[0e1846] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[7eea80] | 4 | /* $Id: longalg.cc,v 1.34 1999-06-22 08:09:14 Singular Exp $ */ |
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[0e1846] | 5 | /* |
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| 6 | * ABSTRACT: algebraic numbers |
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| 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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| 11 | #include "mod2.h" |
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| 12 | #include "tok.h" |
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| 13 | #include "mmemory.h" |
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| 14 | #include "febase.h" |
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| 15 | #include "longrat.h" |
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| 16 | #include "modulop.h" |
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| 17 | #include "numbers.h" |
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| 18 | #include "polys.h" |
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| 19 | #include "ideals.h" |
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| 20 | #include "ipid.h" |
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[be0d84] | 21 | #include "ring.h" |
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[af06ef] | 22 | #ifdef HAVE_FACTORY |
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| 23 | #include "clapsing.h" |
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| 24 | #endif |
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[0e1846] | 25 | #include "longalg.h" |
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[af06ef] | 26 | |
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[0e1846] | 27 | #define FEHLER1 1 |
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| 28 | #define FEHLER2 1 |
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| 29 | #define FEHLER3 1 |
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| 30 | |
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| 31 | struct snaIdeal |
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| 32 | { |
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| 33 | int anz; |
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| 34 | alg *liste; |
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| 35 | }; |
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| 36 | typedef struct snaIdeal * naIdeal; |
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| 37 | |
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| 38 | naIdeal naI=NULL; |
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| 39 | |
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| 40 | //#define RECA_SIZE (sizeof(alg)+sizeof(number)) |
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| 41 | alg naMinimalPoly; |
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| 42 | int naNumbOfPar; |
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[550b4c] | 43 | int napMonomSize; |
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[0e1846] | 44 | char **naParNames; |
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| 45 | static int naIsChar0; |
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| 46 | static int naPrimeM; |
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| 47 | |
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| 48 | #ifdef LDEBUG |
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| 49 | #define naTest(a) naDBTest(a,__FILE__,__LINE__) |
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| 50 | BOOLEAN naDBTest(number a, char *f,int l); |
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| 51 | #else |
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| 52 | #define naTest(a) |
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| 53 | #endif |
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| 54 | |
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| 55 | number (*naMap)(number from); |
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| 56 | /* procedure variables */ |
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| 57 | static numberfunc |
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[5dc4ea] | 58 | nacMult, nacSub, nacAdd, nacDiv, nacIntDiv, nacGcd, nacLcm; |
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[0e1846] | 59 | #ifdef LDEBUG |
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| 60 | static void (*nacDBDelete)(number *a,char *f,int l); |
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| 61 | #define nacDelete(A) nacDBDelete(A,__FILE__,__LINE__) |
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| 62 | #else |
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| 63 | static void (*nacDelete)(number *a); |
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| 64 | #endif |
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| 65 | number (*nacInit)(int i); |
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| 66 | static int (*nacInt)(number &n); |
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| 67 | void (*nacNormalize)(number &a); |
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| 68 | static number (*nacNeg)(number a); |
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| 69 | static void (*nacWrite)(number &a); |
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| 70 | number (*nacCopy)(number a); |
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| 71 | static number (*nacInvers)(number a); |
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| 72 | BOOLEAN (*nacIsZero)(number a); |
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| 73 | static BOOLEAN (*nacIsOne)(number a); |
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| 74 | static BOOLEAN (*nacIsMOne)(number a); |
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| 75 | static BOOLEAN (*nacGreaterZero)(number a); |
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| 76 | static char * (*nacRead) (char *s, number *a); |
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| 77 | extern void napDelete(alg *p); |
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| 78 | static alg napRedp(alg q); |
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| 79 | static alg napTailred(alg q); |
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| 80 | static BOOLEAN napDivPoly(alg p, alg q); |
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| 81 | static int napExpi(int i, alg a, alg b); |
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| 82 | |
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[5dc4ea] | 83 | static number nadGcd( number a, number b) { return nacInit(1); } |
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[0e1846] | 84 | /*2 |
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| 85 | * sets the appropriate operators |
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| 86 | */ |
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| 87 | void naSetChar(int i, BOOLEAN complete, char ** param, int pars) |
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| 88 | { |
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| 89 | if (naI!=NULL) |
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| 90 | { |
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| 91 | int j; |
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| 92 | for (j=naI->anz-1; j>=0; j--) |
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| 93 | napDelete (&naI->liste[j]); |
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| 94 | Free((ADDRESS)naI->liste,naI->anz*sizeof(alg)); |
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| 95 | Free((ADDRESS)naI,sizeof(*naI)); |
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| 96 | naI=NULL; |
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| 97 | } |
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| 98 | naMap = naCopy; |
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| 99 | naMinimalPoly = NULL; |
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| 100 | naParNames=param; |
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| 101 | naNumbOfPar=pars; |
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[550b4c] | 102 | napMonomSize = RECA_SIZE + naNumbOfPar*SIZEOF_PARAMETER; |
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[0e1846] | 103 | if (i == 1) |
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| 104 | { |
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| 105 | naIsChar0 = 1; |
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| 106 | #ifdef LDEBUG |
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| 107 | nacDBDelete = nlDBDelete; |
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| 108 | #else |
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| 109 | nacDelete = nlDelete; |
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| 110 | #endif |
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| 111 | if (complete) |
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| 112 | { |
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| 113 | nacInit = nlInit; |
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| 114 | nacInt = nlInt; |
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| 115 | nacCopy = nlCopy; |
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| 116 | nacAdd = nlAdd; |
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| 117 | nacSub = nlSub; |
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| 118 | nacMult = nlMult; |
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| 119 | nacDiv = nlDiv; |
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[5dc4ea] | 120 | nacIntDiv = nlIntDiv; |
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[0e1846] | 121 | nacInvers = nlInvers; |
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| 122 | nacNormalize = nlNormalize; |
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| 123 | nacNeg = nlNeg; |
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| 124 | nacIsZero = nlIsZero; |
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| 125 | nacRead = nlRead; |
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| 126 | nacWrite = nlWrite; |
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| 127 | nacGreaterZero = nlGreaterZero; |
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| 128 | nacIsOne = nlIsOne; |
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| 129 | nacIsMOne = nlIsMOne; |
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| 130 | nacGcd = nlGcd; |
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| 131 | nacLcm = nlLcm; |
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| 132 | } |
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| 133 | } |
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| 134 | else if (i < 0) |
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| 135 | { |
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| 136 | naIsChar0 = 0; |
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| 137 | #ifdef LDEBUG |
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| 138 | nacDBDelete = nDBDummy1; |
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| 139 | #else |
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| 140 | nacDelete = nDummy1; |
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| 141 | #endif |
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| 142 | if (complete) |
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| 143 | { |
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| 144 | npSetChar(-i); |
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| 145 | nacInit = npInit; |
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| 146 | nacInt = npInt; |
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| 147 | nacCopy = npCopy; |
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| 148 | nacAdd = npAdd; |
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| 149 | nacSub = npSub; |
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| 150 | nacMult = npMult; |
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| 151 | nacDiv = npDiv; |
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[5dc4ea] | 152 | nacIntDiv = npDiv; |
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[0e1846] | 153 | nacInvers = npInvers; |
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| 154 | nacNormalize = nDummy2; |
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| 155 | nacNeg = npNeg; |
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| 156 | nacIsZero = npIsZero; |
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| 157 | nacRead = npRead; |
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| 158 | nacWrite = npWrite; |
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| 159 | nacGreaterZero = npGreaterZero; |
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| 160 | nacIsOne = npIsOne; |
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| 161 | nacIsMOne = npIsMOne; |
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[5dc4ea] | 162 | nacGcd = nadGcd; |
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| 163 | nacLcm = nadGcd; |
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[0e1846] | 164 | } |
