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sagemathgh-36102: sage.schemes: Update # needs
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- Part of: sagemath#29705
- Cherry-picked from: sagemath#35095
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### ⌛ Dependencies

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URL: sagemath#36102
Reported by: Matthias Köppe
Reviewer(s): David Coudert, Enrique Manuel Artal Bartolo, Kwankyu Lee, Matthias Köppe
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2 parents 1842e9d + 3e2de54 commit 025f479
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9 changes: 5 additions & 4 deletions src/sage/modular/abvar/homspace.py
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Expand Up @@ -148,14 +148,15 @@
::
sage: T = E.image_of_hecke_algebra() # long time
sage: T.gens() # long time
sage: # long time
sage: T = E.image_of_hecke_algebra()
sage: T.gens()
(Abelian variety endomorphism of Abelian variety J0(33) of dimension 3,
Abelian variety endomorphism of Abelian variety J0(33) of dimension 3,
Abelian variety endomorphism of Abelian variety J0(33) of dimension 3)
sage: T.index_in(E) # long time
sage: T.index_in(E)
+Infinity
sage: T.index_in_saturation() # long time
sage: T.index_in_saturation()
1
AUTHORS:
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13 changes: 8 additions & 5 deletions src/sage/modular/cusps_nf.py
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@@ -1,3 +1,4 @@
# sage.doctest: needs sage.rings.number_field
r"""
The set `\mathbb{P}^1(K)` of cusps of a number field `K`
Expand Down Expand Up @@ -62,7 +63,7 @@
sage: Gamma0_NFCusps(N)
[Cusp [0: 1] of Number Field in a with defining polynomial x^2 + 5,
Cusp [1: 3] of Number Field in a with defining polynomial x^2 + 5,
Cusp [1: 3] of Number Field in a with defining polynomial x^2 + 5,
...]
"""
# ****************************************************************************
Expand Down Expand Up @@ -859,7 +860,7 @@ def ABmatrix(self):
sage: M = alpha.ABmatrix()
sage: M # random
[-a^2 - a - 1, -3*a - 7, 8, -2*a^2 - 3*a + 4]
sage: M[0] == alpha.numerator() and M[2]==alpha.denominator()
sage: M[0] == alpha.numerator() and M[2] == alpha.denominator()
True
An AB-matrix associated to a cusp alpha will send Infinity to alpha:
Expand All @@ -870,7 +871,7 @@ def ABmatrix(self):
sage: M = alpha.ABmatrix()
sage: (k.ideal(M[1], M[3])*alpha.ideal()).is_principal()
True
sage: M[0] == alpha.numerator() and M[2]==alpha.denominator()
sage: M[0] == alpha.numerator() and M[2] == alpha.denominator()
True
sage: NFCusp(k, oo).apply(M) == alpha
True
Expand Down Expand Up @@ -1249,7 +1250,8 @@ def units_mod_ideal(I):
sage: from sage.modular.cusps_nf import units_mod_ideal
sage: k.<a> = NumberField(x^3 + 11)
sage: k.unit_group()
Unit group with structure C2 x Z of Number Field in a with defining polynomial x^3 + 11
Unit group with structure C2 x Z of
Number Field in a with defining polynomial x^3 + 11
sage: I = k.ideal(5, a + 1)
sage: units_mod_ideal(I)
[1,
Expand All @@ -1261,7 +1263,8 @@ def units_mod_ideal(I):
