Update tests output for pari 2.17

src/sage/arith/misc.py

@@ -2693,7 +2693,7 @@ def factor(n, proof=None, int_=False, algorithm='pari', verbose=0, **kwds):
 
         sage: K.<i> = QuadraticField(-1)                                                # needs sage.rings.number_field
         sage: factor(122 - 454*i)                                                       # needs sage.rings.number_field
-        (-i) * (-i - 2)^3 * (i + 1)^3 * (-2*i + 3) * (i + 4)
+        (-i - 2)^3 * (-i - 1)^3 * (3*i + 2) * (i + 4)
 
     To access the data in a factorization::
 
@@ -2776,7 +2776,7 @@ def radical(n, *args, **kwds):
         ArithmeticError: radical of 0 is not defined
         sage: K.<i> = QuadraticField(-1)                                                # needs sage.rings.number_field
         sage: radical(K(2))                                                             # needs sage.rings.number_field
-        i + 1
+        -i - 1
 
     Tests with numpy and gmpy2 numbers::
 
@@ -3031,7 +3031,7 @@ def is_squarefree(n):
         sage: is_squarefree(O(2))
         False
         sage: O(2).factor()
-        (-I) * (I + 1)^2
+        (-I) * (-I - 1)^2
 
     This method fails on domains which are not Unique Factorization Domains::
 

src/sage/categories/quotient_fields.py

@@ -100,7 +100,7 @@ def gcd(self, other):
                 sage: R = ZZ.extension(x^2 + 1, names='i')
                 sage: i = R.1
                 sage: gcd(5, 3 + 4*i)
-                -i - 2
+                2*i - 1
                 sage: P.<t> = R[]
                 sage: gcd(t, i)
                 Traceback (most recent call last):

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 (2*a + 1)
+            Fractional ideal (-a + 2)
             sage: g = f.conjugate(conj, new_ideal=ideal)
             sage: g.domain().ideal()
-            Fractional ideal (2*a + 1)
+            Fractional ideal (-a + 2)
         """
         if self.domain().is_padic_base():
             return DynamicalSystem_Berkovich(self._system.conjugate(M, adjugate=adjugate))

src/sage/dynamics/arithmetic_dynamics/projective_ds.py

@@ -1790,7 +1790,7 @@ def primes_of_bad_reduction(self, check=True):
             sage: P.<x,y> = ProjectiveSpace(K,1)
             sage: f = DynamicalSystem_projective([1/3*x^2+1/a*y^2, y^2])
             sage: f.primes_of_bad_reduction()                                           # needs sage.rings.function_field
-            [Fractional ideal (a), Fractional ideal (3)]
+            [Fractional ideal (-a), Fractional ideal (3)]
 
         This is an example where ``check=False`` returns extra primes::
 

src/sage/libs/pari/tests.py

@@ -1502,7 +1502,7 @@
     sage: pari(-104).quadclassunit()
     [6, [6], [Qfb(5, -4, 6)], 1]
     sage: pari(109).quadclassunit()
-    [1, [], [], 5.56453508676047]
+    [1, [], [], 5.56453508676047, -1]
     sage: pari(10001).quadclassunit() # random generators
     [16, [16], [Qfb(10, 99, -5, 0.E-38)], 5.29834236561059]
     sage: pari(10001).quadclassunit()[0]
@@ -1749,13 +1749,13 @@
     sage: y = QQ['yy'].0; _ = pari(y) # pari has variable ordering rules
     sage: x = QQ['zz'].0; nf = pari(x^2 + 2).nfinit()
     sage: nf.nfroots(y^2 + 2)
-    [Mod(-zz, zz^2 + 2), Mod(zz, zz^2 + 2)]
+    [Mod(-zz, zz^2 + 2), Mod(zz, zz^2 + 2)]~
     sage: nf = pari(x^3 + 2).nfinit()
     sage: nf.nfroots(y^3 + 2)
-    [Mod(zz, zz^3 + 2)]
+    [Mod(zz, zz^3 + 2)]~
     sage: nf = pari(x^4 + 2).nfinit()
     sage: nf.nfroots(y^4 + 2)
-    [Mod(-zz, zz^4 + 2), Mod(zz, zz^4 + 2)]
+    [Mod(-zz, zz^4 + 2), Mod(zz, zz^4 + 2)]~
 
     sage: nf = pari('x^2 + 1').nfinit()
     sage: nf.nfrootsof1()

