[b46956] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* $Id: longtrans.cc 12469 2011-02-25 13:38:49Z seelisch $ */ |
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| 5 | /* |
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| 6 | * ABSTRACT: numbers in transcendental field extensions, i.e., |
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| 7 | in rational function fields |
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| 8 | */ |
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| 9 | |
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| 10 | #include <stdio.h> |
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| 11 | #include <string.h> |
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| 12 | #include <kernel/mod2.h> |
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| 13 | #include <kernel/structs.h> |
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| 14 | #include <omalloc/omalloc.h> |
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| 15 | #include <kernel/febase.h> |
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| 16 | #include <kernel/longrat.h> |
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| 17 | #include <kernel/modulop.h> |
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| 18 | #include <kernel/numbers.h> |
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| 19 | #include <kernel/polys.h> |
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| 20 | #include <kernel/ideals.h> |
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| 21 | #include <kernel/ring.h> |
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| 22 | #ifdef HAVE_FACTORY |
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| 23 | #define SI_DONT_HAVE_GLOBAL_VARS |
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| 24 | #include <factory/factory.h> |
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| 25 | #include <kernel/clapsing.h> |
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| 26 | #include <kernel/clapconv.h> |
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| 27 | #endif |
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| 28 | #include <kernel/longtrans.h> |
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[661c214] | 29 | #include <kernel/longalg.h> |
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[b46956] | 30 | |
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[661c214] | 31 | ring nacRing; |
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[21972b] | 32 | int ntIsChar0; |
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[661c214] | 33 | ring ntMapRing; |
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[21972b] | 34 | int ntParsToCopy; |
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| 35 | int ntNumbOfPar; |
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| 36 | |
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| 37 | numberfunc nacMult, nacSub, nacAdd, nacDiv, nacIntDiv; |
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| 38 | number (*ntMap)(number from); |
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| 39 | number (*nacGcd)(number a, number b, const ring r); |
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| 40 | number (*nacLcm)(number a, number b, const ring r); |
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| 41 | number (*nacInit)(int i, const ring r); |
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| 42 | int (*nacInt)(number &n, const ring r); |
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| 43 | void (*nacNormalize)(number &a); |
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| 44 | number (*nacNeg)(number a); |
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| 45 | number (*nacCopy)(number a); |
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| 46 | number (*nacInvers)(number a); |
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| 47 | BOOLEAN (*nacIsZero)(number a); |
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| 48 | BOOLEAN (*nacIsOne)(number a); |
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| 49 | BOOLEAN (*nacGreaterZero)(number a); |
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| 50 | number (*nacMap)(number); |
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[b46956] | 51 | |
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| 52 | #ifdef LDEBUG |
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| 53 | #define ntTest(a) ntDBTest(a,__FILE__,__LINE__) |
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| 54 | BOOLEAN ntDBTest(number a, const char *f,const int l); |
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| 55 | #else |
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| 56 | #define ntTest(a) |
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| 57 | #endif |
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| 58 | |
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[21972b] | 59 | static number ntdGcd( number a, number b, const ring r) { return nacInit(1,r); } |
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[b46956] | 60 | /*2 |
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| 61 | * sets the appropriate operators |
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| 62 | */ |
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| 63 | void ntSetChar(int i, ring r) |
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| 64 | { |
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[d0450f] | 65 | assume((r->minpoly == NULL) && |
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| 66 | (r->minideal == NULL) ); |
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| 67 | |
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[661c214] | 68 | if (naI!=NULL) |
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[b46956] | 69 | { |
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| 70 | int j; |
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[661c214] | 71 | for (j=naI->anz-1; j>=0; j--) |
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| 72 | p_Delete (&naI->liste[j],nacRing); |
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| 73 | omFreeSize((ADDRESS)naI->liste,naI->anz*sizeof(napoly)); |
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| 74 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
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| 75 | naI=NULL; |
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[b46956] | 76 | } |
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| 77 | ntMap = ntCopy; |
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[661c214] | 78 | naMinimalPoly = NULL; |
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[b46956] | 79 | |
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[661c214] | 80 | ntNumbOfPar=rPar(r); |
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[b46956] | 81 | if (i == 1) |
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| 82 | ntIsChar0 = 1; |
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| 83 | else if (i < 0) |
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| 84 | { |
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| 85 | ntIsChar0 = 0; |
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| 86 | npSetChar(-i, r->algring); // to be changed HS |
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| 87 | } |
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| 88 | #ifdef TEST |
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| 89 | else |
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| 90 | { |
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| 91 | Print("ntSetChar:c=%d param=%d\n",i,rPar(r)); |
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| 92 | } |
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| 93 | #endif |
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[661c214] | 94 | nacRing = r->algring; |
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[21972b] | 95 | nacInit = nacRing->cf->cfInit; |
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| 96 | nacInt = nacRing->cf->n_Int; |
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| 97 | nacCopy = nacRing->cf->nCopy; |
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| 98 | nacAdd = nacRing->cf->nAdd; |
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| 99 | nacSub = nacRing->cf->nSub; |
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| 100 | nacNormalize = nacRing->cf->nNormalize; |
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| 101 | nacNeg = nacRing->cf->nNeg; |
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| 102 | nacIsZero = nacRing->cf->nIsZero; |
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| 103 | nacGreaterZero = nacRing->cf->nGreaterZero; |
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| 104 | nacIsOne = nacRing->cf->nIsOne; |
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| 105 | nacGcd = nacRing->cf->nGcd; |
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| 106 | nacLcm = nacRing->cf->nLcm; |
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| 107 | nacMult = nacRing->cf->nMult; |
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| 108 | nacDiv = nacRing->cf->nDiv; |
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| 109 | nacIntDiv = nacRing->cf->nIntDiv; |
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| 110 | nacInvers = nacRing->cf->nInvers; |
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[661c214] | 111 | } |
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| 112 | |
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| 113 | /*============= procedure for polynomials: napXXXX =======================*/ |
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[b46956] | 114 | |
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| 115 | #ifdef LDEBUG |
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[661c214] | 116 | void napTest(napoly p) |
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[b46956] | 117 | { |
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[d0450f] | 118 | if (ntIsChar0) |
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[b46956] | 119 | { |
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[d0450f] | 120 | while (p != NULL) |
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| 121 | { |
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[b46956] | 122 | nlDBTest(pGetCoeff(p), "", 0); |
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[d0450f] | 123 | pIter(p); |
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| 124 | } |
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[b46956] | 125 | } |
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| 126 | } |
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| 127 | #else |
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[661c214] | 128 | #define napTest(p) ((void) 0) |
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[b46956] | 129 | #endif |
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| 130 | |
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[d0450f] | 131 | /* creates a new napoly that consists of a |
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| 132 | single coefficient (provided as a number); |
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| 133 | the provided number is NOT const */ |
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[661c214] | 134 | napoly napInitz(number z) |
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[b46956] | 135 | { |
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[661c214] | 136 | napoly a = (napoly)p_Init(nacRing); |
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[b46956] | 137 | pGetCoeff(a) = z; |
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| 138 | return a; |
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| 139 | } |
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| 140 | |
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[d0450f] | 141 | /* creates a new napoly which is the |
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| 142 | negative inverse of the argument; |
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| 143 | keeps p */ |
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| 144 | napoly napCopyNeg(const napoly p) |
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[b46956] | 145 | { |
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[d0450f] | 146 | napoly r = napCopy(p); |
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| 147 | r = (napoly)p_Neg((poly)r, nacRing); |
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[b46956] | 148 | return r; |
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| 149 | } |
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| 150 | |
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[d0450f] | 151 | /* modifies the napoly p to p*z, i.e. |
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| 152 | in-place multiplication of p with the number z; |
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| 153 | keeps z */ |
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| 154 | void napMultN(napoly p, const number z) |
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[b46956] | 155 | { |
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| 156 | number t; |
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[d0450f] | 157 | while (p != NULL) |
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[b46956] | 158 | { |
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[21972b] | 159 | t = nacMult(pGetCoeff(p), z); |