sage: from sage.modular.cusps_nf import units_mod_ideal
sage: k.<a> = NumberField(x^4 - x^3 -21*x^2 + 17*x + 133)
sage: k.unit_group()
Unit group with structure C6 x Z of Number Field in a with defining polynomial x^4 - x^3 - 21*x^2 + 17*x + 133
Unit group with structure C6 x Z of
Number Field in a with defining polynomial x^4 - x^3 - 21*x^2 + 17*x + 133
sage: I = k.ideal(3)
sage: U = units_mod_ideal(I)
sage: all(U[j].is_unit() and (U[j] not in I) for j in range(len(U)))
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11 changes: 6 additions & 5 deletions src/sage/modular/modform/element.py
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Expand Up @@ -2315,13 +2315,14 @@ def minimal_twist(self, p=None):
sage: f.twist(chi, level=11) == g
True
sage: f = Newforms(575, 2, names='a')[4] # long time
sage: g, chi = f.minimal_twist(5) # long time
sage: g # long time
sage: # long time
sage: f = Newforms(575, 2, names='a')[4]
sage: g, chi = f.minimal_twist(5)
sage: g
q + a*q^2 - a*q^3 - 2*q^4 + (1/2*a + 2)*q^5 + O(q^6)
sage: chi # long time
sage: chi
Dirichlet character modulo 5 of conductor 5 mapping 2 |--> 1/2*a
sage: f.twist(chi, level=g.level()) == g # long time
sage: f.twist(chi, level=g.level()) == g
True
"""
if p is None:
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1 change: 1 addition & 0 deletions src/sage/modular/modform_hecketriangle/analytic_type.py
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@@ -1,3 +1,4 @@
# sage.doctest: needs sage.graphs
r"""
Analytic types of modular forms
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24 changes: 16 additions & 8 deletions src/sage/modular/overconvergent/weightspace.py
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@@ -1,4 +1,4 @@
# -*- coding: utf-8 -*-
# sage.doctest: needs sage.rings.padics
r"""
The space of `p`-adic weights
Expand All @@ -17,7 +17,8 @@
sage: W = pAdicWeightSpace(17)
sage: W
Space of 17-adic weight-characters defined over 17-adic Field with capped relative precision 20
Space of 17-adic weight-characters
defined over 17-adic Field with capped relative precision 20
sage: R.<x> = QQ[]
sage: L = Qp(17).extension(x^2 - 17, names='a'); L.rename('L')
sage: W.base_extend(L)
Expand Down Expand Up @@ -101,7 +102,8 @@ def WeightSpace_constructor(p, base_ring=None):
EXAMPLES::
sage: pAdicWeightSpace(3) # indirect doctest
Space of 3-adic weight-characters defined over 3-adic Field with capped relative precision 20
Space of 3-adic weight-characters
defined over 3-adic Field with capped relative precision 20
sage: pAdicWeightSpace(3, QQ)
Space of 3-adic weight-characters defined over Rational Field
sage: pAdicWeightSpace(10)
Expand Down Expand Up @@ -248,11 +250,13 @@ def base_extend(self, R):
sage: W = pAdicWeightSpace(3, QQ)
sage: W.base_extend(Qp(3))
Space of 3-adic weight-characters defined over 3-adic Field with capped relative precision 20
Space of 3-adic weight-characters
defined over 3-adic Field with capped relative precision 20
sage: W.base_extend(IntegerModRing(12))
Traceback (most recent call last):
...