src/sage/matrix/matrix2.pyx

@@ -16583,7 +16583,7 @@ cdef class Matrix(Matrix1):
             ....:   -2*a^2 + 4*a - 2, -2*a^2 + 1, 2*a, a^2 - 6, 3*a^2 - a ])
             sage: r,s,p = m._echelon_form_PID()
             sage: s[2]
-            (0, 0, -3*a^2 - 18*a + 34, -68*a^2 + 134*a - 53, -111*a^2 + 275*a - 90)
+            (0, 0, 3*a^2 + 18*a - 34, 68*a^2 - 134*a + 53, 111*a^2 - 275*a + 90)
             sage: r * m == s and r.det() == 1
             True
 

src/sage/modular/cusps_nf.py

@@ -1184,9 +1184,9 @@ def NFCusps_ideal_reps_for_levelN(N, nlists=1):
         sage: from sage.modular.cusps_nf import NFCusps_ideal_reps_for_levelN
         sage: NFCusps_ideal_reps_for_levelN(N)
         [(Fractional ideal (1),
-          Fractional ideal (67, a + 17),
-          Fractional ideal (127, a + 48),
-          Fractional ideal (157, a - 19))]
+          Fractional ideal (67, -4/7*a^3 + 13/7*a^2 + 39/7*a - 43),
+          Fractional ideal (127, -4/7*a^3 + 13/7*a^2 + 39/7*a - 42),
+          Fractional ideal (157, -4/7*a^3 + 13/7*a^2 + 39/7*a + 48))]
         sage: L = NFCusps_ideal_reps_for_levelN(N, 5)
         sage: all(len(L[i]) == k.class_number() for i in range(len(L)))
         True
@@ -1244,7 +1244,7 @@ def units_mod_ideal(I):
         sage: I = k.ideal(5, a + 1)
         sage: units_mod_ideal(I)
         [1,
-        -2*a^2 - 4*a + 1,
+        2*a^2 + 4*a - 1,
         ...]
 
     ::

src/sage/modular/dirichlet.py

@@ -2395,13 +2395,13 @@ class DirichletGroupFactory(UniqueFactory):
         sage: parent(val)
         Gaussian Integers generated by zeta4 in Cyclotomic Field of order 4 and degree 2
         sage: r4_29_0 = r4.residue_field(K(29).factor()[0][0]); r4_29_0(val)
-        17
+        12
         sage: r4_29_0(val) * GF(29)(3)
-        22
+        7
         sage: r4_29_0(G.gens()[2].values_on_gens()[2]) * 3
-        22
+        7
         sage: parent(r4_29_0(G.gens()[2].values_on_gens()[2]) * 3)
-        Residue field of Fractional ideal (-2*zeta4 + 5)
+        Residue field of Fractional ideal (-2*zeta4 - 5)
 
     ::
 

src/sage/modular/modsym/p1list_nf.py

@@ -61,7 +61,7 @@
 
     sage: alpha = MSymbol(N, a + 2, 3*a^2)
     sage: alpha.lift_to_sl2_Ok()
-    [-1, 4*a^2 - 13*a + 23, a + 2, 5*a^2 + 3*a - 3]
+    [-a - 1, 15*a^2 - 38*a + 86, a + 2, -a^2 + 9*a - 19]
     sage: Ok = k.ring_of_integers()
     sage: M = Matrix(Ok, 2, alpha.lift_to_sl2_Ok())
     sage: det(M)
@@ -977,11 +977,11 @@ def apply_J_epsilon(self, i, e1, e2=1):
             sage: N = k.ideal(5, a + 1)
             sage: P = P1NFList(N)
             sage: u = k.unit_group().gens_values(); u
-            [-1, -2*a^2 - 4*a + 1]
+            [-1, 2*a^2 + 4*a - 1]
             sage: P.apply_J_epsilon(4, -1)
             2
             sage: P.apply_J_epsilon(4, u[0], u[1])
-            5
+            1
 
         ::
 