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| 160 | nacNormalize(t); |
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[661c214] | 161 | n_Delete(&pGetCoeff(p),nacRing); |
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[b46956] | 162 | pGetCoeff(p) = t; |
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| 163 | pIter(p); |
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| 164 | } |
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| 165 | } |
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| 166 | |
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[d0450f] | 167 | /* division of f by g with remainder |
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| 168 | (with respect to the first variable), |
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| 169 | f = g * q + r, |
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| 170 | assumes that the exponent of the first variable |
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| 171 | in f is greater than or equal to that in g |
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| 172 | sets q, r; destroys f; keeps g */ |
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| 173 | void napDivMod(napoly f, const napoly g, napoly *q, napoly *r) |
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[b46956] | 174 | { |
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| 175 | napoly a, h, b, qq; |
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| 176 | |
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[661c214] | 177 | qq = (napoly)p_Init(nacRing); |
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[b46956] | 178 | pNext(qq) = b = NULL; |
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[d0450f] | 179 | p_Normalize(g, nacRing); |
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| 180 | p_Normalize(f, nacRing); |
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[b46956] | 181 | a = f; |
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[d0450f] | 182 | assume(p_GetExp(a, 1, nacRing) >= p_GetExp(g, 1, nacRing)); |
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[b46956] | 183 | do |
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| 184 | { |
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[d0450f] | 185 | napSetExp(qq, 1, p_GetExp(a, 1, nacRing) - p_GetExp(g, 1, nacRing)); |
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| 186 | p_Setm(qq, nacRing); |
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[21972b] | 187 | pGetCoeff(qq) = nacDiv(pGetCoeff(a), pGetCoeff(g)); |
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| 188 | nacNormalize(pGetCoeff(qq)); |
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[661c214] | 189 | b = napAdd(b, napCopy(qq)); |
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[21972b] | 190 | pGetCoeff(qq) = nacNeg(pGetCoeff(qq)); |
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[661c214] | 191 | h = napCopy(g); |
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| 192 | napMultT(h, qq); |
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[d0450f] | 193 | p_Normalize(h, nacRing); |
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| 194 | n_Delete(&pGetCoeff(qq), nacRing); |
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[b46956] | 195 | a = napAdd(a, h); |
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| 196 | } |
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[d0450f] | 197 | while ((a != NULL) && |
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| 198 | (p_GetExp(a, 1, nacRing) >= p_GetExp(g, 1, nacRing))); |
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[b46956] | 199 | omFreeBinAddr(qq); |
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| 200 | *q = b; |
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| 201 | *r = a; |
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| 202 | } |
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| 203 | |
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[d0450f] | 204 | /* remainder of division of f by g |
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| 205 | (with respect to the first variable), |
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| 206 | f = g * q + r, |
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| 207 | assumes that the exponent of the first variable |
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| 208 | in f is greater than or equal to that in g |
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| 209 | destroys f; keeps g; returns r */ |
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| 210 | napoly napRemainder(napoly f, const napoly g) |
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| 211 | { |
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| 212 | napoly a, h, qq; |
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| 213 | |
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| 214 | qq = (napoly)p_Init(nacRing); |
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| 215 | pNext(qq) = NULL; |
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| 216 | p_Normalize(g, nacRing); |
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| 217 | p_Normalize(f, nacRing); |
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| 218 | a = f; |
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| 219 | assume(p_GetExp(a, 1, nacRing) >= p_GetExp(g, 1, nacRing)); |
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| 220 | do |
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| 221 | { |
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| 222 | napSetExp(qq, 1, p_GetExp(a, 1, nacRing) - p_GetExp(g, 1, nacRing)); |
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| 223 | napSetm(qq); |
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| 224 | pGetCoeff(qq) = nacDiv(pGetCoeff(a), pGetCoeff(g)); |
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| 225 | pGetCoeff(qq) = nacNeg(pGetCoeff(qq)); |
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| 226 | nacNormalize(pGetCoeff(qq)); |
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| 227 | h = napCopy(g); |
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| 228 | napMultT(h, qq); |
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| 229 | p_Normalize(h, nacRing); |
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| 230 | n_Delete(&pGetCoeff(qq), nacRing); |
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| 231 | a = napAdd(a, h); |
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| 232 | } |
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| 233 | while ((a != NULL) && |
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| 234 | (p_GetExp(a,1,nacRing) >= p_GetExp(g,1,nacRing))); |
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| 235 | omFreeBinAddr(qq); |
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| 236 | return a; |
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| 237 | } |
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| 238 | |
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| 239 | /* returns z such that z * x mod c = 1; |
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| 240 | if there is no solution, an error is reported and |
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| 241 | some intermediate version of x is returned; |
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| 242 | modifies x; keeps c */ |
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[661c214] | 243 | napoly napInvers(napoly x, const napoly c) |
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[b46956] | 244 | { |
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| 245 | napoly y, r, qa, qn, q; |
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| 246 | number t, h; |
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| 247 | |
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[d0450f] | 248 | if (p_GetExp(x, 1, nacRing) >= p_GetExp(c, 1, nacRing)) |
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| 249 | x = napRemainder(x, c); |
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| 250 | if (x == NULL) |
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[b46956] | 251 | { |
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[d5ad46f] | 252 | WerrorS("zero divisor found - your minpoly is not irreducible"); |
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| 253 | return NULL; |
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[b46956] | 254 | } |
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[d0450f] | 255 | if (p_GetExp(x, 1, nacRing) == 0) |
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[b46956] | 256 | { |
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[21972b] | 257 | if (!nacIsOne(pGetCoeff(x))) |
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[b46956] | 258 | { |
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[21972b] | 259 | nacNormalize(pGetCoeff(x)); |
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| 260 | t = nacInvers(pGetCoeff(x)); |
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| 261 | nacNormalize(t); |
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[d0450f] | 262 | n_Delete(&pGetCoeff(x), nacRing); |
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[b46956] | 263 | pGetCoeff(x) = t; |
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| 264 | } |
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| 265 | return x; |
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| 266 | } |
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[661c214] | 267 | y = napCopy(c); |
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| 268 | napDivMod(y, x, &qa, &r); |
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[d0450f] | 269 | if (r == NULL) |
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[b46956] | 270 | { |
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[8eea06] | 271 | WerrorS("x is not invertible modulo c(1)"); |
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[d0450f] | 272 | return x; |
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[b46956] | 273 | } |
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[d0450f] | 274 | if (p_GetExp(r, 1, nacRing) == 0) |
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[b46956] | 275 | { |
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[21972b] | 276 | nacNormalize(pGetCoeff(r)); |
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| 277 | t = nacInvers(pGetCoeff(r)); |
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| 278 | nacNormalize(t); |
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| 279 | t = nacNeg(t); |
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[661c214] | 280 | napMultN(qa, t); |
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[d0450f] | 281 | n_Delete(&t, nacRing); |
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| 282 | p_Normalize(qa, nacRing); |
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| 283 | p_Delete(&x, nacRing); |
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| 284 | p_Delete(&r, nacRing); |
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[b46956] | 285 | return qa; |
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| 286 | } |
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| 287 | y = x; |
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| 288 | x = r; |
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[661c214] | 289 | napDivMod(y, x, &q, &r); |
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[d0450f] | 290 | if (r == NULL) |
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[b46956] | 291 | { |
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[8eea06] | 292 | WerrorS("x is not invertible modulo c(2)"); |
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[d0450f] | 293 | return x; |
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[b46956] | 294 | } |
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[d0450f] | 295 | if (p_GetExp(r, 1, nacRing) == 0) |
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[b46956] | 296 | { |
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[661c214] | 297 | q = p_Mult_q(q, qa,nacRing); |
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[d0450f] | 298 | q = napAdd(q, p_ISet(1, nacRing)); |
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[21972b] | 299 | nacNormalize(pGetCoeff(r)); |
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| 300 | t = nacInvers(pGetCoeff(r)); |
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[661c214] | 301 | napMultN(q, t); |
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[d0450f] | 302 | p_Normalize(q, nacRing); |
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| 303 | n_Delete(&t, nacRing); |
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| 304 | p_Delete(&x, nacRing); |
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| 305 | p_Delete(&r, nacRing); |
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| 306 | if (p_GetExp(q, 1, nacRing) >= p_GetExp(c, 1, nacRing)) |
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| 307 | q = napRemainder(q, c); |
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[b46956] | 308 | return q; |
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| 309 | } |
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[d0450f] | 310 | q = p_Mult_q(q, napCopy(qa), nacRing); |
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| 311 | q = napAdd(q, p_ISet(1, nacRing)); |