TypeError: No coercion map from 'Rational Field' to 'Ring of integers modulo 12' is defined
TypeError: No coercion map from 'Rational Field'
to 'Ring of integers modulo 12' is defined
"""
if R.has_coerce_map_from(self.base_ring()):
return WeightSpace_constructor(self.prime(), R)
Expand Down Expand Up @@ -356,7 +360,9 @@ def pAdicEisensteinSeries(self, ring, prec=20):
sage: kappa = pAdicWeightSpace(3)(3, DirichletGroup(3,QQ).0)
sage: kappa.pAdicEisensteinSeries(QQ[['q']], 20)
1 - 9*q + 27*q^2 - 9*q^3 - 117*q^4 + 216*q^5 + 27*q^6 - 450*q^7 + 459*q^8 - 9*q^9 - 648*q^10 + 1080*q^11 - 117*q^12 - 1530*q^13 + 1350*q^14 + 216*q^15 - 1845*q^16 + 2592*q^17 + 27*q^18 - 3258*q^19 + O(q^20)
1 - 9*q + 27*q^2 - 9*q^3 - 117*q^4 + 216*q^5 + 27*q^6 - 450*q^7 + 459*q^8
- 9*q^9 - 648*q^10 + 1080*q^11 - 117*q^12 - 1530*q^13 + 1350*q^14 + 216*q^15
- 1845*q^16 + 2592*q^17 + 27*q^18 - 3258*q^19 + O(q^20)
"""
if not self.is_even():
raise ValueError("Eisenstein series not defined for odd weight-characters")
Expand Down Expand Up @@ -570,7 +576,8 @@ def chi(self):
sage: kappa = pAdicWeightSpace(29)(13, DirichletGroup(29, Qp(29)).0^14)
sage: kappa.chi()
Dirichlet character modulo 29 of conductor 29 mapping 2 |--> 28 + 28*29 + 28*29^2 + ... + O(29^20)
Dirichlet character modulo 29 of conductor 29
mapping 2 |--> 28 + 28*29 + 28*29^2 + ... + O(29^20)
"""
return self._chi

Expand Down Expand Up @@ -667,7 +674,8 @@ def Lvalue(self):
sage: pAdicWeightSpace(7)(5, DirichletGroup(7, Qp(7)).0^4).Lvalue()
0
sage: pAdicWeightSpace(7)(6, DirichletGroup(7, Qp(7)).0^4).Lvalue()
1 + 2*7 + 7^2 + 3*7^3 + 3*7^5 + 4*7^6 + 2*7^7 + 5*7^8 + 2*7^9 + 3*7^10 + 6*7^11 + 2*7^12 + 3*7^13 + 5*7^14 + 6*7^15 + 5*7^16 + 3*7^17 + 6*7^18 + O(7^19)
1 + 2*7 + 7^2 + 3*7^3 + 3*7^5 + 4*7^6 + 2*7^7 + 5*7^8 + 2*7^9 + 3*7^10 + 6*7^11
+ 2*7^12 + 3*7^13 + 5*7^14 + 6*7^15 + 5*7^16 + 3*7^17 + 6*7^18 + O(7^19)
"""
if self._k > 0:
return -self._chi.bernoulli(self._k) / self._k
Expand Down
2 changes: 1 addition & 1 deletion src/sage/modular/pollack_stevens/padic_lseries.py
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Original file line number Diff line number Diff line change
@@ -1,4 +1,4 @@
# -*- coding: utf-8 -*-
# sage.doctest: needs sage.ring.padics
r"""
`p`-adic `L`-series attached to overconvergent eigensymbols
Expand Down
39 changes: 20 additions & 19 deletions src/sage/schemes/affine/affine_homset.py
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Expand Up @@ -211,8 +211,8 @@ def points(self, **kwds):
EXAMPLES: The bug reported at #11526 is fixed::
sage: A2 = AffineSpace(ZZ, 2)
sage: F = GF(3) # optional - sage.rings.finite_rings
sage: A2(F).points() # optional - sage.rings.finite_rings
sage: F = GF(3)
sage: A2(F).points()
[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
::
Expand All @@ -228,23 +228,23 @@ def points(self, **kwds):
::
sage: u = QQ['u'].0
sage: K.<v> = NumberField(u^2 + 3) # optional - sage.rings.number_field
sage: A.<x,y> = AffineSpace(K, 2) # optional - sage.rings.number_field
sage: len(A(K).points(bound=2)) # optional - sage.rings.number_field
sage: K.<v> = NumberField(u^2 + 3) # needs sage.rings.number_field
sage: A.<x,y> = AffineSpace(K, 2) # needs sage.rings.number_field
sage: len(A(K).points(bound=2)) # needs sage.rings.number_field
1849
::
sage: A.<x,y> = AffineSpace(QQ, 2)
sage: E = A.subscheme([x^2 + y^2 - 1, y^2 - x^3 + x^2 + x - 1])
sage: E(A.base_ring()).points()
sage: E(A.base_ring()).points() # needs sage.libs.singular
[(-1, 0), (0, -1), (0, 1), (1, 0)]
::
sage: A.<x,y> = AffineSpace(CC, 2)
sage: A.<x,y> = AffineSpace(CC, 2) # needs sage.rings.real_mpfr
sage: E = A.subscheme([y^3 - x^3 - x^2, x*y])
sage: E(A.base_ring()).points()
sage: E(A.base_ring()).points() # needs sage.libs.singular sage.rings.real_mpfr
verbose 0 (...: affine_homset.py, points)
Warning: computations in the numerical fields are inexact;points
may be computed partially or incorrectly.
