[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /*************************************************************** |
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[b84b400] | 5 | * File: p_polys.h |
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[35aab3] | 6 | * Purpose: declaration of poly stuf which are independent of |
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| 7 | * currRing |
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| 8 | * Author: obachman (Olaf Bachmann) |
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| 9 | * Created: 9/00 |
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[341696] | 10 | * Version: $Id$ |
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[35aab3] | 11 | *******************************************************************/ |
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| 12 | #ifndef P_POLYS_H |
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| 13 | #define P_POLYS_H |
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| 14 | |
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[20b794] | 15 | #include <polys/monomials/ring.h> |
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[8a8c9e] | 16 | #include <polys/monomials/monomials.h> |
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[20b794] | 17 | #include <polys/monomials/polys-impl.h> |
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[8a8c9e] | 18 | #include <polys/templates/p_Procs.h> |
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| 19 | #include <polys/templates/p_Procs.h> |
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| 20 | #include <polys/sbuckets.h> |
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[35aab3] | 21 | |
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| 22 | /*************************************************************** |
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| 23 | * |
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| 24 | * Primitives for accessing and setting fields of a poly |
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| 25 | * poly must be != NULL |
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| 26 | * |
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| 27 | ***************************************************************/ |
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| 28 | // next |
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[367c32] | 29 | #define pNext(p) ((p)->next) |
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| 30 | #define pIter(p) ((p) = (p)->next) |
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[35aab3] | 31 | |
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| 32 | // coeff |
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[367c32] | 33 | #define pGetCoeff(p) ((p)->coef) |
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[35aab3] | 34 | // deletes old coeff before setting the new one |
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[367c32] | 35 | #define pSetCoeff0(p,n) (p)->coef=(n) |
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| 36 | #define p_GetCoeff(p,r) pGetCoeff(p) |
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| 37 | #define p_SetCoeff0(p,n,r) pSetCoeff0(p,n) |
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[35aab3] | 38 | |
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| 39 | /*************************************************************** |
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| 40 | * |
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| 41 | * Comparisons: they are all done without regarding coeffs |
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| 42 | * |
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| 43 | ***************************************************************/ |
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| 44 | #define p_LmCmpAction(p, q, r, actionE, actionG, actionS) \ |
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| 45 | _p_LmCmpAction(p, q, r, actionE, actionG, actionS) |
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| 46 | |
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| 47 | // returns 1 if ExpVector(p)==ExpVector(q): does not compare numbers !! |
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| 48 | #define p_LmEqual(p1, p2, r) p_ExpVectorEqual(p1, p2, r) |
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| 49 | |
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| 50 | /*************************************************************** |
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| 51 | * |
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| 52 | * Divisiblity tests, args must be != NULL, except for |
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| 53 | * pDivisbleBy |
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| 54 | * |
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| 55 | ***************************************************************/ |
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| 56 | unsigned long p_GetShortExpVector(poly a, ring r); |
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| 57 | |
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| 58 | /*************************************************************** |
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| 59 | * |
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| 60 | * Misc things on polys |
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| 61 | * |
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| 62 | ***************************************************************/ |
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| 63 | // return the maximal exponent of p in form of the maximal long var |
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[a05493f] | 64 | unsigned long p_GetMaxExpL(poly p, const ring r, unsigned long l_max = 0); |
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[35aab3] | 65 | // return monomial r such that GetExp(r,i) is maximum of all |
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| 66 | // monomials in p; coeff == 0, next == NULL, ord is not set |
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| 67 | poly p_GetMaxExpP(poly p, ring r); |
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| 68 | |
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| 69 | // return the TotalDegree of the long var l |
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[a04c5e] | 70 | static inline unsigned long p_GetTotalDegree(const unsigned long l, const ring r); |
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[35aab3] | 71 | // return the total degree of the long var l containing number_of_exp exponents |
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[a04c5e] | 72 | static inline unsigned long p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps); |
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[35aab3] | 73 | |
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[ba0fc3] | 74 | int p_MinDeg(poly p,intvec *w, const ring R); |
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| 75 | |
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| 76 | long p_DegW(poly p, const short *w, const ring R); |
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| 77 | |
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[35aab3] | 78 | // return TRUE if all monoms have the same component |
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| 79 | BOOLEAN p_OneComp(poly p, ring r); |
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[2f0d83f] | 80 | |
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| 81 | // return i, if head depends only on var(i) |
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[35aab3] | 82 | int p_IsPurePower(const poly p, const ring r); |
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| 83 | |
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[2f0d83f] | 84 | // return i, if poly depends only on var(i) |
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| 85 | int p_IsUnivariate(poly p, const ring r); |
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| 86 | |
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[95450e] | 87 | // set entry e[i] to 1 if var(i) occurs in p, ignore var(j) if e[j]>0 |
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[f46646] | 88 | // return #(e[i]>0) |
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| 89 | int p_GetVariables(poly p, int * e, const ring r); |
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[95450e] | 90 | |
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[35aab3] | 91 | // returns the poly representing the integer i |
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| 92 | poly p_ISet(int i, ring r); |
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[2f0d83f] | 93 | |
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[35aab3] | 94 | // returns the poly representing the number n, destroys n |
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| 95 | poly p_NSet(number n, ring r); |
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| 96 | |
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| 97 | /*************************************************************** |
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| 98 | * |
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| 99 | * Copying/Deletion of polys: args may be NULL |
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| 100 | * |
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| 101 | ***************************************************************/ |
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| 102 | |
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| 103 | // simply deletes monomials, does not free coeffs |
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| 104 | void p_ShallowDelete(poly *p, const ring r); |
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| 105 | |
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[f550e86] | 106 | |
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[35aab3] | 107 | |
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| 108 | /*************************************************************** |
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| 109 | * |
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| 110 | * Copying/Deleteion of polys: args may be NULL |
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| 111 | * - p/q as arg mean a poly |
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| 112 | * - m a monomial |
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| 113 | * - n a number |
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| 114 | * - pp (resp. qq, mm, nn) means arg is constant |
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| 115 | * - p (resp, q, m, n) means arg is destroyed |
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| 116 | * |
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| 117 | ***************************************************************/ |
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| 118 | |
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[bf183f] | 119 | poly p_Sub(poly a, poly b, const ring r); |
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| 120 | |
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| 121 | poly p_Power(poly p, int i, const ring r); |
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[35aab3] | 122 | /*************************************************************** |
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| 123 | * |
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| 124 | * Misc stuff |
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| 125 | * |
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| 126 | ***************************************************************/ |
