[0e1846] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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[32df82] | 4 | /* $Id: longalg.cc,v 1.3 1997-04-02 15:07:21 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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| 21 | #include "longalg.h" |
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| 22 | #define FEHLER1 1 |
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| 23 | #define FEHLER2 1 |
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| 24 | #define FEHLER3 1 |
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| 25 | |
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| 26 | struct snaIdeal |
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| 27 | { |
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| 28 | int anz; |
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| 29 | alg *liste; |
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| 30 | }; |
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| 31 | typedef struct snaIdeal * naIdeal; |
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| 32 | |
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| 33 | naIdeal naI=NULL; |
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| 34 | |
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| 35 | //#define RECA_SIZE (sizeof(alg)+sizeof(number)) |
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| 36 | alg naMinimalPoly; |
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| 37 | int naNumbOfPar; |
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| 38 | char **naParNames; |
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| 39 | static int naIsChar0; |
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| 40 | static int naPrimeM; |
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| 41 | |
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| 42 | #ifdef LDEBUG |
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| 43 | #define naTest(a) naDBTest(a,__FILE__,__LINE__) |
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| 44 | BOOLEAN naDBTest(number a, char *f,int l); |
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| 45 | #else |
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| 46 | #define naTest(a) |
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| 47 | #endif |
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| 48 | |
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| 49 | number (*naMap)(number from); |
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| 50 | /* procedure variables */ |
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| 51 | static numberfunc |
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| 52 | nacMult, nacSub, nacAdd, nacDiv, nacGcd, nacLcm; |
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| 53 | #ifdef LDEBUG |
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| 54 | static void (*nacDBDelete)(number *a,char *f,int l); |
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| 55 | #define nacDelete(A) nacDBDelete(A,__FILE__,__LINE__) |
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| 56 | #else |
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| 57 | static void (*nacDelete)(number *a); |
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| 58 | #endif |
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| 59 | number (*nacInit)(int i); |
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| 60 | static int (*nacInt)(number &n); |
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| 61 | void (*nacNormalize)(number &a); |
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| 62 | static number (*nacNeg)(number a); |
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| 63 | static void (*nacWrite)(number &a); |
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| 64 | number (*nacCopy)(number a); |
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| 65 | static number (*nacInvers)(number a); |
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| 66 | BOOLEAN (*nacIsZero)(number a); |
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| 67 | static BOOLEAN (*nacIsOne)(number a); |
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| 68 | static BOOLEAN (*nacIsMOne)(number a); |
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| 69 | static BOOLEAN (*nacGreaterZero)(number a); |
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| 70 | static char * (*nacRead) (char *s, number *a); |
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| 71 | extern void napDelete(alg *p); |
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| 72 | static alg napRedp(alg q); |
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| 73 | static alg napTailred(alg q); |
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| 74 | static BOOLEAN napDivPoly(alg p, alg q); |
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| 75 | static int napExpi(int i, alg a, alg b); |
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| 76 | |
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| 77 | /*2 |
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| 78 | * sets the appropriate operators |
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| 79 | */ |
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| 80 | void naSetChar(int i, BOOLEAN complete, char ** param, int pars) |
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| 81 | { |
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| 82 | if (naI!=NULL) |
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| 83 | { |
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| 84 | int j; |
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| 85 | for (j=naI->anz-1; j>=0; j--) |
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| 86 | napDelete (&naI->liste[j]); |
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| 87 | Free((ADDRESS)naI->liste,naI->anz*sizeof(alg)); |
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| 88 | Free((ADDRESS)naI,sizeof(*naI)); |
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| 89 | naI=NULL; |
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| 90 | } |
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| 91 | naMap = naCopy; |
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| 92 | naMinimalPoly = NULL; |
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| 93 | naParNames=param; |
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| 94 | naNumbOfPar=pars; |
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| 95 | if (i == 1) |
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| 96 | { |
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| 97 | naIsChar0 = 1; |
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| 98 | #ifdef LDEBUG |
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| 99 | nacDBDelete = nlDBDelete; |
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| 100 | #else |
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| 101 | nacDelete = nlDelete; |
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| 102 | #endif |
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| 103 | if (complete) |
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| 104 | { |
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| 105 | nacInit = nlInit; |
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| 106 | nacInt = nlInt; |
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| 107 | nacCopy = nlCopy; |
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| 108 | nacAdd = nlAdd; |
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| 109 | nacSub = nlSub; |
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| 110 | nacMult = nlMult; |
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| 111 | nacDiv = nlDiv; |
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| 112 | nacInvers = nlInvers; |
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| 113 | nacNormalize = nlNormalize; |
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| 114 | nacNeg = nlNeg; |
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| 115 | nacIsZero = nlIsZero; |
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| 116 | nacRead = nlRead; |
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| 117 | nacWrite = nlWrite; |
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| 118 | nacGreaterZero = nlGreaterZero; |
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| 119 | nacIsOne = nlIsOne; |
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| 120 | nacIsMOne = nlIsMOne; |
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| 121 | nacGcd = nlGcd; |
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| 122 | nacLcm = nlLcm; |
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| 123 | } |
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| 124 | } |
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| 125 | else if (i < 0) |
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| 126 | { |
