[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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[b1dfaf] | 22 | #include <factory/factory.h> |
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[599326] | 23 | #include <kernel/clapsing.h> |
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| 24 | #include <kernel/clapconv.h> |
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[35aab3] | 25 | #endif |
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[599326] | 26 | #include <kernel/longalg.h> |
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[35aab3] | 27 | |
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[a6904c] | 28 | struct snaIdeal |
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[30c2d97] | 29 | { |
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| 30 | int anz; |
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[a6904c] | 31 | napoly *liste; |
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[30c2d97] | 32 | }; |
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[a6904c] | 33 | typedef struct snaIdeal * naIdeal; |
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[30c2d97] | 34 | |
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[a6904c] | 35 | naIdeal naI=NULL; |
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[35aab3] | 36 | |
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[a6904c] | 37 | omBin snaIdeal_bin = omGetSpecBin(sizeof(snaIdeal)); |
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[900802] | 38 | |
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[a6904c] | 39 | int naNumbOfPar; |
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| 40 | napoly naMinimalPoly; |
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| 41 | #define naParNames (currRing->parameter) |
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| 42 | static int naIsChar0; |
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| 43 | static ring naMapRing; |
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[35aab3] | 44 | |
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| 45 | #ifdef LDEBUG |
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[a6904c] | 46 | #define naTest(a) naDBTest(a,__FILE__,__LINE__) |
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| 47 | BOOLEAN naDBTest(number a, const char *f,const int l); |
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[35aab3] | 48 | #else |
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[a6904c] | 49 | #define naTest(a) |
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[35aab3] | 50 | #endif |
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| 51 | |
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[a6904c] | 52 | number (*naMap)(number from); |
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[35aab3] | 53 | /* procedure variables */ |
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| 54 | static numberfunc |
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| 55 | nacMult, nacSub, nacAdd, nacDiv, nacIntDiv; |
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| 56 | static number (*nacGcd)(number a, number b, const ring r); |
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| 57 | static number (*nacLcm)(number a, number b, const ring r); |
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[8391d8] | 58 | static number (*nacInit)(int i, const ring r); |
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[cf74cd6] | 59 | static int (*nacInt)(number &n, const ring r); |
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[b85e37] | 60 | static void (*nacDelete)(number *a, const ring r); |
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| 61 | #undef n_Delete |
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| 62 | #define n_Delete(A,R) nacDelete(A,R) |
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[35aab3] | 63 | void (*nacNormalize)(number &a); |
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| 64 | static number (*nacNeg)(number a); |
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| 65 | number (*nacCopy)(number a); |
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| 66 | static number (*nacInvers)(number a); |
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| 67 | BOOLEAN (*nacIsZero)(number a); |
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| 68 | static BOOLEAN (*nacIsOne)(number a); |
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| 69 | static BOOLEAN (*nacIsMOne)(number a); |
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| 70 | static BOOLEAN (*nacGreaterZero)(number a); |
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[85e68dd] | 71 | static const char * (*nacRead) (const char *s, number *a); |
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[35aab3] | 72 | static napoly napRedp(napoly q); |
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| 73 | static napoly napTailred(napoly q); |
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| 74 | static BOOLEAN napDivPoly(napoly p, napoly q); |
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| 75 | static int napExpi(int i, napoly a, napoly b); |
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[1629ab] | 76 | ring nacRing; |
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[35aab3] | 77 | |
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[dd8668] | 78 | void naCoefNormalize(number pp); |
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| 79 | |
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[b85e37] | 80 | #define napCopy(p) p_Copy(p,nacRing) |
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[a8bb72d] | 81 | |
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[8391d8] | 82 | static number nadGcd( number a, number b, const ring r) { return nacInit(1,r); } |
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[35aab3] | 83 | /*2 |
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| 84 | * sets the appropriate operators |
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| 85 | */ |
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| 86 | void naSetChar(int i, ring r) |
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| 87 | { |
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| 88 | if (naI!=NULL) |
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| 89 | { |
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| 90 | int j; |
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| 91 | for (j=naI->anz-1; j>=0; j--) |
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[1629ab] | 92 | p_Delete (&naI->liste[j],nacRing); |
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[35aab3] | 93 | omFreeSize((ADDRESS)naI->liste,naI->anz*sizeof(napoly)); |
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| 94 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
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| 95 | naI=NULL; |
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| 96 | } |
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| 97 | naMap = naCopy; |
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[9bea6e] | 98 | |
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[35aab3] | 99 | if (r->minpoly!=NULL) |
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[ec7055] | 100 | { |
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[35aab3] | 101 | naMinimalPoly=((lnumber)r->minpoly)->z; |
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[074d3e] | 102 | #ifdef LDEBUG |
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[ec7055] | 103 | omCheckAddr(naMinimalPoly); |
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[074d3e] | 104 | #endif |
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[ec7055] | 105 | } |
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[35aab3] | 106 | else |
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| 107 | naMinimalPoly = NULL; |
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[a8bb72d] | 108 | if (r->minideal!=NULL) |
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| 109 | { |
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| 110 | naI=(naIdeal)omAllocBin(snaIdeal_bin); |
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| 111 | naI->anz=IDELEMS(r->minideal); |
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| 112 | naI->liste=(napoly*)omAlloc(naI->anz*sizeof(napoly)); |
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| 113 | int j; |
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| 114 | for (j=naI->anz-1; j>=0; j--) |
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| 115 | { |
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| 116 | lnumber a = (lnumber)pGetCoeff(r->minideal->m[j]); |
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| 117 | naI->liste[j]=napCopy(a->z); |
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| 118 | } |
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| 119 | } |
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[9bea6e] | 120 | |
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[b3af93] | 121 | naNumbOfPar=rPar(r); |
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[35aab3] | 122 | if (i == 1) |
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| 123 | { |
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| 124 | naIsChar0 = 1; |
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| 125 | } |
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| 126 | else if (i < 0) |
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| 127 | { |
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| 128 | naIsChar0 = 0; |
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| 129 | npSetChar(-i, r->algring); // to be changed HS |
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| 130 | } |
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| 131 | #ifdef TEST |
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| 132 | else |
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| 133 | { |
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| 134 | Print("naSetChar:c=%d param=%d\n",i,rPar(r)); |
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| 135 | } |
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| 136 | #endif |
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| 137 | nacRing = r->algring; |
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[8391d8] | 138 | nacInit = nacRing->cf->cfInit; |
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[cf74cd6] | 139 | nacInt = nacRing->cf->n_Int; |
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[35aab3] | 140 | nacCopy = nacRing->cf->nCopy; |
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| 141 | nacAdd = nacRing->cf->nAdd; |
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| 142 | nacSub = nacRing->cf->nSub; |
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| 143 | nacNormalize = nacRing->cf->nNormalize; |
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| 144 | nacNeg = nacRing->cf->nNeg; |
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| 145 | nacIsZero = nacRing->cf->nIsZero; |
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| 146 | nacRead = nacRing->cf->nRead; |
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| 147 | nacGreaterZero = nacRing->cf->nGreaterZero; |
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| 148 | nacIsOne = nacRing->cf->nIsOne; |
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| 149 | nacIsMOne = nacRing->cf->nIsMOne; |
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| 150 | nacGcd = nacRing->cf->nGcd; |
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| 151 | nacLcm = nacRing->cf->nLcm; |
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| 152 | nacMult = nacRing->cf->nMult; |
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| 153 | nacDiv = nacRing->cf->nDiv; |
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| 154 | nacIntDiv = nacRing->cf->nIntDiv; |
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| 155 | nacInvers = nacRing->cf->nInvers; |
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[b85e37] | 156 | nacDelete = nacRing->cf->cfDelete; |
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[35aab3] | 157 | } |
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| 158 | |
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| 159 | /*============= procedure for polynomials: napXXXX =======================*/ |
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| 160 | |
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| 161 | |
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| 162 | |
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| 163 | #ifdef LDEBUG |
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| 164 | static void napTest(napoly p) |
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| 165 | { |
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| 166 | while (p != NULL) |
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| 167 | { |
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| 168 | if (naIsChar0) |
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[b3af93] | 169 | nlDBTest(pGetCoeff(p), "", 0); |
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[1629ab] | 170 | pIter(p); |
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[35aab3] | 171 | } |
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| 172 | } |
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| 173 | #else |
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| 174 | #define napTest(p) ((void) 0) |
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| 175 | #endif |
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| 176 | |
