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diff --git a/src/sage/lfunctions/dokchitser.py b/src/sage/lfunctions/dokchitser.py
index 680ac17..1bf8953 100644
--- a/src/sage/lfunctions/dokchitser.py
+++ b/src/sage/lfunctions/dokchitser.py
@@ -111,7 +111,7 @@ class Dokchitser(SageObject):
0.000000000000000 + 0.305999773834052*z + 0.186547797268162*z^2 - 0.136791463097188*z^3 + O(z^4)
sage: L.check_functional_equation()
6.11218974700000e-18 # 32-bit
- 6.04442711160669e-18 # 64-bit
+ 6.11218974738703e-18 # 64-bit
RANK 2 ELLIPTIC CURVE:
@@ -670,7 +670,7 @@ class Dokchitser(SageObject):
sage: L = Dokchitser(conductor=1, gammaV=[0], weight=1, eps=1, poles=[1], residues=[-1], init='1')
sage: L.check_functional_equation()
-1.35525271600000e-20 # 32-bit
- -2.71050543121376e-20 # 64-bit
+ -1.35525271560688e-20 # 64-bit
If we choose the sign in functional equation for the
`\zeta` function incorrectly, the functional equation
diff --git a/src/sage/lfunctions/pari.py b/src/sage/lfunctions/pari.py
index c60f944..1daa219 100644
--- a/src/sage/lfunctions/pari.py
+++ b/src/sage/lfunctions/pari.py
@@ -423,7 +423,7 @@ class LFunction(SageObject):
sage: L.taylor_series(1,4)
0.000000000000000 + 0.305999773834052*z + 0.186547797268162*z^2 - 0.136791463097188*z^3 + O(z^4)
sage: L.check_functional_equation()
- 1.08420217248550e-19
+ 4.33680868994202e-19
.. RUBRIC:: Rank 2 elliptic curve
diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 2732f22..6c2a453 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -3433,18 +3433,18 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
Fractional ideal (2, 1/2*a - 1/2)
Fractional ideal (2, 1/2*a + 1/2)
3
- Fractional ideal (3, 1/2*a - 1/2)
Fractional ideal (3, 1/2*a + 1/2)
+ Fractional ideal (3, 1/2*a - 1/2)
4
Fractional ideal (4, 1/2*a + 3/2)
Fractional ideal (2)
Fractional ideal (4, 1/2*a + 5/2)
5
6
- Fractional ideal (1/2*a - 1/2)
- Fractional ideal (6, 1/2*a + 5/2)
Fractional ideal (6, 1/2*a + 7/2)
Fractional ideal (1/2*a + 1/2)
+ Fractional ideal (1/2*a - 1/2)
+ Fractional ideal (6, 1/2*a + 5/2)
7
8
Fractional ideal (1/2*a + 3/2)
@@ -3452,9 +3452,9 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
Fractional ideal (4, a + 1)
Fractional ideal (1/2*a - 3/2)
9
- Fractional ideal (9, 1/2*a + 11/2)
- Fractional ideal (3)
Fractional ideal (9, 1/2*a + 7/2)
+ Fractional ideal (3)
+ Fractional ideal (9, 1/2*a + 11/2)
10
"""
hnf_ideals = self.pari_nf().ideallist(bound)
@@ -4550,7 +4550,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
-1/13*a^2 + 6/13*a + 345/13,
-1,
2/13*a^2 + 1/13*a - 755/13,
- 1/13*a^2 - 19/13*a - 7/13],
+ 1/13*a^2 + 20/13*a - 7/13],
[(Fractional ideal (11, a - 2), 2), (Fractional ideal (19, a + 7), 2)])
Number fields defined by non-monic and non-integral
@@ -4708,9 +4708,9 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
-1/13*a^2 + 6/13*a + 345/13,
-1,
2/13*a^2 + 1/13*a - 755/13,
- 1/13*a^2 - 19/13*a - 7/13,
- -1/13*a^2 + 45/13*a - 97/13,
- 2/13*a^2 + 40/13*a - 27/13]
+ 1/13*a^2 + 20/13*a - 7/13,
+ 1/13*a^2 - 45/13*a + 97/13,
+ -2/13*a^2 - 40/13*a + 27/13]
Verify that :trac:`16708` is fixed::
@@ -5355,7 +5355,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
sage: K.<a> = NumberField(7/9*x^3 + 7/3*x^2 - 56*x + 123)
sage: K.elements_of_norm(7)
- [7/225*a^2 - 7/75*a - 42/25]
+ [28/225*a^2 + 77/75*a - 133/25]
"""
proof = proof_flag(proof)
B = self.pari_bnf(proof).bnfisintnorm(n)
@@ -5458,7 +5458,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
