Fix doctests for 'make pari_bnf() deterministic'

src/sage/dynamics/arithmetic_dynamics/berkovich_ds.py

@@ -690,10 +690,10 @@ def conjugate(self, M, adjugate=False, new_ideal=None):
 
             sage: # needs sage.rings.number_field
             sage: ideal = A.ideal(5).factor()[1][0]; ideal
-            Fractional ideal (-a + 2)
+            Fractional ideal (-2*a - 1)
             sage: g = f.conjugate(conj, new_ideal=ideal)
             sage: g.domain().ideal()
-            Fractional ideal (-a + 2)
+            Fractional ideal (-2*a - 1)
         """
         if self.domain().is_padic_base():
             return DynamicalSystem_Berkovich(self._system.conjugate(M, adjugate=adjugate))

src/sage/rings/finite_rings/residue_field.pyx

@@ -495,9 +495,9 @@ class ResidueField_generic(Field):
 
         sage: # needs sage.rings.number_field
         sage: I = QQ[i].factor(2)[0][0]; I
-        Fractional ideal (-I - 1)
+        Fractional ideal (I - 1)
         sage: k = I.residue_field(); k
-        Residue field of Fractional ideal (-I - 1)
+        Residue field of Fractional ideal (I - 1)
         sage: type(k)
         <class 'sage.rings.finite_rings.residue_field.ResidueFiniteField_prime_modn_with_category'>
 
@@ -1007,7 +1007,7 @@ cdef class ReductionMap(Map):
             sage: cr
             Partially defined reduction map:
               From: Number Field in a with defining polynomial x^2 + 1
-              To:   Residue field of Fractional ideal (-a + 1)
+              To:   Residue field of Fractional ideal (a - 1)
             sage: cr == r                       # not implemented
             True
             sage: r(2 + a) == cr(2 + a)
@@ -1038,7 +1038,7 @@ cdef class ReductionMap(Map):
             sage: cr
             Partially defined reduction map:
               From: Number Field in a with defining polynomial x^2 + 1
-              To:   Residue field of Fractional ideal (-a + 1)
+              To:   Residue field of Fractional ideal (a - 1)
             sage: cr == r                       # not implemented
             True
             sage: r(2 + a) == cr(2 + a)
@@ -1070,7 +1070,7 @@ cdef class ReductionMap(Map):
             sage: r = F.reduction_map(); r
             Partially defined reduction map:
               From: Number Field in a with defining polynomial x^2 + 1
-              To:   Residue field of Fractional ideal (-a + 1)
+              To:   Residue field of Fractional ideal (a - 1)
 
         We test that calling the function also works after copying::
 
@@ -1082,7 +1082,7 @@ cdef class ReductionMap(Map):
             Traceback (most recent call last):
             ...
             ZeroDivisionError: Cannot reduce field element 1/2*a
-            modulo Fractional ideal (-a + 1): it has negative valuation
+            modulo Fractional ideal (a - 1): it has negative valuation
 
             sage: # needs sage.rings.finite_rings
             sage: R.<t> = GF(2)[]; h = t^5 + t^2 + 1

src/sage/rings/integer.pyx

@@ -5585,7 +5585,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
             sage: 5.is_norm(K)
             False
             sage: n.is_norm(K, element=True)
-            (True, 4*beta + 6)
+            (True, -4*beta + 6)
             sage: n.is_norm(K, element=True)[1].norm()
             4
             sage: n = 5

src/sage/rings/number_field/S_unit_solver.py

@@ -1381,7 +1381,7 @@ def defining_polynomial_for_Kp(prime, prec=106):
         sage: from sage.rings.number_field.S_unit_solver import defining_polynomial_for_Kp
         sage: K.<a> = QuadraticField(2)
         sage: p2 = K.prime_above(7); p2
-        Fractional ideal (-2*a + 1)
+        Fractional ideal (2*a - 1)
         sage: defining_polynomial_for_Kp(p2, 10)
         x + 266983762
 