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[b85e37] | 177 | #define napSetCoeff(p,n) {n_Delete(&pGetCoeff(p),nacRing);pGetCoeff(p)=n;} |
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[35aab3] | 178 | #define napComp(p,q) p_LmCmp((poly)p,(poly)q, nacRing) |
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| 179 | #define napMultT(A,E) A=(napoly)p_Mult_mm((poly)A,(poly)E,nacRing) |
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[99bdcf] | 180 | #define napDeg(p) (int)p_Totaldegree(p, nacRing) |
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[35aab3] | 181 | |
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| 182 | /*3 |
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| 183 | * creates an napoly |
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| 184 | */ |
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| 185 | napoly napInitz(number z) |
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| 186 | { |
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| 187 | napoly a = (napoly)p_Init(nacRing); |
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[b3af93] | 188 | pGetCoeff(a) = z; |
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[35aab3] | 189 | return a; |
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| 190 | } |
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| 191 | |
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| 192 | /*3 |
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| 193 | * copy a napoly. poly |
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| 194 | */ |
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| 195 | static napoly napCopyNeg(napoly p) |
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| 196 | { |
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| 197 | napoly r=napCopy(p); |
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| 198 | r=(napoly)p_Neg((poly)r, nacRing); |
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| 199 | return r; |
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| 200 | } |
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| 201 | |
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[b3af93] | 202 | /*3 |
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| 203 | * returns ph * z |
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| 204 | */ |
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| 205 | static void napMultN(napoly p, number z) |
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| 206 | { |
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| 207 | number t; |
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| 208 | |
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| 209 | while (p!=NULL) |
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| 210 | { |
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| 211 | t = nacMult(pGetCoeff(p), z); |
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[fef045c] | 212 | nacNormalize(t); |
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[b85e37] | 213 | n_Delete(&pGetCoeff(p),nacRing); |
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[b3af93] | 214 | pGetCoeff(p) = t; |
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| 215 | pIter(p); |
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| 216 | } |
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| 217 | } |
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| 218 | |
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[35aab3] | 219 | /*3 |
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| 220 | * division with rest; f = g*q + r, returns r and destroy f |
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| 221 | */ |
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[eebfa9] | 222 | napoly napRemainder(napoly f, const napoly g) |
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[35aab3] | 223 | { |
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| 224 | napoly a, h, qq; |
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| 225 | |
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| 226 | qq = (napoly)p_Init(nacRing); |
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[1629ab] | 227 | pNext(qq) = NULL; |
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[aaeb98] | 228 | p_Normalize(g, nacRing); |
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| 229 | p_Normalize(f, nacRing); |
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[35aab3] | 230 | a = f; |
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| 231 | do |
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| 232 | { |
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[b85e37] | 233 | napSetExp(qq,1, p_GetExp(a,1,nacRing) - p_GetExp(g,1,nacRing)); |
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[9bea6e] | 234 | napSetm(qq); |
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[b3af93] | 235 | pGetCoeff(qq) = nacDiv(pGetCoeff(a), pGetCoeff(g)); |
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| 236 | pGetCoeff(qq) = nacNeg(pGetCoeff(qq)); |
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[fef045c] | 237 | nacNormalize(pGetCoeff(qq)); |
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[35aab3] | 238 | h = napCopy(g); |
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| 239 | napMultT(h, qq); |
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[fef045c] | 240 | p_Normalize(h,nacRing); |
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[b85e37] | 241 | n_Delete(&pGetCoeff(qq),nacRing); |
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[35aab3] | 242 | a = napAdd(a, h); |
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| 243 | } |
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[b85e37] | 244 | while ((a!=NULL) && (p_GetExp(a,1,nacRing) >= p_GetExp(g,1,nacRing))); |
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[35aab3] | 245 | omFreeBinAddr(qq); |
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| 246 | return a; |
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| 247 | } |
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| 248 | |
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| 249 | /*3 |
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| 250 | * division with rest; f = g*q + r, destroy f |
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| 251 | */ |
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| 252 | static void napDivMod(napoly f, napoly g, napoly *q, napoly *r) |
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| 253 | { |
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| 254 | napoly a, h, b, qq; |
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| 255 | |
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| 256 | qq = (napoly)p_Init(nacRing); |
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[1629ab] | 257 | pNext(qq) = b = NULL; |
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[aaeb98] | 258 | p_Normalize(g,nacRing); |
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| 259 | p_Normalize(f,nacRing); |
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[35aab3] | 260 | a = f; |
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| 261 | do |
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| 262 | { |
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[b85e37] | 263 | napSetExp(qq,1, p_GetExp(a,1,nacRing) - p_GetExp(g,1,nacRing)); |
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[35aab3] | 264 | p_Setm(qq,nacRing); |
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[b3af93] | 265 | pGetCoeff(qq) = nacDiv(pGetCoeff(a), pGetCoeff(g)); |
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| 266 | nacNormalize(pGetCoeff(qq)); |
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[35aab3] | 267 | b = napAdd(b, napCopy(qq)); |
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[b3af93] | 268 | pGetCoeff(qq) = nacNeg(pGetCoeff(qq)); |
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[35aab3] | 269 | h = napCopy(g); |
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| 270 | napMultT(h, qq); |
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[fef045c] | 271 | p_Normalize(h,nacRing); |
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[b85e37] | 272 | n_Delete(&pGetCoeff(qq),nacRing); |
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[35aab3] | 273 | a = napAdd(a, h); |
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| 274 | } |
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[b85e37] | 275 | while ((a!=NULL) && (p_GetExp(a,1,nacRing) >= p_GetExp(g,1,nacRing))); |
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[35aab3] | 276 | omFreeBinAddr(qq); |
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| 277 | *q = b; |
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| 278 | *r = a; |
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| 279 | } |
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| 280 | |
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| 281 | /*3 |
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| 282 | * returns z with z*x mod c = 1 |
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| 283 | */ |
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| 284 | static napoly napInvers(napoly x, const napoly c) |
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| 285 | { |
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| 286 | napoly y, r, qa, qn, q; |
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| 287 | number t, h; |
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| 288 | |
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[b85e37] | 289 | if (p_GetExp(x,1,nacRing) >= p_GetExp(c,1,nacRing)) |
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[35aab3] | 290 | x = napRemainder(x, c); |
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| 291 | if (x==NULL) |
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| 292 | { |
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| 293 | goto zero_divisor; |
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| 294 | } |
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[b85e37] | 295 | if (p_GetExp(x,1,nacRing)==0) |
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[35aab3] | 296 | { |
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[b3af93] | 297 | if (!nacIsOne(pGetCoeff(x))) |
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[35aab3] | 298 | { |
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[fef045c] | 299 | nacNormalize(pGetCoeff(x)); |
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[b3af93] | 300 | t = nacInvers(pGetCoeff(x)); |
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[35aab3] | 301 | nacNormalize(t); |
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[b85e37] | 302 | n_Delete(&pGetCoeff(x),nacRing); |
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[b3af93] | 303 | pGetCoeff(x) = t; |
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[35aab3] | 304 | } |
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| 305 | return x; |
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| 306 | } |
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| 307 | y = napCopy(c); |
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| 308 | napDivMod(y, x, &qa, &r); |
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| 309 | if (r==NULL) |
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| 310 | { |
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| 311 | goto zero_divisor; |
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| 312 | } |
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[b85e37] | 313 | if (p_GetExp(r,1,nacRing)==0) |
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[35aab3] | 314 | { |
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[fef045c] | 315 | nacNormalize(pGetCoeff(r)); |
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[b3af93] | 316 | t = nacInvers(pGetCoeff(r)); |
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[fef045c] | 317 | nacNormalize(t); |
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[35aab3] | 318 | t = nacNeg(t); |
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[b3af93] | 319 | napMultN(qa, t); |
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[b85e37] | 320 | n_Delete(&t,nacRing); |
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[fef045c] | 321 | p_Normalize(qa,nacRing); |
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[1629ab] | 322 | p_Delete(&x,nacRing); |
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| 323 | p_Delete(&r,nacRing); |
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[35aab3] | 324 | return qa; |
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| 325 | } |
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| 326 | y = x; |
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| 327 | x = r; |
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| 328 | napDivMod(y, x, &q, &r); |
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| 329 | if (r==NULL) |
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| 330 | { |
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| 331 | goto zero_divisor; |
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| 332 | } |
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[b85e37] | 333 | if (p_GetExp(r,1,nacRing)==0) |
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[35aab3] | 334 | { |
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[b85e37] | 335 | q = p_Mult_q(q, qa,nacRing); |
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[6094f4] | 336 | q = napAdd(q, p_ISet(1,nacRing)); |
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[fef045c] | 337 | nacNormalize(pGetCoeff(r)); |
