| 1 | #ifndef POLYS_H |
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| 2 | #define POLYS_H |
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| 3 | /**************************************** |
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| 4 | * Computer Algebra System SINGULAR * |
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| 5 | ****************************************/ |
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| 6 | /* $Id$ */ |
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| 7 | /* |
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| 8 | * ABSTRACT - compatiblity layer for all operations with polys |
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| 9 | */ |
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| 10 | |
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| 11 | #include <polys/monomials/ring.h> |
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| 12 | #include <polys/monomials/p_polys.h> |
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| 13 | |
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| 14 | extern ring currRing; |
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| 15 | void rChangeCurrRing(ring r); |
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| 16 | |
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| 17 | void p_SetGlobals(const ring r, BOOLEAN complete = TRUE); |
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| 18 | |
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| 19 | #include <coeffs/numbers.h> |
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| 20 | inline number nGcd(number a, number b, const ring r = currRing) { return n_Gcd(a, b, r->cf); } |
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| 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 | |
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| 29 | // deletes old coeff before setting the new one |
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| 30 | #define pSetCoeff(p,n) p_SetCoeff(p,n,currRing) |
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| 31 | |
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| 32 | // Order |
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| 33 | #define pGetOrder(p) p_GetOrder(p, currRing) |
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| 34 | |
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| 35 | // Component |
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| 36 | #define pGetComp(p) __p_GetComp(p, currRing) |
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| 37 | #define pSetComp(p,v) p_SetComp(p,v, currRing) |
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| 38 | |
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| 39 | // Exponent |
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| 40 | #define pGetExp(p,i) p_GetExp(p, i, currRing) |
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| 41 | #define pSetExp(p,i,v) p_SetExp(p, i, v, currRing) |
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| 42 | #define pIncrExp(p,i) p_IncrExp(p,i, currRing) |
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| 43 | #define pDecrExp(p,i) p_DecrExp(p,i, currRing) |
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| 44 | #define pAddExp(p,i,v) p_AddExp(p,i,v, currRing) |
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| 45 | #define pSubExp(p,i,v) p_SubExp(p,i,v, currRing) |
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| 46 | #define pMultExp(p,i,v) p_MultExp(p,i,v, currRing) |
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| 47 | #define pGetExpSum(p1, p2, i) p_GetExpSum(p1, p2, i, currRing) |
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| 48 | #define pGetExpDiff(p1, p2, i) p_GetExpDiff(p1, p2, i, currRing) |
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| 49 | |
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| 50 | |
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| 51 | /*************************************************************** |
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| 52 | * |
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| 53 | * Allocation/Initalization/Deletion |
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| 54 | * except for pHead, all polys must be != NULL |
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| 55 | * |
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| 56 | ***************************************************************/ |
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| 57 | // allocates the space for a new monomial -- no initialization !!! |
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| 58 | #define pNew() p_New(currRing) |
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| 59 | // allocates a new monomial and initializes everything to 0 |
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| 60 | #define pInit() p_Init(currRing) |
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| 61 | // like pInit, except that expvector is initialized to that of p, |
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| 62 | // p must be != NULL |
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| 63 | #define pLmInit(p) p_LmInit(p, currRing) |
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| 64 | // returns newly allocated copy of Lm(p), coef is copied, next=NULL, |
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| 65 | // p might be NULL |
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| 66 | #define pHead(p) p_Head(p, currRing) |
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| 67 | // frees the space of the monomial m, assumes m != NULL |
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| 68 | // coef is not freed, m is not advanced |
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| 69 | static inline void pLmFree(poly p) {p_LmFree(p, currRing);} |
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| 70 | // like pLmFree, but advances p |
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| 71 | static inline void pLmFree(poly *p) {p_LmFree(p, currRing);} |
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| 72 | // assumes p != NULL, deletes p, returns pNext(p) |
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| 73 | #define pLmFreeAndNext(p) p_LmFreeAndNext(p, currRing) |