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[b46956] | 312 | qa = napNeg(qa); |
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| 313 | loop |
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| 314 | { |
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| 315 | y = x; |
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| 316 | x = r; |
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[661c214] | 317 | napDivMod(y, x, &qn, &r); |
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[d0450f] | 318 | if (r == NULL) |
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[b46956] | 319 | { |
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[8eea06] | 320 | WerrorS("zero divisor found - your minpoly is not irreducible"); |
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[d0450f] | 321 | return x; |
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[b46956] | 322 | } |
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[d0450f] | 323 | if (p_GetExp(r, 1, nacRing) == 0) |
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[b46956] | 324 | { |
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[d0450f] | 325 | q = p_Mult_q(q, qn, nacRing); |
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[b46956] | 326 | q = napNeg(q); |
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| 327 | q = napAdd(q, qa); |
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[21972b] | 328 | nacNormalize(pGetCoeff(r)); |
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| 329 | t = nacInvers(pGetCoeff(r)); |
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| 330 | //nacNormalize(t); |
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[661c214] | 331 | napMultN(q, t); |
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[d0450f] | 332 | p_Normalize(q, nacRing); |
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| 333 | n_Delete(&t, nacRing); |
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| 334 | p_Delete(&x, nacRing); |
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| 335 | p_Delete(&r, nacRing); |
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| 336 | if (p_GetExp(q, 1, nacRing) >= p_GetExp(c, 1, nacRing)) |
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| 337 | q = napRemainder(q, c); |
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[b46956] | 338 | return q; |
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| 339 | } |
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| 340 | y = q; |
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[661c214] | 341 | q = p_Mult_q(napCopy(q), qn, nacRing); |
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[b46956] | 342 | q = napNeg(q); |
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| 343 | q = napAdd(q, qa); |
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| 344 | qa = y; |
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| 345 | } |
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| 346 | } |
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| 347 | |
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[d0450f] | 348 | /* the degree of a napoly, i.e. the |
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| 349 | maximum of all terms' degrees; |
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| 350 | keeps p */ |
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| 351 | int napMaxDeg(napoly p) |
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[b46956] | 352 | { |
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| 353 | int d = 0; |
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[d0450f] | 354 | while (p != NULL) |
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[b46956] | 355 | { |
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[d0450f] | 356 | d=si_max(d, napDeg(p)); |
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[b46956] | 357 | pIter(p); |
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| 358 | } |
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| 359 | return d; |
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| 360 | } |
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| 361 | |
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[d0450f] | 362 | /* the degree of a napoly, i.e. the |
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| 363 | maximum of all terms' degrees; |
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| 364 | fills l with the number of terms; |
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| 365 | keeps p */ |
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| 366 | int napMaxDegLen(napoly p, int &l) |
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[b46956] | 367 | { |
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[d0450f] | 368 | int d = 0; |
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| 369 | l = 0; |
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| 370 | while (p != NULL) |
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[b46956] | 371 | { |
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[d0450f] | 372 | d = si_max(d, napDeg(p)); |
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[b46956] | 373 | pIter(p); |
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[d0450f] | 374 | l++; |
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[b46956] | 375 | } |
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| 376 | return d; |
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| 377 | } |
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| 378 | |
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| 379 | |
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[d0450f] | 380 | /* writes a napoly, i.e. a number in the ground field; |
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| 381 | if has_denom is TRUE, the output is ready to be |
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| 382 | followed by a non-trivial denominator; |
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| 383 | r is assumed to be a polynomial ring over an algebraic |
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| 384 | or transcendental field extension; |
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| 385 | keeps all arguments */ |
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| 386 | void napWrite(napoly p, const BOOLEAN has_denom, const ring r) |
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[b46956] | 387 | { |
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[d0450f] | 388 | ring nacring = r->algring; |
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| 389 | if (p == NULL) StringAppendS("0"); |
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| 390 | else if (p_LmIsConstant(p, nacring)) |
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[b46956] | 391 | { |
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[d0450f] | 392 | BOOLEAN kl = FALSE; |
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[b46956] | 393 | if (has_denom) |
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| 394 | { |
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[d0450f] | 395 | number den = nacring->cf->cfGetDenom(pGetCoeff(p), nacring); |
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| 396 | kl = !n_IsOne(den, nacring); |
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[661c214] | 397 | n_Delete(&den, nacring); |
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[b46956] | 398 | } |
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| 399 | if (kl) StringAppendS("("); |
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[d0450f] | 400 | n_Write(pGetCoeff(p), nacring); |
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[b46956] | 401 | if (kl) StringAppendS(")"); |
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| 402 | } |
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| 403 | else |
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| 404 | { |
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| 405 | StringAppendS("("); |
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| 406 | loop |
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| 407 | { |
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[d0450f] | 408 | BOOLEAN wroteCoeff = FALSE; |
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| 409 | if ((p_LmIsConstant(p, nacring)) || |
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| 410 | ((!n_IsOne(pGetCoeff(p), nacring)) && |
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| 411 | (!n_IsMOne(pGetCoeff(p),nacring)))) |
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[b46956] | 412 | { |
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[d0450f] | 413 | n_Write(pGetCoeff(p), nacring); |
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| 414 | wroteCoeff = (r->ShortOut == 0); |
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[b46956] | 415 | } |
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[d0450f] | 416 | else if (n_IsMOne(pGetCoeff(p), nacring)) StringAppendS("-"); |
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| 417 | for (int i = 0; i < r->P; i++) |
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[b46956] | 418 | { |
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[d0450f] | 419 | int e = p_GetExp(p, i+1, nacring); |
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[b46956] | 420 | if (e > 0) |
---|
| 421 | { |
---|
[d0450f] | 422 | if (wroteCoeff) StringAppendS("*"); |
---|
| 423 | else wroteCoeff=(r->ShortOut==0); |
---|
[b46956] | 424 | StringAppendS(r->parameter[i]); |
---|
| 425 | if (e > 1) |
---|
| 426 | { |
---|
[d0450f] | 427 | if (r->ShortOut == 0) StringAppendS("^"); |
---|
[b46956] | 428 | StringAppend("%d", e); |
---|
| 429 | } |
---|
| 430 | } |
---|
[d0450f] | 431 | } |
---|
[b46956] | 432 | pIter(p); |
---|
[d0450f] | 433 | if (p == NULL) break; |
---|
| 434 | if (n_GreaterZero(pGetCoeff(p),nacring)) StringAppendS("+"); |
---|
[b46956] | 435 | } |
---|
| 436 | StringAppendS(")"); |
---|
| 437 | } |
---|
| 438 | } |
---|
| 439 | |
---|
[d0450f] | 440 | /* helper for napRead */ |
---|
| 441 | const char* napHandleMons(const char* s, int i, napoly ex) |
---|
[b46956] | 442 | { |
---|
[d0450f] | 443 | int j; |
---|
| 444 | if (strncmp(s, ntParNames[i], strlen(ntParNames[i])) == 0) |
---|
[b46956] | 445 | { |
---|
[d0450f] | 446 | s += strlen(ntParNames[i]); |
---|
[b46956] | 447 | if ((*s >= '0') && (*s <= '9')) |
---|
| 448 | { |
---|
| 449 | s = eati(s, &j); |
---|
[d0450f] | 450 | napAddExp(ex, i+1, j); |
---|
[b46956] | 451 | } |
---|
| 452 | else |
---|
[d0450f] | 453 | napAddExp(ex, i+1, 1); |
---|
[b46956] | 454 | } |
---|
| 455 | return s; |
---|
| 456 | } |
---|
[d0450f] | 457 | |
---|
| 458 | /* helper for napRead */ |
---|
| 459 | const char* napHandlePars(const char *s, int i, napoly ex) |
---|
[b46956] | 460 | { |
---|
[d0450f] | 461 | int j; |
---|
| 462 | if (strcmp(s, ntParNames[i]) == 0) |
---|
[b46956] | 463 | { |
---|
[d0450f] | 464 | s += strlen(ntParNames[i]); |
---|
| 465 | napSetExp(ex, i+1, 1); |
---|
[b46956] | 466 | } |
---|
| 467 | return s; |
---|
| 468 | } |
---|
| 469 | |
---|
[d0450f] | 470 | /* reads a monomial into the napoly b; |
---|
| 471 | returns the latter portion of s which |
---|
| 472 | comes "after" the monomial that has |
---|
| 473 | just been read; |
---|
| 474 | modifies b */ |
---|
| 475 | const char* napRead(const char *s, napoly *b) |
---|
[b46956] | 476 | { |
---|
| 477 | napoly a; |
---|
[d0450f] | 478 | int i; |
---|
[661c214] | 479 | a = (napoly)p_Init(nacRing); |
---|
[b46956] | 480 | if ((*s >= '0') && (*s <= '9')) |
---|
| 481 | { |
---|
[2d3daa] | 482 | s = nacRing->cf->nRead(s, &pGetCoeff(a)); |
---|
[21972b] | 483 | if (nacIsZero(pGetCoeff(a))) |
---|
[b46956] | 484 | { |
---|
[d0450f] | 485 | p_LmDelete(&a, nacRing); |
---|
[b46956] | 486 | *b = NULL; |
---|
| 487 | return s; |
---|
| 488 | } |
---|
| 489 | } |
---|
[d0450f] | 490 | else pGetCoeff(a) = nacInit(1,nacRing); |
---|
[b46956] | 491 | i = 0; |
---|
[d0450f] | 492 | const char* olds = s; |
---|
[b46956] | 493 | loop |
---|
| 494 | { |
---|
[661c214] | 495 | s = napHandlePars(s, i, a); |
---|
[d0450f] | 496 | if (olds == s) i++; |
---|
[b46956] | 497 | else if (*s == '\0') |
---|
| 498 | { |
---|
| 499 | *b = a; |
---|
| 500 | return s; |
---|
| 501 | } |
---|
[d0450f] | 502 | if (i >= ntNumbOfPar) break; |
---|
[b46956] | 503 | } |
---|
[d0450f] | 504 | i = 0; |
---|
[b46956] | 505 | loop |
---|
| 506 | { |
---|
| 507 | olds = s; |
---|
[661c214] | 508 | s = napHandleMons(s, i, a); |
---|
[d0450f] | 509 | if (olds == s) i++; |
---|
| 510 | else i = 0; |
---|
| 511 | if ((*s == '\0') || (i >= ntNumbOfPar)) break; |
---|
[b46956] | 512 | } |
---|
| 513 | *b = a; |
---|
| 514 | return s; |
---|
| 515 | } |
---|
| 516 | |
---|
[d0450f] | 517 | /* considers the lowest terms la of a and lb of b; |
---|
| 518 | returns the minimum of the two exponents of the |
---|
| 519 | first variable in la and lb; |
---|
[152d55] | 520 | assumes a != NULL, b != NULL; |
---|
[d0450f] | 521 | keeps a and b */ |
---|
[661c214] | 522 | int napExp(napoly a, napoly b) |
---|
[b46956] | 523 | { |
---|
[152d55] | 524 | assume(a != NULL); |
---|
| 525 | assume(b != NULL); |
---|
[d0450f] | 526 | while (pNext(a) != NULL) pIter(a); |
---|
| 527 | int m = p_GetExp(a, 1, nacRing); |
---|
| 528 | if (m == 0) return 0; |
---|
| 529 | while (pNext(b) != NULL) pIter(b); |
---|
| 530 | int mm = p_GetExp(b, 1, nacRing); |
---|
[b46956] | 531 | if (m > mm) m = mm; |