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| 127 | naIsChar0 = 0; |
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| 128 | #ifdef LDEBUG |
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| 129 | nacDBDelete = nDBDummy1; |
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| 130 | #else |
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| 131 | nacDelete = nDummy1; |
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| 132 | #endif |
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| 133 | if (complete) |
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| 134 | { |
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| 135 | npSetChar(-i); |
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| 136 | nacInit = npInit; |
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| 137 | nacInt = npInt; |
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| 138 | nacCopy = npCopy; |
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| 139 | nacAdd = npAdd; |
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| 140 | nacSub = npSub; |
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| 141 | nacMult = npMult; |
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| 142 | nacDiv = npDiv; |
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| 143 | nacInvers = npInvers; |
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| 144 | nacNormalize = nDummy2; |
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| 145 | nacNeg = npNeg; |
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| 146 | nacIsZero = npIsZero; |
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| 147 | nacRead = npRead; |
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| 148 | nacWrite = npWrite; |
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| 149 | nacGreaterZero = npGreaterZero; |
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| 150 | nacIsOne = npIsOne; |
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| 151 | nacIsMOne = npIsMOne; |
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| 152 | nacGcd = ndGcd; |
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| 153 | } |
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| 154 | } |
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| 155 | #ifdef TEST |
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| 156 | else |
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| 157 | { |
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| 158 | Print("hier ging was schief:c=%d compl=%d param=%d\n",i,complete,param); |
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| 159 | } |
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| 160 | #endif |
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| 161 | } |
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| 162 | |
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| 163 | /*============= procedure for polynomials: napXXXX =======================*/ |
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| 164 | |
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| 165 | /*3 |
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| 166 | * creates an alg poly |
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| 167 | */ |
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| 168 | static alg napInit(int i) |
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| 169 | { |
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| 170 | alg a = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 171 | |
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| 172 | a->ko = nacInit(i); |
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| 173 | if (!nacIsZero(a->ko)) |
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| 174 | { |
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| 175 | return a; |
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| 176 | } |
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| 177 | else |
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| 178 | { |
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| 179 | Free((ADDRESS)a, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 180 | return NULL; |
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| 181 | } |
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| 182 | } |
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| 183 | |
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| 184 | /*3 |
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| 185 | * creates an alg poly |
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| 186 | */ |
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| 187 | alg napInitz(number z) |
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| 188 | { |
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| 189 | alg a = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 190 | |
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| 191 | a->ko = z; |
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| 192 | return a; |
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| 193 | } |
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| 194 | |
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| 195 | /*3 |
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| 196 | * deletes head of an alg poly |
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| 197 | */ |
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| 198 | static void napDelete1(alg *p) |
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| 199 | { |
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| 200 | alg h = *p; |
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| 201 | |
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| 202 | if (h!=NULL) |
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| 203 | { |
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| 204 | *p = h->ne; |
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| 205 | nacDelete(&(h->ko)); |
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| 206 | Free((ADDRESS)h, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 207 | } |
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| 208 | } |
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| 209 | |
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| 210 | /*3 |
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| 211 | * delete an alg poly |
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| 212 | */ |
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| 213 | void napDelete(alg *p) |
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| 214 | { |
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| 215 | alg w, h = *p; |
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| 216 | |
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| 217 | while (h!=NULL) |
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| 218 | { |
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| 219 | w = h; |
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| 220 | h = h->ne; |
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| 221 | nacDelete(&(w->ko)); |
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| 222 | Free((ADDRESS)w, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 223 | } |
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| 224 | *p = NULL; |
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| 225 | } |
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| 226 | |
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| 227 | |
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| 228 | /*3 |
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| 229 | * copy a alg. poly |
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| 230 | */ |
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| 231 | static alg napCopy(alg p) |
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| 232 | { |
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| 233 | alg w, a; |
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| 234 | |
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| 235 | if (p==NULL) return NULL; |
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| 236 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 237 | a = w = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 238 | memcpy(w->e, p->e, naNumbOfPar * sizeof(int)); |
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| 239 | w->ko = nacCopy(p->ko); |
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| 240 | loop |
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| 241 | { |
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| 242 | p=p->ne; |
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| 243 | if (p==NULL) break; |
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| 244 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 245 | a->ne = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 246 | a = a->ne; |