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[b3af93] | 338 | t = nacInvers(pGetCoeff(r)); |
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| 339 | napMultN(q, t); |
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[fef045c] | 340 | p_Normalize(q,nacRing); |
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[b85e37] | 341 | n_Delete(&t,nacRing); |
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[1629ab] | 342 | p_Delete(&x,nacRing); |
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| 343 | p_Delete(&r,nacRing); |
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[b85e37] | 344 | if (p_GetExp(q,1,nacRing) >= p_GetExp(c,1,nacRing)) |
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[35aab3] | 345 | q = napRemainder(q, c); |
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| 346 | return q; |
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| 347 | } |
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[b85e37] | 348 | q = p_Mult_q(q, napCopy(qa),nacRing); |
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[6094f4] | 349 | q = napAdd(q, p_ISet(1,nacRing)); |
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[35aab3] | 350 | qa = napNeg(qa); |
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| 351 | loop |
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| 352 | { |
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| 353 | y = x; |
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| 354 | x = r; |
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| 355 | napDivMod(y, x, &qn, &r); |
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| 356 | if (r==NULL) |
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| 357 | { |
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| 358 | break; |
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| 359 | } |
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[b85e37] | 360 | if (p_GetExp(r,1,nacRing)==0) |
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[35aab3] | 361 | { |
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[b85e37] | 362 | q = p_Mult_q(q, qn,nacRing); |
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[35aab3] | 363 | q = napNeg(q); |
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| 364 | q = napAdd(q, qa); |
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[fef045c] | 365 | nacNormalize(pGetCoeff(r)); |
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[b3af93] | 366 | t = nacInvers(pGetCoeff(r)); |
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[fef045c] | 367 | //nacNormalize(t); |
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[b3af93] | 368 | napMultN(q, t); |
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[fef045c] | 369 | p_Normalize(q,nacRing); |
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[b85e37] | 370 | n_Delete(&t,nacRing); |
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[1629ab] | 371 | p_Delete(&x,nacRing); |
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| 372 | p_Delete(&r,nacRing); |
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[b85e37] | 373 | if (p_GetExp(q,1,nacRing) >= p_GetExp(c,1,nacRing)) |
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[35aab3] | 374 | q = napRemainder(q, c); |
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| 375 | return q; |
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| 376 | } |
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| 377 | y = q; |
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[b85e37] | 378 | q = p_Mult_q(napCopy(q), qn, nacRing); |
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[35aab3] | 379 | q = napNeg(q); |
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| 380 | q = napAdd(q, qa); |
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| 381 | qa = y; |
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| 382 | } |
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| 383 | // zero divisor found: |
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| 384 | zero_divisor: |
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| 385 | Werror("zero divisor found - your minpoly is not irreducible"); |
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| 386 | return x; |
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| 387 | } |
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| 388 | |
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| 389 | /*3 |
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| 390 | * the max degree of an napoly poly (used for test of "simple" et al.) |
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| 391 | */ |
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| 392 | static int napMaxDeg(napoly p) |
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| 393 | { |
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| 394 | int d = 0; |
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| 395 | while(p!=NULL) |
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| 396 | { |
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| 397 | d=si_max(d,napDeg(p)); |
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[1629ab] | 398 | pIter(p); |
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[35aab3] | 399 | } |
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| 400 | return d; |
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| 401 | } |
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| 402 | |
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| 403 | /*3 |
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| 404 | * the max degree of an napoly poly (used for test of "simple" et al.) |
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| 405 | */ |
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| 406 | static int napMaxDegLen(napoly p, int &l) |
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| 407 | { |
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| 408 | int d = 0; |
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| 409 | int ll=0; |
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| 410 | while(p!=NULL) |
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| 411 | { |
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| 412 | d=si_max(d,napDeg(p)); |
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[1629ab] | 413 | pIter(p); |
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[35aab3] | 414 | ll++; |
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| 415 | } |
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| 416 | l=ll; |
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| 417 | return d; |
---|
| 418 | } |
---|
| 419 | |
---|
| 420 | |
---|
| 421 | /*3 |
---|
| 422 | *writes a polynomial number |
---|
| 423 | */ |
---|
[493225] | 424 | void napWrite(napoly p,const BOOLEAN has_denom, const ring r) |
---|
[35aab3] | 425 | { |
---|
[493225] | 426 | ring nacring=r->algring; |
---|
[35aab3] | 427 | if (p==NULL) |
---|
| 428 | StringAppendS("0"); |
---|
[493225] | 429 | else if (p_LmIsConstant(p,nacring)) |
---|
[35aab3] | 430 | { |
---|
| 431 | BOOLEAN kl=FALSE; |
---|
| 432 | if (has_denom) |
---|
| 433 | { |
---|
[493225] | 434 | number den=nacring->cf->cfGetDenom(pGetCoeff(p),nacring ); |
---|
| 435 | kl=!n_IsOne(den,nacring); |
---|
| 436 | n_Delete(&den, nacring); |
---|
[35aab3] | 437 | } |
---|
| 438 | if (kl) StringAppendS("("); |
---|
| 439 | //StringAppendS("-1"); |
---|
[493225] | 440 | n_Write(pGetCoeff(p),nacring); |
---|
[35aab3] | 441 | if (kl) StringAppendS(")"); |
---|
| 442 | } |
---|
| 443 | else |
---|
| 444 | { |
---|
| 445 | StringAppendS("("); |
---|
| 446 | loop |
---|
| 447 | { |
---|
| 448 | BOOLEAN wroteCoeff=FALSE; |
---|
[493225] | 449 | if ((p_LmIsConstant(p,nacring)) |
---|
| 450 | || ((!n_IsOne(pGetCoeff(p),nacring)) |
---|
| 451 | && (!n_IsMOne(pGetCoeff(p),nacring)))) |
---|
[35aab3] | 452 | { |
---|
[493225] | 453 | n_Write(pGetCoeff(p),nacring); |
---|
| 454 | wroteCoeff=(r->ShortOut==0); |
---|
[35aab3] | 455 | } |
---|
[493225] | 456 | else if (n_IsMOne(pGetCoeff(p),nacring)) |
---|
[35aab3] | 457 | { |
---|
| 458 | StringAppendS("-"); |
---|
| 459 | } |
---|
| 460 | int i; |
---|
[493225] | 461 | for (i = 0; i < r->P; i++) |
---|
[35aab3] | 462 | { |
---|
[493225] | 463 | int e=p_GetExp(p,i+1,nacring); |
---|
[b85e37] | 464 | if (e > 0) |
---|
[35aab3] | 465 | { |
---|
| 466 | if (wroteCoeff) |
---|
| 467 | StringAppendS("*"); |
---|
| 468 | else |
---|
[493225] | 469 | wroteCoeff=(r->ShortOut==0); |
---|
| 470 | StringAppendS(r->parameter[i]); |
---|
[b85e37] | 471 | if (e > 1) |
---|
[35aab3] | 472 | { |
---|
[493225] | 473 | if (r->ShortOut == 0) |
---|
[35aab3] | 474 | StringAppendS("^"); |
---|
[b85e37] | 475 | StringAppend("%d", e); |
---|
[35aab3] | 476 | } |
---|
| 477 | } |
---|
| 478 | } /*for*/ |
---|
[1629ab] | 479 | pIter(p); |
---|
[35aab3] | 480 | if (p==NULL) |
---|
| 481 | break; |
---|
[493225] | 482 | if (n_GreaterZero(pGetCoeff(p),nacring)) |
---|
[35aab3] | 483 | StringAppendS("+"); |
---|
| 484 | } |
---|
| 485 | StringAppendS(")"); |
---|
| 486 | } |
---|
| 487 | } |
---|
| 488 | |
---|
| 489 | |
---|
[85e68dd] | 490 | static const char *napHandleMons(const char *s, int i, napoly ex) |
---|
[35aab3] | 491 | { |
---|
| 492 | int j; |
---|
| 493 | if (strncmp(s,naParNames[i],strlen(naParNames[i]))==0) |
---|
| 494 | { |
---|
| 495 | s+=strlen(naParNames[i]); |
---|
| 496 | if ((*s >= '0') && (*s <= '9')) |
---|
| 497 | { |
---|
| 498 | s = eati(s, &j); |
---|
| 499 | napAddExp(ex,i+1,j); |
---|
| 500 | } |
---|
| 501 | else |
---|
| 502 | napAddExp(ex,i+1,1); |
---|
| 503 | } |
---|
| 504 | return s; |
---|
| 505 | } |
---|
[85e68dd] | 506 | static const char *napHandlePars(const char *s, int i, napoly ex) |
---|
[4ea694] | 507 | { |
---|
| 508 | int j; |
---|
| 509 | if (strcmp(s,naParNames[i])==0) |
---|
| 510 | { |
---|
| 511 | s+=strlen(naParNames[i]); |
---|
| 512 | napSetExp(ex,i+1,1); |
---|
| 513 | } |
---|
| 514 | return s; |
---|
| 515 | } |
---|
[35aab3] | 516 | |
---|
| 517 | /*3 reads a monomial */ |
---|
[85e68dd] | 518 | static const char *napRead(const char *s, napoly *b) |
---|
[35aab3] | 519 | { |
---|
| 520 | napoly a; |
---|
| 521 | int i; |
---|
| 522 | a = (napoly)p_Init(nacRing); |
---|
| 523 | if ((*s >= '0') && (*s <= '9')) |
---|
| 524 | { |
---|
[b3af93] | 525 | s = nacRead(s, &pGetCoeff(a)); |
---|
| 526 | if (nacIsZero(pGetCoeff(a))) |
---|
[35aab3] | 527 | { |
---|
[aa74213] | 528 | p_LmDelete(&a,nacRing); |
---|
[35aab3] | 529 | *b = NULL; |
---|
| 530 | return s; |
---|
| 531 | } |
---|
| 532 | } |
---|
| 533 | else |
---|
[8391d8] | 534 | pGetCoeff(a) = nacInit(1,nacRing); |
---|
[35aab3] | 535 | i = 0; |
---|
[85e68dd] | 536 | const char *olds=s; |
---|
[4ea694] | 537 | loop |
---|
| 538 | { |
---|
| 539 | s = napHandlePars(s, i, a); |
---|
| 540 | if (olds == s) |
---|
| 541 | i++; |
---|
[b85e37] | 542 | else if (*s == '\0') |
---|
[4ea694] | 543 | { |
---|
| 544 | *b = a; |
---|
| 545 | return s; |
---|
| 546 | } |
---|
[b3af93] | 547 | if (i >= naNumbOfPar) |
---|
[4ea694] | 548 | break; |
---|
| 549 | } |
---|
[98203c] | 550 | i=0; |
---|
[35aab3] | 551 | loop |
---|
| 552 | { |
---|
| 553 | olds = s; |
---|
| 554 | s = napHandleMons(s, i, a); |
---|
| 555 | if (olds == s) |
---|
| 556 | i++; |
---|
| 557 | else |
---|
| 558 | i = 0; |
---|
[b3af93] | 559 | if ((*s == '\0') || (i >= naNumbOfPar)) |
---|
[35aab3] | 560 | break; |
---|
| 561 | } |
---|
| 562 | *b = a; |
---|
| 563 | return s; |
---|
| 564 | } |
---|
| 565 | |
---|
| 566 | static int napExp(napoly a, napoly b) |
---|
| 567 | { |
---|
[1629ab] | 568 | while (pNext(a)!=NULL) pIter(a); |
---|
[b85e37] | 569 | int m = p_GetExp(a,1,nacRing); |
---|
[35aab3] | 570 | if (m==0) return 0; |
---|
[1629ab] | 571 | while (pNext(b)!=NULL) pIter(b); |
---|
[b85e37] | 572 | int mm=p_GetExp(b,1,nacRing); |
---|
[35aab3] | 573 | if (m > mm) m = mm; |
---|
| 574 | return m; |
---|
| 575 | } |
---|
| 576 | |
---|
| 577 | /* |
---|
| 578 | * finds the smallest i-th exponent in a and b |
---|
| 579 | * used to find it in a fraction |
---|
| 580 | */ |
---|
| 581 | static int napExpi(int i, napoly a, napoly b) |
---|
| 582 | { |
---|
| 583 | if (a==NULL || b==NULL) return 0; |
---|
[b85e37] | 584 | int m = p_GetExp(a,i+1,nacRing); |
---|
[35aab3] | 585 | if (m==0) return 0; |
---|
[1629ab] | 586 | while (pNext(a) != NULL) |
---|
[35aab3] | 587 | { |
---|
[1629ab] | 588 | pIter(a); |
---|
[b85e37] | 589 | if (m > p_GetExp(a,i+1,nacRing)) |
---|
[35aab3] | 590 | { |
---|
[b85e37] | 591 | m = p_GetExp(a,i+1,nacRing); |
---|
[35aab3] | 592 | if (m==0) return 0; |
---|
| 593 | } |
---|
| 594 | } |
---|
| 595 | do |
---|
| 596 | { |
---|
[b85e37] | 597 | if (m > p_GetExp(b,i+1,nacRing)) |
---|
[35aab3] | 598 | { |
---|
[b85e37] | 599 | m = p_GetExp(b,i+1,nacRing); |
---|
[35aab3] | 600 | if (m==0) return 0; |
---|
| 601 | } |
---|
[1629ab] | 602 | pIter(b); |
---|
[35aab3] | 603 | } |
---|
| 604 | while (b != NULL); |
---|
| 605 | return m; |
---|
| 606 | } |
---|
| 607 | |
---|
| 608 | static void napContent(napoly ph) |
---|
| 609 | { |
---|
| 610 | number h,d; |
---|
| 611 | napoly p; |
---|
| 612 | |
---|
| 613 | p = ph; |
---|
[b3af93] | 614 | if (nacIsOne(pGetCoeff(p))) |
---|
[35aab3] | 615 | return; |
---|
[b3af93] | 616 | h = nacCopy(pGetCoeff(p)); |
---|
[1629ab] | 617 | pIter(p); |
---|
[35aab3] | 618 | do |
---|
| 619 | { |
---|
[b3af93] | 620 | d=nacGcd(pGetCoeff(p), h, nacRing); |
---|
[35aab3] | 621 | if(nacIsOne(d)) |
---|
| 622 | { |
---|
[b85e37] | 623 | n_Delete(&h,nacRing); |
---|
| 624 | n_Delete(&d,nacRing); |
---|
[35aab3] | 625 | return; |
---|
