[35aab3] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[a6904c] | 4 | /* $Id: longalg.cc 12469 2010-01-28 10:39:49Z hannes $ */ |
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[35aab3] | 5 | /* |
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[a6904c] | 6 | * ABSTRACT: algebraic numbers |
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[35aab3] | 7 | */ |
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| 8 | |
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| 9 | #include <stdio.h> |
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| 10 | #include <string.h> |
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[599326] | 11 | #include <kernel/mod2.h> |
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| 12 | #include <kernel/structs.h> |
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[b1dfaf] | 13 | #include <omalloc/omalloc.h> |
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[599326] | 14 | #include <kernel/febase.h> |
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| 15 | #include <kernel/longrat.h> |
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| 16 | #include <kernel/modulop.h> |
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| 17 | #include <kernel/numbers.h> |
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| 18 | #include <kernel/polys.h> |
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| 19 | #include <kernel/ideals.h> |
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| 20 | #include <kernel/ring.h> |
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[35aab3] | 21 | #ifdef HAVE_FACTORY |
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[24fd70] | 22 | #define SI_DONT_HAVE_GLOBAL_VARS |
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[b1dfaf] | 23 | #include <factory/factory.h> |
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[599326] | 24 | #include <kernel/clapsing.h> |
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| 25 | #include <kernel/clapconv.h> |
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[35aab3] | 26 | #endif |
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[599326] | 27 | #include <kernel/longalg.h> |
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[661c214] | 28 | #include <kernel/longtrans.h> |
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[35aab3] | 29 | |
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| 30 | #ifdef LDEBUG |
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[a6904c] | 31 | #define naTest(a) naDBTest(a,__FILE__,__LINE__) |
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| 32 | BOOLEAN naDBTest(number a, const char *f,const int l); |
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[35aab3] | 33 | #else |
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[a6904c] | 34 | #define naTest(a) |
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[35aab3] | 35 | #endif |
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| 36 | |
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[661c214] | 37 | naIdeal naI = NULL; |
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[21972b] | 38 | napoly naMinimalPoly; |
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| 39 | omBin snaIdeal_bin = omGetSpecBin(sizeof(snaIdeal)); |
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| 40 | number (*naMap)(number from); |
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[661c214] | 41 | |
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[9a07cd] | 42 | void redefineFunctionPointers() |
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| 43 | { |
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| 44 | n_Procs_s* n = currRing->cf; |
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| 45 | /* re-defining function pointers */ |
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| 46 | n->cfDelete = naDelete; |
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| 47 | n->nNormalize = naNormalize; |
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| 48 | n->cfInit = naInit; |
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| 49 | n->nPar = naPar; |
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| 50 | n->nParDeg = naParDeg; |
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| 51 | n->n_Int = naInt; |
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| 52 | n->nAdd = naAdd; |
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| 53 | n->nSub = naSub; |
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| 54 | n->nMult = naMult; |
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| 55 | n->nDiv = naDiv; |
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| 56 | n->nExactDiv = naDiv; |
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| 57 | n->nIntDiv = naIntDiv; |
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| 58 | n->nNeg = naNeg; |
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| 59 | n->nInvers = naInvers; |
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| 60 | n->nCopy = naCopy; |
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| 61 | n->cfCopy = na_Copy; |
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| 62 | n->nGreater = naGreater; |
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| 63 | n->nEqual = naEqual; |
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| 64 | n->nIsZero = naIsZero; |
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| 65 | n->nIsOne = naIsOne; |
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| 66 | n->nIsMOne = naIsMOne; |
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| 67 | n->nGreaterZero = naGreaterZero; |
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| 68 | n->cfWrite = naWrite; |
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| 69 | n->nRead = naRead; |
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| 70 | n->nPower = naPower; |
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| 71 | n->nGcd = naGcd; |
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| 72 | n->nLcm = naLcm; |
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| 73 | n->cfSetMap = naSetMap; |
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| 74 | n->nName = naName; |
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| 75 | n->nSize = naSize; |
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| 76 | n->cfGetDenom = napGetDenom; |
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| 77 | n->cfGetNumerator = napGetNumerator; |
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| 78 | #ifdef LDEBUG |
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| 79 | n->nDBTest = naDBTest; |
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| 80 | #endif |
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| 81 | /* re-defining global function pointers */ |
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| 82 | nNormalize=naNormalize; |
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| 83 | nPar = naPar; |
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| 84 | nParDeg= nParDeg; |
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| 85 | n_Int = naInt; |
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| 86 | nAdd = naAdd; |
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| 87 | nSub = naSub; |
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| 88 | nMult = naMult; |
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| 89 | nDiv = naDiv; |
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| 90 | nExactDiv= naDiv; |
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| 91 | nIntDiv= naIntDiv; |
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| 92 | nNeg = naNeg; |
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| 93 | nInvers= naInvers; |
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| 94 | nCopy = naCopy; |
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| 95 | nGreater = naGreater; |
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| 96 | nEqual = naEqual; |
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| 97 | nIsZero = naIsZero; |
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| 98 | nIsOne = naIsOne; |
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| 99 | nIsMOne = naIsMOne; |
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| 100 | nGreaterZero = naGreaterZero; |
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| 101 | nRead = naRead; |
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| 102 | nPower = naPower; |
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| 103 | nGcd = naGcd; |
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| 104 | nLcm = naLcm; |
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| 105 | nName= naName; |
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| 106 | nSize = naSize; |
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| 107 | } |
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| 108 | |
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[21972b] | 109 | static number nadGcd( number a, number b, const ring r) { return nacInit(1,r); } |
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[35aab3] | 110 | /*2 |
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| 111 | * sets the appropriate operators |
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| 112 | */ |
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| 113 | void naSetChar(int i, ring r) |
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| 114 | { |
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[d0450f] | 115 | assume((r->minpoly != NULL) || |
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| 116 | (r->minideal != NULL) ); |
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| 117 | |
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[35aab3] | 118 | if (naI!=NULL) |
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| 119 | { |
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| 120 | int j; |
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| 121 | for (j=naI->anz-1; j>=0; j--) |