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| 247 | memcpy(a->e, p->e, naNumbOfPar * sizeof(int)); |
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| 248 | a->ko = nacCopy(p->ko); |
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| 249 | } |
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| 250 | a->ne = NULL; |
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| 251 | return w; |
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| 252 | } |
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| 253 | |
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| 254 | /*3 |
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| 255 | * copy a alg. poly |
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| 256 | */ |
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| 257 | static alg napCopyNeg(alg p) |
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| 258 | { |
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| 259 | alg w, a; |
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| 260 | |
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| 261 | if (p==NULL) return NULL; |
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| 262 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 263 | a = w = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 264 | memcpy(w->e, p->e, naNumbOfPar * sizeof(int)); |
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| 265 | w->ko = nacNeg(nacCopy(p->ko)); |
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| 266 | loop |
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| 267 | { |
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| 268 | p=p->ne; |
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| 269 | if (p==NULL) break; |
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| 270 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 271 | a->ne = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 272 | a = a->ne; |
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| 273 | memcpy(a->e, p->e, naNumbOfPar * sizeof(int)); |
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| 274 | a->ko = nacNeg(nacCopy(p->ko)); |
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| 275 | } |
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| 276 | a->ne = NULL; |
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| 277 | return w; |
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| 278 | } |
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| 279 | |
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| 280 | /*3 |
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| 281 | * Compare exponents of p and q |
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| 282 | */ |
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| 283 | static int napComp(alg p, alg q) |
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| 284 | { |
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| 285 | int i = 0; |
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| 286 | |
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| 287 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 288 | mmTestP(q,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 289 | while (p->e[i] == q->e[i]) |
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| 290 | { |
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| 291 | i++; |
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| 292 | if (i >= naNumbOfPar) |
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| 293 | return 0; |
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| 294 | } |
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| 295 | if (p->e[i] > q->e[i]) |
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| 296 | return 1; |
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| 297 | else |
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| 298 | return - 1; |
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| 299 | } |
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| 300 | |
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| 301 | /*3 |
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| 302 | * addition of alg. polys |
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| 303 | */ |
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| 304 | alg napAdd(alg p1, alg p2) |
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| 305 | { |
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| 306 | alg a1, p, a2, a; |
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| 307 | int c; number t; |
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| 308 | |
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| 309 | if (p1==NULL) return p2; |
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| 310 | if (p2==NULL) return p1; |
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| 311 | mmTestP(p1,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 312 | mmTestP(p2,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 313 | a1 = p1; |
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| 314 | a2 = p2; |
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| 315 | a = p = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 316 | loop |
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| 317 | { |
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| 318 | c = napComp(a1, a2); |
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| 319 | if (c == 1) |
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| 320 | { |
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| 321 | a = a->ne = a1; |
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| 322 | a1 = a1->ne; |
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| 323 | if (!a1) |
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| 324 | { |
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| 325 | a->ne= a2; |
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| 326 | break; |
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| 327 | } |
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| 328 | mmTestP(a1,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 329 | } |
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| 330 | else if (c == -1) |
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| 331 | { |
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| 332 | a = a->ne = a2; |
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| 333 | a2 = a2->ne; |
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| 334 | if (!a2) |
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| 335 | { |
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| 336 | a->ne = a1; |
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| 337 | break; |
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| 338 | } |
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| 339 | mmTestP(a2,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 340 | } |
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| 341 | else |
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| 342 | { |
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| 343 | t = nacAdd(a1->ko, a2->ko); |
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| 344 | napDelete1(&a2); |
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| 345 | if (nacIsZero(t)) |
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| 346 | { |
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| 347 | nacDelete(&t); |
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| 348 | napDelete1(&a1); |
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| 349 | } |
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| 350 | else |
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| 351 | { |
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| 352 | nacDelete(&(a1->ko)); |
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| 353 | a1->ko = t; |
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| 354 | a = a->ne = a1; |
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| 355 | a1 = a1->ne; |
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| 356 | } |
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| 357 | if (a1==NULL) |
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| 358 | { |
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| 359 | a->ne = a2; |
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| 360 | break; |
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| 361 | } |
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| 362 | else if (a2==NULL) |
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| 363 | { |
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| 364 | a->ne = a1; |
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| 365 | break; |
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| 366 | } |
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| 367 | mmTestP(a1,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 368 | mmTestP(a2,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 369 | } |