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| 165 | } |
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| 166 | #ifdef TEST |
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| 167 | else |
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| 168 | { |
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[667247] | 169 | Print("naSetChar:c=%d compl=%d param=%d\n",i,complete,param); |
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[0e1846] | 170 | } |
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| 171 | #endif |
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| 172 | } |
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| 173 | |
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| 174 | /*============= procedure for polynomials: napXXXX =======================*/ |
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| 175 | |
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[5dc4ea] | 176 | #define napSetCoeff(p,n) {nacDelete(&((p)->ko));(p)->ko=n;} |
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| 177 | #define napIter(A) A=(A)->ne |
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| 178 | |
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| 179 | |
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[0e1846] | 180 | /*3 |
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| 181 | * creates an alg poly |
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| 182 | */ |
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| 183 | static alg napInit(int i) |
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| 184 | { |
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[550b4c] | 185 | alg a = (alg)Alloc0(napMonomSize); |
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[0e1846] | 186 | |
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| 187 | a->ko = nacInit(i); |
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| 188 | if (!nacIsZero(a->ko)) |
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| 189 | { |
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| 190 | return a; |
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| 191 | } |
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| 192 | else |
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| 193 | { |
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[550b4c] | 194 | Free((ADDRESS)a, napMonomSize); |
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[0e1846] | 195 | return NULL; |
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| 196 | } |
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| 197 | } |
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| 198 | |
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| 199 | /*3 |
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| 200 | * creates an alg poly |
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| 201 | */ |
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| 202 | alg napInitz(number z) |
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| 203 | { |
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[550b4c] | 204 | alg a = (alg)Alloc0(napMonomSize); |
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[0e1846] | 205 | |
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| 206 | a->ko = z; |
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| 207 | return a; |
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| 208 | } |
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| 209 | |
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| 210 | /*3 |
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| 211 | * deletes head of an alg poly |
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| 212 | */ |
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| 213 | static void napDelete1(alg *p) |
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| 214 | { |
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| 215 | alg h = *p; |
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| 216 | |
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| 217 | if (h!=NULL) |
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| 218 | { |
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| 219 | *p = h->ne; |
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| 220 | nacDelete(&(h->ko)); |
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[550b4c] | 221 | Free((ADDRESS)h, napMonomSize); |
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[0e1846] | 222 | } |
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| 223 | } |
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| 224 | |
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| 225 | /*3 |
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| 226 | * delete an alg poly |
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| 227 | */ |
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| 228 | void napDelete(alg *p) |
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| 229 | { |
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| 230 | alg w, h = *p; |
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| 231 | |
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| 232 | while (h!=NULL) |
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| 233 | { |
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| 234 | w = h; |
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| 235 | h = h->ne; |
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| 236 | nacDelete(&(w->ko)); |
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[550b4c] | 237 | Free((ADDRESS)w, napMonomSize); |
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[0e1846] | 238 | } |
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| 239 | *p = NULL; |
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| 240 | } |
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| 241 | |
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| 242 | |
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| 243 | /*3 |
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| 244 | * copy a alg. poly |
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| 245 | */ |
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| 246 | static alg napCopy(alg p) |
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| 247 | { |
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[58bbda] | 248 | if (p==NULL) return NULL; |
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| 249 | |
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[0e1846] | 250 | alg w, a; |
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| 251 | |
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[550b4c] | 252 | mmTestP(p,napMonomSize); |
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| 253 | a = w = (alg)Alloc(napMonomSize); |
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| 254 | memcpy(w->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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[0e1846] | 255 | w->ko = nacCopy(p->ko); |
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| 256 | loop |
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| 257 | { |
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| 258 | p=p->ne; |
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| 259 | if (p==NULL) break; |
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[550b4c] | 260 | mmTestP(p,napMonomSize); |
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| 261 | a->ne = (alg)Alloc(napMonomSize); |
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[0e1846] | 262 | a = a->ne; |
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[550b4c] | 263 | memcpy(a->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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[0e1846] | 264 | a->ko = nacCopy(p->ko); |
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| 265 | } |
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| 266 | a->ne = NULL; |
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| 267 | return w; |
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| 268 | } |
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| 269 | |
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| 270 | /*3 |
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| 271 | * copy a alg. poly |
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| 272 | */ |
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| 273 | static alg napCopyNeg(alg p) |
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| 274 | { |
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| 275 | alg w, a; |
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| 276 | |
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| 277 | if (p==NULL) return NULL; |
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[550b4c] | 278 | mmTestP(p,napMonomSize); |
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| 279 | a = w = (alg)Alloc(napMonomSize); |
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| 280 | memcpy(w->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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[0e1846] | 281 | w->ko = nacNeg(nacCopy(p->ko)); |
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| 282 | loop |
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| 283 | { |
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| 284 | p=p->ne; |
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| 285 | if (p==NULL) break; |
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[550b4c] | 286 | mmTestP(p,napMonomSize); |
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| 287 | a->ne = (alg)Alloc(napMonomSize); |
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[0e1846] | 288 | a = a->ne; |
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[550b4c] | 289 | memcpy(a->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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[0e1846] | 290 | a->ko = nacNeg(nacCopy(p->ko)); |
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| 291 | } |
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| 292 | a->ne = NULL; |
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| 293 | return w; |
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| 294 | } |
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| 295 | |
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| 296 | /*3 |
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| 297 | * Compare exponents of p and q |
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| 298 | */ |
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| 299 | static int napComp(alg p, alg q) |
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| 300 | { |
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| 301 | int i = 0; |
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| 302 | |
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[550b4c] | 303 | mmTestP(p,napMonomSize); |
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| 304 | mmTestP(q,napMonomSize); |
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[0e1846] | 305 | while (p->e[i] == q->e[i]) |
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| 306 | { |
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| 307 | i++; |
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| 308 | if (i >= naNumbOfPar) |
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| 309 | return 0; |
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| 310 | } |
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| 311 | if (p->e[i] > q->e[i]) |
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| 312 | return 1; |
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| 313 | else |
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| 314 | return - 1; |
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| 315 | } |
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| 316 | |
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| 317 | /*3 |
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| 318 | * addition of alg. polys |
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| 319 | */ |
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| 320 | alg napAdd(alg p1, alg p2) |
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| 321 | { |
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| 322 | alg a1, p, a2, a; |
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| 323 | int c; number t; |
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| 324 | |
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| 325 | if (p1==NULL) return p2; |
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| 326 | if (p2==NULL) return p1; |
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[550b4c] | 327 | mmTestP(p1,napMonomSize); |
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| 328 | mmTestP(p2,napMonomSize); |
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[0e1846] | 329 | a1 = p1; |
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| 330 | a2 = p2; |
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[550b4c] | 331 | a = p = (alg)Alloc(napMonomSize); |
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[0e1846] | 332 | loop |
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| 333 | { |
