Beispiel #1
0
    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"])
Beispiel #2
0
    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"])
Beispiel #3
0
    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"])
Beispiel #4
0
    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"])
Beispiel #5
0
    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"])