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| 74 | // assume p != NULL, deletes Lm(p)->coef and Lm(p) |
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| 75 | #define pLmDelete(p) p_LmDelete(p, currRing) |
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| 76 | // like pLmDelete, returns pNext(p) |
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| 77 | #define pLmDeleteAndNext(p) p_LmDeleteAndNext(p, currRing) |
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| 78 | |
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| 79 | /*************************************************************** |
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| 80 | * |
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| 81 | * Operation on ExpVectors: assumes polys != NULL |
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| 82 | * |
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| 83 | ***************************************************************/ |
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| 84 | |
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| 85 | #define pExpVectorCopy(d_p, s_p) p_ExpVectorCopy(d_p, s_p, currRing) |
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| 86 | #define pExpVectorAdd(p1, p2) p_ExpVectorAdd(p1, p2, currRing) |
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| 87 | #define pExpVectorSub(p1, p2) p_ExpVectorSub(p1, p2, currRing) |
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| 88 | #define pExpVectorAddSub(p1, p2, p3)p_ExpVectorAddSub(p1, p2, p3, currRing) |
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| 89 | #define pExpVectorSum(pr, p1, p2) p_ExpVectorSum(pr, p1, p2, currRing) |
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| 90 | #define pExpVectorDiff(pr, p1, p2) p_ExpVectorDiff(pr, p1, p2, currRing) |
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| 91 | |
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| 92 | // Gets a copy of (resp. set) the exponent vector, where e is assumed |
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| 93 | // to point to (r->N +1)*sizeof(long) memory. Exponents are |
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| 94 | // filled in as follows: comp, e_1, .., e_n |
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| 95 | #define pGetExpV(p, e) p_GetExpV(p, e, currRing) |
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| 96 | #define pSetExpV(p, e) p_SetExpV(p, e, currRing) |
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| 97 | |
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| 98 | /*************************************************************** |
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| 99 | * |
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| 100 | * Comparisons: they are all done without regarding coeffs |
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| 101 | * |
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| 102 | ***************************************************************/ |
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| 103 | // returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering |
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| 104 | #define pLmCmp(p,q) p_LmCmp(p,q,currRing) |
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| 105 | // executes axtionE|actionG|actionS if p=q|p>q|p<q w.r.t monomial ordering |
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| 106 | // action should be a "goto ..." |
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| 107 | #define pLmCmpAction(p,q, actionE, actionG, actionS) \ |
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| 108 | _p_LmCmpAction(p,q,currRing, actionE, actionG,actionS) |
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| 109 | |
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| 110 | #define pLmEqual(p1, p2) p_ExpVectorEqual(p1, p2, currRing) |
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| 111 | |
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| 112 | // pCmp: args may be NULL |
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| 113 | // returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2))) |
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| 114 | #define pCmp(p1, p2) p_Cmp(p1, p2, currRing) |
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| 115 | |
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| 116 | |
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| 117 | /*************************************************************** |
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| 118 | * |
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| 119 | * Divisiblity tests, args must be != NULL, except for |
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| 120 | * pDivisbleBy |
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| 121 | * |
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| 122 | ***************************************************************/ |
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| 123 | // returns TRUE, if leading monom of a divides leading monom of b |
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| 124 | // i.e., if there exists a expvector c > 0, s.t. b = a + c; |
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| 125 | #define pDivisibleBy(a, b) p_DivisibleBy(a,b,currRing) |
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| 126 | // like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL |
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| 127 | #define pLmDivisibleBy(a,b) p_LmDivisibleBy(a,b,currRing) |
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| 128 | // like pLmDivisibleBy, does not check components |
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| 129 | #define pLmDivisibleByNoComp(a, b) p_LmDivisibleByNoComp(a,b,currRing) |
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| 130 | // Divisibility tests based on Short Exponent vectors |
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| 131 | // sev_a == pGetShortExpVector(a) |
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| 132 | // not_sev_b == ~ pGetShortExpVector(b) |
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| 133 | #define pLmShortDivisibleBy(a, sev_a, b, not_sev_b) \ |