@@ -2170,23 +2170,23 @@ def construct_complement_dictionaries(split_primes_list, SUK, verbose=False):
         sage: SUK = K.S_unit_group(S=K.primes_above(H))
         sage: split_primes_list = [3, 7]
         sage: actual = construct_complement_dictionaries(split_primes_list, SUK)
-        sage: expected = {3: {(1, 1, 0): [(1, 0, 0), (1, 1, 0)],
-        ....:                 (1, 0, 0): [(1, 0, 0), (1, 1, 0)]},
-        ....:             7: {(1, 1, 0): [(1, 0, 0), (1, 4, 4), (1, 2, 2)],
-        ....:                 (1, 3, 2): [(1, 0, 0), (1, 4, 4), (1, 2, 2)],
-        ....:                 (1, 5, 4): [(1, 0, 0), (1, 4, 4), (1, 2, 2)],
-        ....:                 (1, 0, 4): [(1, 2, 4), (1, 4, 0), (1, 0, 2)],
-        ....:                 (1, 2, 0): [(1, 2, 4), (1, 4, 0), (1, 0, 2)],
-        ....:                 (1, 4, 2): [(1, 2, 4), (1, 4, 0), (1, 0, 2)],
-        ....:                 (1, 1, 2): [(1, 1, 2), (1, 3, 4), (1, 5, 0)],
-        ....:                 (1, 3, 4): [(1, 1, 2), (1, 3, 4), (1, 5, 0)],
-        ....:                 (1, 5, 0): [(1, 1, 2), (1, 3, 4), (1, 5, 0)],
-        ....:                 (1, 0, 2): [(1, 0, 4), (1, 4, 2), (1, 2, 0)],
-        ....:                 (1, 2, 4): [(1, 0, 4), (1, 4, 2), (1, 2, 0)],
-        ....:                 (1, 4, 0): [(1, 0, 4), (1, 4, 2), (1, 2, 0)],
-        ....:                 (1, 0, 0): [(1, 5, 4), (1, 3, 2), (1, 1, 0)],
-        ....:                 (1, 2, 2): [(1, 5, 4), (1, 3, 2), (1, 1, 0)],
-        ....:                 (1, 4, 4): [(1, 5, 4), (1, 3, 2), (1, 1, 0)]}}
+        sage: expected = {3: {(0, 1, 0): [(0, 1, 0), (1, 0, 0)],
+        ....:                 (1, 0, 0): [(0, 1, 0), (1, 0, 0)]},
+        ....:             7: {(0, 1, 0): [(1, 0, 0), (1, 2, 2), (1, 4, 4)],
+        ....:                 (0, 1, 2): [(0, 1, 2), (0, 3, 4), (0, 5, 0)],
+        ....:                 (0, 3, 2): [(1, 0, 0), (1, 2, 2), (1, 4, 4)],
+        ....:                 (0, 3, 4): [(0, 1, 2), (0, 3, 4), (0, 5, 0)],
+        ....:                 (0, 5, 0): [(0, 1, 2), (0, 3, 4), (0, 5, 0)],
+        ....:                 (0, 5, 4): [(1, 0, 0), (1, 2, 2), (1, 4, 4)],
+        ....:                 (1, 0, 0): [(0, 1, 0), (0, 3, 2), (0, 5, 4)],
+        ....:                 (1, 0, 2): [(1, 0, 4), (1, 2, 0), (1, 4, 2)],
+        ....:                 (1, 0, 4): [(1, 0, 2), (1, 2, 4), (1, 4, 0)],
+        ....:                 (1, 2, 0): [(1, 0, 2), (1, 2, 4), (1, 4, 0)],
+        ....:                 (1, 2, 2): [(0, 1, 0), (0, 3, 2), (0, 5, 4)],
+        ....:                 (1, 2, 4): [(1, 0, 4), (1, 2, 0), (1, 4, 2)],
+        ....:                 (1, 4, 0): [(1, 0, 4), (1, 2, 0), (1, 4, 2)],
+        ....:                 (1, 4, 2): [(1, 0, 2), (1, 2, 4), (1, 4, 0)],
+        ....:                 (1, 4, 4): [(0, 1, 0), (0, 3, 2), (0, 5, 4)]}}
         sage: all(set(actual[p][vec]) == set(expected[p][vec])
         ....:     for p in [3, 7] for vec in expected[p])
         True