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[1629ab] | 122 | p_Delete (&naI->liste[j],nacRing); |
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[35aab3] | 123 | omFreeSize((ADDRESS)naI->liste,naI->anz*sizeof(napoly)); |
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| 124 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
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| 125 | naI=NULL; |
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| 126 | } |
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| 127 | naMap = naCopy; |
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[9bea6e] | 128 | |
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[35aab3] | 129 | if (r->minpoly!=NULL) |
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[ec7055] | 130 | { |
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[35aab3] | 131 | naMinimalPoly=((lnumber)r->minpoly)->z; |
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[074d3e] | 132 | #ifdef LDEBUG |
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[ec7055] | 133 | omCheckAddr(naMinimalPoly); |
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[074d3e] | 134 | #endif |
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[ec7055] | 135 | } |
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[35aab3] | 136 | else |
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| 137 | naMinimalPoly = NULL; |
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[d0450f] | 138 | |
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[a8bb72d] | 139 | if (r->minideal!=NULL) |
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| 140 | { |
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| 141 | naI=(naIdeal)omAllocBin(snaIdeal_bin); |
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| 142 | naI->anz=IDELEMS(r->minideal); |
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| 143 | naI->liste=(napoly*)omAlloc(naI->anz*sizeof(napoly)); |
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| 144 | int j; |
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| 145 | for (j=naI->anz-1; j>=0; j--) |
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| 146 | { |
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| 147 | lnumber a = (lnumber)pGetCoeff(r->minideal->m[j]); |
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| 148 | naI->liste[j]=napCopy(a->z); |
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| 149 | } |
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| 150 | } |
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[9bea6e] | 151 | |
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[661c214] | 152 | ntNumbOfPar=rPar(r); |
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[35aab3] | 153 | if (i == 1) |
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[661c214] | 154 | ntIsChar0 = 1; |
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[35aab3] | 155 | else if (i < 0) |
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| 156 | { |
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[661c214] | 157 | ntIsChar0 = 0; |
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[35aab3] | 158 | npSetChar(-i, r->algring); // to be changed HS |
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| 159 | } |
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| 160 | #ifdef TEST |
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| 161 | else |
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| 162 | { |
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| 163 | Print("naSetChar:c=%d param=%d\n",i,rPar(r)); |
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| 164 | } |
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| 165 | #endif |
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| 166 | nacRing = r->algring; |
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[21972b] | 167 | nacInit = nacRing->cf->cfInit; |
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| 168 | nacInt = nacRing->cf->n_Int; |
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| 169 | nacCopy = nacRing->cf->nCopy; |
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| 170 | nacAdd = nacRing->cf->nAdd; |
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| 171 | nacSub = nacRing->cf->nSub; |
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| 172 | nacNormalize = nacRing->cf->nNormalize; |
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| 173 | nacNeg = nacRing->cf->nNeg; |
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| 174 | nacIsZero = nacRing->cf->nIsZero; |
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| 175 | nacGreaterZero = nacRing->cf->nGreaterZero; |
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| 176 | nacIsOne = nacRing->cf->nIsOne; |
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| 177 | nacGcd = nacRing->cf->nGcd; |
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| 178 | nacLcm = nacRing->cf->nLcm; |
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| 179 | nacMult = nacRing->cf->nMult; |
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| 180 | nacDiv = nacRing->cf->nDiv; |
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| 181 | nacIntDiv = nacRing->cf->nIntDiv; |
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| 182 | nacInvers = nacRing->cf->nInvers; |
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[35aab3] | 183 | } |
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| 184 | |
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| 185 | /*================ procedure for rational functions: naXXXX =================*/ |
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| 186 | |
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| 187 | /*2 |
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| 188 | * z:= i |
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| 189 | */ |
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[8391d8] | 190 | number naInit(int i, const ring r) |
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[35aab3] | 191 | { |
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| 192 | if (i!=0) |
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| 193 | { |
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[8391d8] | 194 | number c=n_Init(i,r->algring); |
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| 195 | if (!n_IsZero(c,r->algring)) |
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[35aab3] | 196 | { |
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[8391d8] | 197 | poly z=p_Init(r->algring); |
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| 198 | pSetCoeff0(z,c); |
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[35aab3] | 199 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
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| 200 | l->z = z; |
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| 201 | l->s = 2; |
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| 202 | l->n = NULL; |
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| 203 | return (number)l; |
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| 204 | } |
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| 205 | } |
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| 206 | /*else*/ |
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| 207 | return NULL; |
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| 208 | } |
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| 209 | |
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| 210 | number naPar(int i) |
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| 211 | { |
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| 212 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
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| 213 | l->s = 2; |
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[6094f4] | 214 | l->z = p_ISet(1,nacRing); |
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[35aab3] | 215 | napSetExp(l->z,i,1); |
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| 216 | p_Setm(l->z,nacRing); |
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| 217 | l->n = NULL; |
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| 218 | return (number)l; |
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| 219 | } |
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| 220 | |
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| 221 | int naParDeg(number n) /* i := deg(n) */ |
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| 222 | { |
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| 223 | lnumber l = (lnumber)n; |
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| 224 | if (l==NULL) return -1; |
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| 225 | return napDeg(l->z); |
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| 226 | } |
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| 227 | |
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| 228 | //int naParDeg(number n) /* i := deg(n) */ |
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| 229 | //{ |
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| 230 | // lnumber l = (lnumber)n; |
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| 231 | // if (l==NULL) return -1; |
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| 232 | // return napMaxDeg(l->z)+napMaxDeg(l->n); |
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| 233 | //} |
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| 234 | |
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| 235 | int naSize(number n) /* size desc. */ |
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| 236 | { |
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| 237 | lnumber l = (lnumber)n; |
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| 238 | if (l==NULL) return -1; |
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| 239 | int len_z; |
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| 240 | int len_n; |
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| 241 | int o=napMaxDegLen(l->z,len_z)+napMaxDegLen(l->n,len_n); |
