def __init__(self, group, base_ring, red_hom, n): r""" Return the graded ring of (Hecke) 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) modular forms for the given ``group`` and ``base_ring``. EXAMPLES:: sage: from sage.modular.modform_hecketriangle.graded_ring import ModularFormsRing sage: MR = ModularFormsRing() sage: MR ModularFormsRing(n=3) over Integer Ring sage: MR.analytic_type() 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(["holo"])
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 Integer Ring sage: MR in MR.category() True 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=base_ring, category=CommutativeAlgebras(base_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 Complex Field with 53 bits of precision sage: MR in MR.category() True 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=base_ring, category=CommutativeAlgebras(base_ring)) self._analytic_type = self.AT(["cusp"])