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[c1a2b20] | 127 | /*2 |
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| 128 | * returns the length of a (numbers of monomials) |
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| 129 | */ |
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| 130 | static inline int pLength(poly a) |
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| 131 | { |
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| 132 | int l = 0; |
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| 133 | while (a!=NULL) |
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| 134 | { |
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| 135 | pIter(a); |
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| 136 | l++; |
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| 137 | } |
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| 138 | return l; |
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| 139 | } |
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| 140 | |
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[71ba5b8] | 141 | void p_Norm(poly p1, const ring r); |
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[8d1d30c] | 142 | void p_Normalize(poly p,const ring r); |
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| 143 | |
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| 144 | void p_Content(poly p, const ring r); |
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[5698bb] | 145 | //void p_SimpleContent(poly p, int s, const ring r); |
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[8d1d30c] | 146 | |
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| 147 | poly p_Cleardenom(poly p, const ring r); |
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| 148 | void p_Cleardenom_n(poly p, const ring r,number &c); |
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| 149 | number p_GetAllDenom(poly ph, const ring r); |
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| 150 | |
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[fbf8a6] | 151 | int pSize( poly p, const ring r ); |
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| 152 | |
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[4e8ef90] | 153 | // homogenizes p by multiplying certain powers of the varnum-th variable |
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| 154 | poly p_Homogen (poly p, int varnum, const ring r); |
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[a30a39a] | 155 | |
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[4e8ef90] | 156 | BOOLEAN p_IsHomogeneous (poly p, const ring r); |
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| 157 | |
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[a04c5e] | 158 | static inline void p_Setm(poly p, const ring r); |
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[35aab3] | 159 | p_SetmProc p_GetSetmProc(ring r); |
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| 160 | |
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[71ba5b8] | 161 | poly p_Subst(poly p, int n, poly e, const ring r); |
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| 162 | |
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[35aab3] | 163 | // TODO: |
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| 164 | #define p_SetmComp p_Setm |
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| 165 | |
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[20d9284] | 166 | // component |
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| 167 | static inline unsigned long p_SetComp(poly p, unsigned long c, ring r) |
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| 168 | { |
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| 169 | p_LmCheckPolyRing2(p, r); |
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| 170 | pAssume2(rRing_has_Comp(r)); |
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| 171 | __p_GetComp(p,r) = c; |
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| 172 | return c; |
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| 173 | } |
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[a22a82] | 174 | // sets component of poly a to i, returns length of p |
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| 175 | static inline void p_SetCompP(poly p, int i, ring r) |
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[5a3ae8] | 176 | { |
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| 177 | if (p != NULL) |
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| 178 | { |
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| 179 | #ifdef PDEBUG |
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| 180 | poly q = p; |
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| 181 | int l = 0; |
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| 182 | #endif |
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| 183 | |
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| 184 | if (rOrd_SetCompRequiresSetm(r)) |
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| 185 | { |
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| 186 | do |
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| 187 | { |
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| 188 | p_SetComp(p, i, r); |
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| 189 | p_SetmComp(p, r); |
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| 190 | #ifdef PDEBUG |
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| 191 | l++; |
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| 192 | #endif |
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| 193 | pIter(p); |
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| 194 | } |
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| 195 | while (p != NULL); |
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| 196 | } |
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| 197 | else |
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| 198 | { |
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| 199 | do |
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| 200 | { |
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| 201 | p_SetComp(p, i, r); |
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| 202 | #ifdef PDEBUG |
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| 203 | l++; |
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| 204 | #endif |
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| 205 | pIter(p); |
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| 206 | } |
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| 207 | while(p != NULL); |
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| 208 | } |
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| 209 | #ifdef PDEBUG |
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| 210 | p_Test(q, r); |
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| 211 | assume(l == pLength(q)); |
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| 212 | #endif |
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| 213 | } |
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| 214 | } |
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| 215 | |
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[a22a82] | 216 | static inline void p_SetCompP(poly p, int i, ring lmRing, ring tailRing) |
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[5a3ae8] | 217 | { |
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| 218 | if (p != NULL) |
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| 219 | { |
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| 220 | p_SetComp(p, i, lmRing); |
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| 221 | p_SetmComp(p, lmRing); |
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| 222 | p_SetCompP(pNext(p), i, tailRing); |
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| 223 | } |
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| 224 | } |
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[c462b55] | 225 | |
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| 226 | // returns maximal column number in the modul element a (or 0) |
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| 227 | static inline long p_MaxComp(poly p, ring lmRing, ring tailRing) |
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| 228 | { |
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| 229 | long result,i; |
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| 230 | |
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| 231 | if(p==NULL) return 0; |
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| 232 | result = p_GetComp(p, lmRing); |
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| 233 | if (result != 0) |
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| 234 | { |
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| 235 | loop |
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| 236 | { |
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| 237 | pIter(p); |
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| 238 | if(p==NULL) break; |
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| 239 | i = p_GetComp(p, tailRing); |
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| 240 | if (i>result) result = i; |
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| 241 | } |
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| 242 | } |
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| 243 | return result; |
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| 244 | } |
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| 245 | |
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| 246 | static inline long p_MaxComp(poly p,ring lmRing) {return p_MaxComp(p,lmRing,lmRing);} |
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| 247 | |
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| 248 | static inline long p_MinComp(poly p, ring lmRing, ring tailRing) |
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| 249 | { |
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| 250 | long result,i; |
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| 251 | |
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| 252 | if(p==NULL) return 0; |
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| 253 | result = p_GetComp(p,lmRing); |
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| 254 | if (result != 0) |
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| 255 | { |
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| 256 | loop |
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| 257 | { |
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| 258 | pIter(p); |
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| 259 | if(p==NULL) break; |
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| 260 | i = p_GetComp(p,tailRing); |
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| 261 | if (i<result) result = i; |
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| 262 | } |
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| 263 | } |
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| 264 | return result; |
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| 265 | } |
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| 266 | |
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| 267 | static inline long p_MinComp(poly p,ring lmRing) {return p_MinComp(p,lmRing,lmRing);} |
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[35aab3] | 268 | |
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| 269 | /*************************************************************** |
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| 270 | * |
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| 271 | * poly things which are independent of ring |
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| 272 | * |
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| 273 | ***************************************************************/ |