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| 334 | c = napComp(a1, a2); |
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| 335 | if (c == 1) |
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| 336 | { |
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| 337 | a = a->ne = a1; |
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| 338 | a1 = a1->ne; |
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[1a5daea] | 339 | if (a1==NULL) |
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[0e1846] | 340 | { |
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| 341 | a->ne= a2; |
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| 342 | break; |
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| 343 | } |
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[550b4c] | 344 | mmTestP(a1,napMonomSize); |
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[0e1846] | 345 | } |
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| 346 | else if (c == -1) |
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| 347 | { |
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| 348 | a = a->ne = a2; |
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| 349 | a2 = a2->ne; |
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[1a5daea] | 350 | if (a2==NULL) |
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[0e1846] | 351 | { |
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| 352 | a->ne = a1; |
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| 353 | break; |
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| 354 | } |
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[550b4c] | 355 | mmTestP(a2,napMonomSize); |
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[0e1846] | 356 | } |
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| 357 | else |
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| 358 | { |
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| 359 | t = nacAdd(a1->ko, a2->ko); |
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| 360 | napDelete1(&a2); |
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| 361 | if (nacIsZero(t)) |
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| 362 | { |
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| 363 | nacDelete(&t); |
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| 364 | napDelete1(&a1); |
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| 365 | } |
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| 366 | else |
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| 367 | { |
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| 368 | nacDelete(&(a1->ko)); |
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| 369 | a1->ko = t; |
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| 370 | a = a->ne = a1; |
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| 371 | a1 = a1->ne; |
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| 372 | } |
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| 373 | if (a1==NULL) |
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| 374 | { |
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| 375 | a->ne = a2; |
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| 376 | break; |
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| 377 | } |
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| 378 | else if (a2==NULL) |
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| 379 | { |
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| 380 | a->ne = a1; |
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| 381 | break; |
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| 382 | } |
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[550b4c] | 383 | mmTestP(a1,napMonomSize); |
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| 384 | mmTestP(a2,napMonomSize); |
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[0e1846] | 385 | } |
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| 386 | } |
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| 387 | a = p->ne; |
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[550b4c] | 388 | Free((ADDRESS)p, napMonomSize); |
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[0e1846] | 389 | return a; |
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| 390 | } |
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| 391 | |
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| 392 | |
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| 393 | /*3 |
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| 394 | * multiply a alg. poly by -1 |
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| 395 | */ |
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| 396 | static alg napNeg(alg a) |
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| 397 | { |
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| 398 | alg p = a; |
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| 399 | |
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| 400 | while (p!=NULL) |
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| 401 | { |
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[550b4c] | 402 | mmTestP(p,napMonomSize); |
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[0e1846] | 403 | p->ko = nacNeg(p->ko); |
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| 404 | p = p->ne; |
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| 405 | } |
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| 406 | return a; |
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| 407 | } |
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| 408 | |
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| 409 | /*3 |
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| 410 | * returns ph * z |
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| 411 | */ |
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| 412 | static void napMultN(alg p, number z) |
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| 413 | { |
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| 414 | number t; |
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| 415 | |
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| 416 | while (p!=NULL) |
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| 417 | { |
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[550b4c] | 418 | mmTestP(p,napMonomSize); |
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[0e1846] | 419 | t = nacMult(p->ko, z); |
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| 420 | nacNormalize(t); |
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| 421 | nacDelete(&p->ko); |
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| 422 | p->ko = t; |
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| 423 | p = p->ne; |
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| 424 | } |
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| 425 | } |
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| 426 | |
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| 427 | /*3 |
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| 428 | * update the polynomial a by multipying it by |
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| 429 | * the (number) coefficient |
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| 430 | * and the exponent vector (of) exp (a well initialized polynomial) |
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| 431 | */ |
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| 432 | static void napMultT(alg a, alg exp) |
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| 433 | { |
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| 434 | int i; |
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| 435 | number t, h; |
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| 436 | if (a==NULL) |
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| 437 | return; |
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| 438 | h = exp->ko; |
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| 439 | if (nacIsOne(h)) |
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| 440 | { |
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| 441 | do |
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| 442 | { |
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| 443 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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| 444 | a->e[i] += exp->e[i]; |
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| 445 | a = a->ne; |
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| 446 | } |
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| 447 | while (a!=NULL); |
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| 448 | } |
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| 449 | else |
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| 450 | { |
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| 451 | h = nacNeg(h); |
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| 452 | if (nacIsOne(h)) |
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| 453 | { |
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| 454 | h = nacNeg(h); |
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| 455 | do |
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| 456 | { |
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| 457 | a->ko = nacNeg(a->ko); |
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| 458 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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| 459 | a->e[i] += exp->e[i]; |
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| 460 | a = a->ne; |
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| 461 | } |
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| 462 | while (a!=NULL); |
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| 463 | } |
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| 464 | else |
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| 465 | { |
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| 466 | h = nacNeg(h); |
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| 467 | do |
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| 468 | { |
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| 469 | t = nacMult(a->ko, h); |
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| 470 | nacDelete(&(a->ko)); |
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| 471 | a->ko = t; |
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| 472 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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| 473 | a->e[i] += exp->e[i]; |
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| 474 | a = a->ne; |
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| 475 | } |
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| 476 | while (a!=NULL); |
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| 477 | } |
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| 478 | } |
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| 479 | } |
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| 480 | |
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| 481 | /*3 |
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| 482 | * multiplication of alg. polys |
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| 483 | * multiply p1 with p2, p1 and p2 are destroyed |
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| 484 | */ |
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| 485 | static alg napMult(alg p1, alg p2) |
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| 486 | { |
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| 487 | alg a1, a2, b, h; |
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| 488 | if (p1==NULL) |
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| 489 | { |
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| 490 | napDelete(&p2); |
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| 491 | return NULL; |
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| 492 | } |
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| 493 | if (p2==NULL) |
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| 494 | { |
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| 495 | napDelete(&p1); |
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| 496 | return NULL; |
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| 497 | } |
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| 498 | b = NULL; |
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| 499 | a1 = p1; |
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| 500 | a2 = p2; |
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| 501 | if (a2->ne!=NULL) |
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| 502 | { |
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| 503 | if (a1->ne!=NULL) |
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| 504 | { |
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| 505 | do |
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| 506 | { |
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| 507 | a1 = a1->ne; |
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| 508 | a2 = a2->ne; |
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| 509 | } |