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| 242 | return (len_z+len_n)+o; |
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| 243 | } |
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| 244 | |
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| 245 | /*2 |
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| 246 | * convert a number to int (if possible) |
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| 247 | */ |
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[cf74cd6] | 248 | int naInt(number &n, const ring r) |
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[35aab3] | 249 | { |
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| 250 | lnumber l=(lnumber)n; |
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[cf74cd6] | 251 | if ((l!=NULL)&&(l->n==NULL)&&(p_IsConstant(l->z,r->algring))) |
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[35aab3] | 252 | { |
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[21972b] | 253 | return nacInt(pGetCoeff(l->z),r->algring); |
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[35aab3] | 254 | } |
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| 255 | return 0; |
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| 256 | } |
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| 257 | |
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| 258 | /*2 |
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| 259 | * deletes p |
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| 260 | */ |
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| 261 | void naDelete(number *p, const ring r) |
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| 262 | { |
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[ec7055] | 263 | if ((*p)!=r->minpoly) |
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| 264 | { |
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| 265 | lnumber l = (lnumber) * p; |
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| 266 | if (l==NULL) return; |
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[d9ff1b] | 267 | p_Delete(&(l->z),r->algring); |
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| 268 | p_Delete(&(l->n),r->algring); |
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[ec7055] | 269 | omFreeBin((ADDRESS)l, rnumber_bin); |
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| 270 | } |
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[35aab3] | 271 | *p = NULL; |
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| 272 | } |
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| 273 | |
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| 274 | /*2 |
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| 275 | * copy p to erg |
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| 276 | */ |
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| 277 | number naCopy(number p) |
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| 278 | { |
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| 279 | if (p==NULL) return NULL; |
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| 280 | naTest(p); |
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| 281 | lnumber erg; |
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| 282 | lnumber src = (lnumber)p; |
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| 283 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
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[bedece] | 284 | erg->z = p_Copy(src->z, nacRing); |
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| 285 | erg->n = p_Copy(src->n, nacRing); |
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[35aab3] | 286 | erg->s = src->s; |
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| 287 | return (number)erg; |
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| 288 | } |
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| 289 | number na_Copy(number p, const ring r) |
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| 290 | { |
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| 291 | if (p==NULL) return NULL; |
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| 292 | lnumber erg; |
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| 293 | lnumber src = (lnumber)p; |
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| 294 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
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[bedece] | 295 | erg->z = p_Copy(src->z,r->algring); |
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| 296 | erg->n = p_Copy(src->n,r->algring); |
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[35aab3] | 297 | erg->s = src->s; |
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| 298 | return (number)erg; |
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| 299 | } |
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| 300 | |
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[b3af93] | 301 | /*2 |
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| 302 | * addition; lu:= la + lb |
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| 303 | */ |
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| 304 | number naAdd(number la, number lb) |
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| 305 | { |
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[074d3e] | 306 | if (la==NULL) return naCopy(lb); |
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| 307 | if (lb==NULL) return naCopy(la); |
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| 308 | |
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[b3af93] | 309 | napoly x, y; |
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| 310 | lnumber lu; |
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| 311 | lnumber a = (lnumber)la; |
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| 312 | lnumber b = (lnumber)lb; |
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[074d3e] | 313 | #ifdef LDEBUG |
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[b3af93] | 314 | omCheckAddrSize(a,sizeof(snumber)); |
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| 315 | omCheckAddrSize(b,sizeof(snumber)); |
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[074d3e] | 316 | #endif |
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[b85e37] | 317 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
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[b3af93] | 318 | else x = napCopy(a->z); |
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[b85e37] | 319 | if (a->n!=NULL) y = pp_Mult_qq(b->z, a->n,nacRing); |
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[b3af93] | 320 | else y = napCopy(b->z); |
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[074d3e] | 321 | napoly res = napAdd(x, y); |
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| 322 | if (res==NULL) |
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[b3af93] | 323 | { |
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| 324 | return (number)NULL; |
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| 325 | } |
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[074d3e] | 326 | lu = (lnumber)omAllocBin(rnumber_bin); |
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| 327 | lu->z=res; |
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[b3af93] | 328 | if (a->n!=NULL) |
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| 329 | { |
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[b85e37] | 330 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
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[b3af93] | 331 | else x = napCopy(a->n); |
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| 332 | } |
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| 333 | else |
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| 334 | { |
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| 335 | if (b->n!=NULL) x = napCopy(b->n); |
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| 336 | else x = NULL; |
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| 337 | } |
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| 338 | //if (x!=NULL) |
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| 339 | //{ |
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[70f63a] | 340 | // if (p_LmIsConstant(x,nacRing)) |
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[b3af93] | 341 | // { |
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[21972b] | 342 | // number inv=nacInvers(pGetCoeff(x)); |
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[b3af93] | 343 | // napMultN(lu->z,inv); |
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[b85e37] | 344 | // n_Delete(&inv,nacRing); |
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[b3af93] | 345 | // napDelete(&x); |
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| 346 | // } |
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| 347 | //} |
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| 348 | lu->n = x; |
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| 349 | lu->s = FALSE; |
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[074d3e] | 350 | if (/*lu->n*/ x!=NULL) |
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[fef045c] | 351 | { |
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| 352 | number luu=(number)lu; |
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[dd8668] | 353 | //if (p_IsConstant(lu->n,nacRing)) naCoefNormalize(luu); |
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[074d3e] | 354 | //else |
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[dd8668] | 355 | naNormalize(luu); |
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[fef045c] | 356 | lu=(lnumber)luu; |
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| 357 | } |
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[074d3e] | 358 | //else lu->s=2; |
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[b3af93] | 359 | naTest((number)lu); |
