| 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 - all basic methods to manipulate polynomials of the |
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| 9 | currRing |
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| 10 | */ |
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| 11 | |
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| 12 | #include <polys/p_polys.h> |
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| 13 | |
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| 14 | /*************************************************************** |
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| 15 | * |
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| 16 | * Primitives for accessing and setting fields of a poly |
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| 17 | * poly must be != NULL |
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| 18 | * |
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| 19 | ***************************************************************/ |
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| 20 | // deletes old coeff before setting the new one |
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| 21 | #define pSetCoeff(p,n) p_SetCoeff(p,n,currRing) |
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| 22 | |
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| 23 | // Order |
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| 24 | #define pGetOrder(p) p_GetOrder(p, currRing) |
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| 25 | |
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| 26 | // Component |
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| 27 | #define pGetComp(p) _p_GetComp(p, currRing) |
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| 28 | #define pSetComp(p,v) p_SetComp(p,v, currRing) |
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| 29 | |
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| 30 | // Exponent |
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| 31 | #define pGetExp(p,i) p_GetExp(p, i, currRing) |
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| 32 | #define pSetExp(p,i,v) p_SetExp(p, i, v, currRing) |
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| 33 | #define pIncrExp(p,i) p_IncrExp(p,i, currRing) |
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| 34 | #define pDecrExp(p,i) p_DecrExp(p,i, currRing) |
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| 35 | #define pAddExp(p,i,v) p_AddExp(p,i,v, currRing) |
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| 36 | #define pSubExp(p,i,v) p_SubExp(p,i,v, currRing) |
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| 37 | #define pMultExp(p,i,v) p_MultExp(p,i,v, currRing) |
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| 38 | #define pGetExpSum(p1, p2, i) p_GetExpSum(p1, p2, i, currRing) |
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| 39 | #define pGetExpDiff(p1, p2, i) p_GetExpDiff(p1, p2, i, currRing) |
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| 40 | |
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| 41 | /*************************************************************** |
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| 42 | * |
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| 43 | * Allocation/Initalization/Deletion |
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| 44 | * except for pHead, all polys must be != NULL |
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| 45 | * |
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| 46 | ***************************************************************/ |
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| 47 | // allocates the space for a new monomial -- no initialization !!! |
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| 48 | #define pNew() p_New(currRing) |
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| 49 | // allocates a new monomial and initializes everything to 0 |
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| 50 | #define pInit() p_Init(currRing) |
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| 51 | // like pInit, except that expvector is initialized to that of p, |
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| 52 | // p must be != NULL |
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| 53 | #define pLmInit(p) p_LmInit(p, currRing) |
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| 54 | // returns newly allocated copy of Lm(p), coef is copied, next=NULL, |
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| 55 | // p might be NULL |
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| 56 | #define pHead(p) p_Head(p, currRing) |
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| 57 | // frees the space of the monomial m, assumes m != NULL |
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| 58 | // coef is not freed, m is not advanced |
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| 59 | static inline void pLmFree(poly p) {p_LmFree(p, currRing);} |
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| 60 | // like pLmFree, but advances p |
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| 61 | static inline void pLmFree(poly *p) {p_LmFree(p, currRing);} |
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| 62 | // assumes p != NULL, deletes p, returns pNext(p) |
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| 63 | #define pLmFreeAndNext(p) p_LmFreeAndNext(p, currRing) |
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| 64 | // assume p != NULL, deletes Lm(p)->coef and Lm(p) |
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| 65 | #define pLmDelete(p) p_LmDelete(p, currRing) |
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| 66 | // like pLmDelete, returns pNext(p) |
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| 67 | #define pLmDeleteAndNext(p) p_LmDeleteAndNext(p, currRing) |
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| 68 | |
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| 69 | /*************************************************************** |
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| 70 | * |
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| 71 | * Operation on ExpVectors: assumes polys != NULL |
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| 72 | * |
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| 73 | ***************************************************************/ |
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| 74 | |
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| 75 | #define pExpVectorCopy(d_p, s_p) p_ExpVectorCopy(d_p, s_p, currRing) |
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| 76 | #define pExpVectorAdd(p1, p2) p_ExpVectorAdd(p1, p2, currRing) |
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| 77 | #define pExpVectorSub(p1, p2) p_ExpVectorSub(p1, p2, currRing) |
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| 78 | #define pExpVectorAddSub(p1, p2, p3)p_ExpVectorAddSub(p1, p2, p3, currRing) |