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| 510 | while ((a1!=NULL) && (a2!=NULL)); |
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| 511 | if (a1!=NULL) |
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| 512 | { |
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| 513 | a1 = p1; |
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| 514 | a2 = p2; |
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| 515 | } |
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| 516 | else |
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| 517 | { |
---|
| 518 | a1 = p2; |
---|
| 519 | a2 = p1; |
---|
| 520 | } |
---|
| 521 | do |
---|
| 522 | { |
---|
| 523 | if (a2->ne!=NULL) |
---|
| 524 | h = napCopy(a1); |
---|
| 525 | else |
---|
| 526 | h = a1; |
---|
| 527 | napMultT(h, a2); |
---|
| 528 | b = napAdd(h, b); |
---|
| 529 | napDelete1(&a2); |
---|
| 530 | } |
---|
| 531 | while (a2!=NULL); |
---|
| 532 | } |
---|
| 533 | else |
---|
| 534 | { |
---|
| 535 | napMultT(a2, a1); |
---|
| 536 | b = napAdd(a2, b); |
---|
| 537 | napDelete1(&a1); |
---|
| 538 | } |
---|
| 539 | } |
---|
| 540 | else |
---|
| 541 | { |
---|
| 542 | napMultT(a1, a2); |
---|
| 543 | b = napAdd(a1, b); |
---|
| 544 | napDelete1(&a2); |
---|
| 545 | } |
---|
| 546 | return b; |
---|
| 547 | } |
---|
| 548 | |
---|
| 549 | /*3 |
---|
| 550 | * division with rest; f = g*q + r, returns r and destroy f |
---|
| 551 | */ |
---|
| 552 | static alg napRemainder(alg f, const alg g) |
---|
| 553 | { |
---|
| 554 | alg a, h, qq; |
---|
| 555 | |
---|
[550b4c] | 556 | qq = (alg)Alloc(napMonomSize); |
---|
[0e1846] | 557 | qq->ne = NULL; |
---|
| 558 | a = f; |
---|
| 559 | do |
---|
| 560 | { |
---|
[550b4c] | 561 | mmTestP(a,napMonomSize); |
---|
| 562 | mmTestP(g,napMonomSize); |
---|
[0e1846] | 563 | qq->e[0] = a->e[0] - g->e[0]; |
---|
| 564 | qq->ko = nacDiv(a->ko, g->ko); |
---|
| 565 | qq->ko = nacNeg(qq->ko); |
---|
| 566 | h = napCopy(g); |
---|
| 567 | napMultT(h, qq); |
---|
| 568 | nacDelete(&(qq->ko)); |
---|
| 569 | a = napAdd(a, h); |
---|
| 570 | } |
---|
| 571 | while ((a!=NULL) && (a->e[0] >= g->e[0])); |
---|
[550b4c] | 572 | Free((ADDRESS)qq, napMonomSize); |
---|
[0e1846] | 573 | return a; |
---|
| 574 | } |
---|
| 575 | |
---|
| 576 | /*3 |
---|
| 577 | * division with rest; f = g*q + r, destroy f |
---|
| 578 | */ |
---|
| 579 | static void napDivMod(alg f, alg g, alg *q, alg *r) |
---|
| 580 | { |
---|
| 581 | alg a, h, b, qq; |
---|
| 582 | |
---|
[550b4c] | 583 | qq = (alg)Alloc(napMonomSize); |
---|
[0e1846] | 584 | qq->ne = b = NULL; |
---|
| 585 | a = f; |
---|
| 586 | do |
---|
| 587 | { |
---|
[550b4c] | 588 | mmTestP(a,napMonomSize); |
---|
| 589 | mmTestP(g,napMonomSize); |
---|
[0e1846] | 590 | qq->e[0] = a->e[0] - g->e[0]; |
---|
| 591 | qq->ko = nacDiv(a->ko, g->ko); |
---|
| 592 | b = napAdd(b, napCopy(qq)); |
---|
| 593 | qq->ko = nacNeg(qq->ko); |
---|
| 594 | h = napCopy(g); |
---|
| 595 | napMultT(h, qq); |
---|
| 596 | nacDelete(&(qq->ko)); |
---|
| 597 | a = napAdd(a, h); |
---|
| 598 | } |
---|
| 599 | while ((a!=NULL) && (a->e[0] >= g->e[0])); |
---|
[550b4c] | 600 | Free((ADDRESS)qq, napMonomSize); |
---|
[0e1846] | 601 | *q = b; |
---|
| 602 | *r = a; |
---|
| 603 | } |
---|
| 604 | |
---|
| 605 | /*3 |
---|
| 606 | * returns z with z*x mod c = 1 |
---|
| 607 | */ |
---|
| 608 | static alg napInvers(alg x, const alg c) |
---|
| 609 | { |
---|
| 610 | alg y, r, qa, qn, q; |
---|
| 611 | number t, h; |
---|
| 612 | |
---|
| 613 | if (x->e[0] >= c->e[0]) |
---|
| 614 | x = napRemainder(x, c); |
---|
[25ea20d] | 615 | if (x==NULL) |
---|
| 616 | { |
---|
| 617 | goto zero_divisor; |
---|
| 618 | } |
---|
[0e1846] | 619 | if (x->e[0]==0) |
---|
| 620 | { |
---|
| 621 | if (!nacIsOne(x->ko)) |
---|
| 622 | { |
---|
| 623 | h = nacInit(1); |
---|
| 624 | t = nacDiv(h, x->ko); |
---|
| 625 | nacDelete(&(x->ko)); |
---|
| 626 | nacDelete(&h); |
---|
| 627 | x->ko = t; |
---|
| 628 | } |
---|
| 629 | return x; |
---|
| 630 | } |
---|
| 631 | y = napCopy(c); |
---|
| 632 | napDivMod(y, x, &qa, &r); |
---|
[25ea20d] | 633 | if (r==NULL) |
---|
| 634 | { |
---|
| 635 | goto zero_divisor; |
---|
| 636 | } |
---|
[0e1846] | 637 | if (r->e[0]==0) |
---|
| 638 | { |
---|
| 639 | h = nacInit(-1); |
---|
| 640 | t = nacDiv(h, r->ko); |
---|
| 641 | nacNormalize(t); |
---|
| 642 | napMultN(qa, t); |
---|
| 643 | nacDelete(&h); |
---|
| 644 | nacDelete(&t); |
---|
| 645 | napDelete(&x); |
---|
| 646 | napDelete(&r); |
---|
| 647 | return qa; |
---|
| 648 | } |
---|
| 649 | y = x; |
---|
| 650 | x = r; |
---|
| 651 | napDivMod(y, x, &q, &r); |
---|
[25ea20d] | 652 | if (r==NULL) |
---|
| 653 | { |
---|
| 654 | goto zero_divisor; |
---|
| 655 | } |
---|
[0e1846] | 656 | if (r->e[0]==0) |
---|
| 657 | { |
---|
| 658 | q = napMult(q, qa); |
---|
| 659 | q = napAdd(q, napInit(1)); |
---|
| 660 | h = nacInit(1); |
---|
| 661 | t = nacDiv(h, r->ko); |
---|
| 662 | napMultN(q, t); |
---|
| 663 | nacDelete(&h); |
---|
| 664 | nacDelete(&t); |
---|
| 665 | napDelete(&x); |
---|
| 666 | napDelete(&r); |
---|
| 667 | if (q->e[0] >= c->e[0]) |
---|
| 668 | q = napRemainder(q, c); |
---|
| 669 | return q; |
---|
| 670 | } |
---|
| 671 | q = napMult(q, napCopy(qa)); |
---|
| 672 | q = napAdd(q, napInit(1)); |
---|
| 673 | qa = napNeg(qa); |
---|
| 674 | loop |
---|
| 675 | { |
---|
| 676 | y = x; |
---|
| 677 | x = r; |
---|
| 678 | napDivMod(y, x, &qn, &r); |
---|
[25ea20d] | 679 | if (r==NULL) |
---|
| 680 | { |
---|
| 681 | break; |
---|
| 682 | } |
---|
[0e1846] | 683 | if (r->e[0]==0) |
---|
| 684 | { |
---|
| 685 | q = napMult(q, qn); |
---|
| 686 | q = napNeg(q); |
---|
| 687 | q = napAdd(q, qa); |
---|
| 688 | h = nacInit(1); |
---|
| 689 | t = nacDiv(h, r->ko); |
---|
| 690 | napMultN(q, t); |
---|
| 691 | nacDelete(&h); |
---|
| 692 | nacDelete(&t); |
---|
| 693 | napDelete(&x); |
---|
| 694 | napDelete(&r); |
---|
| 695 | if (q->e[0] >= c->e[0]) |
---|
| 696 | q = napRemainder(q, c); |
---|
| 697 | return q; |
---|
| 698 | } |
---|
| 699 | y = q; |
---|
| 700 | q = napMult(napCopy(q), qn); |
---|
| 701 | q = napNeg(q); |
---|
| 702 | q = napAdd(q, qa); |
---|
| 703 | qa = y; |
---|
| 704 | } |
---|
[25ea20d] | 705 | // zero divisor found: |
---|
| 706 | zero_divisor: |
---|
| 707 | Werror("zero divisor found - your minpoly is not irreducible"); |
---|
| 708 | return x; |
---|
[0e1846] | 709 | } |
---|
| 710 | |
---|
| 711 | /*3 |
---|
| 712 | * the degree of an alg poly (used for test of "constant" et al.) |
---|
| 713 | */ |
---|
| 714 | static int napDeg(alg p) |
---|
| 715 | { |
---|
| 716 | int d = 0, i; |
---|
| 717 | |
---|
[550b4c] | 718 | mmTestP(p,napMonomSize); |
---|
[0e1846] | 719 | for (i = naNumbOfPar-1; i>=0; i--) |
---|
| 720 | d += p->e[i]; |
---|
| 721 | return d; |
---|
| 722 | } |
---|
| 723 | |
---|
[f64447] | 724 | /*3 |
---|
| 725 | * the max degree of an alg poly (used for test of "simple" et al.) |
---|
| 726 | */ |
---|
| 727 | static int napMaxDeg(alg p) |
---|
| 728 | { |
---|
| 729 | int d = 0; |
---|
| 730 | mmTestP(p,napMonomSize); |
---|
| 731 | while(p!=NULL) |
---|
| 732 | { |
---|
| 733 | d=max(d,napDeg(p)); |
---|
| 734 | p=p->ne; |
---|
| 735 | } |
---|
| 736 | return d; |
---|
| 737 | } |
---|
| 738 | |
---|
| 739 | /*3 |
---|
| 740 | * the max degree of an alg poly (used for test of "simple" et al.) |
---|
| 741 | */ |
---|
| 742 | static int napMaxDegLen(alg p, int &l) |
---|
| 743 | { |
---|
| 744 | int d = 0; |
---|
| 745 | int ll=0; |
---|
| 746 | mmTestP(p,napMonomSize); |
---|
| 747 | while(p!=NULL) |
---|
| 748 | { |
---|
| 749 | d=max(d,napDeg(p)); |
---|
| 750 | p=p->ne; |
---|
| 751 | ll++; |
---|
| 752 | } |
---|
| 753 | l=ll; |
---|
| 754 | return d; |
---|
| 755 | } |
---|
| 756 | |
---|
| 757 | |
---|
[0e1846] | 758 | /*3 |
---|
| 759 | *writes a polynomial number |
---|
| 760 | */ |
---|
[7b13a2] | 761 | void napWrite(alg p) |
---|
[0e1846] | 762 | { |
---|
| 763 | if (p==NULL) |
---|
| 764 | StringAppendS("0"); |
---|
[be0519] | 765 | else if (napDeg(p)==0) |
---|
| 766 | { |
---|
| 767 | //StringAppendS("-1"); |
---|
| 768 | nacWrite(p->ko); |
---|
| 769 | } |
---|
[0e1846] | 770 | else |
---|
| 771 | { |
---|
| 772 | StringAppendS("("); |
---|
| 773 | loop |
---|
| 774 | { |
---|
| 775 | BOOLEAN wroteCoeff=FALSE; |
---|
[550b4c] | 776 | mmTestP(p,napMonomSize); |
---|
[0e1846] | 777 | if ((napDeg(p)==0) |
---|
[e6578d] | 778 | || ((!nacIsOne(p->ko)) |
---|
| 779 | && (!nacIsMOne(p->ko)))) |
---|
[0e1846] | 780 | { |
---|
| 781 | nacWrite(p->ko); |
---|
| 782 | wroteCoeff=(pShortOut==0); |
---|
| 783 | } |
---|
[e6578d] | 784 | else if (nacIsMOne(p->ko)) |
---|
| 785 | { |
---|
[b45d97] | 786 | StringAppendS("-"); |
---|
[e6578d] | 787 | } |
---|
| 788 | int i; |
---|
[0e1846] | 789 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
| 790 | { |
---|
| 791 | if (p->e[i] > 0) |
---|
| 792 | { |
---|
| 793 | if (wroteCoeff) |
---|
| 794 | StringAppendS("*"); |
---|
| 795 | else |
---|
| 796 | wroteCoeff=(pShortOut==0); |
---|
[b45d97] | 797 | StringAppendS(naParNames[i]); |
---|
[0e1846] | 798 | if (p->e[i] > 1) |
---|
| 799 | { |
---|
| 800 | if (pShortOut == 0) |
---|
| 801 | StringAppendS("^"); |
---|
| 802 | StringAppend("%d", p->e[i]); |
---|
| 803 | } |
---|
| 804 | } |
---|
| 805 | } |
---|
| 806 | p = p->ne; |
---|
| 807 | if (p==NULL) |
---|
| 808 | break; |
---|
| 809 | if (nacGreaterZero(p->ko)) |
---|
| 810 | StringAppendS("+"); |
---|
| 811 | } |
---|
| 812 | StringAppendS(")"); |
---|
| 813 | } |
---|
| 814 | } |
---|
| 815 | |
---|
| 816 | |
---|
[550b4c] | 817 | static char *napHandleMons(char *s, int i, PARAMETER_TYPE *ex) |
---|
[0e1846] | 818 | { |
---|
| 819 | int j; |
---|
| 820 | if (strncmp(s,naParNames[i],strlen(naParNames[i]))==0) |
---|
| 821 | { |
---|
| 822 | s+=strlen(naParNames[i]); |
---|
| 823 | if ((*s >= '0') && (*s <= '9')) |
---|
| 824 | { |
---|
| 825 | s = eati(s, &j); |
---|
| 826 | ex[i] += j; |
---|
| 827 | } |
---|
| 828 | else |
---|
| 829 | ex[i]++; |
---|
| 830 | } |
---|
| 831 | return s; |
---|
| 832 | } |
---|
| 833 | |
---|
| 834 | /*3 reads a monomial */ |
---|
| 835 | static char *napRead(char *s, alg *b) |
---|
| 836 | { |
---|
| 837 | alg a; |
---|
| 838 | int i; |
---|
[550b4c] | 839 | a = (alg)Alloc0(napMonomSize); |
---|
[0e1846] | 840 | if ((*s >= '0') && (*s <= '9')) |
---|
| 841 | { |
---|
| 842 | s = nacRead(s, &(a->ko)); |
---|
| 843 | if (nacIsZero(a->ko)) |
---|
| 844 | { |
---|
| 845 | napDelete1(&a); |
---|
| 846 | *b = NULL; |
---|
| 847 | return s; |
---|
| 848 | } |
---|
| 849 | } |
---|
| 850 | else |
---|
| 851 | a->ko = nacInit(1); |
---|
| 852 | i = 0; |
---|
| 853 | char *olds; |
---|
| 854 | loop |
---|
| 855 | { |
---|
| 856 | olds = s; |
---|
| 857 | s = napHandleMons(s, i, a->e); |
---|
| 858 | if (olds == s) |
---|
| 859 | i++; |
---|
| 860 | else |
---|
| 861 | i = 0; |
---|
| 862 | if ((*s == '\0') || (i >= naNumbOfPar)) |
---|
| 863 | break; |
---|
| 864 | } |
---|
| 865 | *b = a; |
---|
| 866 | return s; |
---|
| 867 | } |
---|
| 868 | |
---|
| 869 | static int napExp(alg a, alg b) |
---|
| 870 | { |
---|
| 871 | while (a->ne!=NULL) a = a->ne; |
---|
| 872 | int m = a->e[0]; |
---|
[af06ef] | 873 | if (m==0) return 0; |
---|
[0e1846] | 874 | while (b->ne!=NULL) b = b->ne; |
---|
| 875 | if (m > b->e[0]) m = b->e[0]; |
---|
| 876 | return m; |
---|
| 877 | } |
---|
| 878 | |
---|
| 879 | #if FEHLER2 |
---|
| 880 | /*meins |
---|
| 881 | * finds the smallest i-th exponent in a and b |
---|
| 882 | * used to find it in a fraction |
---|
| 883 | */ |
---|
| 884 | static int napExpi(int i, alg a, alg b) |
---|
| 885 | { |
---|
| 886 | if (a==NULL || b==NULL) return 0; |
---|
| 887 | int m = a->e[i]; |
---|
| 888 | if (m==0) return 0; |
---|
| 889 | while (a->ne != NULL) |
---|
| 890 | { |
---|
| 891 | a = a->ne; |
---|
| 892 | if (m > a->e[i]) |
---|
| 893 | { |
---|
| 894 | m = a->e[i]; |
---|
| 895 | if (m==0) return 0; |
---|
| 896 | } |
---|
| 897 | } |
---|
| 898 | do |
---|
| 899 | { |
---|
| 900 | if (m > b->e[i]) |
---|
| 901 | { |
---|
| 902 | m = b->e[i]; |
---|
| 903 | if (m==0) return 0; |
---|
| 904 | } |
---|
| 905 | b = b->ne; |
---|
| 906 | } |
---|
| 907 | while (b != NULL); |
---|
| 908 | return m; |
---|
| 909 | } |
---|
| 910 | #endif |
---|
| 911 | |
---|
| 912 | static void napContent(alg ph) |
---|
| 913 | { |
---|
| 914 | number h,d; |
---|
| 915 | alg p; |
---|
| 916 | |
---|
| 917 | p = ph; |
---|
| 918 | if (nacIsOne(p->ko)) |
---|
| 919 | return; |
---|
| 920 | h = nacCopy(p->ko); |
---|
| 921 | p = p->ne; |
---|
| 922 | do |
---|
| 923 | { |
---|
| 924 | d=nacGcd(p->ko, h); |
---|
| 925 | if(nacIsOne(d)) |
---|
| 926 | { |
---|
| 927 | nacDelete(&h); |
---|
| 928 | nacDelete(&d); |
---|
| 929 | return; |
---|
| 930 | } |
---|
| 931 | nacDelete(&h); |
---|
| 932 | h = d; |
---|
| 933 | p = p->ne; |
---|
| 934 | } |
---|
| 935 | while (p!=NULL); |
---|
| 936 | h = nacInvers(d); |
---|
| 937 | nacDelete(&d); |
---|
| 938 | p = ph; |
---|
| 939 | while (p!=NULL) |
---|
| 940 | { |
---|
| 941 | d = nacMult(p->ko, h); |
---|
| 942 | nacDelete(&(p->ko)); |
---|
| 943 | p->ko = d; |
---|
| 944 | p = p->ne; |
---|
| 945 | } |
---|
| 946 | nacDelete(&h); |
---|
| 947 | } |