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| 360 | return (number)lu; |
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| 361 | } |
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| 362 | |
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| 363 | /*2 |
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| 364 | * subtraction; r:= la - lb |
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| 365 | */ |
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| 366 | number naSub(number la, number lb) |
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| 367 | { |
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| 368 | lnumber lu; |
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| 369 | |
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| 370 | if (lb==NULL) return naCopy(la); |
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| 371 | if (la==NULL) |
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| 372 | { |
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| 373 | lu = (lnumber)naCopy(lb); |
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| 374 | lu->z = napNeg(lu->z); |
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| 375 | return (number)lu; |
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| 376 | } |
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| 377 | |
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| 378 | lnumber a = (lnumber)la; |
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| 379 | lnumber b = (lnumber)lb; |
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| 380 | |
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[074d3e] | 381 | #ifdef LDEBUG |
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[b3af93] | 382 | omCheckAddrSize(a,sizeof(snumber)); |
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| 383 | omCheckAddrSize(b,sizeof(snumber)); |
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[074d3e] | 384 | #endif |
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[b3af93] | 385 | |
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| 386 | napoly x, y; |
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[b85e37] | 387 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
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[b3af93] | 388 | else x = napCopy(a->z); |
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[b85e37] | 389 | if (a->n!=NULL) y = p_Mult_q(napCopy(b->z), napCopyNeg(a->n),nacRing); |
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[b3af93] | 390 | else y = napCopyNeg(b->z); |
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[074d3e] | 391 | napoly res = napAdd(x, y); |
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| 392 | if (res==NULL) |
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[b3af93] | 393 | { |
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| 394 | return (number)NULL; |
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| 395 | } |
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[074d3e] | 396 | lu = (lnumber)omAllocBin(rnumber_bin); |
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| 397 | lu->z=res; |
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[b3af93] | 398 | if (a->n!=NULL) |
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| 399 | { |
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[b85e37] | 400 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
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[b3af93] | 401 | else x = napCopy(a->n); |
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| 402 | } |
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| 403 | else |
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| 404 | { |
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| 405 | if (b->n!=NULL) x = napCopy(b->n); |
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| 406 | else x = NULL; |
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| 407 | } |
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| 408 | lu->n = x; |
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| 409 | lu->s = FALSE; |
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[074d3e] | 410 | if (/*lu->n*/ x!=NULL) |
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[fef045c] | 411 | { |
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| 412 | number luu=(number)lu; |
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[dd8668] | 413 | //if (p_IsConstant(lu->n,nacRing)) naCoefNormalize(luu); |
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[074d3e] | 414 | //else |
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[dd8668] | 415 | naNormalize(luu); |
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[fef045c] | 416 | lu=(lnumber)luu; |
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| 417 | } |
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[074d3e] | 418 | //else lu->s=2; |
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[b3af93] | 419 | naTest((number)lu); |
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| 420 | return (number)lu; |
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| 421 | } |
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| 422 | |
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[35aab3] | 423 | /*2 |
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| 424 | * multiplication; r:= la * lb |
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| 425 | */ |
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| 426 | number naMult(number la, number lb) |
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| 427 | { |
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| 428 | if ((la==NULL) || (lb==NULL)) |
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| 429 | return NULL; |
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| 430 | |
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| 431 | lnumber a = (lnumber)la; |
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| 432 | lnumber b = (lnumber)lb; |
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| 433 | lnumber lo; |
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| 434 | napoly x; |
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| 435 | |
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[074d3e] | 436 | #ifdef LDEBUG |
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[35aab3] | 437 | omCheckAddrSize(a,sizeof(snumber)); |
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| 438 | omCheckAddrSize(b,sizeof(snumber)); |
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[074d3e] | 439 | #endif |
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[35aab3] | 440 | naTest(la); |
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| 441 | naTest(lb); |
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| 442 | |
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| 443 | lo = (lnumber)omAllocBin(rnumber_bin); |
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[b85e37] | 444 | lo->z = pp_Mult_qq(a->z, b->z,nacRing); |
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[35aab3] | 445 | |
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| 446 | if (a->n==NULL) |
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| 447 | { |
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| 448 | if (b->n==NULL) |
---|
| 449 | x = NULL; |
---|
| 450 | else |
---|
| 451 | x = napCopy(b->n); |
---|
| 452 | } |
---|
| 453 | else |
---|
| 454 | { |
---|
| 455 | if (b->n==NULL) |
---|
| 456 | { |
---|
| 457 | x = napCopy(a->n); |
---|
| 458 | } |
---|
| 459 | else |
---|
| 460 | { |
---|
[b85e37] | 461 | x = pp_Mult_qq(b->n, a->n, nacRing); |
---|
[35aab3] | 462 | } |
---|
| 463 | } |
---|
| 464 | if (naMinimalPoly!=NULL) |
---|
| 465 | { |
---|
[b85e37] | 466 | if (p_GetExp(lo->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[d0450f] | 467 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
| 468 | if ((x!=NULL) && |
---|
| 469 | (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing))) |
---|
| 470 | x = napRemainder(x, naMinimalPoly); |
---|
[35aab3] | 471 | } |
---|
| 472 | if (naI!=NULL) |
---|
| 473 | { |
---|
| 474 | lo->z = napRedp (lo->z); |
---|
| 475 | if (lo->z != NULL) |
---|
| 476 | lo->z = napTailred (lo->z); |
---|
| 477 | if (x!=NULL) |
---|
| 478 | { |
---|
| 479 | x = napRedp (x); |
---|
| 480 | if (x!=NULL) |
---|
| 481 | x = napTailred (x); |
---|
| 482 | } |
---|
| 483 | } |
---|
[21972b] | 484 | if ((x!=NULL) && (p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
[1629ab] | 485 | p_Delete(&x,nacRing); |
---|
[35aab3] | 486 | lo->n = x; |
---|
[074d3e] | 487 | lo->s = 0; |
---|
[35aab3] | 488 | if(lo->z==NULL) |
---|
| 489 | { |
---|
| 490 | omFreeBin((ADDRESS)lo, rnumber_bin); |
---|
| 491 | lo=NULL; |
---|
| 492 | } |
---|
[fef045c] | 493 | else if (lo->n!=NULL) |
---|
[35aab3] | 494 | { |
---|
[a7b15e0] | 495 | number luu=(number)lo; |
---|
[dd8668] | 496 | // if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 497 | // else |
---|
[dd8668] | 498 | naNormalize(luu); |
---|
[a7b15e0] | 499 | lo=(lnumber)luu; |
---|
[35aab3] | 500 | } |
---|
[074d3e] | 501 | //if (naMinimalPoly==NULL) lo->s=2; |
---|
[35aab3] | 502 | naTest((number)lo); |
---|
| 503 | return (number)lo; |
---|
| 504 | } |
---|
| 505 | |
---|
| 506 | number naIntDiv(number la, number lb) |
---|
| 507 | { |
---|
| 508 | lnumber res; |
---|
| 509 | lnumber a = (lnumber)la; |
---|
| 510 | lnumber b = (lnumber)lb; |
---|
| 511 | if (a==NULL) |
---|
| 512 | { |
---|
| 513 | return NULL; |
---|
| 514 | } |
---|
| 515 | if (b==NULL) |
---|
| 516 | { |
---|
[b7e838] | 517 | WerrorS(nDivBy0); |
---|
[35aab3] | 518 | return NULL; |
---|
| 519 | } |
---|
| 520 | assume(a->z!=NULL && b->z!=NULL); |
---|
| 521 | assume(a->n==NULL && b->n==NULL); |
---|
| 522 | res = (lnumber)omAllocBin(rnumber_bin); |
---|
| 523 | res->z = napCopy(a->z); |
---|
| 524 | res->n = napCopy(b->z); |
---|
| 525 | res->s = 0; |
---|
| 526 | number nres=(number)res; |
---|
| 527 | naNormalize(nres); |
---|
| 528 | |
---|
[b3af93] | 529 | //napDelete(&res->n); |