---|
| 532 | return m; |
---|
| 533 | } |
---|
| 534 | |
---|
[d0450f] | 535 | /* returns the smallest i-th exponent in a and b; |
---|
| 536 | used to find it in a fraction; |
---|
| 537 | keeps a and b */ |
---|
[661c214] | 538 | int napExpi(int i, napoly a, napoly b) |
---|
[b46956] | 539 | { |
---|
[d0450f] | 540 | if (a == NULL || b == NULL) return 0; |
---|
| 541 | int m = p_GetExp(a, i+1, nacRing); |
---|
| 542 | if (m == 0) return 0; |
---|
[b46956] | 543 | while (pNext(a) != NULL) |
---|
| 544 | { |
---|
| 545 | pIter(a); |
---|
[d0450f] | 546 | if (m > p_GetExp(a, i+1, nacRing)) |
---|
[b46956] | 547 | { |
---|
[d0450f] | 548 | m = p_GetExp(a, i+1, nacRing); |
---|
| 549 | if (m == 0) return 0; |
---|
[b46956] | 550 | } |
---|
| 551 | } |
---|
| 552 | do |
---|
| 553 | { |
---|
[d0450f] | 554 | if (m > p_GetExp(b, i+1, nacRing)) |
---|
[b46956] | 555 | { |
---|
[d0450f] | 556 | m = p_GetExp(b, i+1, nacRing); |
---|
| 557 | if (m == 0) return 0; |
---|
[b46956] | 558 | } |
---|
| 559 | pIter(b); |
---|
| 560 | } |
---|
| 561 | while (b != NULL); |
---|
| 562 | return m; |
---|
| 563 | } |
---|
| 564 | |
---|
[d0450f] | 565 | /* divides out the content of the given napoly; |
---|
[152d55] | 566 | assumes that ph != NULL; |
---|
| 567 | modifies ph */ |
---|
[661c214] | 568 | void napContent(napoly ph) |
---|
[b46956] | 569 | { |
---|
[d0450f] | 570 | number h, d; |
---|
[b46956] | 571 | napoly p; |
---|
| 572 | |
---|
[152d55] | 573 | assume(ph != NULL); |
---|
[b46956] | 574 | p = ph; |
---|
[d0450f] | 575 | if (nacIsOne(pGetCoeff(p))) return; |
---|
[21972b] | 576 | h = nacCopy(pGetCoeff(p)); |
---|
[b46956] | 577 | pIter(p); |
---|
[152d55] | 578 | while (p != NULL) |
---|
[b46956] | 579 | { |
---|
[d0450f] | 580 | d = nacGcd(pGetCoeff(p), h, nacRing); |
---|
| 581 | if (nacIsOne(d)) |
---|
[b46956] | 582 | { |
---|
[661c214] | 583 | n_Delete(&h,nacRing); |
---|
| 584 | n_Delete(&d,nacRing); |
---|
[b46956] | 585 | return; |
---|
| 586 | } |
---|
[d0450f] | 587 | n_Delete(&h, nacRing); |
---|
[b46956] | 588 | h = d; |
---|
| 589 | pIter(p); |
---|
| 590 | } |
---|
[21972b] | 591 | h = nacInvers(d); |
---|
[d0450f] | 592 | n_Delete(&d, nacRing); |
---|
[b46956] | 593 | p = ph; |
---|
[d0450f] | 594 | while (p != NULL) |
---|
[b46956] | 595 | { |
---|
[21972b] | 596 | d = nacMult(pGetCoeff(p), h); |
---|
[d0450f] | 597 | n_Delete(&pGetCoeff(p), nacRing); |
---|
[b46956] | 598 | pGetCoeff(p) = d; |
---|
| 599 | pIter(p); |
---|
| 600 | } |
---|
[d0450f] | 601 | n_Delete(&h, nacRing); |
---|
[b46956] | 602 | } |
---|
| 603 | |
---|
[152d55] | 604 | /* removes denominators of coefficients in ph |
---|
| 605 | by multiplication with lcm of those; |
---|
| 606 | if char != 0, then nothing is done; |
---|
| 607 | modifies ph */ |
---|
[661c214] | 608 | void napCleardenom(napoly ph) |
---|
[b46956] | 609 | { |
---|
| 610 | number d, h; |
---|
| 611 | napoly p; |
---|
| 612 | |
---|
[d0450f] | 613 | if (!ntIsChar0) return; |
---|
[b46956] | 614 | p = ph; |
---|
[21972b] | 615 | h = nacInit(1,nacRing); |
---|
[b46956] | 616 | while (p!=NULL) |
---|
| 617 | { |
---|
[152d55] | 618 | d = nacLcm(h, pGetCoeff(p), nacRing); // uses denominator of pGetCoeff(p) |
---|
[661c214] | 619 | n_Delete(&h,nacRing); |
---|
[b46956] | 620 | h = d; |
---|
| 621 | pIter(p); |
---|
| 622 | } |
---|
[21972b] | 623 | if(!nacIsOne(h)) |
---|
[b46956] | 624 | { |
---|
| 625 | p = ph; |
---|
| 626 | while (p!=NULL) |
---|
| 627 | { |
---|
[21972b] | 628 | d=nacMult(h, pGetCoeff(p)); |
---|
[661c214] | 629 | n_Delete(&pGetCoeff(p),nacRing); |
---|
[21972b] | 630 | nacNormalize(d); |
---|
[b46956] | 631 | pGetCoeff(p) = d; |
---|
| 632 | pIter(p); |
---|
| 633 | } |
---|
| 634 | } |
---|
[152d55] | 635 | n_Delete(&h,nacRing); |
---|
[661c214] | 636 | napContent(ph); |
---|
[b46956] | 637 | } |
---|
| 638 | |
---|
[152d55] | 639 | /* returns the gcd of all coefficients in a and b; |
---|
| 640 | assumes a != NULL, b != NULL; |
---|
| 641 | keeps a, keeps b */ |
---|
[661c214] | 642 | napoly napGcd0(napoly a, napoly b) |
---|
[b46956] | 643 | { |
---|
| 644 | number x, y; |
---|
[152d55] | 645 | assume(a != NULL); |
---|
| 646 | assume(b != NULL); |
---|
[d0450f] | 647 | if (!ntIsChar0) return p_ISet(1, nacRing); |
---|
[21972b] | 648 | x = nacCopy(pGetCoeff(a)); |
---|
[152d55] | 649 | if (nacIsOne(x)) return napInitz(x); |
---|
| 650 | pIter(a); |
---|
| 651 | while (a!=NULL) |
---|
[b46956] | 652 | { |
---|
[21972b] | 653 | y = nacGcd(x, pGetCoeff(a), nacRing); |
---|
[661c214] | 654 | n_Delete(&x,nacRing); |
---|
[b46956] | 655 | x = y; |
---|
[152d55] | 656 | if (nacIsOne(x)) return napInitz(x); |
---|
| 657 | pIter(a); |
---|
[b46956] | 658 | } |
---|
| 659 | do |
---|
| 660 | { |
---|
[21972b] | 661 | y = nacGcd(x, pGetCoeff(b), nacRing); |
---|
[661c214] | 662 | n_Delete(&x,nacRing); |
---|
[b46956] | 663 | x = y; |
---|
[152d55] | 664 | if (nacIsOne(x)) return napInitz(x); |
---|
[b46956] | 665 | pIter(b); |
---|
| 666 | } |
---|
| 667 | while (b!=NULL); |
---|
[661c214] | 668 | return napInitz(x); |
---|
[b46956] | 669 | } |
---|
| 670 | |
---|
[152d55] | 671 | /* returns the gcd of a and b; |
---|
| 672 | if char != 0, then the constant poly 1 is returned; |
---|
| 673 | if a = b = 0, then the constant poly 1 is returned; |
---|
| 674 | if a = 0 != b, then b is returned; |
---|
| 675 | if a != 0 = b, then a is returned; |
---|
| 676 | keeps a, keeps b */ |
---|
[661c214] | 677 | napoly napGcd(napoly a, napoly b) |
---|
[b46956] | 678 | { |
---|
| 679 | int i; |
---|
| 680 | napoly g, x, y, h; |
---|
[152d55] | 681 | if (a == NULL) |
---|
[b46956] | 682 | { |
---|
[152d55] | 683 | if (b == NULL) return p_ISet(1,nacRing); |
---|
| 684 | else return napCopy(b); |
---|
[661c214] | 685 | } |
---|
[152d55] | 686 | else if (b == NULL) return napCopy(a); |
---|
| 687 | |
---|
[661c214] | 688 | if (naMinimalPoly != NULL) |
---|
[152d55] | 689 | { // we have an algebraic extension |
---|
[661c214] | 690 | if (p_GetExp(a,1,nacRing) >= p_GetExp(b,1,nacRing)) |
---|
| 691 | { |
---|
| 692 | x = a; |
---|
| 693 | y = b; |
---|
| 694 | } |
---|
| 695 | else |
---|
| 696 | { |
---|
| 697 | x = b; |
---|
| 698 | y = a; |
---|
| 699 | } |
---|
| 700 | if (!ntIsChar0) g = p_ISet(1,nacRing); |
---|
| 701 | else g = napGcd0(x, y); |
---|
| 702 | if (pNext(y)==NULL) |
---|
| 703 | { |
---|
| 704 | napSetExp(g,1, napExp(x, y)); |
---|
| 705 | p_Setm(g,nacRing); |
---|
| 706 | return g; |
---|
| 707 | } |
---|
| 708 | x = napCopy(x); |
---|
| 709 | y = napCopy(y); |
---|
| 710 | loop |
---|
| 711 | { |
---|
[d0450f] | 712 | h = napRemainder(x, y); |
---|
[661c214] | 713 | if (h==NULL) |
---|
| 714 | { |
---|
| 715 | napCleardenom(y); |
---|
[21972b] | 716 | if (!nacIsOne(pGetCoeff(g))) |
---|
[661c214] | 717 | napMultN(y, pGetCoeff(g)); |
---|
| 718 | p_LmDelete(&g,nacRing); |
---|
| 719 | return y; |
---|
| 720 | } |
---|
| 721 | else if (pNext(h)==NULL) |
---|
| 722 | break; |
---|
| 723 | x = y; |
---|
| 724 | y = h; |
---|
| 725 | } |
---|
| 726 | p_Delete(&y,nacRing); |
---|
| 727 | p_LmDelete(&h,nacRing); |
---|
| 728 | napSetExp(g,1, napExp(a, b)); |
---|
| 729 | p_Setm(g,nacRing); |
---|
| 730 | return g; |
---|
[b46956] | 731 | } |
---|
[152d55] | 732 | else |
---|
| 733 | { // we have ntNumbOfPar transcendental variables |
---|
| 734 | if (!ntIsChar0) x = p_ISet(1,nacRing); |
---|
| 735 | else x = napGcd0(a,b); |
---|
| 736 | for (i=(ntNumbOfPar-1); i>=0; i--) |
---|
| 737 | { |
---|
| 738 | napSetExp(x,i+1, napExpi(i,a,b)); |
---|
| 739 | p_Setm(x,nacRing); |
---|
| 740 | } |
---|
| 741 | return x; |
---|
[b46956] | 742 | } |
---|
| 743 | } |
---|
| 744 | |
---|
[152d55] | 745 | /* returns the lcm of all denominators in the coefficients of a; |
---|
| 746 | if char != 0, then the constant poly 1 is returned; |
---|
| 747 | if a = 0, then the constant poly 1 is returned; |
---|
| 748 | keeps a */ |
---|
[661c214] | 749 | number napLcm(napoly a) |
---|
[b46956] | 750 | { |
---|
[21972b] | 751 | number h = nacInit(1,nacRing); |
---|
[b46956] | 752 | if (ntIsChar0) |
---|
| 753 | { |
---|
| 754 | number d; |
---|
| 755 | napoly b = a; |
---|
| 756 | while (b!=NULL) |
---|
| 757 | { |
---|
[152d55] | 758 | d = nacLcm(h, pGetCoeff(b), nacRing); // uses denominator of pGetCoeff(b) |
---|
[661c214] | 759 | n_Delete(&h,nacRing); |
---|
[b46956] | 760 | h = d; |
---|
| 761 | pIter(b); |
---|
| 762 | } |
---|
| 763 | } |
---|
| 764 | return h; |
---|
| 765 | } |
---|
| 766 | |
---|
| 767 | /*2 |
---|
| 768 | * meins (for reduction in algebraic extension) |
---|
| 769 | * checks if head of p divides head of q |
---|
| 770 | * doesn't delete p and q |
---|
| 771 | */ |
---|
[661c214] | 772 | BOOLEAN napDivPoly (napoly p, napoly q) |
---|
[b46956] | 773 | { |
---|
[661c214] | 774 | int j=1; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
[b46956] | 775 | |
---|
[661c214] | 776 | while (p_GetExp(p,j,nacRing) <= p_GetExp(q,j,nacRing)) |
---|
[b46956] | 777 | { |
---|
| 778 | j++; |
---|
[661c214] | 779 | if (j > ntNumbOfPar) |
---|
[b46956] | 780 | return 1; |
---|
| 781 | } |
---|
| 782 | return 0; |
---|
| 783 | } |
---|
| 784 | |
---|
| 785 | |
---|
[d0450f] | 786 | /* |
---|
| 787 | * only used for reduction in algebraic extensions when naI != NULL; |
---|
| 788 | * reduces the tail of poly q which is required to be != NULL; |
---|
| 789 | * modifies q and returns it |
---|
| 790 | */ |
---|
[661c214] | 791 | napoly napRedp (napoly q) |
---|
[b46956] | 792 | { |
---|
[661c214] | 793 | napoly h = (napoly)p_Init(nacRing); |
---|
[b46956] | 794 | int i=0,j; |
---|
| 795 | |
---|
| 796 | loop |
---|
| 797 | { |
---|
[661c214] | 798 | if (napDivPoly (naI->liste[i], q)) |
---|
[b46956] | 799 | { |
---|
[661c214] | 800 | /* h = lt(q)/lt(naI->liste[i])*/ |
---|
[21972b] | 801 | pGetCoeff(h) = nacCopy(pGetCoeff(q)); |
---|
[661c214] | 802 | for (j=ntNumbOfPar; j>0; j--) |
---|
[d0450f] | 803 | napSetExp(h,j, p_GetExp(q,j,nacRing) - p_GetExp(naI->liste[i], |
---|
| 804 | j,nacRing)); |
---|
[661c214] | 805 | p_Setm(h,nacRing); |
---|
| 806 | h = p_Mult_q(h, napCopy(naI->liste[i]),nacRing); |
---|
[b46956] | 807 | h = napNeg (h); |
---|
[661c214] | 808 | q = napAdd (q, napCopy(h)); |
---|
| 809 | p_Delete (&pNext(h),nacRing); |
---|
[b46956] | 810 | if (q == NULL) |
---|
| 811 | { |
---|
[661c214] | 812 | p_Delete(&h,nacRing); |
---|
[b46956] | 813 | return q; |
---|
| 814 | } |
---|
| 815 | /* try to reduce further */ |
---|
| 816 | i = 0; |
---|
| 817 | } |
---|
| 818 | else |
---|
| 819 | { |
---|
| 820 | i++; |
---|
[661c214] | 821 | if (i >= naI->anz) |
---|
[b46956] | 822 | { |
---|
[661c214] | 823 | p_Delete(&h,nacRing); |
---|
[b46956] | 824 | return q; |
---|
| 825 | } |
---|
| 826 | } |
---|
| 827 | } |
---|
| 828 | } |
---|
| 829 | |
---|
| 830 | |
---|
[d0450f] | 831 | /* |
---|
| 832 | * only used for reduction in algebraic extensions when naI != NULL; |
---|
| 833 | * reduces the tail of poly q which is required to be != NULL; |
---|
| 834 | * modifies q and returns it |
---|
| 835 | */ |
---|
[661c214] | 836 | napoly napTailred (napoly q) |
---|
[b46956] | 837 | { |
---|
| 838 | napoly h; |
---|
| 839 | |
---|
| 840 | h = pNext(q); |
---|
| 841 | while (h != NULL) |
---|
| 842 | { |
---|
[661c214] | 843 | h = napRedp (h); |
---|
[b46956] | 844 | if (h == NULL) |
---|
| 845 | return q; |
---|
| 846 | pIter(h); |
---|
| 847 | } |
---|
| 848 | return q; |
---|
| 849 | } |
---|
| 850 | |
---|
[661c214] | 851 | napoly napMap(napoly p) |
---|
| 852 | { |
---|
| 853 | napoly w, a; |
---|
| 854 | |
---|
| 855 | if (p==NULL) return NULL; |
---|
| 856 | a = w = (napoly)p_Init(nacRing); |
---|
| 857 | int i; |
---|
| 858 | for(i=1;i<=ntParsToCopy;i++) |
---|
| 859 | napSetExp(a,i,napGetExpFrom(p,i,ntMapRing)); |
---|
| 860 | p_Setm(a,nacRing); |
---|
[21972b] | 861 | pGetCoeff(w) = nacMap(pGetCoeff(p)); |
---|
[661c214] | 862 | loop |
---|
| 863 | { |
---|
| 864 | pIter(p); |
---|
| 865 | if (p==NULL) break; |
---|
| 866 | pNext(a) = (napoly)p_Init(nacRing); |
---|
| 867 | pIter(a); |
---|
| 868 | for(i=1;i<=ntParsToCopy;i++) |
---|
| 869 | napSetExp(a,i,napGetExpFrom(p,i,ntMapRing)); |
---|
| 870 | p_Setm(a,nacRing); |
---|
[21972b] | 871 | pGetCoeff(a) = nacMap(pGetCoeff(p)); |
---|
[661c214] | 872 | } |
---|
| 873 | pNext(a) = NULL; |
---|
| 874 | return w; |
---|
| 875 | } |
---|
| 876 | |
---|
| 877 | napoly napPerm(napoly p,const int *par_perm,const ring src_ring,const nMapFunc nMap) |
---|
| 878 | { |
---|
| 879 | napoly w, a; |
---|
| 880 | |
---|
| 881 | if (p==NULL) return NULL; |
---|
| 882 | w = (napoly)p_Init(nacRing); |
---|
| 883 | int i; |
---|
| 884 | BOOLEAN not_null=TRUE; |
---|
| 885 | loop |
---|
| 886 | { |
---|
| 887 | for(i=1;i<=rPar(src_ring);i++) |
---|
| 888 | { |
---|
| 889 | int e; |
---|
| 890 | if (par_perm!=NULL) e=par_perm[i-1]; |
---|
| 891 | else e=-i; |
---|
| 892 | int ee=napGetExpFrom(p,i,src_ring); |
---|
| 893 | if (e<0) |
---|
| 894 | napSetExp(w,-e,ee); |
---|
| 895 | else if (ee>0) |
---|
| 896 | not_null=FALSE; |
---|
| 897 | } |
---|
| 898 | pGetCoeff(w) = nMap(pGetCoeff(p)); |
---|
| 899 | p_Setm(w,nacRing); |
---|
| 900 | pIter(p); |
---|
| 901 | if (!not_null) |
---|
| 902 | { |
---|
| 903 | if (p==NULL) |
---|
| 904 | { |
---|
| 905 | p_Delete(&w,nacRing); |
---|
| 906 | return NULL; |
---|
| 907 | } |
---|
| 908 | /* else continue*/ |
---|
| 909 | n_Delete(&(pGetCoeff(w)),nacRing); |
---|
| 910 | } |
---|
| 911 | else |
---|
| 912 | { |
---|
| 913 | if (p==NULL) return w; |
---|
| 914 | else |
---|