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| 79 | #define pExpVectorSum(pr, p1, p2) p_ExpVectorSum(pr, p1, p2, currRing) |
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| 80 | #define pExpVectorDiff(pr, p1, p2) p_ExpVectorDiff(pr, p1, p2, currRing) |
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| 81 | |
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| 82 | // Gets a copy of (resp. set) the exponent vector, where e is assumed |
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| 83 | // to point to (r->N +1)*sizeof(long) memory. Exponents are |
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| 84 | // filled in as follows: comp, e_1, .., e_n |
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| 85 | #define pGetExpV(p, e) p_GetExpV(p, e, currRing) |
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| 86 | #define pSetExpV(p, e) p_SetExpV(p, e, currRing) |
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| 87 | |
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| 88 | /*************************************************************** |
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| 89 | * |
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| 90 | * Comparisons: they are all done without regarding coeffs |
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| 91 | * |
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| 92 | ***************************************************************/ |
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| 93 | // returns 0|1|-1 if p=q|p>q|p<q w.r.t monomial ordering |
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| 94 | #define pLmCmp(p,q) p_LmCmp(p,q,currRing) |
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| 95 | // executes axtionE|actionG|actionS if p=q|p>q|p<q w.r.t monomial ordering |
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| 96 | // action should be a "goto ..." |
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| 97 | #define pLmCmpAction(p,q, actionE, actionG, actionS) \ |
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| 98 | _p_LmCmpAction(p,q,currRing, actionE, actionG,actionS) |
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| 99 | |
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| 100 | #define pLmEqual(p1, p2) p_ExpVectorEqual(p1, p2, currRing) |
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| 101 | |
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| 102 | // pCmp: args may be NULL |
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| 103 | // returns: (p2==NULL ? 1 : (p1 == NULL ? -1 : p_LmCmp(p1, p2))) |
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| 104 | #define pCmp(p1, p2) p_Cmp(p1, p2, currRing) |
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| 105 | |
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| 106 | |
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| 107 | /*************************************************************** |
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| 108 | * |
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| 109 | * Divisiblity tests, args must be != NULL, except for |
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| 110 | * pDivisbleBy |
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| 111 | * |
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| 112 | ***************************************************************/ |
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| 113 | // returns TRUE, if leading monom of a divides leading monom of b |
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| 114 | // i.e., if there exists a expvector c > 0, s.t. b = a + c; |
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| 115 | #define pDivisibleBy(a, b) p_DivisibleBy(a,b,currRing) |
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| 116 | // like pDivisibleBy, except that it is assumed that a!=NULL, b!=NULL |
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| 117 | #define pLmDivisibleBy(a,b) p_LmDivisibleBy(a,b,currRing) |
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| 118 | // like pLmDivisibleBy, does not check components |
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| 119 | #define pLmDivisibleByNoComp(a, b) p_LmDivisibleByNoComp(a,b,currRing) |
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| 120 | // Divisibility tests based on Short Exponent vectors |
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| 121 | // sev_a == pGetShortExpVector(a) |
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| 122 | // not_sev_b == ~ pGetShortExpVector(b) |
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| 123 | #define pLmShortDivisibleBy(a, sev_a, b, not_sev_b) \ |
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| 124 | p_LmShortDivisibleBy(a, sev_a, b, not_sev_b, currRing) |
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| 125 | #define pLmRingShortDivisibleBy(a, sev_a, b, not_sev_b) \ |
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| 126 | p_LmRingShortDivisibleBy(a, sev_a, b, not_sev_b, currRing) |
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| 127 | // returns the "Short Exponent Vector" -- used to speed up divisibility |
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| 128 | // tests (see polys-impl.cc ) |
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| 129 | #define pGetShortExpVector(a) p_GetShortExpVector(a, currRing) |
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| 130 | #ifdef HAVE_RINGS |
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| 131 | /* divisibility check over ground ring (which may contain zero divisors); |
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| 132 | TRUE iff LT(f) divides LT(g), i.e., LT(f)*c*m = LT(g), for some |
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| 133 | coefficient c and some monomial m; |
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| 134 | does not take components into account */ |
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| 135 | BOOLEAN pDivisibleByRingCase(poly f, poly g); |
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| 136 | #endif |
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| 137 | |
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| 138 | /*************************************************************** |
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| 139 | * |
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| 140 | * Copying/Deleteion of polys: args may be NULL |
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| 141 | * |
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| 142 | ***************************************************************/ |
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| 143 | // return a copy of the poly |
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| 144 | #define pCopy(p) p_Copy(p, currRing) |
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| 145 | #define pDelete(p_ptr) p_Delete(p_ptr, currRing) |
