def _wronskian_invdeterminant(self, weight_parity = 0) : r""" The inverse determinant of `W`, which in the considered cases is always a negative power of the eta function. See the thesis of Nils Skoruppa. INPUT: - ``weight_parity`` -- An integer (default: `0`). """ try : if weight_parity % 2 == 0 : wronskian_invdeterminant = self._wronskian_invdeterminant_even else : wronskian_invdeterminant = self._wronskian_invdeterminant_odd except AttributeError : m = self.jacobi_index() if weight_parity % 2 == 0 : pw = (m + 1) * (2 * m + 1) else : pw = (m - 1) * (2 * m - 1) qexp_prec = self._qexp_precision() wronskian_invdeterminant = self.integral_power_series_ring() \ ( [ number_of_partitions(n) for n in xrange(qexp_prec) ] ) \ .add_bigoh(qexp_prec) ** pw if weight_parity % 2 == 0 : self._wronskian_invdeterminant_even = wronskian_invdeterminant else : self._wronskian_invdeterminant_odd = wronskian_invdeterminant return wronskian_invdeterminant
def _wronskian_invdeterminant(self, weight_parity=0): r""" The inverse determinant of `W`, which in the considered cases is always a negative power of the eta function. See the thesis of Nils Skoruppa. INPUT: - ``weight_parity`` -- An integer (default: `0`). """ try: if weight_parity % 2 == 0: wronskian_invdeterminant = self._wronskian_invdeterminant_even else: wronskian_invdeterminant = self._wronskian_invdeterminant_odd except AttributeError: m = self.jacobi_index() if weight_parity % 2 == 0: pw = (m + 1) * (2 * m + 1) else: pw = (m - 1) * (2 * m - 1) qexp_prec = self._qexp_precision() wronskian_invdeterminant = self.integral_power_series_ring() \ ( [ number_of_partitions(n) for n in xrange(qexp_prec) ] ) \ .add_bigoh(qexp_prec) ** pw if weight_parity % 2 == 0: self._wronskian_invdeterminant_even = wronskian_invdeterminant else: self._wronskian_invdeterminant_odd = wronskian_invdeterminant return wronskian_invdeterminant
def _eta_power(self): try: return self.__eta_power except AttributeError: qexp_prec = self._get_maass_form_qexp_prec() self.__eta_power = self.integral_power_series_ring() \ ([number_of_partitions(n) for n in xrange(qexp_prec)], qexp_prec)**6 return self.__eta_power
def _eta_power(self) : try : return self.__eta_power except AttributeError : qexp_prec = self._get_maass_form_qexp_prec() self.__eta_power = self.integral_power_series_ring() \ ([number_of_partitions(n) for n in xrange(qexp_prec)], qexp_prec)**6 return self.__eta_power
def _itgs_iterator(self, base_ring): r""" The isomorphism type generating series is given by `\frac{1}{1-x}`. EXAMPLES:: sage: P = species.PermutationSpecies() sage: g = P.isotype_generating_series() sage: g.coefficients(10) [1, 1, 2, 3, 5, 7, 11, 15, 22, 30] """ from sage.combinat.partition import number_of_partitions for n in _integers_from(0): yield base_ring(number_of_partitions(n))
def _itgs_iterator(self, base_ring): r""" The isomorphism type generating series is given by `\frac{1}{1-x}`. EXAMPLES:: sage: P = species.PartitionSpecies() sage: g = P.isotype_generating_series() sage: g.coefficients(10) [1, 1, 2, 3, 5, 7, 11, 15, 22, 30] """ from sage.combinat.partition import number_of_partitions for n in _integers_from(0): yield self._weight*base_ring(number_of_partitions(n))
def _eta_factor(self): r""" The inverse determinant of `W`, which in these cases is always a negative power of the eta function. """ try: return self.__eta_factor except AttributeError: m = self.__precision.jacobi_index() pw = (m + 1) * (2 * m + 1) qexp_prec = self._qexp_precision() self.__eta_factor = self.integral_power_series_ring() \ ( [ number_of_partitions(n) for n in xrange(qexp_prec) ] ) \ .add_bigoh(qexp_prec) ** pw return self.__eta_factor
def _eta_factor(self) : r""" The inverse determinant of `W`, which in these cases is always a negative power of the eta function. """ try : return self.__eta_factor except AttributeError : m = self.__precision.jacobi_index() pw = (m + 1) * (2 * m + 1) qexp_prec = self._qexp_precision() self.__eta_factor = self.integral_power_series_ring() \ ( [ number_of_partitions(n) for n in xrange(qexp_prec) ] ) \ .add_bigoh(qexp_prec) ** pw return self.__eta_factor