---|
[35aab3] | 530 | naTest(nres); |
---|
| 531 | return nres; |
---|
| 532 | } |
---|
| 533 | |
---|
| 534 | /*2 |
---|
| 535 | * division; lo:= la / lb |
---|
| 536 | */ |
---|
| 537 | number naDiv(number la, number lb) |
---|
| 538 | { |
---|
| 539 | lnumber lo; |
---|
| 540 | lnumber a = (lnumber)la; |
---|
| 541 | lnumber b = (lnumber)lb; |
---|
| 542 | napoly x; |
---|
| 543 | |
---|
[b85e37] | 544 | if (a==NULL) |
---|
[35aab3] | 545 | return NULL; |
---|
| 546 | |
---|
[b85e37] | 547 | if (b==NULL) |
---|
[35aab3] | 548 | { |
---|
[b7e838] | 549 | WerrorS(nDivBy0); |
---|
[35aab3] | 550 | return NULL; |
---|
| 551 | } |
---|
[074d3e] | 552 | #ifdef LDEBUG |
---|
[35aab3] | 553 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 554 | omCheckAddrSize(b,sizeof(snumber)); |
---|
[074d3e] | 555 | #endif |
---|
[35aab3] | 556 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
| 557 | if (b->n!=NULL) |
---|
[b85e37] | 558 | lo->z = pp_Mult_qq(a->z, b->n,nacRing); |
---|
[35aab3] | 559 | else |
---|
| 560 | lo->z = napCopy(a->z); |
---|
| 561 | if (a->n!=NULL) |
---|
[b85e37] | 562 | x = pp_Mult_qq(b->z, a->n, nacRing); |
---|
[35aab3] | 563 | else |
---|
| 564 | x = napCopy(b->z); |
---|
| 565 | if (naMinimalPoly!=NULL) |
---|
| 566 | { |
---|
[b85e37] | 567 | if (p_GetExp(lo->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[d0450f] | 568 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
[b85e37] | 569 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[d0450f] | 570 | x = napRemainder(x, naMinimalPoly); |
---|
[35aab3] | 571 | } |
---|
| 572 | if (naI!=NULL) |
---|
| 573 | { |
---|
| 574 | lo->z = napRedp (lo->z); |
---|
| 575 | if (lo->z != NULL) |
---|
| 576 | lo->z = napTailred (lo->z); |
---|
| 577 | if (x!=NULL) |
---|
| 578 | { |
---|
| 579 | x = napRedp (x); |
---|
| 580 | if (x!=NULL) |
---|
| 581 | x = napTailred (x); |
---|
| 582 | } |
---|
| 583 | } |
---|
[21972b] | 584 | if ((p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
[1629ab] | 585 | p_Delete(&x,nacRing); |
---|
[35aab3] | 586 | lo->n = x; |
---|
[074d3e] | 587 | lo->s = 0; |
---|
[fef045c] | 588 | if (lo->n!=NULL) |
---|
| 589 | { |
---|
| 590 | number luu=(number)lo; |
---|
[dd8668] | 591 | //if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 592 | //else |
---|
[dd8668] | 593 | naNormalize(luu); |
---|
[fef045c] | 594 | lo=(lnumber)luu; |
---|
| 595 | } |
---|
[074d3e] | 596 | //else lo->s=2; |
---|
[35aab3] | 597 | naTest((number)lo); |
---|
| 598 | return (number)lo; |
---|
| 599 | } |
---|
| 600 | |
---|
| 601 | /*2 |
---|
[074d3e] | 602 | * za:= - za, inplace |
---|
[35aab3] | 603 | */ |
---|
| 604 | number naNeg(number za) |
---|
| 605 | { |
---|
| 606 | if (za!=NULL) |
---|
| 607 | { |
---|
| 608 | lnumber e = (lnumber)za; |
---|
| 609 | naTest(za); |
---|
| 610 | e->z = napNeg(e->z); |
---|
| 611 | } |
---|
| 612 | return za; |
---|
| 613 | } |
---|
| 614 | |
---|
| 615 | /*2 |
---|
| 616 | * 1/a |
---|
| 617 | */ |
---|
| 618 | number naInvers(number a) |
---|
| 619 | { |
---|
| 620 | lnumber lo; |
---|
| 621 | lnumber b = (lnumber)a; |
---|
| 622 | napoly x; |
---|
| 623 | |
---|
| 624 | if (b==NULL) |
---|
| 625 | { |
---|
[b7e838] | 626 | WerrorS(nDivBy0); |
---|
[35aab3] | 627 | return NULL; |
---|
| 628 | } |
---|
[074d3e] | 629 | #ifdef LDEBUG |
---|
[35aab3] | 630 | omCheckAddrSize(b,sizeof(snumber)); |
---|
[074d3e] | 631 | #endif |
---|
[35aab3] | 632 | lo = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 633 | lo->s = b->s; |
---|
| 634 | if (b->n!=NULL) |
---|
| 635 | lo->z = napCopy(b->n); |
---|
| 636 | else |
---|
[6094f4] | 637 | lo->z = p_ISet(1,nacRing); |
---|
[35aab3] | 638 | x = b->z; |
---|
[21972b] | 639 | if ((!p_LmIsConstant(x,nacRing)) || !nacIsOne(pGetCoeff(x))) |
---|
[35aab3] | 640 | x = napCopy(x); |
---|
| 641 | else |
---|
| 642 | { |
---|
| 643 | lo->n = NULL; |
---|
| 644 | naTest((number)lo); |
---|
| 645 | return (number)lo; |
---|
| 646 | } |
---|
| 647 | if (naMinimalPoly!=NULL) |
---|
| 648 | { |
---|
| 649 | x = napInvers(x, naMinimalPoly); |
---|
[b85e37] | 650 | x = p_Mult_q(x, lo->z,nacRing); |
---|
| 651 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[d0450f] | 652 | x = napRemainder(x, naMinimalPoly); |
---|
[35aab3] | 653 | lo->z = x; |
---|
| 654 | lo->n = NULL; |
---|
| 655 | while (x!=NULL) |
---|
| 656 | { |
---|
[21972b] | 657 | nacNormalize(pGetCoeff(x)); |
---|
[1629ab] | 658 | pIter(x); |
---|
[35aab3] | 659 | } |
---|
| 660 | } |
---|
| 661 | else |
---|
| 662 | lo->n = x; |
---|
| 663 | if (lo->n!=NULL) |
---|
| 664 | { |
---|
| 665 | number luu=(number)lo; |
---|
[dd8668] | 666 | //if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 667 | //else |
---|
[dd8668] | 668 | naNormalize(luu); |
---|
[35aab3] | 669 | lo=(lnumber)luu; |
---|
| 670 | } |
---|
| 671 | naTest((number)lo); |
---|
| 672 | return (number)lo; |
---|
| 673 | } |
---|
| 674 | |
---|
| 675 | |
---|
| 676 | BOOLEAN naIsZero(number za) |
---|
| 677 | { |
---|
| 678 | lnumber zb = (lnumber)za; |
---|
| 679 | naTest(za); |
---|
| 680 | #ifdef LDEBUG |
---|
| 681 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
| 682 | #endif |
---|
[b85e37] | 683 | return (zb==NULL); |
---|
[35aab3] | 684 | } |
---|
| 685 | |
---|
| 686 | |
---|
| 687 | BOOLEAN naGreaterZero(number za) |
---|
| 688 | { |
---|
| 689 | lnumber zb = (lnumber)za; |
---|
| 690 | #ifdef LDEBUG |
---|
| 691 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
| 692 | #endif |
---|
| 693 | naTest(za); |
---|
[b85e37] | 694 | if (zb!=NULL) |
---|
[35aab3] | 695 | { |
---|
[21972b] | 696 | return (nacGreaterZero(pGetCoeff(zb->z))||(!p_LmIsConstant(zb->z,nacRing))); |
---|
[35aab3] | 697 | } |
---|
[cd3d336] | 698 | /* else */ return FALSE; |
---|
[35aab3] | 699 | } |
---|
| 700 | |
---|
| 701 | |
---|
| 702 | /*2 |
---|
| 703 | * a = b ? |
---|
| 704 | */ |
---|
| 705 | BOOLEAN naEqual (number a, number b) |
---|
| 706 | { |
---|
| 707 | if(a==b) return TRUE; |
---|
| 708 | if((a==NULL)&&(b!=NULL)) return FALSE; |
---|
| 709 | if((b==NULL)&&(a!=NULL)) return FALSE; |
---|
| 710 | |
---|
| 711 | lnumber aa=(lnumber)a; |
---|
| 712 | lnumber bb=(lnumber)b; |
---|
| 713 | |
---|
| 714 | int an_deg=0; |
---|
| 715 | if(aa->n!=NULL) |
---|
| 716 | an_deg=napDeg(aa->n); |
---|
| 717 | int bn_deg=0; |
---|
| 718 | if(bb->n!=NULL) |
---|
| 719 | bn_deg=napDeg(bb->n); |
---|
| 720 | if(an_deg+napDeg(bb->z)!=bn_deg+napDeg(aa->z)) |
---|
| 721 | return FALSE; |
---|
| 722 | #if 0 |
---|
| 723 | naNormalize(a); |
---|
| 724 | aa=(lnumber)a; |
---|
| 725 | naNormalize(b); |
---|
| 726 | bb=(lnumber)b; |
---|
| 727 | if((aa->n==NULL)&&(bb->n!=NULL)) return FALSE; |
---|
| 728 | if((bb->n==NULL)&&(aa->n!=NULL)) return FALSE; |
---|
| 729 | if(napComp(aa->z,bb->z)!=0) return FALSE; |
---|
| 730 | if((aa->n!=NULL) && (napComp(aa->n,bb->n))) return FALSE; |
---|
| 731 | #endif |
---|
| 732 | number h = naSub(a, b); |
---|
| 733 | BOOLEAN bo = naIsZero(h); |
---|
| 734 | naDelete(&h,currRing); |
---|
| 735 | return bo; |
---|
| 736 | } |
---|
| 737 | |
---|
| 738 | |
---|
| 739 | BOOLEAN naGreater (number a, number b) |
---|
| 740 | { |
---|
| 741 | if (naIsZero(a)) |
---|
| 742 | return FALSE; |
---|
| 743 | if (naIsZero(b)) |
---|
| 744 | return TRUE; /* a!= 0)*/ |
---|
| 745 | return napDeg(((lnumber)a)->z)>napDeg(((lnumber)b)->z); |
---|
| 746 | } |
---|
| 747 | |
---|
| 748 | /*2 |
---|
| 749 | * reads a number |
---|
| 750 | */ |
---|
[85e68dd] | 751 | const char *naRead(const char *s, number *p) |
---|
[35aab3] | 752 | { |
---|
| 753 | napoly x; |
---|
| 754 | lnumber a; |
---|
| 755 | s = napRead(s, &x); |
---|
| 756 | if (x==NULL) |
---|
| 757 | { |
---|
| 758 | *p = NULL; |
---|
| 759 | return s; |
---|
| 760 | } |
---|
| 761 | *p = (number)omAlloc0Bin(rnumber_bin); |
---|
| 762 | a = (lnumber)*p; |
---|
| 763 | if ((naMinimalPoly!=NULL) |
---|
[b85e37] | 764 | && (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing))) |
---|
[d0450f] | 765 | a->z = napRemainder(x, naMinimalPoly); |
---|
[35aab3] | 766 | else if (naI!=NULL) |
---|
| 767 | { |
---|
| 768 | a->z = napRedp(x); |
---|
| 769 | if (a->z != NULL) |
---|
| 770 | a->z = napTailred (a->z); |
---|
| 771 | } |
---|
| 772 | else |
---|
| 773 | a->z = x; |
---|
| 774 | if(a->z==NULL) |
---|
| 775 | { |
---|
| 776 | omFreeBin((ADDRESS)*p, rnumber_bin); |
---|
| 777 | *p=NULL; |
---|
| 778 | } |
---|
| 779 | else |
---|
| 780 | { |
---|
| 781 | a->n = NULL; |
---|
| 782 | a->s = 0; |
---|
| 783 | naTest(*p); |
---|
| 784 | } |
---|
| 785 | return s; |
---|
| 786 | } |
---|
| 787 | |
---|
| 788 | /*2 |
---|
| 789 | * tries to convert a number to a name |
---|
| 790 | */ |
---|
| 791 | char * naName(number n) |
---|
| 792 | { |
---|
| 793 | lnumber ph = (lnumber)n; |
---|
[b85e37] | 794 | if (ph==NULL) |
---|
[35aab3] | 795 | return NULL; |
---|
| 796 | int i; |
---|
[661c214] | 797 | char *s=(char *)omAlloc(4* ntNumbOfPar); |
---|
[35aab3] | 798 | char *t=(char *)omAlloc(8); |
---|
| 799 | s[0]='\0'; |
---|
[661c214] | 800 | for (i = 0; i <= ntNumbOfPar - 1; i++) |
---|
[35aab3] | 801 | { |
---|
[b85e37] | 802 | int e=p_GetExp(ph->z,i+1,nacRing); |
---|
| 803 | if (e > 0) |
---|
[35aab3] | 804 | { |
---|
[b85e37] | 805 | if (e >1) |
---|
[35aab3] | 806 | { |
---|
[21972b] | 807 | sprintf(t,"%s%d",ntParNames[i],e); |
---|
[35aab3] | 808 | strcat(s,t); |
---|
| 809 | } |
---|
| 810 | else |
---|
| 811 | { |
---|
[21972b] | 812 | strcat(s,ntParNames[i]); |
---|
[35aab3] | 813 | } |
---|
| 814 | } |
---|
| 815 | } |
---|
| 816 | omFreeSize((ADDRESS)t,8); |
---|
| 817 | if (s[0]=='\0') |
---|
| 818 | { |
---|
| 819 | omFree((ADDRESS)s); |
---|
| 820 | return NULL; |
---|
| 821 | } |
---|
| 822 | return s; |
---|
| 823 | } |
---|
| 824 | |
---|
| 825 | /*2 |
---|
| 826 | * writes a number |
---|
| 827 | */ |
---|
[493225] | 828 | void naWrite(number &phn, const ring r) |
---|
[35aab3] | 829 | { |
---|
| 830 | lnumber ph = (lnumber)phn; |
---|
[b85e37] | 831 | if (ph==NULL) |
---|
[35aab3] | 832 | StringAppendS("0"); |
---|