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[8a8c9e] | 274 | static inline poly pLast(poly a, int &length); |
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[35aab3] | 275 | inline poly pLast(poly a) { int l; return pLast(a, l);} |
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[20d9284] | 276 | static inline poly pReverse(poly p) |
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| 277 | { |
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| 278 | if (p == NULL || pNext(p) == NULL) return p; |
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| 279 | |
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| 280 | poly q = pNext(p), // == pNext(p) |
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| 281 | qn; |
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| 282 | pNext(p) = NULL; |
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| 283 | do |
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| 284 | { |
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| 285 | qn = pNext(q); |
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| 286 | pNext(q) = p; |
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| 287 | p = q; |
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| 288 | q = qn; |
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| 289 | } |
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| 290 | while (qn != NULL); |
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| 291 | return p; |
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| 292 | } |
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[c6a3eb2] | 293 | void pEnlargeSet(poly**p, int length, int increment); |
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[35aab3] | 294 | |
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| 295 | |
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| 296 | /*************************************************************** |
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| 297 | * |
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| 298 | * I/O |
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| 299 | * |
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| 300 | ***************************************************************/ |
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| 301 | char* p_String(poly p, ring lmRing, ring tailRing); |
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| 302 | char* p_String0(poly p, ring lmRing, ring tailRing); |
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| 303 | void p_Write(poly p, ring lmRing, ring tailRing); |
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| 304 | void p_Write0(poly p, ring lmRing, ring tailRing); |
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| 305 | void p_wrp(poly p, ring lmRing, ring tailRing); |
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| 306 | |
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[a04c5e] | 307 | static inline char* p_String(poly p, ring p_ring); |
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| 308 | static inline char* p_String0(poly p, ring p_ring); |
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| 309 | static inline void p_Write(poly p, ring p_ring); |
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| 310 | static inline void p_Write0(poly p, ring p_ring); |
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| 311 | static inline void p_wrp(poly p, ring p_ring); |
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[35aab3] | 312 | |
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| 313 | |
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| 314 | /*************************************************************** |
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| 315 | * |
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| 316 | * Degree stuff -- see p_polys.cc for explainations |
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| 317 | * |
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| 318 | ***************************************************************/ |
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| 319 | extern pLDegProc pLDeg; |
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| 320 | extern pFDegProc pFDeg; |
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[19ae652] | 321 | long p_WFirstTotalDegree(poly p, ring r); |
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| 322 | long p_WTotaldegree(poly p, const ring r); |
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[bf183f] | 323 | long p_WDegree(poly p,const ring r); |
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[35aab3] | 324 | long pLDeg0(poly p,int *l, ring r); |
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| 325 | long pLDeg0c(poly p,int *l, ring r); |
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| 326 | long pLDegb(poly p,int *l, ring r); |
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| 327 | long pLDeg1(poly p,int *l, ring r); |
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| 328 | long pLDeg1c(poly p,int *l, ring r); |
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| 329 | long pLDeg1_Deg(poly p,int *l, ring r); |
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| 330 | long pLDeg1c_Deg(poly p,int *l, ring r); |
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| 331 | long pLDeg1_Totaldegree(poly p,int *l, ring r); |
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| 332 | long pLDeg1c_Totaldegree(poly p,int *l, ring r); |
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| 333 | long pLDeg1_WFirstTotalDegree(poly p,int *l, ring r); |
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| 334 | long pLDeg1c_WFirstTotalDegree(poly p,int *l, ring r); |
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[f82bd3] | 335 | BOOLEAN p_EqualPolys(poly p1, poly p2, const ring r); |
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[c6a3eb2] | 336 | |
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| 337 | long p_Deg(poly a, const ring r); |
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[35aab3] | 338 | /*************************************************************** |
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| 339 | * |
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| 340 | * PDEBUG stuff |
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| 341 | * |
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| 342 | ***************************************************************/ |
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| 343 | #ifdef PDEBUG |
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| 344 | // Returns TRUE if m is monom of p, FALSE otherwise |
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| 345 | BOOLEAN pIsMonomOf(poly p, poly m); |
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| 346 | // Returns TRUE if p and q have common monoms |
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| 347 | BOOLEAN pHaveCommonMonoms(poly p, poly q); |
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| 348 | |
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| 349 | // p_Check* routines return TRUE if everything is ok, |
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| 350 | // else, they report error message and return false |
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| 351 | |
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| 352 | // check if Lm(p) is from ring r |
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| 353 | BOOLEAN p_LmCheckIsFromRing(poly p, ring r); |
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| 354 | // check if Lm(p) != NULL, r != NULL and initialized && Lm(p) is from r |
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| 355 | BOOLEAN p_LmCheckPolyRing(poly p, ring r); |
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| 356 | // check if all monoms of p are from ring r |
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| 357 | BOOLEAN p_CheckIsFromRing(poly p, ring r); |
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| 358 | // check r != NULL and initialized && all monoms of p are from r |
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| 359 | BOOLEAN p_CheckPolyRing(poly p, ring r); |
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| 360 | // check if r != NULL and initialized |
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| 361 | BOOLEAN p_CheckRing(ring r); |
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| 362 | // only do check if cond |
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[14d732] | 363 | |
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| 364 | |
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[35aab3] | 365 | #define pIfThen(cond, check) do {if (cond) {check;}} while (0) |
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| 366 | |
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| 367 | BOOLEAN _p_Test(poly p, ring r, int level); |
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| 368 | BOOLEAN _p_LmTest(poly p, ring r, int level); |
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| 369 | BOOLEAN _pp_Test(poly p, ring lmRing, ring tailRing, int level); |
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| 370 | |
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| 371 | #define p_Test(p,r) _p_Test(p, r, PDEBUG) |
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| 372 | #define p_LmTest(p,r) _p_LmTest(p, r, PDEBUG) |
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| 373 | #define pp_Test(p, lmRing, tailRing) _pp_Test(p, lmRing, tailRing, PDEBUG) |
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| 374 | |
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| 375 | #else // ! PDEBUG |
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| 376 | |
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| 377 | #define pIsMonomOf(p, q) (TRUE) |
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| 378 | #define pHaveCommonMonoms(p, q) (TRUE) |
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| 379 | #define p_LmCheckIsFromRing(p,r) ((void)0) |
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| 380 | #define p_LmCheckPolyRing(p,r) ((void)0) |
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| 381 | #define p_CheckIsFromRing(p,r) ((void)0) |
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| 382 | #define p_CheckPolyRing(p,r) ((void)0) |
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| 383 | #define p_CheckRing(r) ((void)0) |
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| 384 | #define P_CheckIf(cond, check) ((void)0) |
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| 385 | |
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[68fcc8] | 386 | #define p_Test(p,r) (1) |
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| 387 | #define p_LmTest(p,r) (1) |
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| 388 | #define pp_Test(p, lmRing, tailRing) (1) |
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[35aab3] | 389 | |
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| 390 | #endif |
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| 391 | |
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[a04c5e] | 392 | /*************************************************************** |
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| 393 | * |
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| 394 | * Primitives for accessing and setting fields of a poly |
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| 395 | * |
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| 396 | ***************************************************************/ |
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| 397 | |
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| 398 | static inline number p_SetCoeff(poly p, number n, ring r) |