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| 146 | |
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| 147 | /*************************************************************** |
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| 148 | * |
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| 149 | * Copying/Deletion of polys: args may be NULL |
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| 150 | * - p/q as arg mean a poly |
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| 151 | * - m a monomial |
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| 152 | * - n a number |
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| 153 | * - pp (resp. qq, mm, nn) means arg is constant |
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| 154 | * - p (resp, q, m, n) means arg is destroyed |
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| 155 | * |
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| 156 | ***************************************************************/ |
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| 157 | #define pNeg(p) p_Neg(p, currRing) |
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| 158 | #define ppMult_nn(p, n) pp_Mult_nn(p, n, currRing) |
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| 159 | #define pMult_nn(p, n) p_Mult_nn(p, n, currRing) |
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| 160 | #define ppMult_mm(p, m) pp_Mult_mm(p, m, currRing) |
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| 161 | #define pMult_mm(p, m) p_Mult_mm(p, m, currRing) |
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| 162 | #define pAdd(p, q) p_Add_q(p, q, currRing) |
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| 163 | #define pPower(p, q) p_Power(p, q, currRing) |
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| 164 | #define pMinus_mm_Mult_qq(p, m, q) p_Minus_mm_Mult_qq(p, m, q, currRing) |
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| 165 | #define pPlus_mm_Mult_qq(p, m, q) p_Plus_mm_Mult_qq(p, m, q, currRing) |
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| 166 | #define pMult(p, q) p_Mult_q(p, q, currRing) |
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| 167 | #define ppMult_qq(p, q) pp_Mult_qq(p, q, currRing) |
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| 168 | // p*Coeff(m) for such monomials pm of p, for which m is divisble by pm |
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| 169 | #define ppMult_Coeff_mm_DivSelect(p, m) pp_Mult_Coeff_mm_DivSelect(p, m, currRing) |
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| 170 | /************************************************************************* |
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| 171 | * |
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| 172 | * Sort routines |
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| 173 | * |
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| 174 | *************************************************************************/ |
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| 175 | // sorts p, assumes all monomials in p are different |
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| 176 | #define pSortMerger(p) p_SortMerge(p, currRing) |
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| 177 | #define pSort(p) p_SortMerge(p, currRing) |
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| 178 | |
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| 179 | // sorts p, p may have equal monomials |
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| 180 | #define pSortAdd(p) p_SortAdd(p, currRing) |
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| 181 | |
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| 182 | |
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| 183 | // Assume: If considerd only as poly in any component of p |
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| 184 | // (say, monomials of other components of p are set to 0), |
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| 185 | // then p is already sorted correctly |
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| 186 | #define pSortCompCorrect(p) pSort(p) |
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| 187 | |
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| 188 | /*************************************************************** |
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| 189 | * |
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| 190 | * Predicates on polys/Lm's |
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| 191 | * |
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| 192 | ***************************************************************/ |
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| 193 | // return true if all p is eihter NULL, or if all exponents |
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| 194 | // of p are 0 and Comp of p is zero |
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| 195 | #define pIsConstantComp(p) p_IsConstantComp(p, currRing) |
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| 196 | // like above, except that Comp might be != 0 |
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| 197 | #define pIsConstant(p) p_IsConstant(p,currRing) |
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| 198 | // return true if the Lm is a constant <>0 |
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| 199 | #define pIsUnit(p) p_IsUnit(p,currRing) |
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| 200 | // like above, except that p must be != NULL |
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| 201 | #define pLmIsConstantComp(p) p_LmIsConstantComp(p, currRing) |
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| 202 | #define pLmIsConstant(p) p_LmIsConstant(p,currRing) |
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| 203 | |
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| 204 | // return TRUE if all monomials of p are constant |
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| 205 | #define pIsConstantPoly(p) p_IsConstantPoly(p, currRing) |
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| 206 | |
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| 207 | #define pIsPurePower(p) p_IsPurePower(p, currRing) |
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| 208 | #define pIsUnivariate(p) p_IsUnivariate(p, currRing) |
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| 209 | #define pIsVector(p) (pGetComp(p)>0) |
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| 210 | #define pGetVariables(p,e) p_GetVariables(p, e, currRing) |
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| 211 | |
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| 212 | /*************************************************************** |
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| 213 | * |
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| 214 | * Old stuff |
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| 215 | * |
