1 #ifndef INITIAL_H 2 #define INITIAL_H 3 4 /** 5 * various functions to compute the initial form of polynomials and ideals 6 */ 7 #include "gfanlib/gfanlib_vector.h" 8 #include "gfanlib/gfanlib_matrix.h" 9 #include "polys/monomials/p_polys.h" 10 11 /** 12 * Returns the weighted degree of the leading term of p with respect to w 13 */ 14 long wDeg(const poly p, const ring r, const gfan::ZVector &w); 15 16 /** 17 * Returns the weighted multidegree of the leading term of p with respect to (w,W). 18 * The weighted multidegree is a vector of length one higher than the column vectors of W. 19 * The first entry is the weighted degree with respect to w 20 * and the i+1st entry is the weighted degree with respect to the i-th row vector of W. 21 */ 22 gfan::ZVector WDeg(const poly p, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W); 23 24 /** 25 * Returns the initial form of p with respect to w 26 */ 27 poly initial(const poly p, const ring r, const gfan::ZVector &w); 28 29 /** 30 * Returns the initial form of I with respect to w 31 */ 32 ideal initial(const ideal I, const ring r, const gfan::ZVector &w); 33 34 /** 35 * Returns the initial form of p with respect to w and W 36 */ 37 poly initial(const poly p, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W); 38 39 /** 40 * Returns the initial form of I with respect to w and W 41 */ 42 ideal initial(const ideal I, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W); 43 44 /** 45 * Stores the initial form of *pStar with respect to w in pStar 46 */ 47 void initial(poly* pStar, const ring r, const gfan::ZVector &w); 48 49 /** 50 * Stores the initial form of *IStar with respect to w in IStar 51 */ 52 void initial(ideal* IStar, const ring r, const gfan::ZVector &w); 53 54 /** 55 * Stores the initial form of *pStar with respect to w and W in pStar 56 */ 57 void initial(poly* pStar, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W); 58 59 /** 60 * Stores the initial form of *IStar with respect to w and W in IStar 61 */ 62 void initial(ideal* IStar, const ring r, const gfan::ZVector &w, const gfan::ZMatrix &W); 63 64 #endif 65