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| 370 | } |
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| 371 | a = p->ne; |
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| 372 | Free((ADDRESS)p, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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| 373 | return a; |
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| 374 | } |
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| 375 | |
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| 376 | |
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| 377 | /*3 |
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| 378 | * multiply a alg. poly by -1 |
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| 379 | */ |
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| 380 | static alg napNeg(alg a) |
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| 381 | { |
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| 382 | alg p = a; |
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| 383 | |
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| 384 | while (p!=NULL) |
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| 385 | { |
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| 386 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 387 | p->ko = nacNeg(p->ko); |
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| 388 | p = p->ne; |
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| 389 | } |
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| 390 | return a; |
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| 391 | } |
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| 392 | |
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| 393 | /*3 |
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| 394 | * returns ph * z |
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| 395 | */ |
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| 396 | static void napMultN(alg p, number z) |
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| 397 | { |
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| 398 | number t; |
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| 399 | |
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| 400 | while (p!=NULL) |
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| 401 | { |
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| 402 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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| 403 | t = nacMult(p->ko, z); |
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| 404 | nacNormalize(t); |
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| 405 | nacDelete(&p->ko); |
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| 406 | p->ko = t; |
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| 407 | p = p->ne; |
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| 408 | } |
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| 409 | } |
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| 410 | |
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| 411 | /*3 |
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| 412 | * update the polynomial a by multipying it by |
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| 413 | * the (number) coefficient |
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| 414 | * and the exponent vector (of) exp (a well initialized polynomial) |
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| 415 | */ |
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| 416 | static void napMultT(alg a, alg exp) |
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| 417 | { |
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| 418 | int i; |
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| 419 | number t, h; |
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| 420 | if (a==NULL) |
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| 421 | return; |
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| 422 | h = exp->ko; |
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| 423 | if (nacIsOne(h)) |
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| 424 | { |
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| 425 | do |
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| 426 | { |
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| 427 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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| 428 | a->e[i] += exp->e[i]; |
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| 429 | a = a->ne; |
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| 430 | } |
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| 431 | while (a!=NULL); |
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| 432 | } |
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| 433 | else |
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| 434 | { |
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| 435 | h = nacNeg(h); |
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| 436 | if (nacIsOne(h)) |
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| 437 | { |
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| 438 | h = nacNeg(h); |
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| 439 | do |
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| 440 | { |
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| 441 | a->ko = nacNeg(a->ko); |
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| 442 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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| 443 | a->e[i] += exp->e[i]; |
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| 444 | a = a->ne; |
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| 445 | } |
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| 446 | while (a!=NULL); |
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| 447 | } |
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| 448 | else |
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| 449 | { |
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| 450 | h = nacNeg(h); |
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| 451 | do |
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| 452 | { |
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| 453 | t = nacMult(a->ko, h); |
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| 454 | nacDelete(&(a->ko)); |
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| 455 | a->ko = t; |
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| 456 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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| 457 | a->e[i] += exp->e[i]; |
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| 458 | a = a->ne; |
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| 459 | } |
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| 460 | while (a!=NULL); |
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| 461 | } |
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| 462 | } |
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| 463 | } |
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| 464 | |
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| 465 | /*3 |
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| 466 | * multiplication of alg. polys |
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| 467 | * multiply p1 with p2, p1 and p2 are destroyed |
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| 468 | * do not put attention on speed: the procedure is only used in the interpreter |
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| 469 | */ |
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| 470 | static alg napMult(alg p1, alg p2) |
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| 471 | { |
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| 472 | alg a1, a2, b, h; |
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| 473 | if (p1==NULL) |
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| 474 | { |
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| 475 | napDelete(&p2); |
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| 476 | return NULL; |
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| 477 | } |
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| 478 | if (p2==NULL) |
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| 479 | { |
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| 480 | napDelete(&p1); |
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| 481 | return NULL; |
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| 482 | } |
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| 483 | b = NULL; |
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| 484 | a1 = p1; |
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| 485 | a2 = p2; |
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| 486 | if (a2->ne!=NULL) |
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| 487 | { |