| 833 | else |
---|
| 834 | { |
---|
| 835 | phn->s = 0; |
---|
| 836 | BOOLEAN has_denom=(ph->n!=NULL); |
---|
[493225] | 837 | napWrite(ph->z,has_denom/*(ph->n!=NULL)*/,r); |
---|
[35aab3] | 838 | if (has_denom/*(ph->n!=NULL)*/) |
---|
| 839 | { |
---|
| 840 | StringAppendS("/"); |
---|
[493225] | 841 | napWrite(ph->n,TRUE,r); |
---|
[35aab3] | 842 | } |
---|
| 843 | } |
---|
| 844 | } |
---|
| 845 | |
---|
| 846 | /*2 |
---|
| 847 | * za == 1 ? |
---|
| 848 | */ |
---|
| 849 | BOOLEAN naIsOne(number za) |
---|
| 850 | { |
---|
| 851 | lnumber a = (lnumber)za; |
---|
| 852 | napoly x, y; |
---|
| 853 | number t; |
---|
| 854 | if (a==NULL) return FALSE; |
---|
| 855 | #ifdef LDEBUG |
---|
[074d3e] | 856 | omCheckAddrSize(a,sizeof(snumber)); |
---|
[b85e37] | 857 | if (a->z==NULL) |
---|
| 858 | { |
---|
| 859 | WerrorS("internal zero error(4)"); |
---|
| 860 | return FALSE; |
---|
| 861 | } |
---|
[35aab3] | 862 | #endif |
---|
| 863 | if (a->n==NULL) |
---|
| 864 | { |
---|
[70f63a] | 865 | if (p_LmIsConstant(a->z,nacRing)) |
---|
[e6ab52] | 866 | { |
---|
[21972b] | 867 | return nacIsOne(pGetCoeff(a->z)); |
---|
[e6ab52] | 868 | } |
---|
[35aab3] | 869 | else return FALSE; |
---|
| 870 | } |
---|
[1c3aa7] | 871 | #if 0 |
---|
[35aab3] | 872 | x = a->z; |
---|
| 873 | y = a->n; |
---|
| 874 | do |
---|
| 875 | { |
---|
| 876 | if (napComp(x, y)) |
---|
| 877 | return FALSE; |
---|
| 878 | else |
---|
| 879 | { |
---|
[21972b] | 880 | t = nacSub(pGetCoeff(x), pGetCoeff(y)); |
---|
| 881 | if (!nacIsZero(t)) |
---|
[35aab3] | 882 | { |
---|
[b85e37] | 883 | n_Delete(&t,nacRing); |
---|
[35aab3] | 884 | return FALSE; |
---|
| 885 | } |
---|
| 886 | else |
---|
[b85e37] | 887 | n_Delete(&t,nacRing); |
---|
[35aab3] | 888 | } |
---|
[1629ab] | 889 | pIter(x); |
---|
| 890 | pIter(y); |
---|
[35aab3] | 891 | } |
---|
| 892 | while ((x!=NULL) && (y!=NULL)); |
---|
| 893 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
[1629ab] | 894 | p_Delete(&a->z,nacRing); |
---|
| 895 | p_Delete(&a->n,nacRing); |
---|
[6094f4] | 896 | a->z = p_ISet(1,nacRing); |
---|
[35aab3] | 897 | a->n = NULL; |
---|
| 898 | return TRUE; |
---|
[1c3aa7] | 899 | #else |
---|
| 900 | return FALSE; |
---|
| 901 | #endif |
---|
[35aab3] | 902 | } |
---|
| 903 | |
---|
| 904 | /*2 |
---|
| 905 | * za == -1 ? |
---|
| 906 | */ |
---|
| 907 | BOOLEAN naIsMOne(number za) |
---|
| 908 | { |
---|
| 909 | lnumber a = (lnumber)za; |
---|
| 910 | napoly x, y; |
---|
| 911 | number t; |
---|
| 912 | if (a==NULL) return FALSE; |
---|
| 913 | #ifdef LDEBUG |
---|
[074d3e] | 914 | omCheckAddrSize(a,sizeof(snumber)); |
---|
[35aab3] | 915 | if (a->z==NULL) |
---|
| 916 | { |
---|
| 917 | WerrorS("internal zero error(5)"); |
---|
| 918 | return FALSE; |
---|
| 919 | } |
---|
| 920 | #endif |
---|
| 921 | if (a->n==NULL) |
---|
| 922 | { |
---|
[0c2088] | 923 | if (p_LmIsConstant(a->z,nacRing)) return n_IsMOne(pGetCoeff(a->z),nacRing); |
---|
[35aab3] | 924 | /*else return FALSE;*/ |
---|
| 925 | } |
---|
| 926 | return FALSE; |
---|
| 927 | } |
---|
| 928 | |
---|
| 929 | /*2 |
---|
| 930 | * returns the i-th power of p (i>=0) |
---|
| 931 | */ |
---|
| 932 | void naPower(number p, int i, number *rc) |
---|
| 933 | { |
---|
| 934 | number x; |
---|
[785e89] | 935 | *rc = naInit(1,currRing); |
---|
[35aab3] | 936 | for (; i > 0; i--) |
---|
| 937 | { |
---|
| 938 | x = naMult(*rc, p); |
---|
| 939 | naDelete(rc,currRing); |
---|
| 940 | *rc = x; |
---|
| 941 | } |
---|
| 942 | } |
---|
| 943 | |
---|
| 944 | /*2 |
---|
| 945 | * result =gcd(a,b) |
---|
| 946 | */ |
---|
| 947 | number naGcd(number a, number b, const ring r) |
---|
| 948 | { |
---|
[3de9a9] | 949 | if (a==NULL) return naCopy(b); |
---|
| 950 | if (b==NULL) return naCopy(a); |
---|
[b85e37] | 951 | |
---|
[35aab3] | 952 | lnumber x, y; |
---|
| 953 | lnumber result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 954 | |
---|
| 955 | x = (lnumber)a; |
---|
| 956 | y = (lnumber)b; |
---|
[661c214] | 957 | if ((ntNumbOfPar == 1) && (naMinimalPoly!=NULL)) |
---|
[35aab3] | 958 | { |
---|
[1629ab] | 959 | if (pNext(x->z)!=NULL) |
---|
[aaeb98] | 960 | result->z = p_Copy(x->z, r->algring); |
---|
[35aab3] | 961 | else |
---|
[a7b15e0] | 962 | result->z = napGcd0(x->z, y->z); |
---|
[35aab3] | 963 | } |
---|
[a7b15e0] | 964 | else |
---|
[52e2f6] | 965 | #ifndef HAVE_FACTORY |
---|
[e6ab52] | 966 | result->z = napGcd(x->z, y->z); // change from napGcd0 |
---|
| 967 | #else |
---|
[a7b15e0] | 968 | { |
---|
[295c703] | 969 | int c=ABS(nGetChar()); |
---|
| 970 | if (c==1) c=0; |
---|
| 971 | setCharacteristic( c ); |
---|
| 972 | |
---|
[e6ab52] | 973 | napoly rz=napGcd(x->z, y->z); |
---|
| 974 | CanonicalForm F, G, R; |
---|
[b85e37] | 975 | R=convSingPFactoryP(rz,r->algring); |
---|
[aaeb98] | 976 | p_Normalize(x->z,nacRing); |
---|
[b85e37] | 977 | F=convSingPFactoryP(x->z,r->algring)/R; |
---|
[aaeb98] | 978 | p_Normalize(y->z,nacRing); |
---|
[b85e37] | 979 | G=convSingPFactoryP(y->z,r->algring)/R; |
---|
[e6ab52] | 980 | F = gcd( F, G ); |
---|
[b85e37] | 981 | if (F.isOne()) |
---|
[e6ab52] | 982 | result->z= rz; |
---|
| 983 | else |
---|
| 984 | { |
---|
[aaeb98] | 985 | p_Delete(&rz,r->algring); |
---|
| 986 | result->z=convFactoryPSingP( F*R,r->algring ); |
---|
| 987 | p_Normalize(result->z,nacRing); |
---|
[e6ab52] | 988 | } |
---|
[a7b15e0] | 989 | } |
---|
| 990 | #endif |
---|
[35aab3] | 991 | naTest((number)result); |
---|
| 992 | return (number)result; |
---|
| 993 | } |
---|
| 994 | |
---|
[76aef7] | 995 | |
---|
[35aab3] | 996 | /*2 |
---|
[661c214] | 997 | * ntNumbOfPar = 1: |
---|
[35aab3] | 998 | * clears denominator algebraic case; |
---|
| 999 | * tries to simplify ratio transcendental case; |
---|
| 1000 | * |
---|
| 1001 | * cancels monomials |
---|
| 1002 | * occuring in denominator |
---|
[661c214] | 1003 | * and enumerator ? ntNumbOfPar != 1; |
---|
[35aab3] | 1004 | * |
---|
[b3af93] | 1005 | * #defines for Factory: |
---|
| 1006 | * FACTORY_GCD_TEST: do not apply built in gcd for |
---|
| 1007 | * univariate polynomials, always use Factory |
---|
[35aab3] | 1008 | */ |
---|
[b3af93] | 1009 | //#define FACTORY_GCD_TEST |
---|
[b85e37] | 1010 | void naCoefNormalize(number pp) |
---|
| 1011 | { |
---|
| 1012 | if (pp==NULL) return; |
---|
| 1013 | lnumber p = (lnumber)pp; |
---|
| 1014 | number nz; // all denom. of the numerator |
---|
| 1015 | nz=p_GetAllDenom(p->z,nacRing); |
---|
| 1016 | BOOLEAN norm=FALSE; |
---|
| 1017 | if (!n_IsOne(nz,nacRing)) |
---|
| 1018 | { |
---|
| 1019 | norm=TRUE; |
---|
| 1020 | p->z=p_Mult_nn(p->z,nz,nacRing); |
---|
| 1021 | if (p->n==NULL) |
---|
| 1022 | { |
---|
| 1023 | p->n=p_NSet(nz,nacRing); |
---|
| 1024 | } |
---|
| 1025 | else |
---|
| 1026 | { |
---|
| 1027 | p->n=p_Mult_nn(p->n,nz,nacRing); |
---|
| 1028 | n_Delete(&nz, nacRing); |
---|
| 1029 | } |
---|
| 1030 | } |
---|
| 1031 | else |
---|
| 1032 | { |
---|
| 1033 | n_Delete(&nz, nacRing); |
---|
| 1034 | } |
---|
[fef045c] | 1035 | if (norm) |
---|
| 1036 | { |
---|
| 1037 | norm=FALSE; |
---|
| 1038 | p_Normalize(p->z,nacRing); |
---|
| 1039 | p_Normalize(p->n,nacRing); |
---|
| 1040 | } |
---|
| 1041 | number nn; |
---|
| 1042 | nn=p_GetAllDenom(p->n,nacRing); |
---|
[b85e37] | 1043 | if (!n_IsOne(nn,nacRing)) |
---|
| 1044 | { |
---|
| 1045 | norm=TRUE; |
---|
| 1046 | p->n=p_Mult_nn(p->n,nn,nacRing); |
---|
| 1047 | p->z=p_Mult_nn(p->z,nn,nacRing); |
---|
| 1048 | n_Delete(&nn, nacRing); |
---|
| 1049 | } |
---|
| 1050 | else |
---|
| 1051 | { |
---|
| 1052 | n_Delete(&nn, nacRing); |
---|
| 1053 | } |
---|
| 1054 | if (norm) |
---|
| 1055 | { |
---|
| 1056 | p_Normalize(p->z,nacRing); |
---|
| 1057 | p_Normalize(p->n,nacRing); |
---|
| 1058 | } |
---|
[fef045c] | 1059 | // remove common factors in n, z: |
---|
| 1060 | if (p->n!=NULL) |
---|
| 1061 | { |
---|
| 1062 | poly pp=p->z; |
---|
| 1063 | nz=n_Copy(pGetCoeff(pp),nacRing); |
---|
| 1064 | pIter(pp); |
---|
| 1065 | while(pp!=NULL) |
---|
[074d3e] | 1066 | { |
---|
[fef045c] | 1067 | if (n_IsOne(nz,nacRing)) break; |
---|
| 1068 | number d=n_Gcd(nz,pGetCoeff(pp),nacRing); |
---|
| 1069 | n_Delete(&nz,nacRing); nz=d; |
---|
| 1070 | pIter(pp); |
---|
| 1071 | } |
---|
| 1072 | if (!n_IsOne(nz,nacRing)) |
---|
| 1073 | { |
---|
| 1074 | pp=p->n; |
---|
| 1075 | nn=n_Copy(pGetCoeff(pp),nacRing); |
---|
| 1076 | pIter(pp); |
---|
| 1077 | while(pp!=NULL) |
---|
[074d3e] | 1078 | { |
---|
[fef045c] | 1079 | if (n_IsOne(nn,nacRing)) break; |
---|
| 1080 | number d=n_Gcd(nn,pGetCoeff(pp),nacRing); |
---|
| 1081 | n_Delete(&nn,nacRing); nn=d; |
---|
| 1082 | pIter(pp); |
---|
| 1083 | } |
---|
| 1084 | number ng=n_Gcd(nz,nn,nacRing); |
---|
| 1085 | n_Delete(&nn,nacRing); |
---|
| 1086 | if (!n_IsOne(ng,nacRing)) |
---|
| 1087 | { |
---|
| 1088 | number ni=n_Invers(ng,nacRing); |
---|
| 1089 | p->z=p_Mult_nn(p->z,ni,nacRing); |
---|
| 1090 | p->n=p_Mult_nn(p->n,ni,nacRing); |
---|
| 1091 | p_Normalize(p->z,nacRing); |
---|
| 1092 | p_Normalize(p->n,nacRing); |
---|
| 1093 | n_Delete(&ni,nacRing); |
---|
| 1094 | } |
---|
| 1095 | n_Delete(&ng,nacRing); |
---|
| 1096 | } |
---|
| 1097 | n_Delete(&nz,nacRing); |
---|
| 1098 | } |
---|
[dd8668] | 1099 | if (p->n!=NULL) |
---|
[b85e37] | 1100 | { |
---|
[21972b] | 1101 | if(!nacGreaterZero(pGetCoeff(p->n))) |
---|
[dd8668] | 1102 | { |
---|
| 1103 | p->z=napNeg(p->z); |
---|
| 1104 | p->n=napNeg(p->n); |
---|
| 1105 | } |
---|
| 1106 | |
---|
| 1107 | if (/*(p->n!=NULL) && */ |
---|
| 1108 | (p_IsConstant(p->n,nacRing)) |
---|
| 1109 | && (n_IsOne(pGetCoeff(p->n),nacRing))) |
---|
| 1110 | { |
---|
| 1111 | p_Delete(&(p->n), nacRing); |
---|
| 1112 | p->n = NULL; |
---|
| 1113 | } |
---|
[b85e37] | 1114 | } |
---|
| 1115 | } |
---|
[074d3e] | 1116 | |
---|
[35aab3] | 1117 | void naNormalize(number &pp) |
---|
| 1118 | { |
---|
[e1b6a22] | 1119 | |
---|
[35aab3] | 1120 | //naTest(pp); // input may not be "normal" |
---|
| 1121 | lnumber p = (lnumber)pp; |
---|
| 1122 | |
---|
[dd8668] | 1123 | if (p==NULL) |
---|
[35aab3] | 1124 | return; |
