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#ifndef MULTIPLICITY_H_INCLUDED
#define MULTIPLICITY_H_INCLUDED
#include "polynomial.h"
#include "matrix.h"
/**
* By multiplicative coordinate changes in the Laurent polynomial ring this routine produces a simpler ideal (and a ring) with the same multiplicity as g. This routine also preserves the mixed volume of the Newton polytopes.
*/
PolynomialSet idealWithSameMultiplicity(PolynomialSet const &g);
int multiplicity(PolynomialSet const &g);
/* Computes the multiplicity of a d-dimensional ideal with the d-dimensional homogeneity space. The input must be a marked, reduced Gr\"oebner basis */
/**
* Given a marked list of polynomials, this routine will compute the number of monomials not in
* the ideal generated by the marked terms. The number is assumed to be finite.
*/
int numberOfStandardMonomials(PolynomialSet const &markedGroebnerBasis);
Polynomial multiplicativeChangeInv(Polynomial const &p, IntegerMatrix const &lattice, PolynomialRing const &r2);
/**
* Every exponent vector difference of a polynomial in g is assumed to be in the lattice generated by the rows of lattice.
* The output of this routine is a list of Laurent polynomials which are obtained by expressing these differences
* in terms of the lattice generators. The resulting polynomials are in r2 which is a polynomial ring with the same coefficient
* field as that of g and whose number of variables equals the dimension of the lattice.
*/
PolynomialSet multiplicativeChangeInv(PolynomialSet const &g, IntegerMatrix const &lattice, PolynomialRing const &r2);
#endif
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