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| 134 | p_LmShortDivisibleBy(a, sev_a, b, not_sev_b, currRing) |
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| 135 | #define pLmRingShortDivisibleBy(a, sev_a, b, not_sev_b) \ |
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| 136 | p_LmRingShortDivisibleBy(a, sev_a, b, not_sev_b, currRing) |
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| 137 | // returns the "Short Exponent Vector" -- used to speed up divisibility |
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| 138 | // tests (see polys-impl.cc ) |
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| 139 | #define pGetShortExpVector(a) p_GetShortExpVector(a, currRing) |
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| 140 | #ifdef HAVE_RINGS |
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| 141 | /* divisibility check over ground ring (which may contain zero divisors); |
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| 142 | TRUE iff LT(f) divides LT(g), i.e., LT(f)*c*m = LT(g), for some |
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| 143 | coefficient c and some monomial m; |
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| 144 | does not take components into account */ |
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| 145 | #define pDivisibleByRingCase(f,g) p_DivisibleByRingCase(f,g,currRing) |
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| 146 | #endif |
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| 147 | |
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| 148 | /*************************************************************** |
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| 149 | * |
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| 150 | * Copying/Deleteion of polys: args may be NULL |
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| 151 | * |
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| 152 | ***************************************************************/ |
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| 153 | // return a copy of the poly |
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| 154 | #define pCopy(p) p_Copy(p, currRing) |
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| 155 | #define pDelete(p_ptr) p_Delete(p_ptr, currRing) |
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| 156 | |
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| 157 | /*************************************************************** |
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| 158 | * |
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| 159 | * Copying/Deletion of polys: args may be NULL |
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| 160 | * - p/q as arg mean a poly |
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| 161 | * - m a monomial |
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| 162 | * - n a number |
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| 163 | * - pp (resp. qq, mm, nn) means arg is constant |
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| 164 | * - p (resp, q, m, n) means arg is destroyed |
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| 165 | * |
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| 166 | ***************************************************************/ |
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| 167 | #define pNeg(p) p_Neg(p, currRing) |
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| 168 | #define ppMult_nn(p, n) pp_Mult_nn(p, n, currRing) |
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| 169 | #define pMult_nn(p, n) p_Mult_nn(p, n, currRing) |
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| 170 | #define ppMult_mm(p, m) pp_Mult_mm(p, m, currRing) |
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| 171 | #define pMult_mm(p, m) p_Mult_mm(p, m, currRing) |
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| 172 | #define pAdd(p, q) p_Add_q(p, q, currRing) |
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| 173 | #define pPower(p, q) p_Power(p, q, currRing) |
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| 174 | #define pMinus_mm_Mult_qq(p, m, q) p_Minus_mm_Mult_qq(p, m, q, currRing) |
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| 175 | #define pPlus_mm_Mult_qq(p, m, q) p_Plus_mm_Mult_qq(p, m, q, currRing) |
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| 176 | #define pMult(p, q) p_Mult_q(p, q, currRing) |
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| 177 | #define ppMult_qq(p, q) pp_Mult_qq(p, q, currRing) |
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| 178 | // p*Coeff(m) for such monomials pm of p, for which m is divisble by pm |
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| 179 | #define ppMult_Coeff_mm_DivSelect(p, m) pp_Mult_Coeff_mm_DivSelect(p, m, currRing) |
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| 180 | /************************************************************************* |
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| 181 | * |
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| 182 | * Sort routines |
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| 183 | * |
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| 184 | *************************************************************************/ |
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| 185 | // sorts p, assumes all monomials in p are different |
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| 186 | #define pSortMerger(p) p_SortMerge(p, currRing) |
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| 187 | #define pSort(p) p_SortMerge(p, currRing) |
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| 188 | |
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| 189 | // sorts p, p may have equal monomials |
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| 190 | #define pSortAdd(p) p_SortAdd(p, currRing) |
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| 191 | |
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| 192 | |
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| 193 | // Assume: If considerd only as poly in any component of p |
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| 194 | // (say, monomials of other components of p are set to 0), |