---|
[b85e37] | 1125 | naCoefNormalize(pp); |
---|
[e475e3] | 1126 | p->s = 2; |
---|
[35aab3] | 1127 | napoly x = p->z; |
---|
| 1128 | napoly y = p->n; |
---|
[b85e37] | 1129 | |
---|
| 1130 | BOOLEAN norm=FALSE; |
---|
| 1131 | |
---|
[e1b6a22] | 1132 | if ((y!=NULL) && (naMinimalPoly!=NULL)) |
---|
[35aab3] | 1133 | { |
---|
[e1b6a22] | 1134 | y = napInvers(y, naMinimalPoly); |
---|
[b85e37] | 1135 | x = p_Mult_q(x, y,nacRing); |
---|
| 1136 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[d0450f] | 1137 | x = napRemainder(x, naMinimalPoly); |
---|
[e1b6a22] | 1138 | p->z = x; |
---|
| 1139 | p->n = y = NULL; |
---|
[661c214] | 1140 | norm=ntIsChar0; |
---|
[e1b6a22] | 1141 | } |
---|
[b85e37] | 1142 | |
---|
[e1b6a22] | 1143 | /* check for degree of x too high: */ |
---|
| 1144 | if ((x!=NULL) && (naMinimalPoly!=NULL) && (x!=naMinimalPoly) |
---|
[b85e37] | 1145 | && (p_GetExp(x,1,nacRing)>p_GetExp(naMinimalPoly,1,nacRing))) |
---|
[e1b6a22] | 1146 | // DO NOT REDUCE naMinimalPoly with itself |
---|
| 1147 | { |
---|
[d0450f] | 1148 | x = napRemainder(x, naMinimalPoly); |
---|
[e1b6a22] | 1149 | p->z = x; |
---|
[661c214] | 1150 | norm=ntIsChar0; |
---|
[35aab3] | 1151 | } |
---|
| 1152 | /* normalize all coefficients in n and z (if in Q) */ |
---|
[b85e37] | 1153 | if (norm) |
---|
[35aab3] | 1154 | { |
---|
[b85e37] | 1155 | naCoefNormalize(pp); |
---|
[35aab3] | 1156 | x = p->z; |
---|
| 1157 | y = p->n; |
---|
| 1158 | } |
---|
[b85e37] | 1159 | if (y==NULL) return; |
---|
| 1160 | |
---|
[8fa1c2] | 1161 | if ((naMinimalPoly == NULL) && (x!=NULL) && (y!=NULL)) |
---|
[35aab3] | 1162 | { |
---|
| 1163 | int i; |
---|
[661c214] | 1164 | for (i=ntNumbOfPar-1; i>=0; i--) |
---|
[35aab3] | 1165 | { |
---|
| 1166 | napoly xx=x; |
---|
| 1167 | napoly yy=y; |
---|
| 1168 | int m = napExpi(i, yy, xx); |
---|
| 1169 | if (m != 0) // in this case xx!=NULL!=yy |
---|
| 1170 | { |
---|
| 1171 | while (xx != NULL) |
---|
| 1172 | { |
---|
| 1173 | napAddExp(xx,i+1, -m); |
---|
[1629ab] | 1174 | pIter(xx); |
---|
[35aab3] | 1175 | } |
---|
| 1176 | while (yy != NULL) |
---|
| 1177 | { |
---|
| 1178 | napAddExp(yy,i+1, -m); |
---|
[1629ab] | 1179 | pIter(yy); |
---|
[35aab3] | 1180 | } |
---|
| 1181 | } |
---|
| 1182 | } |
---|
| 1183 | } |
---|
[70f63a] | 1184 | if (p_LmIsConstant(y,nacRing)) /* i.e. => simplify to (1/c)*z / monom */ |
---|
[35aab3] | 1185 | { |
---|
[21972b] | 1186 | if (nacIsOne(pGetCoeff(y))) |
---|
[35aab3] | 1187 | { |
---|
[aa74213] | 1188 | p_LmDelete(&y,nacRing); |
---|
[35aab3] | 1189 | p->n = NULL; |
---|
| 1190 | naTest(pp); |
---|
| 1191 | return; |
---|
| 1192 | } |
---|
[21972b] | 1193 | number h1 = nacInvers(pGetCoeff(y)); |
---|
| 1194 | nacNormalize(h1); |
---|
[b3af93] | 1195 | napMultN(x, h1); |
---|
[b85e37] | 1196 | n_Delete(&h1,nacRing); |
---|
[aa74213] | 1197 | p_LmDelete(&y,nacRing); |
---|
[35aab3] | 1198 | p->n = NULL; |
---|
| 1199 | naTest(pp); |
---|
| 1200 | return; |
---|
| 1201 | } |
---|
[b3af93] | 1202 | #ifndef FACTORY_GCD_TEST |
---|
[661c214] | 1203 | if (ntNumbOfPar == 1) /* apply built-in gcd */ |
---|
[35aab3] | 1204 | { |
---|
| 1205 | napoly x1,y1; |
---|
[b85e37] | 1206 | if (p_GetExp(x,1,nacRing) >= p_GetExp(y,1,nacRing)) |
---|
[35aab3] | 1207 | { |
---|
| 1208 | x1 = napCopy(x); |
---|
| 1209 | y1 = napCopy(y); |
---|
| 1210 | } |
---|
| 1211 | else |
---|
| 1212 | { |
---|
| 1213 | x1 = napCopy(y); |
---|
| 1214 | y1 = napCopy(x); |
---|
| 1215 | } |
---|
| 1216 | napoly r; |
---|
| 1217 | loop |
---|
| 1218 | { |
---|
[d0450f] | 1219 | r = napRemainder(x1, y1); |
---|
[1629ab] | 1220 | if ((r==NULL) || (pNext(r)==NULL)) break; |
---|
[35aab3] | 1221 | x1 = y1; |
---|
| 1222 | y1 = r; |
---|
| 1223 | } |
---|
| 1224 | if (r!=NULL) |
---|
| 1225 | { |
---|
[1629ab] | 1226 | p_Delete(&r,nacRing); |
---|
| 1227 | p_Delete(&y1,nacRing); |
---|
[35aab3] | 1228 | } |
---|
| 1229 | else |
---|
| 1230 | { |
---|
| 1231 | napDivMod(x, y1, &(p->z), &r); |
---|
| 1232 | napDivMod(y, y1, &(p->n), &r); |
---|
[1629ab] | 1233 | p_Delete(&y1,nacRing); |
---|
[35aab3] | 1234 | } |
---|
| 1235 | x = p->z; |
---|
| 1236 | y = p->n; |
---|
| 1237 | /* collect all denoms from y and multiply x and y by it */ |
---|
[661c214] | 1238 | if (ntIsChar0) |
---|
[35aab3] | 1239 | { |
---|
| 1240 | number n=napLcm(y); |
---|
[b3af93] | 1241 | napMultN(x,n); |
---|
| 1242 | napMultN(y,n); |
---|
[b85e37] | 1243 | n_Delete(&n,nacRing); |
---|
[35aab3] | 1244 | while(x!=NULL) |
---|
| 1245 | { |
---|
[21972b] | 1246 | nacNormalize(pGetCoeff(x)); |
---|
[1629ab] | 1247 | pIter(x); |
---|
[35aab3] | 1248 | } |
---|
| 1249 | x = p->z; |
---|
| 1250 | while(y!=NULL) |
---|
| 1251 | { |
---|
[21972b] | 1252 | nacNormalize(pGetCoeff(y)); |
---|
[1629ab] | 1253 | pIter(y); |
---|
[35aab3] | 1254 | } |
---|
| 1255 | y = p->n; |
---|
| 1256 | } |
---|
[1629ab] | 1257 | if (pNext(y)==NULL) |
---|
[35aab3] | 1258 | { |
---|
[21972b] | 1259 | if (nacIsOne(pGetCoeff(y))) |
---|
[35aab3] | 1260 | { |
---|
[b85e37] | 1261 | if (p_GetExp(y,1,nacRing)==0) |
---|
[35aab3] | 1262 | { |
---|
[aa74213] | 1263 | p_LmDelete(&y,nacRing); |
---|
[35aab3] | 1264 | p->n = NULL; |
---|
| 1265 | } |
---|
| 1266 | naTest(pp); |
---|
| 1267 | return; |
---|
| 1268 | } |
---|
| 1269 | } |
---|
| 1270 | } |
---|
[b3af93] | 1271 | #endif /* FACTORY_GCD_TEST */ |
---|
[35aab3] | 1272 | #ifdef HAVE_FACTORY |
---|
[b3af93] | 1273 | #ifndef FACTORY_GCD_TEST |
---|
[35aab3] | 1274 | else |
---|
[b3af93] | 1275 | #endif |
---|
[35aab3] | 1276 | { |
---|
| 1277 | napoly xx,yy; |
---|
| 1278 | singclap_algdividecontent(x,y,xx,yy); |
---|
| 1279 | if (xx!=NULL) |
---|
| 1280 | { |
---|
| 1281 | p->z=xx; |
---|
| 1282 | p->n=yy; |
---|
[1629ab] | 1283 | p_Delete(&x,nacRing); |
---|
| 1284 | p_Delete(&y,nacRing); |
---|
[35aab3] | 1285 | } |
---|
| 1286 | } |
---|
| 1287 | #endif |
---|
| 1288 | /* remove common factors from z and n */ |
---|
| 1289 | x=p->z; |
---|
| 1290 | y=p->n; |
---|
[21972b] | 1291 | if(!nacGreaterZero(pGetCoeff(y))) |
---|
[35aab3] | 1292 | { |
---|
| 1293 | x=napNeg(x); |
---|
| 1294 | y=napNeg(y); |
---|
| 1295 | } |
---|
[21972b] | 1296 | number g=nacCopy(pGetCoeff(x)); |
---|
[1629ab] | 1297 | pIter(x); |
---|
[35aab3] | 1298 | while (x!=NULL) |
---|
| 1299 | { |
---|
[21972b] | 1300 | number d=nacGcd(g,pGetCoeff(x), nacRing); |
---|
| 1301 | if(nacIsOne(d)) |
---|
[35aab3] | 1302 | { |
---|
[b85e37] | 1303 | n_Delete(&g,nacRing); |
---|
| 1304 | n_Delete(&d,nacRing); |
---|
[35aab3] | 1305 | naTest(pp); |
---|
| 1306 | return; |
---|
| 1307 | } |
---|
[b85e37] | 1308 | n_Delete(&g,nacRing); |
---|
[35aab3] | 1309 | g = d; |
---|
[1629ab] | 1310 | pIter(x); |
---|
[35aab3] | 1311 | } |
---|
| 1312 | while (y!=NULL) |
---|
| 1313 | { |
---|
[21972b] | 1314 | number d=nacGcd(g,pGetCoeff(y), nacRing); |
---|
| 1315 | if(nacIsOne(d)) |
---|
[35aab3] | 1316 | { |
---|
[b85e37] | 1317 | n_Delete(&g,nacRing); |
---|
| 1318 | n_Delete(&d,nacRing); |
---|
[35aab3] | 1319 | naTest(pp); |
---|
| 1320 | return; |
---|
| 1321 | } |
---|
[b85e37] | 1322 | n_Delete(&g,nacRing); |
---|
[35aab3] | 1323 | g = d; |
---|
[1629ab] | 1324 | pIter(y); |
---|
[35aab3] | 1325 | } |
---|
| 1326 | x=p->z; |
---|
| 1327 | y=p->n; |
---|
| 1328 | while (x!=NULL) |
---|
| 1329 | { |
---|
[21972b] | 1330 | number d = nacIntDiv(pGetCoeff(x),g); |
---|
[35aab3] | 1331 | napSetCoeff(x,d); |
---|
[1629ab] | 1332 | pIter(x); |
---|
[35aab3] | 1333 | } |
---|
| 1334 | while (y!=NULL) |
---|
| 1335 | { |
---|
[21972b] | 1336 | number d = nacIntDiv(pGetCoeff(y),g); |
---|
[35aab3] | 1337 | napSetCoeff(y,d); |
---|
[1629ab] | 1338 | pIter(y); |
---|
[35aab3] | 1339 | } |
---|
[b85e37] | 1340 | n_Delete(&g,nacRing); |
---|
[35aab3] | 1341 | naTest(pp); |
---|
| 1342 | } |
---|
| 1343 | |
---|
| 1344 | /*2 |
---|
| 1345 | * returns in result->n 1 |
---|
| 1346 | * and in result->z the lcm(a->z,b->n) |
---|
| 1347 | */ |
---|
| 1348 | number naLcm(number la, number lb, const ring r) |
---|
| 1349 | { |
---|
| 1350 | lnumber result; |
---|
| 1351 | lnumber a = (lnumber)la; |
---|
| 1352 | lnumber b = (lnumber)lb; |
---|
| 1353 | result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1354 | naTest(la); |
---|
| 1355 | naTest(lb); |
---|
[aaeb98] | 1356 | napoly x = p_Copy(a->z, r->algring); |
---|
[35aab3] | 1357 | number t = napLcm(b->z); // get all denom of b->z |
---|
[21972b] | 1358 | if (!nacIsOne(t)) |
---|
[35aab3] | 1359 | { |
---|
[aaeb98] | 1360 | number bt, rr; |
---|
[35aab3] | 1361 | napoly xx=x; |
---|
| 1362 | while (xx!=NULL) |
---|
| 1363 | { |
---|
[21972b] | 1364 | bt = nacGcd(t, pGetCoeff(xx), r->algring); |
---|
| 1365 | rr = nacMult(t, pGetCoeff(xx)); |
---|
[b85e37] | 1366 | n_Delete(&pGetCoeff(xx),r->algring); |
---|
[21972b] | 1367 | pGetCoeff(xx) = nacDiv(rr, bt); |
---|
| 1368 | nacNormalize(pGetCoeff(xx)); |
---|
[b85e37] | 1369 | n_Delete(&bt,r->algring); |
---|
| 1370 | n_Delete(&rr,r->algring); |
---|
[1629ab] | 1371 | pIter(xx); |
---|
[35aab3] | 1372 | } |
---|
| 1373 | } |
---|
[b85e37] | 1374 | n_Delete(&t,r->algring); |
---|
[35aab3] | 1375 | result->z = x; |
---|
| 1376 | #ifdef HAVE_FACTORY |
---|
| 1377 | if (b->n!=NULL) |
---|
| 1378 | { |
---|
| 1379 | result->z=singclap_alglcm(result->z,b->n); |
---|
[aaeb98] | 1380 | p_Delete(&x,r->algring); |
---|
[35aab3] | 1381 | } |
---|
| 1382 | #endif |
---|
| 1383 | naTest(la); |
---|
| 1384 | naTest(lb); |
---|
| 1385 | naTest((number)result); |
---|
| 1386 | return ((number)result); |
---|
| 1387 | } |
---|
| 1388 | |
---|
| 1389 | /*2 |
---|
| 1390 | * input: a set of constant polynomials |
---|
| 1391 | * sets the global variable naI |
---|
| 1392 | */ |
---|
| 1393 | void naSetIdeal(ideal I) |
---|
| 1394 | { |
---|
| 1395 | int i; |
---|
| 1396 | |
---|
| 1397 | if (idIs0(I)) |
---|
| 1398 | { |
---|
| 1399 | for (i=naI->anz-1; i>=0; i--) |
---|
[1629ab] | 1400 | p_Delete(&naI->liste[i],nacRing); |
---|
[35aab3] | 1401 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
---|
| 1402 | naI=NULL; |
---|