| 915 | { |
---|
| 916 | pNext(w)=napPerm(p,par_perm,src_ring,nMap); |
---|
| 917 | return w; |
---|
| 918 | } |
---|
| 919 | } |
---|
| 920 | } |
---|
| 921 | } |
---|
| 922 | |
---|
| 923 | /*2 |
---|
| 924 | * convert a napoly number into a poly |
---|
| 925 | */ |
---|
| 926 | poly napPermNumber(number z, int * par_perm, int P, ring oldRing) |
---|
| 927 | { |
---|
| 928 | if (z==NULL) return NULL; |
---|
| 929 | poly res=NULL; |
---|
| 930 | poly p; |
---|
| 931 | napoly za=((lnumber)z)->z; |
---|
| 932 | napoly zb=((lnumber)z)->n; |
---|
[d0450f] | 933 | nMapFunc nMap=naSetMap(oldRing,currRing); /* todo: check naSetMap |
---|
| 934 | vs. ntSetMap */ |
---|
[661c214] | 935 | if (currRing->parameter!=NULL) |
---|
| 936 | nMap=currRing->algring->cf->cfSetMap(oldRing->algring, nacRing); |
---|
| 937 | else |
---|
| 938 | nMap=currRing->cf->cfSetMap(oldRing->algring, currRing); |
---|
| 939 | if (nMap==NULL) return NULL; /* emergency exit only */ |
---|
[528f5b7] | 940 | while(za!=NULL) |
---|
[661c214] | 941 | { |
---|
| 942 | p = pInit(); |
---|
| 943 | pNext(p)=NULL; |
---|
| 944 | nNew(&pGetCoeff(p)); |
---|
| 945 | int i; |
---|
| 946 | for(i=pVariables;i;i--) |
---|
| 947 | pSetExp(p,i, 0); |
---|
| 948 | if (rRing_has_Comp(currRing)) pSetComp(p, 0); |
---|
| 949 | napoly pa=NULL; |
---|
| 950 | lnumber pan; |
---|
| 951 | if (currRing->parameter!=NULL) |
---|
| 952 | { |
---|
| 953 | assume(oldRing->algring!=NULL); |
---|
| 954 | pGetCoeff(p)=(number)omAlloc0Bin(rnumber_bin); |
---|
| 955 | pan=(lnumber)pGetCoeff(p); |
---|
| 956 | pan->s=2; |
---|
| 957 | pan->z=napInitz(nMap(pGetCoeff(za))); |
---|
| 958 | pa=pan->z; |
---|
| 959 | } |
---|
| 960 | else |
---|
| 961 | { |
---|
| 962 | pGetCoeff(p)=nMap(pGetCoeff(za)); |
---|
| 963 | } |
---|
| 964 | for(i=0;i<P;i++) |
---|
| 965 | { |
---|
| 966 | if(napGetExpFrom(za,i+1,oldRing)!=0) |
---|
| 967 | { |
---|
| 968 | if(par_perm==NULL) |
---|
| 969 | { |
---|
| 970 | if ((rPar(currRing)>=i) && (pa!=NULL)) |
---|
| 971 | { |
---|
| 972 | napSetExp(pa,i+1,napGetExpFrom(za,i+1,oldRing)); |
---|
| 973 | p_Setm(pa,nacRing); |
---|
| 974 | } |
---|
| 975 | else |
---|
| 976 | { |
---|
| 977 | pDelete(&p); |
---|
| 978 | break; |
---|
| 979 | } |
---|
| 980 | } |
---|
| 981 | else if(par_perm[i]>0) |
---|
| 982 | pSetExp(p,par_perm[i],napGetExpFrom(za,i+1,oldRing)); |
---|
| 983 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
| 984 | { |
---|
| 985 | napSetExp(pa,-par_perm[i], napGetExpFrom(za,i+1,oldRing)); |
---|
| 986 | p_Setm(pa,nacRing); |
---|
| 987 | } |
---|
| 988 | else |
---|
| 989 | { |
---|
| 990 | pDelete(&p); |
---|
| 991 | break; |
---|
| 992 | } |
---|
| 993 | } |
---|
| 994 | } |
---|
| 995 | if (p!=NULL) |
---|
| 996 | { |
---|
| 997 | pSetm(p); |
---|
| 998 | if (zb!=NULL) |
---|
| 999 | { |
---|
| 1000 | if (currRing->P>0) |
---|
| 1001 | { |
---|
| 1002 | pan->n=napPerm(zb,par_perm,oldRing,nMap); |
---|
| 1003 | if(pan->n==NULL) /* error in mapping or mapping to variable */ |
---|
| 1004 | pDelete(&p); |
---|
| 1005 | } |
---|
| 1006 | else |
---|
| 1007 | pDelete(&p); |
---|
| 1008 | } |
---|
| 1009 | pTest(p); |
---|
| 1010 | res=pAdd(res,p); |
---|
| 1011 | } |
---|
| 1012 | pIter(za); |
---|
| 1013 | } |
---|
| 1014 | pTest(res); |
---|
| 1015 | return res; |
---|
| 1016 | } |
---|
| 1017 | |
---|
| 1018 | number napGetDenom(number &n, const ring r) |
---|
| 1019 | { |
---|
| 1020 | lnumber x=(lnumber)n; |
---|
| 1021 | if (x->n!=NULL) |
---|
| 1022 | { |
---|
| 1023 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1024 | rr->z=p_Copy(x->n,r->algring); |
---|
| 1025 | rr->s = 2; |
---|
| 1026 | return (number)rr; |
---|
| 1027 | } |
---|
| 1028 | return n_Init(1,r); |
---|
| 1029 | } |
---|
| 1030 | |
---|
| 1031 | number napGetNumerator(number &n, const ring r) |
---|
| 1032 | { |
---|
| 1033 | lnumber x=(lnumber)n; |
---|
| 1034 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1035 | rr->z=p_Copy(x->z,r->algring); |
---|
| 1036 | rr->s = 2; |
---|
| 1037 | return (number)rr; |
---|
| 1038 | } |
---|
[b46956] | 1039 | |
---|
| 1040 | /*================ procedure for rational functions: ntXXXX =================*/ |
---|
| 1041 | |
---|
| 1042 | /*2 |
---|
| 1043 | * z:= i |
---|
| 1044 | */ |
---|
| 1045 | number ntInit(int i, const ring r) |
---|
| 1046 | { |
---|
| 1047 | if (i!=0) |
---|
| 1048 | { |
---|
| 1049 | number c=n_Init(i,r->algring); |
---|
| 1050 | if (!n_IsZero(c,r->algring)) |
---|
| 1051 | { |
---|
| 1052 | poly z=p_Init(r->algring); |
---|
| 1053 | pSetCoeff0(z,c); |
---|
| 1054 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1055 | l->z = z; |
---|
| 1056 | l->s = 2; |
---|
| 1057 | l->n = NULL; |
---|
| 1058 | return (number)l; |
---|
| 1059 | } |
---|
| 1060 | } |
---|
| 1061 | /*else*/ |
---|
| 1062 | return NULL; |
---|
| 1063 | } |
---|
| 1064 | |
---|
[661c214] | 1065 | /*3 |
---|
| 1066 | * division with remainder: f = g*q + r, |
---|
| 1067 | * returns r and destroys f |
---|
| 1068 | */ |
---|
| 1069 | napoly ntRemainder(napoly f, const napoly g) |
---|
| 1070 | { |
---|
| 1071 | napoly a, h, qq; |
---|
| 1072 | |
---|
| 1073 | qq = (napoly)p_Init(nacRing); |
---|
| 1074 | pNext(qq) = NULL; |
---|
| 1075 | p_Normalize(g, nacRing); |
---|
| 1076 | p_Normalize(f, nacRing); |
---|
| 1077 | a = f; |
---|
| 1078 | do |
---|
| 1079 | { |
---|
| 1080 | napSetExp(qq,1, p_GetExp(a,1,nacRing) - p_GetExp(g,1,nacRing)); |
---|
| 1081 | napSetm(qq); |
---|
[21972b] | 1082 | pGetCoeff(qq) = nacDiv(pGetCoeff(a), pGetCoeff(g)); |
---|
| 1083 | pGetCoeff(qq) = nacNeg(pGetCoeff(qq)); |
---|
| 1084 | nacNormalize(pGetCoeff(qq)); |
---|
[661c214] | 1085 | h = napCopy(g); |
---|
| 1086 | napMultT(h, qq); |
---|
| 1087 | p_Normalize(h,nacRing); |
---|
| 1088 | n_Delete(&pGetCoeff(qq),nacRing); |
---|
| 1089 | a = napAdd(a, h); |
---|
| 1090 | } |
---|
| 1091 | while ((a!=NULL) && (p_GetExp(a,1,nacRing) >= p_GetExp(g,1,nacRing))); |
---|
| 1092 | omFreeBinAddr(qq); |
---|
| 1093 | return a; |
---|
| 1094 | } |
---|
| 1095 | |
---|
[b46956] | 1096 | number ntPar(int i) |
---|
| 1097 | { |
---|
| 1098 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1099 | l->s = 2; |
---|
[661c214] | 1100 | l->z = p_ISet(1,nacRing); |
---|
[b46956] | 1101 | napSetExp(l->z,i,1); |
---|
[661c214] | 1102 | p_Setm(l->z,nacRing); |
---|
[b46956] | 1103 | l->n = NULL; |
---|
| 1104 | return (number)l; |
---|
| 1105 | } |
---|
| 1106 | |
---|
| 1107 | int ntParDeg(number n) /* i := deg(n) */ |
---|
| 1108 | { |
---|
| 1109 | lnumber l = (lnumber)n; |
---|
| 1110 | if (l==NULL) return -1; |
---|
[661c214] | 1111 | return napDeg(l->z); |
---|
[b46956] | 1112 | } |
---|
| 1113 | |
---|
| 1114 | //int ntParDeg(number n) /* i := deg(n) */ |
---|
| 1115 | //{ |
---|
| 1116 | // lnumber l = (lnumber)n; |
---|
| 1117 | // if (l==NULL) return -1; |
---|
[661c214] | 1118 | // return napMaxDeg(l->z)+napMaxDeg(l->n); |
---|
[b46956] | 1119 | //} |
---|
| 1120 | |
---|
| 1121 | int ntSize(number n) /* size desc. */ |
---|
| 1122 | { |
---|
| 1123 | lnumber l = (lnumber)n; |
---|
| 1124 | if (l==NULL) return -1; |
---|
| 1125 | int len_z; |
---|
| 1126 | int len_n; |
---|
[661c214] | 1127 | int o=napMaxDegLen(l->z,len_z)+napMaxDegLen(l->n,len_n); |
---|
[b46956] | 1128 | return (len_z+len_n)+o; |
---|
| 1129 | } |
---|
| 1130 | |
---|
| 1131 | /*2 |
---|
| 1132 | * convert a number to int (if possible) |
---|
| 1133 | */ |
---|
| 1134 | int ntInt(number &n, const ring r) |
---|
| 1135 | { |
---|
| 1136 | lnumber l=(lnumber)n; |
---|
| 1137 | if ((l!=NULL)&&(l->n==NULL)&&(p_IsConstant(l->z,r->algring))) |
---|
| 1138 | { |
---|
[21972b] | 1139 | return nacInt(pGetCoeff(l->z),r->algring); |
---|
[b46956] | 1140 | } |
---|
| 1141 | return 0; |
---|
| 1142 | } |
---|
| 1143 | |
---|
| 1144 | /*2 |
---|
| 1145 | * deletes p |
---|
| 1146 | */ |
---|
| 1147 | void ntDelete(number *p, const ring r) |
---|
| 1148 | { |
---|
| 1149 | if ((*p)!=NULL) |
---|
| 1150 | { |
---|
| 1151 | lnumber l = (lnumber) * p; |
---|
| 1152 | if (l==NULL) return; |
---|
| 1153 | p_Delete(&(l->z),r->algring); |
---|
| 1154 | p_Delete(&(l->n),r->algring); |
---|
| 1155 | omFreeBin((ADDRESS)l, rnumber_bin); |
---|
| 1156 | } |
---|
| 1157 | *p = NULL; |
---|
| 1158 | } |
---|
| 1159 | |
---|
| 1160 | /*2 |
---|
| 1161 | * copy p to erg |
---|
| 1162 | */ |
---|
| 1163 | number ntCopy(number p) |
---|
| 1164 | { |
---|
| 1165 | if (p==NULL) return NULL; |
---|
| 1166 | ntTest(p); |
---|
| 1167 | lnumber erg; |
---|
| 1168 | lnumber src = (lnumber)p; |
---|
| 1169 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
[661c214] | 1170 | erg->z = p_Copy(src->z, nacRing); |
---|
| 1171 | erg->n = p_Copy(src->n, nacRing); |
---|
[b46956] | 1172 | erg->s = src->s; |
---|
| 1173 | return (number)erg; |
---|
| 1174 | } |
---|
| 1175 | number nt_Copy(number p, const ring r) |
---|
| 1176 | { |
---|
| 1177 | if (p==NULL) return NULL; |
---|
| 1178 | lnumber erg; |
---|
| 1179 | lnumber src = (lnumber)p; |
---|
| 1180 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1181 | erg->z = p_Copy(src->z,r->algring); |
---|
| 1182 | erg->n = p_Copy(src->n,r->algring); |
---|
| 1183 | erg->s = src->s; |
---|
| 1184 | return (number)erg; |
---|
| 1185 | } |
---|
| 1186 | |
---|
| 1187 | /*2 |
---|
| 1188 | * addition; lu:= la + lb |
---|
| 1189 | */ |
---|
| 1190 | number ntAdd(number la, number lb) |
---|
| 1191 | { |
---|
| 1192 | if (la==NULL) return ntCopy(lb); |
---|
| 1193 | if (lb==NULL) return ntCopy(la); |
---|
| 1194 | |
---|
| 1195 | napoly x, y; |
---|
| 1196 | lnumber lu; |
---|
| 1197 | lnumber a = (lnumber)la; |
---|
| 1198 | lnumber b = (lnumber)lb; |
---|
| 1199 | #ifdef LDEBUG |
---|
| 1200 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1201 | omCheckAddrSize(b,sizeof(snumber)); |
---|
| 1202 | #endif |
---|
[661c214] | 1203 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
---|
| 1204 | else x = napCopy(a->z); |
---|
| 1205 | if (a->n!=NULL) y = pp_Mult_qq(b->z, a->n,nacRing); |
---|
| 1206 | else y = napCopy(b->z); |
---|
[b46956] | 1207 | napoly res = napAdd(x, y); |
---|
| 1208 | if (res==NULL) |
---|
| 1209 | { |
---|
| 1210 | return (number)NULL; |
---|
| 1211 | } |
---|
| 1212 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1213 | lu->z=res; |
---|
| 1214 | if (a->n!=NULL) |
---|
| 1215 | { |
---|
[661c214] | 1216 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
---|
| 1217 | else x = napCopy(a->n); |
---|
[b46956] | 1218 | } |
---|
| 1219 | else |
---|
| 1220 | { |
---|
[661c214] | 1221 | if (b->n!=NULL) x = napCopy(b->n); |
---|
[b46956] | 1222 | else x = NULL; |
---|
| 1223 | } |
---|
| 1224 | //if (x!=NULL) |
---|
| 1225 | //{ |
---|
[661c214] | 1226 | // if (p_LmIsConstant(x,nacRing)) |
---|
[b46956] | 1227 | // { |
---|
[21972b] | 1228 | // number inv=nacInvers(pGetCoeff(x)); |
---|
[661c214] | 1229 | // napMultN(lu->z,inv); |
---|
| 1230 | // n_Delete(&inv,nacRing); |
---|
| 1231 | // napDelete(&x); |
---|
[b46956] | 1232 | // } |
---|
| 1233 | //} |
---|
| 1234 | lu->n = x; |
---|
| 1235 | lu->s = FALSE; |
---|
| 1236 | if (/*lu->n*/ x!=NULL) |
---|
| 1237 | { |
---|
| 1238 | number luu=(number)lu; |
---|
[661c214] | 1239 | //if (p_IsConstant(lu->n,nacRing)) ntCoefNormalize(luu); |
---|
[b46956] | 1240 | //else |
---|
| 1241 | ntNormalize(luu); |
---|
| 1242 | lu=(lnumber)luu; |
---|
| 1243 | } |
---|
| 1244 | //else lu->s=2; |
---|
| 1245 | ntTest((number)lu); |
---|
| 1246 | return (number)lu; |
---|
| 1247 | } |
---|
| 1248 | |
---|
| 1249 | /*2 |
---|
| 1250 | * subtraction; r:= la - lb |
---|
| 1251 | */ |
---|
| 1252 | number ntSub(number la, number lb) |
---|
| 1253 | { |
---|
| 1254 | lnumber lu; |
---|
| 1255 | |
---|
| 1256 | if (lb==NULL) return ntCopy(la); |
---|
| 1257 | if (la==NULL) |
---|
| 1258 | { |
---|
| 1259 | lu = (lnumber)ntCopy(lb); |
---|
| 1260 | lu->z = napNeg(lu->z); |
---|
| 1261 | return (number)lu; |
---|
| 1262 | } |
---|
| 1263 | |
---|
| 1264 | lnumber a = (lnumber)la; |
---|
| 1265 | lnumber b = (lnumber)lb; |
---|
| 1266 | |
---|
| 1267 | #ifdef LDEBUG |
---|
| 1268 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1269 | omCheckAddrSize(b,sizeof(snumber)); |
---|
| 1270 | #endif |
---|
| 1271 | |
---|
| 1272 | napoly x, y; |
---|
[661c214] | 1273 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
---|
| 1274 | else x = napCopy(a->z); |
---|
| 1275 | if (a->n!=NULL) y = p_Mult_q(napCopy(b->z), napCopyNeg(a->n),nacRing); |
---|
| 1276 | else y = napCopyNeg(b->z); |
---|
[b46956] | 1277 | napoly res = napAdd(x, y); |
---|
| 1278 | if (res==NULL) |
---|
| 1279 | { |
---|
| 1280 | return (number)NULL; |
---|
| 1281 | } |
---|
| 1282 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1283 | lu->z=res; |
---|
| 1284 | if (a->n!=NULL) |
---|
| 1285 | { |
---|
[661c214] | 1286 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
---|
| 1287 | else x = napCopy(a->n); |
---|
[b46956] | 1288 | } |
---|
| 1289 | else |
---|
| 1290 | { |
---|
[661c214] | 1291 | if (b->n!=NULL) x = napCopy(b->n); |
---|
[b46956] | 1292 | else x = NULL; |
---|
| 1293 | } |
---|
| 1294 | lu->n = x; |
---|
| 1295 | lu->s = FALSE; |
---|
| 1296 | if (/*lu->n*/ x!=NULL) |
---|
| 1297 | { |
---|
| 1298 | number luu=(number)lu; |
---|
[661c214] | 1299 | //if (p_IsConstant(lu->n,nacRing)) ntCoefNormalize(luu); |
---|
[b46956] | 1300 | //else |
---|
| 1301 | ntNormalize(luu); |
---|
| 1302 | lu=(lnumber)luu; |
---|
| 1303 | } |
---|
| 1304 | //else lu->s=2; |
---|
| 1305 | ntTest((number)lu); |
---|
| 1306 | return (number)lu; |
---|
| 1307 | } |
