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Original file line number | Diff line number | Diff line change |
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@@ -168,15 +168,15 @@ | |
- Craig Citro, Robert Bradshaw (2008-03): Rewrote with modabvar overhaul | ||
""" | ||
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#***************************************************************************** | ||
# **************************************************************************** | ||
# Copyright (C) 2007 William Stein <[email protected]> | ||
# | ||
# This program is free software: you can redistribute it and/or modify | ||
# it under the terms of the GNU General Public License as published by | ||
# the Free Software Foundation, either version 2 of the License, or | ||
# (at your option) any later version. | ||
# http://www.gnu.org/licenses/ | ||
#***************************************************************************** | ||
# https://www.gnu.org/licenses/ | ||
# **************************************************************************** | ||
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from copy import copy | ||
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@@ -188,7 +188,6 @@ | |
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from . import morphism | ||
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import sage.rings.integer_ring | ||
from sage.rings.infinity import Infinity | ||
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from sage.rings.ring import Ring | ||
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@@ -276,7 +275,7 @@ def _matrix_space(self): | |
sage: Hom(J0(11), J0(22))._matrix_space | ||
Full MatrixSpace of 2 by 4 dense matrices over Integer Ring | ||
""" | ||
return MatrixSpace(ZZ,2*self.domain().dimension(), 2*self.codomain().dimension()) | ||
return MatrixSpace(ZZ, 2*self.domain().dimension(), 2*self.codomain().dimension()) | ||
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def _element_constructor_from_element_class(self, *args, **keywords): | ||
""" | ||
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@@ -479,7 +478,7 @@ def free_module(self): | |
""" | ||
self.calculate_generators() | ||
V = ZZ**(4*self.domain().dimension() * self.codomain().dimension()) | ||
return V.submodule([ V(m.matrix().list()) for m in self.gens() ]) | ||
return V.submodule([V(m.matrix().list()) for m in self.gens()]) | ||
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def gen(self, i=0): | ||
""" | ||
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@@ -570,7 +569,7 @@ def calculate_generators(self): | |
return | ||
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if (self.domain() == self.codomain()) and (self.domain().dimension() == 1): | ||
self._gens = ( identity_matrix(ZZ,2), ) | ||
self._gens = (identity_matrix(ZZ, 2),) | ||
return | ||
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phi = self.domain()._isogeny_to_product_of_powers() | ||
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@@ -583,9 +582,9 @@ def calculate_generators(self): | |
Mt = psi.complementary_isogeny().matrix() | ||
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R = ZZ**(4*self.domain().dimension()*self.codomain().dimension()) | ||
gens = R.submodule([ (M*self._get_matrix(g)*Mt).list() | ||
for g in im_gens ]).saturation().basis() | ||
self._gens = tuple([ self._get_matrix(g) for g in gens ]) | ||
gens = R.submodule([(M*self._get_matrix(g)*Mt).list() | ||
for g in im_gens]).saturation().basis() | ||
self._gens = tuple([self._get_matrix(g) for g in gens]) | ||
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def _calculate_product_gens(self): | ||
""" | ||
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@@ -746,7 +745,8 @@ def _calculate_simple_gens(self): | |
Mf = f.matrix() | ||
Mg = g.matrix() | ||
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return [ Mf * self._get_matrix(e) * Mg for e in ls ] | ||
return [Mf * self._get_matrix(e) * Mg for e in ls] | ||
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# NOTE/WARNING/TODO: Below in the __init__, etc. we do *not* check | ||
# that the input gens are give something that spans a sub*ring*, as apposed | ||
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@@ -820,7 +820,7 @@ def __init__(self, A, gens=None, category=None): | |
if gens is None: | ||
self._gens = None | ||
else: | ||
self._gens = tuple([ self._get_matrix(g) for g in gens ]) | ||
self._gens = tuple([self._get_matrix(g) for g in gens]) | ||
self._is_full_ring = gens is None | ||
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def _repr_(self): | ||
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@@ -903,7 +903,7 @@ def index_in_saturation(self): | |
A = self.abelian_variety() | ||
d = A.dimension() | ||
M = ZZ**(4*d**2) | ||
gens = [ x.matrix().list() for x in self.gens() ] | ||
gens = [x.matrix().list() for x in self.gens()] | ||
R = M.submodule(gens) | ||
return R.index_in_saturation() | ||
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@@ -934,8 +934,8 @@ def discriminant(self): | |
2 | ||
""" | ||
g = self.gens() | ||
M = Matrix(ZZ,len(g), [ (g[i]*g[j]).trace() | ||
for i in range(len(g)) for j in range(len(g)) ]) | ||
M = Matrix(ZZ, len(g), [(g[i]*g[j]).trace() | ||
for i in range(len(g)) for j in range(len(g))]) | ||
return M.determinant() | ||
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def image_of_hecke_algebra(self, check_every=1): | ||
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@@ -1002,18 +1002,18 @@ def image_of_hecke_algebra(self, check_every=1): | |
EndVecZ = ZZ**(4*d**2) | ||
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if d == 1: | ||
self.__hecke_algebra_image = EndomorphismSubring(A, [[1,0,0,1]]) | ||
self.__hecke_algebra_image = EndomorphismSubring(A, [[1, 0, 0, 1]]) | ||
return self.__hecke_algebra_image | ||
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V = EndVecZ.submodule([A.hecke_operator(1).matrix().list()]) | ||
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for n in range(2,M.sturm_bound()+1): | ||
for n in range(2, M.sturm_bound()+1): | ||
if (check_every > 0 and | ||
n % check_every == 0 and | ||
V.dimension() == d and | ||
V.index_in_saturation() == 1): | ||
break | ||
V += EndVecZ.submodule([ A.hecke_operator(n).matrix().list() ]) | ||
V += EndVecZ.submodule([A.hecke_operator(n).matrix().list()]) | ||
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self.__hecke_algebra_image = EndomorphismSubring(A, V.basis()) | ||
return self.__hecke_algebra_image |