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| 195 | // then p is already sorted correctly |
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| 196 | #define pSortCompCorrect(p) pSort(p) |
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| 197 | |
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| 198 | /*************************************************************** |
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| 199 | * |
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| 200 | * Predicates on polys/Lm's |
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| 201 | * |
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| 202 | ***************************************************************/ |
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| 203 | // return true if all p is eihter NULL, or if all exponents |
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| 204 | // of p are 0 and Comp of p is zero |
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| 205 | #define pIsConstantComp(p) p_IsConstantComp(p, currRing) |
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| 206 | // like above, except that Comp might be != 0 |
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| 207 | #define pIsConstant(p) p_IsConstant(p,currRing) |
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| 208 | // return true if the Lm is a constant <>0 |
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| 209 | #define pIsUnit(p) p_IsUnit(p,currRing) |
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| 210 | // like above, except that p must be != NULL |
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| 211 | #define pLmIsConstantComp(p) p_LmIsConstantComp(p, currRing) |
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| 212 | #define pLmIsConstant(p) p_LmIsConstant(p,currRing) |
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| 213 | |
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| 214 | // return TRUE if all monomials of p are constant |
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| 215 | #define pIsConstantPoly(p) p_IsConstantPoly(p, currRing) |
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| 216 | |
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| 217 | #define pIsPurePower(p) p_IsPurePower(p, currRing) |
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| 218 | #define pIsUnivariate(p) p_IsUnivariate(p, currRing) |
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| 219 | #define pIsVector(p) (pGetComp(p)>0) |
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| 220 | #define pGetVariables(p,e) p_GetVariables(p, e, currRing) |
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| 221 | |
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| 222 | /*************************************************************** |
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| 223 | * |
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| 224 | * Old stuff |
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| 225 | * |
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| 226 | ***************************************************************/ |
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| 227 | |
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| 228 | typedef poly* polyset; |
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| 229 | // // // extern poly ppNoether; // use currRing -> ppNoether!!! |
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| 230 | extern BOOLEAN pVectorOut; |
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| 231 | |
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| 232 | /*-------------predicate on polys ----------------------*/ |
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| 233 | #define pHasNotCF(p1,p2) p_HasNotCF(p1,p2,currRing) |
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| 234 | /*has no common factor ?*/ |
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| 235 | #define pSplit(p,r) p_Split(p,r) |
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| 236 | /*p => IN(p), r => REST(p) */ |
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| 237 | |
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| 238 | |
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| 239 | |
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| 240 | /*-----------the ordering of monomials:-------------*/ |
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| 241 | #define pSetm(p) p_Setm(p, currRing) |
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| 242 | // TODO: |
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| 243 | #define pSetmComp(p) p_Setm(p, currRing) |
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| 244 | |
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| 245 | /*************************************************************** |
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| 246 | * |
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| 247 | * Degree stuff -- see p_polys.cc for explainations |
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| 248 | * |
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| 249 | ***************************************************************/ |
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| 250 | inline int pWeight(int i, const ring R = currRing){ return p_Weight(i, R); } |
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| 251 | inline long pDeg(poly p, const ring R = currRing) { return p_Deg(p, R); } |
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| 252 | |
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| 253 | |
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| 254 | static inline long pTotaldegree(poly p) { return p_Totaldegree(p,currRing); } |
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| 255 | #define pWTotaldegree(p) p_WTotaldegree(p,currRing) |
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| 256 | #define pWDegree(p) p_WDegree(p,currRing) |
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| 257 | |
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| 258 | /*-------------operations on polynomials:------------*/ |
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| 259 | #define pSub(a,b) p_Sub(a,b,currRing) |
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| 260 | |