src/sage/rings/number_field/class_group.py

@@ -524,9 +524,9 @@ def gens_ideals(self):
             Class group of order 68 with structure C34 x C2 of Number Field
             in a with defining polynomial x^2 + x + 23899
             sage: C.gens()
-            (Fractional ideal class (7, a + 5), Fractional ideal class (5, a + 3))
+            (Fractional ideal class (83, a + 21), Fractional ideal class (15, a + 8))
             sage: C.gens_ideals()
-            (Fractional ideal (7, a + 5), Fractional ideal (5, a + 3))
+            (Fractional ideal (83, a + 21), Fractional ideal (15, a + 8))
         """
         return self.gens_values()
 

src/sage/rings/number_field/number_field.py

@@ -7136,7 +7136,7 @@ def units(self, proof=None):
 
             sage: K.<a> = NumberField(1/2*x^2 - 1/6)
             sage: K.units()
-            (-3*a + 2,)
+            (3*a + 2,)
         """
         proof = proof_flag(proof)
 

src/sage/rings/number_field/number_field_element.pyx

@@ -1954,7 +1954,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             sage: x = polygen(ZZ, 'x')
             sage: K.<i> = NumberField(x^2 + 1)
             sage: (6*i + 6).factor()
-            (i) * (-i - 1)^3 * 3
+            (i - 1)^3 * 3
 
         In the following example, the class number is 2.  If a factorization
         in prime elements exists, we will find it::
@@ -2043,7 +2043,7 @@ cdef class NumberFieldElement(NumberFieldElement_base):
             0
             sage: R = K.maximal_order()
             sage: R(i+1).gcd(2)
-            i + 1
+            i - 1
             sage: R = K.order(2*i)
             sage: R(1).gcd(R(4*i))
             1

src/sage/rings/number_field/number_field_ideal_rel.py

@@ -189,7 +189,7 @@ def absolute_ideal(self, names='a'):
             sage: J.absolute_norm()
             2
             sage: J.ideal_below()
-            Fractional ideal (b)
+            Fractional ideal (-b)
             sage: J.ideal_below().norm()
             2
         """
@@ -385,7 +385,7 @@ def relative_norm(self):
             sage: K.<a> = NumberField(x^2 + 6)
             sage: L.<b> = K.extension(K['x'].gen()^4 + a)
             sage: N = L.ideal(b).relative_norm(); N
-            Fractional ideal (a)
+            Fractional ideal (-a)
             sage: N.parent()
             Monoid of ideals of Number Field in a with defining polynomial x^2 + 6
             sage: N.ring()
@@ -916,7 +916,7 @@ def is_NumberFieldFractionalIdeal_rel(x):
         sage: is_NumberFieldFractionalIdeal_rel(I)
         True
         sage: N = I.relative_norm(); N
-        Fractional ideal (a)
+        Fractional ideal (-a)
         sage: is_NumberFieldFractionalIdeal_rel(N)
         False
     """

src/sage/rings/number_field/order.py

@@ -496,7 +496,7 @@ def fractional_ideal(self, *args, **kwds):
             sage: K.<a> = NumberField(x^2 + 2)
             sage: R = K.maximal_order()
             sage: R.fractional_ideal(2/3 + 7*a, a)
-            Fractional ideal (-1/3*a)
+            Fractional ideal (1/3*a)
         """
         return self.number_field().fractional_ideal(*args, **kwds)
 