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| 216 | ***************************************************************/ |
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| 217 | |
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| 218 | typedef poly* polyset; |
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| 219 | extern int pOrdSgn; |
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| 220 | extern BOOLEAN pLexOrder; |
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| 221 | extern poly ppNoether; |
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| 222 | extern BOOLEAN pVectorOut; |
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| 223 | |
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| 224 | /*-------------predicate on polys ----------------------*/ |
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| 225 | #define pHasNotCF(p1,p2) p_HasNotCF(p1,p2,currRing) |
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| 226 | /*has no common factor ?*/ |
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| 227 | #define pSplit(p,r) p_Split(p,r) |
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| 228 | /*p => IN(p), r => REST(p) */ |
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| 229 | |
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| 230 | |
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| 231 | |
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| 232 | /*-----------the ordering of monomials:-------------*/ |
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| 233 | #define pSetm(p) p_Setm(p, currRing) |
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| 234 | // TODO: |
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| 235 | #define pSetmComp(p) p_Setm(p, currRing) |
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| 236 | |
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| 237 | /*************************************************************** |
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| 238 | * |
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| 239 | * Degree stuff -- see p_polys.cc for explainations |
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| 240 | * |
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| 241 | ***************************************************************/ |
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| 242 | static inline long pFDeg(const poly p, const ring r) { return r->pFDeg(p,r); } |
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| 243 | static inline long pLDeg(const poly p, int *l, const ring r) { return r->pLDeg(p,l,r); } |
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| 244 | #define pWeight(c) p_Weight(c,currRing) |
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| 245 | #define pDeg(p) p_Deg(p,currRing) |
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| 246 | static inline long pTotaldegree(poly p) { return p_Totaldegree(p,currRing); } |
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| 247 | #define pWTotaldegree(p) p_WTotaldegree(p,currRing) |
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| 248 | #define pWDegree(poly p) p_WDegree(p,currRing) |
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| 249 | |
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| 250 | /*-------------operations on polynomials:------------*/ |
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| 251 | #define pSub(a,b) p_Sub(a,b,currRing) |
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| 252 | |
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| 253 | #define pmInit(a,b) p_mInit(a,b,currRing) |
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| 254 | |
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| 255 | // ----------------- define to enable new p_procs -----*/ |
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| 256 | |
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| 257 | #define pDivide(a,b) p_Divide(a,b,currRing) |
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| 258 | #define pLcm(a,b,m) p_Lcm(a,b,m,currRing) |
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| 259 | #define pDiff(a,b) p_Diff(a,b,currRing) |
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| 260 | #define pDiffOp(a,b,m) p_DiffOp(a,b,m,currRing) |
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| 261 | |
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| 262 | #define pMaxComp(p) p_MaxComp(p, currRing) |
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| 263 | #define pMinComp(p) p_MinComp(p, currRing) |
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| 264 | |
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| 265 | #define pOneComp(p) p_OneComp(p, currRing) |
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| 266 | #define pSetCompP(a,i) p_SetCompP(a, i, currRing) |
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| 267 | |
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| 268 | // let's inline those, so that we can call them from the debugger |
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| 269 | inline char* pString(poly p) {return p_String(p, currRing, currRing);} |
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| 270 | inline char* pString0(poly p) {return p_String0(p, currRing, currRing);} |
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| 271 | inline void pWrite(poly p) {p_Write(p, currRing, currRing);} |
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| 272 | inline void pWrite0(poly p) {p_Write0(p, currRing, currRing);} |
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| 273 | inline void wrp(poly p) {p_wrp(p, currRing, currRing);} |
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| 274 | |
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| 275 | void pEnlargeSet(polyset *p, int length, int increment); |
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| 276 | #define pISet(i) p_ISet(i,currRing) |
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| 277 | #define pNSet(n) p_NSet(n,currRing) |
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| 278 | |
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| 279 | #define pOne() p_One(currRing) |
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| 280 | |
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| 281 | #define pNormalize(p) p_Normalize(p,currRing) |
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| 282 | #define pSize(p) p_Size(p,currRing) |
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| 283 | |
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| 284 | |
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| 285 | // homogenizes p by multiplying certain powers of the varnum-th variable |
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| 286 | #define pHomogen(p,varnum) p_Homogen(p,varnum,currRing) |
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| 287 | |
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| 288 | BOOLEAN pIsHomogeneous (poly p); |