| 626 | } |
---|
[b85e37] | 627 | n_Delete(&h,nacRing); |
---|
[35aab3] | 628 | h = d; |
---|
[1629ab] | 629 | pIter(p); |
---|
[35aab3] | 630 | } |
---|
| 631 | while (p!=NULL); |
---|
| 632 | h = nacInvers(d); |
---|
[b85e37] | 633 | n_Delete(&d,nacRing); |
---|
[35aab3] | 634 | p = ph; |
---|
| 635 | while (p!=NULL) |
---|
| 636 | { |
---|
[b3af93] | 637 | d = nacMult(pGetCoeff(p), h); |
---|
[b85e37] | 638 | n_Delete(&pGetCoeff(p),nacRing); |
---|
[b3af93] | 639 | pGetCoeff(p) = d; |
---|
[1629ab] | 640 | pIter(p); |
---|
[35aab3] | 641 | } |
---|
[b85e37] | 642 | n_Delete(&h,nacRing); |
---|
[35aab3] | 643 | } |
---|
| 644 | |
---|
| 645 | static void napCleardenom(napoly ph) |
---|
| 646 | { |
---|
| 647 | number d, h; |
---|
| 648 | napoly p; |
---|
| 649 | |
---|
| 650 | if (!naIsChar0) |
---|
| 651 | return; |
---|
| 652 | p = ph; |
---|
[8391d8] | 653 | h = nacInit(1,nacRing); |
---|
[35aab3] | 654 | while (p!=NULL) |
---|
| 655 | { |
---|
[b3af93] | 656 | d = nacLcm(h, pGetCoeff(p), nacRing); |
---|
[b85e37] | 657 | n_Delete(&h,nacRing); |
---|
[35aab3] | 658 | h = d; |
---|
[1629ab] | 659 | pIter(p); |
---|
[35aab3] | 660 | } |
---|
| 661 | if(!nacIsOne(h)) |
---|
| 662 | { |
---|
| 663 | p = ph; |
---|
[b3af93] | 664 | while (p!=NULL) |
---|
| 665 | { |
---|
| 666 | d=nacMult(h, pGetCoeff(p)); |
---|
[b85e37] | 667 | n_Delete(&pGetCoeff(p),nacRing); |
---|
[b3af93] | 668 | nacNormalize(d); |
---|
| 669 | pGetCoeff(p) = d; |
---|
| 670 | pIter(p); |
---|
| 671 | } |
---|
[b85e37] | 672 | n_Delete(&h,nacRing); |
---|
[35aab3] | 673 | } |
---|
| 674 | napContent(ph); |
---|
| 675 | } |
---|
| 676 | |
---|
| 677 | static napoly napGcd0(napoly a, napoly b) |
---|
| 678 | { |
---|
| 679 | number x, y; |
---|
| 680 | if (!naIsChar0) |
---|
[6094f4] | 681 | return p_ISet(1,nacRing); |
---|
[b3af93] | 682 | x = nacCopy(pGetCoeff(a)); |
---|
[35aab3] | 683 | if (nacIsOne(x)) |
---|
| 684 | return napInitz(x); |
---|
[1629ab] | 685 | while (pNext(a)!=NULL) |
---|
[35aab3] | 686 | { |
---|
[1629ab] | 687 | pIter(a); |
---|
[b3af93] | 688 | y = nacGcd(x, pGetCoeff(a), nacRing); |
---|
[b85e37] | 689 | n_Delete(&x,nacRing); |
---|
[35aab3] | 690 | x = y; |
---|
| 691 | if (nacIsOne(x)) |
---|
| 692 | return napInitz(x); |
---|
| 693 | } |
---|
| 694 | do |
---|
| 695 | { |
---|
[b3af93] | 696 | y = nacGcd(x, pGetCoeff(b), nacRing); |
---|
[b85e37] | 697 | n_Delete(&x,nacRing); |
---|
[35aab3] | 698 | x = y; |
---|
| 699 | if (nacIsOne(x)) |
---|
| 700 | return napInitz(x); |
---|
[1629ab] | 701 | pIter(b); |
---|
[35aab3] | 702 | } |
---|
| 703 | while (b!=NULL); |
---|
| 704 | return napInitz(x); |
---|
| 705 | } |
---|
| 706 | |
---|
| 707 | /*3 |
---|
| 708 | * result =gcd(a,b) |
---|
| 709 | */ |
---|
| 710 | static napoly napGcd(napoly a, napoly b) |
---|
| 711 | { |
---|
| 712 | int i; |
---|
| 713 | napoly g, x, y, h; |
---|
| 714 | if ((a==NULL) |
---|
[b3af93] | 715 | || ((pNext(a)==NULL)&&(nacIsZero(pGetCoeff(a))))) |
---|
[35aab3] | 716 | { |
---|
| 717 | if ((b==NULL) |
---|
[b3af93] | 718 | || ((pNext(b)==NULL)&&(nacIsZero(pGetCoeff(b))))) |
---|
[35aab3] | 719 | { |
---|
[6094f4] | 720 | return p_ISet(1,nacRing); |
---|
[35aab3] | 721 | } |
---|
| 722 | return napCopy(b); |
---|
| 723 | } |
---|
| 724 | else |
---|
| 725 | if ((b==NULL) |
---|
[b3af93] | 726 | || ((pNext(b)==NULL)&&(nacIsZero(pGetCoeff(b))))) |
---|
[35aab3] | 727 | { |
---|
| 728 | return napCopy(a); |
---|
| 729 | } |
---|
| 730 | if (naMinimalPoly != NULL) |
---|
| 731 | { |
---|
[b85e37] | 732 | if (p_GetExp(a,1,nacRing) >= p_GetExp(b,1,nacRing)) |
---|
[35aab3] | 733 | { |
---|
| 734 | x = a; |
---|
| 735 | y = b; |
---|
| 736 | } |
---|
| 737 | else |
---|
| 738 | { |
---|
| 739 | x = b; |
---|
| 740 | y = a; |
---|
| 741 | } |
---|
[6094f4] | 742 | if (!naIsChar0) g = p_ISet(1,nacRing); |
---|
[35aab3] | 743 | else g = napGcd0(x, y); |
---|
[1629ab] | 744 | if (pNext(y)==NULL) |
---|
[35aab3] | 745 | { |
---|
| 746 | napSetExp(g,1, napExp(x, y)); |
---|
| 747 | p_Setm(g,nacRing); |
---|
| 748 | return g; |
---|
| 749 | } |
---|
| 750 | x = napCopy(x); |
---|
| 751 | y = napCopy(y); |
---|
| 752 | loop |
---|
| 753 | { |
---|
| 754 | h = napRemainder(x, y); |
---|
| 755 | if (h==NULL) |
---|
| 756 | { |
---|
| 757 | napCleardenom(y); |
---|
[b3af93] | 758 | if (!nacIsOne(pGetCoeff(g))) |
---|
| 759 | napMultN(y, pGetCoeff(g)); |
---|
[aa74213] | 760 | p_LmDelete(&g,nacRing); |
---|
[35aab3] | 761 | return y; |
---|
| 762 | } |
---|
[1629ab] | 763 | else if (pNext(h)==NULL) |
---|
[35aab3] | 764 | break; |
---|
| 765 | x = y; |
---|
| 766 | y = h; |
---|
| 767 | } |
---|
[1629ab] | 768 | p_Delete(&y,nacRing); |
---|
[aa74213] | 769 | p_LmDelete(&h,nacRing); |
---|
[35aab3] | 770 | napSetExp(g,1, napExp(a, b)); |
---|
| 771 | p_Setm(g,nacRing); |
---|
| 772 | return g; |
---|
| 773 | } |
---|
| 774 | // Hmm ... this is a memory leak |
---|
| 775 | // x = (napoly)p_Init(nacRing); |
---|
| 776 | g=a; |
---|
| 777 | h=b; |
---|
[6094f4] | 778 | if (!naIsChar0) x = p_ISet(1,nacRing); |
---|
[35aab3] | 779 | else x = napGcd0(g,h); |
---|
[b3af93] | 780 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
[35aab3] | 781 | { |
---|
| 782 | napSetExp(x,i+1, napExpi(i,a,b)); |
---|
| 783 | p_Setm(x,nacRing); |
---|
| 784 | } |
---|
| 785 | return x; |
---|
| 786 | } |
---|
| 787 | |
---|
| 788 | |
---|
| 789 | number napLcm(napoly a) |
---|
| 790 | { |
---|
[8391d8] | 791 | number h = nacInit(1,nacRing); |
---|
[35aab3] | 792 | |
---|
| 793 | if (naIsChar0) |
---|
| 794 | { |
---|
| 795 | number d; |
---|
| 796 | napoly b = a; |
---|
| 797 | |
---|
| 798 | while (b!=NULL) |
---|
| 799 | { |
---|
[b3af93] | 800 | d = nacLcm(h, pGetCoeff(b), nacRing); |
---|
[b85e37] | 801 | n_Delete(&h,nacRing); |
---|
[35aab3] | 802 | h = d; |
---|
[1629ab] | 803 | pIter(b); |
---|
[35aab3] | 804 | } |
---|
| 805 | } |
---|
| 806 | return h; |
---|
| 807 | } |
---|
| 808 | |
---|
| 809 | |
---|
| 810 | /*2 |
---|
| 811 | * meins (for reduction in algebraic extension) |
---|
| 812 | * checks if head of p divides head of q |
---|
| 813 | * doesn't delete p and q |
---|
| 814 | */ |
---|
| 815 | static BOOLEAN napDivPoly (napoly p, napoly q) |
---|
| 816 | { |
---|
| 817 | int j=1; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
| 818 | |
---|
[b85e37] | 819 | while (p_GetExp(p,j,nacRing) <= p_GetExp(q,j,nacRing)) |
---|
[35aab3] | 820 | { |
---|
| 821 | j++; |
---|
[b3af93] | 822 | if (j > naNumbOfPar) |
---|
[35aab3] | 823 | return 1; |
---|
| 824 | } |
---|
| 825 | return 0; |
---|
| 826 | } |
---|
| 827 | |
---|
| 828 | |
---|
| 829 | /*2 |
---|
| 830 | * meins (for reduction in algebraic extension) |
---|
| 831 | * Normalform of poly with naI |
---|
| 832 | * changes q and returns it |
---|
| 833 | */ |
---|
| 834 | napoly napRedp (napoly q) |
---|
| 835 | { |
---|
| 836 | napoly h = (napoly)p_Init(nacRing); |
---|
| 837 | int i=0,j; |
---|
| 838 | |
---|
| 839 | loop |
---|
| 840 | { |
---|
| 841 | if (napDivPoly (naI->liste[i], q)) |
---|
| 842 | { |
---|
| 843 | /* h = lt(q)/lt(naI->liste[i])*/ |
---|
[b3af93] | 844 | pGetCoeff(h) = nacCopy(pGetCoeff(q)); |
---|
| 845 | for (j=naNumbOfPar; j>0; j--) |
---|
[b85e37] | 846 | napSetExp(h,j, p_GetExp(q,j,nacRing) - p_GetExp(naI->liste[i],j,nacRing)); |
---|
[35aab3] | 847 | p_Setm(h,nacRing); |
---|
[b85e37] | 848 | h = p_Mult_q(h, napCopy(naI->liste[i]),nacRing); |
---|
[35aab3] | 849 | h = napNeg (h); |
---|
| 850 | q = napAdd (q, napCopy(h)); |
---|
[1629ab] | 851 | p_Delete (&pNext(h),nacRing); |
---|
[35aab3] | 852 | if (q == NULL) |
---|
| 853 | { |
---|
[1629ab] | 854 | p_Delete(&h,nacRing); |
---|
[35aab3] | 855 | return q; |
---|
| 856 | } |
---|
| 857 | /* try to reduce further */ |
---|
| 858 | i = 0; |
---|
| 859 | } |
---|
| 860 | else |
---|
| 861 | { |
---|
| 862 | i++; |
---|
| 863 | if (i >= naI->anz) |
---|
| 864 | { |
---|
[1629ab] | 865 | p_Delete(&h,nacRing); |
---|
[35aab3] | 866 | return q; |
---|
| 867 | } |
---|
| 868 | } |
---|
| 869 | } |
---|
| 870 | } |
---|
| 871 | |
---|
| 872 | |
---|
| 873 | /*2 |
---|
| 874 | * meins (for reduction in algebraic extension) |
---|
| 875 | * reduces the tail of Poly q |
---|
| 876 | * needs q != NULL |
---|
| 877 | * changes q and returns it |
---|
| 878 | */ |
---|
| 879 | napoly napTailred (napoly q) |
---|
| 880 | { |
---|
| 881 | napoly h; |
---|
| 882 | |
---|
[1629ab] | 883 | h = pNext(q); |
---|
[35aab3] | 884 | while (h != NULL) |
---|
| 885 | { |
---|
| 886 | h = napRedp (h); |
---|
| 887 | if (h == NULL) |
---|
| 888 | return q; |
---|
[1629ab] | 889 | pIter(h); |
---|
[35aab3] | 890 | } |
---|
| 891 | return q; |
---|
| 892 | } |
---|
| 893 | |
---|
| 894 | |
---|
| 895 | /*================ procedure for rational functions: naXXXX =================*/ |
---|
| 896 | |
---|
| 897 | /*2 |
---|
| 898 | * z:= i |
---|
| 899 | */ |
---|
[8391d8] | 900 | number naInit(int i, const ring r) |
---|
[35aab3] | 901 | { |
---|
| 902 | if (i!=0) |
---|
| 903 | { |
---|
[8391d8] | 904 | number c=n_Init(i,r->algring); |
---|
| 905 | if (!n_IsZero(c,r->algring)) |
---|
[35aab3] | 906 | { |
---|
[8391d8] | 907 | poly z=p_Init(r->algring); |
---|
| 908 | pSetCoeff0(z,c); |
---|
[35aab3] | 909 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
| 910 | l->z = z; |
---|
| 911 | l->s = 2; |
---|
| 912 | l->n = NULL; |
---|
| 913 | return (number)l; |
---|
| 914 | } |
---|
| 915 | } |
---|
| 916 | /*else*/ |
---|
| 917 | return NULL; |
---|
| 918 | } |
---|
| 919 | |
---|
| 920 | number naPar(int i) |
---|
| 921 | { |
---|
| 922 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
| 923 | l->s = 2; |
---|
[6094f4] | 924 | l->z = p_ISet(1,nacRing); |
---|
[35aab3] | 925 | napSetExp(l->z,i,1); |
---|
| 926 | p_Setm(l->z,nacRing); |
---|
| 927 | l->n = NULL; |
---|
| 928 | return (number)l; |
---|
| 929 | } |
---|
| 930 | |
---|
| 931 | int naParDeg(number n) /* i := deg(n) */ |
---|
| 932 | { |
---|
| 933 | lnumber l = (lnumber)n; |
---|
| 934 | if (l==NULL) return -1; |
---|
| 935 | return napDeg(l->z); |
---|
| 936 | } |
---|
| 937 | |
---|
| 938 | //int naParDeg(number n) /* i := deg(n) */ |
---|
| 939 | //{ |
---|
| 940 | // lnumber l = (lnumber)n; |
---|
| 941 | // if (l==NULL) return -1; |
---|
| 942 | // return napMaxDeg(l->z)+napMaxDeg(l->n); |
---|
| 943 | //} |
---|
| 944 | |
---|
| 945 | int naSize(number n) /* size desc. */ |
---|
| 946 | { |
---|
| 947 | lnumber l = (lnumber)n; |
---|
| 948 | if (l==NULL) return -1; |
---|
| 949 | int len_z; |
---|
| 950 | int len_n; |
---|
| 951 | int o=napMaxDegLen(l->z,len_z)+napMaxDegLen(l->n,len_n); |
---|
| 952 | return (len_z+len_n)+o; |
---|
| 953 | } |
---|
| 954 | |
---|
| 955 | /*2 |
---|
| 956 | * convert a number to int (if possible) |
---|
| 957 | */ |
---|
[cf74cd6] | 958 | int naInt(number &n, const ring r) |
---|
[35aab3] | 959 | { |
---|
| 960 | lnumber l=(lnumber)n; |
---|
[cf74cd6] | 961 | if ((l!=NULL)&&(l->n==NULL)&&(p_IsConstant(l->z,r->algring))) |
---|
[35aab3] | 962 | { |
---|
[cf74cd6] | 963 | return nacInt(pGetCoeff(l->z),r->algring); |
---|
[35aab3] | 964 | } |
---|
| 965 | return 0; |
---|
| 966 | } |
---|
| 967 | |
---|
| 968 | /*2 |
---|
| 969 | * deletes p |
---|
| 970 | */ |
---|
| 971 | void naDelete(number *p, const ring r) |
---|
| 972 | { |
---|
[ec7055] | 973 | if ((*p)!=r->minpoly) |
---|
| 974 | { |
---|
| 975 | lnumber l = (lnumber) * p; |
---|
| 976 | if (l==NULL) return; |
---|
[d9ff1b] | 977 | p_Delete(&(l->z),r->algring); |
---|
| 978 | p_Delete(&(l->n),r->algring); |
---|
[ec7055] | 979 | omFreeBin((ADDRESS)l, rnumber_bin); |
---|
| 980 | } |
---|
[35aab3] | 981 | *p = NULL; |
---|
| 982 | } |
---|
| 983 | |
---|
| 984 | /*2 |
---|
| 985 | * copy p to erg |
---|
| 986 | */ |
---|
| 987 | number naCopy(number p) |
---|
| 988 | { |
---|
| 989 | if (p==NULL) return NULL; |
---|
| 990 | naTest(p); |
---|
| 991 | lnumber erg; |
---|
| 992 | lnumber src = (lnumber)p; |
---|
| 993 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
[bedece] | 994 | erg->z = p_Copy(src->z, nacRing); |
---|
| 995 | erg->n = p_Copy(src->n, nacRing); |
---|
[35aab3] | 996 | erg->s = src->s; |
---|
| 997 | return (number)erg; |
---|
| 998 | } |
---|
| 999 | number na_Copy(number p, const ring r) |
---|
| 1000 | { |
---|
| 1001 | if (p==NULL) return NULL; |
---|
| 1002 | lnumber erg; |
---|
| 1003 | lnumber src = (lnumber)p; |
---|
| 1004 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
[bedece] | 1005 | erg->z = p_Copy(src->z,r->algring); |
---|
| 1006 | erg->n = p_Copy(src->n,r->algring); |
---|
[35aab3] | 1007 | erg->s = src->s; |
---|
| 1008 | return (number)erg; |
---|
| 1009 | } |
---|
| 1010 | |
---|
[b3af93] | 1011 | /*2 |
---|
| 1012 | * addition; lu:= la + lb |
---|
| 1013 | */ |
---|
| 1014 | number naAdd(number la, number lb) |
---|
| 1015 | { |
---|
[074d3e] | 1016 | if (la==NULL) return naCopy(lb); |
---|
| 1017 | if (lb==NULL) return naCopy(la); |
---|
| 1018 | |
---|
[b3af93] | 1019 | napoly x, y; |
---|
| 1020 | lnumber lu; |
---|
| 1021 | lnumber a = (lnumber)la; |
---|
| 1022 | lnumber b = (lnumber)lb; |
---|
[074d3e] | 1023 | #ifdef LDEBUG |
---|
[b3af93] | 1024 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1025 | omCheckAddrSize(b,sizeof(snumber)); |
---|
[074d3e] | 1026 | #endif |
---|
[b85e37] | 1027 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
---|
[b3af93] | 1028 | else x = napCopy(a->z); |
---|
[b85e37] | 1029 | if (a->n!=NULL) y = pp_Mult_qq(b->z, a->n,nacRing); |
---|
[b3af93] | 1030 | else y = napCopy(b->z); |
---|
[074d3e] | 1031 | napoly res = napAdd(x, y); |
---|
| 1032 | if (res==NULL) |
---|
[b3af93] | 1033 | { |
---|
| 1034 | return (number)NULL; |
---|
| 1035 | } |
---|