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| 399 | { |
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| 400 | p_LmCheckPolyRing2(p, r); |
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[8a8c9e] | 401 | n_Delete(&(p->coef), r->cf); |
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[a04c5e] | 402 | (p)->coef=n; |
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| 403 | return n; |
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| 404 | } |
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| 405 | |
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| 406 | // order |
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| 407 | static inline long p_GetOrder(poly p, ring r) |
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| 408 | { |
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| 409 | p_LmCheckPolyRing2(p, r); |
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| 410 | if (r->typ==NULL) return ((p)->exp[r->pOrdIndex]); |
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| 411 | int i=0; |
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| 412 | loop |
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| 413 | { |
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| 414 | switch(r->typ[i].ord_typ) |
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| 415 | { |
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| 416 | case ro_wp_neg: |
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| 417 | return (((long)((p)->exp[r->pOrdIndex]))-POLY_NEGWEIGHT_OFFSET); |
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| 418 | case ro_syzcomp: |
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| 419 | case ro_syz: |
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| 420 | case ro_cp: |
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| 421 | i++; |
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| 422 | break; |
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| 423 | //case ro_dp: |
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| 424 | //case ro_wp: |
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| 425 | default: |
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| 426 | return ((p)->exp[r->pOrdIndex]); |
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| 427 | } |
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| 428 | } |
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| 429 | } |
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| 430 | |
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| 431 | // Setm |
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| 432 | static inline void p_Setm(poly p, const ring r) |
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| 433 | { |
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| 434 | p_CheckRing2(r); |
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| 435 | r->p_Setm(p, r); |
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| 436 | } |
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| 437 | |
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[20d9284] | 438 | |
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[a04c5e] | 439 | static inline unsigned long p_AddComp(poly p, unsigned long v, ring r) |
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| 440 | { |
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| 441 | p_LmCheckPolyRing2(p, r); |
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| 442 | pAssume2(rRing_has_Comp(r)); |
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| 443 | return __p_GetComp(p,r) += v; |
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| 444 | } |
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| 445 | static inline unsigned long p_SubComp(poly p, unsigned long v, ring r) |
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| 446 | { |
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| 447 | p_LmCheckPolyRing2(p, r); |
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| 448 | pAssume2(rRing_has_Comp(r)); |
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[8a8c9e] | 449 | _pPolyAssume2(__p_GetComp(p,r) >= v,p,r); |
---|
[a04c5e] | 450 | return __p_GetComp(p,r) -= v; |
---|
| 451 | } |
---|
| 452 | static inline int p_Comp_k_n(poly a, poly b, int k, ring r) |
---|
| 453 | { |
---|
| 454 | if ((a==NULL) || (b==NULL) ) return FALSE; |
---|
| 455 | p_LmCheckPolyRing2(a, r); |
---|
| 456 | p_LmCheckPolyRing2(b, r); |
---|
| 457 | pAssume2(k > 0 && k <= r->N); |
---|
| 458 | int i=k; |
---|
| 459 | for(;i<=r->N;i++) |
---|
| 460 | { |
---|
| 461 | if (p_GetExp(a,i,r) != p_GetExp(b,i,r)) return FALSE; |
---|
| 462 | // if (a->exp[(r->VarOffset[i] & 0xffffff)] != b->exp[(r->VarOffset[i] & 0xffffff)]) return FALSE; |
---|
| 463 | } |
---|
| 464 | return TRUE; |
---|
| 465 | } |
---|
| 466 | |
---|
| 467 | #ifndef HAVE_EXPSIZES |
---|
| 468 | |
---|
| 469 | /// get a single variable exponent |
---|
| 470 | /// @Note: |
---|
| 471 | /// the integer VarOffset encodes: |
---|
| 472 | /// 1. the position of a variable in the exponent vector p->exp (lower 24 bits) |
---|
| 473 | /// 2. number of bits to shift to the right in the upper 8 bits (which takes at most 6 bits for 64 bit) |
---|
| 474 | /// Thus VarOffset always has 2 zero higher bits! |
---|
| 475 | static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset) |
---|
| 476 | { |
---|
| 477 | pAssume2((VarOffset >> (24 + 6)) == 0); |
---|
| 478 | #if 0 |
---|
| 479 | int pos=(VarOffset & 0xffffff); |
---|
| 480 | int bitpos=(VarOffset >> 24); |
---|
| 481 | unsigned long exp=(p->exp[pos] >> bitmask) & iBitmask; |
---|
| 482 | return exp; |
---|
| 483 | #else |
---|
| 484 | return (long) |
---|
| 485 | ((p->exp[(VarOffset & 0xffffff)] >> (VarOffset >> 24)) |
---|
| 486 | & iBitmask); |
---|
| 487 | #endif |
---|
| 488 | } |
---|
| 489 | |
---|
| 490 | |
---|
| 491 | /// set a single variable exponent |
---|
| 492 | /// @Note: |
---|
| 493 | /// VarOffset encodes the position in p->exp @see p_GetExp |
---|
| 494 | static inline unsigned long p_SetExp(poly p, const unsigned long e, const unsigned long iBitmask, const int VarOffset) |
---|
| 495 | { |
---|
| 496 | pAssume2(e>=0); |
---|
| 497 | pAssume2(e<=iBitmask); |
---|
| 498 | pAssume2((VarOffset >> (24 + 6)) == 0); |
---|
| 499 | |
---|
| 500 | // shift e to the left: |
---|
| 501 | register int shift = VarOffset >> 24; |
---|
| 502 | unsigned long ee = e << shift /*(VarOffset >> 24)*/; |
---|
| 503 | // find the bits in the exponent vector |
---|
| 504 | register int offset = (VarOffset & 0xffffff); |
---|
| 505 | // clear the bits in the exponent vector: |
---|
| 506 | p->exp[offset] &= ~( iBitmask << shift ); |
---|
| 507 | // insert e with | |
---|
| 508 | p->exp[ offset ] |= ee; |
---|
| 509 | return e; |
---|
| 510 | } |
---|
| 511 | |
---|
| 512 | |
---|
| 513 | #else // #ifdef HAVE_EXPSIZES // EXPERIMENTAL!!! |
---|
| 514 | |
---|
| 515 | static inline unsigned long BitMask(unsigned long bitmask, int twobits) |
---|
| 516 | { |
---|
| 517 | // bitmask = 00000111111111111 |
---|
| 518 | // 0 must give bitmask! |
---|
| 519 | // 1, 2, 3 - anything like 00011..11 |
---|
| 520 | pAssume2((twobits >> 2) == 0); |
---|
| 521 | static const unsigned long _bitmasks[4] = {-1, 0x7fff, 0x7f, 0x3}; |
---|
| 522 | return bitmask & _bitmasks[twobits]; |
---|
| 523 | } |
---|
| 524 | |
---|
| 525 | |
---|
| 526 | /// @Note: we may add some more info (6 ) into VarOffset and thus encode |
---|
| 527 | static inline long p_GetExp(const poly p, const unsigned long iBitmask, const int VarOffset) |
---|
| 528 | { |
---|
| 529 | int pos =(VarOffset & 0xffffff); |
---|
| 530 | int hbyte= (VarOffset >> 24); // the highest byte |
---|
| 531 | int bitpos = hbyte & 0x3f; // last 6 bits |
---|
| 532 | long bitmask = BitMask(iBitmask, hbyte >> 6); |
---|
| 533 | |
---|
| 534 | long exp=(p->exp[pos] >> bitpos) & bitmask; |
---|
| 535 | return exp; |
---|
| 536 | |
---|
| 537 | } |
---|
| 538 | |
---|
| 539 | static inline long p_SetExp(poly p, const long e, const unsigned long iBitmask, const int VarOffset) |
---|
| 540 | { |
---|
| 541 | pAssume2(e>=0); |
---|
| 542 | pAssume2(e <= BitMask(iBitmask, VarOffset >> 30)); |
---|
| 543 | |
---|
| 544 | // shift e to the left: |
---|
| 545 | register int hbyte = VarOffset >> 24; |
---|
| 546 | int bitmask = BitMask(iBitmask, hbyte >> 6); |
---|
| 547 | register int shift = hbyte & 0x3f; |
---|
| 548 | long ee = e << shift; |
---|
| 549 | // find the bits in the exponent vector |
---|
| 550 | register int offset = (VarOffset & 0xffffff); |
---|
| 551 | // clear the bits in the exponent vector: |
---|
| 552 | p->exp[offset] &= ~( bitmask << shift ); |
---|
| 553 | // insert e with | |
---|
| 554 | p->exp[ offset ] |= ee; |
---|
| 555 | return e; |
---|
| 556 | } |
---|
| 557 | |
---|
| 558 | #endif // #ifndef HAVE_EXPSIZES |
---|
| 559 | |
---|
| 560 | |
---|
| 561 | static inline long p_GetExp(const poly p, const ring r, const int VarOffset) |
---|
| 562 | { |
---|
| 563 | p_LmCheckPolyRing2(p, r); |
---|
| 564 | pAssume2(VarOffset != -1); |
---|
| 565 | return p_GetExp(p, r->bitmask, VarOffset); |
---|
| 566 | } |
---|
| 567 | |
---|
| 568 | static inline long p_SetExp(poly p, const long e, const ring r, const int VarOffset) |
---|
| 569 | { |
---|
| 570 | p_LmCheckPolyRing2(p, r); |
---|
| 571 | pAssume2(VarOffset != -1); |
---|
| 572 | return p_SetExp(p, e, r->bitmask, VarOffset); |
---|
| 573 | } |
---|
| 574 | |
---|
| 575 | |
---|
| 576 | |
---|
| 577 | /// get v^th exponent for a monomial |
---|
| 578 | static inline long p_GetExp(const poly p, const int v, const ring r) |
---|
| 579 | { |
---|
| 580 | p_LmCheckPolyRing2(p, r); |
---|
| 581 | pAssume2(v>0 && v <= r->N); |
---|
| 582 | pAssume2(r->VarOffset[v] != -1); |
---|
| 583 | return p_GetExp(p, r->bitmask, r->VarOffset[v]); |
---|
| 584 | } |
---|
| 585 | |
---|
| 586 | |
---|
| 587 | /// set v^th exponent for a monomial |
---|
| 588 | static inline long p_SetExp(poly p, const int v, const long e, const ring r) |
---|
| 589 | { |
---|
| 590 | p_LmCheckPolyRing2(p, r); |
---|
| 591 | pAssume2(v>0 && v <= r->N); |
---|
| 592 | pAssume2(r->VarOffset[v] != -1); |
---|
| 593 | return p_SetExp(p, e, r->bitmask, r->VarOffset[v]); |
---|
| 594 | } |
---|
| 595 | |
---|
| 596 | |
---|
| 597 | |
---|
| 598 | |
---|
| 599 | |
---|
| 600 | // the following should be implemented more efficiently |
---|
| 601 | static inline long p_IncrExp(poly p, int v, ring r) |
---|
| 602 | { |
---|
| 603 | p_LmCheckPolyRing2(p, r); |
---|
| 604 | int e = p_GetExp(p,v,r); |
---|
| 605 | e++; |
---|
| 606 | return p_SetExp(p,v,e,r); |
---|
| 607 | } |
---|
| 608 | static inline long p_DecrExp(poly p, int v, ring r) |
---|
| 609 | { |
---|
| 610 | p_LmCheckPolyRing2(p, r); |
---|
| 611 | int e = p_GetExp(p,v,r); |
---|
| 612 | pAssume2(e > 0); |
---|
| 613 | e--; |
---|
| 614 | return p_SetExp(p,v,e,r); |
---|
| 615 | } |
---|
| 616 | static inline long p_AddExp(poly p, int v, long ee, ring r) |
---|
| 617 | { |
---|
| 618 | p_LmCheckPolyRing2(p, r); |
---|
| 619 | int e = p_GetExp(p,v,r); |
---|
| 620 | e += ee; |
---|
| 621 | return p_SetExp(p,v,e,r); |
---|
| 622 | } |
---|
| 623 | static inline long p_SubExp(poly p, int v, long ee, ring r) |
---|
| 624 | { |
---|
| 625 | p_LmCheckPolyRing2(p, r); |
---|
| 626 | long e = p_GetExp(p,v,r); |
---|
| 627 | pAssume2(e >= ee); |
---|
| 628 | e -= ee; |
---|
| 629 | return p_SetExp(p,v,e,r); |
---|
| 630 | } |
---|
| 631 | static inline long p_MultExp(poly p, int v, long ee, ring r) |
---|
| 632 | { |
---|
| 633 | p_LmCheckPolyRing2(p, r); |
---|
| 634 | long e = p_GetExp(p,v,r); |
---|
| 635 | e *= ee; |
---|
| 636 | return p_SetExp(p,v,e,r); |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | static inline long p_GetExpSum(poly p1, poly p2, int i, ring r) |
---|
| 640 | { |
---|
| 641 | p_LmCheckPolyRing2(p1, r); |
---|
