['trig2exp'](self,*args) @@ -17566,9 +17566,9 @@ cdef class GiacMethods_base: Help for trigcos: trigcos(Expr) Simplifies the argument with the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) privileging cosine. - See also: 1/ trigsin 2/ trigtan + See also: 1/ trigsin 2/ trigtan Ex1:trigcos(sin(x)^4+sin(x)^2) - + ''' return GiacMethods['trigcos'](self,*args) @@ -17577,9 +17577,9 @@ cdef class GiacMethods_base: Help for trigexpand: trigexpand(Expr) Expands trigonometric functions. - See also: 1/ texpand 2/ lnexpand 3/ expexpand + See also: 1/ texpand 2/ lnexpand 3/ expexpand Ex1:trigexpand(sin(3*x)) - + ''' return GiacMethods['trigexpand'](self,*args) @@ -17588,10 +17588,10 @@ cdef class GiacMethods_base: Help for triginterp: triginterp(List,Var=xmin..xmax) Returns a trigonometric polynomial interpolation (with respect to variable x) of the points with ordinate given in list y and the abscissa equally spaced between a and b. - See also: 1/ lagrange 2/ thiele + See also: 1/ lagrange 2/ thiele Ex1:triginterp([11,10,17,24,32,26,23,19],x=0..21) Ex2:triginterp([11,10,17,24,32,26,23,19],0,21,x) - + ''' return GiacMethods['triginterp'](self,*args) @@ -17600,9 +17600,9 @@ cdef class GiacMethods_base: Help for trigsimplify: trigsimplify(Expr) Simplifies a trigonometric expression. - See also: 1/ simplify + See also: 1/ simplify Ex1:trigsimplify(3*sin(x)-4*sin(x)^3) - + ''' return GiacMethods['trigsimplify'](self,*args) @@ -17611,9 +17611,9 @@ cdef class GiacMethods_base: Help for trigsin: trigsin(Expr) Simplifies the argument with the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) privileging sine. - See also: 1/ trigcos 2/ trigtan + See also: 1/ trigcos 2/ trigtan Ex1:trigsin(cos(x)^4+sin(x)^2) - + ''' return GiacMethods['trigsin'](self,*args) @@ -17622,9 +17622,9 @@ cdef class GiacMethods_base: Help for trigtan: trigtan(Expr) Simplifies the argument with the formulas sin(x)^2+cos(x)^2=1 and tan(x)=sin(x)/cos(x) privileging tangent. - See also: 1/ trigsin 2/ trigcos + See also: 1/ trigsin 2/ trigcos Ex1:trigtan(cos(x)^4+sin(x)^2) - + ''' return GiacMethods['trigtan'](self,*args) @@ -17633,9 +17633,9 @@ cdef class GiacMethods_base: Help for trn: trn(Mtrx) Returns the adjoint matrix of A =tran(conj(A)). - See also: 1/ tran 2/ conj + See also: 1/ tran 2/ conj Ex1:trn([[1,2+i],[3,4]]) - + ''' return GiacMethods['trn'](self,*args) @@ -17644,9 +17644,9 @@ cdef class GiacMethods_base: Help for true: true() Boolean equal to true or 1. - See also: 1/ false + See also: 1/ false Ex1: a:=true - + ''' return GiacMethods['true'](self,*args) @@ -17655,13 +17655,13 @@ cdef class GiacMethods_base: Help for trunc: trunc(Real||LstReal,Int(n)) Truncates value to n decimal places (by default n=0). Accepts complex numbers.(type=DOM_COMPLEX or DOM_FLOAT). - See also: 1/ fPart 2/ floor 3/ iPart + See also: 1/ fPart 2/ floor 3/ iPart Ex1:trunc(4.3) Ex2:trunc(sqrt(2),3) Ex3:trunc([4.3333,sqrt(2)]) Ex4:trunc([4.3333,sqrt(2)],2) Ex5:trunc(sqrt(2)+i*sqrt(5),4) - + ''' return GiacMethods['trunc'](self,*args) @@ -17670,9 +17670,9 @@ cdef class GiacMethods_base: Help for truncate: truncate(Poly(P),Intg(n)) Truncates the polynomial P at order n. - See also: 1/ series + See also: 1/ series Ex1:truncate((x^2+x)^2,3) - + ''' return GiacMethods['truncate'](self,*args) @@ -17681,9 +17681,9 @@ cdef class GiacMethods_base: Help for truncate_graph: truncate_graph(Graph(G)) Returns the graph obtained by truncating the biconnected planar graph G. - See also: 1/ is_biconnected 2/ is_planar 3/ plane_dual + See also: 1/ is_biconnected 2/ is_planar 3/ plane_dual Ex1:truncate_graph(graph("tetrahedron")) - + ''' return GiacMethods['truncate_graph'](self,*args) @@ -17692,9 +17692,9 @@ cdef class GiacMethods_base: Help for tsimplify: tsimplify(Expr) Lowers the number of non rational variables. - See also: 1/ simplify + See also: 1/ simplify Ex1:tsimplify(exp(2*x)+exp(x)) - + ''' return GiacMethods['tsimplify'](self,*args) @@ -17703,9 +17703,9 @@ cdef class GiacMethods_base: Help for tuer: tuer(NULL) Stop step-by-step execution of a program (with debug). - See also: 1/ + See also: 1/ Ex1:tuer() - + ''' return GiacMethods['tuer'](self,*args) @@ -17714,9 +17714,9 @@ cdef class GiacMethods_base: Help for tukey_window: tukey_window(Lst,[Real(a)],[Interval(n1..n2)]) Applies the Tukey windowing function with parameter a in [0,1] (by default a=0.5) to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ bartlett_hann_window 14/ welch_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ bartlett_hann_window 14/ welch_window Ex1: scatterplot(tukey_window(randvector(1000,0..1),0.4)) - + ''' return GiacMethods['tukey_window'](self,*args) @@ -17725,10 +17725,10 @@ cdef class GiacMethods_base: Help for tutte_polynomial: tutte_polynomial(Graph(G),[Var(x),Var(y)]) Returns the Tutte polynomial [or its value at point (x,y)] of undirected graph G. If G is weighted, all weights must be positive integers and are interpreted as edge multiplicities. - See also: 1/ chromatic_polynomial 2/ flow_polynomial 3/ reliability_polynomial 4/ delete_edge 5/ contract_edge + See also: 1/ chromatic_polynomial 2/ flow_polynomial 3/ reliability_polynomial 4/ delete_edge 5/ contract_edge Ex1:tutte_polynomial(graph("tetrahedron")) Ex2:tutte_polynomial(graph("tetrahedron"),1,1) - + ''' return GiacMethods['tutte_polynomial'](self,*args) @@ -17737,9 +17737,9 @@ cdef class GiacMethods_base: Help for two_edge_connected_components: two_edge_connected_components(Graph(G)) Returns the list of two-edge-connected components of undirected graph G, each of them represented by the list of its vertices. - See also: 1/ is_two_edge_connected 2/ connected_components + See also: 1/ is_two_edge_connected 2/ connected_components Ex1:two_edge_connected_components(graph(trail(1,2,3,4,5,3,1),trail(5,6,7,8,6))) - + ''' return GiacMethods['two_edge_connected_components'](self,*args) @@ -17748,9 +17748,9 @@ cdef class GiacMethods_base: Help for ufactor: ufactor(Unit,Unit) Factors a unit in a unit object. - See also: 1/ convert 2/ mksa 3/ usimplify + See also: 1/ convert 2/ mksa 3/ usimplify Ex1:ufactor(100_C,1_A) - + ''' return GiacMethods['ufactor'](self,*args) @@ -17759,10 +17759,10 @@ cdef class GiacMethods_base: Help for ugamma: ugamma(Real(a),Real(x),[1]) Calculates ugamma function at a point (a,x):if a and x>=0 ugamma(a,x)=int(e^{-t}*t^{a-1},t=x..inf),(ugamma(a,x)+igamma(a,x)=Gamma(a)). - See also: 1/ Psi 2/ Beta 3/ Gamma 4/ igamma + See also: 1/ Psi 2/ Beta 3/ Gamma 4/ igamma Ex1:ugamma(5.0,2.0) Ex2:ugamma(-5.1,2.1) - + ''' return GiacMethods['ugamma'](self,*args) @@ -17771,10 +17771,10 @@ cdef class GiacMethods_base: Help for unapply: unapply(Expr,Var) Returns a function defined by an expression. - See also: 1/ apply + See also: 1/ apply Ex1:unapply(2*x^2,x) Ex2: f(x):=x*exp(x);g:=unapply(diff(f(x),x),x) - + ''' return GiacMethods['unapply'](self,*args) @@ -17783,10 +17783,10 @@ cdef class GiacMethods_base: Help for unarchive: unarchive(Str(namefich),Seq(Var)) Reads the value of a variable or of a list of variables which are in the file given as argument (file created with archive). - See also: 1/ archive 2/ Archive 3/ Unarchiv + See also: 1/ archive 2/ Archive 3/ Unarchiv Ex1:unarchive("toto") Ex2:unarchive("aa.txt") - + ''' return GiacMethods['unarchive'](self,*args) @@ -17795,9 +17795,9 @@ cdef class GiacMethods_base: Help for underlying_graph: underlying_graph(Graph(G)) Returns the graph obtained by stripping directions and weights from arcs (pairs of arcs connecting the