@@ -570,7 +570,7 @@ def __mul__(self, right):
             sage: k.<a> = NumberField(x^2 + 5077); G = k.class_group(); G
             Class group of order 22 with structure C22 of Number Field in a with defining polynomial x^2 + 5077
             sage: G.0 ^ -9
-            Fractional ideal class (67, a + 45)
+            Fractional ideal class (43, a + 13)
             sage: Ok = k.maximal_order(); Ok
             Maximal Order generated by a in Number Field in a with defining polynomial x^2 + 5077
             sage: Ok * (11, a + 7)
@@ -2933,7 +2933,7 @@ def GaussianIntegers(names='I', latex_name='i'):
         sage: ZZI
         Gaussian Integers generated by I in Number Field in I with defining polynomial x^2 + 1 with I = 1*I
         sage: factor(3 + I)
-        (-I) * (I - 2) * (-I + 1)
+        (-2*I - 1) * (I - 1)
         sage: CC(I)
         1.00000000000000*I
         sage: I.minpoly()
@@ -2964,7 +2964,7 @@ def EisensteinIntegers(names='omega'):
          with defining polynomial x^2 + x + 1
          with omega = -0.50000000000000000? + 0.866025403784439?*I
         sage: factor(3 + omega)
-        (omega + 1) * (-2*omega + 1)
+        (omega) * (-3*omega - 2)
         sage: CC(omega)
         -0.500000000000000 + 0.866025403784439*I
         sage: omega.minpoly()

src/sage/rings/number_field/selmer_group.py

@@ -489,9 +489,9 @@ def pSelmerGroup(K, S, p, proof=None, debug=False):
 
         sage: [K.ideal(g).factor() for g in gens]
         [(Fractional ideal (2, a + 1)) * (Fractional ideal (3, a + 1)),
-        Fractional ideal (a),
-        (Fractional ideal (2, a + 1))^2,
-        1]
+         Fractional ideal (-a),
+         (Fractional ideal (2, a + 1))^2,
+         1]
 
         sage: toKS2(10)
         (0, 0, 1, 1)

src/sage/rings/polynomial/polynomial_quotient_ring.py

@@ -1877,7 +1877,7 @@ def selmer_generators(self, S, m, proof=True):
             sage: D.selmer_generators([K.ideal(2, -a + 1),
             ....:                      K.ideal(3, a + 1),
             ....:                      K.ideal(a)], 3)
-            [2, a + 1, -a]
+            [2, a + 1, a]
         """
         fields, isos, iso_classes = self._S_decomposition(tuple(S))
         n = len(fields)

src/sage/rings/rational.pyx

@@ -1446,7 +1446,7 @@ cdef class Rational(sage.structure.element.FieldElement):
             sage: 0.is_norm(K)
             True
             sage: (1/7).is_norm(K, element=True)
-            (True, -3/7*beta + 5/7)
+            (True, 1/7*beta + 3/7)
             sage: (1/10).is_norm(K, element=True)
             (False, None)
             sage: (1/691).is_norm(QQ, element=True)
@@ -1558,7 +1558,7 @@ cdef class Rational(sage.structure.element.FieldElement):
         EXAMPLES::
 
             sage: QQ(2)._bnfisnorm(QuadraticField(-1, 'i'))                             # needs sage.rings.number_field
-            (-i + 1, 1)
+            (i - 1, 1)
             sage: x = polygen(QQ, 'x')
             sage: 7._bnfisnorm(NumberField(x^3 - 2, 'b'))                               # needs sage.rings.number_field
             (1, 7)

src/sage/schemes/berkovich/berkovich_space.py

@@ -201,7 +201,7 @@ def ideal(self):
             sage: ideal = A.prime_above(5)
             sage: B = Berkovich_Cp_Projective(A, ideal)
             sage: B.ideal()
-            Fractional ideal (-a - 2)
+            Fractional ideal (2*a - 1)
 
         ::
 

src/sage/schemes/plane_conics/con_number_field.py

@@ -121,7 +121,7 @@ def has_rational_point(self, point=False, obstruction=False,
             sage: K.<i> = QuadraticField(-1)
             sage: C = Conic(K, [1, 3, -5])
             sage: C.has_rational_point(point=True, obstruction=True)
-            (False, Fractional ideal (i + 2))
+            (False, Fractional ideal (2*i - 1))
             sage: C.has_rational_point(algorithm='rnfisnorm')
             False
             sage: C.has_rational_point(algorithm='rnfisnorm', obstruction=True,