[074d3e] | 1036 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1037 | lu->z=res; |
---|
[b3af93] | 1038 | if (a->n!=NULL) |
---|
| 1039 | { |
---|
[b85e37] | 1040 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
---|
[b3af93] | 1041 | else x = napCopy(a->n); |
---|
| 1042 | } |
---|
| 1043 | else |
---|
| 1044 | { |
---|
| 1045 | if (b->n!=NULL) x = napCopy(b->n); |
---|
| 1046 | else x = NULL; |
---|
| 1047 | } |
---|
| 1048 | //if (x!=NULL) |
---|
| 1049 | //{ |
---|
[70f63a] | 1050 | // if (p_LmIsConstant(x,nacRing)) |
---|
[b3af93] | 1051 | // { |
---|
| 1052 | // number inv=nacInvers(pGetCoeff(x)); |
---|
| 1053 | // napMultN(lu->z,inv); |
---|
[b85e37] | 1054 | // n_Delete(&inv,nacRing); |
---|
[b3af93] | 1055 | // napDelete(&x); |
---|
| 1056 | // } |
---|
| 1057 | //} |
---|
| 1058 | lu->n = x; |
---|
| 1059 | lu->s = FALSE; |
---|
[074d3e] | 1060 | if (/*lu->n*/ x!=NULL) |
---|
[fef045c] | 1061 | { |
---|
| 1062 | number luu=(number)lu; |
---|
[dd8668] | 1063 | //if (p_IsConstant(lu->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 1064 | //else |
---|
[dd8668] | 1065 | naNormalize(luu); |
---|
[fef045c] | 1066 | lu=(lnumber)luu; |
---|
| 1067 | } |
---|
[074d3e] | 1068 | //else lu->s=2; |
---|
[b3af93] | 1069 | naTest((number)lu); |
---|
| 1070 | return (number)lu; |
---|
| 1071 | } |
---|
| 1072 | |
---|
| 1073 | /*2 |
---|
| 1074 | * subtraction; r:= la - lb |
---|
| 1075 | */ |
---|
| 1076 | number naSub(number la, number lb) |
---|
| 1077 | { |
---|
| 1078 | lnumber lu; |
---|
| 1079 | |
---|
| 1080 | if (lb==NULL) return naCopy(la); |
---|
| 1081 | if (la==NULL) |
---|
| 1082 | { |
---|
| 1083 | lu = (lnumber)naCopy(lb); |
---|
| 1084 | lu->z = napNeg(lu->z); |
---|
| 1085 | return (number)lu; |
---|
| 1086 | } |
---|
| 1087 | |
---|
| 1088 | lnumber a = (lnumber)la; |
---|
| 1089 | lnumber b = (lnumber)lb; |
---|
| 1090 | |
---|
[074d3e] | 1091 | #ifdef LDEBUG |
---|
[b3af93] | 1092 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1093 | omCheckAddrSize(b,sizeof(snumber)); |
---|
[074d3e] | 1094 | #endif |
---|
[b3af93] | 1095 | |
---|
| 1096 | napoly x, y; |
---|
[b85e37] | 1097 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
---|
[b3af93] | 1098 | else x = napCopy(a->z); |
---|
[b85e37] | 1099 | if (a->n!=NULL) y = p_Mult_q(napCopy(b->z), napCopyNeg(a->n),nacRing); |
---|
[b3af93] | 1100 | else y = napCopyNeg(b->z); |
---|
[074d3e] | 1101 | napoly res = napAdd(x, y); |
---|
| 1102 | if (res==NULL) |
---|
[b3af93] | 1103 | { |
---|
| 1104 | return (number)NULL; |
---|
| 1105 | } |
---|
[074d3e] | 1106 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1107 | lu->z=res; |
---|
[b3af93] | 1108 | if (a->n!=NULL) |
---|
| 1109 | { |
---|
[b85e37] | 1110 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
---|
[b3af93] | 1111 | else x = napCopy(a->n); |
---|
| 1112 | } |
---|
| 1113 | else |
---|
| 1114 | { |
---|
| 1115 | if (b->n!=NULL) x = napCopy(b->n); |
---|
| 1116 | else x = NULL; |
---|
| 1117 | } |
---|
| 1118 | lu->n = x; |
---|
| 1119 | lu->s = FALSE; |
---|
[074d3e] | 1120 | if (/*lu->n*/ x!=NULL) |
---|
[fef045c] | 1121 | { |
---|
| 1122 | number luu=(number)lu; |
---|
[dd8668] | 1123 | //if (p_IsConstant(lu->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 1124 | //else |
---|
[dd8668] | 1125 | naNormalize(luu); |
---|
[fef045c] | 1126 | lu=(lnumber)luu; |
---|
| 1127 | } |
---|
[074d3e] | 1128 | //else lu->s=2; |
---|
[b3af93] | 1129 | naTest((number)lu); |
---|
| 1130 | return (number)lu; |
---|
| 1131 | } |
---|
| 1132 | |
---|
[35aab3] | 1133 | /*2 |
---|
| 1134 | * multiplication; r:= la * lb |
---|
| 1135 | */ |
---|
| 1136 | number naMult(number la, number lb) |
---|
| 1137 | { |
---|
| 1138 | if ((la==NULL) || (lb==NULL)) |
---|
| 1139 | return NULL; |
---|
| 1140 | |
---|
| 1141 | lnumber a = (lnumber)la; |
---|
| 1142 | lnumber b = (lnumber)lb; |
---|
| 1143 | lnumber lo; |
---|
| 1144 | napoly x; |
---|
| 1145 | |
---|
[074d3e] | 1146 | #ifdef LDEBUG |
---|
[35aab3] | 1147 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1148 | omCheckAddrSize(b,sizeof(snumber)); |
---|
[074d3e] | 1149 | #endif |
---|
[35aab3] | 1150 | naTest(la); |
---|
| 1151 | naTest(lb); |
---|
| 1152 | |
---|
| 1153 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
[b85e37] | 1154 | lo->z = pp_Mult_qq(a->z, b->z,nacRing); |
---|
[35aab3] | 1155 | |
---|
| 1156 | if (a->n==NULL) |
---|
| 1157 | { |
---|
| 1158 | if (b->n==NULL) |
---|
| 1159 | x = NULL; |
---|
| 1160 | else |
---|
| 1161 | x = napCopy(b->n); |
---|
| 1162 | } |
---|
| 1163 | else |
---|
| 1164 | { |
---|
| 1165 | if (b->n==NULL) |
---|
| 1166 | { |
---|
| 1167 | x = napCopy(a->n); |
---|
| 1168 | } |
---|
| 1169 | else |
---|
| 1170 | { |
---|
[b85e37] | 1171 | x = pp_Mult_qq(b->n, a->n, nacRing); |
---|
[35aab3] | 1172 | } |
---|
| 1173 | } |
---|
| 1174 | if (naMinimalPoly!=NULL) |
---|
| 1175 | { |
---|
[b85e37] | 1176 | if (p_GetExp(lo->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 1177 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
[b85e37] | 1178 | if ((x!=NULL) && (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing))) |
---|
[35aab3] | 1179 | x = napRemainder(x, naMinimalPoly); |
---|
| 1180 | } |
---|
| 1181 | if (naI!=NULL) |
---|
| 1182 | { |
---|
| 1183 | lo->z = napRedp (lo->z); |
---|
| 1184 | if (lo->z != NULL) |
---|
| 1185 | lo->z = napTailred (lo->z); |
---|
| 1186 | if (x!=NULL) |
---|
| 1187 | { |
---|
| 1188 | x = napRedp (x); |
---|
| 1189 | if (x!=NULL) |
---|
| 1190 | x = napTailred (x); |
---|
| 1191 | } |
---|
| 1192 | } |
---|
[70f63a] | 1193 | if ((x!=NULL) && (p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
[1629ab] | 1194 | p_Delete(&x,nacRing); |
---|
[35aab3] | 1195 | lo->n = x; |
---|
[074d3e] | 1196 | lo->s = 0; |
---|
[35aab3] | 1197 | if(lo->z==NULL) |
---|
| 1198 | { |
---|
| 1199 | omFreeBin((ADDRESS)lo, rnumber_bin); |
---|
| 1200 | lo=NULL; |
---|
| 1201 | } |
---|
[fef045c] | 1202 | else if (lo->n!=NULL) |
---|
[35aab3] | 1203 | { |
---|
[a7b15e0] | 1204 | number luu=(number)lo; |
---|
[dd8668] | 1205 | // if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 1206 | // else |
---|
[dd8668] | 1207 | naNormalize(luu); |
---|
[a7b15e0] | 1208 | lo=(lnumber)luu; |
---|
[35aab3] | 1209 | } |
---|
[074d3e] | 1210 | //if (naMinimalPoly==NULL) lo->s=2; |
---|
[35aab3] | 1211 | naTest((number)lo); |
---|
| 1212 | return (number)lo; |
---|
| 1213 | } |
---|
| 1214 | |
---|
| 1215 | number naIntDiv(number la, number lb) |
---|
| 1216 | { |
---|
| 1217 | lnumber res; |
---|
| 1218 | lnumber a = (lnumber)la; |
---|
| 1219 | lnumber b = (lnumber)lb; |
---|
| 1220 | if (a==NULL) |
---|
| 1221 | { |
---|
| 1222 | return NULL; |
---|
| 1223 | } |
---|
| 1224 | if (b==NULL) |
---|
| 1225 | { |
---|
[b7e838] | 1226 | WerrorS(nDivBy0); |
---|
[35aab3] | 1227 | return NULL; |
---|
| 1228 | } |
---|
| 1229 | assume(a->z!=NULL && b->z!=NULL); |
---|
| 1230 | assume(a->n==NULL && b->n==NULL); |
---|
| 1231 | res = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1232 | res->z = napCopy(a->z); |
---|
| 1233 | res->n = napCopy(b->z); |
---|
| 1234 | res->s = 0; |
---|
| 1235 | number nres=(number)res; |
---|
| 1236 | naNormalize(nres); |
---|
| 1237 | |
---|
[b3af93] | 1238 | //napDelete(&res->n); |
---|
[35aab3] | 1239 | naTest(nres); |
---|
| 1240 | return nres; |
---|
| 1241 | } |
---|
| 1242 | |
---|
| 1243 | /*2 |
---|
| 1244 | * division; lo:= la / lb |
---|
| 1245 | */ |
---|
| 1246 | number naDiv(number la, number lb) |
---|
| 1247 | { |
---|
| 1248 | lnumber lo; |
---|
| 1249 | lnumber a = (lnumber)la; |
---|
| 1250 | lnumber b = (lnumber)lb; |
---|
| 1251 | napoly x; |
---|
| 1252 | |
---|
[b85e37] | 1253 | if (a==NULL) |
---|
[35aab3] | 1254 | return NULL; |
---|
| 1255 | |
---|
[b85e37] | 1256 | if (b==NULL) |
---|
[35aab3] | 1257 | { |
---|
[b7e838] | 1258 | WerrorS(nDivBy0); |
---|
[35aab3] | 1259 | return NULL; |
---|
| 1260 | } |
---|
[074d3e] | 1261 | #ifdef LDEBUG |
---|
[35aab3] | 1262 | omCheckAddrSize(a,sizeof(snumber)); |
---|
| 1263 | omCheckAddrSize(b,sizeof(snumber)); |
---|
[074d3e] | 1264 | #endif |
---|
[35aab3] | 1265 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
| 1266 | if (b->n!=NULL) |
---|
[b85e37] | 1267 | lo->z = pp_Mult_qq(a->z, b->n,nacRing); |
---|
[35aab3] | 1268 | else |
---|
| 1269 | lo->z = napCopy(a->z); |
---|
| 1270 | if (a->n!=NULL) |
---|
[b85e37] | 1271 | x = pp_Mult_qq(b->z, a->n, nacRing); |
---|
[35aab3] | 1272 | else |
---|
| 1273 | x = napCopy(b->z); |
---|
| 1274 | if (naMinimalPoly!=NULL) |
---|
| 1275 | { |
---|
[b85e37] | 1276 | if (p_GetExp(lo->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 1277 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
[b85e37] | 1278 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 1279 | x = napRemainder(x, naMinimalPoly); |
---|
| 1280 | } |
---|
| 1281 | if (naI!=NULL) |
---|
| 1282 | { |
---|
| 1283 | lo->z = napRedp (lo->z); |
---|
| 1284 | if (lo->z != NULL) |
---|
| 1285 | lo->z = napTailred (lo->z); |
---|
| 1286 | if (x!=NULL) |
---|
| 1287 | { |
---|
| 1288 | x = napRedp (x); |
---|
| 1289 | if (x!=NULL) |
---|
| 1290 | x = napTailred (x); |
---|
| 1291 | } |
---|
| 1292 | } |
---|
[70f63a] | 1293 | if ((p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
[1629ab] | 1294 | p_Delete(&x,nacRing); |
---|
[35aab3] | 1295 | lo->n = x; |
---|
[074d3e] | 1296 | lo->s = 0; |
---|
[fef045c] | 1297 | if (lo->n!=NULL) |
---|
| 1298 | { |
---|
| 1299 | number luu=(number)lo; |
---|
[dd8668] | 1300 | //if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 1301 | //else |
---|
[dd8668] | 1302 | naNormalize(luu); |
---|
[fef045c] | 1303 | lo=(lnumber)luu; |
---|
| 1304 | } |
---|
[074d3e] | 1305 | //else lo->s=2; |
---|
[35aab3] | 1306 | naTest((number)lo); |
---|
| 1307 | return (number)lo; |
---|
| 1308 | } |
---|
| 1309 | |
---|
| 1310 | /*2 |
---|
[074d3e] | 1311 | * za:= - za, inplace |
---|
[35aab3] | 1312 | */ |
---|
| 1313 | number naNeg(number za) |
---|
| 1314 | { |
---|
| 1315 | if (za!=NULL) |
---|
| 1316 | { |
---|
| 1317 | lnumber e = (lnumber)za; |
---|
| 1318 | naTest(za); |
---|
| 1319 | e->z = napNeg(e->z); |
---|
| 1320 | } |
---|
| 1321 | return za; |
---|
| 1322 | } |
---|
| 1323 | |
---|
| 1324 | /*2 |
---|
| 1325 | * 1/a |
---|
| 1326 | */ |
---|
| 1327 | number naInvers(number a) |
---|
| 1328 | { |
---|
| 1329 | lnumber lo; |
---|
| 1330 | lnumber b = (lnumber)a; |
---|
| 1331 | napoly x; |
---|
| 1332 | |
---|
| 1333 | if (b==NULL) |
---|
| 1334 | { |
---|
[b7e838] | 1335 | WerrorS(nDivBy0); |
---|
[35aab3] | 1336 | return NULL; |
---|
| 1337 | } |
---|
[074d3e] | 1338 | #ifdef LDEBUG |
---|
[35aab3] | 1339 | omCheckAddrSize(b,sizeof(snumber)); |
---|
[074d3e] | 1340 | #endif |
---|
[35aab3] | 1341 | lo = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1342 | lo->s = b->s; |
---|
| 1343 | if (b->n!=NULL) |
---|
| 1344 | lo->z = napCopy(b->n); |
---|
| 1345 | else |
---|
[6094f4] | 1346 | lo->z = p_ISet(1,nacRing); |
---|
[35aab3] | 1347 | x = b->z; |
---|
[70f63a] | 1348 | if ((!p_LmIsConstant(x,nacRing)) || !nacIsOne(pGetCoeff(x))) |
---|
[35aab3] | 1349 | x = napCopy(x); |
---|
| 1350 | else |
---|
| 1351 | { |
---|
| 1352 | lo->n = NULL; |
---|
| 1353 | naTest((number)lo); |
---|
| 1354 | return (number)lo; |
---|
| 1355 | } |
---|
| 1356 | if (naMinimalPoly!=NULL) |
---|
| 1357 | { |
---|
| 1358 | x = napInvers(x, naMinimalPoly); |
---|
[b85e37] | 1359 | x = p_Mult_q(x, lo->z,nacRing); |
---|
| 1360 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 1361 | x = napRemainder(x, naMinimalPoly); |
---|
| 1362 | lo->z = x; |
---|
| 1363 | lo->n = NULL; |
---|
| 1364 | while (x!=NULL) |
---|
| 1365 | { |
---|
[b3af93] | 1366 | nacNormalize(pGetCoeff(x)); |
---|
[1629ab] | 1367 | pIter(x); |
---|
[35aab3] | 1368 | } |
---|
| 1369 | } |
---|
| 1370 | else |
---|
| 1371 | lo->n = x; |
---|
| 1372 | if (lo->n!=NULL) |
---|
| 1373 | { |
---|
| 1374 | number luu=(number)lo; |
---|
[dd8668] | 1375 | //if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
[074d3e] | 1376 | //else |
---|
[dd8668] | 1377 | naNormalize(luu); |
---|
[35aab3] | 1378 | lo=(lnumber)luu; |
---|
| 1379 | } |
---|
| 1380 | naTest((number)lo); |
---|
| 1381 | return (number)lo; |
---|
| 1382 | } |
---|
| 1383 | |
---|
| 1384 | |
---|
| 1385 | BOOLEAN naIsZero(number za) |
---|
| 1386 | { |
---|
| 1387 | lnumber zb = (lnumber)za; |
---|
| 1388 | naTest(za); |
---|
| 1389 | #ifdef LDEBUG |
---|
| 1390 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
| 1391 | #endif |
---|
[b85e37] | 1392 | return (zb==NULL); |
---|
[35aab3] | 1393 | } |
---|
| 1394 | |
---|
| 1395 | |
---|
| 1396 | BOOLEAN naGreaterZero(number za) |
---|
| 1397 | { |
---|
| 1398 | lnumber zb = (lnumber)za; |
---|
| 1399 | #ifdef LDEBUG |
---|
| 1400 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
| 1401 | #endif |
---|
| 1402 | naTest(za); |
---|
[b85e37] | 1403 | if (zb!=NULL) |
---|
[35aab3] | 1404 | { |
---|
[70f63a] | 1405 | return (nacGreaterZero(pGetCoeff(zb->z))||(!p_LmIsConstant(zb->z,nacRing))); |
---|
[35aab3] | 1406 | } |
---|
[cd3d336] | 1407 | /* else */ return FALSE; |
---|
[35aab3] | 1408 | } |
---|
| 1409 | |
---|
| 1410 | |
---|
| 1411 | /*2 |
---|
| 1412 | * a = b ? |
---|
| 1413 | */ |
---|
| 1414 | BOOLEAN naEqual (number a, number b) |
---|
| 1415 | { |
---|
| 1416 | if(a==b) return TRUE; |
---|
| 1417 | if((a==NULL)&&(b!=NULL)) return FALSE; |
---|
| 1418 | if((b==NULL)&&(a!=NULL)) return FALSE; |
---|
| 1419 | |
---|
| 1420 | lnumber aa=(lnumber)a; |
---|
| 1421 | lnumber bb=(lnumber)b; |
---|
| 1422 | |
---|
| 1423 | int an_deg=0; |
---|
| 1424 | if(aa->n!=NULL) |
---|
| 1425 | an_deg=napDeg(aa->n); |
---|
| 1426 | int bn_deg=0; |