---|
| 1308 | |
---|
| 1309 | /*2 |
---|
| 1310 | * multiplication; r:= la * lb |
---|
| 1311 | */ |
---|
| 1312 | number ntMult(number la, number lb) |
---|
| 1313 | { |
---|
| 1314 | if ((la==NULL) || (lb==NULL)) |
---|
| 1315 | return NULL; |
---|
| 1316 | |
---|
| 1317 | lnumber a = (lnumber)la; |
---|
| 1318 | lnumber b = (lnumber)lb; |
---|
| 1319 | lnumber lo; |
---|
| 1320 | napoly x; |
---|
| 1321 | |
---|
| 1322 | #ifdef LDEBUG |
---|
| 1323 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1324 | omCheckAddrSize(b,sizeof(snumber)); |
---|
| 1325 | #endif |
---|
| 1326 | ntTest(la); |
---|
| 1327 | ntTest(lb); |
---|
| 1328 | |
---|
| 1329 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
[661c214] | 1330 | lo->z = pp_Mult_qq(a->z, b->z,nacRing); |
---|
[b46956] | 1331 | |
---|
| 1332 | if (a->n==NULL) |
---|
| 1333 | { |
---|
| 1334 | if (b->n==NULL) |
---|
| 1335 | x = NULL; |
---|
| 1336 | else |
---|
[661c214] | 1337 | x = napCopy(b->n); |
---|
[b46956] | 1338 | } |
---|
| 1339 | else |
---|
| 1340 | { |
---|
| 1341 | if (b->n==NULL) |
---|
| 1342 | { |
---|
[661c214] | 1343 | x = napCopy(a->n); |
---|
[b46956] | 1344 | } |
---|
| 1345 | else |
---|
| 1346 | { |
---|
[661c214] | 1347 | x = pp_Mult_qq(b->n, a->n, nacRing); |
---|
[b46956] | 1348 | } |
---|
| 1349 | } |
---|
[21972b] | 1350 | if ((x!=NULL) && (p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
[661c214] | 1351 | p_Delete(&x,nacRing); |
---|
[b46956] | 1352 | lo->n = x; |
---|
| 1353 | lo->s = 0; |
---|
| 1354 | if(lo->z==NULL) |
---|
| 1355 | { |
---|
| 1356 | omFreeBin((ADDRESS)lo, rnumber_bin); |
---|
| 1357 | lo=NULL; |
---|
| 1358 | } |
---|
| 1359 | else if (lo->n!=NULL) |
---|
| 1360 | { |
---|
| 1361 | number luu=(number)lo; |
---|
[661c214] | 1362 | // if (p_IsConstant(lo->n,nacRing)) ntCoefNormalize(luu); |
---|
[b46956] | 1363 | // else |
---|
| 1364 | ntNormalize(luu); |
---|
| 1365 | lo=(lnumber)luu; |
---|
| 1366 | } |
---|
| 1367 | //if (naMinimalPoly==NULL) lo->s=2; |
---|
| 1368 | ntTest((number)lo); |
---|
| 1369 | return (number)lo; |
---|
| 1370 | } |
---|
| 1371 | |
---|
| 1372 | number ntIntDiv(number la, number lb) |
---|
| 1373 | { |
---|
[f115489] | 1374 | ntTest(la); |
---|
| 1375 | ntTest(lb); |
---|
[b46956] | 1376 | lnumber res; |
---|
| 1377 | lnumber a = (lnumber)la; |
---|
| 1378 | lnumber b = (lnumber)lb; |
---|
| 1379 | if (a==NULL) |
---|
| 1380 | { |
---|
| 1381 | return NULL; |
---|
| 1382 | } |
---|
| 1383 | if (b==NULL) |
---|
| 1384 | { |
---|
| 1385 | WerrorS(nDivBy0); |
---|
| 1386 | return NULL; |
---|
| 1387 | } |
---|
[f115489] | 1388 | #ifdef LDEBUG |
---|
| 1389 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1390 | omCheckAddrSize(b,sizeof(snumber)); |
---|
| 1391 | #endif |
---|
[b46956] | 1392 | assume(a->z!=NULL && b->z!=NULL); |
---|
| 1393 | assume(a->n==NULL && b->n==NULL); |
---|
| 1394 | res = (lnumber)omAllocBin(rnumber_bin); |
---|
[661c214] | 1395 | res->z = napCopy(a->z); |
---|
| 1396 | res->n = napCopy(b->z); |
---|
[b46956] | 1397 | res->s = 0; |
---|
| 1398 | number nres=(number)res; |
---|
| 1399 | ntNormalize(nres); |
---|
| 1400 | |
---|
[661c214] | 1401 | //napDelete(&res->n); |
---|
[b46956] | 1402 | ntTest(nres); |
---|
| 1403 | return nres; |
---|
| 1404 | } |
---|
| 1405 | |
---|
| 1406 | /*2 |
---|
| 1407 | * division; lo:= la / lb |
---|
| 1408 | */ |
---|
| 1409 | number ntDiv(number la, number lb) |
---|
| 1410 | { |
---|
| 1411 | lnumber lo; |
---|
| 1412 | lnumber a = (lnumber)la; |
---|
| 1413 | lnumber b = (lnumber)lb; |
---|
| 1414 | napoly x; |
---|
| 1415 | |
---|
| 1416 | if (a==NULL) |
---|
| 1417 | return NULL; |
---|
| 1418 | |
---|
| 1419 | if (b==NULL) |
---|
| 1420 | { |
---|
| 1421 | WerrorS(nDivBy0); |
---|
| 1422 | return NULL; |
---|
| 1423 | } |
---|
| 1424 | #ifdef LDEBUG |
---|
| 1425 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1426 | omCheckAddrSize(b,sizeof(snumber)); |
---|
| 1427 | #endif |
---|
| 1428 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1429 | if (b->n!=NULL) |
---|
[661c214] | 1430 | lo->z = pp_Mult_qq(a->z, b->n,nacRing); |
---|
[b46956] | 1431 | else |
---|
[661c214] | 1432 | lo->z = napCopy(a->z); |
---|
[b46956] | 1433 | if (a->n!=NULL) |
---|
[661c214] | 1434 | x = pp_Mult_qq(b->z, a->n, nacRing); |
---|
[b46956] | 1435 | else |
---|
[661c214] | 1436 | x = napCopy(b->z); |
---|
[21972b] | 1437 | if ((p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
[661c214] | 1438 | p_Delete(&x,nacRing); |
---|
[b46956] | 1439 | lo->n = x; |
---|
| 1440 | lo->s = 0; |
---|
| 1441 | if (lo->n!=NULL) |
---|
| 1442 | { |
---|
| 1443 | number luu=(number)lo; |
---|
[661c214] | 1444 | //if (p_IsConstant(lo->n,nacRing)) ntCoefNormalize(luu); |
---|
[b46956] | 1445 | //else |
---|
| 1446 | ntNormalize(luu); |
---|
| 1447 | lo=(lnumber)luu; |
---|
| 1448 | } |
---|
| 1449 | //else lo->s=2; |
---|
| 1450 | ntTest((number)lo); |
---|
| 1451 | return (number)lo; |
---|
| 1452 | } |
---|
| 1453 | |
---|
| 1454 | /*2 |
---|
| 1455 | * za:= - za, inplace |
---|
| 1456 | */ |
---|
| 1457 | number ntNeg(number za) |
---|
| 1458 | { |
---|
| 1459 | if (za!=NULL) |
---|
| 1460 | { |
---|
| 1461 | lnumber e = (lnumber)za; |
---|
| 1462 | ntTest(za); |
---|
| 1463 | e->z = napNeg(e->z); |
---|
| 1464 | } |
---|
| 1465 | return za; |
---|
| 1466 | } |
---|
| 1467 | |
---|
| 1468 | /*2 |
---|
| 1469 | * 1/a |
---|
| 1470 | */ |
---|
| 1471 | number ntInvers(number a) |
---|
| 1472 | { |
---|
| 1473 | lnumber lo; |
---|
| 1474 | lnumber b = (lnumber)a; |
---|
| 1475 | napoly x; |
---|
| 1476 | |
---|
| 1477 | if (b==NULL) |
---|
| 1478 | { |
---|
| 1479 | WerrorS(nDivBy0); |
---|
| 1480 | return NULL; |
---|
| 1481 | } |
---|
| 1482 | #ifdef LDEBUG |
---|
| 1483 | omCheckAddrSize(b,sizeof(snumber)); |
---|
| 1484 | #endif |
---|
| 1485 | lo = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1486 | lo->s = b->s; |
---|
| 1487 | if (b->n!=NULL) |
---|
[661c214] | 1488 | lo->z = napCopy(b->n); |
---|
[b46956] | 1489 | else |
---|
[661c214] | 1490 | lo->z = p_ISet(1,nacRing); |
---|
[b46956] | 1491 | x = b->z; |
---|
[21972b] | 1492 | if ((!p_LmIsConstant(x,nacRing)) || !nacIsOne(pGetCoeff(x))) |
---|
[661c214] | 1493 | x = napCopy(x); |
---|
[b46956] | 1494 | else |
---|
| 1495 | { |
---|
| 1496 | lo->n = NULL; |
---|
| 1497 | ntTest((number)lo); |
---|
| 1498 | return (number)lo; |
---|
| 1499 | } |
---|
| 1500 | lo->n = x; |
---|
| 1501 | if (lo->n!=NULL) |
---|
| 1502 | { |
---|
| 1503 | number luu=(number)lo; |
---|
[661c214] | 1504 | //if (p_IsConstant(lo->n,nacRing)) ntCoefNormalize(luu); |
---|
[b46956] | 1505 | //else |
---|
| 1506 | ntNormalize(luu); |
---|
| 1507 | lo=(lnumber)luu; |
---|
| 1508 | } |
---|
| 1509 | ntTest((number)lo); |
---|
| 1510 | return (number)lo; |
---|
| 1511 | } |
---|
| 1512 | |
---|
| 1513 | |
---|
| 1514 | BOOLEAN ntIsZero(number za) |
---|
| 1515 | { |
---|
| 1516 | lnumber zb = (lnumber)za; |
---|
| 1517 | ntTest(za); |
---|
| 1518 | #ifdef LDEBUG |
---|
| 1519 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
| 1520 | #endif |
---|
| 1521 | return (zb==NULL); |
---|
| 1522 | } |
---|
| 1523 | |
---|
| 1524 | |
---|
| 1525 | BOOLEAN ntGreaterZero(number za) |
---|
| 1526 | { |
---|
| 1527 | lnumber zb = (lnumber)za; |
---|
| 1528 | #ifdef LDEBUG |
---|
| 1529 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
| 1530 | #endif |
---|
| 1531 | ntTest(za); |
---|
| 1532 | if (zb!=NULL) |
---|
| 1533 | { |
---|
[21972b] | 1534 | return (nacGreaterZero(pGetCoeff(zb->z))||(!p_LmIsConstant(zb->z,nacRing))); |
---|
[b46956] | 1535 | } |
---|
| 1536 | /* else */ return FALSE; |
---|
| 1537 | } |
---|
| 1538 | |
---|
| 1539 | |
---|
| 1540 | /*2 |
---|
| 1541 | * a = b ? |
---|
| 1542 | */ |
---|
| 1543 | BOOLEAN ntEqual (number a, number b) |
---|
| 1544 | { |
---|
| 1545 | if(a==b) return TRUE; |
---|
| 1546 | if((a==NULL)&&(b!=NULL)) return FALSE; |
---|
| 1547 | if((b==NULL)&&(a!=NULL)) return FALSE; |
---|
| 1548 | |
---|
| 1549 | lnumber aa=(lnumber)a; |
---|
| 1550 | lnumber bb=(lnumber)b; |
---|
| 1551 | |
---|
| 1552 | int an_deg=0; |
---|
| 1553 | if(aa->n!=NULL) |
---|
[661c214] | 1554 | an_deg=napDeg(aa->n); |
---|
[b46956] | 1555 | int bn_deg=0; |
---|
| 1556 | if(bb->n!=NULL) |
---|
[661c214] | 1557 | bn_deg=napDeg(bb->n); |
---|
| 1558 | if(an_deg+napDeg(bb->z)!=bn_deg+napDeg(aa->z)) |
---|
[b46956] | 1559 | return FALSE; |
---|
| 1560 | #if 0 |
---|
| 1561 | ntNormalize(a); |
---|
| 1562 | aa=(lnumber)a; |
---|
| 1563 | ntNormalize(b); |
---|
| 1564 | bb=(lnumber)b; |
---|
| 1565 | if((aa->n==NULL)&&(bb->n!=NULL)) return FALSE; |
---|
| 1566 | if((bb->n==NULL)&&(aa->n!=NULL)) return FALSE; |
---|
[661c214] | 1567 | if(napComp(aa->z,bb->z)!=0) return FALSE; |
---|
| 1568 | if((aa->n!=NULL) && (napComp(aa->n,bb->n))) return FALSE; |
---|
[b46956] | 1569 | #endif |
---|
| 1570 | number h = ntSub(a, b); |
---|
| 1571 | BOOLEAN bo = ntIsZero(h); |
---|
| 1572 | ntDelete(&h,currRing); |
---|
| 1573 | return bo; |
---|
| 1574 | } |
---|
| 1575 | |
---|
| 1576 | |
---|
| 1577 | BOOLEAN ntGreater (number a, number b) |
---|
| 1578 | { |
---|
| 1579 | if (ntIsZero(a)) |
---|
| 1580 | return FALSE; |
---|
| 1581 | if (ntIsZero(b)) |
---|
| 1582 | return TRUE; /* a!= 0)*/ |
---|
[661c214] | 1583 | return napDeg(((lnumber)a)->z)>napDeg(((lnumber)b)->z); |
---|
[b46956] | 1584 | } |
---|
| 1585 | |
---|
| 1586 | /*2 |
---|
| 1587 | * reads a number |
---|
| 1588 | */ |
---|
| 1589 | const char *ntRead(const char *s, number *p) |
---|
| 1590 | { |
---|
| 1591 | napoly x; |
---|
| 1592 | lnumber a; |
---|
[661c214] | 1593 | s = napRead(s, &x); |
---|
[b46956] | 1594 | if (x==NULL) |
---|
| 1595 | { |
---|
| 1596 | *p = NULL; |
---|
| 1597 | return s; |
---|
| 1598 | } |
---|
| 1599 | *p = (number)omAlloc0Bin(rnumber_bin); |
---|
| 1600 | a = (lnumber)*p; |
---|
[d0450f] | 1601 | a->z = x; |
---|
[b46956] | 1602 | if(a->z==NULL) |
---|
| 1603 | { |
---|
| 1604 | omFreeBin((ADDRESS)*p, rnumber_bin); |
---|
| 1605 | *p=NULL; |
---|
| 1606 | } |
---|
| 1607 | else |
---|
| 1608 | { |
---|
| 1609 | a->n = NULL; |
---|
| 1610 | a->s = 0; |
---|
| 1611 | ntTest(*p); |
---|
| 1612 | } |
---|
| 1613 | return s; |
---|
| 1614 | } |
---|
| 1615 | |
---|
| 1616 | /*2 |
---|
| 1617 | * tries to convert a number to a name |
---|
| 1618 | */ |
---|
| 1619 | char * ntName(number n) |
---|
| 1620 | { |
---|
| 1621 | lnumber ph = (lnumber)n; |
---|
| 1622 | if (ph==NULL) |
---|
| 1623 | return NULL; |
---|
| 1624 | int i; |
---|
[661c214] | 1625 | char *s=(char *)omAlloc(4* ntNumbOfPar); |
---|
[b46956] | 1626 | char *t=(char *)omAlloc(8); |
---|
| 1627 | s[0]='\0'; |
---|
[661c214] | 1628 | for (i = 0; i <= ntNumbOfPar - 1; i++) |
---|
[b46956] | 1629 | { |
---|
[661c214] | 1630 | int e=p_GetExp(ph->z,i+1,nacRing); |
---|
[b46956] | 1631 | if (e > 0) |
---|
| 1632 | { |
---|
| 1633 | if (e >1) |
---|
| 1634 | { |
---|
[21972b] | 1635 | sprintf(t,"%s%d",ntParNames[i],e); |
---|
[b46956] | 1636 | strcat(s,t); |
---|
| 1637 | } |
---|
| 1638 | else |
---|
| 1639 | { |
---|
[21972b] | 1640 | strcat(s,ntParNames[i]); |
---|
[b46956] | 1641 | } |
---|
| 1642 | } |
---|
| 1643 | } |
---|
| 1644 | omFreeSize((ADDRESS)t,8); |
---|
| 1645 | if (s[0]=='\0') |
---|
| 1646 | { |
---|
| 1647 | omFree((ADDRESS)s); |
---|
| 1648 | return NULL; |
---|
| 1649 | } |
---|
| 1650 | return s; |
---|
| 1651 | } |
---|
| 1652 | |
---|
| 1653 | /*2 |
---|
| 1654 | * writes a number |
---|
| 1655 | */ |
---|
| 1656 | void ntWrite(number &phn, const ring r) |
---|
| 1657 | { |
---|
| 1658 | lnumber ph = (lnumber)phn; |
---|
| 1659 | if (ph==NULL) |
---|
| 1660 | StringAppendS("0"); |
---|
| 1661 | else |
---|
| 1662 | { |
---|
| 1663 | phn->s = 0; |
---|
| 1664 | BOOLEAN has_denom=(ph->n!=NULL); |
---|
[661c214] | 1665 | napWrite(ph->z,has_denom/*(ph->n!=NULL)*/,r); |
---|
[b46956] | 1666 | if (has_denom/*(ph->n!=NULL)*/) |
---|
| 1667 | { |
---|
| 1668 | StringAppendS("/"); |
---|
[661c214] | 1669 | napWrite(ph->n,TRUE,r); |
---|
[b46956] | 1670 | } |
---|
| 1671 | } |
---|
| 1672 | } |
---|
| 1673 | |
---|
| 1674 | /*2 |
---|
| 1675 | * za == 1 ? |
---|
| 1676 | */ |
---|
| 1677 | BOOLEAN ntIsOne(number za) |
---|
| 1678 | { |
---|
| 1679 | lnumber a = (lnumber)za; |
---|
| 1680 | napoly x, y; |
---|
| 1681 | number t; |
---|
| 1682 | if (a==NULL) return FALSE; |
---|
| 1683 | #ifdef LDEBUG |
---|
| 1684 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1685 | if (a->z==NULL) |
---|
| 1686 | { |
---|
| 1687 | WerrorS("internal zero error(4)"); |
---|
| 1688 | return FALSE; |
---|
| 1689 | } |
---|
| 1690 | #endif |
---|
| 1691 | if (a->n==NULL) |
---|
| 1692 | { |
---|
[661c214] | 1693 | if (p_LmIsConstant(a->z,nacRing)) |
---|
[b46956] | 1694 | { |
---|
[21972b] | 1695 | return nacIsOne(pGetCoeff(a->z)); |
---|
[b46956] | 1696 | } |
---|
| 1697 | else return FALSE; |
---|
| 1698 | } |
---|
| 1699 | #if 0 |
---|
| 1700 | x = a->z; |
---|
| 1701 | y = a->n; |
---|
| 1702 | do |
---|
| 1703 | { |
---|
[661c214] | 1704 | if (napComp(x, y)) |
---|
[b46956] | 1705 | return FALSE; |
---|
| 1706 | else |
---|
| 1707 | { |
---|
[21972b] | 1708 | t = nacSub(pGetCoeff(x), pGetCoeff(y)); |
---|
| 1709 | if (!nacIsZero(t)) |
---|
[b46956] | 1710 | { |
---|
[661c214] | 1711 | n_Delete(&t,nacRing); |
---|
[b46956] | 1712 | return FALSE; |
---|
| 1713 | } |
---|
| 1714 | else |
---|
[661c214] | 1715 | n_Delete(&t,nacRing); |
---|
[b46956] | 1716 | } |
---|
| 1717 | pIter(x); |
---|
| 1718 | pIter(y); |
---|
| 1719 | } |
---|
