def _multiply_basis(self, left, right): """ EXAMPLES:: sage: p1 = Permutation([3,2,1]) sage: p2 = Permutation([2,1,3]) sage: X = SchubertPolynomialRing(QQ) sage: X._multiply_basis(p1,p2) {[4, 2, 1, 3]: 1} """ return symmetrica.mult_schubert_schubert(left, right).monomial_coefficients()
def product_on_basis(self, left, right): """ EXAMPLES:: sage: p1 = Permutation([3,2,1]) sage: p2 = Permutation([2,1,3]) sage: X = SchubertPolynomialRing(QQ) sage: X.product_on_basis(p1,p2) X[4, 2, 1, 3] """ return symmetrica.mult_schubert_schubert(left, right)