---|
| 1427 | if(bb->n!=NULL) |
---|
| 1428 | bn_deg=napDeg(bb->n); |
---|
| 1429 | if(an_deg+napDeg(bb->z)!=bn_deg+napDeg(aa->z)) |
---|
| 1430 | return FALSE; |
---|
| 1431 | #if 0 |
---|
| 1432 | naNormalize(a); |
---|
| 1433 | aa=(lnumber)a; |
---|
| 1434 | naNormalize(b); |
---|
| 1435 | bb=(lnumber)b; |
---|
| 1436 | if((aa->n==NULL)&&(bb->n!=NULL)) return FALSE; |
---|
| 1437 | if((bb->n==NULL)&&(aa->n!=NULL)) return FALSE; |
---|
| 1438 | if(napComp(aa->z,bb->z)!=0) return FALSE; |
---|
| 1439 | if((aa->n!=NULL) && (napComp(aa->n,bb->n))) return FALSE; |
---|
| 1440 | #endif |
---|
| 1441 | number h = naSub(a, b); |
---|
| 1442 | BOOLEAN bo = naIsZero(h); |
---|
| 1443 | naDelete(&h,currRing); |
---|
| 1444 | return bo; |
---|
| 1445 | } |
---|
| 1446 | |
---|
| 1447 | |
---|
| 1448 | BOOLEAN naGreater (number a, number b) |
---|
| 1449 | { |
---|
| 1450 | if (naIsZero(a)) |
---|
| 1451 | return FALSE; |
---|
| 1452 | if (naIsZero(b)) |
---|
| 1453 | return TRUE; /* a!= 0)*/ |
---|
| 1454 | return napDeg(((lnumber)a)->z)>napDeg(((lnumber)b)->z); |
---|
| 1455 | } |
---|
| 1456 | |
---|
| 1457 | /*2 |
---|
| 1458 | * reads a number |
---|
| 1459 | */ |
---|
[85e68dd] | 1460 | const char *naRead(const char *s, number *p) |
---|
[35aab3] | 1461 | { |
---|
| 1462 | napoly x; |
---|
| 1463 | lnumber a; |
---|
| 1464 | s = napRead(s, &x); |
---|
| 1465 | if (x==NULL) |
---|
| 1466 | { |
---|
| 1467 | *p = NULL; |
---|
| 1468 | return s; |
---|
| 1469 | } |
---|
| 1470 | *p = (number)omAlloc0Bin(rnumber_bin); |
---|
| 1471 | a = (lnumber)*p; |
---|
| 1472 | if ((naMinimalPoly!=NULL) |
---|
[b85e37] | 1473 | && (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing))) |
---|
[35aab3] | 1474 | a->z = napRemainder(x, naMinimalPoly); |
---|
| 1475 | else if (naI!=NULL) |
---|
| 1476 | { |
---|
| 1477 | a->z = napRedp(x); |
---|
| 1478 | if (a->z != NULL) |
---|
| 1479 | a->z = napTailred (a->z); |
---|
| 1480 | } |
---|
| 1481 | else |
---|
| 1482 | a->z = x; |
---|
| 1483 | if(a->z==NULL) |
---|
| 1484 | { |
---|
| 1485 | omFreeBin((ADDRESS)*p, rnumber_bin); |
---|
| 1486 | *p=NULL; |
---|
| 1487 | } |
---|
| 1488 | else |
---|
| 1489 | { |
---|
| 1490 | a->n = NULL; |
---|
| 1491 | a->s = 0; |
---|
| 1492 | naTest(*p); |
---|
| 1493 | } |
---|
| 1494 | return s; |
---|
| 1495 | } |
---|
| 1496 | |
---|
| 1497 | /*2 |
---|
| 1498 | * tries to convert a number to a name |
---|
| 1499 | */ |
---|
| 1500 | char * naName(number n) |
---|
| 1501 | { |
---|
| 1502 | lnumber ph = (lnumber)n; |
---|
[b85e37] | 1503 | if (ph==NULL) |
---|
[35aab3] | 1504 | return NULL; |
---|
| 1505 | int i; |
---|
[b3af93] | 1506 | char *s=(char *)omAlloc(4* naNumbOfPar); |
---|
[35aab3] | 1507 | char *t=(char *)omAlloc(8); |
---|
| 1508 | s[0]='\0'; |
---|
[b3af93] | 1509 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
[35aab3] | 1510 | { |
---|
[b85e37] | 1511 | int e=p_GetExp(ph->z,i+1,nacRing); |
---|
| 1512 | if (e > 0) |
---|
[35aab3] | 1513 | { |
---|
[b85e37] | 1514 | if (e >1) |
---|
[35aab3] | 1515 | { |
---|
[b85e37] | 1516 | sprintf(t,"%s%d",naParNames[i],e); |
---|
[35aab3] | 1517 | strcat(s,t); |
---|
| 1518 | } |
---|
| 1519 | else |
---|
| 1520 | { |
---|
| 1521 | strcat(s,naParNames[i]); |
---|
| 1522 | } |
---|
| 1523 | } |
---|
| 1524 | } |
---|
| 1525 | omFreeSize((ADDRESS)t,8); |
---|
| 1526 | if (s[0]=='\0') |
---|
| 1527 | { |
---|
| 1528 | omFree((ADDRESS)s); |
---|
| 1529 | return NULL; |
---|
| 1530 | } |
---|
| 1531 | return s; |
---|
| 1532 | } |
---|
| 1533 | |
---|
| 1534 | /*2 |
---|
| 1535 | * writes a number |
---|
| 1536 | */ |
---|
[493225] | 1537 | void naWrite(number &phn, const ring r) |
---|
[35aab3] | 1538 | { |
---|
| 1539 | lnumber ph = (lnumber)phn; |
---|
[b85e37] | 1540 | if (ph==NULL) |
---|
[35aab3] | 1541 | StringAppendS("0"); |
---|
| 1542 | else |
---|
| 1543 | { |
---|
| 1544 | phn->s = 0; |
---|
| 1545 | BOOLEAN has_denom=(ph->n!=NULL); |
---|
[493225] | 1546 | napWrite(ph->z,has_denom/*(ph->n!=NULL)*/,r); |
---|
[35aab3] | 1547 | if (has_denom/*(ph->n!=NULL)*/) |
---|
| 1548 | { |
---|
| 1549 | StringAppendS("/"); |
---|
[493225] | 1550 | napWrite(ph->n,TRUE,r); |
---|
[35aab3] | 1551 | } |
---|
| 1552 | } |
---|
| 1553 | } |
---|
| 1554 | |
---|
| 1555 | /*2 |
---|
| 1556 | * za == 1 ? |
---|
| 1557 | */ |
---|
| 1558 | BOOLEAN naIsOne(number za) |
---|
| 1559 | { |
---|
| 1560 | lnumber a = (lnumber)za; |
---|
| 1561 | napoly x, y; |
---|
| 1562 | number t; |
---|
| 1563 | if (a==NULL) return FALSE; |
---|
| 1564 | #ifdef LDEBUG |
---|
[074d3e] | 1565 | omCheckAddrSize(a,sizeof(snumber)); |
---|
[b85e37] | 1566 | if (a->z==NULL) |
---|
| 1567 | { |
---|
| 1568 | WerrorS("internal zero error(4)"); |
---|
| 1569 | return FALSE; |
---|
| 1570 | } |
---|
[35aab3] | 1571 | #endif |
---|
| 1572 | if (a->n==NULL) |
---|
| 1573 | { |
---|
[70f63a] | 1574 | if (p_LmIsConstant(a->z,nacRing)) |
---|
[e6ab52] | 1575 | { |
---|
[b85e37] | 1576 | return nacIsOne(pGetCoeff(a->z)); |
---|
[e6ab52] | 1577 | } |
---|
[35aab3] | 1578 | else return FALSE; |
---|
| 1579 | } |
---|
[1c3aa7] | 1580 | #if 0 |
---|
[35aab3] | 1581 | x = a->z; |
---|
| 1582 | y = a->n; |
---|
| 1583 | do |
---|
| 1584 | { |
---|
| 1585 | if (napComp(x, y)) |
---|
| 1586 | return FALSE; |
---|
| 1587 | else |
---|
| 1588 | { |
---|
[b3af93] | 1589 | t = nacSub(pGetCoeff(x), pGetCoeff(y)); |
---|
[35aab3] | 1590 | if (!nacIsZero(t)) |
---|
| 1591 | { |
---|
[b85e37] | 1592 | n_Delete(&t,nacRing); |
---|
[35aab3] | 1593 | return FALSE; |
---|
| 1594 | } |
---|
| 1595 | else |
---|
[b85e37] | 1596 | n_Delete(&t,nacRing); |
---|
[35aab3] | 1597 | } |
---|
[1629ab] | 1598 | pIter(x); |
---|
| 1599 | pIter(y); |
---|
[35aab3] | 1600 | } |
---|
| 1601 | while ((x!=NULL) && (y!=NULL)); |
---|
| 1602 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
[1629ab] | 1603 | p_Delete(&a->z,nacRing); |
---|
| 1604 | p_Delete(&a->n,nacRing); |
---|
[6094f4] | 1605 | a->z = p_ISet(1,nacRing); |
---|
[35aab3] | 1606 | a->n = NULL; |
---|
| 1607 | return TRUE; |
---|
[1c3aa7] | 1608 | #else |
---|
| 1609 | return FALSE; |
---|
| 1610 | #endif |
---|
[35aab3] | 1611 | } |
---|
| 1612 | |
---|
| 1613 | /*2 |
---|
| 1614 | * za == -1 ? |
---|
| 1615 | */ |
---|
| 1616 | BOOLEAN naIsMOne(number za) |
---|
| 1617 | { |
---|
| 1618 | lnumber a = (lnumber)za; |
---|
| 1619 | napoly x, y; |
---|
| 1620 | number t; |
---|
| 1621 | if (a==NULL) return FALSE; |
---|
| 1622 | #ifdef LDEBUG |
---|
[074d3e] | 1623 | omCheckAddrSize(a,sizeof(snumber)); |
---|
[35aab3] | 1624 | if (a->z==NULL) |
---|
| 1625 | { |
---|
| 1626 | WerrorS("internal zero error(5)"); |
---|
| 1627 | return FALSE; |
---|
| 1628 | } |
---|
| 1629 | #endif |
---|
| 1630 | if (a->n==NULL) |
---|
| 1631 | { |
---|
[70f63a] | 1632 | if (p_LmIsConstant(a->z,nacRing)) return nacIsMOne(pGetCoeff(a->z)); |
---|
[35aab3] | 1633 | /*else return FALSE;*/ |
---|
| 1634 | } |
---|
| 1635 | return FALSE; |
---|
| 1636 | } |
---|
| 1637 | |
---|
| 1638 | /*2 |
---|
| 1639 | * returns the i-th power of p (i>=0) |
---|
| 1640 | */ |
---|
| 1641 | void naPower(number p, int i, number *rc) |
---|
| 1642 | { |
---|
| 1643 | number x; |
---|
[785e89] | 1644 | *rc = naInit(1,currRing); |
---|
[35aab3] | 1645 | for (; i > 0; i--) |
---|
| 1646 | { |
---|
| 1647 | x = naMult(*rc, p); |
---|
| 1648 | naDelete(rc,currRing); |
---|
| 1649 | *rc = x; |
---|
| 1650 | } |
---|
| 1651 | } |
---|
| 1652 | |
---|
| 1653 | /*2 |
---|
| 1654 | * result =gcd(a,b) |
---|
| 1655 | */ |
---|
| 1656 | number naGcd(number a, number b, const ring r) |
---|
| 1657 | { |
---|
[3de9a9] | 1658 | if (a==NULL) return naCopy(b); |
---|
| 1659 | if (b==NULL) return naCopy(a); |
---|
[b85e37] | 1660 | |
---|
[35aab3] | 1661 | lnumber x, y; |
---|
| 1662 | lnumber result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 1663 | |
---|
| 1664 | x = (lnumber)a; |
---|
| 1665 | y = (lnumber)b; |
---|
[b3af93] | 1666 | if ((naNumbOfPar == 1) && (naMinimalPoly!=NULL)) |
---|
[35aab3] | 1667 | { |
---|
[1629ab] | 1668 | if (pNext(x->z)!=NULL) |
---|
[aaeb98] | 1669 | result->z = p_Copy(x->z, r->algring); |
---|
[35aab3] | 1670 | else |
---|
[a7b15e0] | 1671 | result->z = napGcd0(x->z, y->z); |
---|
[35aab3] | 1672 | } |
---|
[a7b15e0] | 1673 | else |
---|
[52e2f6] | 1674 | #ifndef HAVE_FACTORY |
---|
[e6ab52] | 1675 | result->z = napGcd(x->z, y->z); // change from napGcd0 |
---|
| 1676 | #else |
---|
[a7b15e0] | 1677 | { |
---|
[295c703] | 1678 | int c=ABS(nGetChar()); |
---|
| 1679 | if (c==1) c=0; |
---|
| 1680 | setCharacteristic( c ); |
---|
| 1681 | |
---|
[e6ab52] | 1682 | napoly rz=napGcd(x->z, y->z); |
---|
| 1683 | CanonicalForm F, G, R; |
---|
[b85e37] | 1684 | R=convSingPFactoryP(rz,r->algring); |
---|
[aaeb98] | 1685 | p_Normalize(x->z,nacRing); |
---|
[b85e37] | 1686 | F=convSingPFactoryP(x->z,r->algring)/R; |
---|
[aaeb98] | 1687 | p_Normalize(y->z,nacRing); |
---|
[b85e37] | 1688 | G=convSingPFactoryP(y->z,r->algring)/R; |
---|
[e6ab52] | 1689 | F = gcd( F, G ); |
---|
[b85e37] | 1690 | if (F.isOne()) |
---|
[e6ab52] | 1691 | result->z= rz; |
---|
| 1692 | else |
---|
| 1693 | { |
---|
[aaeb98] | 1694 | p_Delete(&rz,r->algring); |
---|
| 1695 | result->z=convFactoryPSingP( F*R,r->algring ); |
---|
| 1696 | p_Normalize(result->z,nacRing); |
---|
[e6ab52] | 1697 | } |
---|
[a7b15e0] | 1698 | } |
---|
| 1699 | #endif |
---|
[35aab3] | 1700 | naTest((number)result); |
---|
| 1701 | return (number)result; |
---|
| 1702 | } |
---|
| 1703 | |
---|
[76aef7] | 1704 | |
---|
[35aab3] | 1705 | /*2 |
---|
[b3af93] | 1706 | * naNumbOfPar = 1: |
---|
[35aab3] | 1707 | * clears denominator algebraic case; |
---|
| 1708 | * tries to simplify ratio transcendental case; |
---|
| 1709 | * |
---|
| 1710 | * cancels monomials |
---|
| 1711 | * occuring in denominator |
---|
[b3af93] | 1712 | * and enumerator ? naNumbOfPar != 1; |
---|
[35aab3] | 1713 | * |
---|
[b3af93] | 1714 | * #defines for Factory: |
---|
| 1715 | * FACTORY_GCD_TEST: do not apply built in gcd for |
---|
| 1716 | * univariate polynomials, always use Factory |
---|
[35aab3] | 1717 | */ |
---|
[b3af93] | 1718 | //#define FACTORY_GCD_TEST |
---|
[b85e37] | 1719 | void naCoefNormalize(number pp) |
---|
| 1720 | { |
---|
| 1721 | if (pp==NULL) return; |
---|
| 1722 | lnumber p = (lnumber)pp; |
---|
| 1723 | number nz; // all denom. of the numerator |
---|
| 1724 | nz=p_GetAllDenom(p->z,nacRing); |
---|
| 1725 | BOOLEAN norm=FALSE; |
---|
| 1726 | if (!n_IsOne(nz,nacRing)) |
---|
| 1727 | { |
---|
| 1728 | norm=TRUE; |
---|
| 1729 | p->z=p_Mult_nn(p->z,nz,nacRing); |
---|
| 1730 | if (p->n==NULL) |
---|
| 1731 | { |
---|
| 1732 | p->n=p_NSet(nz,nacRing); |
---|
| 1733 | } |
---|
| 1734 | else |
---|
| 1735 | { |
---|
| 1736 | p->n=p_Mult_nn(p->n,nz,nacRing); |
---|
| 1737 | n_Delete(&nz, nacRing); |
---|
| 1738 | } |
---|
| 1739 | } |
---|
| 1740 | else |
---|
| 1741 | { |
---|
| 1742 | n_Delete(&nz, nacRing); |
---|
| 1743 | } |
---|
[fef045c] | 1744 | if (norm) |
---|
| 1745 | { |
---|
| 1746 | norm=FALSE; |
---|
| 1747 | p_Normalize(p->z,nacRing); |
---|
| 1748 | p_Normalize(p->n,nacRing); |
---|
| 1749 | } |
---|
| 1750 | number nn; |
---|
| 1751 | nn=p_GetAllDenom(p->n,nacRing); |
---|
[b85e37] | 1752 | if (!n_IsOne(nn,nacRing)) |
---|
| 1753 | { |
---|
| 1754 | norm=TRUE; |
---|
| 1755 | p->n=p_Mult_nn(p->n,nn,nacRing); |
---|
| 1756 | p->z=p_Mult_nn(p->z,nn,nacRing); |
---|
| 1757 | n_Delete(&nn, nacRing); |
---|
| 1758 | } |
---|
| 1759 | else |
---|
| 1760 | { |
---|
| 1761 | n_Delete(&nn, nacRing); |
---|
| 1762 | } |
---|
| 1763 | if (norm) |
---|
| 1764 | { |
---|
| 1765 | p_Normalize(p->z,nacRing); |
---|
| 1766 | p_Normalize(p->n,nacRing); |
---|
| 1767 | } |
---|
[fef045c] | 1768 | // remove common factors in n, z: |
---|
| 1769 | if (p->n!=NULL) |
---|
| 1770 | { |
---|
| 1771 | poly pp=p->z; |
---|
| 1772 | nz=n_Copy(pGetCoeff(pp),nacRing); |
---|
| 1773 | pIter(pp); |
---|
| 1774 | while(pp!=NULL) |
---|
[074d3e] | 1775 | { |
---|
[fef045c] | 1776 | if (n_IsOne(nz,nacRing)) break; |
---|
| 1777 | number d=n_Gcd(nz,pGetCoeff(pp),nacRing); |
---|
| 1778 | n_Delete(&nz,nacRing); nz=d; |
---|
| 1779 | pIter(pp); |
---|
| 1780 | } |
---|
| 1781 | if (!n_IsOne(nz,nacRing)) |
---|
| 1782 | { |
---|
| 1783 | pp=p->n; |
---|
| 1784 | nn=n_Copy(pGetCoeff(pp),nacRing); |
---|
| 1785 | pIter(pp); |
---|
| 1786 | while(pp!=NULL) |
---|
[074d3e] | 1787 | { |
---|
[fef045c] | 1788 | if (n_IsOne(nn,nacRing)) break; |
---|
| 1789 | number d=n_Gcd(nn,pGetCoeff(pp),nacRing); |
---|
| 1790 | n_Delete(&nn,nacRing); nn=d; |
---|
| 1791 | pIter(pp); |
---|
| 1792 | } |
---|
| 1793 | number ng=n_Gcd(nz,nn,nacRing); |
---|
| 1794 | n_Delete(&nn,nacRing); |
---|
| 1795 | if (!n_IsOne(ng,nacRing)) |
---|
| 1796 | { |
---|
| 1797 | number ni=n_Invers(ng,nacRing); |
---|
| 1798 | p->z=p_Mult_nn(p->z,ni,nacRing); |
---|
| 1799 | p->n=p_Mult_nn(p->n,ni,nacRing); |
---|
| 1800 | p_Normalize(p->z,nacRing); |
---|
| 1801 | p_Normalize(p->n,nacRing); |
---|
| 1802 | n_Delete(&ni,nacRing); |
---|
| 1803 | } |
---|
| 1804 | n_Delete(&ng,nacRing); |
---|
| 1805 | } |
---|
| 1806 | n_Delete(&nz,nacRing); |
---|
| 1807 | } |
---|
[dd8668] | 1808 | if (p->n!=NULL) |
---|
[b85e37] | 1809 | { |
---|
[dd8668] | 1810 | if(!nacGreaterZero(pGetCoeff(p->n))) |
---|
| 1811 | { |
---|
| 1812 | p->z=napNeg(p->z); |
---|
| 1813 | p->n=napNeg(p->n); |
---|
| 1814 | } |
---|
| 1815 | |
---|
| 1816 | if (/*(p->n!=NULL) && */ |
---|
| 1817 | (p_IsConstant(p->n,nacRing)) |
---|
| 1818 | && (n_IsOne(pGetCoeff(p->n),nacRing))) |
---|
| 1819 | { |
---|
| 1820 | p_Delete(&(p->n), nacRing); |
---|
| 1821 | p->n = NULL; |
---|
| 1822 | } |
---|
[b85e37] | 1823 | } |
---|
