initial.h

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#ifndef INITIAL_H
#define INITIAL_H
 
/**
 * various functions to compute the initial form of polynomials and ideals
 */
#include "gfanlib/gfanlib_vector.h"
#include "gfanlib/gfanlib_matrix.h"
#include "polys/monomials/p_polys.h"
 
/**
 * Returns the weighted degree of the leading term of p with respect to w
 */
long wDeg(const poly p, const ring r, const gfan::ZVector &w);
 
/**
 * Returns the weighted multidegree of the leading term of p with respect to (w,W).
 * The weighted multidegree is a vector of length one higher than the column vectors of W.
 * The first entry is the weighted degree with respect to w
 * and the i+1st entry is the weighted degree with respect to the i-th row vector of W.
 */
gfan::ZVector WDeg(const poly p, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W);
 
/**
 * Returns the initial form of p with respect to w
 */
poly initial(const poly p, const ring r, const gfan::ZVector &w);
 
/**
 * Returns the initial form of I with respect to w
 */
ideal initial(const ideal I, const ring r, const gfan::ZVector &w);
 
/**
 * Returns the initial form of p with respect to w and W
 */
poly initial(const poly p, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W);
 
/**
 * Returns the initial form of I with respect to w and W
 */
ideal initial(const ideal I, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W);
 
/**
 * Stores the initial form of *pStar with respect to w in pStar
 */
void initial(poly* pStar, const ring r, const gfan::ZVector &w);
 
/**
 * Stores the initial form of *IStar with respect to w in IStar
 */
void initial(ideal* IStar, const ring r, const gfan::ZVector &w);
 
/**
 * Stores the initial form of *pStar with respect to w and W in pStar
 */
void initial(poly* pStar, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W);
 
/**
 * Stores the initial form of *IStar with respect to w and W in IStar
 */
void initial(ideal* IStar, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W);
 
#endif