same vertices are merged to a single edge). - See also: 1/ is_directed 2/ is_weighted 3/ make_directed 4/ make_weighted + See also: 1/ is_directed 2/ is_weighted 3/ make_directed 4/ make_weighted Ex1:underlying_graph(digraph(trail(1,2,3,4,1))) - + ''' return GiacMethods['underlying_graph'](self,*args) @@ -17806,13 +17806,13 @@ cdef class GiacMethods_base: Help for unfactored: unfactored(Opt.) Option of the plotimplicit command. - See also: 1/ plotimplicit + See also: 1/ plotimplicit Ex1: plotimplicit(x^2+y^2-1,x,y,unfactored) Ex2: plotimplicit(x^2+y^2-1,[x,y],unfactored) Ex3: plotimplicit(x^2+y^2+z^2-1,x,y,z,xstep=0.2,ystep=0.2,zstep=0.2,unfactored) Ex4: plotimplicit(x^2+y^2+z^2-1,[x,y,z],xstep=0.2,ystep=0.2,zstep=0.2,unfactored) Ex5: plotimplicit(x^2+y^2+z^2-1,x=0..1,y=0..1,z=0..1,xstep=0.2,ystep=0.2,zstep=0.2,unfactored) - + ''' return GiacMethods['unfactored'](self,*args) @@ -17821,12 +17821,12 @@ cdef class GiacMethods_base: Help for uniform: uniform(Real(a),Real(b),Real(x)) Returns the probability density at x of the uniform law on [a,b]. - See also: 1/ uniform_cdf 2/ uniform_icdf 3/ randvector 4/ ranm + See also: 1/ uniform_cdf 2/ uniform_icdf 3/ randvector 4/ ranm Ex1:uniform(2,5,4) Ex2:uniform(1.2,3.5,3) Ex3: randvector(3,uniform,1.2,3.5) Ex4: ranm(4,3,uniform,1.2,3.5) - + ''' return GiacMethods['uniform'](self,*args) @@ -17835,10 +17835,10 @@ cdef class GiacMethods_base: Help for uniform_cdf: uniform_cdf(Real(a),Real(b),Real(x0),[Real(y0)]) Returns the probability that a uniform random variable on [a,b] is less than x0 (or between x0 and y0). - See also: 1/ uniformd 2/ uniform_icdf + See also: 1/ uniformd 2/ uniform_icdf Ex1:uniform_cdf(3.2,5.7,4.4) Ex2:uniform_cdf(3.2,5.7,4.4,5.4) - + ''' return GiacMethods['uniform_cdf'](self,*args) @@ -17847,10 +17847,10 @@ cdef class GiacMethods_base: Help for uniform_icdf: uniform_icdf(Real(a),Real(b),Real(p)) Returns h such that the probability that a uniform random variable on [a,b] is less than h is p (0<=p<=1). - See also: 1/ uniform_cdf 2/ uniformd + See also: 1/ uniform_cdf 2/ uniformd Ex1:uniform_icdf(4.2,10.3,0.95) Ex2:uniform_icdf(3.2,5.7,0.48) - + ''' return GiacMethods['uniform_icdf'](self,*args) @@ -17859,12 +17859,12 @@ cdef class GiacMethods_base: Help for uniformd: uniformd(Real(a),Real(b),Real(x)) Returns the probability density at x of the uniform law on [a,b]. - See also: 1/ uniform_cdf 2/ uniform_icdf 3/ randvector 4/ ranm + See also: 1/ uniform_cdf 2/ uniform_icdf 3/ randvector 4/ ranm Ex1:uniformd(2,5,4) Ex2:uniformd(1.2,3.5,3) Ex3: randvector(3,uniform,1.2,3.5) Ex4: ranm(4,3,uniform,1.2,3.5) - + ''' return GiacMethods['uniformd'](self,*args) @@ -17873,10 +17873,10 @@ cdef class GiacMethods_base: Help for uniformd_cdf: uniformd_cdf(Real(a),Real(b),Real(x0),[Real(y0)]) Returns the probability that a uniform random variable on [a,b] is less than x0 (or between x0 and y0). - See also: 1/ uniformd 2/ uniform_icdf + See also: 1/ uniformd 2/ uniform_icdf Ex1:uniformd_cdf(3.2,5.7,4.4) Ex2:uniformd_cdf(3.2,5.7,4.4,5.4) - + ''' return GiacMethods['uniformd_cdf'](self,*args) @@ -17885,10 +17885,10 @@ cdef class GiacMethods_base: Help for uniformd_icdf: uniformd_icdf(Real(a),Real(b),Real(p)) Returns h such that the probability that a uniform random variable on [a,b] is less than h is p (0<=p<=1). - See also: 1/ uniform_cdf 2/ uniformd + See also: 1/ uniform_cdf 2/ uniformd Ex1:uniformd_icdf(4.2,10.3,0.95) Ex2:uniformd_icdf(3.2,5.7,0.48) - + ''' return GiacMethods['uniformd_icdf'](self,*args) @@ -17897,12 +17897,12 @@ cdef class GiacMethods_base: Help for unitV: unitV(Lst||Cplx) Returns the vector divided by its l2norm. It is also an option for plotfield. - See also: 1/ l2norm + See also: 1/ l2norm Ex1:unitV(3+4*i) Ex2:unitV([3,4]) Ex3: fieldplot(-t*y,[t,y],normalize) Ex4: fieldplot(-t*y,[t,y],normalize,xstep=0.5,ystep=0.5) - + ''' return GiacMethods['unitV'](self,*args) @@ -17911,9 +17911,9 @@ cdef class GiacMethods_base: Help for unquote: unquote(Expr) Evaluates a quoted expression (for example purge(c);a:=c;unquote(a):=3; put 3 in the variables a and c). - See also: 1/ quote + See also: 1/ quote Ex1:unquote(a) - + ''' return GiacMethods['unquote'](self,*args) @@ -17922,10 +17922,10 @@ cdef class GiacMethods_base: Help for upper: upper(Mtrx||Strng) Returns the upper triangular matrix (over the diagonal, included) or writes a string in uppercase. - See also: 1/ diag 2/ lower + See also: 1/ diag 2/ lower Ex1:upper([[1,2,3],[4,5,6],[7,8,9]]) Ex2:upper("hello") - + ''' return GiacMethods['upper'](self,*args) @@ -17934,10 +17934,10 @@ cdef class GiacMethods_base: Help for user_operator: user_operator(Str(R),Fnc(f),Opt(Binary||Unary||Delete)) Defines a binary operator and returns 0 (failure) or 1(success). - See also: 1/ + See also: 1/ Ex1:user_operator("R",(x,y)->x*y+x+y,Binary) Ex2:user_operator("R",(x,y)->x*y+x+y,Delete) - + ''' return GiacMethods['user_operator'](self,*args) @@ -17946,9 +17946,9 @@ cdef class GiacMethods_base: Help for usimplify: usimplify(Unit) Simplifies a unit in a unit object. - See also: 1/ convert 2/ mksa 3/ ufactor + See also: 1/ convert 2/ mksa 3/ ufactor Ex1:usimplify(100_(W*s)) - + ''' return GiacMethods['usimplify'](self,*args) @@ -17957,12 +17957,12 @@ cdef class GiacMethods_base: Help for valuation: valuation(Poly(P)) Returns the valuation (degree of the term of lowest degree) of the polynomial P. - See also: 1/ degree 2/ tcoeff + See also: 1/ degree 2/ tcoeff Ex1:valuation(x^4+x^3) Ex2:valuation([1,1,0,0,0]) Ex3:valuation(x^5+3*x^2) Ex4:valuation([5,0,0,3,0,0]) - + ''' return GiacMethods['valuation'](self,*args) @@ -17971,9 +17971,9 @@ cdef class GiacMethods_base: Help for vandermonde: vandermonde(Vect(V)) Returns the Vandermonde matrix=[V^0,V^1,..]. - See also: 1/ det + See also: 1/ det Ex1:vandermonde([1,2,a]) - + ''' return GiacMethods['vandermonde'](self,*args) @@ -17982,10 +17982,10 @@ cdef class GiacMethods_base: Help for variables_are_files: variables_are_files(:=Intg(0 or 1)) Pseudo-variable to specify if you want to save the variables as file "nameofthevariable.cas". - See also: 1/ cas_setup + See also: 1/ cas_setup Ex1: variables_are_files:=1 Ex2: variables_are_files:=0 - + ''' return GiacMethods['variables_are_files'](self,*args) @@ -17994,11 +17994,11 @@ cdef class GiacMethods_base: Help for variance: variance(Lst||Mtrx,[Lst]) Returns the variance of a list with the second argument as weights or the list of variances of the columns of a matrix. - See also: 1/ stddev 2/ mean + See also: 1/ stddev 2/ mean Ex1:variance([3,4,2]) Ex2:variance([1,2,3],[1,2,1]) Ex3:variance([[1,2,3],[5,6,7]]) - + ''' return GiacMethods['variance'](self,*args) @@ -18007,9 +18007,9 @@ cdef class GiacMethods_base: Help for version: version(NULL) Returns the giac version number; for example, you are using : giac 0.4.0 - See also: 1/ + See also: 1/ Ex1:version() - + ''' return GiacMethods['version'](self,*args) @@ -18018,11 +18018,11 @@ cdef class GiacMethods_base: Help for vertex_connectivity: vertex_connectivity(Graph(G)) Returns the largest integer k such that undirected connected graph G remains connected when fewer than k vertices are removed. - See also: 1/ edge_connectivity 2/ is_connected + See also: 1/ edge_connectivity 2/ is_connected Ex1:vertex_connectivity(graph("petersen")) Ex2:vertex_connectivity(graph("clebsch")) Ex3:vertex_connectivity(complete_graph(5)) - + ''' return GiacMethods['vertex_connectivity'](self,*args) @@ -18031,9 +18031,9 @@ cdef class GiacMethods_base: Help for vertex_degree: vertex_degree(Graph(G),Vrtx(v)) Returns the degree of the vertex v in G (i.e. the number of edges incident to v). - See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_in_degree 6/ vertex_out_degree + See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_in_degree 6/ vertex_out_degree Ex1:vertex_degree(digraph(trail(1,2,3,4,2)),2) - + ''' return GiacMethods['vertex_degree'](self,*args) @@ -18042,10 +18042,10 @@ cdef class GiacMethods_base: Help for vertex_distance: vertex_distance(Graph(G),Vrtx(s),Vrtx(t)||Lst(T)) Returns the number of edges in the shortest path from vertex s to vertex t in G. If such path does not exist, returns +infinity. For vector T of vertices from G returns the list of distances from s to each vertex t in T. - See also: 1/ allpairs_distance 2/ graph_diameter 3/ dijkstra 4/ shortest_path + See also: 1/ allpairs_distance 2/ graph_diameter 3/ dijkstra 4/ shortest_path Ex1:vertex_distance(graph("petersen"),1,4) Ex2:vertex_distance(graph("petersen"),1,[2,4]) - + ''' return GiacMethods['vertex_distance'](self,*args) @@ -18054,9 +18054,9 @@ cdef class GiacMethods_base: Help for vertex_in_degree: vertex_in_degree(Graph(G),Vrtx(v)) Returns the number of arcs in G entering the vertex v. - See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_degree 6/ vertex_out_degree + See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_degree 6/ vertex_out_degree Ex1:vertex_in_degree(digraph(trail(1,2,3,4,2)),2) - + ''' return GiacMethods['vertex_in_degree'](self,*args) @@ -18065,9 +18065,9 @@ cdef class GiacMethods_base: Help for vertex_out_degree: vertex_out_degree(Graph(G),Vrtx(v)) Returns the number of arcs in G emanating from the vertex v. - See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_degree 6/ vertex_in_degree + See also: 1/ degree_sequence 2/ is_regular 3/ maximum_degree 4/ minimum_degree 5/ vertex_degree 6/ vertex_in_degree Ex1:vertex_out_degree(digraph(trail(1,2,3,4,2)),2) - + ''' return GiacMethods['vertex_out_degree'](self,*args) @@ -18076,11 +18076,11 @@ cdef class GiacMethods_base: Help for vertices: vertices(Polygon or Polyedr(P)) Returns the list of the vertices of the polygon or polyhedron P. - See also: 1/ isosceles_triangle 2/ polyhedron + See also: 1/ isosceles_triangle 2/ polyhedron Ex1:vertices(isosceles_triangle(0,1,pi/4)) Ex2:vertices(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex3:vertices(isosceles_triangle(0,1,pi/4))[2] - + ''' return GiacMethods['vertices'](self,*args) @@ -18089,11 +18089,11 @@ cdef class GiacMethods_base: Help for vertices_abc: vertices_abc(Polygon or Polyedr(P)) Returns the list of the vertices of the polygon or polyhedron P. - See also: 1/ isosceles_triangle 2/ polyhedron + See also: 1/ isosceles_triangle 2/ polyhedron Ex1:vertices_abc(isosceles_triangle(0,1,pi/4)) Ex2:vertices_abc(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex3:vertices_abc(isosceles_triangle(0,1,pi/4))[2] - + ''' return GiacMethods['vertices_abc'](self,*args) @@ -18102,11 +18102,11 @@ cdef class GiacMethods_base: Help for vertices_abca: vertices_abca(Polygon or Polyedr(P)) Returns the closed list [A,B,...A] of the vertices of the polygon or polyhedron P. - See also: 1/ isosceles_triangle 2/ polyhedron + See also: 1/ isosceles_triangle 2/ polyhedron Ex1:vertices_abca(isosceles_triangle(0,1,pi/4)) Ex2:vertices_abca(polyhedron([0,0,0],[0,5,0],[0,0,5],[1,2,6])) Ex3:vertices_abca(isosceles_triangle(0,1,pi/4))[2] - + ''' return GiacMethods['vertices_abca'](self,*args) @@ -18115,9 +18115,9 @@ cdef class GiacMethods_base: Help for vpotential: vpotential(Vect(V),LstVar) Returns U such that curl(U)=V. - See also: 1/ curl 2/ potential + See also: 1/ curl 2/ potential Ex1:vpotential([2*x*y+3,x^2-4*z,-2*y*z],[x,y,z]) - + ''' return