---|
| 948 | |
---|
| 949 | static void napCleardenom(alg ph) |
---|
| 950 | { |
---|
| 951 | number d, h; |
---|
| 952 | alg p; |
---|
| 953 | |
---|
| 954 | if (!naIsChar0) |
---|
| 955 | return; |
---|
| 956 | p = ph; |
---|
| 957 | h = nacInit(1); |
---|
| 958 | while (p!=NULL) |
---|
| 959 | { |
---|
| 960 | d = nacLcm(h, p->ko); |
---|
| 961 | nacDelete(&h); |
---|
| 962 | h = d; |
---|
| 963 | p = p->ne; |
---|
| 964 | } |
---|
| 965 | if(!nacIsOne(h)) |
---|
| 966 | { |
---|
| 967 | p = ph; |
---|
| 968 | while (p!=NULL) |
---|
| 969 | { |
---|
| 970 | d=nacMult(h, p->ko); |
---|
| 971 | nacDelete(&(p->ko)); |
---|
| 972 | p->ko = d; |
---|
| 973 | p = p->ne; |
---|
| 974 | } |
---|
| 975 | nacDelete(&h); |
---|
| 976 | } |
---|
| 977 | napContent(ph); |
---|
| 978 | } |
---|
| 979 | |
---|
| 980 | static alg napGcd0(alg a, alg b) |
---|
| 981 | { |
---|
| 982 | number x, y; |
---|
| 983 | if (!naIsChar0) |
---|
| 984 | return napInit(1); |
---|
| 985 | x = nacCopy(a->ko); |
---|
| 986 | if (nacIsOne(x)) |
---|
| 987 | return napInitz(x); |
---|
| 988 | while (a->ne!=NULL) |
---|
| 989 | { |
---|
| 990 | a = a->ne; |
---|
| 991 | y = nacGcd(x, a->ko); |
---|
| 992 | nacDelete(&x); |
---|
| 993 | x = y; |
---|
| 994 | if (nacIsOne(x)) |
---|
| 995 | return napInitz(x); |
---|
| 996 | } |
---|
| 997 | do |
---|
| 998 | { |
---|
| 999 | y = nacGcd(x, b->ko); |
---|
| 1000 | nacDelete(&x); |
---|
| 1001 | x = y; |
---|
| 1002 | if (nacIsOne(x)) |
---|
| 1003 | return napInitz(x); |
---|
| 1004 | b = b->ne; |
---|
| 1005 | } |
---|
| 1006 | while (b!=NULL); |
---|
| 1007 | return napInitz(x); |
---|
| 1008 | } |
---|
| 1009 | |
---|
| 1010 | /*3 |
---|
| 1011 | * result =gcd(a,b) |
---|
| 1012 | */ |
---|
| 1013 | static alg napGcd(alg a, alg b) |
---|
| 1014 | { |
---|
| 1015 | int i; |
---|
| 1016 | alg g, x, y, h; |
---|
| 1017 | if ((a==NULL) |
---|
| 1018 | || ((a->ne==NULL)&&(nacIsZero(a->ko)))) |
---|
| 1019 | { |
---|
| 1020 | if ((b==NULL) |
---|
| 1021 | || ((b->ne==NULL)&&(nacIsZero(b->ko)))) |
---|
| 1022 | { |
---|
| 1023 | return napInit(1); |
---|
| 1024 | } |
---|
| 1025 | return napCopy(b); |
---|
| 1026 | } |
---|
[c8bd75] | 1027 | else |
---|
| 1028 | if ((b==NULL) |
---|
| 1029 | || ((b->ne==NULL)&&(nacIsZero(b->ko)))) |
---|
| 1030 | { |
---|
| 1031 | return napCopy(a); |
---|
| 1032 | } |
---|
[0e1846] | 1033 | if (naMinimalPoly != NULL) |
---|
| 1034 | { |
---|
| 1035 | if (a->e[0] >= b->e[0]) |
---|
| 1036 | { |
---|
| 1037 | x = a; |
---|
| 1038 | y = b; |
---|
| 1039 | } |
---|
| 1040 | else |
---|
| 1041 | { |
---|
| 1042 | x = b; |
---|
| 1043 | y = a; |
---|
| 1044 | } |
---|
[c8bd75] | 1045 | if (!naIsChar0) g = napInit(1); |
---|
| 1046 | else g = napGcd0(x, y); |
---|
[0e1846] | 1047 | if (y->ne==NULL) |
---|
| 1048 | { |
---|
| 1049 | g->e[0] = napExp(x, y); |
---|
| 1050 | return g; |
---|
| 1051 | } |
---|
| 1052 | x = napCopy(x); |
---|
| 1053 | y = napCopy(y); |
---|
| 1054 | loop |
---|
| 1055 | { |
---|
| 1056 | h = napRemainder(x, y); |
---|
| 1057 | if (h==NULL) |
---|
| 1058 | { |
---|
| 1059 | napCleardenom(y); |
---|
| 1060 | if (!nacIsOne(g->ko)) napMultN(y, g->ko); |
---|
| 1061 | napDelete1(&g); |
---|
| 1062 | return y; |
---|
| 1063 | } |
---|
| 1064 | else if (h->ne==NULL) |
---|
| 1065 | break; |
---|
| 1066 | x = y; |
---|
| 1067 | y = h; |
---|
| 1068 | } |
---|
| 1069 | napDelete(&y); |
---|
| 1070 | napDelete1(&h); |
---|
| 1071 | g->e[0] = napExp(a, b); |
---|
| 1072 | return g; |
---|
| 1073 | } |
---|
[550b4c] | 1074 | x = (alg)Alloc0(napMonomSize); |
---|
[0e1846] | 1075 | g=a; |
---|
| 1076 | h=b; |
---|
[c8bd75] | 1077 | if (!naIsChar0) x = napInit(1); |
---|
| 1078 | else x = napGcd0(g,h); |
---|
[0e1846] | 1079 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
[c8bd75] | 1080 | { |
---|
[0e1846] | 1081 | x->e[i] = napExpi(i,a,b); |
---|
[c8bd75] | 1082 | } |
---|
[0e1846] | 1083 | return x; |
---|
| 1084 | } |
---|
| 1085 | |
---|
| 1086 | |
---|
| 1087 | number napLcm(alg a) |
---|
| 1088 | { |
---|
[af06ef] | 1089 | number h = nacInit(1); |
---|
[0e1846] | 1090 | |
---|
[af06ef] | 1091 | if (naIsChar0) |
---|
[0e1846] | 1092 | { |
---|
[af06ef] | 1093 | number d; |
---|
| 1094 | alg b = a; |
---|
| 1095 | |
---|
| 1096 | while (b!=NULL) |
---|
| 1097 | { |
---|
| 1098 | d = nacLcm(h, b->ko); |
---|
| 1099 | nacDelete(&h); |
---|
| 1100 | h = d; |
---|
| 1101 | b = b->ne; |
---|
| 1102 | } |
---|
[0e1846] | 1103 | } |
---|
| 1104 | return h; |
---|
| 1105 | } |
---|
| 1106 | |
---|
| 1107 | |
---|
| 1108 | /*2 |
---|
| 1109 | * meins (for reduction in algebraic extension) |
---|
| 1110 | * checks if head of p divides head of q |
---|
| 1111 | * doesn't delete p and q |
---|
| 1112 | */ |
---|
| 1113 | BOOLEAN napDivPoly (alg p, alg q) |
---|
| 1114 | { |
---|
| 1115 | int j=0; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
| 1116 | |
---|
| 1117 | while (p->e[j] <= q->e[j]) |
---|
| 1118 | { |
---|
| 1119 | j++; |
---|
| 1120 | if (j >= naNumbOfPar) |
---|
| 1121 | return 1; |
---|
| 1122 | } |
---|
| 1123 | return 0; |
---|
| 1124 | } |
---|
| 1125 | |
---|
| 1126 | |
---|
| 1127 | /*2 |
---|
| 1128 | * meins (for reduction in algebraic extension) |
---|
| 1129 | * Normalform of poly with naI |
---|
| 1130 | * changes q and returns it |
---|
| 1131 | */ |
---|
| 1132 | alg napRedp (alg q) |
---|
| 1133 | { |
---|
[550b4c] | 1134 | alg h = (alg)Alloc0(napMonomSize); |
---|
[0e1846] | 1135 | int i=0,j; |
---|
| 1136 | |
---|
| 1137 | loop |
---|
| 1138 | { |
---|
| 1139 | if (napDivPoly (naI->liste[i], q)) |
---|
| 1140 | { |
---|
[550b4c] | 1141 | mmTestP((ADDRESS)q,napMonomSize); |
---|
[af06ef] | 1142 | //StringSetS(""); |
---|
| 1143 | //napWrite(q); |
---|
| 1144 | //napWrite(naI->liste[i]); |
---|
| 1145 | //Print(StringAppendS("\n")); |
---|
[0e1846] | 1146 | /* h = lt(q)/lt(naI->liste[i])*/ |
---|
| 1147 | h->ko = nacCopy(q->ko); |
---|
| 1148 | for (j=naNumbOfPar-1; j>=0; j--) |
---|
| 1149 | h->e[j] = q->e[j] - naI->liste[i]->e[j]; |
---|
| 1150 | h = napMult (h, napCopy(naI->liste[i])); |
---|
| 1151 | h = napNeg (h); |
---|
| 1152 | q = napAdd (q, napCopy(h)); |
---|
| 1153 | napDelete (&(h->ne)); |
---|
| 1154 | if (q == NULL) |
---|
| 1155 | { |
---|
| 1156 | napDelete(&h); |
---|
| 1157 | return q; |
---|
| 1158 | } |
---|
| 1159 | /* try to reduce further */ |
---|
| 1160 | i = 0; |
---|
| 1161 | } |
---|
| 1162 | else |
---|
| 1163 | { |
---|
| 1164 | i++; |
---|
| 1165 | if (i >= naI->anz) |
---|
| 1166 | { |
---|
| 1167 | napDelete(&h); |
---|
| 1168 | return q; |
---|
| 1169 | } |
---|
| 1170 | } |
---|
| 1171 | } |
---|
| 1172 | } |
---|
| 1173 | |
---|
| 1174 | |
---|
| 1175 | /*2 |
---|
| 1176 | * meins (for reduction in algebraic extension) |
---|
| 1177 | * reduces the tail of Poly q |
---|
| 1178 | * needs q != NULL |
---|
| 1179 | * changes q and returns it |
---|
| 1180 | */ |
---|
| 1181 | alg napTailred (alg q) |
---|
| 1182 | { |
---|
| 1183 | alg h; |
---|
| 1184 | |
---|
| 1185 | h = q->ne; |
---|
| 1186 | while (h != NULL) |
---|
| 1187 | { |
---|
| 1188 | h = napRedp (h); |
---|
| 1189 | if (h == NULL) |
---|
| 1190 | return q; |
---|
| 1191 | h = h->ne; |
---|
| 1192 | } |
---|
| 1193 | return q; |
---|
| 1194 | } |
---|
| 1195 | |
---|
| 1196 | |
---|
| 1197 | /*================ procedure for rational functions: naXXXX =================*/ |
---|
| 1198 | |
---|
| 1199 | /*2 |
---|
| 1200 | * z:= i |
---|
| 1201 | */ |
---|
| 1202 | number naInit(int i) |
---|
| 1203 | { |
---|
| 1204 | if (i!=0) |
---|
| 1205 | { |
---|
| 1206 | lnumber l = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1207 | l->z = napInit(i); |
---|
| 1208 | if (l->z==NULL) |
---|
| 1209 | { |
---|
| 1210 | Free((ADDRESS)l, sizeof(rnumber)); |
---|
| 1211 | return NULL; |
---|
| 1212 | } |
---|
| 1213 | l->s = 2; |
---|
| 1214 | l->n = NULL; |
---|
| 1215 | return (number)l; |
---|
| 1216 | } |
---|
| 1217 | /*else*/ |
---|
| 1218 | return NULL; |
---|
| 1219 | } |
---|
| 1220 | |
---|
| 1221 | number naPar(int i) |
---|
| 1222 | { |
---|
| 1223 | lnumber l = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1224 | l->s = 2; |
---|
| 1225 | l->z = napInit(1); |
---|
| 1226 | l->z->e[i-1]=1; |
---|
| 1227 | l->n = NULL; |
---|
| 1228 | return (number)l; |
---|
| 1229 | } |
---|
| 1230 | |
---|
| 1231 | int naParDeg(number n) /* i := deg(n) */ |
---|
| 1232 | { |
---|
| 1233 | lnumber l = (lnumber)n; |
---|
| 1234 | if (l==NULL) return -1; |
---|
| 1235 | return napDeg(l->z); |
---|
| 1236 | } |
---|
| 1237 | |
---|
[f64447] | 1238 | //int naParDeg(number n) /* i := deg(n) */ |
---|
| 1239 | //{ |
---|
| 1240 | // lnumber l = (lnumber)n; |
---|
| 1241 | // if (l==NULL) return -1; |
---|
| 1242 | // return napMaxDeg(l->z)+napMaxDeg(l->n); |
---|
| 1243 | //} |
---|
| 1244 | |
---|
| 1245 | int naSize(number n) /* size desc. */ |
---|
| 1246 | { |
---|
| 1247 | lnumber l = (lnumber)n; |
---|
| 1248 | if (l==NULL) return -1; |
---|
| 1249 | int len_z; |
---|
| 1250 | int len_n; |
---|
| 1251 | int o=napMaxDegLen(l->z,len_z)+napMaxDegLen(l->n,len_n); |
---|
| 1252 | return (len_z+len_n)+o; |
---|
| 1253 | } |
---|
| 1254 | |
---|
[0e1846] | 1255 | /*2 |
---|
| 1256 | * convert a number to int (if possible) |
---|
| 1257 | */ |
---|
| 1258 | int naInt(number &n) |
---|
| 1259 | { |
---|
| 1260 | lnumber l=(lnumber)n; |
---|
| 1261 | if ((l!=NULL)&&(l->n==NULL)&&(napDeg(l->z)==0)) |
---|
| 1262 | { |
---|
| 1263 | return nacInt(l->z->ko); |
---|
| 1264 | } |
---|
| 1265 | return 0; |
---|
| 1266 | } |
---|
| 1267 | |
---|
| 1268 | /*2 |
---|
| 1269 | * deletes p |
---|
| 1270 | */ |
---|
| 1271 | #ifdef LDEBUG |
---|
| 1272 | void naDBDelete(number *p,char *f, int lno) |
---|
| 1273 | #else |
---|
| 1274 | void naDelete(number *p) |
---|
| 1275 | #endif |
---|
| 1276 | { |
---|
| 1277 | lnumber l = (lnumber) * p; |
---|
| 1278 | if (l==NULL) return; |
---|
| 1279 | napDelete(&(l->z)); |
---|
| 1280 | napDelete(&(l->n)); |
---|
| 1281 | #if defined(MDEBUG) && defined(LDEBUG) |
---|
| 1282 | mmDBFreeBlock((ADDRESS)l, sizeof(rnumber),f,lno); |
---|
| 1283 | #else |
---|
| 1284 | Free((ADDRESS)l, sizeof(rnumber)); |
---|
| 1285 | #endif |
---|
| 1286 | *p = NULL; |
---|
| 1287 | } |
---|
| 1288 | |
---|
| 1289 | /*2 |
---|
| 1290 | * copy p to erg |
---|
| 1291 | */ |
---|
| 1292 | number naCopy(number p) |
---|
| 1293 | { |
---|
| 1294 | if (p==NULL) return NULL; |
---|
| 1295 | naTest(p); |
---|
| 1296 | lnumber erg; |
---|
| 1297 | lnumber src = (lnumber)p; |
---|
| 1298 | erg = (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 1299 | erg->z = napCopy(src->z); |
---|
| 1300 | erg->n = napCopy(src->n); |
---|
| 1301 | erg->s = src->s; |
---|
| 1302 | return (number)erg; |
---|
| 1303 | } |
---|
| 1304 | |
---|
| 1305 | /*2 |
---|
| 1306 | * a dummy number: 0 |
---|
| 1307 | */ |
---|
| 1308 | void naNew(number *z) |
---|
| 1309 | { |
---|
| 1310 | *z = NULL; |
---|
| 1311 | } |
---|
| 1312 | |
---|
| 1313 | /*2 |
---|
| 1314 | * addition; lu:= la + lb |
---|
| 1315 | */ |
---|
| 1316 | number naAdd(number la, number lb) |
---|
| 1317 | { |
---|
| 1318 | alg x, y; |
---|
| 1319 | lnumber lu; |
---|
| 1320 | lnumber a = (lnumber)la; |
---|
| 1321 | lnumber b = (lnumber)lb; |
---|
| 1322 | if (a==NULL) return naCopy(lb); |
---|
| 1323 | if (b==NULL) return naCopy(la); |
---|
| 1324 | mmTestP(a,sizeof(rnumber)); |
---|
| 1325 | mmTestP(b,sizeof(rnumber)); |
---|
| 1326 | lu = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1327 | if (b->n!=NULL) x = napMult(napCopy(a->z), napCopy(b->n)); |
---|
| 1328 | else x = napCopy(a->z); |
---|
| 1329 | if (a->n!=NULL) y = napMult(napCopy(b->z), napCopy(a->n)); |
---|
| 1330 | else y = napCopy(b->z); |
---|
| 1331 | lu->z = napAdd(x, y); |
---|
| 1332 | if (lu->z==NULL) |
---|
| 1333 | { |
---|
| 1334 | Free((ADDRESS)lu, sizeof(rnumber)); |
---|
| 1335 | return (number)NULL; |
---|
| 1336 | } |
---|
| 1337 | if (a->n!=NULL) |
---|
| 1338 | { |
---|
| 1339 | if (b->n!=NULL) x = napMult(napCopy(a->n), napCopy(b->n)); |
---|
| 1340 | else x = napCopy(a->n); |
---|
| 1341 | } |
---|
| 1342 | else |
---|
| 1343 | { |
---|
| 1344 | if (b->n!=NULL) x = napCopy(b->n); |
---|
| 1345 | else x = NULL; |
---|
| 1346 | } |
---|
| 1347 | if ((x!=NULL) && (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1348 | napDelete(&x); |
---|
| 1349 | lu->n = x; |
---|
| 1350 | lu->s = 0; |
---|
| 1351 | naTest((number)lu); |
---|
| 1352 | return (number)lu; |
---|
| 1353 | } |
---|
| 1354 | |
---|
| 1355 | /*2 |
---|
| 1356 | * subtraction; r:= la - lb |
---|
| 1357 | */ |
---|
| 1358 | number naSub(number la, number lb) |
---|
| 1359 | { |
---|
| 1360 | lnumber lu; |
---|
| 1361 | |
---|
| 1362 | if (lb==NULL) return naCopy(la); |
---|
| 1363 | if (la==NULL) |
---|
| 1364 | { |
---|
| 1365 | //if (lb!=NULL) |
---|
| 1366 | //{ |
---|
| 1367 | lu = (lnumber)naCopy(lb); |
---|
| 1368 | lu->z = napNeg(lu->z); |
---|
| 1369 | return (number)lu; |
---|
| 1370 | //} |
---|
| 1371 | //else |
---|
| 1372 | // return NULL; |
---|
| 1373 | } |
---|
| 1374 | |
---|
| 1375 | alg x, y; |
---|
| 1376 | lnumber a = (lnumber)la; |
---|
| 1377 | lnumber b = (lnumber)lb; |
---|
| 1378 | |
---|
| 1379 | mmTestP(a,sizeof(rnumber)); |
---|