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| 488 | if (a1->ne!=NULL) |
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| 489 | { |
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| 490 | do |
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| 491 | { |
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| 492 | a1 = a1->ne; |
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| 493 | a2 = a2->ne; |
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| 494 | } |
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| 495 | while ((a1!=NULL) && (a2!=NULL)); |
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| 496 | if (a1!=NULL) |
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| 497 | { |
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| 498 | a1 = p1; |
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| 499 | a2 = p2; |
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| 500 | } |
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| 501 | else |
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| 502 | { |
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| 503 | a1 = p2; |
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| 504 | a2 = p1; |
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| 505 | } |
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| 506 | do |
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| 507 | { |
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| 508 | if (a2->ne!=NULL) |
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| 509 | h = napCopy(a1); |
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| 510 | else |
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| 511 | h = a1; |
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| 512 | napMultT(h, a2); |
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| 513 | b = napAdd(h, b); |
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| 514 | napDelete1(&a2); |
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| 515 | } |
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| 516 | while (a2!=NULL); |
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| 517 | } |
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| 518 | else |
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| 519 | { |
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| 520 | napMultT(a2, a1); |
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| 521 | b = napAdd(a2, b); |
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| 522 | napDelete1(&a1); |
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| 523 | } |
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| 524 | } |
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| 525 | else |
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| 526 | { |
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| 527 | napMultT(a1, a2); |
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| 528 | b = napAdd(a1, b); |
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| 529 | napDelete1(&a2); |
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| 530 | } |
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| 531 | return b; |
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| 532 | } |
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| 533 | |
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| 534 | /*3 |
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| 535 | * division with rest; f = g*q + r, returns r and destroy f |
---|
| 536 | */ |
---|
| 537 | static alg napRemainder(alg f, const alg g) |
---|
| 538 | { |
---|
| 539 | alg a, h, qq; |
---|
| 540 | |
---|
| 541 | qq = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 542 | qq->ne = NULL; |
---|
| 543 | a = f; |
---|
| 544 | do |
---|
| 545 | { |
---|
| 546 | mmTestP(a,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
| 547 | mmTestP(g,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
| 548 | qq->e[0] = a->e[0] - g->e[0]; |
---|
| 549 | qq->ko = nacDiv(a->ko, g->ko); |
---|
| 550 | qq->ko = nacNeg(qq->ko); |
---|
| 551 | h = napCopy(g); |
---|
| 552 | napMultT(h, qq); |
---|
| 553 | nacDelete(&(qq->ko)); |
---|
| 554 | a = napAdd(a, h); |
---|
| 555 | } |
---|
| 556 | while ((a!=NULL) && (a->e[0] >= g->e[0])); |
---|
| 557 | Free((ADDRESS)qq, RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 558 | return a; |
---|
| 559 | } |
---|
| 560 | |
---|
| 561 | /*3 |
---|
| 562 | * division with rest; f = g*q + r, destroy f |
---|
| 563 | */ |
---|
| 564 | static void napDivMod(alg f, alg g, alg *q, alg *r) |
---|
| 565 | { |
---|
| 566 | alg a, h, b, qq; |
---|
| 567 | |
---|
| 568 | qq = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 569 | qq->ne = b = NULL; |
---|
| 570 | a = f; |
---|
| 571 | do |
---|
| 572 | { |
---|
| 573 | mmTestP(a,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
| 574 | mmTestP(g,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
| 575 | qq->e[0] = a->e[0] - g->e[0]; |
---|
| 576 | qq->ko = nacDiv(a->ko, g->ko); |
---|
| 577 | b = napAdd(b, napCopy(qq)); |
---|
| 578 | qq->ko = nacNeg(qq->ko); |
---|
| 579 | h = napCopy(g); |
---|
| 580 | napMultT(h, qq); |
---|
| 581 | nacDelete(&(qq->ko)); |
---|
| 582 | a = napAdd(a, h); |
---|
| 583 | } |
---|
| 584 | while ((a!=NULL) && (a->e[0] >= g->e[0])); |
---|
| 585 | Free((ADDRESS)qq, RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 586 | *q = b; |
---|
| 587 | *r = a; |
---|
| 588 | } |
---|
| 589 | |
---|
| 590 | /*3 |
---|
| 591 | * returns z with z*x mod c = 1 |
---|
| 592 | */ |
---|
| 593 | static alg napInvers(alg x, const alg c) |
---|
| 594 | { |
---|
| 595 | alg y, r, qa, qn, q; |
---|
| 596 | number t, h; |
---|
| 597 | |
---|
| 598 | if (x->e[0] >= c->e[0]) |
---|
| 599 | x = napRemainder(x, c); |
---|
| 600 | if (x->e[0]==0) |
---|
| 601 | { |
---|
| 602 | if (!nacIsOne(x->ko)) |
---|
| 603 | { |
---|
| 604 | h = nacInit(1); |
---|
| 605 | t = nacDiv(h, x->ko); |
---|
| 606 | nacDelete(&(x->ko)); |
---|
| 607 | nacDelete(&h); |
---|
| 608 | x->ko = t; |
---|
| 609 | } |
---|
| 610 | return x; |
---|
| 611 | } |
---|
| 612 | y = napCopy(c); |
---|
| 613 | napDivMod(y, x, &qa, &r); |
---|
| 614 | if (r->e[0]==0) |
---|
| 615 | { |
---|
| 616 | h = nacInit(-1); |
---|
| 617 | t = nacDiv(h, r->ko); |
---|
| 618 | nacNormalize(t); |
---|
| 619 | napMultN(qa, t); |
---|
| 620 | nacDelete(&h); |
---|
| 621 | nacDelete(&t); |
---|
| 622 | napDelete(&x); |
---|
| 623 | napDelete(&r); |
---|
| 624 | return qa; |
---|
| 625 | } |
---|
| 626 | y = x; |
---|
| 627 | x = r; |
---|
| 628 | napDivMod(y, x, &q, &r); |
---|
| 629 | if (r->e[0]==0) |
---|
| 630 | { |
---|
| 631 | q = napMult(q, qa); |
---|
| 632 | q = napAdd(q, napInit(1)); |
---|
| 633 | h = nacInit(1); |
---|
| 634 | t = nacDiv(h, r->ko); |
---|
| 635 | napMultN(q, t); |
---|
| 636 | nacDelete(&h); |
---|
| 637 | nacDelete(&t); |
---|
| 638 | napDelete(&x); |
---|
| 639 | napDelete(&r); |
---|
| 640 | if (q->e[0] >= c->e[0]) |
---|
| 641 | q = napRemainder(q, c); |
---|
| 642 | return q; |
---|
| 643 | } |
---|
| 644 | q = napMult(q, napCopy(qa)); |
---|
| 645 | q = napAdd(q, napInit(1)); |
---|
| 646 | qa = napNeg(qa); |
---|
| 647 | loop |
---|
| 648 | { |
---|
| 649 | y = x; |
---|
| 650 | x = r; |
---|
| 651 | napDivMod(y, x, &qn, &r); |
---|
| 652 | if (r->e[0]==0) |
---|
| 653 | { |
---|
| 654 | q = napMult(q, qn); |
---|
| 655 | q = napNeg(q); |
---|
| 656 | q = napAdd(q, qa); |
---|
| 657 | h = nacInit(1); |
---|
| 658 | t = nacDiv(h, r->ko); |
---|
| 659 | napMultN(q, t); |
---|
| 660 | nacDelete(&h); |
---|
| 661 | nacDelete(&t); |
---|
| 662 | napDelete(&x); |
---|
| 663 | napDelete(&r); |
---|
| 664 | if (q->e[0] >= c->e[0]) |
---|
| 665 | q = napRemainder(q, c); |
---|
| 666 | return q; |
---|
| 667 | } |
---|
| 668 | y = q; |
---|
| 669 | q = napMult(napCopy(q), qn); |
---|
| 670 | q = napNeg(q); |
---|
| 671 | q = napAdd(q, qa); |
---|
| 672 | qa = y; |
---|
| 673 | } |
---|
| 674 | } |
---|
| 675 | |
---|
| 676 | /*3 |
---|
| 677 | * the degree of an alg poly (used for test of "constant" et al.) |
---|
| 678 | */ |
---|
| 679 | static int napDeg(alg p) |
---|
| 680 | { |
---|
| 681 | int d = 0, i; |
---|
| 682 | |
---|
| 683 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
| 684 | for (i = naNumbOfPar-1; i>=0; i--) |
---|
| 685 | d += p->e[i]; |
---|
| 686 | return d; |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | /*3 |
---|
| 690 | *writes a polynomial number |
---|
| 691 | */ |
---|
| 692 | static void napWrite(alg p) |
---|
| 693 | { |
---|
| 694 | int i; |
---|
| 695 | if (p==NULL) |
---|
| 696 | StringAppendS("0"); |
---|
| 697 | else |
---|
| 698 | { |
---|
| 699 | StringAppendS("("); |
---|
| 700 | loop |
---|
| 701 | { |
---|
| 702 | BOOLEAN wroteCoeff=FALSE; |
---|
| 703 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
| 704 | if ((napDeg(p)==0) |
---|
| 705 | || (!nacIsOne(p->ko))) |
---|
| 706 | { |
---|
| 707 | nacWrite(p->ko); |
---|
| 708 | wroteCoeff=(pShortOut==0); |
---|