| 642 | p_LmCheckPolyRing2(p2, r); |
---|
| 643 | return p_GetExp(p1,i,r) + p_GetExp(p2,i,r); |
---|
| 644 | } |
---|
| 645 | static inline long p_GetExpDiff(poly p1, poly p2, int i, ring r) |
---|
| 646 | { |
---|
| 647 | return p_GetExp(p1,i,r) - p_GetExp(p2,i,r); |
---|
| 648 | } |
---|
| 649 | |
---|
| 650 | |
---|
| 651 | /*************************************************************** |
---|
| 652 | * |
---|
| 653 | * Allocation/Initalization/Deletion |
---|
| 654 | * |
---|
| 655 | ***************************************************************/ |
---|
| 656 | static inline poly p_New(ring r, omBin bin) |
---|
| 657 | { |
---|
| 658 | p_CheckRing2(r); |
---|
| 659 | pAssume2(bin != NULL && r->PolyBin->sizeW == bin->sizeW); |
---|
| 660 | poly p; |
---|
| 661 | omTypeAllocBin(poly, p, bin); |
---|
| 662 | p_SetRingOfLm(p, r); |
---|
| 663 | return p; |
---|
| 664 | } |
---|
| 665 | |
---|
| 666 | static inline poly p_New(ring r) |
---|
| 667 | { |
---|
| 668 | return p_New(r, r->PolyBin); |
---|
| 669 | } |
---|
| 670 | |
---|
| 671 | static inline void p_LmFree(poly p, ring r) |
---|
| 672 | { |
---|
| 673 | p_LmCheckPolyRing2(p, r); |
---|
| 674 | omFreeBinAddr(p); |
---|
| 675 | } |
---|
| 676 | static inline void p_LmFree(poly *p, ring r) |
---|
| 677 | { |
---|
| 678 | p_LmCheckPolyRing2(*p, r); |
---|
| 679 | poly h = *p; |
---|
| 680 | *p = pNext(h); |
---|
| 681 | omFreeBinAddr(h); |
---|
| 682 | } |
---|
| 683 | static inline poly p_LmFreeAndNext(poly p, ring r) |
---|
| 684 | { |
---|
| 685 | p_LmCheckPolyRing2(p, r); |
---|
| 686 | poly pnext = pNext(p); |
---|
| 687 | omFreeBinAddr(p); |
---|
| 688 | return pnext; |
---|
| 689 | } |
---|
[8a8c9e] | 690 | static inline void p_LmDelete(poly p, const ring r) |
---|
[a04c5e] | 691 | { |
---|
| 692 | p_LmCheckPolyRing2(p, r); |
---|
[8a8c9e] | 693 | n_Delete(&pGetCoeff(p), r->cf); |
---|
[a04c5e] | 694 | omFreeBinAddr(p); |
---|
| 695 | } |
---|
[8a8c9e] | 696 | static inline void p_LmDelete(poly *p, const ring r) |
---|
[a04c5e] | 697 | { |
---|
| 698 | p_LmCheckPolyRing2(*p, r); |
---|
| 699 | poly h = *p; |
---|
| 700 | *p = pNext(h); |
---|
[8a8c9e] | 701 | n_Delete(&pGetCoeff(h), r->cf); |
---|
[a04c5e] | 702 | omFreeBinAddr(h); |
---|
| 703 | } |
---|
[8a8c9e] | 704 | static inline poly p_LmDeleteAndNext(poly p, const ring r) |
---|
[a04c5e] | 705 | { |
---|
| 706 | p_LmCheckPolyRing2(p, r); |
---|
| 707 | poly pnext = pNext(p); |
---|
[8a8c9e] | 708 | n_Delete(&pGetCoeff(p), r->cf); |
---|
[a04c5e] | 709 | omFreeBinAddr(p); |
---|
| 710 | return pnext; |
---|
| 711 | } |
---|
| 712 | |
---|
| 713 | /*************************************************************** |
---|
| 714 | * |
---|
| 715 | * Misc routines |
---|
| 716 | * |
---|
| 717 | ***************************************************************/ |
---|
[20d9284] | 718 | |
---|
| 719 | // pCmp: args may be NULL |
---|
| 720 | // returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2))) |
---|
[a04c5e] | 721 | static inline int p_Cmp(poly p1, poly p2, ring r) |
---|
| 722 | { |
---|
| 723 | if (p2==NULL) |
---|
| 724 | return 1; |
---|
| 725 | if (p1==NULL) |
---|
| 726 | return -1; |
---|
| 727 | return p_LmCmp(p1,p2,r); |
---|
| 728 | } |
---|
| 729 | |
---|
| 730 | static inline unsigned long p_GetMaxExp(const poly p, const ring r) |
---|
| 731 | { |
---|
| 732 | return p_GetMaxExp(p_GetMaxExpL(p, r), r); |
---|
| 733 | } |
---|
| 734 | |
---|
| 735 | static inline unsigned long p_GetMaxExp(const unsigned long l, const ring r) |
---|
| 736 | { |
---|
| 737 | unsigned long bitmask = r->bitmask; |
---|
| 738 | unsigned long max = (l & bitmask); |
---|
| 739 | unsigned long j = r->ExpPerLong - 1; |
---|
| 740 | |
---|
| 741 | if (j > 0) |
---|
| 742 | { |
---|
| 743 | unsigned long i = r->BitsPerExp; |
---|
| 744 | long e; |
---|
| 745 | loop |
---|
| 746 | { |
---|
| 747 | e = ((l >> i) & bitmask); |
---|
| 748 | if ((unsigned long) e > max) |
---|
| 749 | max = e; |
---|
| 750 | j--; |
---|
| 751 | if (j==0) break; |
---|
| 752 | i += r->BitsPerExp; |
---|
| 753 | } |
---|
| 754 | } |
---|
| 755 | return max; |
---|
| 756 | } |
---|
| 757 | |
---|
| 758 | static inline unsigned long |
---|
| 759 | p_GetTotalDegree(const unsigned long l, const ring r, const int number_of_exps) |
---|
| 760 | { |
---|
| 761 | const unsigned long bitmask = r->bitmask; |
---|
| 762 | unsigned long sum = (l & bitmask); |
---|
| 763 | unsigned long j = number_of_exps - 1; |
---|
| 764 | |
---|
| 765 | if (j > 0) |
---|
| 766 | { |
---|
| 767 | unsigned long i = r->BitsPerExp; |
---|
| 768 | loop |
---|
| 769 | { |
---|
| 770 | sum += ((l >> i) & bitmask); |
---|
| 771 | j--; |
---|
| 772 | if (j==0) break; |
---|
| 773 | i += r->BitsPerExp; |
---|
| 774 | } |
---|
| 775 | } |
---|
| 776 | return sum; |
---|
| 777 | } |
---|
| 778 | |
---|
| 779 | static inline unsigned long |
---|
| 780 | p_GetTotalDegree(const unsigned long l, const ring r) |
---|
| 781 | { |
---|
| 782 | return p_GetTotalDegree(l, r, r->ExpPerLong); |
---|
| 783 | } |
---|
| 784 | |
---|
| 785 | /*************************************************************** |
---|
| 786 | * |
---|
| 787 | * Dispatcher to r->p_Procs, they do the tests/checks |
---|
| 788 | * |
---|
| 789 | ***************************************************************/ |
---|
| 790 | // returns a copy of p |
---|
| 791 | static inline poly p_Copy(poly p, const ring r) |
---|
| 792 | { |
---|
| 793 | #ifdef PDEBUG |
---|
| 794 | poly pp= r->p_Procs->p_Copy(p, r); |
---|
| 795 | p_Test(pp,r); |
---|
| 796 | return pp; |
---|
| 797 | #else |
---|
| 798 | return r->p_Procs->p_Copy(p, r); |
---|
| 799 | #endif |
---|
| 800 | } |
---|
| 801 | |
---|
[20d9284] | 802 | static inline poly p_Head(poly p, const ring r) |
---|
| 803 | { |
---|
| 804 | if (p == NULL) return NULL; |
---|
| 805 | p_LmCheckPolyRing1(p, r); |
---|
| 806 | poly np; |
---|
| 807 | omTypeAllocBin(poly, np, r->PolyBin); |
---|
| 808 | p_SetRingOfLm(np, r); |
---|
| 809 | p_MemCopy_LengthGeneral(np->exp, p->exp, r->ExpL_Size); |
---|
| 810 | pNext(np) = NULL; |
---|
| 811 | pSetCoeff0(np, n_Copy(pGetCoeff(p), r->cf)); |
---|
| 812 | return np; |
---|
| 813 | } |
---|
| 814 | |
---|
| 815 | // returns a copy of p with Lm(p) from lmRing and Tail(p) from tailRing |
---|
[a04c5e] | 816 | static inline poly p_Copy(poly p, const ring lmRing, const ring tailRing) |
---|
| 817 | { |
---|
| 818 | #ifndef PDEBUG |
---|
| 819 | if (tailRing == lmRing) |
---|
| 820 | return tailRing->p_Procs->p_Copy(p, tailRing); |
---|
| 821 | #endif |
---|
| 822 | if (p != NULL) |
---|
| 823 | { |
---|
| 824 | poly pres = p_Head(p, lmRing); |
---|
| 825 | pNext(pres) = tailRing->p_Procs->p_Copy(pNext(p), tailRing); |
---|
| 826 | return pres; |
---|
| 827 | } |
---|
| 828 | else |
---|
| 829 | return NULL; |
---|
| 830 | } |
---|
| 831 | |
---|
| 832 | // deletes *p, and sets *p to NULL |
---|
| 833 | static inline void p_Delete(poly *p, const ring r) |
---|
| 834 | { |
---|
| 835 | r->p_Procs->p_Delete(p, r); |
---|
| 836 | } |
---|
| 837 | |
---|
| 838 | static inline void p_Delete(poly *p, const ring lmRing, const ring tailRing) |
---|
| 839 | { |
---|
| 840 | #ifndef PDEBUG |
---|
| 841 | if (tailRing == lmRing) |
---|
| 842 | { |
---|
| 843 | tailRing->p_Procs->p_Delete(p, tailRing); |
---|
| 844 | return; |
---|
| 845 | } |
---|
| 846 | #endif |
---|
| 847 | if (*p != NULL) |
---|
| 848 | { |
---|
| 849 | if (pNext(*p) != NULL) |
---|
| 850 | tailRing->p_Procs->p_Delete(&pNext(*p), tailRing); |
---|
| 851 | p_LmDelete(p, lmRing); |
---|
| 852 | } |
---|
| 853 | } |
---|
| 854 | |
---|
[20d9284] | 855 | // copys monomials of p, allocates new monomials from bin, |
---|
| 856 | // deletes monomoals of p |
---|
[a04c5e] | 857 | static inline poly p_ShallowCopyDelete(poly p, const ring r, omBin bin) |
---|
| 858 | { |
---|
| 859 | p_LmCheckPolyRing2(p, r); |
---|
| 860 | pAssume2(r->PolyBin->sizeW == bin->sizeW); |
---|
| 861 | return r->p_Procs->p_ShallowCopyDelete(p, r, bin); |
---|
| 862 | } |
---|
| 863 | |
---|
| 864 | // returns p+q, destroys p and q |
---|
| 865 | static inline poly p_Add_q(poly p, poly q, const ring r) |
---|
| 866 | { |
---|
| 867 | int shorter; |
---|
| 868 | return r->p_Procs->p_Add_q(p, q, shorter, r); |
---|
| 869 | } |
---|
| 870 | |
---|
[20d9284] | 871 | /// like p_Add_q, except that if lp == pLength(lp) lq == pLength(lq) then lp == pLength(p+q) |
---|
[a04c5e] | 872 | static inline poly p_Add_q(poly p, poly q, int &lp, int lq, const ring r) |
---|
| 873 | { |
---|
| 874 | int shorter; |
---|
| 875 | poly res = r->p_Procs->p_Add_q(p, q, shorter, r); |
---|
| 876 | lp = (lp + lq) - shorter; |
---|
| 877 | return res; |
---|
| 878 | } |
---|
[35aab3] | 879 | |
---|
[a04c5e] | 880 | // returns p*n, destroys p |
---|
| 881 | static inline poly p_Mult_nn(poly p, number n, const ring r) |
---|
| 882 | { |
---|
[8a8c9e] | 883 | if (n_IsOne(n, r->cf)) |
---|
[a04c5e] | 884 | return p; |
---|
| 885 | else |
---|
| 886 | return r->p_Procs->p_Mult_nn(p, n, r); |
---|
| 887 | } |
---|
| 888 | |
---|
| 889 | static inline poly p_Mult_nn(poly p, number n, const ring lmRing, |
---|
| 890 | const ring tailRing) |
---|
| 891 | { |
---|
| 892 | #ifndef PDEBUG |
---|
| 893 | if (lmRing == tailRing) |
---|
| 894 | { |
---|
| 895 | return p_Mult_nn(p, n, tailRing); |
---|
| 896 | } |
---|
| 897 | #endif |
---|
| 898 | poly pnext = pNext(p); |
---|
| 899 | pNext(p) = NULL; |
---|
| 900 | p = lmRing->p_Procs->p_Mult_nn(p, n, lmRing); |
---|
| 901 | pNext(p) = tailRing->p_Procs->p_Mult_nn(pnext, n, tailRing); |
---|
| 902 | return p; |
---|
| 903 | } |
---|
| 904 | |
---|
| 905 | // returns p*n, does not destroy p |
---|
| 906 | static inline poly pp_Mult_nn(poly p, number n, const ring r) |
---|
| 907 | { |
---|
[8a8c9e] | 908 | if (n_IsOne(n, r->cf)) |
---|
[a04c5e] | 909 | return p_Copy(p, r); |
---|
| 910 | else |
---|
| 911 | return r->p_Procs->pp_Mult_nn(p, n, r); |
---|
| 912 | } |
---|
| 913 | |
---|
[20d9284] | 914 | // test if the monomial is a constant as a vector component |
---|
| 915 | // i.e., test if all exponents are zero |
---|
| 916 | static inline BOOLEAN p_LmIsConstantComp(const poly p, const ring r) |
---|
| 917 | { |
---|
| 918 | //p_LmCheckPolyRing(p, r); |
---|
| 919 | int i = r->VarL_Size - 1; |
---|
| 920 | |
---|
| 921 | do |
---|
| 922 | { |
---|
| 923 | if (p->exp[r->VarL_Offset[i]] != 0) |
---|
| 924 | return FALSE; |
---|
| 925 | i--; |
---|
| 926 | } |
---|
| 927 | while (i >= 0); |
---|
| 928 | return TRUE; |
---|
| 929 | } |
---|
| 930 | |
---|
| 931 | // test if monomial is a constant, i.e. if all exponents and the component |
---|
| 932 | // is zero |
---|
| 933 | static inline BOOLEAN p_LmIsConstant(const poly p, const ring r) |
---|
| 934 | { |
---|
| 935 | if (p_LmIsConstantComp(p, r)) |
---|
| 936 | return (p_GetComp(p, r) == 0); |
---|
| 937 | return FALSE; |
---|
| 938 | } |
---|
| 939 | |
---|
[a04c5e] | 940 | // returns Copy(p)*m, does neither destroy p nor m |
---|
| 941 | static inline poly pp_Mult_mm(poly p, poly m, const ring r) |
---|
| 942 | { |
---|
| 943 | if (p_LmIsConstant(m, r)) |
---|
| 944 | return pp_Mult_nn(p, pGetCoeff(m), r); |
---|
| 945 | else |
---|
| 946 | { |
---|
| 947 | poly last; |
---|
| 948 | return r->p_Procs->pp_Mult_mm(p, m, r, last); |
---|
| 949 | } |
---|
| 950 | } |
---|
| 951 | |
---|
| 952 | // returns p*m, destroys p, const: m |
---|
| 953 | static inline poly p_Mult_mm(poly p, poly m, const ring r) |
---|
| 954 | { |
---|
| 955 | if (p_LmIsConstant(m, r)) |
---|
| 956 | return p_Mult_nn(p, pGetCoeff(m), r); |
---|
| 957 | else |
---|
| 958 | return r->p_Procs->p_Mult_mm(p, m, r); |
---|
| 959 | } |
---|
| 960 | |
---|
| 961 | // return p - m*Copy(q), destroys p; const: p,m |
---|
| 962 | static inline poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, const ring r) |
---|
| 963 | { |
---|
| 964 | #ifdef HAVE_PLURAL |
---|
| 965 | if (rIsPluralRing(r)) |
---|