| 1380 | mmTestP(b,sizeof(rnumber)); |
---|
| 1381 | lu = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1382 | if (b->n!=NULL) x = napMult(napCopy(a->z), napCopy(b->n)); |
---|
| 1383 | else x = napCopy(a->z); |
---|
| 1384 | if (a->n!=NULL) y = napMult(napCopy(b->z), napCopyNeg(a->n)); |
---|
| 1385 | else y = napCopyNeg(b->z); |
---|
| 1386 | lu->z = napAdd(x, y); |
---|
| 1387 | if (lu->z==NULL) |
---|
| 1388 | { |
---|
| 1389 | Free((ADDRESS)lu, sizeof(rnumber)); |
---|
| 1390 | return (number)NULL; |
---|
| 1391 | } |
---|
| 1392 | if (a->n!=NULL) |
---|
| 1393 | { |
---|
| 1394 | if (b->n!=NULL) x = napMult(napCopy(a->n), napCopy(b->n)); |
---|
| 1395 | else x = napCopy(a->n); |
---|
| 1396 | } |
---|
| 1397 | else |
---|
| 1398 | { |
---|
| 1399 | if (b->n!=NULL) x = napCopy(b->n); |
---|
| 1400 | else x = NULL; |
---|
| 1401 | } |
---|
| 1402 | if ((x!=NULL)&& (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1403 | napDelete(&x); |
---|
| 1404 | lu->n = x; |
---|
| 1405 | lu->s = 0; |
---|
| 1406 | naTest((number)lu); |
---|
| 1407 | return (number)lu; |
---|
| 1408 | } |
---|
| 1409 | |
---|
| 1410 | /*2 |
---|
| 1411 | * multiplication; r:= la * lb |
---|
| 1412 | */ |
---|
| 1413 | number naMult(number la, number lb) |
---|
| 1414 | { |
---|
| 1415 | if ((la==NULL) || (lb==NULL)) |
---|
| 1416 | return NULL; |
---|
| 1417 | |
---|
| 1418 | lnumber a = (lnumber)la; |
---|
| 1419 | lnumber b = (lnumber)lb; |
---|
| 1420 | lnumber lo; |
---|
| 1421 | alg x; |
---|
| 1422 | |
---|
[4b5c87] | 1423 | mmTestP(a,sizeof(rnumber)); |
---|
| 1424 | mmTestP(b,sizeof(rnumber)); |
---|
[58bbda] | 1425 | naTest(la); |
---|
| 1426 | naTest(lb); |
---|
[4b5c87] | 1427 | |
---|
| 1428 | lo = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1429 | lo->z = napMult(napCopy(a->z), napCopy(b->z)); |
---|
| 1430 | |
---|
[0e1846] | 1431 | if (a->n==NULL) |
---|
| 1432 | { |
---|
| 1433 | if (b->n==NULL) |
---|
| 1434 | x = NULL; |
---|
| 1435 | else |
---|
| 1436 | x = napCopy(b->n); |
---|
| 1437 | } |
---|
| 1438 | else |
---|
| 1439 | { |
---|
| 1440 | if (b->n==NULL) |
---|
[58bbda] | 1441 | { |
---|
[0e1846] | 1442 | x = napCopy(a->n); |
---|
[58bbda] | 1443 | } |
---|
[0e1846] | 1444 | else |
---|
[58bbda] | 1445 | { |
---|
[0e1846] | 1446 | x = napMult(napCopy(b->n), napCopy(a->n)); |
---|
[58bbda] | 1447 | } |
---|
[0e1846] | 1448 | } |
---|
| 1449 | if (naMinimalPoly!=NULL) |
---|
| 1450 | { |
---|
| 1451 | if (lo->z->e[0] >= naMinimalPoly->e[0]) |
---|
| 1452 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
| 1453 | if ((x!=NULL) && (x->e[0] >= naMinimalPoly->e[0])) |
---|
| 1454 | x = napRemainder(x, naMinimalPoly); |
---|
| 1455 | } |
---|
| 1456 | #if FEHLER1 |
---|
| 1457 | if (naI!=NULL) |
---|
| 1458 | { |
---|
| 1459 | lo->z = napRedp (lo->z); |
---|
| 1460 | if (lo->z != NULL) |
---|
| 1461 | lo->z = napTailred (lo->z); |
---|
| 1462 | if (x!=NULL) |
---|
| 1463 | { |
---|
| 1464 | x = napRedp (x); |
---|
| 1465 | if (x!=NULL) |
---|
| 1466 | x = napTailred (x); |
---|
| 1467 | } |
---|
| 1468 | } |
---|
| 1469 | #endif |
---|
| 1470 | if ((x!=NULL) && (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1471 | napDelete(&x); |
---|
| 1472 | lo->n = x; |
---|
| 1473 | lo->s = 0; |
---|
| 1474 | if(lo->z==NULL) |
---|
| 1475 | { |
---|
| 1476 | Free((ADDRESS)lo,sizeof(rnumber)); |
---|
| 1477 | lo=NULL; |
---|
| 1478 | } |
---|
| 1479 | naTest((number)lo); |
---|
| 1480 | return (number)lo; |
---|
| 1481 | } |
---|
| 1482 | |
---|
| 1483 | number naIntDiv(number la, number lb) |
---|
| 1484 | { |
---|
| 1485 | lnumber res; |
---|
| 1486 | lnumber a = (lnumber)la; |
---|
| 1487 | lnumber b = (lnumber)lb; |
---|
| 1488 | if ((a==NULL) || (a->z==NULL)) |
---|
| 1489 | return NULL; |
---|
| 1490 | if ((b==NULL) || (b->z==NULL)) |
---|
| 1491 | { |
---|
| 1492 | WerrorS("div. by 0"); |
---|
| 1493 | return NULL; |
---|
| 1494 | } |
---|
| 1495 | res = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1496 | res->z = napCopy(a->z); |
---|
| 1497 | res->n = napCopy(b->z); |
---|
| 1498 | res->s = 0; |
---|
| 1499 | number nres=(number)res; |
---|
| 1500 | naNormalize(nres); |
---|
| 1501 | |
---|
| 1502 | //napDelete(&res->n); |
---|
| 1503 | naTest(nres); |
---|
| 1504 | return nres; |
---|
| 1505 | } |
---|
| 1506 | |
---|
| 1507 | /*2 |
---|
| 1508 | * division; lo:= la / lb |
---|
| 1509 | */ |
---|
| 1510 | number naDiv(number la, number lb) |
---|
| 1511 | { |
---|
| 1512 | lnumber lo; |
---|
| 1513 | lnumber a = (lnumber)la; |
---|
| 1514 | lnumber b = (lnumber)lb; |
---|
| 1515 | alg x; |
---|
| 1516 | |
---|
| 1517 | if ((a==NULL) || (a->z==NULL)) |
---|
| 1518 | return NULL; |
---|
| 1519 | |
---|
| 1520 | if ((b==NULL) || (b->z==NULL)) |
---|
| 1521 | { |
---|
| 1522 | WerrorS("div. by 0"); |
---|
| 1523 | return NULL; |
---|
| 1524 | } |
---|
| 1525 | mmTestP(a,sizeof(rnumber)); |
---|
| 1526 | mmTestP(b,sizeof(rnumber)); |
---|
| 1527 | lo = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1528 | if (b->n!=NULL) |
---|
| 1529 | lo->z = napMult(napCopy(a->z), napCopy(b->n)); |
---|
| 1530 | else |
---|
| 1531 | lo->z = napCopy(a->z); |
---|
| 1532 | if (a->n!=NULL) |
---|
| 1533 | x = napMult(napCopy(b->z), napCopy(a->n)); |
---|
| 1534 | else |
---|
| 1535 | x = napCopy(b->z); |
---|
| 1536 | if (naMinimalPoly!=NULL) |
---|
| 1537 | { |
---|
| 1538 | if (lo->z->e[0] >= naMinimalPoly->e[0]) |
---|
| 1539 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
| 1540 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
| 1541 | x = napRemainder(x, naMinimalPoly); |
---|
| 1542 | } |
---|
| 1543 | #if FEHLER1 |
---|
| 1544 | if (naI!=NULL) |
---|
| 1545 | { |
---|
| 1546 | lo->z = napRedp (lo->z); |
---|
| 1547 | if (lo->z != NULL) |
---|
| 1548 | lo->z = napTailred (lo->z); |
---|
| 1549 | if (x!=NULL) |
---|
| 1550 | { |
---|
| 1551 | x = napRedp (x); |
---|
| 1552 | if (x!=NULL) |
---|
| 1553 | x = napTailred (x); |
---|
| 1554 | } |
---|
| 1555 | } |
---|
| 1556 | #endif |
---|
| 1557 | if ((napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1558 | napDelete(&x); |
---|
| 1559 | lo->s = 0; |
---|
| 1560 | lo->n = x; |
---|
| 1561 | naTest((number)lo); |
---|
| 1562 | return (number)lo; |
---|
| 1563 | } |
---|
| 1564 | |
---|
| 1565 | /*2 |
---|
| 1566 | * za:= - za |
---|
| 1567 | */ |
---|
| 1568 | number naNeg(number za) |
---|
| 1569 | { |
---|
| 1570 | if (za!=NULL) |
---|
| 1571 | { |
---|
| 1572 | lnumber e = (lnumber)za; |
---|
| 1573 | naTest(za); |
---|
| 1574 | e->z = napNeg(e->z); |
---|
| 1575 | } |
---|
| 1576 | return za; |
---|
| 1577 | } |
---|
| 1578 | |
---|
| 1579 | /*2 |
---|
| 1580 | * 1/a |
---|
| 1581 | */ |
---|
| 1582 | number naInvers(number a) |
---|
| 1583 | { |
---|
| 1584 | lnumber lo; |
---|
| 1585 | lnumber b = (lnumber)a; |
---|
| 1586 | alg x; |
---|
| 1587 | |
---|
| 1588 | if (b==NULL) |
---|
| 1589 | { |
---|
| 1590 | WerrorS("div. by 0"); |
---|
| 1591 | return NULL; |
---|
| 1592 | } |
---|
| 1593 | mmTestP(b,sizeof(rnumber)); |
---|
| 1594 | lo = (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 1595 | lo->s = b->s; |
---|
| 1596 | if (b->n!=NULL) |
---|
| 1597 | lo->z = napCopy(b->n); |
---|
| 1598 | else |
---|
| 1599 | lo->z = napInit(1); |
---|
| 1600 | x = b->z; |
---|
| 1601 | if ((napDeg(x)!=0) || !nacIsOne(x->ko)) |
---|
| 1602 | x = napCopy(x); |
---|
| 1603 | else |
---|
| 1604 | { |
---|
| 1605 | lo->n = NULL; |
---|
| 1606 | naTest((number)lo); |
---|
| 1607 | return (number)lo; |
---|
| 1608 | } |
---|
| 1609 | if (naMinimalPoly!=NULL) |
---|
| 1610 | { |
---|
| 1611 | x = napInvers(x, naMinimalPoly); |
---|
| 1612 | x = napMult(x, lo->z); |
---|
| 1613 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
| 1614 | x = napRemainder(x, naMinimalPoly); |
---|
| 1615 | lo->z = x; |
---|
| 1616 | lo->n = NULL; |
---|
| 1617 | lo->s = 2; |
---|
| 1618 | while (x!=NULL) |
---|
| 1619 | { |
---|
| 1620 | nacNormalize(x->ko); |
---|
| 1621 | x = x->ne; |
---|
| 1622 | } |
---|
| 1623 | } |
---|
| 1624 | else |
---|
| 1625 | lo->n = x; |
---|
| 1626 | naTest((number)lo); |
---|
| 1627 | return (number)lo; |
---|
| 1628 | } |
---|
| 1629 | |
---|
| 1630 | |
---|
| 1631 | BOOLEAN naIsZero(number za) |
---|
| 1632 | { |
---|
| 1633 | lnumber zb = (lnumber)za; |
---|
| 1634 | naTest(za); |
---|
| 1635 | #ifdef TEST |
---|
| 1636 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
| 1637 | #endif |
---|
| 1638 | return ((zb==NULL) || (zb->z==NULL)); |
---|
| 1639 | } |
---|
| 1640 | |
---|
| 1641 | |
---|
| 1642 | BOOLEAN naGreaterZero(number za) |
---|
| 1643 | { |
---|
| 1644 | lnumber zb = (lnumber)za; |
---|
| 1645 | #ifdef TEST |
---|
| 1646 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
| 1647 | #endif |
---|
| 1648 | naTest(za); |
---|
[be0519] | 1649 | if ((zb!=NULL) && (zb->z!=NULL)) |
---|
| 1650 | { |
---|
| 1651 | if (zb->n!=NULL) return TRUE; |
---|
| 1652 | if ((napDeg(zb->z)==0) && !nacGreaterZero(zb->z->ko)) return FALSE; |
---|
| 1653 | } |
---|
| 1654 | return TRUE; |
---|
[0e1846] | 1655 | } |
---|
| 1656 | |
---|
| 1657 | |
---|
| 1658 | /*2 |
---|
| 1659 | * a = b ? |
---|
| 1660 | */ |
---|
| 1661 | BOOLEAN naEqual (number a, number b) |
---|
| 1662 | { |
---|
[3eccafa] | 1663 | if(a==b) return TRUE; |
---|
| 1664 | if((a==NULL)&&(b!=NULL)) return FALSE; |
---|
| 1665 | if((b==NULL)&&(a!=NULL)) return FALSE; |
---|
| 1666 | |
---|
| 1667 | lnumber aa=(lnumber)a; |
---|
| 1668 | lnumber bb=(lnumber)b; |
---|
| 1669 | |
---|
| 1670 | int an_deg=0; |
---|
| 1671 | if(aa->n!=NULL) |
---|
| 1672 | an_deg=napDeg(aa->n); |
---|
| 1673 | int bn_deg=0; |
---|
| 1674 | if(bb->n!=NULL) |
---|
| 1675 | bn_deg=napDeg(bb->n); |
---|
| 1676 | if(an_deg+napDeg(bb->z)!=bn_deg+napDeg(aa->z)) |
---|
| 1677 | return FALSE; |
---|
| 1678 | #if 0 |
---|
| 1679 | naNormalize(a); |
---|
| 1680 | aa=(lnumber)a; |
---|
| 1681 | naNormalize(b); |
---|
| 1682 | bb=(lnumber)b; |
---|
| 1683 | if((aa->n==NULL)&&(bb->n!=NULL)) return FALSE; |
---|
| 1684 | if((bb->n==NULL)&&(aa->n!=NULL)) return FALSE; |
---|
| 1685 | if(napComp(aa->z,bb->z)!=0) return FALSE; |
---|
| 1686 | if((aa->n!=NULL) && (napComp(aa->n,bb->n))) return FALSE; |
---|
| 1687 | #endif |
---|
| 1688 | number h = naSub(a, b); |
---|
| 1689 | BOOLEAN bo = naIsZero(h); |
---|
[0e1846] | 1690 | naDelete(&h); |
---|
| 1691 | return bo; |
---|
| 1692 | } |
---|
| 1693 | |
---|
| 1694 | |
---|
| 1695 | BOOLEAN naGreater (number a, number b) |
---|
| 1696 | { |
---|
| 1697 | if (naIsZero(a)) |
---|
| 1698 | return FALSE; |
---|
| 1699 | if (naIsZero(b)) |
---|
| 1700 | return TRUE; /* a!= 0)*/ |
---|
[5c1c8fb] | 1701 | return napDeg(((lnumber)a)->z)>napDeg(((lnumber)b)->z); |
---|
[0e1846] | 1702 | } |
---|
| 1703 | |
---|
| 1704 | /*2 |
---|
| 1705 | * reads a number |
---|
| 1706 | */ |
---|
| 1707 | char *naRead(char *s, number *p) |
---|
| 1708 | { |
---|
| 1709 | alg x; |
---|
| 1710 | lnumber a; |
---|
| 1711 | s = napRead(s, &x); |
---|
| 1712 | if (x==NULL) |
---|
| 1713 | { |
---|
| 1714 | *p = NULL; |
---|
| 1715 | return s; |
---|
| 1716 | } |
---|
| 1717 | *p = (number)Alloc0(sizeof(rnumber)); |
---|
| 1718 | a = (lnumber)*p; |
---|
| 1719 | if ((naMinimalPoly!=NULL) && (x->e[0] >= naMinimalPoly->e[0])) |
---|
| 1720 | a->z = napRemainder(x, naMinimalPoly); |
---|
| 1721 | #if FEHLER3 |
---|
| 1722 | else if (naI!=NULL) |
---|
| 1723 | { |
---|
| 1724 | a->z = napRedp(x); |
---|
| 1725 | if (a->z != NULL) |
---|
| 1726 | a->z = napTailred (a->z); |
---|
| 1727 | } |
---|
| 1728 | #endif |
---|
| 1729 | else |
---|
| 1730 | a->z = x; |
---|
| 1731 | if(a->z==NULL) |
---|
| 1732 | { |
---|
| 1733 | Free((ADDRESS)*p,sizeof(rnumber)); |
---|
| 1734 | *p=NULL; |
---|
| 1735 | } |
---|
| 1736 | else |
---|
| 1737 | { |
---|
| 1738 | a->n = NULL; |
---|
| 1739 | a->s = 0; |
---|
| 1740 | naTest(*p); |
---|
| 1741 | } |
---|
| 1742 | return s; |
---|
| 1743 | } |
---|
| 1744 | |
---|
| 1745 | /*2 |
---|
| 1746 | * tries to convert a number to a name |
---|
| 1747 | */ |
---|
| 1748 | char * naName(number n) |
---|
| 1749 | { |
---|
| 1750 | lnumber ph = (lnumber)n; |
---|
| 1751 | if ((ph==NULL)||(ph->z==NULL)) |
---|
| 1752 | return NULL; |
---|
| 1753 | int i; |
---|
| 1754 | char *s=(char *)AllocL(4* naNumbOfPar); |
---|
| 1755 | char *t=(char *)Alloc(8); |
---|
| 1756 | s[0]='\0'; |
---|
| 1757 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
| 1758 | { |
---|
| 1759 | if (ph->z->e[i] > 0) |
---|
| 1760 | { |
---|
| 1761 | if (ph->z->e[i] >1) |
---|
| 1762 | { |
---|
| 1763 | sprintf(t,"%s%d",naParNames[i],ph->z->e[i]); |
---|
| 1764 | strcat(s,t); |
---|
| 1765 | } |
---|
| 1766 | else |
---|
| 1767 | { |
---|
| 1768 | strcat(s,naParNames[i]); |
---|
| 1769 | } |
---|
| 1770 | } |
---|
| 1771 | } |
---|
| 1772 | Free((ADDRESS)t,8); |
---|
| 1773 | if (s[0]=='\0') |
---|
| 1774 | { |
---|
| 1775 | FreeL((ADDRESS)s); |
---|
| 1776 | return NULL; |
---|
| 1777 | } |
---|
| 1778 | return s; |
---|
| 1779 | } |
---|
| 1780 | |
---|
| 1781 | /*2 |
---|
| 1782 | * writes a number |
---|
| 1783 | */ |
---|
| 1784 | void naWrite(number &phn) |
---|
| 1785 | { |
---|
| 1786 | lnumber ph = (lnumber)phn; |
---|
| 1787 | if ((ph==NULL)||(ph->z==NULL)) |
---|
| 1788 | StringAppendS("0"); |
---|
| 1789 | else |
---|