| 709 | } |
---|
| 710 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
| 711 | { |
---|
| 712 | if (p->e[i] > 0) |
---|
| 713 | { |
---|
| 714 | if (wroteCoeff) |
---|
| 715 | StringAppendS("*"); |
---|
| 716 | else |
---|
| 717 | wroteCoeff=(pShortOut==0); |
---|
| 718 | StringAppend(naParNames[i]); |
---|
| 719 | if (p->e[i] > 1) |
---|
| 720 | { |
---|
| 721 | if (pShortOut == 0) |
---|
| 722 | StringAppendS("^"); |
---|
| 723 | StringAppend("%d", p->e[i]); |
---|
| 724 | } |
---|
| 725 | } |
---|
| 726 | } |
---|
| 727 | p = p->ne; |
---|
| 728 | if (p==NULL) |
---|
| 729 | break; |
---|
| 730 | if (nacGreaterZero(p->ko)) |
---|
| 731 | StringAppendS("+"); |
---|
| 732 | } |
---|
| 733 | StringAppendS(")"); |
---|
| 734 | } |
---|
| 735 | } |
---|
| 736 | |
---|
| 737 | |
---|
| 738 | static char *napHandleMons(char *s, int i, int *ex) |
---|
| 739 | { |
---|
| 740 | int j; |
---|
| 741 | if (strncmp(s,naParNames[i],strlen(naParNames[i]))==0) |
---|
| 742 | { |
---|
| 743 | s+=strlen(naParNames[i]); |
---|
| 744 | if ((*s >= '0') && (*s <= '9')) |
---|
| 745 | { |
---|
| 746 | s = eati(s, &j); |
---|
| 747 | ex[i] += j; |
---|
| 748 | } |
---|
| 749 | else |
---|
| 750 | ex[i]++; |
---|
| 751 | } |
---|
| 752 | return s; |
---|
| 753 | } |
---|
| 754 | |
---|
| 755 | /*3 reads a monomial */ |
---|
| 756 | static char *napRead(char *s, alg *b) |
---|
| 757 | { |
---|
| 758 | alg a; |
---|
| 759 | int i; |
---|
| 760 | a = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 761 | if ((*s >= '0') && (*s <= '9')) |
---|
| 762 | { |
---|
| 763 | s = nacRead(s, &(a->ko)); |
---|
| 764 | if (nacIsZero(a->ko)) |
---|
| 765 | { |
---|
| 766 | napDelete1(&a); |
---|
| 767 | *b = NULL; |
---|
| 768 | return s; |
---|
| 769 | } |
---|
| 770 | } |
---|
| 771 | else |
---|
| 772 | a->ko = nacInit(1); |
---|
| 773 | i = 0; |
---|
| 774 | char *olds; |
---|
| 775 | loop |
---|
| 776 | { |
---|
| 777 | olds = s; |
---|
| 778 | s = napHandleMons(s, i, a->e); |
---|
| 779 | if (olds == s) |
---|
| 780 | i++; |
---|
| 781 | else |
---|
| 782 | i = 0; |
---|
| 783 | if ((*s == '\0') || (i >= naNumbOfPar)) |
---|
| 784 | break; |
---|
| 785 | } |
---|
| 786 | *b = a; |
---|
| 787 | return s; |
---|
| 788 | } |
---|
| 789 | |
---|
| 790 | static int napExp(alg a, alg b) |
---|
| 791 | { |
---|
| 792 | while (a->ne!=NULL) a = a->ne; |
---|
| 793 | int m = a->e[0]; |
---|
| 794 | if (m==0) return m; |
---|
| 795 | while (b->ne!=NULL) b = b->ne; |
---|
| 796 | if (m > b->e[0]) m = b->e[0]; |
---|
| 797 | return m; |
---|
| 798 | } |
---|
| 799 | |
---|
| 800 | #if FEHLER2 |
---|
| 801 | /*meins |
---|
| 802 | * finds the smallest i-th exponent in a and b |
---|
| 803 | * used to find it in a fraction |
---|
| 804 | */ |
---|
| 805 | static int napExpi(int i, alg a, alg b) |
---|
| 806 | { |
---|
| 807 | if (a==NULL || b==NULL) return 0; |
---|
| 808 | int m = a->e[i]; |
---|
| 809 | if (m==0) return 0; |
---|
| 810 | while (a->ne != NULL) |
---|
| 811 | { |
---|
| 812 | a = a->ne; |
---|
| 813 | if (m > a->e[i]) |
---|
| 814 | { |
---|
| 815 | m = a->e[i]; |
---|
| 816 | if (m==0) return 0; |
---|
| 817 | } |
---|
| 818 | } |
---|
| 819 | do |
---|
| 820 | { |
---|
| 821 | if (m > b->e[i]) |
---|
| 822 | { |
---|
| 823 | m = b->e[i]; |
---|
| 824 | if (m==0) return 0; |
---|
| 825 | } |
---|
| 826 | b = b->ne; |
---|
| 827 | } |
---|
| 828 | while (b != NULL); |
---|
| 829 | return m; |
---|
| 830 | } |
---|
| 831 | #endif |
---|
| 832 | |
---|
| 833 | static void napContent(alg ph) |
---|
| 834 | { |
---|
| 835 | number h,d; |
---|
| 836 | alg p; |
---|
| 837 | |
---|
| 838 | p = ph; |
---|
| 839 | if (nacIsOne(p->ko)) |
---|
| 840 | return; |
---|
| 841 | h = nacCopy(p->ko); |
---|
| 842 | p = p->ne; |
---|
| 843 | do |
---|
| 844 | { |
---|
| 845 | d=nacGcd(p->ko, h); |
---|
| 846 | if(nacIsOne(d)) |
---|
| 847 | { |
---|
| 848 | nacDelete(&h); |
---|
| 849 | nacDelete(&d); |
---|
| 850 | return; |
---|
| 851 | } |
---|
| 852 | nacDelete(&h); |
---|
| 853 | h = d; |
---|
| 854 | p = p->ne; |
---|
| 855 | } |
---|
| 856 | while (p!=NULL); |
---|
| 857 | h = nacInvers(d); |
---|
| 858 | nacDelete(&d); |
---|
| 859 | p = ph; |
---|
| 860 | while (p!=NULL) |
---|
| 861 | { |
---|
| 862 | d = nacMult(p->ko, h); |
---|
| 863 | nacDelete(&(p->ko)); |
---|
| 864 | p->ko = d; |
---|
| 865 | p = p->ne; |
---|
| 866 | } |
---|
| 867 | nacDelete(&h); |
---|
| 868 | } |
---|
| 869 | |
---|
| 870 | static void napCleardenom(alg ph) |
---|
| 871 | { |
---|
| 872 | number d, h; |
---|
| 873 | alg p; |
---|
| 874 | |
---|
| 875 | if (!naIsChar0) |
---|
| 876 | return; |
---|
| 877 | p = ph; |
---|
| 878 | h = nacInit(1); |
---|
| 879 | while (p!=NULL) |
---|
| 880 | { |
---|
| 881 | d = nacLcm(h, p->ko); |
---|
| 882 | nacDelete(&h); |
---|
| 883 | h = d; |
---|
| 884 | p = p->ne; |
---|
| 885 | } |
---|
| 886 | if(!nacIsOne(h)) |
---|
| 887 | { |
---|
| 888 | p = ph; |
---|
| 889 | while (p!=NULL) |
---|
| 890 | { |
---|
| 891 | d=nacMult(h, p->ko); |
---|
| 892 | nacDelete(&(p->ko)); |
---|
| 893 | p->ko = d; |
---|
| 894 | p = p->ne; |
---|
| 895 | } |
---|
| 896 | nacDelete(&h); |
---|
| 897 | } |
---|
| 898 | napContent(ph); |
---|
| 899 | } |
---|
| 900 | |
---|
| 901 | static alg napGcd0(alg a, alg b) |
---|
| 902 | { |
---|
| 903 | number x, y; |
---|
| 904 | if (!naIsChar0) |
---|
| 905 | return napInit(1); |
---|
| 906 | x = nacCopy(a->ko); |
---|
| 907 | if (nacIsOne(x)) |
---|
| 908 | return napInitz(x); |
---|
| 909 | while (a->ne!=NULL) |
---|
| 910 | { |
---|
| 911 | a = a->ne; |
---|
| 912 | y = nacGcd(x, a->ko); |
---|
| 913 | nacDelete(&x); |
---|
| 914 | x = y; |
---|
| 915 | if (nacIsOne(x)) |
---|
| 916 | return napInitz(x); |
---|
| 917 | } |
---|
| 918 | do |
---|
| 919 | { |
---|
| 920 | y = nacGcd(x, b->ko); |
---|
| 921 | nacDelete(&x); |
---|
| 922 | x = y; |
---|
| 923 | if (nacIsOne(x)) |
---|
| 924 | return napInitz(x); |
---|
| 925 | b = b->ne; |
---|
| 926 | } |
---|
| 927 | while (b!=NULL); |
---|
| 928 | return napInitz(x); |
---|
| 929 | } |
---|
| 930 | |
---|
| 931 | /*3 |
---|
| 932 | * result =gcd(a,b) |
---|
| 933 | */ |
---|
| 934 | static alg napGcd(alg a, alg b) |
---|
| 935 | { |
---|
| 936 | int i; |
---|
| 937 | alg g, x, y, h; |
---|
| 938 | if ((a==NULL) |
---|
| 939 | || ((a->ne==NULL)&&(nacIsZero(a->ko)))) |
---|
| 940 | { |
---|
| 941 | if ((b==NULL) |
---|
| 942 | || ((b->ne==NULL)&&(nacIsZero(b->ko)))) |
---|
| 943 | { |
---|
| 944 | return napInit(1); |
---|
| 945 | } |
---|
| 946 | return napCopy(b); |
---|
| 947 | } |
---|
| 948 | if (naMinimalPoly != NULL) |
---|
| 949 | { |
---|
| 950 | if (a->e[0] >= b->e[0]) |
---|
| 951 | { |
---|
| 952 | x = a; |
---|
| 953 | y = b; |
---|
| 954 | } |
---|
| 955 | else |
---|
| 956 | { |
---|
| 957 | x = b; |
---|
| 958 | y = a; |
---|
| 959 | } |
---|
| 960 | g = napGcd0(x, y); |
---|
| 961 | if (y->ne==NULL) |
---|
| 962 | { |
---|
| 963 | g->e[0] = napExp(x, y); |
---|
| 964 | return g; |
---|
| 965 | } |
---|
| 966 | x = napCopy(x); |
---|
| 967 | y = napCopy(y); |
---|
| 968 | loop |
---|
| 969 | { |
---|
| 970 | h = napRemainder(x, y); |
---|
| 971 | if (h==NULL) |
---|
| 972 | { |
---|
| 973 | napCleardenom(y); |
---|
| 974 | if (!nacIsOne(g->ko)) napMultN(y, g->ko); |
---|
| 975 | napDelete1(&g); |
---|
| 976 | return y; |
---|
| 977 | } |
---|
| 978 | else if (h->ne==NULL) |
---|
| 979 | break; |
---|
| 980 | x = y; |
---|
| 981 | y = h; |
---|
| 982 | } |
---|
| 983 | napDelete(&y); |
---|
| 984 | napDelete1(&h); |
---|
| 985 | g->e[0] = napExp(a, b); |
---|
| 986 | return g; |
---|
| 987 | } |
---|
| 988 | x = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 989 | g=a; |
---|
| 990 | h=b; |
---|
| 991 | x = napGcd0(g,h); |
---|
| 992 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
| 993 | x->e[i] = napExpi(i,a,b); |
---|
| 994 | return x; |
---|
| 995 | } |
---|
| 996 | |
---|
| 997 | |
---|
| 998 | number napLcm(alg a) |
---|
| 999 | { |
---|
| 1000 | number d, h; |
---|
| 1001 | alg b; |
---|
| 1002 | |
---|
| 1003 | h = nacInit(1); |
---|
| 1004 | b = a; |
---|
| 1005 | while (b!=NULL) |
---|
| 1006 | { |
---|
| 1007 | d = nacLcm(h, b->ko); |
---|
| 1008 | nacDelete(&h); |
---|
| 1009 | h = d; |
---|
| 1010 | b = b->ne; |
---|
| 1011 | } |
---|
| 1012 | return h; |
---|
| 1013 | } |
---|
| 1014 | |
---|
| 1015 | |
---|
| 1016 | /*2 |
---|
| 1017 | * meins (for reduction in algebraic extension) |
---|
| 1018 | * checks if head of p divides head of q |
---|
| 1019 | * doesn't delete p and q |
---|
| 1020 | */ |
---|
| 1021 | BOOLEAN napDivPoly (alg p, alg q) |
---|
| 1022 | { |
---|
| 1023 | int j=0; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
| 1024 | |
---|
| 1025 | while (p->e[j] <= q->e[j]) |
---|
| 1026 | { |
---|
| 1027 | j++; |
---|
| 1028 | if (j >= naNumbOfPar) |
---|
| 1029 | return 1; |
---|
| 1030 | } |
---|
| 1031 | return 0; |
---|
| 1032 | } |
---|
| 1033 | |
---|
| 1034 | |
---|
| 1035 | /*2 |
---|
