Module: sage.modular.modsym.boundary
Space of boundary modular symbols.
Used mainly for computing the cuspidal subspace of modular symbols.
Module-level Functions
) |
Class: BoundarySpace
This class is an abstract base class, so only derived classes should be instantiated.
Input:
self, [group=Congruence Subgroup Gamma0(1)], [weight=2], [sign=0], [base_ring=Rational Field], [character=None]) |
Initialize a space of boundary symbols.
Functions: character,
element,
filename,
free_module,
gen,
group,
is_ambient,
rank,
sign,
weight
self) |
Return the Dirichlet character assocaited to this space of boundary modular symbols.
self, x) |
Creates and returns an element of self from a modular or sage symbol, if possible. Input:
self) |
Returns the filename of self that should be used to store self in the database. Input:
self, [i=0]) |
Return the i-th generator of this space.
self) |
Return the congruence subgroup associated to this space of boundary modular symbols.
self) |
The rank of the space generated by boundary symbols that have been found so far in the course of computing the boundary map.
WARNING: This number may change as more elements are coerced into this space!! (This is an implementation detail that will likely change.)
self) |
Return the sign of the complex conjugation involution on this space of boundary modular symbols.
self) |
Return the weight of this space of boundary modular symbols.
Special Functions: __call__,
__init__,
__len__,
_coerce_impl,
_coerce_in_manin_symbol,
_cusp_index,
_known_cusps,
_repr_
self, x) |
Coerce x into a boundary symbol space.
If x is a modular symbol (with the same group, weight, character, sign, and base field), this returns the image of that modular symbol under the boundary map.
self) |
Return cusps found so far.
Class: BoundarySpace_wtk_eps
self, eps, weight, [sign=0]) |
Space of boundary modular symbols with given weight, character, and sign.
Input:
Special Functions: __init__,
_coerce_cusp,
_cusp_index,
_is_equiv,
_repr_
self, c) |
Coerce symbol into a boundary symbol space.
Class: BoundarySpace_wtk_g0
self, level, weight, sign, F) |
Initialize a space of boundary symbols of weight k for Gamma_0(N), over F.
For weight 2, it is faster to use BoundarySpace_wt2_g0.
Input:
Special Functions: __init__,
_coerce_cusp,
_is_equiv,
_repr_
self, c) |
Coerce cusp into a boundary symbol space.
Class: BoundarySpace_wtk_g1
self, level, weight, sign, F) |
Initialize a space of boundary modular symbols for Gamma1(N).
Input:
sage: from sage.modular.modsym.boundary import BoundarySpace_wtk_g1 sage: BoundarySpace_wtk_g1(17, 2, 0, QQ) Boundary Modular Symbols space for Gamma_1(17) of weight 2 over Rational Field
Special Functions: __init__,
_coerce_cusp,
_cusp_index,
_is_equiv,
_repr_
self, c) |
Coerce symbol into a boundary symbol space.
Class: BoundarySpace_wtk_gamma_h
self, group, weight, sign, F) |
Initialize a space of boundary modular symbols for GammaH(N).
Input:
sage: from sage.modular.modsym.boundary import BoundarySpace_wtk_gamma_h sage: BoundarySpace_wtk_gamma_h(GammaH(13,[3]), 2, 0, QQ) Boundary Modular Symbols space for Congruence Subgroup Gamma_H(13) with H generated by [3] of weight 2 over Rational Field
Special Functions: __init__,
_coerce_cusp,
_cusp_index,
_is_equiv,
_repr_
self, c) |
Coerce symbol into a boundary symbol space.
Class: BoundarySpaceElement
self, parent, x) |
Create a boundary symbol.
Input:
Functions: coordinate_vector
Special Functions: __init__,
__neg__,
_add_,
_lmul_,
_repr_,
_rmul_,
_sub_
self) |
Returns a string representation for self for printing purposes.
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