Module: sage.modular.hecke.algebra
Hecke algebras and modules
Module-level Functions
M) |
M) |
x) |
Class: HeckeAlgebra_anemic
Functions: gens,
hecke_operator,
is_anemic
self) |
Return a generator over all Hecke operator
for
, with
coprime to the level.
This is an infinite sequence.
sage: T = ModularSymbols(12,2).anemic_hecke_algebra() sage: g = T.gens() sage: g.next() Hecke operator T_1 on Modular Symbols space of dimension 5 for Gamma_0(12) of weight 2 with sign 0 over Rational Field sage: g.next() Hecke operator T_5 on Modular Symbols space of dimension 5 for Gamma_0(12) of weight 2 with sign 0 over Rational Field
self, n) |
Return the
-th Hecke operator, for
any positive integer
coprime to the level.
sage: T = ModularSymbols(Gamma1(5),3).anemic_hecke_algebra() sage: T.hecke_operator(2) Hecke operator T_2 on Modular Symbols space of dimension 4 for Gamma_1(5) of weight 3 with sign 0 and over Rational Field sage: T.hecke_operator(5) Traceback (most recent call last): ... IndexError: Hecke operator T_5 not defined in the anemic Hecke algebra
Special Functions: __cmp__,
_latex_,
_repr_
Class: HeckeAlgebra_base
self, M) |
Input:
Functions: basis,
discriminant,
gen,
gens,
hecke_matrix,
hecke_operator,
is_noetherian,
level,
module,
ngens,
rank
self, n) |
Return the
-th Hecke operator.
sage: T = ModularSymbols(11).hecke_algebra() sage: T.gen(2) Hecke operator T_2 on Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign 0 over Rational Field
self) |
Return a generator over all Hecke operator
for
. This is infinite.
sage: T = ModularSymbols(1,12).hecke_algebra() sage: g = T.gens() sage: g.next() Hecke operator T_1 on Modular Symbols space of dimension 3 for Gamma_0(1) of weight 12 with sign 0 over Rational Field sage: g.next() Hecke operator T_2 on Modular Symbols space of dimension 3 for Gamma_0(1) of weight 12 with sign 0 over Rational Field
self, n) |
Return the matrix of the n-th Hecke operator
.
sage: T = ModularSymbols(1,12).hecke_algebra() sage: T.hecke_matrix(2) [ -24 0 0] [ 0 -24 0] [4860 0 2049]
self, n) |
Return the n-th Hecke operator
.
sage: T = ModularSymbols(1,12).hecke_algebra() sage: T.hecke_operator(2) Hecke operator T_2 on Modular Symbols space of dimension 3 for Gamma_0(1) of weight 12 with sign 0 over Rational Field
self) |
Return True if this Hecke algebra is Noetherian as a ring.
self) |
sage: T = ModularSymbols(1,12).hecke_algebra() sage: T.module() Modular Symbols space of dimension 3 for Gamma_0(1) of weight 12 with sign 0 over Rational Field
Special Functions: __call__,
__contains__,
__init__,
_coerce_impl,
_HeckeAlgebra_base__matrix_space,
_latex_,
_repr_
self, x) |
sage: T = ModularSymbols(11).hecke_algebra() sage: T.gen(2) in T True sage: 5 in T False
Class: HeckeAlgebra_full
Functions: is_anemic
self) |
Return True if this is an anemic Hecke algebra.
Special Functions: __cmp__,
_repr_