| 1036 | * meins (for reduction in algebraic extension) |
---|
| 1037 | * Normalform of poly with naI |
---|
| 1038 | * changes q and returns it |
---|
| 1039 | */ |
---|
| 1040 | alg napRedp (alg q) |
---|
| 1041 | { |
---|
| 1042 | alg h = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 1043 | int i=0,j; |
---|
| 1044 | |
---|
| 1045 | loop |
---|
| 1046 | { |
---|
| 1047 | if (napDivPoly (naI->liste[i], q)) |
---|
| 1048 | { |
---|
| 1049 | mmTestP((ADDRESS)q,RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 1050 | StringSetS(""); |
---|
| 1051 | napWrite(q); |
---|
| 1052 | napWrite(naI->liste[i]); |
---|
| 1053 | Print(StringAppendS("\n")); |
---|
| 1054 | /* h = lt(q)/lt(naI->liste[i])*/ |
---|
| 1055 | h->ko = nacCopy(q->ko); |
---|
| 1056 | for (j=naNumbOfPar-1; j>=0; j--) |
---|
| 1057 | h->e[j] = q->e[j] - naI->liste[i]->e[j]; |
---|
| 1058 | h = napMult (h, napCopy(naI->liste[i])); |
---|
| 1059 | h = napNeg (h); |
---|
| 1060 | q = napAdd (q, napCopy(h)); |
---|
| 1061 | napDelete (&(h->ne)); |
---|
| 1062 | if (q == NULL) |
---|
| 1063 | { |
---|
| 1064 | napDelete(&h); |
---|
| 1065 | return q; |
---|
| 1066 | } |
---|
| 1067 | /* try to reduce further */ |
---|
| 1068 | i = 0; |
---|
| 1069 | } |
---|
| 1070 | else |
---|
| 1071 | { |
---|
| 1072 | i++; |
---|
| 1073 | if (i >= naI->anz) |
---|
| 1074 | { |
---|
| 1075 | napDelete(&h); |
---|
| 1076 | return q; |
---|
| 1077 | } |
---|
| 1078 | } |
---|
| 1079 | } |
---|
| 1080 | } |
---|
| 1081 | |
---|
| 1082 | |
---|
| 1083 | /*2 |
---|
| 1084 | * meins (for reduction in algebraic extension) |
---|
| 1085 | * reduces the tail of Poly q |
---|
| 1086 | * needs q != NULL |
---|
| 1087 | * changes q and returns it |
---|
| 1088 | */ |
---|
| 1089 | alg napTailred (alg q) |
---|
| 1090 | { |
---|
| 1091 | alg h; |
---|
| 1092 | |
---|
| 1093 | h = q->ne; |
---|
| 1094 | while (h != NULL) |
---|
| 1095 | { |
---|
| 1096 | h = napRedp (h); |
---|
| 1097 | if (h == NULL) |
---|
| 1098 | return q; |
---|
| 1099 | h = h->ne; |
---|
| 1100 | } |
---|
| 1101 | return q; |
---|
| 1102 | } |
---|
| 1103 | |
---|
| 1104 | |
---|
| 1105 | /*================ procedure for rational functions: naXXXX =================*/ |
---|
| 1106 | |
---|
| 1107 | /*2 |
---|
| 1108 | * z:= i |
---|
| 1109 | */ |
---|
| 1110 | number naInit(int i) |
---|
| 1111 | { |
---|
| 1112 | if (i!=0) |
---|
| 1113 | { |
---|
| 1114 | lnumber l = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1115 | l->z = napInit(i); |
---|
| 1116 | if (l->z==NULL) |
---|
| 1117 | { |
---|
| 1118 | Free((ADDRESS)l, sizeof(rnumber)); |
---|
| 1119 | return NULL; |
---|
| 1120 | } |
---|
| 1121 | l->s = 2; |
---|
| 1122 | l->n = NULL; |
---|
| 1123 | return (number)l; |
---|
| 1124 | } |
---|
| 1125 | /*else*/ |
---|
| 1126 | return NULL; |
---|
| 1127 | } |
---|
| 1128 | |
---|
| 1129 | number naPar(int i) |
---|
| 1130 | { |
---|
| 1131 | lnumber l = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1132 | l->s = 2; |
---|
| 1133 | l->z = napInit(1); |
---|
| 1134 | l->z->e[i-1]=1; |
---|
| 1135 | l->n = NULL; |
---|
| 1136 | return (number)l; |
---|
| 1137 | } |
---|
| 1138 | |
---|
| 1139 | int naParDeg(number n) /* i := deg(n) */ |
---|
| 1140 | { |
---|
| 1141 | lnumber l = (lnumber)n; |
---|
| 1142 | if (l==NULL) return -1; |
---|
| 1143 | return napDeg(l->z); |
---|
| 1144 | } |
---|
| 1145 | |
---|
| 1146 | /*2 |
---|
| 1147 | * convert a number to int (if possible) |
---|
| 1148 | */ |
---|
| 1149 | int naInt(number &n) |
---|
| 1150 | { |
---|
| 1151 | lnumber l=(lnumber)n; |
---|
| 1152 | if ((l!=NULL)&&(l->n==NULL)&&(napDeg(l->z)==0)) |
---|
| 1153 | { |
---|
| 1154 | return nacInt(l->z->ko); |
---|
| 1155 | } |
---|
| 1156 | return 0; |
---|
| 1157 | } |
---|
| 1158 | |
---|
| 1159 | /*2 |
---|
| 1160 | * deletes p |
---|
| 1161 | */ |
---|
| 1162 | #ifdef LDEBUG |
---|
| 1163 | void naDBDelete(number *p,char *f, int lno) |
---|
| 1164 | #else |
---|
| 1165 | void naDelete(number *p) |
---|
| 1166 | #endif |
---|
| 1167 | { |
---|
| 1168 | lnumber l = (lnumber) * p; |
---|
| 1169 | if (l==NULL) return; |
---|
| 1170 | napDelete(&(l->z)); |
---|
| 1171 | napDelete(&(l->n)); |
---|
| 1172 | #if defined(MDEBUG) && defined(LDEBUG) |
---|
| 1173 | mmDBFreeBlock((ADDRESS)l, sizeof(rnumber),f,lno); |
---|
| 1174 | #else |
---|
| 1175 | Free((ADDRESS)l, sizeof(rnumber)); |
---|
| 1176 | #endif |
---|
| 1177 | *p = NULL; |
---|
| 1178 | } |
---|
| 1179 | |
---|
| 1180 | /*2 |
---|
| 1181 | * copy p to erg |
---|
| 1182 | */ |
---|
| 1183 | number naCopy(number p) |
---|
| 1184 | { |
---|
| 1185 | if (p==NULL) return NULL; |
---|
| 1186 | naTest(p); |
---|
| 1187 | lnumber erg; |
---|
| 1188 | lnumber src = (lnumber)p; |
---|
| 1189 | erg = (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 1190 | erg->z = napCopy(src->z); |
---|
| 1191 | erg->n = napCopy(src->n); |
---|
| 1192 | erg->s = src->s; |
---|
| 1193 | return (number)erg; |
---|
| 1194 | } |
---|
| 1195 | |
---|
| 1196 | /*2 |
---|
| 1197 | * a dummy number: 0 |
---|
| 1198 | */ |
---|
| 1199 | void naNew(number *z) |
---|
| 1200 | { |
---|
| 1201 | *z = NULL; |
---|
| 1202 | } |
---|
| 1203 | |
---|
| 1204 | /*2 |
---|
| 1205 | * addition; lu:= la + lb |
---|
| 1206 | */ |
---|
| 1207 | number naAdd(number la, number lb) |
---|
| 1208 | { |
---|
| 1209 | alg x, y; |
---|
| 1210 | lnumber lu; |
---|
| 1211 | lnumber a = (lnumber)la; |
---|
| 1212 | lnumber b = (lnumber)lb; |
---|
| 1213 | if (a==NULL) return naCopy(lb); |
---|
| 1214 | if (b==NULL) return naCopy(la); |
---|
| 1215 | mmTestP(a,sizeof(rnumber)); |
---|
| 1216 | mmTestP(b,sizeof(rnumber)); |
---|
| 1217 | lu = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1218 | if (b->n!=NULL) x = napMult(napCopy(a->z), napCopy(b->n)); |
---|
| 1219 | else x = napCopy(a->z); |
---|
| 1220 | if (a->n!=NULL) y = napMult(napCopy(b->z), napCopy(a->n)); |
---|
| 1221 | else y = napCopy(b->z); |
---|
| 1222 | lu->z = napAdd(x, y); |
---|
| 1223 | if (lu->z==NULL) |
---|
| 1224 | { |
---|
| 1225 | Free((ADDRESS)lu, sizeof(rnumber)); |
---|
| 1226 | return (number)NULL; |
---|
| 1227 | } |
---|
| 1228 | if (a->n!=NULL) |
---|
| 1229 | { |
---|
| 1230 | if (b->n!=NULL) x = napMult(napCopy(a->n), napCopy(b->n)); |
---|
| 1231 | else x = napCopy(a->n); |
---|
| 1232 | } |
---|
| 1233 | else |
---|
| 1234 | { |
---|
| 1235 | if (b->n!=NULL) x = napCopy(b->n); |
---|
| 1236 | else x = NULL; |
---|
| 1237 | } |
---|
| 1238 | if ((x!=NULL) && (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1239 | napDelete(&x); |
---|
| 1240 | lu->n = x; |
---|
| 1241 | lu->s = 0; |
---|
| 1242 | naTest((number)lu); |
---|
| 1243 | return (number)lu; |
---|
| 1244 | } |
---|
| 1245 | |
---|
| 1246 | /*2 |
---|
| 1247 | * subtraction; r:= la - lb |
---|
| 1248 | */ |
---|
| 1249 | number naSub(number la, number lb) |
---|
| 1250 | { |
---|
| 1251 | lnumber lu; |
---|
| 1252 | |
---|
| 1253 | if (lb==NULL) return naCopy(la); |
---|
| 1254 | if (la==NULL) |
---|
| 1255 | { |
---|
| 1256 | //if (lb!=NULL) |
---|
| 1257 | //{ |
---|
| 1258 | lu = (lnumber)naCopy(lb); |
---|
| 1259 | lu->z = napNeg(lu->z); |
---|
| 1260 | return (number)lu; |
---|
| 1261 | //} |
---|
| 1262 | //else |
---|
| 1263 | // return NULL; |
---|
| 1264 | } |
---|
| 1265 | |
---|
| 1266 | alg x, y; |
---|
| 1267 | lnumber a = (lnumber)la; |
---|
| 1268 | lnumber b = (lnumber)lb; |
---|
| 1269 | |
---|
| 1270 | mmTestP(a,sizeof(rnumber)); |
---|
| 1271 | mmTestP(b,sizeof(rnumber)); |
---|
| 1272 | lu = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1273 | if (b->n!=NULL) x = napMult(napCopy(a->z), napCopy(b->n)); |
---|
| 1274 | else x = napCopy(a->z); |
---|
| 1275 | if (a->n!=NULL) y = napMult(napCopy(b->z), napCopyNeg(a->n)); |
---|
| 1276 | else y = napCopyNeg(b->z); |
---|
| 1277 | lu->z = napAdd(x, y); |
---|
| 1278 | if (lu->z==NULL) |
---|
| 1279 | { |
---|
| 1280 | Free((ADDRESS)lu, sizeof(rnumber)); |
---|
| 1281 | return (number)NULL; |
---|
| 1282 | } |
---|
| 1283 | if (a->n!=NULL) |
---|
| 1284 | { |
---|
| 1285 | if (b->n!=NULL) x = napMult(napCopy(a->n), napCopy(b->n)); |
---|
| 1286 | else x = napCopy(a->n); |
---|
| 1287 | } |
---|
| 1288 | else |
---|
| 1289 | { |
---|
| 1290 | if (b->n!=NULL) x = napCopy(b->n); |
---|
| 1291 | else x = NULL; |
---|
| 1292 | } |
---|
| 1293 | if ((x!=NULL)&& (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1294 | napDelete(&x); |
---|
| 1295 | lu->n = x; |
---|
| 1296 | lu->s = 0; |
---|
| 1297 | naTest((number)lu); |
---|
| 1298 | return (number)lu; |
---|
| 1299 | } |
---|
| 1300 | |
---|
| 1301 | /*2 |
---|
| 1302 | * multiplication; r:= la * lb |
---|
| 1303 | */ |
---|
| 1304 | number naMult(number la, number lb) |
---|
| 1305 | { |
---|
| 1306 | if ((la==NULL) || (lb==NULL)) |
---|
| 1307 | return NULL; |
---|
| 1308 | |
---|
| 1309 | lnumber a = (lnumber)la; |
---|
| 1310 | lnumber b = (lnumber)lb; |
---|
| 1311 | lnumber lo; |
---|
| 1312 | alg x; |
---|
| 1313 | |
---|
| 1314 | mmTestP(a,sizeof(rnumber)); |