| 1403 | } |
---|
| 1404 | else |
---|
| 1405 | { |
---|
| 1406 | lnumber h; |
---|
| 1407 | number a; |
---|
| 1408 | napoly x; |
---|
| 1409 | |
---|
| 1410 | naI=(naIdeal)omAllocBin(snaIdeal_bin); |
---|
| 1411 | naI->anz=IDELEMS(I); |
---|
| 1412 | naI->liste=(napoly*)omAlloc(naI->anz*sizeof(napoly)); |
---|
| 1413 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
| 1414 | { |
---|
| 1415 | h=(lnumber)pGetCoeff(I->m[i]); |
---|
| 1416 | /* We only need the enumerator of h, as we expect it to be a polynomial */ |
---|
| 1417 | naI->liste[i]=napCopy(h->z); |
---|
| 1418 | /* If it isn't normalized (lc = 1) do this */ |
---|
[21972b] | 1419 | if (!nacIsOne(pGetCoeff(naI->liste[i]))) |
---|
[35aab3] | 1420 | { |
---|
| 1421 | x=naI->liste[i]; |
---|
[21972b] | 1422 | nacNormalize(pGetCoeff(x)); |
---|
| 1423 | a=nacCopy(pGetCoeff(x)); |
---|
| 1424 | number aa=nacInvers(a); |
---|
[b85e37] | 1425 | n_Delete(&a,nacRing); |
---|
[b3af93] | 1426 | napMultN(x,aa); |
---|
[b85e37] | 1427 | n_Delete(&aa,nacRing); |
---|
[35aab3] | 1428 | } |
---|
| 1429 | } |
---|
| 1430 | } |
---|
| 1431 | } |
---|
| 1432 | |
---|
| 1433 | /*2 |
---|
| 1434 | * map Z/p -> Q(a) |
---|
| 1435 | */ |
---|
| 1436 | number naMapP0(number c) |
---|
| 1437 | { |
---|
| 1438 | if (npIsZero(c)) return NULL; |
---|
| 1439 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 1440 | l->s=2; |
---|
| 1441 | l->z=(napoly)p_Init(nacRing); |
---|
[7447d8] | 1442 | int i=(int)((long)c); |
---|
[661c214] | 1443 | if (i>((long)ntMapRing->ch>>2)) i-=(long)ntMapRing->ch; |
---|
[8391d8] | 1444 | pGetCoeff(l->z)=nlInit(i, nacRing); |
---|
[35aab3] | 1445 | l->n=NULL; |
---|
| 1446 | return (number)l; |
---|
| 1447 | } |
---|
| 1448 | |
---|
| 1449 | /*2 |
---|
| 1450 | * map Q -> Q(a) |
---|
| 1451 | */ |
---|
| 1452 | number naMap00(number c) |
---|
| 1453 | { |
---|
| 1454 | if (nlIsZero(c)) return NULL; |
---|
| 1455 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 1456 | l->s=0; |
---|
| 1457 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 1458 | pGetCoeff(l->z)=nlCopy(c); |
---|
[35aab3] | 1459 | l->n=NULL; |
---|
| 1460 | return (number)l; |
---|
| 1461 | } |
---|
| 1462 | |
---|
| 1463 | /*2 |
---|
| 1464 | * map Z/p -> Z/p(a) |
---|
| 1465 | */ |
---|
| 1466 | number naMapPP(number c) |
---|
| 1467 | { |
---|
| 1468 | if (npIsZero(c)) return NULL; |
---|
| 1469 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 1470 | l->s=2; |
---|
| 1471 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 1472 | pGetCoeff(l->z)=c; /* omit npCopy, because npCopy is a no-op */ |
---|
[35aab3] | 1473 | l->n=NULL; |
---|
| 1474 | return (number)l; |
---|
| 1475 | } |
---|
| 1476 | |
---|
| 1477 | /*2 |
---|
| 1478 | * map Z/p' -> Z/p(a) |
---|
| 1479 | */ |
---|
| 1480 | number naMapPP1(number c) |
---|
| 1481 | { |
---|
| 1482 | if (npIsZero(c)) return NULL; |
---|
[7447d8] | 1483 | int i=(int)((long)c); |
---|
[661c214] | 1484 | if (i>(long)ntMapRing->ch) i-=(long)ntMapRing->ch; |
---|
| 1485 | number n=npInit(i,ntMapRing); |
---|
[35aab3] | 1486 | if (npIsZero(n)) return NULL; |
---|
| 1487 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 1488 | l->s=2; |
---|
| 1489 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 1490 | pGetCoeff(l->z)=n; |
---|
[35aab3] | 1491 | l->n=NULL; |
---|
| 1492 | return (number)l; |
---|
| 1493 | } |
---|
| 1494 | |
---|
| 1495 | /*2 |
---|
| 1496 | * map Q -> Z/p(a) |
---|
| 1497 | */ |
---|
| 1498 | number naMap0P(number c) |
---|
| 1499 | { |
---|
| 1500 | if (nlIsZero(c)) return NULL; |
---|
[8391d8] | 1501 | number n=npInit(nlModP(c,npPrimeM),nacRing); |
---|
[35aab3] | 1502 | if (npIsZero(n)) return NULL; |
---|
[f1e33bb] | 1503 | npTest(n); |
---|
[35aab3] | 1504 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 1505 | l->s=2; |
---|
| 1506 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 1507 | pGetCoeff(l->z)=n; |
---|
[35aab3] | 1508 | l->n=NULL; |
---|
| 1509 | return (number)l; |
---|
| 1510 | } |
---|
| 1511 | |
---|
| 1512 | /*2 |
---|
| 1513 | * map _(a) -> _(b) |
---|
| 1514 | */ |
---|
| 1515 | number naMapQaQb(number c) |
---|
| 1516 | { |
---|
| 1517 | if (c==NULL) return NULL; |
---|
| 1518 | lnumber erg= (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1519 | lnumber src =(lnumber)c; |
---|
| 1520 | erg->s=src->s; |
---|
| 1521 | erg->z=napMap(src->z); |
---|
| 1522 | erg->n=napMap(src->n); |
---|
| 1523 | if (naMinimalPoly!=NULL) |
---|
| 1524 | { |
---|
[b85e37] | 1525 | if (p_GetExp(erg->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 1526 | { |
---|
[d0450f] | 1527 | erg->z = napRemainder(erg->z, naMinimalPoly); |
---|
[35aab3] | 1528 | if (erg->z==NULL) |
---|
| 1529 | { |
---|
| 1530 | number t_erg=(number)erg; |
---|
| 1531 | naDelete(&t_erg,currRing); |
---|
| 1532 | return (number)NULL; |
---|
| 1533 | } |
---|
| 1534 | } |
---|
| 1535 | if (erg->n!=NULL) |
---|
| 1536 | { |
---|
[b85e37] | 1537 | if (p_GetExp(erg->n,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[d0450f] | 1538 | erg->n = napRemainder(erg->n, naMinimalPoly); |
---|
[21972b] | 1539 | if ((p_IsConstant(erg->n,nacRing)) && nacIsOne(pGetCoeff(erg->n))) |
---|
[1629ab] | 1540 | p_Delete(&(erg->n),nacRing); |
---|
[35aab3] | 1541 | } |
---|
| 1542 | } |
---|
| 1543 | return (number)erg; |
---|
| 1544 | } |
---|
| 1545 | |
---|
[208e0c] | 1546 | nMapFunc naSetMap(const ring src, const ring dst) |
---|
[35aab3] | 1547 | { |
---|
[661c214] | 1548 | ntMapRing=src; |
---|
[35aab3] | 1549 | if (rField_is_Q_a(dst)) /* -> Q(a) */ |
---|
| 1550 | { |
---|
| 1551 | if (rField_is_Q(src)) |
---|
| 1552 | { |
---|
| 1553 | return naMap00; /*Q -> Q(a)*/ |
---|
| 1554 | } |
---|
| 1555 | if (rField_is_Zp(src)) |
---|
| 1556 | { |
---|
| 1557 | return naMapP0; /* Z/p -> Q(a)*/ |
---|
| 1558 | } |
---|
| 1559 | if (rField_is_Q_a(src)) |
---|
| 1560 | { |
---|
| 1561 | int i; |
---|
[661c214] | 1562 | ntParsToCopy=0; |
---|
[35aab3] | 1563 | for(i=0;i<rPar(src);i++) |
---|
| 1564 | { |
---|
| 1565 | if ((i>=rPar(dst)) |
---|
| 1566 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
| 1567 | return NULL; |
---|
[661c214] | 1568 | ntParsToCopy++; |
---|
[35aab3] | 1569 | } |
---|
[21972b] | 1570 | nacMap=nacCopy; |
---|
[661c214] | 1571 | if ((ntParsToCopy==rPar(dst))&&(ntParsToCopy==rPar(src))) |
---|
[eb3df5] | 1572 | return naCopy; /* Q(a) -> Q(a) */ |
---|
| 1573 | return naMapQaQb; /* Q(a..) -> Q(a..) */ |
---|
[35aab3] | 1574 | } |
---|
| 1575 | } |
---|
| 1576 | /*-----------------------------------------------------*/ |
---|
| 1577 | if (rField_is_Zp_a(dst)) /* -> Z/p(a) */ |
---|
| 1578 | { |
---|
| 1579 | if (rField_is_Q(src)) |
---|
| 1580 | { |
---|
| 1581 | return naMap0P; /*Q -> Z/p(a)*/ |
---|
| 1582 | } |
---|
| 1583 | if (rField_is_Zp(src)) |
---|
| 1584 | { |
---|
[8391d8] | 1585 | if (src->ch==dst->ch) |
---|
[35aab3] | 1586 | { |
---|
| 1587 | return naMapPP; /* Z/p -> Z/p(a)*/ |
---|
| 1588 | } |
---|
| 1589 | else |
---|
| 1590 | { |
---|
| 1591 | return naMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
| 1592 | } |
---|
| 1593 | } |
---|
| 1594 | if (rField_is_Zp_a(src)) |
---|
| 1595 | { |
---|
| 1596 | if (rChar(src)==rChar(dst)) |
---|
| 1597 | { |
---|
[21972b] | 1598 | nacMap=nacCopy; |
---|
[35aab3] | 1599 | } |
---|
| 1600 | else |
---|
| 1601 | { |
---|
[21972b] | 1602 | nacMap = npMapP; |
---|
[35aab3] | 1603 | } |
---|
| 1604 | int i; |
---|
[661c214] | 1605 | ntParsToCopy=0; |
---|
[35aab3] | 1606 | for(i=0;i<rPar(src);i++) |
---|
| 1607 | { |
---|
| 1608 | if ((i>=rPar(dst)) |
---|
| 1609 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
| 1610 | return NULL; |
---|
[661c214] | 1611 | ntParsToCopy++; |
---|
[35aab3] | 1612 | } |
---|
[661c214] | 1613 | if ((ntParsToCopy==rPar(dst))&&(ntParsToCopy==rPar(src)) |
---|
[21972b] | 1614 | && (nacMap==nacCopy)) |
---|
[eb3df5] | 1615 | return naCopy; /* Z/p(a) -> Z/p(a) */ |
---|
[35aab3] | 1616 | return naMapQaQb; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
| 1617 | } |
---|
| 1618 | } |
---|
| 1619 | return NULL; /* default */ |
---|
| 1620 | } |
---|
| 1621 | |
---|
| 1622 | #ifdef LDEBUG |
---|
[85e68dd] | 1623 | BOOLEAN naDBTest(number a, const char *f,const int l) |
---|
[35aab3] | 1624 | { |
---|
| 1625 | lnumber x=(lnumber)a; |
---|
| 1626 | if (x == NULL) |
---|
| 1627 | return TRUE; |
---|
[074d3e] | 1628 | #ifdef LDEBUG |
---|
[35aab3] | 1629 | omCheckAddrSize(a, sizeof(snumber)); |
---|
[074d3e] | 1630 | #endif |
---|
[35aab3] | 1631 | napoly p = x->z; |
---|
| 1632 | if (p==NULL) |
---|
| 1633 | { |
---|
| 1634 | Print("0/* in %s:%d\n",f,l); |
---|
| 1635 | return FALSE; |
---|
| 1636 | } |
---|
| 1637 | while(p!=NULL) |
---|
| 1638 | { |
---|
[d0450f] | 1639 | if (( ntIsChar0 && nlIsZero(pGetCoeff(p))) |
---|
[661c214] | 1640 | || ((!ntIsChar0) && npIsZero(pGetCoeff(p)))) |
---|
[35aab3] | 1641 | { |
---|
| 1642 | Print("coeff 0 in %s:%d\n",f,l); |
---|
| 1643 | return FALSE; |
---|
| 1644 | } |
---|
[b85e37] | 1645 | if((naMinimalPoly!=NULL) |
---|
| 1646 | &&(p_GetExp(p,1,nacRing)>p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 1647 | &&(p!=naMinimalPoly)) |
---|
| 1648 | { |
---|
| 1649 | Print("deg>minpoly in %s:%d\n",f,l); |
---|
| 1650 | return FALSE; |
---|
| 1651 | } |
---|
[661c214] | 1652 | //if (ntIsChar0 && (((int)p->ko &3) == 0) && (p->ko->s==0) && (x->s==2)) |
---|
[35aab3] | 1653 | //{ |
---|
| 1654 | // Print("normalized with non-normal coeffs in %s:%d\n",f,l); |
---|
| 1655 | // return FALSE; |
---|
| 1656 | //} |
---|
[661c214] | 1657 | if (ntIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
[35aab3] | 1658 | return FALSE; |
---|
[1629ab] | 1659 | pIter(p); |
---|
[35aab3] | 1660 | } |
---|
[b3af93] | 1661 | p = x->n; |
---|
[35aab3] | 1662 | while(p!=NULL) |
---|
| 1663 | { |
---|
[661c214] | 1664 | if (ntIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
[35aab3] | 1665 | return FALSE; |
---|
[1629ab] | 1666 | pIter(p); |
---|
[35aab3] | 1667 | } |
---|
| 1668 | return TRUE; |
---|
| 1669 | } |
---|
| 1670 | #endif |
---|