sage: pari('setrand(2)')
sage: L.<b> = K.extension(x^2 - 7)
sage: f = L.factor(a + 1); f
- (Fractional ideal (1/2*a*b - a + 1/2)) * (Fractional ideal (-1/2*a*b - a + 1/2))
+ (Fractional ideal (-1/2*b + 1/2*a + 1)) * (Fractional ideal (-1/2*a*b - a + 1/2))
sage: f.value() == a+1
True
@@ -6535,7 +6535,7 @@ class NumberField_generic(WithEqualityById, number_field_base.NumberField):
sage: [K.uniformizer(P) for P,e in factor(K.ideal(5))]
[t^2 - t + 1, t + 2, t - 2]
sage: [K.uniformizer(P) for P,e in factor(K.ideal(7))]
- [t^2 + 3*t + 1]
+ [t^2 - 4*t + 1]
sage: [K.uniformizer(P) for P,e in factor(K.ideal(67))]
[t + 23, t + 26, t - 32, t - 18]
@@ -7805,11 +7805,11 @@ class NumberField_absolute(NumberField_generic):
Ring morphism:
From: Number Field in a1 with defining polynomial x^3 - 7*x - 7
To: Number Field in a with defining polynomial 7/9*x^3 + 7/3*x^2 - 56*x + 123
- Defn: a1 |--> 7/225*a^2 - 7/75*a - 42/25,
+ Defn: a1 |--> 28/225*a^2 + 77/75*a - 133/25,
Ring morphism:
From: Number Field in a with defining polynomial 7/9*x^3 + 7/3*x^2 - 56*x + 123
To: Number Field in a1 with defining polynomial x^3 - 7*x - 7
- Defn: a |--> -15/7*a1^2 + 9)
+ Defn: a |--> -60/7*a1^2 + 15*a1 + 39)
"""
if name is None:
name = self.variable_names()
diff --git a/src/sage/rings/number_field/number_field_element.pyx b/src/sage/rings/number_field/number_field_element.pyx
index 59bab07..079eaaa 100644
--- a/src/sage/rings/number_field/number_field_element.pyx
+++ b/src/sage/rings/number_field/number_field_element.pyx
@@ -1733,7 +1733,7 @@ cdef class NumberFieldElement(FieldElement):
sage: P.<X> = K[]
sage: L = NumberField(X^2 + a^2 + 2*a + 1, 'b')
sage: K(17)._rnfisnorm(L)
- ((a^2 - 2)*b - 4, 1)
+ ((a^2 - 2)*b + 4, 1)
sage: K.<a> = NumberField(x^3 + x + 1)
sage: Q.<X> = K[]
diff --git a/src/sage/rings/number_field/number_field_ideal.py b/src/sage/rings/number_field/number_field_ideal.py
index b4eabe8..d746dcb 100644
--- a/src/sage/rings/number_field/number_field_ideal.py
+++ b/src/sage/rings/number_field/number_field_ideal.py
@@ -1827,7 +1827,7 @@ class NumberFieldFractionalIdeal(MultiplicativeGroupElement, NumberFieldIdeal):
sage: F.<a> = NumberField(2*x^3 + x + 1)
sage: fact = F.factor(2); fact
- (Fractional ideal (2*a^2 + 1))^2 * (Fractional ideal (-2*a^2))
+ (Fractional ideal (-2*a^2 - 1))^2 * (Fractional ideal (2*a^2))
sage: [p[0].norm() for p in fact]
[2, 2]
"""
@@ -2418,7 +2418,7 @@ class NumberFieldFractionalIdeal(MultiplicativeGroupElement, NumberFieldIdeal):
sage: A.is_coprime(B)
False
sage: lam = A.idealcoprime(B); lam
- -1/6*a + 1/6
+ 1/6*a - 1/6
sage: (lam*A).is_coprime(B)
True
diff --git a/src/sage/rings/number_field/unit_group.py b/src/sage/rings/number_field/unit_group.py
index 6ed0aea..529e23a 100644
--- a/src/sage/rings/number_field/unit_group.py
+++ b/src/sage/rings/number_field/unit_group.py
@@ -279,7 +279,7 @@ class UnitGroup(AbelianGroupWithValues_class):
sage: K.unit_group()
Unit group with structure C2 x Z x Z of Number Field in a with defining polynomial 7/9*x^3 + 7/3*x^2 - 56*x + 123
sage: UnitGroup(K, S=tuple(K.primes_above(7)))
- S-unit group with structure C2 x Z x Z x Z of Number Field in a with defining polynomial 7/9*x^3 + 7/3*x^2 - 56*x + 123 with S = (Fractional ideal (7/225*a^2 - 7/75*a - 42/25),)
+ S-unit group with structure C2 x Z x Z x Z of Number Field in a with defining polynomial 7/9*x^3 + 7/3*x^2 - 56*x + 123 with S = (Fractional ideal (28/225*a^2 + 77/75*a - 133/25),)