| 966 | { |
---|
| 967 | int lp, lq; |
---|
| 968 | poly spNoether; |
---|
| 969 | return nc_p_Minus_mm_Mult_qq(p, m, q, lp, lq, spNoether, r); |
---|
| 970 | } |
---|
| 971 | #endif |
---|
| 972 | |
---|
| 973 | int shorter; |
---|
| 974 | poly last; |
---|
| 975 | |
---|
| 976 | return r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r, last); // !!! |
---|
| 977 | } |
---|
| 978 | |
---|
[20d9284] | 979 | // like p_Minus_mm_Mult_qq, except that if lp == pLength(lp) lq == pLength(lq) |
---|
| 980 | // then lp == pLength(p -m*q) |
---|
[a04c5e] | 981 | static inline poly p_Minus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, |
---|
| 982 | poly spNoether, const ring r) |
---|
| 983 | { |
---|
| 984 | #ifdef HAVE_PLURAL |
---|
| 985 | if (rIsPluralRing(r)) |
---|
| 986 | return nc_p_Minus_mm_Mult_qq(p, m, q, lp, lq, spNoether, r); |
---|
| 987 | #endif |
---|
| 988 | |
---|
| 989 | int shorter; |
---|
| 990 | poly last,res; |
---|
| 991 | res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, spNoether, r, last); |
---|
| 992 | lp = (lp + lq) - shorter; |
---|
| 993 | return res; |
---|
| 994 | } |
---|
| 995 | |
---|
[20d9284] | 996 | // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm |
---|
[a04c5e] | 997 | static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, const poly m, const ring r) |
---|
| 998 | { |
---|
| 999 | int shorter; |
---|
| 1000 | return r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r); |
---|
| 1001 | } |
---|
| 1002 | |
---|
[20d9284] | 1003 | // returns p*Coeff(m) for such monomials pm of p, for which m is divisble by pm |
---|
| 1004 | // if lp is length of p on input then lp is length of returned poly on output |
---|
[a04c5e] | 1005 | static inline poly pp_Mult_Coeff_mm_DivSelect(poly p, int &lp, const poly m, const ring r) |
---|
| 1006 | { |
---|
| 1007 | int shorter; |
---|
| 1008 | poly pp = r->p_Procs->pp_Mult_Coeff_mm_DivSelect(p, m, shorter, r); |
---|
| 1009 | lp -= shorter; |
---|
| 1010 | return pp; |
---|
| 1011 | } |
---|
| 1012 | |
---|
| 1013 | // returns -p, destroys p |
---|
| 1014 | static inline poly p_Neg(poly p, const ring r) |
---|
| 1015 | { |
---|
| 1016 | return r->p_Procs->p_Neg(p, r); |
---|
| 1017 | } |
---|
| 1018 | |
---|
| 1019 | extern poly _p_Mult_q(poly p, poly q, const int copy, const ring r); |
---|
| 1020 | // returns p*q, destroys p and q |
---|
| 1021 | static inline poly p_Mult_q(poly p, poly q, const ring r) |
---|
| 1022 | { |
---|
| 1023 | if (p == NULL) |
---|
| 1024 | { |
---|
| 1025 | r->p_Procs->p_Delete(&q, r); |
---|
| 1026 | return NULL; |
---|
| 1027 | } |
---|
| 1028 | if (q == NULL) |
---|
| 1029 | { |
---|
| 1030 | r->p_Procs->p_Delete(&p, r); |
---|
| 1031 | return NULL; |
---|
| 1032 | } |
---|
| 1033 | |
---|
| 1034 | if (pNext(p) == NULL) |
---|
| 1035 | { |
---|
| 1036 | #ifdef HAVE_PLURAL |
---|
| 1037 | if (rIsPluralRing(r)) |
---|
| 1038 | q = nc_mm_Mult_p(p, q, r); |
---|
| 1039 | else |
---|
| 1040 | #endif /* HAVE_PLURAL */ |
---|
| 1041 | q = r->p_Procs->p_Mult_mm(q, p, r); |
---|
| 1042 | |
---|
| 1043 | r->p_Procs->p_Delete(&p, r); |
---|
| 1044 | return q; |
---|
| 1045 | } |
---|
| 1046 | |
---|
| 1047 | if (pNext(q) == NULL) |
---|
| 1048 | { |
---|
| 1049 | // NEEDED |
---|
| 1050 | #ifdef HAVE_PLURAL |
---|
| 1051 | /* if (rIsPluralRing(r)) |
---|
| 1052 | p = gnc_p_Mult_mm(p, q, r); // ??? |
---|
| 1053 | else*/ |
---|
| 1054 | #endif /* HAVE_PLURAL */ |
---|
| 1055 | p = r->p_Procs->p_Mult_mm(p, q, r); |
---|
| 1056 | |
---|
| 1057 | r->p_Procs->p_Delete(&q, r); |
---|
| 1058 | return p; |
---|
| 1059 | } |
---|
| 1060 | #ifdef HAVE_PLURAL |
---|
| 1061 | if (rIsPluralRing(r)) |
---|
| 1062 | return _nc_p_Mult_q(p, q, r); |
---|
| 1063 | else |
---|
| 1064 | #endif |
---|
| 1065 | return _p_Mult_q(p, q, 0, r); |
---|
| 1066 | } |
---|
| 1067 | |
---|
| 1068 | // returns p*q, does neither destroy p nor q |
---|
| 1069 | static inline poly pp_Mult_qq(poly p, poly q, const ring r) |
---|
| 1070 | { |
---|
| 1071 | poly last; |
---|
| 1072 | if (p == NULL || q == NULL) return NULL; |
---|
| 1073 | |
---|
| 1074 | if (pNext(p) == NULL) |
---|
| 1075 | { |
---|
| 1076 | #ifdef HAVE_PLURAL |
---|
| 1077 | if (rIsPluralRing(r)) |
---|
| 1078 | return nc_mm_Mult_pp(p, q, r); |
---|
| 1079 | #endif |
---|
| 1080 | return r->p_Procs->pp_Mult_mm(q, p, r, last); |
---|
| 1081 | } |
---|
| 1082 | |
---|
| 1083 | if (pNext(q) == NULL) |
---|
| 1084 | { |
---|
| 1085 | return r->p_Procs->pp_Mult_mm(p, q, r, last); |
---|
| 1086 | } |
---|
| 1087 | |
---|
| 1088 | poly qq = q; |
---|
| 1089 | if (p == q) |
---|
| 1090 | qq = p_Copy(q, r); |
---|
| 1091 | |
---|
| 1092 | poly res; |
---|
| 1093 | #ifdef HAVE_PLURAL |
---|
| 1094 | if (rIsPluralRing(r)) |
---|
| 1095 | res = _nc_pp_Mult_qq(p, qq, r); |
---|
| 1096 | else |
---|
| 1097 | #endif |
---|
| 1098 | res = _p_Mult_q(p, qq, 1, r); |
---|
| 1099 | |
---|
| 1100 | if (qq != q) |
---|
| 1101 | p_Delete(&qq, r); |
---|
| 1102 | return res; |
---|
| 1103 | } |
---|
| 1104 | |
---|
| 1105 | // returns p + m*q destroys p, const: q, m |
---|
| 1106 | static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, int &lp, int lq, |
---|
| 1107 | const ring r) |
---|
| 1108 | { |
---|
| 1109 | #ifdef HAVE_PLURAL |
---|
| 1110 | if (rIsPluralRing(r)) |
---|
| 1111 | return nc_p_Plus_mm_Mult_qq(p, m, q, lp, lq, r); |
---|
| 1112 | #endif |
---|
| 1113 | |
---|
| 1114 | // this should be implemented more efficiently |
---|
| 1115 | poly res, last; |
---|
| 1116 | int shorter; |
---|
| 1117 | number n_old = pGetCoeff(m); |
---|
[8a8c9e] | 1118 | number n_neg = n_Copy(n_old, r->cf); |
---|
| 1119 | n_neg = n_Neg(n_neg, r->cf); |
---|
[a04c5e] | 1120 | pSetCoeff0(m, n_neg); |
---|
| 1121 | res = r->p_Procs->p_Minus_mm_Mult_qq(p, m, q, shorter, NULL, r, last); |
---|
| 1122 | lp = (lp + lq) - shorter; |
---|
| 1123 | pSetCoeff0(m, n_old); |
---|
[8a8c9e] | 1124 | n_Delete(&n_neg, r->cf); |
---|
[a04c5e] | 1125 | return res; |
---|
| 1126 | } |
---|
| 1127 | |
---|
| 1128 | static inline poly p_Plus_mm_Mult_qq(poly p, poly m, poly q, const ring r) |
---|
| 1129 | { |
---|
| 1130 | int lp = 0, lq = 0; |
---|
| 1131 | return p_Plus_mm_Mult_qq(p, m, q, lp, lq, r); |
---|
| 1132 | } |
---|
| 1133 | |
---|
[20d9284] | 1134 | // returns merged p and q, assumes p and q have no monomials which are equal |
---|
[a04c5e] | 1135 | static inline poly p_Merge_q(poly p, poly q, const ring r) |
---|
| 1136 | { |
---|
| 1137 | return r->p_Procs->p_Merge_q(p, q, r); |
---|
| 1138 | } |
---|
| 1139 | |
---|
[20d9284] | 1140 | // like p_SortMerge, except that p may have equal monimals |
---|
| 1141 | static inline poly p_SortAdd(poly p, const ring r, BOOLEAN revert= FALSE) |
---|
[a04c5e] | 1142 | { |
---|
| 1143 | if (revert) p = pReverse(p); |
---|
| 1144 | return sBucketSortAdd(p, r); |
---|
| 1145 | } |
---|
| 1146 | |
---|
[20d9284] | 1147 | // sorts p using bucket sort: returns sorted poly |
---|
| 1148 | // assumes that monomials of p are all different |
---|
| 1149 | // reverses it first, if revert == TRUE, use this if input p is "almost" sorted |
---|
| 1150 | // correctly |
---|
| 1151 | static inline poly p_SortMerge(poly p, const ring r, BOOLEAN revert= FALSE) |
---|
[a04c5e] | 1152 | { |
---|
| 1153 | if (revert) p = pReverse(p); |
---|
| 1154 | return sBucketSortMerge(p, r); |
---|
| 1155 | } |
---|
| 1156 | |
---|
| 1157 | /*************************************************************** |
---|
| 1158 | * |
---|
| 1159 | * I/O |
---|
| 1160 | * |
---|
| 1161 | ***************************************************************/ |
---|
| 1162 | static inline char* p_String(poly p, ring p_ring) |
---|
| 1163 | { |
---|
| 1164 | return p_String(p, p_ring, p_ring); |
---|
| 1165 | } |
---|
| 1166 | static inline char* p_String0(poly p, ring p_ring) |
---|
| 1167 | { |
---|
| 1168 | return p_String0(p, p_ring, p_ring); |
---|
| 1169 | } |
---|
| 1170 | static inline void p_Write(poly p, ring p_ring) |
---|
| 1171 | { |
---|
| 1172 | p_Write(p, p_ring, p_ring); |
---|
| 1173 | } |
---|
| 1174 | static inline void p_Write0(poly p, ring p_ring) |
---|
| 1175 | { |
---|
| 1176 | p_Write0(p, p_ring, p_ring); |
---|
| 1177 | } |
---|
| 1178 | static inline void p_wrp(poly p, ring p_ring) |
---|
| 1179 | { |
---|
| 1180 | p_wrp(p, p_ring, p_ring); |
---|
| 1181 | } |
---|
| 1182 | |
---|
| 1183 | /*************************************************************** |
---|
| 1184 | * Purpose: implementation of poly procs which iter over ExpVector |
---|
| 1185 | * Author: obachman (Olaf Bachmann) |
---|
| 1186 | * Created: 8/00 |
---|
| 1187 | * Version: $Id$ |
---|
| 1188 | *******************************************************************/ |
---|
[6bec87] | 1189 | #include <misc/mylimits.h> |
---|
[20b794] | 1190 | #include <polys/templates/p_MemCmp.h> |
---|
| 1191 | // #include <polys/structs.h> |
---|
| 1192 | #include <polys/monomials/ring.h> |
---|
| 1193 | #include <coeffs/coeffs.h> |
---|
[a04c5e] | 1194 | |
---|
| 1195 | #if PDEBUG > 0 |
---|
| 1196 | |
---|
| 1197 | #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \ |
---|
| 1198 | do \ |
---|
| 1199 | { \ |
---|
| 1200 | int _cmp = p_LmCmp(p,q,r); \ |
---|
| 1201 | if (_cmp == 0) actionE; \ |
---|
| 1202 | if (_cmp == 1) actionG; \ |
---|
| 1203 | actionS; \ |
---|
| 1204 | } \ |
---|
| 1205 | while(0) |
---|
| 1206 | |
---|
| 1207 | #else |
---|
| 1208 | |
---|
| 1209 | #define _p_LmCmpAction(p, q, r, actionE, actionG, actionS) \ |
---|
| 1210 | p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, \ |
---|
| 1211 | actionE, actionG, actionS) |
---|
| 1212 | |
---|
| 1213 | #endif |
---|
| 1214 | |
---|
| 1215 | #define pDivAssume(x) ((void)0) |
---|
| 1216 | |
---|
[20b794] | 1217 | #include <omalloc/omalloc.h> |
---|
| 1218 | #include <coeffs/coeffs.h> |
---|
[6bec87] | 1219 | #include <polys/monomials/p_polys.h> |
---|
[20b794] | 1220 | #include <polys/templates/p_MemAdd.h> |
---|
| 1221 | #include <polys/templates/p_MemCopy.h> |
---|
[a04c5e] | 1222 | |
---|
| 1223 | /*************************************************************** |
---|
| 1224 | * |
---|
| 1225 | * Allocation/Initalization/Deletion |
---|
| 1226 | * |
---|
| 1227 | ***************************************************************/ |
---|
| 1228 | // adjustments for negative weights |
---|
| 1229 | static inline void p_MemAdd_NegWeightAdjust(poly p, const ring r) |
---|
| 1230 | { |
---|
| 1231 | if (r->NegWeightL_Offset != NULL) |
---|
| 1232 | { |
---|
| 1233 | for (int i=r->NegWeightL_Size-1; i>=0; i--) |
---|
| 1234 | { |
---|
| 1235 | p->exp[r->NegWeightL_Offset[i]] -= POLY_NEGWEIGHT_OFFSET; |
---|
| 1236 | } |
---|
| 1237 | } |
---|
| 1238 | } |
---|
| 1239 | static inline void p_MemSub_NegWeightAdjust(poly p, const ring r) |
---|
| 1240 | { |
---|
| 1241 | if (r->NegWeightL_Offset != NULL) |
---|
| 1242 | { |
---|
| 1243 | for (int i=r->NegWeightL_Size-1; i>=0; i--) |
---|
| 1244 | { |
---|
| 1245 | p->exp[r->NegWeightL_Offset[i]] += POLY_NEGWEIGHT_OFFSET; |
---|
| 1246 | } |
---|
| 1247 | } |
---|
| 1248 | } |
---|
| 1249 | // ExpVextor(d_p) = ExpVector(s_p) |
---|
| 1250 | static inline void p_ExpVectorCopy(poly d_p, poly s_p, const ring r) |
---|
| 1251 | { |
---|
| 1252 | p_LmCheckPolyRing1(d_p, r); |
---|
| 1253 | p_LmCheckPolyRing1(s_p, r); |
---|
| 1254 | p_MemCopy_LengthGeneral(d_p->exp, s_p->exp, r->ExpL_Size); |
---|
| 1255 | } |
---|
| 1256 | |
---|
| 1257 | static inline poly p_Init(const ring r, omBin bin) |
---|
| 1258 | { |
---|
| 1259 | p_CheckRing1(r); |
---|
| 1260 | pAssume1(bin != NULL && r->PolyBin->sizeW == bin->sizeW); |
---|
| 1261 | poly p; |
---|
| 1262 | omTypeAlloc0Bin(poly, p, bin); |
---|
| 1263 | p_MemAdd_NegWeightAdjust(p, r); |
---|
| 1264 | p_SetRingOfLm(p, r); |
---|
| 1265 | return p; |
---|
| 1266 | } |
---|
| 1267 | static inline poly p_Init(const ring r) |
---|
| 1268 | { |
---|
| 1269 | return p_Init(r, r->PolyBin); |
---|