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| 261 | #define pmInit(a,b) p_mInit(a,b,currRing) |
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| 262 | |
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| 263 | // ----------------- define to enable new p_procs -----*/ |
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| 264 | |
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| 265 | #define pDivide(a,b) p_Divide(a,b,currRing) |
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| 266 | #define pDivideM(a,b) p_DivideM(a,b,currRing) |
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| 267 | #define pLcm(a,b,m) p_Lcm(a,b,m,currRing) |
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| 268 | #define pDiff(a,b) p_Diff(a,b,currRing) |
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| 269 | #define pDiffOp(a,b,m) p_DiffOp(a,b,m,currRing) |
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| 270 | |
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| 271 | #define pMaxComp(p) p_MaxComp(p, currRing) |
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| 272 | #define pMinComp(p) p_MinComp(p, currRing) |
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| 273 | |
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| 274 | #define pOneComp(p) p_OneComp(p, currRing) |
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| 275 | #define pSetCompP(a,i) p_SetCompP(a, i, currRing) |
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| 276 | |
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| 277 | // let's inline those, so that we can call them from the debugger |
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| 278 | inline char* pString(poly p) {return p_String(p, currRing, currRing);} |
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| 279 | inline char* pString0(poly p) {return p_String0(p, currRing, currRing);} |
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| 280 | inline void pWrite(poly p) {p_Write(p, currRing, currRing);} |
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| 281 | inline void pWrite0(poly p) {p_Write0(p, currRing, currRing);} |
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| 282 | inline void wrp(poly p) {p_wrp(p, currRing, currRing);} |
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| 283 | |
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| 284 | #define pISet(i) p_ISet(i,currRing) |
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| 285 | #define pNSet(n) p_NSet(n,currRing) |
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| 286 | |
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| 287 | #define pOne() p_One(currRing) |
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| 288 | |
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| 289 | #define pNormalize(p) p_Normalize(p,currRing) |
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| 290 | #define pSize(p) p_Size(p,currRing) |
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| 291 | |
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| 292 | |
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| 293 | // homogenizes p by multiplying certain powers of the varnum-th variable |
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| 294 | #define pHomogen(p,varnum) p_Homogen(p,varnum,currRing) |
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| 295 | |
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| 296 | BOOLEAN pIsHomogeneous (poly p); |
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| 297 | // // replaces the maximal powers of the leading monomial of p2 in p1 by |
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| 298 | // // the same powers of n, utility for dehomogenization |
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| 299 | // #define pDehomogen(p1,p2,n) p_Dehomgen(p1,p2,n,currRing) |
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| 300 | // #define pIsHomogen(p) p_IsHomggen(p,currRing) |
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| 301 | #define pIsHomogen(p) p_IsHomogen(p,currRing) |
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| 302 | |
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| 303 | /*BOOLEAN pVectorHasUnitM(poly p, int * k);*/ |
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| 304 | #define pVectorHasUnitB(p,k) p_VectorHasUnitB(p,k,currRing) |
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| 305 | #define pVectorHasUnit(p,k,l) p_VectorHasUnit(p,k,l,currRing) |
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| 306 | #define pTakeOutComp1(p,k) p_TakeOutComp1(p,k,currRing) |
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| 307 | |
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| 308 | // Splits *p into two polys: *q which consists of all monoms with |
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| 309 | // component == comp and *p of all other monoms *lq == pLength(*q) |
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| 310 | // On return all components pf *q == 0 |
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| 311 | inline void pTakeOutComp(poly *p, long comp, poly *q, int *lq, const ring R = currRing) |
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| 312 | { |
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| 313 | return p_TakeOutComp(p, comp, q, lq, R); |
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| 314 | } |
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| 315 | |
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| 316 | |
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| 317 | // This is something weird -- Don't use it, unless you know what you are doing |
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| 318 | inline poly pTakeOutComp(poly * p, int k, const ring R = currRing) |
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| 319 | { |
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| 320 | return p_TakeOutComp(p, k, R); |
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| 321 | } |
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| 322 | |
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| 323 | /* old spielwiese |
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| 324 | #define pTakeOutComp(p,k,q,lq) p_TakeOutComp(p,k,q,lq,currRing) |