Conversion from unit group to a number field and back
gives the right results (:trac:`25874`)::
diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py
index 1e2052c..2c05db9 100644
--- a/src/sage/rings/polynomial/polynomial_quotient_ring.py
+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py
@@ -1293,9 +1293,9 @@ class PolynomialQuotientRing_generic(CommutativeRing):
1/16*a*xbar^3 + (-1/16*a - 1/8)*xbar^2 + 23/16*a*xbar - 23/16*a - 23/8),
6),
((-5/4*xbar^2 - 115/4,
- 1/4*a*xbar^2 + 23/4*a,
- -1/16*xbar^3 - 7/16*xbar^2 - 23/16*xbar - 161/16,
- 1/16*a*xbar^3 - 1/16*a*xbar^2 + 23/16*a*xbar - 23/16*a),
+ (1/8*a - 5/8)*xbar^2 + 23/8*a - 115/8,
+ -1/16*xbar^3 - 17/16*xbar^2 - 23/16*xbar - 391/16,
+ 1/16*a*xbar^3 + (-1/16*a - 5/8)*xbar^2 + 23/16*a*xbar - 23/16*a - 115/8),
2)]
By using the ideal `(a)`, we cut the part of the class group coming from
@@ -1425,9 +1425,9 @@ class PolynomialQuotientRing_generic(CommutativeRing):
1/16*a*xbar^3 + (-1/16*a - 1/8)*xbar^2 + 23/16*a*xbar - 23/16*a - 23/8),
6),
((-5/4*xbar^2 - 115/4,
- 1/4*a*xbar^2 + 23/4*a,
- -1/16*xbar^3 - 7/16*xbar^2 - 23/16*xbar - 161/16,
- 1/16*a*xbar^3 - 1/16*a*xbar^2 + 23/16*a*xbar - 23/16*a),
+ (1/8*a - 5/8)*xbar^2 + 23/8*a - 115/8,
+ -1/16*xbar^3 - 17/16*xbar^2 - 23/16*xbar - 391/16,
+ 1/16*a*xbar^3 + (-1/16*a - 5/8)*xbar^2 + 23/16*a*xbar - 23/16*a - 115/8),
2)]
Note that all the returned values live where we expect them to::
diff --git a/src/sage/schemes/elliptic_curves/ell_number_field.py b/src/sage/schemes/elliptic_curves/ell_number_field.py
index 2967f08..300278b 100644
--- a/src/sage/schemes/elliptic_curves/ell_number_field.py
+++ b/src/sage/schemes/elliptic_curves/ell_number_field.py
@@ -302,7 +302,8 @@ class EllipticCurve_number_field(EllipticCurve_field):
(3,
3,
[(0 : 0 : 1),
- (-1/2*zeta43_0^2 - 1/2*zeta43_0 + 7 : -3/2*zeta43_0^2 - 5/2*zeta43_0 + 18 : 1)])
+ (-1/2*zeta43_0^2 - 1/2*zeta43_0 + 7 : -3/2*zeta43_0^2 - 5/2*zeta43_0 + 18 : 1),
+ (5/8*zeta43_0^2 + 17/8*zeta43_0 - 9/4 : -27/16*zeta43_0^2 - 103/16*zeta43_0 + 39/8 : 1)])
"""
verbose = int(verbose)
if known_points is None:
@@ -810,7 +811,7 @@ class EllipticCurve_number_field(EllipticCurve_field):
sage: K.<v> = NumberField(x^2 + 161*x - 150)
sage: E = EllipticCurve([25105/216*v - 3839/36, 634768555/7776*v - 98002625/1296, 634768555/7776*v - 98002625/1296, 0, 0])
sage: E.global_integral_model()
- Elliptic Curve defined by y^2 + (2094779518028859*v-1940492905300351)*x*y + (477997268472544193101178234454165304071127500*v-442791377441346852919930773849502871958097500)*y = x^3 + (26519784690047674853185542622500*v-24566525306469707225840460652500)*x^2 over Number Field in v with defining polynomial x^2 + 161*x - 150
+ Elliptic Curve defined by y^2 + (33872485050625*v-31078224284250)*x*y + (2020602604156076340058146664245468750000*v-1871778534673615560803175189398437500000)*y = x^3 + (6933305282258321342920781250*v-6422644400723486559914062500)*x^2 over Number Field in v with defining polynomial x^2 + 161*x - 150
:trac:`14476`::
@@ -923,10 +924,10 @@ class EllipticCurve_number_field(EllipticCurve_field):
sage: E1 = E.scale_curve(u^5)
sage: E1.ainvs()
(0,
- 0,
- 0,
- 28087920796764302856*a + 88821804456186580548,
- -77225139016967233228487820912*a - 244207331916752959911655344864)
+ 0,
+ 0,
+ 193309837823322216*a - 611299381639464252,
+ -3379649566176127326923323632*a + 10687390322316522207588229536)
sage: E1._scale_by_units().ainvs()
(0, 0, 0, 4536*a + 14148, -163728*a - 474336)
|