| 1270 | } |
---|
| 1271 | |
---|
| 1272 | static inline poly p_LmInit(poly p, const ring r) |
---|
| 1273 | { |
---|
| 1274 | p_LmCheckPolyRing1(p, r); |
---|
| 1275 | poly np; |
---|
| 1276 | omTypeAllocBin(poly, np, r->PolyBin); |
---|
| 1277 | p_SetRingOfLm(np, r); |
---|
| 1278 | p_MemCopy_LengthGeneral(np->exp, p->exp, r->ExpL_Size); |
---|
| 1279 | pNext(np) = NULL; |
---|
| 1280 | pSetCoeff0(np, NULL); |
---|
| 1281 | return np; |
---|
| 1282 | } |
---|
| 1283 | static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r, omBin d_bin) |
---|
| 1284 | { |
---|
| 1285 | p_LmCheckPolyRing1(s_p, s_r); |
---|
| 1286 | p_CheckRing(d_r); |
---|
| 1287 | pAssume1(d_r->N <= s_r->N); |
---|
| 1288 | poly d_p = p_Init(d_r, d_bin); |
---|
| 1289 | for (int i=d_r->N; i>0; i--) |
---|
| 1290 | { |
---|
| 1291 | p_SetExp(d_p, i, p_GetExp(s_p, i,s_r), d_r); |
---|
| 1292 | } |
---|
| 1293 | if (rRing_has_Comp(d_r)) |
---|
| 1294 | { |
---|
| 1295 | p_SetComp(d_p, p_GetComp(s_p,s_r), d_r); |
---|
| 1296 | } |
---|
| 1297 | p_Setm(d_p, d_r); |
---|
| 1298 | return d_p; |
---|
| 1299 | } |
---|
| 1300 | static inline poly p_LmInit(poly s_p, const ring s_r, const ring d_r) |
---|
| 1301 | { |
---|
| 1302 | pAssume1(d_r != NULL); |
---|
| 1303 | return p_LmInit(s_p, s_r, d_r, d_r->PolyBin); |
---|
| 1304 | } |
---|
[20d9284] | 1305 | |
---|
[f550e86] | 1306 | // set all exponents l..k to 0, assume exp. k+1..n and 1..l-1 are in |
---|
[a04c5e] | 1307 | // different blocks |
---|
| 1308 | // set coeff to 1 |
---|
| 1309 | static inline poly p_GetExp_k_n(poly p, int l, int k, const ring r) |
---|
| 1310 | { |
---|
| 1311 | if (p == NULL) return NULL; |
---|
| 1312 | p_LmCheckPolyRing1(p, r); |
---|
| 1313 | poly np; |
---|
| 1314 | omTypeAllocBin(poly, np, r->PolyBin); |
---|
| 1315 | p_SetRingOfLm(np, r); |
---|
| 1316 | p_MemCopy_LengthGeneral(np->exp, p->exp, r->ExpL_Size); |
---|
| 1317 | pNext(np) = NULL; |
---|
[8a8c9e] | 1318 | pSetCoeff0(np, n_Init(1, r->cf)); |
---|
[a04c5e] | 1319 | int i; |
---|
| 1320 | for(i=l;i<=k;i++) |
---|
| 1321 | { |
---|
| 1322 | //np->exp[(r->VarOffset[i] & 0xffffff)] =0; |
---|
| 1323 | p_SetExp(np,i,0,r); |
---|
| 1324 | } |
---|
| 1325 | p_Setm(np,r); |
---|
| 1326 | return np; |
---|
| 1327 | } |
---|
| 1328 | |
---|
[20d9284] | 1329 | // simialar to p_ShallowCopyDelete but does it only for leading monomial |
---|
[a04c5e] | 1330 | static inline poly p_LmShallowCopyDelete(poly p, const ring r, omBin bin) |
---|
| 1331 | { |
---|
| 1332 | p_LmCheckPolyRing1(p, r); |
---|
| 1333 | pAssume1(bin->sizeW == r->PolyBin->sizeW); |
---|
| 1334 | poly new_p = p_New(r); |
---|
| 1335 | p_MemCopy_LengthGeneral(new_p->exp, p->exp, r->ExpL_Size); |
---|
| 1336 | pSetCoeff0(new_p, pGetCoeff(p)); |
---|
| 1337 | pNext(new_p) = pNext(p); |
---|
| 1338 | omFreeBinAddr(p); |
---|
| 1339 | return new_p; |
---|
| 1340 | } |
---|
| 1341 | |
---|
| 1342 | /*************************************************************** |
---|
| 1343 | * |
---|
| 1344 | * Operation on ExpVectors |
---|
| 1345 | * |
---|
| 1346 | ***************************************************************/ |
---|
| 1347 | // ExpVector(p1) += ExpVector(p2) |
---|
| 1348 | static inline void p_ExpVectorAdd(poly p1, poly p2, const ring r) |
---|
| 1349 | { |
---|
| 1350 | p_LmCheckPolyRing1(p1, r); |
---|
| 1351 | p_LmCheckPolyRing1(p2, r); |
---|
| 1352 | #if PDEBUG >= 1 |
---|
| 1353 | for (int i=1; i<=r->N; i++) |
---|
| 1354 | pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask); |
---|
| 1355 | pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0); |
---|
| 1356 | #endif |
---|
| 1357 | |
---|
| 1358 | p_MemAdd_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size); |
---|
| 1359 | p_MemAdd_NegWeightAdjust(p1, r); |
---|
| 1360 | } |
---|
| 1361 | // ExpVector(p1) -= ExpVector(p2) |
---|
| 1362 | static inline void p_ExpVectorSub(poly p1, poly p2, const ring r) |
---|
| 1363 | { |
---|
| 1364 | p_LmCheckPolyRing1(p1, r); |
---|
| 1365 | p_LmCheckPolyRing1(p2, r); |
---|
| 1366 | #if PDEBUG >= 1 |
---|
| 1367 | for (int i=1; i<=r->N; i++) |
---|
| 1368 | pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r)); |
---|
| 1369 | pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0 || |
---|
| 1370 | p_GetComp(p1, r) == p_GetComp(p2, r)); |
---|
| 1371 | #endif |
---|
| 1372 | |
---|
| 1373 | p_MemSub_LengthGeneral(p1->exp, p2->exp, r->ExpL_Size); |
---|
| 1374 | p_MemSub_NegWeightAdjust(p1, r); |
---|
| 1375 | |
---|
| 1376 | } |
---|
| 1377 | // ExpVector(p1) += ExpVector(p2) - ExpVector(p3) |
---|
| 1378 | static inline void p_ExpVectorAddSub(poly p1, poly p2, poly p3, const ring r) |
---|
| 1379 | { |
---|
| 1380 | p_LmCheckPolyRing1(p1, r); |
---|
| 1381 | p_LmCheckPolyRing1(p2, r); |
---|
| 1382 | p_LmCheckPolyRing1(p3, r); |
---|
| 1383 | #if PDEBUG >= 1 |
---|
| 1384 | for (int i=1; i<=r->N; i++) |
---|
| 1385 | pAssume1(p_GetExp(p1, i, r) + p_GetExp(p2, i, r) >= p_GetExp(p3, i, r)); |
---|
| 1386 | pAssume1(p_GetComp(p1, r) == 0 || |
---|
| 1387 | (p_GetComp(p2, r) - p_GetComp(p3, r) == 0) || |
---|
| 1388 | (p_GetComp(p1, r) == p_GetComp(p2, r) - p_GetComp(p3, r))); |
---|
| 1389 | #endif |
---|
| 1390 | |
---|
| 1391 | p_MemAddSub_LengthGeneral(p1->exp, p2->exp, p3->exp, r->ExpL_Size); |
---|
| 1392 | // no need to adjust in case of NegWeights |
---|
| 1393 | } |
---|
| 1394 | |
---|
| 1395 | // ExpVector(pr) = ExpVector(p1) + ExpVector(p2) |
---|
| 1396 | static inline void p_ExpVectorSum(poly pr, poly p1, poly p2, const ring r) |
---|
| 1397 | { |
---|
| 1398 | p_LmCheckPolyRing1(p1, r); |
---|
| 1399 | p_LmCheckPolyRing1(p2, r); |
---|
| 1400 | p_LmCheckPolyRing1(pr, r); |
---|
| 1401 | #if PDEBUG >= 1 |
---|
| 1402 | for (int i=1; i<=r->N; i++) |
---|
| 1403 | pAssume1((unsigned long) (p_GetExp(p1, i, r) + p_GetExp(p2, i, r)) <= r->bitmask); |
---|
| 1404 | pAssume1(p_GetComp(p1, r) == 0 || p_GetComp(p2, r) == 0); |
---|
| 1405 | #endif |
---|
| 1406 | |
---|
| 1407 | p_MemSum_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size); |
---|
| 1408 | p_MemAdd_NegWeightAdjust(pr, r); |
---|
| 1409 | } |
---|
| 1410 | // ExpVector(pr) = ExpVector(p1) - ExpVector(p2) |
---|
| 1411 | static inline void p_ExpVectorDiff(poly pr, poly p1, poly p2, const ring r) |
---|
| 1412 | { |
---|
| 1413 | p_LmCheckPolyRing1(p1, r); |
---|
| 1414 | p_LmCheckPolyRing1(p2, r); |
---|
| 1415 | p_LmCheckPolyRing1(pr, r); |
---|
| 1416 | #if PDEBUG >= 2 |
---|
| 1417 | for (int i=1; i<=r->N; i++) |
---|
| 1418 | pAssume1(p_GetExp(p1, i, r) >= p_GetExp(p2, i, r)); |
---|
| 1419 | pAssume1(!rRing_has_Comp(r) || p_GetComp(p1, r) == p_GetComp(p2, r)); |
---|
| 1420 | #endif |
---|
| 1421 | |
---|
| 1422 | p_MemDiff_LengthGeneral(pr->exp, p1->exp, p2->exp, r->ExpL_Size); |
---|
| 1423 | p_MemSub_NegWeightAdjust(pr, r); |
---|
| 1424 | } |
---|
| 1425 | |
---|
| 1426 | static inline BOOLEAN p_ExpVectorEqual(poly p1, poly p2, const ring r) |
---|
| 1427 | { |
---|
| 1428 | p_LmCheckPolyRing1(p1, r); |
---|
| 1429 | p_LmCheckPolyRing1(p2, r); |
---|
| 1430 | |
---|
| 1431 | int i = r->ExpL_Size; |
---|
| 1432 | unsigned long *ep = p1->exp; |
---|
| 1433 | unsigned long *eq = p2->exp; |
---|
| 1434 | |
---|
| 1435 | do |
---|
| 1436 | { |
---|
| 1437 | i--; |
---|
| 1438 | if (ep[i] != eq[i]) return FALSE; |
---|
| 1439 | } |
---|
| 1440 | while (i); |
---|
| 1441 | return TRUE; |
---|
| 1442 | } |
---|
| 1443 | |
---|
| 1444 | static inline long p_Totaldegree(poly p, const ring r) |
---|
| 1445 | { |
---|
| 1446 | p_LmCheckPolyRing1(p, r); |
---|
| 1447 | unsigned long s = p_GetTotalDegree(p->exp[r->VarL_Offset[0]], |
---|
| 1448 | r, |
---|
| 1449 | r->MinExpPerLong); |
---|
| 1450 | for (int i=r->VarL_Size-1; i>0; i--) |
---|
| 1451 | { |
---|
| 1452 | s += p_GetTotalDegree(p->exp[r->VarL_Offset[i]], r); |
---|
| 1453 | } |
---|
| 1454 | return (long)s; |
---|
| 1455 | } |
---|
| 1456 | |
---|
| 1457 | static inline void p_GetExpV(poly p, int *ev, const ring r) |
---|
| 1458 | { |
---|
| 1459 | p_LmCheckPolyRing1(p, r); |
---|
| 1460 | for (int j = r->N; j; j--) |
---|
| 1461 | ev[j] = p_GetExp(p, j, r); |
---|
| 1462 | |
---|
| 1463 | ev[0] = p_GetComp(p, r); |
---|
| 1464 | } |
---|
| 1465 | static inline void p_SetExpV(poly p, int *ev, const ring r) |
---|
| 1466 | { |
---|
| 1467 | p_LmCheckPolyRing1(p, r); |
---|
| 1468 | for (int j = r->N; j; j--) |
---|
| 1469 | p_SetExp(p, j, ev[j], r); |
---|
| 1470 | |
---|
| 1471 | p_SetComp(p, ev[0],r); |
---|
| 1472 | p_Setm(p, r); |
---|
| 1473 | } |
---|
| 1474 | |
---|
| 1475 | /*************************************************************** |
---|
| 1476 | * |
---|
| 1477 | * Comparison w.r.t. monomial ordering |
---|
| 1478 | * |
---|
| 1479 | ***************************************************************/ |
---|
| 1480 | static inline int p_LmCmp(poly p, poly q, const ring r) |
---|
| 1481 | { |
---|
| 1482 | p_LmCheckPolyRing1(p, r); |
---|
| 1483 | p_LmCheckPolyRing1(q, r); |
---|
| 1484 | |
---|
| 1485 | p_MemCmp_LengthGeneral_OrdGeneral(p->exp, q->exp, r->CmpL_Size, r->ordsgn, |
---|
| 1486 | return 0, return 1, return -1); |
---|
| 1487 | } |
---|
| 1488 | |
---|
| 1489 | |
---|
| 1490 | /*************************************************************** |
---|
| 1491 | * |
---|
| 1492 | * divisibility |
---|
| 1493 | * |
---|
| 1494 | ***************************************************************/ |
---|
| 1495 | // return: FALSE, if there exists i, such that a->exp[i] > b->exp[i] |
---|
| 1496 | // TRUE, otherwise |
---|
| 1497 | // (1) Consider long vars, instead of single exponents |
---|
| 1498 | // (2) Clearly, if la > lb, then FALSE |
---|
| 1499 | // (3) Suppose la <= lb, and consider first bits of single exponents in l: |
---|
| 1500 | // if TRUE, then value of these bits is la ^ lb |
---|
| 1501 | // if FALSE, then la-lb causes an "overflow" into one of those bits, i.e., |
---|
| 1502 | // la ^ lb != la - lb |
---|
| 1503 | static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, poly b, const ring r) |
---|
| 1504 | { |
---|
| 1505 | int i=r->VarL_Size - 1; |
---|
| 1506 | unsigned long divmask = r->divmask; |
---|
| 1507 | unsigned long la, lb; |
---|
| 1508 | |
---|
| 1509 | if (r->VarL_LowIndex >= 0) |
---|
| 1510 | { |
---|
| 1511 | i += r->VarL_LowIndex; |
---|
| 1512 | do |
---|
| 1513 | { |
---|
| 1514 | la = a->exp[i]; |
---|
| 1515 | lb = b->exp[i]; |
---|
| 1516 | if ((la > lb) || |
---|
| 1517 | (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask))) |
---|
| 1518 | { |
---|
| 1519 | pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == FALSE); |
---|
| 1520 | return FALSE; |
---|
| 1521 | } |
---|
| 1522 | i--; |
---|
| 1523 | } |
---|
| 1524 | while (i>=r->VarL_LowIndex); |
---|
| 1525 | } |
---|
| 1526 | else |
---|
| 1527 | { |
---|
| 1528 | do |
---|
| 1529 | { |
---|
| 1530 | la = a->exp[r->VarL_Offset[i]]; |
---|
| 1531 | lb = b->exp[r->VarL_Offset[i]]; |
---|
| 1532 | if ((la > lb) || |
---|
| 1533 | (((la & divmask) ^ (lb & divmask)) != ((lb - la) & divmask))) |
---|
| 1534 | { |
---|
| 1535 | pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == FALSE); |
---|
| 1536 | return FALSE; |
---|
| 1537 | } |
---|
| 1538 | i--; |
---|
| 1539 | } |
---|
| 1540 | while (i>=0); |
---|
| 1541 | } |
---|
| 1542 | #ifdef HAVE_RINGS |
---|
| 1543 | pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == nDivBy(p_GetCoeff(b, r), p_GetCoeff(a, r))); |
---|
[8a8c9e] | 1544 | return (!rField_is_Ring(r)) || n_DivBy(p_GetCoeff(b, r), p_GetCoeff(a, r), r->cf); |
---|
[a04c5e] | 1545 | #else |
---|
| 1546 | pDivAssume(p_DebugLmDivisibleByNoComp(a, b, r) == TRUE); |
---|
| 1547 | return TRUE; |
---|
| 1548 | #endif |
---|
| 1549 | } |
---|
| 1550 | |
---|
| 1551 | static inline BOOLEAN _p_LmDivisibleByNoComp(poly a, const ring r_a, poly b, const ring r_b) |
---|
| 1552 | { |
---|
| 1553 | int i=r_a->N; |
---|
| 1554 | pAssume1(r_a->N == r_b->N); |
---|
| 1555 | |
---|
| 1556 | do |
