CoCalc -- modularform

Harvard Workshop: Distribution of modular symbols and L-values
code / alex / psage / psage / modform / fourier_expansion_framework / modularforms / modularform_element.py
²⁴¹⁸⁵² views
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from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_ambient import GradedExpansionAmbient_abstract
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r"""
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A orthogonal modular form, namely a graded expansion providing additional features.
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AUTHOR :
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    -- Martin Raum (2009 - 07 - 30) Initial version
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"""
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#===============================================================================
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# 
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# Copyright (C) 2009 Martin Raum
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# 
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# This program is free software; you can redistribute it and/or
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# modify it under the terms of the GNU General Public License
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# as published by the Free Software Foundation; either version 3
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# of the License, or (at your option) any later version.
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# 
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# This program is distributed in the hope that it will be useful, 
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# but WITHOUT ANY WARRANTY; without even the implied warranty of
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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# General Public License for more details.
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# 
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# You should have received a copy of the GNU General Public License
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# along with this program; if not, see <http://www.gnu.org/licenses/>.
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#
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#===============================================================================
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from psage.modform.fourier_expansion_framework.gradedexpansions.gradedexpansion_element import GradedExpansion_class, \
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                            GradedExpansionVector_class, GradedExpansion_abstract
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class ModularForm_abstract (object) :
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    """
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    NOTE:
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        We assume that the deriving classes also derive (indirectly)
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        from GradedExpansion_abstract.
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    """
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    def is_cusp_form(self) :
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        """
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        Whether ``self`` is a cusp form or not.
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        OUTPUT:
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            A boolean.
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: ma.0.is_cusp_form()
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            Traceback (most recent call last):
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            ...
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            NotImplementedError
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        """
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        raise NotImplementedError
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    def is_eisenstein_series(self) :
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        """
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        Whether ``self`` is an Eisenstein series or not.
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        OUTPUT:
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            A boolean.
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: ma.0.is_eisenstein_series()
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            Traceback (most recent call last):
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            ...
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            NotImplementedError
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        """
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        raise NotImplementedError
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    def _lmul_(self, c) :
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        """
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: mavv = ModularFormsAmbient( QQ, ModularFormTestType_vectorvalued(), NNFilter(5) )
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            sage: (mavv.0 * ma.0).polynomial()
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            g1*v1
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            sage: (ma.0 * 5).polynomial()
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            5*g1
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        """
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        ## For vector valued forms we use an extended base ring, which
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        ## needs conversion before we can multiply
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        if self.parent().type().is_vector_valued() :
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            return self.parent()._element_class( self.parent(),
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               c.polynomial().subs(c.parent().type()._hom_to_vector_valued(self.parent().relations().base_ring())) \
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             * self.polynomial() )
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        else :
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            return super(ModularForm_abstract, self)._lmul_(c)
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    def _rmul_(self, c) :
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        """
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        TESTS::
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_ambient import *
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            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *
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            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *
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            sage: ma = ModularFormsAmbient( QQ, ModularFormTestType_scalar(), NNFilter(5) )
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            sage: mavv = ModularFormsAmbient( QQ, ModularFormTestType_vectorvalued(), NNFilter(5) )
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            sage: (ma.0 * mavv.0).polynomial()
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            g1*v1
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            sage: (5 * ma.0).polynomial()
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            5*g1
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        """
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        ## For vector valued forms we use an extended base ring, which
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        ## needs conversion before we can multiply
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        if self.parent().type().is_vector_valued() :
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            return self.parent()._element_class( self.parent(),
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               c.polynomial().subs(c.parent().type()._hom_to_vector_valued(self.parent().relations().base_ring())) \
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             * self.polynomial() )
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        else :
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            return super(ModularForm_abstract, self)._rmul_(c)
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class ModularForm_generic ( ModularForm_abstract, GradedExpansion_class ) :
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    weight = GradedExpansion_class.grading_index
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class ModularFormVector_generic ( ModularForm_abstract, GradedExpansionVector_class ) :
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    weight = GradedExpansionVector_class.grading_index
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