| 1824 | } |
---|
[074d3e] | 1825 | |
---|
[35aab3] | 1826 | void naNormalize(number &pp) |
---|
| 1827 | { |
---|
[e1b6a22] | 1828 | |
---|
[35aab3] | 1829 | //naTest(pp); // input may not be "normal" |
---|
| 1830 | lnumber p = (lnumber)pp; |
---|
| 1831 | |
---|
[dd8668] | 1832 | if (p==NULL) |
---|
[35aab3] | 1833 | return; |
---|
[b85e37] | 1834 | naCoefNormalize(pp); |
---|
[e475e3] | 1835 | p->s = 2; |
---|
[35aab3] | 1836 | napoly x = p->z; |
---|
| 1837 | napoly y = p->n; |
---|
[b85e37] | 1838 | |
---|
| 1839 | BOOLEAN norm=FALSE; |
---|
| 1840 | |
---|
[e1b6a22] | 1841 | if ((y!=NULL) && (naMinimalPoly!=NULL)) |
---|
[35aab3] | 1842 | { |
---|
[e1b6a22] | 1843 | y = napInvers(y, naMinimalPoly); |
---|
[b85e37] | 1844 | x = p_Mult_q(x, y,nacRing); |
---|
| 1845 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 1846 | x = napRemainder(x, naMinimalPoly); |
---|
[e1b6a22] | 1847 | p->z = x; |
---|
| 1848 | p->n = y = NULL; |
---|
[b85e37] | 1849 | norm=naIsChar0; |
---|
[e1b6a22] | 1850 | } |
---|
[b85e37] | 1851 | |
---|
[e1b6a22] | 1852 | /* check for degree of x too high: */ |
---|
| 1853 | if ((x!=NULL) && (naMinimalPoly!=NULL) && (x!=naMinimalPoly) |
---|
[b85e37] | 1854 | && (p_GetExp(x,1,nacRing)>p_GetExp(naMinimalPoly,1,nacRing))) |
---|
[e1b6a22] | 1855 | // DO NOT REDUCE naMinimalPoly with itself |
---|
| 1856 | { |
---|
| 1857 | x = napRemainder(x, naMinimalPoly); |
---|
| 1858 | p->z = x; |
---|
[b85e37] | 1859 | norm=naIsChar0; |
---|
[35aab3] | 1860 | } |
---|
| 1861 | /* normalize all coefficients in n and z (if in Q) */ |
---|
[b85e37] | 1862 | if (norm) |
---|
[35aab3] | 1863 | { |
---|
[b85e37] | 1864 | naCoefNormalize(pp); |
---|
[35aab3] | 1865 | x = p->z; |
---|
| 1866 | y = p->n; |
---|
| 1867 | } |
---|
[b85e37] | 1868 | if (y==NULL) return; |
---|
| 1869 | |
---|
[8fa1c2] | 1870 | if ((naMinimalPoly == NULL) && (x!=NULL) && (y!=NULL)) |
---|
[35aab3] | 1871 | { |
---|
| 1872 | int i; |
---|
[b3af93] | 1873 | for (i=naNumbOfPar-1; i>=0; i--) |
---|
[35aab3] | 1874 | { |
---|
| 1875 | napoly xx=x; |
---|
| 1876 | napoly yy=y; |
---|
| 1877 | int m = napExpi(i, yy, xx); |
---|
| 1878 | if (m != 0) // in this case xx!=NULL!=yy |
---|
| 1879 | { |
---|
| 1880 | while (xx != NULL) |
---|
| 1881 | { |
---|
| 1882 | napAddExp(xx,i+1, -m); |
---|
[1629ab] | 1883 | pIter(xx); |
---|
[35aab3] | 1884 | } |
---|
| 1885 | while (yy != NULL) |
---|
| 1886 | { |
---|
| 1887 | napAddExp(yy,i+1, -m); |
---|
[1629ab] | 1888 | pIter(yy); |
---|
[35aab3] | 1889 | } |
---|
| 1890 | } |
---|
| 1891 | } |
---|
| 1892 | } |
---|
[70f63a] | 1893 | if (p_LmIsConstant(y,nacRing)) /* i.e. => simplify to (1/c)*z / monom */ |
---|
[35aab3] | 1894 | { |
---|
[b3af93] | 1895 | if (nacIsOne(pGetCoeff(y))) |
---|
[35aab3] | 1896 | { |
---|
[aa74213] | 1897 | p_LmDelete(&y,nacRing); |
---|
[35aab3] | 1898 | p->n = NULL; |
---|
| 1899 | naTest(pp); |
---|
| 1900 | return; |
---|
| 1901 | } |
---|
[b3af93] | 1902 | number h1 = nacInvers(pGetCoeff(y)); |
---|
[35aab3] | 1903 | nacNormalize(h1); |
---|
[b3af93] | 1904 | napMultN(x, h1); |
---|
[b85e37] | 1905 | n_Delete(&h1,nacRing); |
---|
[aa74213] | 1906 | p_LmDelete(&y,nacRing); |
---|
[35aab3] | 1907 | p->n = NULL; |
---|
| 1908 | naTest(pp); |
---|
| 1909 | return; |
---|
| 1910 | } |
---|
[b3af93] | 1911 | #ifndef FACTORY_GCD_TEST |
---|
| 1912 | if (naNumbOfPar == 1) /* apply built-in gcd */ |
---|
[35aab3] | 1913 | { |
---|
| 1914 | napoly x1,y1; |
---|
[b85e37] | 1915 | if (p_GetExp(x,1,nacRing) >= p_GetExp(y,1,nacRing)) |
---|
[35aab3] | 1916 | { |
---|
| 1917 | x1 = napCopy(x); |
---|
| 1918 | y1 = napCopy(y); |
---|
| 1919 | } |
---|
| 1920 | else |
---|
| 1921 | { |
---|
| 1922 | x1 = napCopy(y); |
---|
| 1923 | y1 = napCopy(x); |
---|
| 1924 | } |
---|
| 1925 | napoly r; |
---|
| 1926 | loop |
---|
| 1927 | { |
---|
| 1928 | r = napRemainder(x1, y1); |
---|
[1629ab] | 1929 | if ((r==NULL) || (pNext(r)==NULL)) break; |
---|
[35aab3] | 1930 | x1 = y1; |
---|
| 1931 | y1 = r; |
---|
| 1932 | } |
---|
| 1933 | if (r!=NULL) |
---|
| 1934 | { |
---|
[1629ab] | 1935 | p_Delete(&r,nacRing); |
---|
| 1936 | p_Delete(&y1,nacRing); |
---|
[35aab3] | 1937 | } |
---|
| 1938 | else |
---|
| 1939 | { |
---|
| 1940 | napDivMod(x, y1, &(p->z), &r); |
---|
| 1941 | napDivMod(y, y1, &(p->n), &r); |
---|
[1629ab] | 1942 | p_Delete(&y1,nacRing); |
---|
[35aab3] | 1943 | } |
---|
| 1944 | x = p->z; |
---|
| 1945 | y = p->n; |
---|
| 1946 | /* collect all denoms from y and multiply x and y by it */ |
---|
| 1947 | if (naIsChar0) |
---|
| 1948 | { |
---|
| 1949 | number n=napLcm(y); |
---|
[b3af93] | 1950 | napMultN(x,n); |
---|
| 1951 | napMultN(y,n); |
---|
[b85e37] | 1952 | n_Delete(&n,nacRing); |
---|
[35aab3] | 1953 | while(x!=NULL) |
---|
| 1954 | { |
---|
[b3af93] | 1955 | nacNormalize(pGetCoeff(x)); |
---|
[1629ab] | 1956 | pIter(x); |
---|
[35aab3] | 1957 | } |
---|
| 1958 | x = p->z; |
---|
| 1959 | while(y!=NULL) |
---|
| 1960 | { |
---|
[b3af93] | 1961 | nacNormalize(pGetCoeff(y)); |
---|
[1629ab] | 1962 | pIter(y); |
---|
[35aab3] | 1963 | } |
---|
| 1964 | y = p->n; |
---|
| 1965 | } |
---|
[1629ab] | 1966 | if (pNext(y)==NULL) |
---|
[35aab3] | 1967 | { |
---|
[b3af93] | 1968 | if (nacIsOne(pGetCoeff(y))) |
---|
[35aab3] | 1969 | { |
---|
[b85e37] | 1970 | if (p_GetExp(y,1,nacRing)==0) |
---|
[35aab3] | 1971 | { |
---|
[aa74213] | 1972 | p_LmDelete(&y,nacRing); |
---|
[35aab3] | 1973 | p->n = NULL; |
---|
| 1974 | } |
---|
| 1975 | naTest(pp); |
---|
| 1976 | return; |
---|
| 1977 | } |
---|
| 1978 | } |
---|
| 1979 | } |
---|
[b3af93] | 1980 | #endif /* FACTORY_GCD_TEST */ |
---|
[35aab3] | 1981 | #ifdef HAVE_FACTORY |
---|
[b3af93] | 1982 | #ifndef FACTORY_GCD_TEST |
---|
[35aab3] | 1983 | else |
---|
[b3af93] | 1984 | #endif |
---|
[35aab3] | 1985 | { |
---|
| 1986 | napoly xx,yy; |
---|
| 1987 | singclap_algdividecontent(x,y,xx,yy); |
---|
| 1988 | if (xx!=NULL) |
---|
| 1989 | { |
---|
| 1990 | p->z=xx; |
---|
| 1991 | p->n=yy; |
---|
[1629ab] | 1992 | p_Delete(&x,nacRing); |
---|
| 1993 | p_Delete(&y,nacRing); |
---|
[35aab3] | 1994 | } |
---|
| 1995 | } |
---|
| 1996 | #endif |
---|
| 1997 | /* remove common factors from z and n */ |
---|
| 1998 | x=p->z; |
---|
| 1999 | y=p->n; |
---|
[b3af93] | 2000 | if(!nacGreaterZero(pGetCoeff(y))) |
---|
[35aab3] | 2001 | { |
---|
| 2002 | x=napNeg(x); |
---|
| 2003 | y=napNeg(y); |
---|
| 2004 | } |
---|
[b3af93] | 2005 | number g=nacCopy(pGetCoeff(x)); |
---|
[1629ab] | 2006 | pIter(x); |
---|
[35aab3] | 2007 | while (x!=NULL) |
---|
| 2008 | { |
---|
[b3af93] | 2009 | number d=nacGcd(g,pGetCoeff(x), nacRing); |
---|
[35aab3] | 2010 | if(nacIsOne(d)) |
---|
| 2011 | { |
---|
[b85e37] | 2012 | n_Delete(&g,nacRing); |
---|
| 2013 | n_Delete(&d,nacRing); |
---|
[35aab3] | 2014 | naTest(pp); |
---|
| 2015 | return; |
---|
| 2016 | } |
---|
[b85e37] | 2017 | n_Delete(&g,nacRing); |
---|
[35aab3] | 2018 | g = d; |
---|
[1629ab] | 2019 | pIter(x); |
---|
[35aab3] | 2020 | } |
---|
| 2021 | while (y!=NULL) |
---|
| 2022 | { |
---|
[b3af93] | 2023 | number d=nacGcd(g,pGetCoeff(y), nacRing); |
---|
[35aab3] | 2024 | if(nacIsOne(d)) |
---|
| 2025 | { |
---|
[b85e37] | 2026 | n_Delete(&g,nacRing); |
---|
| 2027 | n_Delete(&d,nacRing); |
---|
[35aab3] | 2028 | naTest(pp); |
---|
| 2029 | return; |
---|
| 2030 | } |
---|
[b85e37] | 2031 | n_Delete(&g,nacRing); |
---|
[35aab3] | 2032 | g = d; |
---|
[1629ab] | 2033 | pIter(y); |
---|
[35aab3] | 2034 | } |
---|
| 2035 | x=p->z; |
---|
| 2036 | y=p->n; |
---|
| 2037 | while (x!=NULL) |
---|
| 2038 | { |
---|
[b3af93] | 2039 | number d = nacIntDiv(pGetCoeff(x),g); |
---|
[35aab3] | 2040 | napSetCoeff(x,d); |
---|
[1629ab] | 2041 | pIter(x); |
---|
[35aab3] | 2042 | } |
---|
| 2043 | while (y!=NULL) |
---|
| 2044 | { |
---|
[b3af93] | 2045 | number d = nacIntDiv(pGetCoeff(y),g); |
---|
[35aab3] | 2046 | napSetCoeff(y,d); |
---|
[1629ab] | 2047 | pIter(y); |
---|
[35aab3] | 2048 | } |
---|
[b85e37] | 2049 | n_Delete(&g,nacRing); |
---|
[35aab3] | 2050 | naTest(pp); |
---|
| 2051 | } |
---|
| 2052 | |
---|
| 2053 | /*2 |
---|
| 2054 | * returns in result->n 1 |
---|
| 2055 | * and in result->z the lcm(a->z,b->n) |
---|
| 2056 | */ |
---|
| 2057 | number naLcm(number la, number lb, const ring r) |
---|
| 2058 | { |
---|
| 2059 | lnumber result; |
---|
| 2060 | lnumber a = (lnumber)la; |
---|
| 2061 | lnumber b = (lnumber)lb; |
---|
| 2062 | result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 2063 | //if (((naMinimalPoly==NULL) && (naI==NULL)) || !naIsChar0) |
---|
| 2064 | //{ |
---|
[6094f4] | 2065 | // result->z = p_ISet(1,nacRing); |
---|
[35aab3] | 2066 | // return (number)result; |
---|
| 2067 | //} |
---|
[1c3aa7] | 2068 | //naNormalize(lb); |
---|
[35aab3] | 2069 | naTest(la); |
---|
| 2070 | naTest(lb); |
---|
[aaeb98] | 2071 | napoly x = p_Copy(a->z, r->algring); |
---|
[35aab3] | 2072 | number t = napLcm(b->z); // get all denom of b->z |
---|
| 2073 | if (!nacIsOne(t)) |
---|
| 2074 | { |
---|
[aaeb98] | 2075 | number bt, rr; |
---|
[35aab3] | 2076 | napoly xx=x; |
---|
| 2077 | while (xx!=NULL) |
---|
| 2078 | { |
---|
[aaeb98] | 2079 | bt = nacGcd(t, pGetCoeff(xx), r->algring); |
---|
| 2080 | rr = nacMult(t, pGetCoeff(xx)); |
---|
[b85e37] | 2081 | n_Delete(&pGetCoeff(xx),r->algring); |
---|
[aaeb98] | 2082 | pGetCoeff(xx) = nacDiv(rr, bt); |
---|
[b3af93] | 2083 | nacNormalize(pGetCoeff(xx)); |
---|
[b85e37] | 2084 | n_Delete(&bt,r->algring); |
---|
| 2085 | n_Delete(&rr,r->algring); |
---|
[1629ab] | 2086 | pIter(xx); |
---|
[35aab3] | 2087 | } |
---|
| 2088 | } |
---|
[b85e37] | 2089 | n_Delete(&t,r->algring); |
---|
[35aab3] | 2090 | result->z = x; |
---|
| 2091 | #ifdef HAVE_FACTORY |
---|
| 2092 | if (b->n!=NULL) |
---|
| 2093 | { |
---|
| 2094 | result->z=singclap_alglcm(result->z,b->n); |
---|
[aaeb98] | 2095 | p_Delete(&x,r->algring); |
---|
[35aab3] | 2096 | } |
---|
| 2097 | #endif |
---|
| 2098 | naTest(la); |
---|
| 2099 | naTest(lb); |
---|
| 2100 | naTest((number)result); |
---|
| 2101 | return ((number)result); |
---|
| 2102 | } |
---|
| 2103 | |
---|
| 2104 | /*2 |
---|
| 2105 | * input: a set of constant polynomials |
---|
| 2106 | * sets the global variable naI |
---|
| 2107 | */ |
---|
| 2108 | void naSetIdeal(ideal I) |
---|
| 2109 | { |
---|
| 2110 | int i; |
---|
| 2111 | |
---|
| 2112 | if (idIs0(I)) |
---|
| 2113 | { |
---|
| 2114 | for (i=naI->anz-1; i>=0; i--) |
---|
[1629ab] | 2115 | p_Delete(&naI->liste[i],nacRing); |
---|
[35aab3] | 2116 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
---|
| 2117 | naI=NULL; |
---|
| 2118 | } |
---|
| 2119 | else |
---|
| 2120 | { |
---|
| 2121 | lnumber h; |
---|
| 2122 | number a; |
---|
| 2123 | napoly x; |
---|
| 2124 | |
---|
| 2125 | naI=(naIdeal)omAllocBin(snaIdeal_bin); |
---|
| 2126 | naI->anz=IDELEMS(I); |
---|
| 2127 | naI->liste=(napoly*)omAlloc(naI->anz*sizeof(napoly)); |
---|
| 2128 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
| 2129 | { |
---|
| 2130 | h=(lnumber)pGetCoeff(I->m[i]); |
---|
| 2131 | /* We only need the enumerator of h, as we expect it to be a polynomial */ |
---|
| 2132 | naI->liste[i]=napCopy(h->z); |
---|
| 2133 | /* If it isn't normalized (lc = 1) do this */ |
---|
[b3af93] | 2134 | if (!nacIsOne(pGetCoeff(naI->liste[i]))) |
---|
[35aab3] | 2135 | { |
---|
| 2136 | x=naI->liste[i]; |
---|
[b3af93] | 2137 | nacNormalize(pGetCoeff(x)); |
---|
| 2138 | a=nacCopy(pGetCoeff(x)); |
---|
[35aab3] | 2139 | number aa=nacInvers(a); |
---|
[b85e37] | 2140 | n_Delete(&a,nacRing); |
---|
[b3af93] | 2141 | napMultN(x,aa); |
---|
[b85e37] | 2142 | n_Delete(&aa,nacRing); |
---|
[35aab3] | 2143 | } |
---|
| 2144 | } |
---|
| 2145 | } |
---|
| 2146 | } |
---|
| 2147 | |
---|
| 2148 | /*2 |
---|
| 2149 | * map Z/p -> Q(a) |
---|
| 2150 | */ |
---|
| 2151 | number naMapP0(number c) |
---|
| 2152 | { |
---|
| 2153 | if (npIsZero(c)) return NULL; |
---|
| 2154 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2155 | l->s=2; |
---|
| 2156 | l->z=(napoly)p_Init(nacRing); |
---|
[7447d8] | 2157 | int i=(int)((long)c); |
---|
[8391d8] | 2158 | if (i>((long)naMapRing->ch>>2)) i-=(long)naMapRing->ch; |
---|
| 2159 | pGetCoeff(l->z)=nlInit(i, nacRing); |
---|
[35aab3] | 2160 | l->n=NULL; |
---|
| 2161 | return (number)l; |
---|
| 2162 | } |
---|
| 2163 | |
---|
| 2164 | /*2 |
---|
| 2165 | * map Q -> Q(a) |
---|
| 2166 | */ |
---|
| 2167 | number naMap00(number c) |
---|
| 2168 | { |
---|
| 2169 | if (nlIsZero(c)) return NULL; |
---|
| 2170 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2171 | l->s=0; |
---|
| 2172 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 2173 | pGetCoeff(l->z)=nlCopy(c); |
---|
[35aab3] | 2174 | l->n=NULL; |
---|
| 2175 | return (number)l; |
---|
| 2176 | } |
---|
| 2177 | |
---|
| 2178 | /*2 |
---|
| 2179 | * map Z/p -> Z/p(a) |
---|
| 2180 | */ |
---|
| 2181 | number naMapPP(number c) |
---|
| 2182 | { |
---|
| 2183 | if (npIsZero(c)) return NULL; |
---|
| 2184 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2185 | l->s=2; |
---|
| 2186 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 2187 | pGetCoeff(l->z)=c; /* omit npCopy, because npCopy is a no-op */ |
---|
[35aab3] | 2188 | l->n=NULL; |
---|
| 2189 | return (number)l; |
---|
| 2190 | } |
---|
| 2191 | |
---|
| 2192 | /*2 |
---|
| 2193 | * map Z/p' -> Z/p(a) |
---|
| 2194 | */ |
---|
| 2195 | number naMapPP1(number c) |
---|
| 2196 | { |
---|
| 2197 | if (npIsZero(c)) return NULL; |
---|
[7447d8] | 2198 | int i=(int)((long)c); |
---|
[8391d8] | 2199 | if (i>(long)naMapRing->ch) i-=(long)naMapRing->ch; |
---|
| 2200 | number n=npInit(i,naMapRing); |
---|
[35aab3] | 2201 | if (npIsZero(n)) return NULL; |
---|