@@ -1122,7 +1122,7 @@ def lift_to_sl2_Ok(N, c, d):
         sage: M = Matrix(Ok, 2, lift_to_sl2_Ok(N, 0, 7))
         Traceback (most recent call last):
         ...
-        ValueError: <0> + <7> and the Fractional ideal (7, a) are not coprime.
+        ValueError: <0> + <7> and the Fractional ideal (7, -4/7*a^3 + 13/7*a^2 + 39/7*a - 19) are not coprime.
     """
     k = N.number_field()
     # check the input

src/sage/quadratic_forms/binary_qf.py

@@ -1646,7 +1646,7 @@ def solve_integer(self, n, *, algorithm='general', _flag=2):
             sage: Q = BinaryQF([1, 0, 12345])
             sage: n = 2^99 + 5273
             sage: Q.solve_integer(n)                                                    # needs sage.libs.pari
-            (-67446480057659, 7139620553488)
+            (67446480057659, 7139620553488)
             sage: Q.solve_integer(n, algorithm='cornacchia')                            # needs sage.libs.pari
             (67446480057659, 7139620553488)
             sage: timeit('Q.solve_integer(n)')                          # not tested
@@ -1661,7 +1661,7 @@ def solve_integer(self, n, *, algorithm='general', _flag=2):
             sage: Qs
             [x^2 + x*y + 6*y^2, 2*x^2 - x*y + 3*y^2, 2*x^2 + x*y + 3*y^2]
             sage: [Q.solve_integer(3) for Q in Qs]
-            [None, (0, -1), (0, -1)]
+            [None, (0, 1), (0, 1)]
             sage: [Q.solve_integer(5) for Q in Qs]
             [None, None, None]
             sage: [Q.solve_integer(6) for Q in Qs]
@@ -1741,11 +1741,11 @@ def solve_integer(self, n, *, algorithm='general', _flag=2):
             sage: # needs sage.libs.pari
             sage: Q = BinaryQF([1, 0, 5])
             sage: Q.solve_integer(126, _flag=1)
-            [(11, -1), (-1, -5), (-1, 5), (-11, -1)]
+            [(-11, -1), (-1, -5), (-1, 5), (11, -1)]
             sage: Q.solve_integer(126, _flag=2)
             (11, -1)
             sage: Q.solve_integer(126, _flag=3)
-            [(11, -1), (-1, -5), (-1, 5), (-11, -1), (-9, -3), (9, -3)]
+            [(-11, -1), (-9, -3), (-1, -5), (-1, 5), (9, -3), (11, -1)]
         """
         if self.is_negative_definite():  # not supported by PARI
             return (-self).solve_integer(-n)

src/sage/rings/finite_rings/finite_field_prime_modn.py

@@ -114,9 +114,9 @@ def _coerce_map_from_(self, S):
             sage: RF13 = K.residue_field(pp)
             sage: RF13.hom([GF(13)(1)])
             Ring morphism:
-             From: Residue field of Fractional ideal (-w - 18)
-             To:   Finite Field of size 13
-             Defn: 1 |--> 1
+              From: Residue field of Fractional ideal (w + 18)
+              To:   Finite Field of size 13
+              Defn: 1 |--> 1
 
         Check that :issue:`19573` is resolved::
 

src/sage/rings/finite_rings/residue_field.pyx

@@ -22,14 +22,13 @@ monogenic (i.e., 2 is an essential discriminant divisor)::
     sage: # needs sage.rings.number_field
     sage: K.<a> = NumberField(x^3 + x^2 - 2*x + 8)
     sage: F = K.factor(2); F
-    (Fractional ideal (-1/2*a^2 + 1/2*a - 1)) * (Fractional ideal (-a^2 + 2*a - 3))
-    * (Fractional ideal (3/2*a^2 - 5/2*a + 4))
+    (Fractional ideal (-1/2*a^2 + 1/2*a - 1)) * (Fractional ideal (a^2 - 2*a + 3)) * (Fractional ideal (-3/2*a^2 + 5/2*a - 4))
     sage: F[0][0].residue_field()
     Residue field of Fractional ideal (-1/2*a^2 + 1/2*a - 1)
     sage: F[1][0].residue_field()
-    Residue field of Fractional ideal (-a^2 + 2*a - 3)
+    Residue field of Fractional ideal (a^2 - 2*a + 3)
     sage: F[2][0].residue_field()
-    Residue field of Fractional ideal (3/2*a^2 - 5/2*a + 4)
+    Residue field of Fractional ideal (-3/2*a^2 + 5/2*a - 4)
 
 We can also form residue fields from `\ZZ`::
 
@@ -126,10 +125,10 @@ First over a small non-prime field::
     sage: I = ideal([ubar*X + Y]); I
     Ideal (ubar*X + Y) of Multivariate Polynomial Ring in X, Y over
      Residue field in ubar of Fractional ideal
-      (47, 517/55860*u^5 + 235/3724*u^4 + 9829/13965*u^3
-            + 54106/13965*u^2 + 64517/27930*u + 755696/13965)
+      (47, 4841/93100*u^5 + 34451/139650*u^4 + 303697/69825*u^3
+            + 297893/27930*u^2 + 1649764/23275*u + 2633506/69825)
     sage: I.groebner_basis()                                                            # needs sage.libs.singular
-    [X + (-19*ubar^2 - 5*ubar - 17)*Y]
+    [X + (-15*ubar^2 + 3*ubar - 2)*Y]
 