| 1720 | while ((x!=NULL) && (y!=NULL)); |
---|
| 1721 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
[661c214] | 1722 | p_Delete(&a->z,nacRing); |
---|
| 1723 | p_Delete(&a->n,nacRing); |
---|
| 1724 | a->z = p_ISet(1,nacRing); |
---|
[b46956] | 1725 | a->n = NULL; |
---|
| 1726 | return TRUE; |
---|
| 1727 | #else |
---|
| 1728 | return FALSE; |
---|
| 1729 | #endif |
---|
| 1730 | } |
---|
| 1731 | |
---|
| 1732 | /*2 |
---|
| 1733 | * za == -1 ? |
---|
| 1734 | */ |
---|
| 1735 | BOOLEAN ntIsMOne(number za) |
---|
| 1736 | { |
---|
| 1737 | lnumber a = (lnumber)za; |
---|
| 1738 | napoly x, y; |
---|
| 1739 | number t; |
---|
| 1740 | if (a==NULL) return FALSE; |
---|
| 1741 | #ifdef LDEBUG |
---|
| 1742 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1743 | if (a->z==NULL) |
---|
| 1744 | { |
---|
| 1745 | WerrorS("internal zero error(5)"); |
---|
| 1746 | return FALSE; |
---|
| 1747 | } |
---|
| 1748 | #endif |
---|
| 1749 | if (a->n==NULL) |
---|
| 1750 | { |
---|
[0c2088] | 1751 | if (p_LmIsConstant(a->z,nacRing)) return n_IsMOne(pGetCoeff(a->z),nacRing); |
---|
[b46956] | 1752 | /*else return FALSE;*/ |
---|
| 1753 | } |
---|
| 1754 | return FALSE; |
---|
| 1755 | } |
---|
| 1756 | |
---|
| 1757 | /*2 |
---|
| 1758 | * returns the i-th power of p (i>=0) |
---|
| 1759 | */ |
---|
| 1760 | void ntPower(number p, int i, number *rc) |
---|
| 1761 | { |
---|
| 1762 | number x; |
---|
| 1763 | *rc = ntInit(1,currRing); |
---|
| 1764 | for (; i > 0; i--) |
---|
| 1765 | { |
---|
| 1766 | x = ntMult(*rc, p); |
---|
| 1767 | ntDelete(rc,currRing); |
---|
| 1768 | *rc = x; |
---|
| 1769 | } |
---|
| 1770 | } |
---|
| 1771 | |
---|
| 1772 | /*2 |
---|
| 1773 | * result =gcd(a,b) |
---|
| 1774 | */ |
---|
| 1775 | number ntGcd(number a, number b, const ring r) |
---|
| 1776 | { |
---|
| 1777 | if (a==NULL) return ntCopy(b); |
---|
| 1778 | if (b==NULL) return ntCopy(a); |
---|
| 1779 | |
---|
| 1780 | lnumber x, y; |
---|
| 1781 | lnumber result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1782 | |
---|
| 1783 | x = (lnumber)a; |
---|
| 1784 | y = (lnumber)b; |
---|
| 1785 | #ifndef HAVE_FACTORY |
---|
[661c214] | 1786 | result->z = napGcd(x->z, y->z); // change from napGcd0 |
---|
[b46956] | 1787 | #else |
---|
| 1788 | int c=ABS(nGetChar()); |
---|
| 1789 | if (c==1) c=0; |
---|
| 1790 | setCharacteristic( c ); |
---|
| 1791 | |
---|
[661c214] | 1792 | napoly rz=napGcd(x->z, y->z); |
---|
[b46956] | 1793 | CanonicalForm F, G, R; |
---|
| 1794 | R=convSingPFactoryP(rz,r->algring); |
---|
[661c214] | 1795 | p_Normalize(x->z,nacRing); |
---|
[b46956] | 1796 | F=convSingPFactoryP(x->z,r->algring)/R; |
---|
[661c214] | 1797 | p_Normalize(y->z,nacRing); |
---|
[b46956] | 1798 | G=convSingPFactoryP(y->z,r->algring)/R; |
---|
| 1799 | F = gcd( F, G ); |
---|
| 1800 | if (F.isOne()) |
---|
| 1801 | result->z= rz; |
---|
| 1802 | else |
---|
| 1803 | { |
---|
| 1804 | p_Delete(&rz,r->algring); |
---|
| 1805 | result->z=convFactoryPSingP( F*R,r->algring ); |
---|
[661c214] | 1806 | p_Normalize(result->z,nacRing); |
---|
[b46956] | 1807 | } |
---|
| 1808 | #endif |
---|
| 1809 | ntTest((number)result); |
---|
| 1810 | return (number)result; |
---|
| 1811 | } |
---|
| 1812 | |
---|
| 1813 | |
---|
| 1814 | /*2 |
---|
[661c214] | 1815 | * ntNumbOfPar = 1: |
---|
[b46956] | 1816 | * clears denominator algebraic case; |
---|
| 1817 | * tries to simplify ratio transcendental case; |
---|
| 1818 | * |
---|
| 1819 | * cancels monomials |
---|
| 1820 | * occuring in denominator |
---|
[661c214] | 1821 | * and enumerator ? ntNumbOfPar != 1; |
---|
[b46956] | 1822 | * |
---|
| 1823 | * #defines for Factory: |
---|
| 1824 | * FACTORY_GCD_TEST: do not apply built in gcd for |
---|
| 1825 | * univariate polynomials, always use Factory |
---|
| 1826 | */ |
---|
| 1827 | //#define FACTORY_GCD_TEST |
---|
| 1828 | void ntCoefNormalize(number pp) |
---|
| 1829 | { |
---|
| 1830 | if (pp==NULL) return; |
---|
| 1831 | lnumber p = (lnumber)pp; |
---|
| 1832 | number nz; // all denom. of the numerator |
---|
[661c214] | 1833 | nz=p_GetAllDenom(p->z,nacRing); |
---|
[b46956] | 1834 | BOOLEAN norm=FALSE; |
---|
[661c214] | 1835 | if (!n_IsOne(nz,nacRing)) |
---|
[b46956] | 1836 | { |
---|
| 1837 | norm=TRUE; |
---|
[661c214] | 1838 | p->z=p_Mult_nn(p->z,nz,nacRing); |
---|
[b46956] | 1839 | if (p->n==NULL) |
---|
| 1840 | { |
---|
[661c214] | 1841 | p->n=p_NSet(nz,nacRing); |
---|
[b46956] | 1842 | } |
---|
| 1843 | else |
---|
| 1844 | { |
---|
[661c214] | 1845 | p->n=p_Mult_nn(p->n,nz,nacRing); |
---|
| 1846 | n_Delete(&nz, nacRing); |
---|
[b46956] | 1847 | } |
---|
| 1848 | } |
---|
| 1849 | else |
---|
| 1850 | { |
---|
[661c214] | 1851 | n_Delete(&nz, nacRing); |
---|
[b46956] | 1852 | } |
---|
| 1853 | if (norm) |
---|
| 1854 | { |
---|
| 1855 | norm=FALSE; |
---|
[661c214] | 1856 | p_Normalize(p->z,nacRing); |
---|
| 1857 | p_Normalize(p->n,nacRing); |
---|
[b46956] | 1858 | } |
---|
| 1859 | number nn; |
---|
[661c214] | 1860 | nn=p_GetAllDenom(p->n,nacRing); |
---|
| 1861 | if (!n_IsOne(nn,nacRing)) |
---|
[b46956] | 1862 | { |
---|
| 1863 | norm=TRUE; |
---|
[661c214] | 1864 | p->n=p_Mult_nn(p->n,nn,nacRing); |
---|
| 1865 | p->z=p_Mult_nn(p->z,nn,nacRing); |
---|
| 1866 | n_Delete(&nn, nacRing); |
---|
[b46956] | 1867 | } |
---|
| 1868 | else |
---|
| 1869 | { |
---|
[661c214] | 1870 | n_Delete(&nn, nacRing); |
---|
[b46956] | 1871 | } |
---|
| 1872 | if (norm) |
---|
| 1873 | { |
---|
[661c214] | 1874 | p_Normalize(p->z,nacRing); |
---|
| 1875 | p_Normalize(p->n,nacRing); |
---|
[b46956] | 1876 | } |
---|
| 1877 | // remove common factors in n, z: |
---|
| 1878 | if (p->n!=NULL) |
---|
| 1879 | { |
---|
| 1880 | poly pp=p->z; |
---|
[661c214] | 1881 | nz=n_Copy(pGetCoeff(pp),nacRing); |
---|
[b46956] | 1882 | pIter(pp); |
---|
| 1883 | while(pp!=NULL) |
---|
| 1884 | { |
---|
[661c214] | 1885 | if (n_IsOne(nz,nacRing)) break; |
---|
| 1886 | number d=n_Gcd(nz,pGetCoeff(pp),nacRing); |
---|
| 1887 | n_Delete(&nz,nacRing); nz=d; |
---|
[b46956] | 1888 | pIter(pp); |
---|
| 1889 | } |
---|
[661c214] | 1890 | if (!n_IsOne(nz,nacRing)) |
---|
[b46956] | 1891 | { |
---|
| 1892 | pp=p->n; |
---|
[661c214] | 1893 | nn=n_Copy(pGetCoeff(pp),nacRing); |
---|
[b46956] | 1894 | pIter(pp); |
---|
| 1895 | while(pp!=NULL) |
---|
| 1896 | { |
---|
[661c214] | 1897 | if (n_IsOne(nn,nacRing)) break; |
---|
| 1898 | number d=n_Gcd(nn,pGetCoeff(pp),nacRing); |
---|
| 1899 | n_Delete(&nn,nacRing); nn=d; |
---|
[b46956] | 1900 | pIter(pp); |
---|
| 1901 | } |
---|
[661c214] | 1902 | number ng=n_Gcd(nz,nn,nacRing); |
---|
| 1903 | n_Delete(&nn,nacRing); |
---|
| 1904 | if (!n_IsOne(ng,nacRing)) |
---|
[b46956] | 1905 | { |
---|
[661c214] | 1906 | number ni=n_Invers(ng,nacRing); |
---|
| 1907 | p->z=p_Mult_nn(p->z,ni,nacRing); |
---|
| 1908 | p->n=p_Mult_nn(p->n,ni,nacRing); |
---|
| 1909 | p_Normalize(p->z,nacRing); |
---|
| 1910 | p_Normalize(p->n,nacRing); |
---|
| 1911 | n_Delete(&ni,nacRing); |
---|
[b46956] | 1912 | } |
---|
[661c214] | 1913 | n_Delete(&ng,nacRing); |
---|
[b46956] | 1914 | } |
---|
[661c214] | 1915 | n_Delete(&nz,nacRing); |
---|
[b46956] | 1916 | } |
---|
| 1917 | if (p->n!=NULL) |
---|
| 1918 | { |
---|
[21972b] | 1919 | if(!nacGreaterZero(pGetCoeff(p->n))) |
---|
[b46956] | 1920 | { |
---|
| 1921 | p->z=napNeg(p->z); |
---|
| 1922 | p->n=napNeg(p->n); |
---|
| 1923 | } |
---|
| 1924 | |
---|
| 1925 | if (/*(p->n!=NULL) && */ |
---|
[661c214] | 1926 | (p_IsConstant(p->n,nacRing)) |
---|
| 1927 | && (n_IsOne(pGetCoeff(p->n),nacRing))) |
---|
[b46956] | 1928 | { |
---|
[661c214] | 1929 | p_Delete(&(p->n), nacRing); |
---|
[b46956] | 1930 | p->n = NULL; |
---|
| 1931 | } |
---|
| 1932 | } |
---|
| 1933 | } |
---|
| 1934 | |
---|
| 1935 | void ntNormalize(number &pp) |
---|
| 1936 | { |
---|
| 1937 | |
---|
| 1938 | //ntTest(pp); // input may not be "normal" |
---|
| 1939 | lnumber p = (lnumber)pp; |
---|
| 1940 | |
---|
| 1941 | if (p==NULL) |
---|
| 1942 | return; |
---|
| 1943 | ntCoefNormalize(pp); |
---|
| 1944 | p->s = 2; |
---|
| 1945 | napoly x = p->z; |
---|
| 1946 | napoly y = p->n; |
---|
| 1947 | |
---|
| 1948 | BOOLEAN norm=FALSE; |
---|
| 1949 | |
---|
| 1950 | if (y==NULL) return; |
---|
| 1951 | |
---|
| 1952 | if ((x!=NULL) && (y!=NULL)) |
---|
| 1953 | { |
---|
| 1954 | int i; |
---|
[661c214] | 1955 | for (i=ntNumbOfPar-1; i>=0; i--) |
---|
[b46956] | 1956 | { |
---|
| 1957 | napoly xx=x; |
---|
| 1958 | napoly yy=y; |
---|
[661c214] | 1959 | int m = napExpi(i, yy, xx); |
---|
[b46956] | 1960 | if (m != 0) // in this case xx!=NULL!=yy |
---|
| 1961 | { |
---|
| 1962 | while (xx != NULL) |
---|
| 1963 | { |
---|
| 1964 | napAddExp(xx,i+1, -m); |
---|
| 1965 | pIter(xx); |
---|
| 1966 | } |
---|
| 1967 | while (yy != NULL) |
---|
| 1968 | { |
---|
| 1969 | napAddExp(yy,i+1, -m); |
---|
| 1970 | pIter(yy); |
---|
| 1971 | } |
---|
| 1972 | } |
---|
| 1973 | } |
---|
| 1974 | } |
---|
[661c214] | 1975 | if (p_LmIsConstant(y,nacRing)) /* i.e. => simplify to (1/c)*z / monom */ |
---|
[b46956] | 1976 | { |
---|
[21972b] | 1977 | if (nacIsOne(pGetCoeff(y))) |
---|
[b46956] | 1978 | { |
---|
[661c214] | 1979 | p_LmDelete(&y,nacRing); |
---|
[b46956] | 1980 | p->n = NULL; |
---|
| 1981 | ntTest(pp); |
---|
| 1982 | return; |
---|
| 1983 | } |
---|
[21972b] | 1984 | number h1 = nacInvers(pGetCoeff(y)); |
---|
| 1985 | nacNormalize(h1); |
---|
[661c214] | 1986 | napMultN(x, h1); |
---|
| 1987 | n_Delete(&h1,nacRing); |
---|
| 1988 | p_LmDelete(&y,nacRing); |
---|
[b46956] | 1989 | p->n = NULL; |
---|
| 1990 | ntTest(pp); |
---|
| 1991 | return; |
---|
| 1992 | } |
---|
| 1993 | #ifndef FACTORY_GCD_TEST |
---|
[661c214] | 1994 | if (ntNumbOfPar == 1) /* apply built-in gcd */ |
---|
[b46956] | 1995 | { |
---|
| 1996 | napoly x1,y1; |
---|
[661c214] | 1997 | if (p_GetExp(x,1,nacRing) >= p_GetExp(y,1,nacRing)) |
---|
[b46956] | 1998 | { |
---|
[661c214] | 1999 | x1 = napCopy(x); |
---|
| 2000 | y1 = napCopy(y); |
---|
[b46956] | 2001 | } |
---|
| 2002 | else |
---|
| 2003 | { |
---|
[661c214] | 2004 | x1 = napCopy(y); |
---|
| 2005 | y1 = napCopy(x); |
---|
[b46956] | 2006 | } |
---|
| 2007 | napoly r; |
---|
| 2008 | loop |
---|
| 2009 | { |
---|
[661c214] | 2010 | r = ntRemainder(x1, y1); |
---|
[b46956] | 2011 | if ((r==NULL) || (pNext(r)==NULL)) break; |
---|
| 2012 | x1 = y1; |
---|
| 2013 | y1 = r; |
---|
| 2014 | } |
---|
| 2015 | if (r!=NULL) |
---|
| 2016 | { |
---|
[661c214] | 2017 | p_Delete(&r,nacRing); |
---|
| 2018 | p_Delete(&y1,nacRing); |
---|
[b46956] | 2019 | } |
---|
| 2020 | else |
---|
| 2021 | { |
---|
[661c214] | 2022 | napDivMod(x, y1, &(p->z), &r); |
---|
| 2023 | napDivMod(y, y1, &(p->n), &r); |
---|
| 2024 | p_Delete(&y1,nacRing); |
---|
[b46956] | 2025 | } |
---|
| 2026 | x = p->z; |
---|
| 2027 | y = p->n; |
---|
| 2028 | /* collect all denoms from y and multiply x and y by it */ |
---|
| 2029 | if (ntIsChar0) |
---|
| 2030 | { |
---|
[661c214] | 2031 | number n=napLcm(y); |
---|
| 2032 | napMultN(x,n); |
---|
| 2033 | napMultN(y,n); |
---|
| 2034 | n_Delete(&n,nacRing); |
---|
[b46956] | 2035 | while(x!=NULL) |
---|
| 2036 | { |
---|
[21972b] | 2037 | nacNormalize(pGetCoeff(x)); |
---|
[b46956] | 2038 | pIter(x); |
---|
| 2039 | } |
---|
| 2040 | x = p->z; |
---|
| 2041 | while(y!=NULL) |
---|
| 2042 | { |
---|
[21972b] | 2043 | nacNormalize(pGetCoeff(y)); |
---|
[b46956] | 2044 | pIter(y); |
---|
| 2045 | } |
---|
| 2046 | y = p->n; |
---|
| 2047 | } |
---|
| 2048 | if (pNext(y)==NULL) |
---|
| 2049 | { |
---|
[21972b] | 2050 | if (nacIsOne(pGetCoeff(y))) |
---|
[b46956] | 2051 | { |
---|
[661c214] | 2052 | if (p_GetExp(y,1,nacRing)==0) |
---|
[b46956] | 2053 | { |
---|
[661c214] | 2054 | p_LmDelete(&y,nacRing); |
---|
[b46956] | 2055 | p->n = NULL; |
---|
| 2056 | } |
---|
| 2057 | ntTest(pp); |
---|
| 2058 | return; |
---|
| 2059 | } |
---|
| 2060 | } |
---|
| 2061 | } |
---|
| 2062 | #endif /* FACTORY_GCD_TEST */ |
---|
| 2063 | #ifdef HAVE_FACTORY |
---|
| 2064 | #ifndef FACTORY_GCD_TEST |
---|
| 2065 | else |
---|
| 2066 | #endif |
---|
| 2067 | { |
---|
| 2068 | napoly xx,yy; |
---|
| 2069 | singclap_algdividecontent(x,y,xx,yy); |
---|
| 2070 | if (xx!=NULL) |
---|
| 2071 | { |
---|
| 2072 | p->z=xx; |
---|
| 2073 | p->n=yy; |
---|
[661c214] | 2074 | p_Delete(&x,nacRing); |
---|
| 2075 | p_Delete(&y,nacRing); |
---|
[b46956] | 2076 | } |
---|
| 2077 | } |
---|
| 2078 | #endif |
---|
| 2079 | /* remove common factors from z and n */ |
---|
| 2080 | x=p->z; |
---|
| 2081 | y=p->n; |
---|
[21972b] | 2082 | if(!nacGreaterZero(pGetCoeff(y))) |
---|
[b46956] | 2083 | { |
---|
| 2084 | x=napNeg(x); |
---|
| 2085 | y=napNeg(y); |
---|
| 2086 | } |
---|
[21972b] | 2087 | number g=nacCopy(pGetCoeff(x)); |
---|
[b46956] | 2088 | pIter(x); |
---|
| 2089 | while (x!=NULL) |
---|
| 2090 | { |
---|
[21972b] | 2091 | number d=nacGcd(g,pGetCoeff(x), nacRing); |
---|
| 2092 | if(nacIsOne(d)) |
---|
[b46956] | 2093 | { |
---|
[661c214] | 2094 | n_Delete(&g,nacRing); |
---|
| 2095 | n_Delete(&d,nacRing); |
---|
[b46956] | 2096 | ntTest(pp); |
---|
| 2097 | return; |
---|
| 2098 | } |
---|
[661c214] | 2099 | n_Delete(&g,nacRing); |
---|
[b46956] | 2100 | g = d; |
---|
| 2101 | pIter(x); |
---|
| 2102 | } |
---|
| 2103 | while (y!=NULL) |
---|
| 2104 | { |
---|
[21972b] | 2105 | number d=nacGcd(g,pGetCoeff(y), nacRing); |
---|
| 2106 | if(nacIsOne(d)) |
---|
[b46956] | 2107 | { |
---|
[661c214] | 2108 | n_Delete(&g,nacRing); |
---|
| 2109 | n_Delete(&d,nacRing); |
---|
[b46956] | 2110 | ntTest(pp); |
---|
