more doctests

src/sage/algebras/lie_algebras/lie_algebra_element.pyx

@@ -356,7 +356,7 @@ cdef class LieAlgebraElementWrapper(ElementWrapper):
             sage: x = L.gen(2); x
             (1,2,3)
             sage: y = L.gen(1); y
-            (1,3,2)
+            (1,3)
             sage: u = x*3; u
             3*(1,2,3)
             sage: parent(u) == L
@@ -366,13 +366,13 @@ cdef class LieAlgebraElementWrapper(ElementWrapper):
             sage: parent(u) == L
             True
             sage: elt = x*y - y*x; elt
-            0
+            -b3 + b5
             sage: xp, yp = x.lift_associative(), y.lift_associative()
             sage: eltp = xp*yp - yp*xp; eltp
-            0
+            -(2,3) + (1,2)
             sage: G = list(S.basis())
             sage: G[4] - G[5]
-            -(1,2) + (1,3)
+            -(1,2) + (1,3,2)
 
         TESTS::
 

src/sage/categories/finite_dimensional_algebras_with_basis.py

@@ -885,10 +885,10 @@ def peirce_decomposition(self, idempotents=None, check=True):
                 sage: [[decomposition[i][j].dimension()          # long time (4s)
                 ....:   for j in range(len(decomposition))]
                 ....:  for i in range(len(decomposition))]
-                [[9, 0, 0, 0, 0],
+                [[1, 0, 0, 0, 0],
                  [0, 9, 0, 0, 0],
                  [0, 0, 4, 0, 0],
-                 [0, 0, 0, 1, 0],
+                 [0, 0, 0, 9, 0],
                  [0, 0, 0, 0, 1]]
 
             The dimension of each block is `d^2`, where `d` is the

src/sage/categories/finite_dimensional_lie_algebras_with_basis.py

@@ -334,7 +334,7 @@ def structure_coefficients(self, include_zeros=False):
                 sage: S = GroupAlgebra(G, QQ)
                 sage: L = LieAlgebra(associative=S)
                 sage: L.structure_coefficients()
-                Finite family {((1,3,2), (1,3)): (2,3) - (1,2), ((1,2,3), (1,3)): -(2,3) + (1,2), ((1,3,2), (1,2)): -(2,3) + (1,3), ((2,3), (1,3)): -(1,2,3) + (1,3,2), ((1,2,3), (1,2)): (2,3) - (1,3), ((1,3), (1,2)): -(1,2,3) + (1,3,2), ((2,3), (1,2)): (1,2,3) - (1,3,2), ((1,3,2), (2,3)): (1,2) - (1,3), ((1,2,3), (2,3)): -(1,2) + (1,3)}
+                Finite family {((1,3), (2,3)): (1,2,3) - (1,3,2), ((2,3), (1,3,2)): -(1,2) + (1,3), ((1,3), (1,3,2)): -(2,3) + (1,2), ((1,3,2), (1,2)): -(2,3) + (1,3), ((1,3), (1,2,3)): (2,3) - (1,2), ((1,2,3), (1,2)): (2,3) - (1,3), ((1,3), (1,2)): -(1,2,3) + (1,3,2), ((2,3), (1,2)): (1,2,3) - (1,3,2), ((1,2,3), (2,3)): -(1,2) + (1,3)}
                 """
             d = {}
             B = self.basis()

src/sage/categories/groups.py

@@ -401,9 +401,9 @@ class provides even greater flexibility, including changing
                 k| a b c a b c b a c b a c
                 l| a b c a b c c b a c b a
                 sage: trans = T.translation()
-                sage: comm = [trans['a'], trans['d'],trans['h']]
+                sage: comm = [trans['a'], trans['b'],trans['c']]
                 sage: comm
-                [(), (1,2)(3,4), (1,4,2,3)(5,6)]
+                [(), (5,6,7), (5,7,6)]
                 sage: P=G.cayley_table(elements=comm)
                 sage: P
                 *  a b c

src/sage/categories/modules_with_basis.py

@@ -771,7 +771,7 @@ def submodule(self, gens, check=True, already_echelonized=False,
                 sage: S3A = S3.algebra(QQ)
                 sage: basis = S3A.annihilator_basis(S3A.algebra_generators(), S3A.bracket)
                 sage: basis
-                ((), (1,2,3) + (1,3,2), (2,3) + (1,2) + (1,3))
+                ((), (2,3) + (1,2) + (1,3), (1,2,3) + (1,3,2))
                 sage: center = S3A.submodule(basis,
                 ....:                        category=AlgebrasWithBasis(QQ).Subobjects(),
                 ....:                        already_echelonized=True)
@@ -782,7 +782,7 @@ def submodule(self, gens, check=True, already_echelonized=False,
                 sage: center.print_options(prefix='c')
                 sage: c = center.basis()
                 sage: c[1].lift()
-                (1,2,3) + (1,3,2)
+                (2,3) + (1,2) + (1,3)
                 sage: c[0]^2
                 c[0]
                 sage: e = 1/6*(c[0]+c[1]+c[2])