GiacMethods['vpotential'](self,*args) @@ -18126,9 +18126,9 @@ cdef class GiacMethods_base: Help for web_graph: web_graph(Intg(a),Intg(b)) Returns a web graph on a*b vertices, where a>=3 and b>=2. - See also: 1/ prism_graph 2/ wheel_graph + See also: 1/ prism_graph 2/ wheel_graph Ex1:web_graph(5,3) - + ''' return GiacMethods['web_graph'](self,*args) @@ -18137,11 +18137,11 @@ cdef class GiacMethods_base: Help for weibull: weibull(Real(k),Real(lambda),Real(theta),Real(x)) Returns the density of probability at x of the Weibull law with parameters k, lambda, theta (by default theta=0). - See also: 1/ weibull_cdf 2/ weibull_icdf + See also: 1/ weibull_cdf 2/ weibull_icdf Ex1:weibull(2.1,1.2,1.3) Ex2:weibull(2.1,1.2,0.0,1.3) Ex3:weibull(2.1,1.2,0.5,1.8) - + ''' return GiacMethods['weibull'](self,*args) @@ -18150,13 +18150,13 @@ cdef class GiacMethods_base: Help for weibull_cdf: weibull_cdf(Real(k),Real(lambda),Real(theta),Real(x0)) Returns the probability that a Weibull random variable of parameters k, lambda, theta is less than x0. - See also: 1/ weibulld 2/ weibull_icdf + See also: 1/ weibulld 2/ weibull_icdf Ex1:weibull_cdf(2.1,1.2,1.9) Ex2:weibull_cdf(2.1,1.2,0.0,1.9) Ex3:weibull_cdf(2.2,1.5,0.4,1.9) Ex4:weibull_cdf(2.2,1.5,0.4,1.2) Ex5:weibull_cdf(2.2,1.5,0.4,1.2,1.9) - + ''' return GiacMethods['weibull_cdf'](self,*args) @@ -18165,10 +18165,10 @@ cdef class GiacMethods_base: Help for weibull_icdf: weibull_icdf(Real(k),Real(lambda),Real(theta),Real(p)) Returns h such that the probability that a Weibull random variable of parameters k, lambda, theta is less than h is p (0<=p<=1). - See also: 1/ weibull_cdf 2/ weibull + See also: 1/ weibull_cdf 2/ weibull Ex1:weibull_icdf(4.2,1.3,0.0,0.95) Ex2:weibull_icdf(2.2,1.5,0.4,0.632) - + ''' return GiacMethods['weibull_icdf'](self,*args) @@ -18177,11 +18177,11 @@ cdef class GiacMethods_base: Help for weibulld: weibulld(Real(k),Real(lambda),Real(theta),Real(x)) Returns the density of probability at x of the Weibull law with parameters k, lambda, theta (by default theta=0). - See also: 1/ weibull_cdf 2/ weibull_icdf + See also: 1/ weibull_cdf 2/ weibull_icdf Ex1:weibulld(2.1,1.2,1.3) Ex2:weibulld(2.1,1.2,0.0,1.3) Ex3:weibulld(2.1,1.2,0.5,1.8) - + ''' return GiacMethods['weibulld'](self,*args) @@ -18190,13 +18190,13 @@ cdef class GiacMethods_base: Help for weibulld_cdf: weibulld_cdf(Real(k),Real(lambda),Real(theta),Real(x0)) Returns the probability that a Weibull random variable of parameters k, lambda, theta is less than x0. - See also: 1/ weibulld 2/ weibull_icdf + See also: 1/ weibulld 2/ weibull_icdf Ex1:weibulld_cdf(2.1,1.2,1.9) Ex2:weibulld_cdf(2.1,1.2,0.0,1.9) Ex3:weibulld_cdf(2.2,1.5,0.4,1.9) Ex4:weibulld_cdf(2.2,1.5,0.4,1.2) Ex5:weibulld_cdf(2.2,1.5,0.4,1.2,1.9) - + ''' return GiacMethods['weibulld_cdf'](self,*args) @@ -18205,10 +18205,10 @@ cdef class GiacMethods_base: Help for weibulld_icdf: weibulld_icdf(Real(k),Real(lambda),Real(theta),Real(p)) Returns h such that the probability that a Weibull random variable of parameters k, lambda, theta is less than h is p (0<=p<=1). - See also: 1/ weibull_cdf 2/ weibull + See also: 1/ weibull_cdf 2/ weibull Ex1:weibulld_icdf(4.2,1.3,0.0,0.95) Ex2:weibulld_icdf(2.2,1.5,0.4,0.632) - + ''' return GiacMethods['weibulld_icdf'](self,*args) @@ -18217,10 +18217,10 @@ cdef class GiacMethods_base: Help for weibullvariate: weibullvariate(Real(a),Real(b)) Returns a random real according to the Weibull distribution with parameters a>0 and b>0. - See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector + See also: 1/ rand 2/ randpoly 3/ randnorm 4/ randvector Ex1:weibullvariate(1,2) Ex2:weibullvariate(1.5,4) - + ''' return GiacMethods['weibullvariate'](self,*args) @@ -18229,9 +18229,9 @@ cdef class GiacMethods_base: Help