---|
| 1557 | { |
---|
| 1558 | if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b)) |
---|
| 1559 | return FALSE; |
---|
| 1560 | i--; |
---|
| 1561 | } |
---|
| 1562 | while (i); |
---|
| 1563 | #ifdef HAVE_RINGS |
---|
[8a8c9e] | 1564 | return n_DivBy(p_GetCoeff(b, r_b), p_GetCoeff(a, r_a), r_a->cf); |
---|
[a04c5e] | 1565 | #else |
---|
| 1566 | return TRUE; |
---|
| 1567 | #endif |
---|
| 1568 | } |
---|
| 1569 | |
---|
| 1570 | #ifdef HAVE_RATGRING |
---|
| 1571 | static inline BOOLEAN _p_LmDivisibleByNoCompPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end) |
---|
| 1572 | { |
---|
| 1573 | int i=end; |
---|
| 1574 | pAssume1(r_a->N == r_b->N); |
---|
| 1575 | |
---|
| 1576 | do |
---|
| 1577 | { |
---|
| 1578 | if (p_GetExp(a,i,r_a) > p_GetExp(b,i,r_b)) |
---|
| 1579 | return FALSE; |
---|
| 1580 | i--; |
---|
| 1581 | } |
---|
| 1582 | while (i>=start); |
---|
| 1583 | #ifdef HAVE_RINGS |
---|
| 1584 | return nDivBy(p_GetCoeff(b, r), p_GetCoeff(a, r)); |
---|
| 1585 | #else |
---|
| 1586 | return TRUE; |
---|
| 1587 | #endif |
---|
| 1588 | } |
---|
| 1589 | static inline BOOLEAN _p_LmDivisibleByPart(poly a, const ring r_a, poly b, const ring r_b,const int start, const int end) |
---|
| 1590 | { |
---|
| 1591 | if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b)) |
---|
| 1592 | return _p_LmDivisibleByNoCompPart(a, r_a, b, r_b,start,end); |
---|
| 1593 | return FALSE; |
---|
| 1594 | } |
---|
| 1595 | static inline BOOLEAN p_LmDivisibleByPart(poly a, poly b, const ring r,const int start, const int end) |
---|
| 1596 | { |
---|
| 1597 | p_LmCheckPolyRing1(b, r); |
---|
| 1598 | pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r)); |
---|
| 1599 | if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)) |
---|
| 1600 | return _p_LmDivisibleByNoCompPart(a, r, b, r,start, end); |
---|
| 1601 | return FALSE; |
---|
| 1602 | } |
---|
| 1603 | #endif |
---|
| 1604 | static inline BOOLEAN _p_LmDivisibleBy(poly a, poly b, const ring r) |
---|
| 1605 | { |
---|
| 1606 | if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)) |
---|
| 1607 | return _p_LmDivisibleByNoComp(a, b, r); |
---|
| 1608 | return FALSE; |
---|
| 1609 | } |
---|
| 1610 | static inline BOOLEAN _p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b) |
---|
| 1611 | { |
---|
| 1612 | if (p_GetComp(a, r_a) == 0 || p_GetComp(a,r_a) == p_GetComp(b,r_b)) |
---|
| 1613 | return _p_LmDivisibleByNoComp(a, r_a, b, r_b); |
---|
| 1614 | return FALSE; |
---|
| 1615 | } |
---|
| 1616 | static inline BOOLEAN p_LmDivisibleByNoComp(poly a, poly b, const ring r) |
---|
| 1617 | { |
---|
| 1618 | p_LmCheckPolyRing1(a, r); |
---|
| 1619 | p_LmCheckPolyRing1(b, r); |
---|
| 1620 | return _p_LmDivisibleByNoComp(a, b, r); |
---|
| 1621 | } |
---|
| 1622 | static inline BOOLEAN p_LmDivisibleBy(poly a, poly b, const ring r) |
---|
| 1623 | { |
---|
| 1624 | p_LmCheckPolyRing1(b, r); |
---|
| 1625 | pIfThen1(a != NULL, p_LmCheckPolyRing1(b, r)); |
---|
| 1626 | if (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r)) |
---|
| 1627 | return _p_LmDivisibleByNoComp(a, b, r); |
---|
| 1628 | return FALSE; |
---|
| 1629 | } |
---|
| 1630 | |
---|
| 1631 | static inline BOOLEAN p_DivisibleBy(poly a, poly b, const ring r) |
---|
| 1632 | { |
---|
| 1633 | pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r)); |
---|
| 1634 | pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r)); |
---|
| 1635 | |
---|
| 1636 | if (a != NULL && (p_GetComp(a, r) == 0 || p_GetComp(a,r) == p_GetComp(b,r))) |
---|
| 1637 | return _p_LmDivisibleByNoComp(a,b,r); |
---|
| 1638 | return FALSE; |
---|
| 1639 | } |
---|
| 1640 | static inline BOOLEAN p_DivisibleBy(poly a, const ring r_a, poly b, const ring r_b) |
---|
| 1641 | { |
---|
| 1642 | pIfThen1(b!=NULL, p_LmCheckPolyRing1(b, r_b)); |
---|
| 1643 | pIfThen1(a!=NULL, p_LmCheckPolyRing1(a, r_a)); |
---|
| 1644 | if (a != NULL) { |
---|
| 1645 | return _p_LmDivisibleBy(a, r_a, b, r_b); |
---|
| 1646 | } |
---|
| 1647 | return FALSE; |
---|
| 1648 | } |
---|
| 1649 | static inline BOOLEAN p_LmDivisibleBy(poly a, const ring r_a, poly b, const ring r_b) |
---|
| 1650 | { |
---|
| 1651 | p_LmCheckPolyRing(a, r_a); |
---|
| 1652 | p_LmCheckPolyRing(b, r_b); |
---|
| 1653 | return _p_LmDivisibleBy(a, r_a, b, r_b); |
---|
| 1654 | } |
---|
| 1655 | static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, |
---|
| 1656 | poly b, unsigned long not_sev_b, const ring r) |
---|
| 1657 | { |
---|
| 1658 | p_LmCheckPolyRing1(a, r); |
---|
| 1659 | p_LmCheckPolyRing1(b, r); |
---|
| 1660 | #ifndef PDIV_DEBUG |
---|
[8a8c9e] | 1661 | _pPolyAssume2(p_GetShortExpVector(a, r) == sev_a, a, r); |
---|
| 1662 | _pPolyAssume2(p_GetShortExpVector(b, r) == ~ not_sev_b, b, r); |
---|
[a04c5e] | 1663 | |
---|
| 1664 | if (sev_a & not_sev_b) |
---|
| 1665 | { |
---|
| 1666 | pAssume1(p_LmDivisibleByNoComp(a, b, r) == FALSE); |
---|
| 1667 | return FALSE; |
---|
| 1668 | } |
---|
| 1669 | return p_LmDivisibleBy(a, b, r); |
---|
| 1670 | #else |
---|
| 1671 | return pDebugLmShortDivisibleBy(a, sev_a, r, b, not_sev_b, r); |
---|
| 1672 | #endif |
---|
| 1673 | } |
---|
| 1674 | |
---|
| 1675 | static inline BOOLEAN p_LmShortDivisibleBy(poly a, unsigned long sev_a, const ring r_a, |
---|
| 1676 | poly b, unsigned long not_sev_b, const ring r_b) |
---|
| 1677 | { |
---|
| 1678 | p_LmCheckPolyRing1(a, r_a); |
---|
| 1679 | p_LmCheckPolyRing1(b, r_b); |
---|
| 1680 | #ifndef PDIV_DEBUG |
---|
[8a8c9e] | 1681 | _pPolyAssume2(p_GetShortExpVector(a, r_a) == sev_a, a, r_a); |
---|
| 1682 | _pPolyAssume2(p_GetShortExpVector(b, r_b) == ~ not_sev_b, b, r_b); |
---|
[a04c5e] | 1683 | |
---|
| 1684 | if (sev_a & not_sev_b) |
---|
| 1685 | { |
---|
| 1686 | pAssume1(_p_LmDivisibleByNoComp(a, r_a, b, r_b) == FALSE); |
---|
| 1687 | return FALSE; |
---|
| 1688 | } |
---|
| 1689 | return _p_LmDivisibleBy(a, r_a, b, r_b); |
---|
| 1690 | #else |
---|
| 1691 | return pDebugLmShortDivisibleBy(a, sev_a, r_a, b, not_sev_b, r_b); |
---|
| 1692 | #endif |
---|
| 1693 | } |
---|
| 1694 | |
---|
| 1695 | /*************************************************************** |
---|
| 1696 | * |
---|
| 1697 | * Misc things on Lm |
---|
| 1698 | * |
---|
| 1699 | ***************************************************************/ |
---|
| 1700 | |
---|
| 1701 | |
---|
| 1702 | // like the respective p_LmIs* routines, except that p might be empty |
---|
| 1703 | static inline BOOLEAN p_IsConstantComp(const poly p, const ring r) |
---|
| 1704 | { |
---|
| 1705 | if (p == NULL) return TRUE; |
---|
| 1706 | return (pNext(p)==NULL) && p_LmIsConstantComp(p, r); |
---|
| 1707 | } |
---|
| 1708 | |
---|
| 1709 | static inline BOOLEAN p_IsConstant(const poly p, const ring r) |
---|
| 1710 | { |
---|
| 1711 | if (p == NULL) return TRUE; |
---|
| 1712 | return (pNext(p)==NULL) && p_LmIsConstant(p, r); |
---|
| 1713 | } |
---|
| 1714 | |
---|
[20d9284] | 1715 | static inline BOOLEAN p_IsConstantPoly(const poly p, const ring r) |
---|
| 1716 | { |
---|
| 1717 | poly pp=p; |
---|
| 1718 | while(pp!=NULL) |
---|
| 1719 | { |
---|
| 1720 | if (! p_LmIsConstantComp(pp, r)) |
---|
| 1721 | return FALSE; |
---|
| 1722 | pIter(pp); |
---|
| 1723 | } |
---|
| 1724 | return TRUE; |
---|
| 1725 | } |
---|
| 1726 | |
---|
[a04c5e] | 1727 | static inline BOOLEAN p_IsUnit(const poly p, const ring r) |
---|
| 1728 | { |
---|
| 1729 | if (p == NULL) return FALSE; |
---|
| 1730 | #ifdef HAVE_RINGS |
---|
| 1731 | if (rField_is_Ring(r)) |
---|
| 1732 | return (p_LmIsConstant(p, r) && nIsUnit(pGetCoeff(p),r->cf)); |
---|
| 1733 | #endif |
---|
| 1734 | return p_LmIsConstant(p, r); |
---|
| 1735 | } |
---|
| 1736 | |
---|
| 1737 | static inline BOOLEAN p_LmExpVectorAddIsOk(const poly p1, const poly p2, |
---|
| 1738 | const ring r) |
---|
| 1739 | { |
---|
| 1740 | p_LmCheckPolyRing(p1, r); |
---|
| 1741 | p_LmCheckPolyRing(p2, r); |
---|
| 1742 | unsigned long l1, l2, divmask = r->divmask; |
---|
| 1743 | int i; |
---|
| 1744 | |
---|
| 1745 | for (i=0; i<r->VarL_Size; i++) |
---|
| 1746 | { |
---|
| 1747 | l1 = p1->exp[r->VarL_Offset[i]]; |
---|
| 1748 | l2 = p2->exp[r->VarL_Offset[i]]; |
---|
| 1749 | // do the divisiblity trick |
---|
| 1750 | if ( (l1 > ULONG_MAX - l2) || |
---|
| 1751 | (((l1 & divmask) ^ (l2 & divmask)) != ((l1 + l2) & divmask))) |
---|
| 1752 | return FALSE; |
---|
| 1753 | } |
---|
| 1754 | return TRUE; |
---|
| 1755 | } |
---|
[f34215] | 1756 | void p_Split(poly p, poly * r); /*p => IN(p), r => REST(p) */ |
---|
| 1757 | BOOLEAN p_HasNotCF(poly p1, poly p2, const ring r); |
---|
| 1758 | poly p_mInit(const char *s, BOOLEAN &ok, const ring r); /* monom s -> poly, interpreter */ |
---|
| 1759 | const char * p_Read(const char *s, poly &p,const ring r); /* monom -> poly */ |
---|
[fb4075b] | 1760 | poly p_Divide(poly a, poly b, const ring r); |
---|
| 1761 | poly p_DivideM(poly a, poly b, const ring r); |
---|
[a7ee69] | 1762 | void p_Lcm(poly a, poly b, poly m, const ring r); |
---|
[ac0bd6] | 1763 | poly p_Diff(poly a, int k, const ring r); |
---|
[5162db] | 1764 | poly p_DiffOp(poly a, poly b,BOOLEAN multiply, const ring r); |
---|
[bf183f] | 1765 | int p_Weight(int c, const ring r); |
---|
| 1766 | |
---|
[cd246b] | 1767 | /* syszygy stuff */ |
---|
| 1768 | BOOLEAN p_VectorHasUnitB(poly p, int * k, const ring r); |
---|
| 1769 | void p_VectorHasUnit(poly p, int * k, int * len, const ring r); |
---|
| 1770 | poly p_TakeOutComp1(poly * p, int k, const ring r); |
---|
[74021a] | 1771 | // Splits *p into two polys: *q which consists of all monoms with |
---|
| 1772 | // component == comp and *p of all other monoms *lq == pLength(*q) |
---|
| 1773 | // On return all components pf *q == 0 |
---|
| 1774 | void p_TakeOutComp(poly *p, long comp, poly *q, int *lq, const ring r); |
---|
| 1775 | |
---|
| 1776 | // This is something weird -- Don't use it, unless you know what you are doing |
---|
| 1777 | poly p_TakeOutComp(poly * p, int k); |
---|
| 1778 | |
---|
| 1779 | void p_DeleteComp(poly * p,int k, const ring r); |
---|
| 1780 | |
---|
[5c39a9] | 1781 | /*-------------ring management:----------------------*/ |
---|
| 1782 | void p_SetGlobals(const ring r, BOOLEAN complete = TRUE); |
---|
| 1783 | |
---|
[949e57] | 1784 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
---|
| 1785 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
---|
| 1786 | // only uses pFDeg (and not pDeg, or pTotalDegree, etc). |
---|
| 1787 | // If you use this, make sure your procs does not make any assumptions |
---|
| 1788 | // on ordering and/or OrdIndex -- otherwise they might return wrong results |
---|
| 1789 | // on strat->tailRing |
---|
[8a8c9e] | 1790 | void pSetDegProcs(ring r, pFDegProc new_FDeg, pLDegProc new_lDeg = NULL); |
---|
[949e57] | 1791 | // restores pFDeg and pLDeg: |
---|
[8a8c9e] | 1792 | void pRestoreDegProcs(ring r, pFDegProc old_FDeg, pLDegProc old_lDeg); |
---|
[949e57] | 1793 | |
---|
[5bc2461] | 1794 | /*-------------pComp for syzygies:-------------------*/ |
---|
| 1795 | void p_SetModDeg(intvec *w, ring r); |
---|
[949e57] | 1796 | |
---|
[f550e86] | 1797 | /*------------ Jet ----------------------------------*/ |
---|
| 1798 | poly pp_Jet(poly p, int m, const ring R); |
---|
| 1799 | poly p_Jet(poly p, int m,const ring R); |
---|
| 1800 | poly pp_JetW(poly p, int m, short *w, const ring R); |
---|
| 1801 | poly p_JetW(poly p, int m, short *w, const ring R); |
---|
[deca086] | 1802 | |
---|
| 1803 | |
---|
| 1804 | poly p_PermPoly (poly p, int * perm,const ring OldRing, const ring dst, |
---|
| 1805 | nMapFunc nMap, int *par_perm=NULL, int OldPar=0); |
---|
| 1806 | |
---|
[a4081e5] | 1807 | /*----------------------------------------------------*/ |
---|
| 1808 | poly p_Series(int n,poly p,poly u, intvec *w, const ring R); |
---|
| 1809 | poly p_Invers(int n,poly u,intvec *w, const ring R); |
---|
| 1810 | |
---|
| 1811 | |
---|
[35aab3] | 1812 | #endif // P_POLYS_H |
---|
| 1813 | |
---|