src/sage/combinat/constellation.py

@@ -1202,8 +1202,8 @@ def braid_group_action(self):
             sage: C = Constellations(3,3)
             sage: C.braid_group_action()
             [Looped multi-digraph on 3 vertices,
-             Looped multi-digraph on 1 vertex,
-             Looped multi-digraph on 3 vertices]
+             Looped multi-digraph on 3 vertices,
+             Looped multi-digraph on 1 vertex]
         """
         G = []
         for c in self:
@@ -1226,9 +1226,9 @@ def braid_group_orbits(self):
             sage: [x.profile() for x in O[0]]
             [([1, 1, 1], [3], [3]), ([3], [1, 1, 1], [3]), ([3], [3], [1, 1, 1])]
             sage: [x.profile() for x in O[1]]
-            [([3], [3], [3])]
-            sage: [x.profile() for x in O[2]]
             [([2, 1], [2, 1], [3]), ([2, 1], [3], [2, 1]), ([3], [2, 1], [2, 1])]
+            sage: [x.profile() for x in O[2]]
+            [([3], [3], [3])]
         """
         return [g.vertices() for g in self.braid_group_action()]
 

src/sage/combinat/symmetric_group_algebra.py

@@ -93,7 +93,7 @@ def SymmetricGroupAlgebra(R, W, category=None):
         sage: SGA.group()
         Symmetric group of order 4! as a permutation group
         sage: SGA.an_element()
-        () + (1,2,3,4) + 2*(1,3)(2,4) + 3*(1,4)(2,3)
+        () + (1,2,3,4) + 3*(1,2,4) + 2*(1,4)
 
         sage: SGA = SymmetricGroupAlgebra(QQ, WeylGroup(["A",3], prefix='s')); SGA
         Symmetric group algebra of order 4 over Rational Field
@@ -247,7 +247,7 @@ def __init__(self, R, W, category):
             sage: G = SymmetricGroup(4).algebra(QQ)
             sage: S = SymmetricGroupAlgebra(QQ,4)
             sage: S(G.an_element())
-            [1, 2, 3, 4] + [2, 3, 4, 1] + 2*[3, 4, 1, 2] + 3*[4, 3, 2, 1]
+            [1, 2, 3, 4] + [2, 3, 4, 1] + 3*[2, 4, 3, 1] + 2*[4, 2, 3, 1]
             sage: G(S.an_element())
             () + 2*(3,4) + 3*(2,3) + (1,4,3,2)
 
@@ -936,7 +936,7 @@ def retract_okounkov_vershik(self, f, m):
 
             sage: G = SymmetricGroup(4).algebra(QQ)
             sage: G.retract_okounkov_vershik(G.an_element(), 3)
-            () + 3*(2,3) + (1,2,3) + 2*(1,3)
+            3*() + 3*(1,2) + (1,2,3)
 
         .. SEEALSO::
 

src/sage/graphs/generic_graph.py

@@ -17781,7 +17781,7 @@ def _color_by_label(self, format='hex', as_function=False, default_color = "blac
 
             sage: f = G._color_by_label(as_function=True)
             sage: [f(1), f(2), f(3)]
-            ['#ff0000', '#0000ff', '#00ff00']
+            ['#0000ff', '#ff0000', '#00ff00']
             sage: f = G._color_by_label({1: "blue", 2: "red", 3: "green"}, as_function=True)
             sage: [f(1), f(2), f(3)]
             ['blue', 'red', 'green']
@@ -17795,9 +17795,9 @@ def _color_by_label(self, format='hex', as_function=False, default_color = "blac
         The default output is a dictionary assigning edges to colors::
 
             sage: G._color_by_label()
-            {'#0000ff': [((1,3,2,4), (1,2,4), 2), ...],
+            {'#0000ff': [((1,3,2,4), (1,3)(2,4), 1), ...],
              '#00ff00': [((1,3,2,4), (1,4)(2,3), 3), ...],
-             '#ff0000': [((1,3,2,4), (1,3)(2,4), 1), ...]}
+             '#ff0000': [((1,3,2,4), (1,2,4), 2), ...]}
 
             sage: G._color_by_label({1: "blue", 2: "red", 3: "green"})
             {'blue': [((1,3,2,4), (1,3)(2,4), 1), ...],