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| 325 | |
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| 326 | // Similar to pTakeOutComp, except that only those components are |
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| 327 | // taken out whose Order == order |
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| 328 | // ASSUME: monomial ordering is Order compatible, i.e., if m1, m2 Monoms then |
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| 329 | // m1 >= m2 ==> pGetOrder(m1) >= pGetOrder(m2) |
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| 330 | #define pDecrOrdTakeOutComp(p,c,o,q,lq) p_DecrOrdTakeOutComp(p,c,o,q,lq,currRing) |
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| 331 | */ |
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| 332 | void pSetPolyComp(poly p, int comp); |
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| 333 | #define pDeleteComp(p,k) p_DeleteComp(p,k,currRing) |
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| 334 | |
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| 335 | inline void pNorm(poly p, const ring R = currRing){ p_Norm(p, R); } |
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| 336 | |
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| 337 | |
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| 338 | #define pSubst(p,n,e) p_Subst(p,n,e,currRing) |
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| 339 | #define ppJet(p,m) pp_Jet(p,m,currRing) |
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| 340 | #define pJet(p,m) p_Jet(p,m,currRing) |
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| 341 | #define ppJetW(p,m,iv) pp_JetW(p,m,iv,currRing) |
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| 342 | #define pJetW(p,m,iv) p_JetW(p,m,iv,currRing) |
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| 343 | #define pMinDeg(p,w) p_MinDeg(p,w,currRing) |
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| 344 | #define pSeries(n,p,u,w) p_Series(n,p,u,w,currRing) |
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| 345 | #define pInvers(n,p,w) p_Invers(n,p,w,currRing) |
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| 346 | // maximum weigthed degree of all monomials of p, w is indexed from |
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| 347 | // 1..pVariables |
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| 348 | #define pDegW(p,w) p_DegW(p,w,currRing) |
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| 349 | |
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| 350 | /*-----------type conversions ----------------------------*/ |
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| 351 | // void pVec2Polys(poly v, polyset *p, int *len); |
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| 352 | #define pVar(m) p_Var(m,currRing) |
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| 353 | |
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| 354 | /*-----------specials for spoly-computations--------------*/ |
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| 355 | |
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| 356 | /// Returns TRUE if |
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| 357 | /// * LM(p) | LM(lcm) |
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| 358 | /// * LC(p) | LC(lcm) only if ring |
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| 359 | /// * Exists i, j: |
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| 360 | /// * LE(p, i) != LE(lcm, i) |
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| 361 | /// * LE(p1, i) != LE(lcm, i) ==> LCM(p1, p) != lcm |
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| 362 | /// * LE(p, j) != LE(lcm, j) |
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| 363 | /// * LE(p2, j) != LE(lcm, j) ==> LCM(p2, p) != lcm |
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| 364 | BOOLEAN pCompareChain (poly p, poly p1, poly p2, poly lcm, const ring R = currRing); |
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| 365 | |
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| 366 | #define pEqualPolys(p1,p2) p_EqualPolys(p1,p2,currRing) |
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| 367 | |
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| 368 | |
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| 369 | |
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| 370 | // returns the length of a polynomial (numbers of monomials) |
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| 371 | // respect syzComp |
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| 372 | static inline poly pLast(poly a, int &length) { return p_Last (a, length, currRing); } |
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| 373 | static inline poly pLast(poly a) { int l; return pLast(a, l); } |
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| 374 | |
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| 375 | /*************************************************************** |
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| 376 | * |
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| 377 | * PDEBUG stuff |
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| 378 | * |
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| 379 | ***************************************************************/ |
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| 380 | #ifdef PDEBUG |
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| 381 | #define pTest(p) _p_Test(p, currRing, PDEBUG) |
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| 382 | #define pLmTest(p) _p_LmTest(p, currRing, PDEBUG) |
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| 383 | |
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| 384 | #else // ! PDEBUG |
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| 385 | |
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| 386 | #define pTest(p) ((void)0) |
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| 387 | #define pLmTest(p) ((void)0) |
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| 388 | #endif |
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| 389 | |
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| 390 | #endif // POLYS_H |
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