| 1790 | { |
---|
[af06ef] | 1791 | phn->s = 0; |
---|
[0e1846] | 1792 | naNormalize(phn); |
---|
| 1793 | napWrite(ph->z); |
---|
| 1794 | if (ph->n!=NULL) |
---|
| 1795 | { |
---|
| 1796 | StringAppendS("/"); |
---|
| 1797 | napWrite(ph->n); |
---|
| 1798 | } |
---|
| 1799 | } |
---|
| 1800 | } |
---|
| 1801 | |
---|
| 1802 | /*2 |
---|
| 1803 | * za == 1 ? |
---|
| 1804 | */ |
---|
| 1805 | BOOLEAN naIsOne(number za) |
---|
| 1806 | { |
---|
| 1807 | lnumber a = (lnumber)za; |
---|
| 1808 | alg x, y; |
---|
| 1809 | number t; |
---|
| 1810 | if (a==NULL) return FALSE; |
---|
| 1811 | mmTestP(a,sizeof(rnumber)); |
---|
| 1812 | #ifdef TEST |
---|
| 1813 | if (a->z==NULL) WerrorS("internal zero error(4)"); |
---|
| 1814 | #endif |
---|
| 1815 | if (a->n==NULL) |
---|
| 1816 | { |
---|
| 1817 | if (napDeg(a->z)==0) return nacIsOne(a->z->ko); |
---|
| 1818 | else return FALSE; |
---|
| 1819 | } |
---|
| 1820 | x = a->z; |
---|
| 1821 | y = a->n; |
---|
| 1822 | do |
---|
| 1823 | { |
---|
| 1824 | if (napComp(x, y)) |
---|
| 1825 | return FALSE; |
---|
| 1826 | else |
---|
| 1827 | { |
---|
| 1828 | t = nacSub(x->ko, y->ko); |
---|
| 1829 | if (!nacIsZero(t)) |
---|
| 1830 | { |
---|
| 1831 | nacDelete(&t); |
---|
| 1832 | return FALSE; |
---|
| 1833 | } |
---|
| 1834 | else |
---|
| 1835 | nacDelete(&t); |
---|
| 1836 | } |
---|
| 1837 | x = x->ne; |
---|
| 1838 | y = y->ne; |
---|
| 1839 | } |
---|
| 1840 | while ((x!=NULL) && (y!=NULL)); |
---|
| 1841 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
| 1842 | napDelete(&a->z); |
---|
| 1843 | napDelete(&a->n); |
---|
| 1844 | a->z = napInit(1); |
---|
| 1845 | a->n = NULL; |
---|
| 1846 | a->s = 2; |
---|
| 1847 | return TRUE; |
---|
| 1848 | } |
---|
| 1849 | |
---|
| 1850 | /*2 |
---|
| 1851 | * za == -1 ? |
---|
| 1852 | */ |
---|
| 1853 | BOOLEAN naIsMOne(number za) |
---|
| 1854 | { |
---|
| 1855 | lnumber a = (lnumber)za; |
---|
| 1856 | alg x, y; |
---|
| 1857 | number t; |
---|
| 1858 | if (a==NULL) return FALSE; |
---|
| 1859 | mmTestP(a,sizeof(rnumber)); |
---|
| 1860 | #ifdef TEST |
---|
[116a98] | 1861 | if (a->z==NULL) |
---|
| 1862 | { |
---|
| 1863 | WerrorS("internal zero error(5)"); |
---|
| 1864 | return FALSE; |
---|
| 1865 | } |
---|
[0e1846] | 1866 | #endif |
---|
| 1867 | if (a->n==NULL) |
---|
| 1868 | { |
---|
| 1869 | if (napDeg(a->z)==0) return nacIsMOne(a->z->ko); |
---|
[c999df4] | 1870 | /*else return FALSE;*/ |
---|
[0e1846] | 1871 | } |
---|
[c999df4] | 1872 | return FALSE; |
---|
[0e1846] | 1873 | } |
---|
| 1874 | |
---|
| 1875 | /*2 |
---|
| 1876 | * returns the i-th power of p (i>=0) |
---|
| 1877 | */ |
---|
| 1878 | void naPower(number p, int i, number *rc) |
---|
| 1879 | { |
---|
| 1880 | number x; |
---|
| 1881 | *rc = naInit(1); |
---|
| 1882 | for (; i > 0; i--) |
---|
| 1883 | { |
---|
| 1884 | x = naMult(*rc, p); |
---|
| 1885 | naDelete(rc); |
---|
| 1886 | *rc = x; |
---|
| 1887 | } |
---|
| 1888 | } |
---|
| 1889 | |
---|
| 1890 | /*2 |
---|
| 1891 | * result =gcd(a,b) |
---|
| 1892 | */ |
---|
| 1893 | number naGcd(number a, number b) |
---|
| 1894 | { |
---|
| 1895 | lnumber x, y; |
---|
| 1896 | lnumber result = (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 1897 | |
---|
| 1898 | x = (lnumber)a; |
---|
| 1899 | y = (lnumber)b; |
---|
| 1900 | if (naNumbOfPar == 1) |
---|
| 1901 | { |
---|
| 1902 | if (naMinimalPoly!=NULL) |
---|
| 1903 | { |
---|
| 1904 | if (x->z->ne!=NULL) |
---|
| 1905 | result->z = napCopy(x->z); |
---|
| 1906 | else |
---|
| 1907 | result->z = napGcd0(x->z, y->z); |
---|
| 1908 | } |
---|
| 1909 | else |
---|
| 1910 | result->z = napGcd(x->z, y->z); |
---|
| 1911 | } |
---|
| 1912 | else |
---|
[c8bd75] | 1913 | result->z = napGcd(x->z, y->z); // change frpm napGcd0 |
---|
[0e1846] | 1914 | naTest((number)result); |
---|
| 1915 | return (number)result; |
---|
| 1916 | } |
---|
| 1917 | |
---|
| 1918 | /*2 |
---|
| 1919 | * naNumbOfPar = 1: |
---|
| 1920 | * clears denominator algebraic case; |
---|
| 1921 | * tries to simplify ratio transcendental case; |
---|
| 1922 | * |
---|
| 1923 | * cancels monomials |
---|
| 1924 | * occuring in denominator |
---|
| 1925 | * and enumerator ? naNumbOfPar != 1; |
---|
[e4b0ec] | 1926 | * |
---|
| 1927 | * #defines for Factory: |
---|
| 1928 | * FACTORY_GCD_TEST: do not apply built in gcd for |
---|
| 1929 | * univariate polynomials, always use Factory |
---|
[0e1846] | 1930 | */ |
---|
| 1931 | void naNormalize(number &pp) |
---|
| 1932 | { |
---|
| 1933 | |
---|
[af06ef] | 1934 | naTest(pp); |
---|
[0e1846] | 1935 | lnumber p = (lnumber)pp; |
---|
| 1936 | |
---|
| 1937 | if ((p==NULL) /*|| (p->s==2)*/) |
---|
| 1938 | return; |
---|
| 1939 | p->s = 2; |
---|
[af06ef] | 1940 | alg x = p->z; |
---|
| 1941 | alg y = p->n; |
---|
[0e1846] | 1942 | if ((y!=NULL) && (naMinimalPoly!=NULL)) |
---|
| 1943 | { |
---|
| 1944 | y = napInvers(y, naMinimalPoly); |
---|
| 1945 | x = napMult(x, y); |
---|
| 1946 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
| 1947 | x = napRemainder(x, naMinimalPoly); |
---|
| 1948 | p->z = x; |
---|
| 1949 | p->n = y = NULL; |
---|
| 1950 | } |
---|
[af06ef] | 1951 | /* normalize all coefficients in n and z (if in Q) */ |
---|
| 1952 | if (naIsChar0) |
---|
[0e1846] | 1953 | { |
---|
[af06ef] | 1954 | while(x!=NULL) |
---|
[0e1846] | 1955 | { |
---|
[af06ef] | 1956 | nacNormalize(x->ko); |
---|
| 1957 | x=x->ne; |
---|
[0e1846] | 1958 | } |
---|
[af06ef] | 1959 | x = p->z; |
---|
| 1960 | } |
---|
| 1961 | if (y==NULL) return; |
---|
| 1962 | if (naIsChar0) |
---|
| 1963 | { |
---|
| 1964 | while(y!=NULL) |
---|
| 1965 | { |
---|
| 1966 | nacNormalize(y->ko); |
---|
| 1967 | y=y->ne; |
---|
| 1968 | } |
---|
| 1969 | y = p->n; |
---|
[0e1846] | 1970 | } |
---|
| 1971 | // p->n !=NULL: |
---|
[af06ef] | 1972 | /* collect all denoms from y and multiply x and y by it */ |
---|
| 1973 | if (naIsChar0) |
---|
| 1974 | { |
---|
| 1975 | number n=napLcm(y); |
---|
| 1976 | napMultN(x,n); |
---|
| 1977 | napMultN(y,n); |
---|
| 1978 | nacDelete(&n); |
---|
| 1979 | while(x!=NULL) |
---|
| 1980 | { |
---|
| 1981 | nacNormalize(x->ko); |
---|
| 1982 | x=x->ne; |
---|
| 1983 | } |
---|
| 1984 | x = p->z; |
---|
| 1985 | while(y!=NULL) |
---|
| 1986 | { |
---|
| 1987 | nacNormalize(y->ko); |
---|
| 1988 | y=y->ne; |
---|
| 1989 | } |
---|
| 1990 | y = p->n; |
---|
| 1991 | } |
---|
[0e1846] | 1992 | #if FEHLER1 |
---|
| 1993 | if (naMinimalPoly == NULL) |
---|
| 1994 | { |
---|
[af06ef] | 1995 | int i; |
---|
| 1996 | for (i=naNumbOfPar-1; i>=0; i--) |
---|
[0e1846] | 1997 | { |
---|
[f64447] | 1998 | alg xx=x; |
---|
| 1999 | alg yy=y; |
---|
[af06ef] | 2000 | int m = napExpi(i, yy, xx); |
---|
[0e1846] | 2001 | if (m != 0) // in this case xx!=NULL!=yy |
---|
| 2002 | { |
---|
| 2003 | while (xx != NULL) |
---|
| 2004 | { |
---|
| 2005 | xx->e[i] -= m; |
---|
| 2006 | xx = xx->ne; |
---|
| 2007 | } |
---|
| 2008 | while (yy != NULL) |
---|
| 2009 | { |
---|
| 2010 | yy->e[i] -= m; |
---|
| 2011 | yy = yy->ne; |
---|
| 2012 | } |
---|
| 2013 | } |
---|
| 2014 | } |
---|
| 2015 | } |
---|
| 2016 | #endif |
---|
[af06ef] | 2017 | if (napDeg(y)==0) /* i.e. y=const => simplify to (1/c)*z / monom */ |
---|
[0e1846] | 2018 | { |
---|
| 2019 | if (nacIsOne(y->ko)) |
---|
| 2020 | { |
---|
| 2021 | napDelete1(&y); |
---|
| 2022 | p->n = NULL; |
---|
| 2023 | return; |
---|
| 2024 | } |
---|
[af06ef] | 2025 | number h1 = nacInvers(y->ko); |
---|
[0e1846] | 2026 | nacNormalize(h1); |
---|
| 2027 | napMultN(x, h1); |
---|
| 2028 | nacDelete(&h1); |
---|
| 2029 | napDelete1(&y); |
---|
| 2030 | p->n = NULL; |
---|
| 2031 | return; |
---|
| 2032 | } |
---|
[e4b0ec] | 2033 | #ifndef FACTORY_GCD_TEST |
---|
[af06ef] | 2034 | if (naNumbOfPar == 1) /* apply built-in gcd */ |
---|
[0e1846] | 2035 | { |
---|
[af06ef] | 2036 | alg x1,y1; |
---|
| 2037 | if (x->e[0] >= y->e[0]) |
---|
[0e1846] | 2038 | { |
---|
[af06ef] | 2039 | x1 = napCopy(x); |
---|
| 2040 | y1 = napCopy(y); |
---|
[0e1846] | 2041 | } |
---|
[af06ef] | 2042 | else |
---|
[0e1846] | 2043 | { |
---|
[af06ef] | 2044 | x1 = napCopy(y); |
---|
| 2045 | y1 = napCopy(x); |
---|
[0e1846] | 2046 | } |
---|
[af06ef] | 2047 | alg r; |
---|
| 2048 | loop |
---|
[0e1846] | 2049 | { |
---|
[af06ef] | 2050 | r = napRemainder(x1, y1); |
---|
| 2051 | if ((r==NULL) || (r->ne==NULL)) break; |
---|
| 2052 | x1 = y1; |
---|
| 2053 | y1 = r; |
---|
[0e1846] | 2054 | } |
---|
[af06ef] | 2055 | if (r!=NULL) |
---|
[0e1846] | 2056 | { |
---|
[af06ef] | 2057 | napDelete(&r); |
---|
| 2058 | napDelete(&y1); |
---|
[0e1846] | 2059 | } |
---|
| 2060 | else |
---|
| 2061 | { |
---|
[af06ef] | 2062 | napDivMod(x, y1, &(p->z), &r); |
---|
| 2063 | napDivMod(y, y1, &(p->n), &r); |
---|
| 2064 | napDelete(&y1); |
---|
[0e1846] | 2065 | } |
---|
[af06ef] | 2066 | x = p->z; |
---|
| 2067 | y = p->n; |
---|
| 2068 | /* collect all denoms from y and multiply x and y by it */ |
---|
| 2069 | if (naIsChar0) |
---|
[0e1846] | 2070 | { |
---|
[af06ef] | 2071 | number n=napLcm(y); |
---|
| 2072 | napMultN(x,n); |
---|
| 2073 | napMultN(y,n); |
---|
| 2074 | nacDelete(&n); |
---|
| 2075 | while(x!=NULL) |
---|
[0e1846] | 2076 | { |
---|
[af06ef] | 2077 | nacNormalize(x->ko); |
---|
| 2078 | x=x->ne; |
---|
[0e1846] | 2079 | } |
---|
[af06ef] | 2080 | x = p->z; |
---|
| 2081 | while(y!=NULL) |
---|
| 2082 | { |
---|
| 2083 | nacNormalize(y->ko); |
---|
| 2084 | y=y->ne; |
---|
| 2085 | } |
---|
| 2086 | y = p->n; |
---|
[0e1846] | 2087 | } |
---|
[af06ef] | 2088 | if (y->ne==NULL) |
---|
[0e1846] | 2089 | { |
---|
[af06ef] | 2090 | if (nacIsOne(y->ko)) |
---|
| 2091 | { |
---|
| 2092 | if (y->e[0]==0) |
---|
| 2093 | { |
---|
| 2094 | napDelete1(&y); |
---|
| 2095 | p->n = NULL; |
---|
| 2096 | } |
---|
| 2097 | return; |
---|
| 2098 | } |
---|
[0e1846] | 2099 | } |
---|
[af06ef] | 2100 | } |
---|
[e4b0ec] | 2101 | #endif /* FACTORY_GCD_TEST */ |
---|
[af06ef] | 2102 | #ifdef HAVE_FACTORY |
---|
[e4b0ec] | 2103 | #ifndef FACTORY_GCD_TEST |
---|
[af06ef] | 2104 | else |
---|
[e4b0ec] | 2105 | #endif |
---|
[af06ef] | 2106 | { |
---|
[1a5daea] | 2107 | alg xx,yy; |
---|
| 2108 | singclap_algdividecontent(x,y,xx,yy); |
---|
| 2109 | if (xx!=NULL) |
---|
[0e1846] | 2110 | { |
---|
[1a5daea] | 2111 | p->z=xx; |
---|
| 2112 | p->n=yy; |
---|
| 2113 | napDelete(&x); |
---|
| 2114 | napDelete(&y); |
---|
[4b5c87] | 2115 | } |
---|
[0e1846] | 2116 | } |
---|
[af06ef] | 2117 | #endif |
---|
[5dc4ea] | 2118 | /* remove common factors from z and n */ |
---|
| 2119 | x=p->z; |
---|
| 2120 | y=p->n; |
---|
| 2121 | if(!nacGreaterZero(napGetCoeff(y))) |
---|
| 2122 | { |
---|
| 2123 | x=napNeg(x); |
---|
| 2124 | y=napNeg(y); |
---|
| 2125 | } |
---|
| 2126 | number g=nacCopy(napGetCoeff(x)); |
---|
| 2127 | napIter(x); |
---|
| 2128 | while (x!=NULL) |
---|
| 2129 | { |
---|
| 2130 | number d=nacGcd(g,napGetCoeff(x)); |
---|
| 2131 | if(nacIsOne(d)) |
---|
| 2132 | { |
---|
| 2133 | nacDelete(&g); |
---|
| 2134 | nacDelete(&d); |
---|
| 2135 | return; |
---|
| 2136 | } |
---|
| 2137 | nacDelete(&g); |
---|
| 2138 | g = d; |
---|
| 2139 | napIter(x); |
---|
| 2140 | } |
---|
| 2141 | while (y!=NULL) |
---|
| 2142 | { |
---|
| 2143 | number d=nacGcd(g,napGetCoeff(y)); |
---|
| 2144 | if(nacIsOne(d)) |
---|
| 2145 | { |
---|
| 2146 | nacDelete(&g); |
---|
| 2147 | nacDelete(&d); |
---|
| 2148 | return; |
---|
| 2149 | } |
---|
| 2150 | nacDelete(&g); |
---|
| 2151 | g = d; |
---|
| 2152 | napIter(y); |
---|
| 2153 | } |
---|
| 2154 | x=p->z; |
---|
| 2155 | y=p->n; |
---|
| 2156 | while (x!=NULL) |
---|
| 2157 | { |
---|
| 2158 | number d = nacIntDiv(napGetCoeff(x),g); |
---|
| 2159 | napSetCoeff(x,d); |
---|
| 2160 | napIter(x); |
---|
| 2161 | } |
---|
| 2162 | while (y!=NULL) |
---|
| 2163 | { |
---|
| 2164 | number d = nacIntDiv(napGetCoeff(y),g); |
---|
| 2165 | napSetCoeff(y,d); |
---|
| 2166 | napIter(y); |
---|
| 2167 | } |
---|
| 2168 | nacDelete(&g); |
---|
[0e1846] | 2169 | } |
---|
| 2170 | |
---|
| 2171 | /*2 |
---|
| 2172 | * returns in result->n 1 |
---|
| 2173 | * and in result->z the lcm(a->z,b->n) |
---|
| 2174 | */ |
---|
| 2175 | number naLcm(number la, number lb) |
---|
| 2176 | { |
---|
| 2177 | lnumber result; |
---|
| 2178 | lnumber a = (lnumber)la; |
---|
| 2179 | lnumber b = (lnumber)lb; |
---|
| 2180 | result = (lnumber)Alloc0(sizeof(rnumber)); |
---|
[fd702f] | 2181 | //if (((naMinimalPoly==NULL) && (naI==NULL)) || !naIsChar0) |
---|
| 2182 | //{ |
---|
| 2183 | // result->z = napInit(1); |
---|
| 2184 | // return (number)result; |
---|
| 2185 | //} |
---|
[0e1846] | 2186 | naNormalize(lb); |
---|
[af06ef] | 2187 | naTest(la); |
---|
| 2188 | naTest(lb); |
---|
| 2189 | alg x = napCopy(a->z); |
---|
| 2190 | number t = napLcm(b->z); // get all denom of b->z |
---|
[0e1846] | 2191 | if (!nacIsOne(t)) |
---|
| 2192 | { |
---|
[af06ef] | 2193 | number bt, r; |
---|
| 2194 | alg xx=x; |
---|
| 2195 | while (xx!=NULL) |
---|
| 2196 | { |
---|
| 2197 | bt = nacGcd(t, xx->ko); |
---|
| 2198 | r = nacMult(t, xx->ko); |
---|
| 2199 | nacDelete(&(xx->ko)); |
---|
| 2200 | xx->ko = nacDiv(r, bt); |
---|
| 2201 | nacNormalize(xx->ko); |
---|
| 2202 | nacDelete(&bt); |
---|
| 2203 | nacDelete(&r); |
---|
| 2204 | xx=xx->ne; |
---|
| 2205 | } |
---|
