Graded rings of modular forms for Hecke triangle groups

AUTHORS:

• Jonas Jermann (2013): initial version

class sage.modular.modform_hecketriangle.graded_ring.CuspFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) cusp forms for the given group and base ring

class sage.modular.modform_hecketriangle.graded_ring.MeromorphicModularFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) meromorphic modular forms for the given group and base ring

class sage.modular.modform_hecketriangle.graded_ring.ModularFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) modular forms for the given group and base ring

class sage.modular.modform_hecketriangle.graded_ring.QuasiCuspFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) quasi cusp forms for the given group and base ring.

class sage.modular.modform_hecketriangle.graded_ring.QuasiMeromorphicModularFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) quasi meromorphic modular forms for the given group and base ring.

class sage.modular.modform_hecketriangle.graded_ring.QuasiModularFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) quasi modular forms for the given group and base ring

class sage.modular.modform_hecketriangle.graded_ring.QuasiWeakModularFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) quasi weakly holomorphic modular forms for the given group and base ring.

class sage.modular.modform_hecketriangle.graded_ring.WeakModularFormsRing(group, base_ring, red_hom, n)

Bases: FormsRing_abstract, UniqueRepresentation

Graded ring of (Hecke) weakly holomorphic modular forms for the given group and base ring

sage.modular.modform_hecketriangle.graded_ring.canonical_parameters(group, base_ring, red_hom, n=None)

Return a canonical version of the parameters.

EXAMPLES:

Sage

sage: from sage.modular.modform_hecketriangle.graded_ring import canonical_parameters
sage: canonical_parameters(4, ZZ, 1)
(Hecke triangle group for n = 4, Integer Ring, True, 4)
sage: canonical_parameters(infinity, RR, 0)
(Hecke triangle group for n = +Infinity, Real Field with 53 bits of precision, False, +Infinity)

Python

>>> from sage.all import *
>>> from sage.modular.modform_hecketriangle.graded_ring import canonical_parameters
>>> canonical_parameters(Integer(4), ZZ, Integer(1))
(Hecke triangle group for n = 4, Integer Ring, True, 4)
>>> canonical_parameters(infinity, RR, Integer(0))
(Hecke triangle group for n = +Infinity, Real Field with 53 bits of precision, False, +Infinity)

Sage Live

from sage.modular.modform_hecketriangle.graded_ring import canonical_parameters
canonical_parameters(4, ZZ, 1)
canonical_parameters(infinity, RR, 0)

Make live