Expand All @@ -253,9 +253,9 @@ def points(self, **kwds):
::
sage: A.<x1,x2> = AffineSpace(CDF, 2)
sage: E = A.subscheme([x1^2 + x2^2 + x1*x2, x1 + x2])
sage: E(A.base_ring()).points()
sage: A.<x1,x2> = AffineSpace(CDF, 2) # needs sage.rings.complex_double
sage: E = A.subscheme([x1^2 + x2^2 + x1*x2, x1 + x2]) # needs sage.libs.singular sage.rings.complex_double
sage: E(A.base_ring()).points() # needs sage.libs.singular sage.rings.complex_double
verbose 0 (...: affine_homset.py, points)
Warning: computations in the numerical fields are inexact;points
may be computed partially or incorrectly.
Expand Down Expand Up @@ -393,28 +393,29 @@ def numerical_points(self, F=None, **kwds):
EXAMPLES::
sage: K.<v> = QuadraticField(3) # optional - sage.rings.number_field
sage: A.<x,y> = AffineSpace(K, 2) # optional - sage.rings.number_field
sage: X = A.subscheme([x^3 - v^2*y, y - v*x^2 + 3]) # optional - sage.rings.number_field
sage: L = X(K).numerical_points(F=RR); L # abs tol 1e-14 # optional - sage.rings.number_field
sage: # needs sage.rings.number_field
sage: K.<v> = QuadraticField(3)
sage: A.<x,y> = AffineSpace(K, 2)
sage: X = A.subscheme([x^3 - v^2*y, y - v*x^2 + 3])
sage: L = X(K).numerical_points(F=RR); L # abs tol 1e-14
[(-1.18738247880014, -0.558021142104134),
(1.57693558184861, 1.30713548084184),
(4.80659931965815, 37.0162574656220)]
sage: L[0].codomain() # optional - sage.rings.number_field
sage: L[0].codomain()
Affine Space of dimension 2 over Real Field with 53 bits of precision
::
sage: A.<x,y> = AffineSpace(QQ, 2)
sage: X = A.subscheme([y^2 - x^2 - 3*x, x^2 - 10*y])
sage: len(X(QQ).numerical_points(F=ComplexField(100)))
sage: len(X(QQ).numerical_points(F=ComplexField(100))) # needs sage.libs.singular
4
::
sage: A.<x1, x2> = AffineSpace(QQ, 2)
sage: E = A.subscheme([30*x1^100 + 1000*x2^2 + 2000*x1*x2 + 1, x1 + x2])
sage: len(E(A.base_ring()).numerical_points(F=CDF, zero_tolerance=1e-9))
sage: len(E(A.base_ring()).numerical_points(F=CDF, zero_tolerance=1e-9)) # needs sage.libs.singular
100
TESTS::
Expand All @@ -430,7 +431,7 @@ def numerical_points(self, F=None, **kwds):
sage: A.<x,y> = AffineSpace(QQ, 2)
sage: X = A.subscheme([y^2 - x^2 - 3*x, x^2 - 10*y])
sage: X(QQ).numerical_points(F=CC, zero_tolerance=-1)
sage: X(QQ).numerical_points(F=CC, zero_tolerance=-1) # needs sage.libs.singular
Traceback (most recent call last):
...
ValueError: tolerance must be positive
Expand Down
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