for weight_matrix: weight_matrix(Graph(G)) Returns the weight matrix of G. - See also: 1/ set_edge_weight 2/ get_edge_weights 3/ is_weighted 4/ make_weighted 5/ assign_edge_weights + See also: 1/ set_edge_weight 2/ get_edge_weights 3/ is_weighted 4/ make_weighted 5/ assign_edge_weights Ex1:weight_matrix(graph(%{[[1,2],2],[[2,3],1]%}) - + ''' return GiacMethods['weight_matrix'](self,*args) @@ -18240,8 +18240,8 @@ cdef class GiacMethods_base: Help for weighted: weighted(Opt) Option for graph and digraph commands. - See also: 1/ directed 2/ graph 3/ digraph - + See also: 1/ directed 2/ graph 3/ digraph + ''' return GiacMethods['weighted'](self,*args) @@ -18250,8 +18250,8 @@ cdef class GiacMethods_base: Help for weights: weights(Opt) Option for the edges command. - See also: 1/ edges - + See also: 1/ edges + ''' return GiacMethods['weights'](self,*args) @@ -18260,9 +18260,9 @@ cdef class GiacMethods_base: Help for welch_window: welch_window(Lst,[Interval(n1..n2)]) Applies the Welch windowing function to the given signal u (or to the elements with indices between n1 and n2) and returns the result in a new list. - See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ bartlett_hann_window + See also: 1/ blackman_harris_window 2/ blackman_window 3/ bohman_window 4/ cosine_window 5/ gaussian_window 6/ hamming_window 7/ hann_poisson_window 8/ hann_window 9/ parzen_window 10/ poisson_window 11/ riemann_window 12/ triangle_window 13/ tukey_window 14/ bartlett_hann_window Ex1: scatterplot(welch_window(randvector(1000,0..1))) - + ''' return GiacMethods['welch_window'](self,*args) @@ -18271,9 +18271,9 @@ cdef class GiacMethods_base: Help for wheel_graph: wheel_graph(Intg(n)) Returns a wheel graph with n+1 vertices. - See also: 1/ star_graph 2/ web_graph + See also: 1/ star_graph 2/ web_graph Ex1:wheel_graph(5) - + ''' return GiacMethods['wheel_graph'](self,*args) @@ -18282,11 +18282,11 @@ cdef class GiacMethods_base: Help for widget_size: widget_size(Intg(n)) Changes the character sizes of the display on the xcas screen (size=n) and with more parameters define the general configuration. - See also: 1/ cas_setup + See also: 1/ cas_setup Ex1:widget_size(20) Ex2:widget_size(8) Ex3:widget_size(20,58,49,697,563,1,1,0) - + ''' return GiacMethods['widget_size'](self,*args) @@ -18295,10 +18295,10 @@ cdef class GiacMethods_base: Help for wilcoxonp: wilcoxonp(Intg,[Intg]) Distribution of the Wilcoxon or Mann-Whitney test for one or two samples. - See also: 1/ wilcoxont 2/ wilcoxons + See also: 1/ wilcoxont 2/ wilcoxons Ex1:wilcoxonp(4) Ex2:wilcoxonp(7,5) - + ''' return GiacMethods['wilcoxonp'](self,*args) @@ -18307,10 +18307,10 @@ cdef class GiacMethods_base: Help for wilcoxons: wilcoxons(List,List || Real) Rank statistic of Wilcoxon or Mann-Whitney for 1 sample and one median or 2 samples. - See also: 1/ wilcoxont 2/ wilcoxonp + See also: 1/ wilcoxont 2/ wilcoxonp Ex1:wilcoxons([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , [2, 6, 10, 11, 13, 14, 15, 18, 19, 20]) Ex2:wilcoxons([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , 10) - + ''' return GiacMethods['wilcoxons'](self,*args) @@ -18319,12 +18319,12 @@ cdef class GiacMethods_base: Help for wilcoxont: wilcoxont(List,List || Real,[Func],[Real]) Wilcoxon or Mann-Whitney test for one sample and a median or 2 samples. - See also: 1/ wilcoxonp 2/ wilcoxons 3/ studentt 4/ normalt + See also: 1/ wilcoxonp 2/ wilcoxons 3/ studentt 4/ normalt Ex1:wilcoxont([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , [2, 6, 10, 11, 13, 14, 15, 18, 19, 20]) Ex2:wilcoxont([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , [2, 6, 10, 11, 13, 14, 15, 18, 19, 20],0.01) Ex3:wilcoxont([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , 10,'>') Ex4:wilcoxont([1, 