[0e1846] | 2206 | } |
---|
| 2207 | nacDelete(&t); |
---|
| 2208 | result->z = x; |
---|
[af06ef] | 2209 | #ifdef HAVE_FACTORY |
---|
| 2210 | if (b->n!=NULL) |
---|
| 2211 | { |
---|
| 2212 | result->z=singclap_alglcm(result->z,b->n); |
---|
| 2213 | napDelete(&x); |
---|
| 2214 | } |
---|
| 2215 | #endif |
---|
| 2216 | naTest(la); |
---|
| 2217 | naTest(lb); |
---|
[0e1846] | 2218 | naTest((number)result); |
---|
[af06ef] | 2219 | return ((number)result); |
---|
[0e1846] | 2220 | } |
---|
| 2221 | |
---|
| 2222 | /*2 |
---|
| 2223 | * input: a set of constant polynomials |
---|
| 2224 | * sets the global variable naI |
---|
| 2225 | */ |
---|
| 2226 | void naSetIdeal(ideal I) |
---|
| 2227 | { |
---|
| 2228 | int i; |
---|
| 2229 | |
---|
| 2230 | if (idIs0(I)) |
---|
| 2231 | { |
---|
| 2232 | for (i=naI->anz-1; i>=0; i--) |
---|
| 2233 | napDelete(&naI->liste[i]); |
---|
| 2234 | Free((ADDRESS)naI,sizeof(*naI)); |
---|
| 2235 | naI=NULL; |
---|
| 2236 | } |
---|
| 2237 | else |
---|
| 2238 | { |
---|
| 2239 | lnumber h; |
---|
| 2240 | number a; |
---|
| 2241 | alg x; |
---|
| 2242 | |
---|
| 2243 | naI=(naIdeal)Alloc(sizeof(*naI)); |
---|
| 2244 | naI->anz=IDELEMS(I); |
---|
| 2245 | naI->liste=(alg*)Alloc(naI->anz*sizeof(alg)); |
---|
| 2246 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
| 2247 | { |
---|
| 2248 | h=(lnumber)pGetCoeff(I->m[i]); |
---|
| 2249 | /* We only need the enumerator of h, as we expect it to be a polynomial */ |
---|
| 2250 | naI->liste[i]=napCopy(h->z); |
---|
| 2251 | /* If it isn't normalized (lc = 1) do this */ |
---|
| 2252 | if (!nacIsOne(naI->liste[i]->ko)) |
---|
| 2253 | { |
---|
| 2254 | x=naI->liste[i]; |
---|
| 2255 | a=nacCopy(x->ko); |
---|
| 2256 | a=nacDiv(nacInit(1),a); |
---|
| 2257 | napMultN(x,a); |
---|
| 2258 | nacDelete(&a); |
---|
| 2259 | } |
---|
| 2260 | } |
---|
| 2261 | } |
---|
| 2262 | } |
---|
| 2263 | |
---|
| 2264 | /*2 |
---|
| 2265 | * map Z/p -> Q(a) |
---|
| 2266 | */ |
---|
| 2267 | number naMapP0(number c) |
---|
| 2268 | { |
---|
| 2269 | if (npIsZero(c)) return NULL; |
---|
| 2270 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2271 | l->s=2; |
---|
[550b4c] | 2272 | l->z=(alg)Alloc0(napMonomSize); |
---|
[0e1846] | 2273 | int i=(int)c; |
---|
| 2274 | if (i>(naPrimeM>>2)) i-=naPrimeM; |
---|
| 2275 | l->z->ko=nlInit(i); |
---|
| 2276 | l->n=NULL; |
---|
| 2277 | return (number)l; |
---|
| 2278 | } |
---|
| 2279 | |
---|
| 2280 | /*2 |
---|
| 2281 | * map Q -> Q(a) |
---|
| 2282 | */ |
---|
| 2283 | number naMap00(number c) |
---|
| 2284 | { |
---|
| 2285 | if (nlIsZero(c)) return NULL; |
---|
| 2286 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2287 | l->s=0; |
---|
[550b4c] | 2288 | l->z=(alg)Alloc0(napMonomSize); |
---|
[0e1846] | 2289 | l->z->ko=nlCopy(c); |
---|
| 2290 | l->n=NULL; |
---|
| 2291 | return (number)l; |
---|
| 2292 | } |
---|
| 2293 | |
---|
| 2294 | /*2 |
---|
| 2295 | * map Z/p -> Z/p(a) |
---|
| 2296 | */ |
---|
| 2297 | number naMapPP(number c) |
---|
| 2298 | { |
---|
| 2299 | if (npIsZero(c)) return NULL; |
---|
| 2300 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2301 | l->s=2; |
---|
[550b4c] | 2302 | l->z=(alg)Alloc0(napMonomSize); |
---|
[0e1846] | 2303 | l->z->ko=c; /* omit npCopy, because npCopy is a no-op */ |
---|
| 2304 | l->n=NULL; |
---|
| 2305 | return (number)l; |
---|
| 2306 | } |
---|
| 2307 | |
---|
| 2308 | /*2 |
---|
| 2309 | * map Z/p' -> Z/p(a) |
---|
| 2310 | */ |
---|
| 2311 | number naMapPP1(number c) |
---|
| 2312 | { |
---|
| 2313 | if (npIsZero(c)) return NULL; |
---|
| 2314 | int i=(int)c; |
---|
| 2315 | if (i>naPrimeM) i-=naPrimeM; |
---|
| 2316 | number n=npInit(i); |
---|
| 2317 | if (npIsZero(n)) return NULL; |
---|
| 2318 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2319 | l->s=2; |
---|
[550b4c] | 2320 | l->z=(alg)Alloc0(napMonomSize); |
---|
[0e1846] | 2321 | l->z->ko=n; |
---|
| 2322 | l->n=NULL; |
---|
| 2323 | return (number)l; |
---|
| 2324 | } |
---|
| 2325 | |
---|
| 2326 | /*2 |
---|
| 2327 | * map Q -> Z/p(a) |
---|
| 2328 | */ |
---|
| 2329 | number naMap0P(number c) |
---|
| 2330 | { |
---|
| 2331 | if (nlIsZero(c)) return NULL; |
---|
| 2332 | number n=npInit(nlInt(c)); |
---|
| 2333 | if (npIsZero(n)) return NULL; |
---|
| 2334 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2335 | l->s=2; |
---|
[550b4c] | 2336 | l->z=(alg)Alloc0(napMonomSize); |
---|
[0e1846] | 2337 | l->z->ko=n; |
---|
| 2338 | l->n=NULL; |
---|
| 2339 | return (number)l; |
---|
| 2340 | } |
---|
| 2341 | |
---|
| 2342 | static number (*nacMap)(number); |
---|
| 2343 | static int naParsToCopy; |
---|
| 2344 | static alg napMap(alg p) |
---|
| 2345 | { |
---|
| 2346 | alg w, a; |
---|
| 2347 | |
---|
| 2348 | if (p==NULL) return NULL; |
---|
[550b4c] | 2349 | a = w = (alg)Alloc0(napMonomSize); |
---|
| 2350 | memcpy(a->e, p->e, naParsToCopy * SIZEOF_PARAMETER); |
---|
[0e1846] | 2351 | w->ko = nacMap(p->ko); |
---|
| 2352 | loop |
---|
| 2353 | { |
---|
| 2354 | p=p->ne; |
---|
| 2355 | if (p==NULL) break; |
---|
[550b4c] | 2356 | a->ne = (alg)Alloc0(napMonomSize); |
---|
[0e1846] | 2357 | a = a->ne; |
---|
[550b4c] | 2358 | memcpy(a->e, p->e, naParsToCopy * SIZEOF_PARAMETER); |
---|
[0e1846] | 2359 | a->ko = nacMap(p->ko); |
---|
| 2360 | } |
---|
| 2361 | a->ne = NULL; |
---|
| 2362 | return w; |
---|
| 2363 | } |
---|
| 2364 | |
---|
| 2365 | /*2 |
---|
| 2366 | * map _(a) -> _(b) |
---|
| 2367 | */ |
---|
| 2368 | number naMapQaQb(number c) |
---|
| 2369 | { |
---|
| 2370 | if (c==NULL) return NULL; |
---|
| 2371 | lnumber erg= (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 2372 | lnumber src =(lnumber)c; |
---|
| 2373 | erg->s=src->s; |
---|
| 2374 | erg->z=napMap(src->z); |
---|
| 2375 | erg->n=napMap(src->n); |
---|
| 2376 | return (number)erg; |
---|
| 2377 | } |
---|
| 2378 | |
---|
| 2379 | BOOLEAN naSetMap(int c, char ** par, int nop, number minpol) |
---|
| 2380 | { |
---|
[be0d84] | 2381 | if (rField_is_Q_a()) /* -> Q(a) */ |
---|
[0e1846] | 2382 | { |
---|
| 2383 | if (c == 0) |
---|
| 2384 | { |
---|
| 2385 | nMap = naMap00; /*Q -> Q(a)*/ |
---|
| 2386 | return TRUE; |
---|
| 2387 | } |
---|
| 2388 | if (c>1) |
---|
| 2389 | { |
---|
| 2390 | if (par==NULL) |
---|
| 2391 | { |
---|
| 2392 | naPrimeM = c; |
---|
| 2393 | nMap = naMapP0; /* Z/p -> Q(a)*/ |
---|
| 2394 | return TRUE; |
---|
| 2395 | } |
---|
| 2396 | else |
---|
| 2397 | { |
---|
| 2398 | return FALSE; /* GF(q) -> Q(a) */ |
---|
| 2399 | } |
---|
| 2400 | } |
---|
| 2401 | if (c<0) |
---|
| 2402 | { |
---|
| 2403 | return FALSE; /* Z/p(a) -> Q(b)*/ |
---|
| 2404 | } |
---|
| 2405 | if (c==1) |
---|
| 2406 | { |
---|
| 2407 | int i; |
---|
| 2408 | naParsToCopy=0; |
---|
| 2409 | for(i=0;i<nop;i++) |
---|
| 2410 | { |
---|
[17e692] | 2411 | if ((i>=rPar(currRing)) |
---|
[0e1846] | 2412 | ||(strcmp(par[i],currRing->parameter[i])!=0)) |
---|
| 2413 | return FALSE; |
---|
| 2414 | naParsToCopy++; |
---|
| 2415 | } |
---|
| 2416 | nacMap=nacCopy; |
---|
| 2417 | nMap=naMapQaQb; |
---|
| 2418 | return TRUE; /* Q(a) -> Q(a) */ |
---|
| 2419 | } |
---|
| 2420 | } |
---|
| 2421 | /*-----------------------------------------------------*/ |
---|
[be0d84] | 2422 | if (rField_is_Zp_a()) /* -> Z/p(a) */ |
---|
[0e1846] | 2423 | { |
---|
| 2424 | if (c == 0) |
---|
| 2425 | { |
---|
| 2426 | nMap = naMap0P; /*Q -> Z/p(a)*/ |
---|
| 2427 | return TRUE; |
---|
| 2428 | } |
---|
| 2429 | if (c>1) |
---|
| 2430 | { |
---|
| 2431 | if (par==NULL) |
---|
| 2432 | { |
---|
| 2433 | if (c==npPrimeM) |
---|
| 2434 | { |
---|
| 2435 | nMap = naMapPP; /* Z/p -> Z/p(a)*/ |
---|
| 2436 | return TRUE; |
---|
| 2437 | } |
---|
| 2438 | else |
---|
| 2439 | { |
---|
| 2440 | naPrimeM = c; |
---|
| 2441 | nMap = naMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
| 2442 | return TRUE; |
---|
| 2443 | } |
---|
| 2444 | } |
---|
| 2445 | else |
---|
| 2446 | { |
---|
| 2447 | return FALSE; /* GF(q) ->Z/p(a) */ |
---|
| 2448 | } |
---|
| 2449 | } |
---|
| 2450 | if (c<0) |
---|
| 2451 | { |
---|
[be0d84] | 2452 | if (c==rChar()) |
---|
[0e1846] | 2453 | { |
---|
| 2454 | nacMap=nacCopy; |
---|
| 2455 | } |
---|
| 2456 | else |
---|
| 2457 | { |
---|
| 2458 | npMapPrime=-c; |
---|
| 2459 | nacMap = npMapP; |
---|
| 2460 | } |
---|
| 2461 | int i; |
---|
| 2462 | naParsToCopy=0; |
---|
| 2463 | for(i=0;i<nop;i++) |
---|
| 2464 | { |
---|
[17e692] | 2465 | if ((i>=rPar(currRing)) |
---|
[0e1846] | 2466 | ||(strcmp(par[i],currRing->parameter[i])!=0)) |
---|
| 2467 | return FALSE; |
---|
| 2468 | naParsToCopy++; |
---|
| 2469 | } |
---|
| 2470 | nMap=naMapQaQb; |
---|
| 2471 | return TRUE; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
| 2472 | } |
---|
| 2473 | if (c==1) |
---|
| 2474 | { |
---|
| 2475 | return FALSE; /* Q(a) -> Z/p(b) */ |
---|
| 2476 | } |
---|
| 2477 | } |
---|
| 2478 | return FALSE; /* default */ |
---|
| 2479 | } |
---|
| 2480 | |
---|
| 2481 | /*2 |
---|
| 2482 | * convert a alg number into a poly |
---|
| 2483 | */ |
---|
| 2484 | poly naPermNumber(number z, int * par_perm, int P) |
---|
| 2485 | { |
---|
| 2486 | if (z==NULL) return NULL; |
---|
| 2487 | poly res=NULL; |
---|
| 2488 | poly p; |
---|
| 2489 | napoly za=((lnumber)z)->z; |
---|
| 2490 | do |
---|
| 2491 | { |
---|
[e78cce] | 2492 | p=pInit(); |
---|
[0e1846] | 2493 | pNext(p)=NULL; |
---|
| 2494 | nNew(&pGetCoeff(p)); |
---|
| 2495 | int i; |
---|
[51c163] | 2496 | for(i=pVariables;i;i--) |
---|
| 2497 | pSetExp(p,i, 0); |
---|
| 2498 | pSetComp(p, 0); |
---|
[0e1846] | 2499 | napoly pa=NULL; |
---|
| 2500 | if (currRing->parameter!=NULL) |
---|
| 2501 | { |
---|
| 2502 | pGetCoeff(p)=(number)Alloc0(sizeof(rnumber)); |
---|
| 2503 | ((lnumber)pGetCoeff(p))->s=2; |
---|
| 2504 | ((lnumber)pGetCoeff(p))->z=napInitz(nacCopy(napGetCoeff(za))); |
---|
| 2505 | pa=((lnumber)pGetCoeff(p))->z; |
---|
| 2506 | } |
---|
| 2507 | else |
---|
| 2508 | { |
---|
| 2509 | pGetCoeff(p)=nCopy(napGetCoeff(za)); |
---|
| 2510 | } |
---|
| 2511 | for(i=0;i<P;i++) |
---|
| 2512 | { |
---|
| 2513 | if(za->e[i]!=0) |
---|
| 2514 | { |
---|
| 2515 | if(par_perm[i]>0) |
---|
[51c163] | 2516 | pSetExp(p,par_perm[i],za->e[i]); |
---|
[0e1846] | 2517 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
| 2518 | pa->e[-par_perm[i]-1]=za->e[i]; |
---|
| 2519 | else |
---|
| 2520 | { |
---|
| 2521 | pDelete(&p); |
---|
| 2522 | break; |
---|
| 2523 | } |
---|
| 2524 | } |
---|
| 2525 | } |
---|
| 2526 | if (p!=NULL) |
---|
| 2527 | { |
---|
| 2528 | pSetm(p); |
---|
| 2529 | pTest(p); |
---|
| 2530 | res=pAdd(res,p); |
---|
| 2531 | } |
---|
| 2532 | za=za->ne; |
---|
| 2533 | } |
---|
| 2534 | while (za!=NULL); |
---|
| 2535 | pTest(res); |
---|
| 2536 | return res; |
---|
| 2537 | } |
---|
| 2538 | |
---|
[7eea80] | 2539 | number naGetDenom(number &n) |
---|
[0f0974] | 2540 | { |
---|
[7eea80] | 2541 | naNormalize(n); |
---|
[0f0974] | 2542 | lnumber x=(lnumber)n; |
---|
| 2543 | if (x->n!=NULL) |
---|
| 2544 | { |
---|
| 2545 | lnumber r=(lnumber)Alloc0(sizeof(rnumber)); |
---|
| 2546 | r->z=napCopy(naGetDenom0(x)); |
---|
| 2547 | r->s = 2; |
---|
| 2548 | return (number)r; |
---|
| 2549 | } |
---|
| 2550 | return naInit(1); |
---|
| 2551 | } |
---|
| 2552 | |
---|
[0e1846] | 2553 | #ifdef LDEBUG |
---|
| 2554 | BOOLEAN naDBTest(number a, char *f,int l) |
---|
| 2555 | { |
---|
| 2556 | lnumber x=(lnumber)a; |
---|
| 2557 | if (x == NULL) |
---|
| 2558 | return TRUE; |
---|
| 2559 | #ifdef MDEBUG |
---|
[de47d79] | 2560 | mmDBTestBlock(a,sizeof(rnumber),f,l); |
---|
[0e1846] | 2561 | #endif |
---|
| 2562 | alg p = x->z; |
---|
| 2563 | if (p==NULL) |
---|
| 2564 | { |
---|
| 2565 | Print("0/* in %s:%d\n",f,l); |
---|
| 2566 | return FALSE; |
---|
| 2567 | } |
---|
| 2568 | while(p!=NULL) |
---|
| 2569 | { |
---|
[bd00313] | 2570 | if ((naIsChar0 && nlIsZero(p->ko)) |
---|
| 2571 | || ((!naIsChar0) && npIsZero(p->ko))) |
---|
[de47d79] | 2572 | { |
---|
| 2573 | Print("coeff 0 in %s:%d\n",f,l); |
---|
| 2574 | return FALSE; |
---|
| 2575 | } |
---|
[0e1846] | 2576 | if((naMinimalPoly!=NULL)&&(p->e[0]>naMinimalPoly->e[0]) |
---|
| 2577 | &&(p!=naMinimalPoly)) |
---|
| 2578 | { |
---|
| 2579 | Print("deg>minpoly in %s:%d\n",f,l); |
---|
| 2580 | return FALSE; |
---|
| 2581 | } |
---|
| 2582 | //if (naIsChar0 && (((int)p->ko &3) == 0) && (p->ko->s==0) && (x->s==2)) |
---|
| 2583 | //{ |
---|
| 2584 | // Print("normalized with non-normal coeffs in %s:%d\n",f,l); |
---|
| 2585 | // return FALSE; |
---|
| 2586 | //} |
---|
[a38f5ea] | 2587 | if (naIsChar0 && !(nlDBTest(p->ko,f,l))) |
---|
[0e1846] | 2588 | return FALSE; |
---|
| 2589 | #ifdef MDEBUG |
---|
[550b4c] | 2590 | mmDBTestBlock(p,napMonomSize,f,l); |
---|
[0e1846] | 2591 | #endif |
---|
| 2592 | p = p->ne; |
---|
| 2593 | } |
---|
[0f0974] | 2594 | p = naGetDenom0(x); |
---|
[0e1846] | 2595 | while(p!=NULL) |
---|
| 2596 | { |
---|
[a38f5ea] | 2597 | if (naIsChar0 && !(nlDBTest(p->ko,f,l))) |
---|
[0e1846] | 2598 | return FALSE; |
---|
| 2599 | #ifdef MDEBUG |
---|
[550b4c] | 2600 | if (!mmDBTestBlock(p,napMonomSize,f,l)) |
---|
[0e1846] | 2601 | return FALSE; |
---|
| 2602 | #endif |
---|
| 2603 | p = p->ne; |
---|
| 2604 | } |
---|
| 2605 | return TRUE; |
---|
| 2606 | } |
---|
| 2607 | #endif |
---|
| 2608 | |
---|