Module: sage.modular.modsym.boundary
Used mainly for computing the cuspidal subspace of modular symbols.
Module-level Functions
x) |
Class: BoundarySpace
This class is an abstract base class, so only derived classes should be instantiated.
INPUT: weight - int, the weight group - congroup.CongruenceGroup, a congruence subgroup. sign - int, either -1, 0, or 1 base_ring - rings.Ring (defaults to the rational numbers)
self, [group=None], [weight=Rational Field], [sign=0], [base_ring=2], [character=Congruence Subgroup Gamma0(1)]) |
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: x -- an object of one of the following types: ModularSymbol, ManinSymbol. We ignore the group, weight, and character of the input modular or sage symbol. OUTPUT: ModularSymbol -- a modular symbol with parent self.
self) |
Returns the filename of self that should be used to store self in the database.
INPUT: self -- space of modular symbols OUTPUT: str -- a string
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__,
__len__,
_coerce_in_manin_symbol,
_cusp_index,
_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.
Class: BoundarySpace_wtk_eps
self, eps, weight, [sign=0]) |
Space of boundary modular symbols with given weight, character, and sign.
INPUT: eps -- dirichlet.DirichletCharacter, the "Nebentypus" character. weight -- int, the weight >= 2 sign -- int, either -1, 0, or 1
Special Functions: _coerce_cusp,
_cusp_index,
_is_equiv,
_repr_
self, c) |
Coerce symbol into a boundary symbol space.
Class: BoundarySpace_wtk_g0_Q
self, level, weight, [sign=0]) |
Initialize a space of boundary symbols of weight k for Gamma_0(N), over Q.
For weight 2, it is faster to use BoundarySpace_wt2_g0_Q.
INPUT: level -- int, the level weight -- integer weight >= 2. sign -- int, either -1, 0, or 1
Special Functions: _coerce_cusp,
_is_equiv,
_repr_
self, c) |
Coerce cusp into a boundary symbol space.
Class: BoundarySpace_wtk_g1_Q
self, level, weight, [sign=0]) |
Initialize a space of boundayr modular symbols for Gamma1(N).
INPUT: level -- int, the level weight -- int, the weight >= 2 sign -- int, either -1, 0, or 1
sage: from sage.modular.modsym.boundary import BoundarySpace_wtk_g1_Q sage: BoundarySpace_wtk_g1_Q(17,2) Boundary Modular Symbols space for Gamma_1(17) of weight 2 over Rational Field
Special Functions: _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: parent -- BoundarySpace; a space of boundary modular symbols x -- a dict with integer keys and values in the base field of parent.
Functions: element,
parent
Special Functions: __add__,
__mul__,
__neg__,
__sub__,
_repr_
self) |
Returns a string representation for self for printing purposes.
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