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_field - rings.Ring (defaults to the rational numbers)
[group=None], [weight=Rational Field], [sign=0], [base_field=2], [character=Gamma0(1)]) |
Initialize a space of boundary symbols.
base_field,
character,
dimension,
element,
filename,
gens,
group,
level,
sign,
vector_space,
weight
Further documentation:
) |
Return the base field of this space of boundary modular symbols.
) |
Return the Dirichlet character assocaited to this space of boundary modular symbols.
) |
The dimension 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!!
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.
) |
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
[i=0]) |
Return the i-th generator of this space.
) |
Return the congruence subgroup associated to this space of boundary modular symbols.
) |
Return the level of the congruence subgroup of this space.
) |
Return the sign of the complex conjugation involution on this space of boundary modular symbols.
) |
Return the weight of this space of boundary modular symbols.
Instances of class BoundarySymbols also have the following special functions:
__call__,
__len__
Further documentation:
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.
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