| 2202 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2203 | l->s=2; |
---|
| 2204 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 2205 | pGetCoeff(l->z)=n; |
---|
[35aab3] | 2206 | l->n=NULL; |
---|
| 2207 | return (number)l; |
---|
| 2208 | } |
---|
| 2209 | |
---|
| 2210 | /*2 |
---|
| 2211 | * map Q -> Z/p(a) |
---|
| 2212 | */ |
---|
| 2213 | number naMap0P(number c) |
---|
| 2214 | { |
---|
| 2215 | if (nlIsZero(c)) return NULL; |
---|
[8391d8] | 2216 | number n=npInit(nlModP(c,npPrimeM),nacRing); |
---|
[35aab3] | 2217 | if (npIsZero(n)) return NULL; |
---|
[f1e33bb] | 2218 | npTest(n); |
---|
[35aab3] | 2219 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
| 2220 | l->s=2; |
---|
| 2221 | l->z=(napoly)p_Init(nacRing); |
---|
[b3af93] | 2222 | pGetCoeff(l->z)=n; |
---|
[35aab3] | 2223 | l->n=NULL; |
---|
| 2224 | return (number)l; |
---|
| 2225 | } |
---|
| 2226 | |
---|
| 2227 | static number (*nacMap)(number); |
---|
| 2228 | static int naParsToCopy; |
---|
| 2229 | static napoly napMap(napoly p) |
---|
| 2230 | { |
---|
| 2231 | napoly w, a; |
---|
| 2232 | |
---|
| 2233 | if (p==NULL) return NULL; |
---|
| 2234 | a = w = (napoly)p_Init(nacRing); |
---|
| 2235 | int i; |
---|
| 2236 | for(i=1;i<=naParsToCopy;i++) |
---|
[8391d8] | 2237 | napSetExp(a,i,napGetExpFrom(p,i,naMapRing)); |
---|
[35aab3] | 2238 | p_Setm(a,nacRing); |
---|
[b3af93] | 2239 | pGetCoeff(w) = nacMap(pGetCoeff(p)); |
---|
[35aab3] | 2240 | loop |
---|
| 2241 | { |
---|
[1629ab] | 2242 | pIter(p); |
---|
[35aab3] | 2243 | if (p==NULL) break; |
---|
[1629ab] | 2244 | pNext(a) = (napoly)p_Init(nacRing); |
---|
| 2245 | pIter(a); |
---|
[35aab3] | 2246 | for(i=1;i<=naParsToCopy;i++) |
---|
[8391d8] | 2247 | napSetExp(a,i,napGetExpFrom(p,i,naMapRing)); |
---|
[35aab3] | 2248 | p_Setm(a,nacRing); |
---|
[b3af93] | 2249 | pGetCoeff(a) = nacMap(pGetCoeff(p)); |
---|
[35aab3] | 2250 | } |
---|
[1629ab] | 2251 | pNext(a) = NULL; |
---|
[35aab3] | 2252 | return w; |
---|
| 2253 | } |
---|
| 2254 | |
---|
[836ebdb] | 2255 | static napoly napPerm(napoly p,const int *par_perm,const ring src_ring,const nMapFunc nMap) |
---|
| 2256 | { |
---|
| 2257 | napoly w, a; |
---|
| 2258 | |
---|
| 2259 | if (p==NULL) return NULL; |
---|
| 2260 | w = (napoly)p_Init(nacRing); |
---|
| 2261 | int i; |
---|
| 2262 | BOOLEAN not_null=TRUE; |
---|
| 2263 | loop |
---|
| 2264 | { |
---|
| 2265 | for(i=1;i<=rPar(src_ring);i++) |
---|
| 2266 | { |
---|
[b506079] | 2267 | int e; |
---|
| 2268 | if (par_perm!=NULL) e=par_perm[i-1]; |
---|
| 2269 | else e=-i; |
---|
[836ebdb] | 2270 | int ee=napGetExpFrom(p,i,src_ring); |
---|
| 2271 | if (e<0) |
---|
| 2272 | napSetExp(w,-e,ee); |
---|
| 2273 | else if (ee>0) |
---|
| 2274 | not_null=FALSE; |
---|
| 2275 | } |
---|
[b3af93] | 2276 | pGetCoeff(w) = nMap(pGetCoeff(p)); |
---|
[836ebdb] | 2277 | p_Setm(w,nacRing); |
---|
[1629ab] | 2278 | pIter(p); |
---|
[836ebdb] | 2279 | if (!not_null) |
---|
| 2280 | { |
---|
| 2281 | if (p==NULL) |
---|
| 2282 | { |
---|
[b30ac0] | 2283 | p_Delete(&w,nacRing); |
---|
[836ebdb] | 2284 | return NULL; |
---|
| 2285 | } |
---|
| 2286 | /* else continue*/ |
---|
[b85e37] | 2287 | n_Delete(&(pGetCoeff(w)),nacRing); |
---|
[836ebdb] | 2288 | } |
---|
| 2289 | else |
---|
| 2290 | { |
---|
| 2291 | if (p==NULL) return w; |
---|
| 2292 | else |
---|
| 2293 | { |
---|
[1629ab] | 2294 | pNext(w)=napPerm(p,par_perm,src_ring,nMap); |
---|
[836ebdb] | 2295 | return w; |
---|
| 2296 | } |
---|
| 2297 | } |
---|
| 2298 | } |
---|
| 2299 | } |
---|
| 2300 | |
---|
[35aab3] | 2301 | /*2 |
---|
| 2302 | * map _(a) -> _(b) |
---|
| 2303 | */ |
---|
| 2304 | number naMapQaQb(number c) |
---|
| 2305 | { |
---|
| 2306 | if (c==NULL) return NULL; |
---|
| 2307 | lnumber erg= (lnumber)omAlloc0Bin(rnumber_bin); |
---|
| 2308 | lnumber src =(lnumber)c; |
---|
| 2309 | erg->s=src->s; |
---|
| 2310 | erg->z=napMap(src->z); |
---|
| 2311 | erg->n=napMap(src->n); |
---|
| 2312 | if (naMinimalPoly!=NULL) |
---|
| 2313 | { |
---|
[b85e37] | 2314 | if (p_GetExp(erg->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 2315 | { |
---|
| 2316 | erg->z = napRemainder(erg->z, naMinimalPoly); |
---|
| 2317 | if (erg->z==NULL) |
---|
| 2318 | { |
---|
| 2319 | number t_erg=(number)erg; |
---|
| 2320 | naDelete(&t_erg,currRing); |
---|
| 2321 | return (number)NULL; |
---|
| 2322 | } |
---|
| 2323 | } |
---|
| 2324 | if (erg->n!=NULL) |
---|
| 2325 | { |
---|
[b85e37] | 2326 | if (p_GetExp(erg->n,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 2327 | erg->n = napRemainder(erg->n, naMinimalPoly); |
---|
[074d3e] | 2328 | if ((p_IsConstant(erg->n,nacRing)) && nacIsOne(pGetCoeff(erg->n))) |
---|
[1629ab] | 2329 | p_Delete(&(erg->n),nacRing); |
---|
[35aab3] | 2330 | } |
---|
| 2331 | } |
---|
| 2332 | return (number)erg; |
---|
| 2333 | } |
---|
| 2334 | |
---|
[208e0c] | 2335 | nMapFunc naSetMap(const ring src, const ring dst) |
---|
[35aab3] | 2336 | { |
---|
[8391d8] | 2337 | naMapRing=src; |
---|
[35aab3] | 2338 | if (rField_is_Q_a(dst)) /* -> Q(a) */ |
---|
| 2339 | { |
---|
| 2340 | if (rField_is_Q(src)) |
---|
| 2341 | { |
---|
| 2342 | return naMap00; /*Q -> Q(a)*/ |
---|
| 2343 | } |
---|
| 2344 | if (rField_is_Zp(src)) |
---|
| 2345 | { |
---|
| 2346 | return naMapP0; /* Z/p -> Q(a)*/ |
---|
| 2347 | } |
---|
| 2348 | if (rField_is_Q_a(src)) |
---|
| 2349 | { |
---|
| 2350 | int i; |
---|
| 2351 | naParsToCopy=0; |
---|
| 2352 | for(i=0;i<rPar(src);i++) |
---|
| 2353 | { |
---|
| 2354 | if ((i>=rPar(dst)) |
---|
| 2355 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
| 2356 | return NULL; |
---|
| 2357 | naParsToCopy++; |
---|
| 2358 | } |
---|
| 2359 | nacMap=nacCopy; |
---|
[eb3df5] | 2360 | if ((naParsToCopy==rPar(dst))&&(naParsToCopy==rPar(src))) |
---|
| 2361 | return naCopy; /* Q(a) -> Q(a) */ |
---|
| 2362 | return naMapQaQb; /* Q(a..) -> Q(a..) */ |
---|
[35aab3] | 2363 | } |
---|
| 2364 | } |
---|
| 2365 | /*-----------------------------------------------------*/ |
---|
| 2366 | if (rField_is_Zp_a(dst)) /* -> Z/p(a) */ |
---|
| 2367 | { |
---|
| 2368 | if (rField_is_Q(src)) |
---|
| 2369 | { |
---|
| 2370 | return naMap0P; /*Q -> Z/p(a)*/ |
---|
| 2371 | } |
---|
| 2372 | if (rField_is_Zp(src)) |
---|
| 2373 | { |
---|
[8391d8] | 2374 | if (src->ch==dst->ch) |
---|
[35aab3] | 2375 | { |
---|
| 2376 | return naMapPP; /* Z/p -> Z/p(a)*/ |
---|
| 2377 | } |
---|
| 2378 | else |
---|
| 2379 | { |
---|
| 2380 | return naMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
| 2381 | } |
---|
| 2382 | } |
---|
| 2383 | if (rField_is_Zp_a(src)) |
---|
| 2384 | { |
---|
| 2385 | if (rChar(src)==rChar(dst)) |
---|
| 2386 | { |
---|
| 2387 | nacMap=nacCopy; |
---|
| 2388 | } |
---|
| 2389 | else |
---|
| 2390 | { |
---|
| 2391 | nacMap = npMapP; |
---|
| 2392 | } |
---|
| 2393 | int i; |
---|
| 2394 | naParsToCopy=0; |
---|
| 2395 | for(i=0;i<rPar(src);i++) |
---|
| 2396 | { |
---|
| 2397 | if ((i>=rPar(dst)) |
---|
| 2398 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
| 2399 | return NULL; |
---|
| 2400 | naParsToCopy++; |
---|
| 2401 | } |
---|
[eb3df5] | 2402 | if ((naParsToCopy==rPar(dst))&&(naParsToCopy==rPar(src)) |
---|
| 2403 | && (nacMap==nacCopy)) |
---|
| 2404 | return naCopy; /* Z/p(a) -> Z/p(a) */ |
---|
[35aab3] | 2405 | return naMapQaQb; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
| 2406 | } |
---|
| 2407 | } |
---|
| 2408 | return NULL; /* default */ |
---|
| 2409 | } |
---|
| 2410 | |
---|
| 2411 | /*2 |
---|
| 2412 | * convert a napoly number into a poly |
---|
| 2413 | */ |
---|
[b30ac0] | 2414 | poly naPermNumber(number z, int * par_perm, int P, ring oldRing) |
---|
[35aab3] | 2415 | { |
---|
| 2416 | if (z==NULL) return NULL; |
---|
| 2417 | poly res=NULL; |
---|
| 2418 | poly p; |
---|
| 2419 | napoly za=((lnumber)z)->z; |
---|
[836ebdb] | 2420 | napoly zb=((lnumber)z)->n; |
---|
[b30ac0] | 2421 | nMapFunc nMap=naSetMap(oldRing,currRing); |
---|
[35aab3] | 2422 | if (currRing->parameter!=NULL) |
---|
[b30ac0] | 2423 | nMap=currRing->algring->cf->cfSetMap(oldRing->algring, nacRing); |
---|
[35aab3] | 2424 | else |
---|
[b30ac0] | 2425 | nMap=currRing->cf->cfSetMap(oldRing->algring, currRing); |
---|
[35aab3] | 2426 | if (nMap==NULL) return NULL; /* emergency exit only */ |
---|
| 2427 | do |
---|
| 2428 | { |
---|
| 2429 | p = pInit(); |
---|
| 2430 | pNext(p)=NULL; |
---|
| 2431 | nNew(&pGetCoeff(p)); |
---|
| 2432 | int i; |
---|
| 2433 | for(i=pVariables;i;i--) |
---|
| 2434 | pSetExp(p,i, 0); |
---|
[672bbc] | 2435 | if (rRing_has_Comp(currRing)) pSetComp(p, 0); |
---|
[35aab3] | 2436 | napoly pa=NULL; |
---|
[836ebdb] | 2437 | lnumber pan; |
---|
[35aab3] | 2438 | if (currRing->parameter!=NULL) |
---|
| 2439 | { |
---|
[b30ac0] | 2440 | assume(oldRing->algring!=NULL); |
---|
[35aab3] | 2441 | pGetCoeff(p)=(number)omAlloc0Bin(rnumber_bin); |
---|
[836ebdb] | 2442 | pan=(lnumber)pGetCoeff(p); |
---|
| 2443 | pan->s=2; |
---|
[b3af93] | 2444 | pan->z=napInitz(nMap(pGetCoeff(za))); |
---|
[836ebdb] | 2445 | pa=pan->z; |
---|
[35aab3] | 2446 | } |
---|
| 2447 | else |
---|
| 2448 | { |
---|
[b3af93] | 2449 | pGetCoeff(p)=nMap(pGetCoeff(za)); |
---|
[35aab3] | 2450 | } |
---|
| 2451 | for(i=0;i<P;i++) |
---|
| 2452 | { |
---|
[b30ac0] | 2453 | if(napGetExpFrom(za,i+1,oldRing)!=0) |
---|
[35aab3] | 2454 | { |
---|
| 2455 | if(par_perm==NULL) |
---|
| 2456 | { |
---|
| 2457 | if ((rPar(currRing)>=i) && (pa!=NULL)) |
---|
[836ebdb] | 2458 | { |
---|
[b30ac0] | 2459 | napSetExp(pa,i+1,napGetExpFrom(za,i+1,oldRing)); |
---|
[35aab3] | 2460 | p_Setm(pa,nacRing); |
---|
| 2461 | } |
---|
| 2462 | else |
---|
| 2463 | { |
---|
| 2464 | pDelete(&p); |
---|
| 2465 | break; |
---|
| 2466 | } |
---|
| 2467 | } |
---|
| 2468 | else if(par_perm[i]>0) |
---|
[b30ac0] | 2469 | pSetExp(p,par_perm[i],napGetExpFrom(za,i+1,oldRing)); |
---|
[35aab3] | 2470 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
[836ebdb] | 2471 | { |
---|
[b30ac0] | 2472 | napSetExp(pa,-par_perm[i], napGetExpFrom(za,i+1,oldRing)); |
---|
[35aab3] | 2473 | p_Setm(pa,nacRing); |
---|
[836ebdb] | 2474 | } |
---|
[35aab3] | 2475 | else |
---|
| 2476 | { |
---|
| 2477 | pDelete(&p); |
---|
| 2478 | break; |
---|
| 2479 | } |
---|
| 2480 | } |
---|
| 2481 | } |
---|
| 2482 | if (p!=NULL) |
---|
| 2483 | { |
---|
| 2484 | pSetm(p); |
---|
[836ebdb] | 2485 | if (zb!=NULL) |
---|
| 2486 | { |
---|
[64345a4] | 2487 | if (currRing->P>0) |
---|
| 2488 | { |
---|
| 2489 | pan->n=napPerm(zb,par_perm,oldRing,nMap); |
---|
| 2490 | if(pan->n==NULL) /* error in mapping or mapping to variable */ |
---|
| 2491 | pDelete(&p); |
---|
| 2492 | } |
---|
| 2493 | else |
---|
[836ebdb] | 2494 | pDelete(&p); |
---|
| 2495 | } |
---|
[35aab3] | 2496 | pTest(p); |
---|
| 2497 | res=pAdd(res,p); |
---|
| 2498 | } |
---|
[1629ab] | 2499 | pIter(za); |
---|
[35aab3] | 2500 | } |
---|
| 2501 | while (za!=NULL); |
---|
| 2502 | pTest(res); |
---|
| 2503 | return res; |
---|
| 2504 | } |
---|
| 2505 | |
---|
| 2506 | number naGetDenom(number &n, const ring r) |
---|
| 2507 | { |
---|
| 2508 | lnumber x=(lnumber)n; |
---|
| 2509 | if (x->n!=NULL) |
---|
| 2510 | { |
---|
| 2511 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
[bedece] | 2512 | rr->z=p_Copy(x->n,r->algring); |
---|
[35aab3] | 2513 | rr->s = 2; |
---|
| 2514 | return (number)rr; |
---|
| 2515 | } |
---|
[8391d8] | 2516 | return n_Init(1,r); |
---|
[35aab3] | 2517 | } |
---|
[b3af93] | 2518 | |
---|
[355201] | 2519 | number naGetNumerator(number &n, const ring r) |
---|
[e803ec] | 2520 | { |
---|
| 2521 | lnumber x=(lnumber)n; |
---|
[b3af93] | 2522 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
[bedece] | 2523 | rr->z=p_Copy(x->z,r->algring); |
---|
[b3af93] | 2524 | rr->s = 2; |
---|
| 2525 | return (number)rr; |
---|
[e803ec] | 2526 | } |
---|
[35aab3] | 2527 | |
---|
| 2528 | #ifdef LDEBUG |
---|
[85e68dd] | 2529 | BOOLEAN naDBTest(number a, const char *f,const int l) |
---|
[35aab3] | 2530 | { |
---|
| 2531 | lnumber x=(lnumber)a; |
---|
| 2532 | if (x == NULL) |
---|
| 2533 | return TRUE; |
---|
[074d3e] | 2534 | #ifdef LDEBUG |
---|
[35aab3] | 2535 | omCheckAddrSize(a, sizeof(snumber)); |
---|
[074d3e] | 2536 | #endif |
---|
[35aab3] | 2537 | napoly p = x->z; |
---|
| 2538 | if (p==NULL) |
---|
| 2539 | { |
---|
| 2540 | Print("0/* in %s:%d\n",f,l); |
---|
| 2541 | return FALSE; |
---|
| 2542 | } |
---|
| 2543 | while(p!=NULL) |
---|
| 2544 | { |
---|
[b3af93] | 2545 | if ((naIsChar0 && nlIsZero(pGetCoeff(p))) |
---|
| 2546 | || ((!naIsChar0) && npIsZero(pGetCoeff(p)))) |
---|
[35aab3] | 2547 | { |
---|
| 2548 | Print("coeff 0 in %s:%d\n",f,l); |
---|
| 2549 | return FALSE; |
---|
| 2550 | } |
---|
[b85e37] | 2551 | if((naMinimalPoly!=NULL) |
---|
| 2552 | &&(p_GetExp(p,1,nacRing)>p_GetExp(naMinimalPoly,1,nacRing)) |
---|
[35aab3] | 2553 | &&(p!=naMinimalPoly)) |
---|
| 2554 | { |
---|
| 2555 | Print("deg>minpoly in %s:%d\n",f,l); |
---|
| 2556 | return FALSE; |
---|
| 2557 | } |
---|
| 2558 | //if (naIsChar0 && (((int)p->ko &3) == 0) && (p->ko->s==0) && (x->s==2)) |
---|
| 2559 | //{ |
---|
| 2560 | // Print("normalized with non-normal coeffs in %s:%d\n",f,l); |
---|
| 2561 | // return FALSE; |
---|
| 2562 | //} |
---|
[b3af93] | 2563 | if (naIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
[35aab3] | 2564 | return FALSE; |
---|
[1629ab] | 2565 | pIter(p); |
---|
[35aab3] | 2566 | } |
---|
[b3af93] | 2567 | p = x->n; |
---|
[35aab3] | 2568 | while(p!=NULL) |
---|
| 2569 | { |
---|
[b3af93] | 2570 | if (naIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
[35aab3] | 2571 | return FALSE; |
---|
[1629ab] | 2572 | pIter(p); |
---|
[35aab3] | 2573 | } |
---|
| 2574 | return TRUE; |
---|
| 2575 | } |
---|
| 2576 | #endif |
---|