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.partitions import number_of_partitions for n in _integers_from(0): yield self._weight*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.PermutationSpecies() sage: g = P.isotype_generating_series() sage: g.coefficients(10) [1, 1, 2, 3, 5, 7, 11, 15, 22, 30] """ from sage.combinat.partitions import number_of_partitions for n in _integers_from(0): yield base_ring(number_of_partitions(n))