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| 289 | // // replaces the maximal powers of the leading monomial of p2 in p1 by |
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| 290 | // // the same powers of n, utility for dehomogenization |
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| 291 | // #define pDehomogen(p1,p2,n) p_Dehomgen(p1,p2,n,currRing) |
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| 292 | // #define pIsHomogen(p) p_IsHomggen(p,currRing) |
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| 293 | #define pIsHomogen(p) p_IsHomogen(p,currRing) |
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| 294 | |
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| 295 | /*BOOLEAN pVectorHasUnitM(poly p, int * k);*/ |
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| 296 | #define pVectorHasUnitB(p,k) p_VectorHasUnitB(p,k,currRing) |
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| 297 | #define pVectorHasUnit(p,k,l) p_VectorHasUnit(p,k,l,currRing) |
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| 298 | #define pTakeOutComp1(p,k) p_TakeOutComp1(p,k,currRing) |
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| 299 | |
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| 300 | // Splits *p into two polys: *q which consists of all monoms with |
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| 301 | // component == comp and *p of all other monoms *lq == pLength(*q) |
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| 302 | // On return all components pf *q == 0 |
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| 303 | void pTakeOutComp(poly *p, long comp, poly *q, int *lq); |
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| 304 | |
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| 305 | // This is something weird -- Don't use it, unless you know what you are doing |
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| 306 | poly pTakeOutComp(poly * p, int k); |
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| 307 | /* old spielwiese |
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| 308 | #define pTakeOutComp(p,k,q,lq) p_TakeOutComp(p,k,q,lq,currRing) |
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| 309 | |
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| 310 | // Similar to pTakeOutComp, except that only those components are |
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| 311 | // taken out whose Order == order |
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| 312 | // ASSUME: monomial ordering is Order compatible, i.e., if m1, m2 Monoms then |
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| 313 | // m1 >= m2 ==> pGetOrder(m1) >= pGetOrder(m2) |
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| 314 | #define pDecrOrdTakeOutComp(p,c,o,q,lq) p_DecrOrdTakeOutComp(p,c,o,q,lq,currRing) |
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| 315 | */ |
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| 316 | void pSetPolyComp(poly p, int comp); |
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| 317 | #define pDeleteComp(p,k) p_DeleteComp(p,k,currRing) |
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| 318 | void pNorm(poly p); |
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| 319 | poly pSubst(poly p, int n, poly e); |
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| 320 | poly ppJet(poly p, int m); |
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| 321 | poly pJet(poly p, int m); |
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| 322 | poly ppJetW(poly p, int m, short * iv); |
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| 323 | poly pJetW(poly p, int m, short * iv); |
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| 324 | int pMinDeg(poly p,intvec *w=NULL); |
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| 325 | poly pSeries(int n,poly p,poly u=NULL,intvec *w=NULL); |
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| 326 | poly pInvers(int n, poly p,intvec *w=NULL); |
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| 327 | // maximum weigthed degree of all monomials of p, w is indexed from |
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| 328 | // 1..pVariables |
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| 329 | long pDegW(poly p, const short *w); |
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| 330 | |
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| 331 | /*-----------type conversions ----------------------------*/ |
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| 332 | void pVec2Polys(poly v, polyset *p, int *len); |
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| 333 | int p_Var(poly mi,const ring r); |
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| 334 | #define pVar(m) p_Var(m,currRing) |
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| 335 | |
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| 336 | /*-----------specials for spoly-computations--------------*/ |
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| 337 | BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm); |
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| 338 | BOOLEAN pCompareChainPart (poly p,poly p1,poly p2,poly lcm); |
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| 339 | #define pEqualPolys(p1,p2) p_EqualPolys(p1,p2,currRing) |
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| 340 | BOOLEAN pComparePolys(poly p1,poly p2); |
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| 341 | |
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| 342 | |
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| 343 | |
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| 344 | /*************************************************************** |
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| 345 | * |
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| 346 | * PDEBUG stuff |
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| 347 | * |
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| 348 | ***************************************************************/ |
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| 349 | #ifdef PDEBUG |
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| 350 | #define pTest(p) _p_Test(p, currRing, PDEBUG) |
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| 351 | #define pLmTest(p) _p_LmTest(p, currRing, PDEBUG) |
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| 352 | |
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| 353 | #else // ! PDEBUG |
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| 354 | |
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| 355 | #define pTest(p) ((void)0) |
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| 356 | #define pLmTest(p) ((void)0) |
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| 357 | #endif |
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| 358 | |
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| 359 | #endif // POLYS_H |
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