def __init__(self, group, base_ring, red_hom):
r"""
Return the graded ring of (Hecke) quasi meromorphic modular forms
for the given ``group`` and ``base_ring``.
INPUT:
- ``group`` - The Hecke triangle group (default: ``HeckeTriangleGroup(3)``)
- ``base_ring`` - The base_ring (default: ``ZZ``).
- ``red_hom`` - If True then results of binary operations are considered
homogeneous whenever it makes sense (default: False).
This is mainly used by the homogeneous spaces.
OUTPUT:
The corresponding graded ring of (Hecke) quasi meromorphic modular forms
for the given ``group`` and ``base_ring``.
EXAMPLES::
sage: MR = QMModularFormsRing(4, ZZ, 1)
sage: MR
QuasiMeromorphicModularFormsRing(n=4) over Integer Ring
sage: MR.analytic_type()
quasi meromorphic modular
sage: MR.category()
Category of commutative algebras over Fraction Field of Univariate Polynomial Ring in d over Integer Ring
"""
FormsRing_abstract.__init__(self, group=group, base_ring=base_ring, red_hom=red_hom)
CommutativeAlgebra.__init__(self, base_ring=self.coeff_ring(), category=CommutativeAlgebras(self.coeff_ring()))
self._analytic_type = self.AT(["quasi", "mero"])
def __init__(self, group, base_ring, red_hom):
r"""
Return the graded ring of (Hecke) cusp forms
for the given ``group`` and ``base_ring``.
INPUT:
- ``group`` - The Hecke triangle group (default: ``HeckeTriangleGroup(3)``)
- ``base_ring`` - The base_ring (default: ``ZZ``).
- ``red_hom`` - If True then results of binary operations are considered
homogeneous whenever it makes sense (default: False).
This is mainly used by the homogeneous spaces.
OUTPUT:
The corresponding graded ring of (Hecke) cusp forms
for the given ``group`` and ``base_ring``.
EXAMPLES::
sage: MR = CuspFormsRing(5, CC, True)
sage: MR
CuspFormsRing(n=5) over Complex Field with 53 bits of precision
sage: MR.analytic_type()
cuspidal
sage: MR.category()
Category of commutative algebras over Fraction Field of Univariate Polynomial Ring in d over Complex Field with 53 bits of precision
"""
FormsRing_abstract.__init__(self, group=group, base_ring=base_ring, red_hom=red_hom)
CommutativeAlgebra.__init__(self, base_ring=self.coeff_ring(), category=CommutativeAlgebras(self.coeff_ring()))
self._analytic_type = self.AT(["cusp"])
def __init__(self, group, base_ring, red_hom, n):
r"""
Return the graded ring of (Hecke) weakly holomorphic modular forms
for the given ``group`` and ``base_ring``.
INPUT:
- ``group`` -- The Hecke triangle group (default: ``HeckeTriangleGroup(3)``)
- ``base_ring`` -- The base_ring (default: ``ZZ``).
- ``red_hom`` -- If True then results of binary operations are considered
homogeneous whenever it makes sense (default: False).
This is mainly used by the spaces of homogeneous elements.
OUTPUT:
The corresponding graded ring of (Hecke) weakly holomorphic modular forms
for the given ``group`` and ``base_ring``.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.graded_ring import WeakModularFormsRing
sage: MR = WeakModularFormsRing(5, ZZ, 0)
sage: MR
WeakModularFormsRing(n=5) over Integer Ring
sage: MR.analytic_type()
weakly holomorphic modular
sage: MR.category()
Category of commutative algebras over Fraction Field of Univariate Polynomial Ring in d over Integer Ring
"""
FormsRing_abstract.__init__(self, group=group, base_ring=base_ring, red_hom=red_hom, n=n)
CommutativeAlgebra.__init__(self, base_ring=self.coeff_ring(), category=CommutativeAlgebras(self.coeff_ring()))
self._analytic_type = self.AT(["weak"])
def __init__(self, group, base_ring, red_hom, n):
r"""
Return the graded ring of (Hecke) quasi meromorphic modular forms
for the given ``group`` and ``base_ring``.
INPUT:
- ``group`` -- The Hecke triangle group (default: ``HeckeTriangleGroup(3)``)
- ``base_ring`` -- The base_ring (default: ``ZZ``).
- ``red_hom`` -- If True then results of binary operations are considered
homogeneous whenever it makes sense (default: False).
This is mainly used by the spaces of homogeneous elements.
OUTPUT:
The corresponding graded ring of (Hecke) quasi meromorphic modular forms
for the given ``group`` and ``base_ring``.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.graded_ring import QuasiMeromorphicModularFormsRing
sage: MR = QuasiMeromorphicModularFormsRing(4, ZZ, 1)
sage: MR
QuasiMeromorphicModularFormsRing(n=4) over Integer Ring
sage: MR.analytic_type()
quasi meromorphic modular
sage: MR.category()
Category of commutative algebras over Fraction Field of Univariate Polynomial Ring in d over Integer Ring
sage: QuasiMeromorphicModularFormsRing(n=infinity)
QuasiMeromorphicModularFormsRing(n=+Infinity) over Integer Ring
"""
FormsRing_abstract.__init__(self,
group=group,
base_ring=base_ring,
red_hom=red_hom,
n=n)
CommutativeAlgebra.__init__(self,
base_ring=self.coeff_ring(),
category=CommutativeAlgebras(
self.coeff_ring()))
self._analytic_type = self.AT(["quasi", "mero"])
def __init__(self, group, base_ring, red_hom, n):
r"""
Return the graded ring of (Hecke) cusp forms
for the given ``group`` and ``base_ring``.
INPUT:
- ``group`` -- The Hecke triangle group (default: ``HeckeTriangleGroup(3)``)
- ``base_ring`` -- The base_ring (default: ``ZZ``).
- ``red_hom`` -- If True then results of binary operations are considered
homogeneous whenever it makes sense (default: False).
This is mainly used by the spaces of homogeneous elements.
OUTPUT:
The corresponding graded ring of (Hecke) cusp forms
for the given ``group`` and ``base_ring``.
EXAMPLES::
sage: from sage.modular.modform_hecketriangle.graded_ring import CuspFormsRing
sage: MR = CuspFormsRing(5, CC, True)
sage: MR
CuspFormsRing(n=5) over Complex Field with 53 bits of precision
sage: MR.analytic_type()
cuspidal
sage: MR.category()
Category of commutative algebras over Fraction Field of Univariate Polynomial Ring in d over Complex Field with 53 bits of precision
sage: CuspFormsRing(n=infinity, base_ring=CC, red_hom=True)
CuspFormsRing(n=+Infinity) over Complex Field with 53 bits of precision
"""
FormsRing_abstract.__init__(self,
group=group,
base_ring=base_ring,
red_hom=red_hom,
n=n)
CommutativeAlgebra.__init__(self,
base_ring=self.coeff_ring(),
category=CommutativeAlgebras(
self.coeff_ring()))
self._analytic_type = self.AT(["cusp"])