 And now over a large prime field::
 
@@ -496,9 +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'>
 
@@ -1008,7 +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)
@@ -1039,7 +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)
@@ -1071,7 +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::
 
@@ -1083,7 +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
@@ -1105,11 +1104,11 @@ cdef class ReductionMap(Map):
             sage: # needs sage.rings.number_field
             sage: K.<i> = NumberField(x^2 + 1)
             sage: P1, P2 = [g[0] for g in K.factor(5)]; P1, P2
-            (Fractional ideal (-i - 2), Fractional ideal (2*i + 1))
+            (Fractional ideal (2*i - 1), Fractional ideal (-2*i - 1))
             sage: a = 1/(1+2*i)
             sage: F1, F2 = [g.residue_field() for g in [P1,P2]]; F1, F2
-            (Residue field of Fractional ideal (-i - 2),
-             Residue field of Fractional ideal (2*i + 1))
+            (Residue field of Fractional ideal (2*i - 1),
+             Residue field of Fractional ideal (-2*i - 1))
             sage: a.valuation(P1)
             0
             sage: F1(i/7)
@@ -1122,7 +1121,7 @@ cdef class ReductionMap(Map):
             Traceback (most recent call last):
             ...
             ZeroDivisionError: Cannot reduce field element -2/5*i + 1/5
-            modulo Fractional ideal (2*i + 1): it has negative valuation
+            modulo Fractional ideal (-2*i - 1): it has negative valuation
         """
         # The reduction map is just x |--> F(to_vs(x) * (PB**(-1))) if
         # either x is integral or the denominator of x is coprime to
@@ -1188,8 +1187,7 @@ cdef class ReductionMap(Map):
             sage: f = k.convert_map_from(K)
             sage: s = f.section(); s
             Lifting map:
-              From: Residue field in abar of
-                    Fractional ideal (-14*a^4 + 24*a^3 + 26*a^2 - 58*a + 15)
+              From: Residue field in abar of Fractional ideal (14*a^4 - 24*a^3 - 26*a^2 + 58*a - 15)
               To:   Number Field in a with defining polynomial x^5 - 5*x + 2
             sage: s(k.gen())
             a
@@ -1424,8 +1422,7 @@ cdef class ResidueFieldHomomorphism_global(RingHomomorphism):
             sage: f = k.coerce_map_from(K.ring_of_integers())
             sage: s = f.section(); s
             Lifting map:
-              From: Residue field in abar of
-                    Fractional ideal (-14*a^4 + 24*a^3 + 26*a^2 - 58*a + 15)
+              From: Residue field in abar of Fractional ideal (14*a^4 - 24*a^3 - 26*a^2 + 58*a - 15)
               To:   Maximal Order generated by a in Number Field in a with defining polynomial x^5 - 5*x + 2
             sage: s(k.gen())
             a
@@ -1678,7 +1675,7 @@ cdef class LiftingMap(Section):
             sage: F.<tmod> = K.factor(7)[0][0].residue_field()
             sage: F.lift_map() #indirect doctest
             Lifting map:
-              From: Residue field in tmod of Fractional ideal (theta_12^2 + 2)
+              From: Residue field in tmod of Fractional ideal (2*theta_12^3 + theta_12)
               To:   Maximal Order generated by theta_12 in Cyclotomic Field of order 12 and degree 4
         """
         return "Lifting"

src/sage/rings/finite_rings/residue_field_pari_ffelt.pyx

@@ -103,7 +103,7 @@ class ResidueFiniteField_pari_ffelt(ResidueField_generic, FiniteField_pari_ffelt
             sage: P.residue_class_degree()
             2
             sage: ff.<alpha> = P.residue_field(); ff
-            Residue field in alpha of Fractional ideal (-12*aa^2 + 189*aa - 475)
+            Residue field in alpha of Fractional ideal (12*aa^2 - 189*aa + 475)
             sage: type(ff)
             <class 'sage.rings.finite_rings.residue_field_pari_ffelt.ResidueFiniteField_pari_ffelt_with_category'>
             sage: ff(alpha^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