3, 4, 5, 7, 8, 8, 12, 15, 17] , 10,'>',0.05) - + ''' return GiacMethods['wilcoxont'](self,*args) @@ -18333,11 +18333,11 @@ cdef class GiacMethods_base: Help for writergb: writergb(Str(s),Lst) Write a PNG picture file named s either from a list [[number_channels,width,height],red,green,alpha,blue] where red,green,alpha,blue are matrices of pixels color or from a matrix of grey pixels or from 3 matrices of RGB colored pixels. - See also: 1/ readrgb + See also: 1/ readrgb Ex1:writergb("image.png",[[255,0],[0,255]]) Ex2:writergb("image.png",[[255,0],[0,0]],[[0,255],[0,0]],[[0,0],[255,0]]) Ex3: a:=readrgb("rgb_image.png");writergb("brg_image.png",[a[0],a[4],a[1],a[3],a[2]]) - + ''' return GiacMethods['writergb'](self,*args) @@ -18346,10 +18346,10 @@ cdef class GiacMethods_base: Help for writewav: writewav(Str(s),Lst(l)) Writes a WAV sound file. - See also: 1/ readwav + See also: 1/ readwav Ex1:writewav("la.wav",2^14*(sin(2*pi*440*soundsec(1)))) Ex2:writewav("beep.wav",[[1,16,44100,80000],[65000$10000,0$10000,65000$10000,0$10000]]) - + ''' return GiacMethods['writewav'](self,*args) @@ -18358,10 +18358,10 @@ cdef class GiacMethods_base: Help for xcas_mode: xcas_mode(Intg(0) or 1 or 2 or 3) Switches to mode Xcas (0), Maple (1), Mupad (2), TI89 (3). - See also: 1/ python_compat + See also: 1/ python_compat Ex1:xcas_mode(1) Ex2:xcas_mode(0) - + ''' return GiacMethods['xcas_mode'](self,*args) @@ -18370,9 +18370,9 @@ cdef class GiacMethods_base: Help for xml_print: xml_print(Str) Indents a XML code given in a string (pretty print). - See also: 1/ export_mathml + See also: 1/ export_mathml Ex1:xml_print(export_mathml(a+2*b)) - + ''' return GiacMethods['xml_print'](self,*args) @@ -18382,7 +18382,7 @@ cdef class GiacMethods_base: xyztrange(SeqReal) xyztrange puts or erases the axes on the graphic-screen (cf button Cfg). Ex1:xyztrange(-5.0,5.0,-5.0,2.0,-10.0,10.0,-1.0,6.0,-5.0,5.0,-1.2384,2.0,1,0.0,1.0) - + ''' return GiacMethods['xyztrange'](self,*args) @@ -18391,12 +18391,12 @@ cdef class GiacMethods_base: Help for zeros: zeros(Expr,[Var]) Returns the zeros (real or complex according to the mode) of the expression (or the matrix where the lines are the solutions of the system : expression1=0,expression2=0...). - See also: 1/ + See also: 1/ Ex1:zeros(x^2+4) Ex2:zeros(ln(x)^2-4) Ex3:zeros(ln(y)^2-2,y) Ex4:zeros([x^2-1,x^2-y^2],[x,y]) - + ''' return GiacMethods['zeros'](self,*args) @@ -18405,10 +18405,10 @@ cdef class GiacMethods_base: Help for ztrans: ztrans(Expr,[Var],[ZtransVar]) z transform of a sequence. - See also: 1/ invztrans 2/ laplace 3/ invlaplace + See also: 1/ invztrans 2/ laplace 3/ invlaplace Ex1:ztrans(a^x) Ex2:ztrans(a^n,n,z) - + ''' return GiacMethods['ztrans'](self,*args) @@ -18417,10 +18417,10 @@ cdef class GiacMethods_base: Help for type: type(Expr) Returns n in [1..12] that defines the type of the argument. - See also: 1/ DOM_FLOAT 2/ DOM_INT 3/ DOM_COMPLEX 4/ DOM_IDENT 5/ DOM_LIST 6/ DOM_SYMBOLIC 7/ DOM_RAT 8/ DOM_STRING 9/ DOM_FUNC 10/ subtype + See also: 1/ DOM_FLOAT 2/ DOM_INT 3/ DOM_COMPLEX 4/ DOM_IDENT 5/ DOM_LIST 6/ DOM_SYMBOLIC 7/ DOM_RAT 8/ DOM_STRING 9/ DOM_FUNC 10/ subtype Ex1:type("abc") Ex2:type([1,2,3]) - + ''' return GiacMethods['type'](self,*args) @@ -18429,12 +18429,12 @@ cdef class GiacMethods_base: Help for zip: zip(Fnc2d(f),Lst(l1),Lst(l2),[Val(default)]) Returns a list whose j-th entry is f(l1[j],l2[j]): without default value its length is the minimum of the lengths of the two input lists and otherwise the shorter list is padded with the default value. - See also: 1/ + See also: 1/ Ex1:zip('+',[a,b,c,d], [1,2,3,4]) Ex2:zip('+',[a,b,c,d], [1,2,3]) Ex3:zip('+',[a,b,c,d], [1,2,3],5) Ex4:zip(sum,[a,b,c,d], [1,2,3,4]) - + ''' return GiacMethods['zip'](self,*args)