src/sage/groups/libgap_mixin.py

@@ -398,13 +398,13 @@ def character_table(self):
             [ 2 -1  0]
             [ 1  1  1]
             sage: MatrixGroup(SymmetricGroup(5)).character_table()
+            [ 1  1  1  1  1  1  1]
             [ 1 -1 -1  1 -1  1  1]
             [ 4  0  1 -1 -2  1  0]
+            [ 4  0 -1 -1  2  1  0]
+            [ 5 -1  1  0  1 -1  1]
             [ 5  1 -1  0 -1 -1  1]
             [ 6  0  0  1  0  0 -2]
-            [ 5 -1  1  0  1 -1  1]
-            [ 4  0 -1 -1  2  1  0]
-            [ 1  1  1  1  1  1  1]
         """
         #code from function in permgroup.py, but modified for
         #how gap handles these groups.

src/sage/matrix/operation_table.py

@@ -316,9 +316,9 @@ class OperationTable(SageObject):
     group ``H``, using a simple ``for`` loop::
 
         sage: L = H.list()    #list of elements of the group H
-        sage: elts = [L[i] for i in {0, 2}]
+        sage: elts = [L[i] for i in {0, 1}]
         sage: elts
-        [(), (1,4,3,2)]
+        [(), (1,3)(2,4)]
         sage: OperationTable(H, operator.mul, elements=elts)
         *  a b
          +----

src/sage/tests/books/judson-abstract-algebra/groups-sage.py

@@ -132,7 +132,7 @@
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
     sage: [[a(x) for x in triangle.domain()] for a in triangle]
-    [[1, 2, 3], [3, 1, 2], [2, 3, 1], [1, 3, 2], [3, 2, 1], [2, 1, 3]]
+    [[1, 2, 3], [3, 2, 1], [2, 3, 1], [1, 3, 2], [3, 1, 2], [2, 1, 3]]
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
@@ -165,35 +165,35 @@
     *  a b c d e f
      +------------
     a| a b c d e f
-    b| b c a f d e
-    c| c a b e f d
+    b| b a d c f e
+    c| c f e b a d
     d| d e f a b c
-    e| e f d c a b
-    f| f d e b c a
+    e| e d a f c b
+    f| f c b e d a
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
     sage: triangle.cayley_table(names='elements')
-          *       () (1,3,2) (1,2,3)   (2,3)   (1,3)   (1,2)
+          *       ()   (1,3) (1,2,3)   (2,3) (1,3,2)   (1,2)
            +------------------------------------------------
-         ()|      () (1,3,2) (1,2,3)   (2,3)   (1,3)   (1,2)
-    (1,3,2)| (1,3,2) (1,2,3)      ()   (1,2)   (2,3)   (1,3)
-    (1,2,3)| (1,2,3)      () (1,3,2)   (1,3)   (1,2)   (2,3)
-      (2,3)|   (2,3)   (1,3)   (1,2)      () (1,3,2) (1,2,3)
-      (1,3)|   (1,3)   (1,2)   (2,3) (1,2,3)      () (1,3,2)
-      (1,2)|   (1,2)   (2,3)   (1,3) (1,3,2) (1,2,3)      ()
+         ()|      ()   (1,3) (1,2,3)   (2,3) (1,3,2)   (1,2)
+      (1,3)|   (1,3)      ()   (2,3) (1,2,3)   (1,2) (1,3,2)
+    (1,2,3)| (1,2,3)   (1,2) (1,3,2)   (1,3)      ()   (2,3)
+      (2,3)|   (2,3) (1,3,2)   (1,2)      ()   (1,3) (1,2,3)
+    (1,3,2)| (1,3,2)   (2,3)      ()   (1,2) (1,2,3)   (1,3)
+      (1,2)|   (1,2) (1,2,3)   (1,3) (1,3,2)   (2,3)      ()
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::
 
     sage: triangle.cayley_table(names=['id','u3','r1','r2','u1','u2'])
      *  id u3 r1 r2 u1 u2
       +------------------
     id| id u3 r1 r2 u1 u2
-    u3| u3 r1 id u2 r2 u1
-    r1| r1 id u3 u1 u2 r2
+    u3| u3 id r2 r1 u2 u1
+    r1| r1 u2 u1 u3 id r2
     r2| r2 u1 u2 id u3 r1
-    u1| u1 u2 r2 r1 id u3
-    u2| u2 r2 u1 u3 r1 id
+    u1| u1 r2 id u2 r1 u3
+    u2| u2 r1 u3 u1 r2 id
 
 ~~~~~~~~~~~~~~~~~~~~~~ ::