| 2111 | return; |
---|
| 2112 | } |
---|
[661c214] | 2113 | n_Delete(&g,nacRing); |
---|
[b46956] | 2114 | g = d; |
---|
| 2115 | pIter(y); |
---|
| 2116 | } |
---|
| 2117 | x=p->z; |
---|
| 2118 | y=p->n; |
---|
| 2119 | while (x!=NULL) |
---|
| 2120 | { |
---|
[21972b] | 2121 | number d = nacIntDiv(pGetCoeff(x),g); |
---|
[661c214] | 2122 | napSetCoeff(x,d); |
---|
[b46956] | 2123 | pIter(x); |
---|
| 2124 | } |
---|
| 2125 | while (y!=NULL) |
---|
| 2126 | { |
---|
[21972b] | 2127 | number d = nacIntDiv(pGetCoeff(y),g); |
---|
[661c214] | 2128 | napSetCoeff(y,d); |
---|
[b46956] | 2129 | pIter(y); |
---|
| 2130 | } |
---|
[661c214] | 2131 | n_Delete(&g,nacRing); |
---|
[b46956] | 2132 | ntTest(pp); |
---|
| 2133 | } |
---|
| 2134 | |
---|
| 2135 | /*2 |
---|
| 2136 | * returns in result->n 1 |
---|
| 2137 | * and in result->z the lcm(a->z,b->n) |
---|
| 2138 | */ |
---|
| 2139 | number ntLcm(number la, number lb, const ring r) |
---|
| 2140 | { |
---|
| 2141 | lnumber result; |
---|
| 2142 | lnumber a = (lnumber)la; |
---|
| 2143 | lnumber b = (lnumber)lb; |
---|
| 2144 | result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 2145 | ntTest(la); |
---|
| 2146 | ntTest(lb); |
---|
| 2147 | napoly x = p_Copy(a->z, r->algring); |
---|
[661c214] | 2148 | number t = napLcm(b->z); // get all denom of b->z |
---|
[21972b] | 2149 | if (!nacIsOne(t)) |
---|
[b46956] | 2150 | { |
---|
| 2151 | number bt, rr; |
---|
| 2152 | napoly xx=x; |
---|
| 2153 | while (xx!=NULL) |
---|
| 2154 | { |
---|
[21972b] | 2155 | bt = nacGcd(t, pGetCoeff(xx), r->algring); |
---|
| 2156 | rr = nacMult(t, pGetCoeff(xx)); |
---|
[b46956] | 2157 | n_Delete(&pGetCoeff(xx),r->algring); |
---|
[21972b] | 2158 | pGetCoeff(xx) = nacDiv(rr, bt); |
---|
| 2159 | nacNormalize(pGetCoeff(xx)); |
---|
[b46956] | 2160 | n_Delete(&bt,r->algring); |
---|
| 2161 | n_Delete(&rr,r->algring); |
---|
| 2162 | pIter(xx); |
---|
| 2163 | } |
---|
| 2164 | } |
---|
| 2165 | n_Delete(&t,r->algring); |
---|
| 2166 | result->z = x; |
---|
| 2167 | #ifdef HAVE_FACTORY |
---|
| 2168 | if (b->n!=NULL) |
---|
| 2169 | { |
---|
| 2170 | result->z=singclap_alglcm(result->z,b->n); |
---|
| 2171 | p_Delete(&x,r->algring); |
---|
| 2172 | } |
---|
| 2173 | #endif |
---|
| 2174 | ntTest(la); |
---|
| 2175 | ntTest(lb); |
---|
| 2176 | ntTest((number)result); |
---|
| 2177 | return ((number)result); |
---|
| 2178 | } |
---|
| 2179 | |
---|
| 2180 | /*2 |
---|
| 2181 | * map Z/p -> Q(a) |
---|
| 2182 | */ |
---|
| 2183 | number ntMapP0(number c) |
---|
| 2184 | { |
---|
| 2185 | if (npIsZero(c)) return NULL; |
---|
| 2186 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2187 | l->s=2; |
---|
[661c214] | 2188 | l->z=(napoly)p_Init(nacRing); |
---|
[b46956] | 2189 | int i=(int)((long)c); |
---|
| 2190 | if (i>((long)ntMapRing->ch>>2)) i-=(long)ntMapRing->ch; |
---|
[661c214] | 2191 | pGetCoeff(l->z)=nlInit(i, nacRing); |
---|
[b46956] | 2192 | l->n=NULL; |
---|
| 2193 | return (number)l; |
---|
| 2194 | } |
---|
| 2195 | |
---|
| 2196 | /*2 |
---|
| 2197 | * map Q -> Q(a) |
---|
| 2198 | */ |
---|
| 2199 | number ntMap00(number c) |
---|
| 2200 | { |
---|
| 2201 | if (nlIsZero(c)) return NULL; |
---|
| 2202 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2203 | l->s=0; |
---|
[661c214] | 2204 | l->z=(napoly)p_Init(nacRing); |
---|
[b46956] | 2205 | pGetCoeff(l->z)=nlCopy(c); |
---|
| 2206 | l->n=NULL; |
---|
| 2207 | return (number)l; |
---|
| 2208 | } |
---|
| 2209 | |
---|
| 2210 | /*2 |
---|
| 2211 | * map Z/p -> Z/p(a) |
---|
| 2212 | */ |
---|
| 2213 | number ntMapPP(number c) |
---|
| 2214 | { |
---|
| 2215 | if (npIsZero(c)) return NULL; |
---|
| 2216 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2217 | l->s=2; |
---|
[661c214] | 2218 | l->z=(napoly)p_Init(nacRing); |
---|
[b46956] | 2219 | pGetCoeff(l->z)=c; /* omit npCopy, because npCopy is a no-op */ |
---|
| 2220 | l->n=NULL; |
---|
| 2221 | return (number)l; |
---|
| 2222 | } |
---|
| 2223 | |
---|
| 2224 | /*2 |
---|
| 2225 | * map Z/p' -> Z/p(a) |
---|
| 2226 | */ |
---|
| 2227 | number ntMapPP1(number c) |
---|
| 2228 | { |
---|
| 2229 | if (npIsZero(c)) return NULL; |
---|
| 2230 | int i=(int)((long)c); |
---|
| 2231 | if (i>(long)ntMapRing->ch) i-=(long)ntMapRing->ch; |
---|
| 2232 | number n=npInit(i,ntMapRing); |
---|
| 2233 | if (npIsZero(n)) return NULL; |
---|
| 2234 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2235 | l->s=2; |
---|
[661c214] | 2236 | l->z=(napoly)p_Init(nacRing); |
---|
[b46956] | 2237 | pGetCoeff(l->z)=n; |
---|
| 2238 | l->n=NULL; |
---|
| 2239 | return (number)l; |
---|
| 2240 | } |
---|
| 2241 | |
---|
| 2242 | /*2 |
---|
| 2243 | * map Q -> Z/p(a) |
---|
| 2244 | */ |
---|
| 2245 | number ntMap0P(number c) |
---|
| 2246 | { |
---|
| 2247 | if (nlIsZero(c)) return NULL; |
---|
[661c214] | 2248 | number n=npInit(nlModP(c,npPrimeM),nacRing); |
---|
[b46956] | 2249 | if (npIsZero(n)) return NULL; |
---|
| 2250 | npTest(n); |
---|
| 2251 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2252 | l->s=2; |
---|
[661c214] | 2253 | l->z=(napoly)p_Init(nacRing); |
---|
[b46956] | 2254 | pGetCoeff(l->z)=n; |
---|
| 2255 | l->n=NULL; |
---|
| 2256 | return (number)l; |
---|
| 2257 | } |
---|
| 2258 | |
---|
| 2259 | /*2 |
---|
| 2260 | * map _(a) -> _(b) |
---|
| 2261 | */ |
---|
| 2262 | number ntMapQaQb(number c) |
---|
| 2263 | { |
---|
| 2264 | if (c==NULL) return NULL; |
---|
| 2265 | lnumber erg= (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 2266 | lnumber src =(lnumber)c; |
---|
| 2267 | erg->s=src->s; |
---|
[661c214] | 2268 | erg->z=napMap(src->z); |
---|
| 2269 | erg->n=napMap(src->n); |
---|
[b46956] | 2270 | return (number)erg; |
---|
| 2271 | } |
---|
| 2272 | |
---|
| 2273 | nMapFunc ntSetMap(const ring src, const ring dst) |
---|
| 2274 | { |
---|
| 2275 | ntMapRing=src; |
---|
| 2276 | if (rField_is_Q_a(dst)) /* -> Q(a) */ |
---|
| 2277 | { |
---|
| 2278 | if (rField_is_Q(src)) |
---|
| 2279 | { |
---|
| 2280 | return ntMap00; /*Q -> Q(a)*/ |
---|
| 2281 | } |
---|
| 2282 | if (rField_is_Zp(src)) |
---|
| 2283 | { |
---|
| 2284 | return ntMapP0; /* Z/p -> Q(a)*/ |
---|
| 2285 | } |
---|
| 2286 | if (rField_is_Q_a(src)) |
---|
| 2287 | { |
---|
| 2288 | int i; |
---|
| 2289 | ntParsToCopy=0; |
---|
| 2290 | for(i=0;i<rPar(src);i++) |
---|
| 2291 | { |
---|
| 2292 | if ((i>=rPar(dst)) |
---|
| 2293 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
| 2294 | return NULL; |
---|
| 2295 | ntParsToCopy++; |
---|
| 2296 | } |
---|
[21972b] | 2297 | nacMap=nacCopy; |
---|
[b46956] | 2298 | if ((ntParsToCopy==rPar(dst))&&(ntParsToCopy==rPar(src))) |
---|
| 2299 | return ntCopy; /* Q(a) -> Q(a) */ |
---|
| 2300 | return ntMapQaQb; /* Q(a..) -> Q(a..) */ |
---|
| 2301 | } |
---|
| 2302 | } |
---|
| 2303 | /*-----------------------------------------------------*/ |
---|
| 2304 | if (rField_is_Zp_a(dst)) /* -> Z/p(a) */ |
---|
| 2305 | { |
---|
| 2306 | if (rField_is_Q(src)) |
---|
| 2307 | { |
---|
| 2308 | return ntMap0P; /*Q -> Z/p(a)*/ |
---|
| 2309 | } |
---|
| 2310 | if (rField_is_Zp(src)) |
---|
| 2311 | { |
---|
| 2312 | if (src->ch==dst->ch) |
---|
| 2313 | { |
---|
| 2314 | return ntMapPP; /* Z/p -> Z/p(a)*/ |
---|
| 2315 | } |
---|
| 2316 | else |
---|
| 2317 | { |
---|
| 2318 | return ntMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
| 2319 | } |
---|
| 2320 | } |
---|
| 2321 | if (rField_is_Zp_a(src)) |
---|
| 2322 | { |
---|
| 2323 | if (rChar(src)==rChar(dst)) |
---|
| 2324 | { |
---|
[21972b] | 2325 | nacMap=nacCopy; |
---|
[b46956] | 2326 | } |
---|
| 2327 | else |
---|
| 2328 | { |
---|
[21972b] | 2329 | nacMap = npMapP; |
---|
[b46956] | 2330 | } |
---|
| 2331 | int i; |
---|
| 2332 | ntParsToCopy=0; |
---|
| 2333 | for(i=0;i<rPar(src);i++) |
---|
| 2334 | { |
---|
| 2335 | if ((i>=rPar(dst)) |
---|
| 2336 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
| 2337 | return NULL; |
---|
| 2338 | ntParsToCopy++; |
---|
| 2339 | } |
---|
| 2340 | if ((ntParsToCopy==rPar(dst))&&(ntParsToCopy==rPar(src)) |
---|
[21972b] | 2341 | && (nacMap==nacCopy)) |
---|
[b46956] | 2342 | return ntCopy; /* Z/p(a) -> Z/p(a) */ |
---|
| 2343 | return ntMapQaQb; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
| 2344 | } |
---|
| 2345 | } |
---|
| 2346 | return NULL; /* default */ |
---|
| 2347 | } |
---|
| 2348 | |
---|
| 2349 | /*2 |
---|
| 2350 | * convert a napoly number into a poly |
---|
| 2351 | */ |
---|
| 2352 | poly ntPermNumber(number z, int * par_perm, int P, ring oldRing) |
---|
| 2353 | { |
---|
| 2354 | if (z==NULL) return NULL; |
---|
| 2355 | poly res=NULL; |
---|
| 2356 | poly p; |
---|
| 2357 | napoly za=((lnumber)z)->z; |
---|
| 2358 | napoly zb=((lnumber)z)->n; |
---|
| 2359 | nMapFunc nMap=ntSetMap(oldRing,currRing); |
---|
| 2360 | if (currRing->parameter!=NULL) |
---|
[661c214] | 2361 | nMap=currRing->algring->cf->cfSetMap(oldRing->algring, nacRing); |
---|
[b46956] | 2362 | else |
---|
| 2363 | nMap=currRing->cf->cfSetMap(oldRing->algring, currRing); |
---|
| 2364 | if (nMap==NULL) return NULL; /* emergency exit only */ |
---|
| 2365 | do |
---|
| 2366 | { |
---|
| 2367 | p = pInit(); |
---|
| 2368 | pNext(p)=NULL; |
---|
| 2369 | nNew(&pGetCoeff(p)); |
---|
| 2370 | int i; |
---|
| 2371 | for(i=pVariables;i;i--) |
---|
| 2372 | pSetExp(p,i, 0); |
---|
| 2373 | if (rRing_has_Comp(currRing)) pSetComp(p, 0); |
---|
| 2374 | napoly pa=NULL; |
---|
| 2375 | lnumber pan; |
---|
| 2376 | if (currRing->parameter!=NULL) |
---|
| 2377 | { |
---|
| 2378 | assume(oldRing->algring!=NULL); |
---|
| 2379 | pGetCoeff(p)=(number)omAlloc0Bin(rnumber_bin); |
---|
| 2380 | pan=(lnumber)pGetCoeff(p); |
---|
| 2381 | pan->s=2; |
---|
[661c214] | 2382 | pan->z=napInitz(nMap(pGetCoeff(za))); |
---|
[b46956] | 2383 | pa=pan->z; |
---|
| 2384 | } |
---|
| 2385 | else |
---|
| 2386 | { |
---|
| 2387 | pGetCoeff(p)=nMap(pGetCoeff(za)); |
---|
| 2388 | } |
---|
| 2389 | for(i=0;i<P;i++) |
---|
| 2390 | { |
---|
| 2391 | if(napGetExpFrom(za,i+1,oldRing)!=0) |
---|
| 2392 | { |
---|
| 2393 | if(par_perm==NULL) |
---|
| 2394 | { |
---|
| 2395 | if ((rPar(currRing)>=i) && (pa!=NULL)) |
---|
| 2396 | { |
---|
| 2397 | napSetExp(pa,i+1,napGetExpFrom(za,i+1,oldRing)); |
---|
[661c214] | 2398 | p_Setm(pa,nacRing); |
---|
[b46956] | 2399 | } |
---|
| 2400 | else |
---|
| 2401 | { |
---|
| 2402 | pDelete(&p); |
---|
| 2403 | break; |
---|
| 2404 | } |
---|
| 2405 | } |
---|
| 2406 | else if(par_perm[i]>0) |
---|
| 2407 | pSetExp(p,par_perm[i],napGetExpFrom(za,i+1,oldRing)); |
---|
| 2408 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
| 2409 | { |
---|
| 2410 | napSetExp(pa,-par_perm[i], napGetExpFrom(za,i+1,oldRing)); |
---|
[661c214] | 2411 | p_Setm(pa,nacRing); |
---|
[b46956] | 2412 | } |
---|
| 2413 | else |
---|
| 2414 | { |
---|
| 2415 | pDelete(&p); |
---|
| 2416 | break; |
---|
| 2417 | } |
---|
| 2418 | } |
---|
| 2419 | } |
---|
| 2420 | if (p!=NULL) |
---|
| 2421 | { |
---|
| 2422 | pSetm(p); |
---|
| 2423 | if (zb!=NULL) |
---|
| 2424 | { |
---|
| 2425 | if (currRing->P>0) |
---|
| 2426 | { |
---|
[661c214] | 2427 | pan->n=napPerm(zb,par_perm,oldRing,nMap); |
---|
[b46956] | 2428 | if(pan->n==NULL) /* error in mapping or mapping to variable */ |
---|
| 2429 | pDelete(&p); |
---|
| 2430 | } |
---|
| 2431 | else |
---|
| 2432 | pDelete(&p); |
---|
| 2433 | } |
---|
| 2434 | pTest(p); |
---|
| 2435 | res=pAdd(res,p); |
---|
| 2436 | } |
---|
| 2437 | pIter(za); |
---|
| 2438 | } |
---|
| 2439 | while (za!=NULL); |
---|
| 2440 | pTest(res); |
---|
| 2441 | return res; |
---|
| 2442 | } |
---|
| 2443 | |
---|
| 2444 | number ntGetDenom(number &n, const ring r) |
---|
| 2445 | { |
---|
| 2446 | lnumber x=(lnumber)n; |
---|
| 2447 | if (x->n!=NULL) |
---|
| 2448 | { |
---|
| 2449 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 2450 | rr->z=p_Copy(x->n,r->algring); |
---|
| 2451 | rr->s = 2; |
---|
| 2452 | return (number)rr; |
---|
| 2453 | } |
---|
| 2454 | return n_Init(1,r); |
---|
| 2455 | } |
---|
| 2456 | |
---|
| 2457 | number ntGetNumerator(number &n, const ring r) |
---|
| 2458 | { |
---|
| 2459 | lnumber x=(lnumber)n; |
---|
| 2460 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 2461 | rr->z=p_Copy(x->z,r->algring); |
---|
| 2462 | rr->s = 2; |
---|
| 2463 | return (number)rr; |
---|
| 2464 | } |
---|
| 2465 | |
---|
| 2466 | #ifdef LDEBUG |
---|
| 2467 | BOOLEAN ntDBTest(number a, const char *f,const int l) |
---|
| 2468 | { |
---|
| 2469 | lnumber x=(lnumber)a; |
---|
| 2470 | if (x == NULL) |
---|
| 2471 | return TRUE; |
---|
| 2472 | #ifdef LDEBUG |
---|
| 2473 | omCheckAddrSize(a, sizeof(snumber)); |
---|
| 2474 | #endif |
---|
| 2475 | napoly p = x->z; |
---|
| 2476 | if (p==NULL) |
---|
| 2477 | { |
---|
| 2478 | Print("0/* in %s:%d\n",f,l); |
---|
| 2479 | return FALSE; |
---|
| 2480 | } |
---|
| 2481 | while(p!=NULL) |
---|
| 2482 | { |
---|
[d0450f] | 2483 | if (( ntIsChar0 && nlIsZero(pGetCoeff(p))) |
---|
[b46956] | 2484 | || ((!ntIsChar0) && npIsZero(pGetCoeff(p)))) |
---|
| 2485 | { |
---|
| 2486 | Print("coeff 0 in %s:%d\n",f,l); |
---|
| 2487 | return FALSE; |
---|
| 2488 | } |
---|
| 2489 | if (ntIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
| 2490 | return FALSE; |
---|
| 2491 | pIter(p); |
---|
| 2492 | } |
---|
| 2493 | p = x->n; |
---|
| 2494 | while(p!=NULL) |
---|
| 2495 | { |
---|
| 2496 | if (ntIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
| 2497 | return FALSE; |
---|
| 2498 | pIter(p); |
---|
| 2499 | } |
---|
| 2500 | return TRUE; |
---|
| 2501 | } |
---|
| 2502 | #endif |
---|