---|
| 1315 | mmTestP(b,sizeof(rnumber)); |
---|
| 1316 | lo = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1317 | lo->z = napMult(napCopy(a->z), napCopy(b->z)); |
---|
| 1318 | if (a->n==NULL) |
---|
| 1319 | { |
---|
| 1320 | if (b->n==NULL) |
---|
| 1321 | x = NULL; |
---|
| 1322 | else |
---|
| 1323 | x = napCopy(b->n); |
---|
| 1324 | } |
---|
| 1325 | else |
---|
| 1326 | { |
---|
| 1327 | if (b->n==NULL) |
---|
| 1328 | x = napCopy(a->n); |
---|
| 1329 | else |
---|
| 1330 | x = napMult(napCopy(b->n), napCopy(a->n)); |
---|
| 1331 | } |
---|
| 1332 | if (naMinimalPoly!=NULL) |
---|
| 1333 | { |
---|
| 1334 | if (lo->z->e[0] >= naMinimalPoly->e[0]) |
---|
| 1335 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
| 1336 | if ((x!=NULL) && (x->e[0] >= naMinimalPoly->e[0])) |
---|
| 1337 | x = napRemainder(x, naMinimalPoly); |
---|
| 1338 | } |
---|
| 1339 | #if FEHLER1 |
---|
| 1340 | if (naI!=NULL) |
---|
| 1341 | { |
---|
| 1342 | lo->z = napRedp (lo->z); |
---|
| 1343 | if (lo->z != NULL) |
---|
| 1344 | lo->z = napTailred (lo->z); |
---|
| 1345 | if (x!=NULL) |
---|
| 1346 | { |
---|
| 1347 | x = napRedp (x); |
---|
| 1348 | if (x!=NULL) |
---|
| 1349 | x = napTailred (x); |
---|
| 1350 | } |
---|
| 1351 | } |
---|
| 1352 | #endif |
---|
| 1353 | if ((x!=NULL) && (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1354 | napDelete(&x); |
---|
| 1355 | lo->n = x; |
---|
| 1356 | lo->s = 0; |
---|
| 1357 | if(lo->z==NULL) |
---|
| 1358 | { |
---|
| 1359 | Free((ADDRESS)lo,sizeof(rnumber)); |
---|
| 1360 | lo=NULL; |
---|
| 1361 | } |
---|
| 1362 | naTest((number)lo); |
---|
| 1363 | return (number)lo; |
---|
| 1364 | } |
---|
| 1365 | |
---|
| 1366 | number naIntDiv(number la, number lb) |
---|
| 1367 | { |
---|
| 1368 | lnumber res; |
---|
| 1369 | lnumber a = (lnumber)la; |
---|
| 1370 | lnumber b = (lnumber)lb; |
---|
| 1371 | if ((a==NULL) || (a->z==NULL)) |
---|
| 1372 | return NULL; |
---|
| 1373 | if ((b==NULL) || (b->z==NULL)) |
---|
| 1374 | { |
---|
| 1375 | WerrorS("div. by 0"); |
---|
| 1376 | return NULL; |
---|
| 1377 | } |
---|
| 1378 | res = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1379 | res->z = napCopy(a->z); |
---|
| 1380 | res->n = napCopy(b->z); |
---|
| 1381 | res->s = 0; |
---|
| 1382 | number nres=(number)res; |
---|
| 1383 | naNormalize(nres); |
---|
| 1384 | |
---|
| 1385 | //napDelete(&res->n); |
---|
| 1386 | naTest(nres); |
---|
| 1387 | return nres; |
---|
| 1388 | } |
---|
| 1389 | |
---|
| 1390 | /*2 |
---|
| 1391 | * division; lo:= la / lb |
---|
| 1392 | */ |
---|
| 1393 | number naDiv(number la, number lb) |
---|
| 1394 | { |
---|
| 1395 | lnumber lo; |
---|
| 1396 | lnumber a = (lnumber)la; |
---|
| 1397 | lnumber b = (lnumber)lb; |
---|
| 1398 | alg x; |
---|
| 1399 | |
---|
| 1400 | if ((a==NULL) || (a->z==NULL)) |
---|
| 1401 | return NULL; |
---|
| 1402 | |
---|
| 1403 | if ((b==NULL) || (b->z==NULL)) |
---|
| 1404 | { |
---|
| 1405 | WerrorS("div. by 0"); |
---|
| 1406 | return NULL; |
---|
| 1407 | } |
---|
| 1408 | mmTestP(a,sizeof(rnumber)); |
---|
| 1409 | mmTestP(b,sizeof(rnumber)); |
---|
| 1410 | lo = (lnumber)Alloc(sizeof(rnumber)); |
---|
| 1411 | if (b->n!=NULL) |
---|
| 1412 | lo->z = napMult(napCopy(a->z), napCopy(b->n)); |
---|
| 1413 | else |
---|
| 1414 | lo->z = napCopy(a->z); |
---|
| 1415 | if (a->n!=NULL) |
---|
| 1416 | x = napMult(napCopy(b->z), napCopy(a->n)); |
---|
| 1417 | else |
---|
| 1418 | x = napCopy(b->z); |
---|
| 1419 | if (naMinimalPoly!=NULL) |
---|
| 1420 | { |
---|
| 1421 | if (lo->z->e[0] >= naMinimalPoly->e[0]) |
---|
| 1422 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
| 1423 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
| 1424 | x = napRemainder(x, naMinimalPoly); |
---|
| 1425 | } |
---|
| 1426 | #if FEHLER1 |
---|
| 1427 | if (naI!=NULL) |
---|
| 1428 | { |
---|
| 1429 | lo->z = napRedp (lo->z); |
---|
| 1430 | if (lo->z != NULL) |
---|
| 1431 | lo->z = napTailred (lo->z); |
---|
| 1432 | if (x!=NULL) |
---|
| 1433 | { |
---|
| 1434 | x = napRedp (x); |
---|
| 1435 | if (x!=NULL) |
---|
| 1436 | x = napTailred (x); |
---|
| 1437 | } |
---|
| 1438 | } |
---|
| 1439 | #endif |
---|
| 1440 | if ((napDeg(x)==0) && nacIsOne(x->ko)) |
---|
| 1441 | napDelete(&x); |
---|
| 1442 | lo->s = 0; |
---|
| 1443 | lo->n = x; |
---|
| 1444 | naTest((number)lo); |
---|
| 1445 | return (number)lo; |
---|
| 1446 | } |
---|
| 1447 | |
---|
| 1448 | /*2 |
---|
| 1449 | * za:= - za |
---|
| 1450 | */ |
---|
| 1451 | number naNeg(number za) |
---|
| 1452 | { |
---|
| 1453 | if (za!=NULL) |
---|
| 1454 | { |
---|
| 1455 | lnumber e = (lnumber)za; |
---|
| 1456 | naTest(za); |
---|
| 1457 | e->z = napNeg(e->z); |
---|
| 1458 | } |
---|
| 1459 | return za; |
---|
| 1460 | } |
---|
| 1461 | |
---|
| 1462 | /*2 |
---|
| 1463 | * 1/a |
---|
| 1464 | */ |
---|
| 1465 | number naInvers(number a) |
---|
| 1466 | { |
---|
| 1467 | lnumber lo; |
---|
| 1468 | lnumber b = (lnumber)a; |
---|
| 1469 | alg x; |
---|
| 1470 | |
---|
| 1471 | if (b==NULL) |
---|
| 1472 | { |
---|
| 1473 | WerrorS("div. by 0"); |
---|
| 1474 | return NULL; |
---|
| 1475 | } |
---|
| 1476 | mmTestP(b,sizeof(rnumber)); |
---|
| 1477 | lo = (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 1478 | lo->s = b->s; |
---|
| 1479 | if (b->n!=NULL) |
---|
| 1480 | lo->z = napCopy(b->n); |
---|
| 1481 | else |
---|
| 1482 | lo->z = napInit(1); |
---|
| 1483 | x = b->z; |
---|
| 1484 | if ((napDeg(x)!=0) || !nacIsOne(x->ko)) |
---|
| 1485 | x = napCopy(x); |
---|
| 1486 | else |
---|
| 1487 | { |
---|
| 1488 | lo->n = NULL; |
---|
| 1489 | naTest((number)lo); |
---|
| 1490 | return (number)lo; |
---|
| 1491 | } |
---|
| 1492 | if (naMinimalPoly!=NULL) |
---|
| 1493 | { |
---|
| 1494 | x = napInvers(x, naMinimalPoly); |
---|
| 1495 | x = napMult(x, lo->z); |
---|
| 1496 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
| 1497 | x = napRemainder(x, naMinimalPoly); |
---|
| 1498 | lo->z = x; |
---|
| 1499 | lo->n = NULL; |
---|
| 1500 | lo->s = 2; |
---|
| 1501 | while (x!=NULL) |
---|
| 1502 | { |
---|
| 1503 | nacNormalize(x->ko); |
---|
| 1504 | x = x->ne; |
---|
| 1505 | } |
---|
| 1506 | } |
---|
| 1507 | else |
---|
| 1508 | lo->n = x; |
---|
| 1509 | naTest((number)lo); |
---|
| 1510 | return (number)lo; |
---|
| 1511 | } |
---|
| 1512 | |
---|
| 1513 | |
---|
| 1514 | BOOLEAN naIsZero(number za) |
---|
| 1515 | { |
---|
| 1516 | lnumber zb = (lnumber)za; |
---|
| 1517 | naTest(za); |
---|
| 1518 | #ifdef TEST |
---|
| 1519 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
| 1520 | #endif |
---|
| 1521 | return ((zb==NULL) || (zb->z==NULL)); |
---|
| 1522 | } |
---|
| 1523 | |
---|
| 1524 | |
---|
| 1525 | BOOLEAN naGreaterZero(number za) |
---|
| 1526 | { |
---|
| 1527 | lnumber zb = (lnumber)za; |
---|
| 1528 | #ifdef TEST |
---|
| 1529 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
| 1530 | #endif |
---|
| 1531 | naTest(za); |
---|
| 1532 | return ((zb!=NULL) && (zb->z!=NULL)); |
---|
| 1533 | } |
---|
| 1534 | |
---|
| 1535 | |
---|
| 1536 | /*2 |
---|
| 1537 | * a = b ? |
---|
| 1538 | */ |
---|
| 1539 | BOOLEAN naEqual (number a, number b) |
---|
| 1540 | { |
---|
| 1541 | number h; |
---|
| 1542 | BOOLEAN bo; |
---|
| 1543 | h = naSub(a, b); |
---|
| 1544 | bo = naIsZero(h); |
---|
| 1545 | naDelete(&h); |
---|
| 1546 | return bo; |
---|
| 1547 | } |
---|
| 1548 | |
---|
| 1549 | |
---|
| 1550 | BOOLEAN naGreater (number a, number b) |
---|
| 1551 | { |
---|
| 1552 | if (naIsZero(a)) |
---|
| 1553 | return FALSE; |
---|
| 1554 | if (naIsZero(b)) |
---|
| 1555 | return TRUE; /* a!= 0)*/ |
---|
| 1556 | return napDeg(((lnumber)a)->n)>napDeg(((lnumber)b)->n); |
---|
| 1557 | } |
---|
| 1558 | |
---|
| 1559 | /*2 |
---|
| 1560 | * reads a number |
---|
| 1561 | */ |
---|
| 1562 | char *naRead(char *s, number *p) |
---|
| 1563 | { |
---|
| 1564 | alg x; |
---|
| 1565 | lnumber a; |
---|
| 1566 | s = napRead(s, &x); |
---|
| 1567 | if (x==NULL) |
---|
| 1568 | { |
---|
| 1569 | *p = NULL; |
---|
| 1570 | return s; |
---|
| 1571 | } |
---|
| 1572 | *p = (number)Alloc0(sizeof(rnumber)); |
---|
| 1573 | a = (lnumber)*p; |
---|
| 1574 | if ((naMinimalPoly!=NULL) && (x->e[0] >= naMinimalPoly->e[0])) |
---|
| 1575 | a->z = napRemainder(x, naMinimalPoly); |
---|
| 1576 | #if FEHLER3 |
---|
| 1577 | else if (naI!=NULL) |
---|
| 1578 | { |
---|
| 1579 | a->z = napRedp(x); |
---|
| 1580 | if (a->z != NULL) |
---|
| 1581 | a->z = napTailred (a->z); |
---|
| 1582 | } |
---|
| 1583 | #endif |
---|
| 1584 | else |
---|
| 1585 | a->z = x; |
---|
| 1586 | if(a->z==NULL) |
---|
| 1587 | { |
---|
| 1588 | Free((ADDRESS)*p,sizeof(rnumber)); |
---|
| 1589 | *p=NULL; |
---|
| 1590 | } |
---|
| 1591 | else |
---|
| 1592 | { |
---|
| 1593 | a->n = NULL; |
---|
| 1594 | a->s = 0; |
---|
| 1595 | naTest(*p); |
---|
| 1596 | } |
---|
| 1597 | return s; |
---|
| 1598 | } |
---|
| 1599 | |
---|
| 1600 | /*2 |
---|
| 1601 | * tries to convert a number to a name |
---|
| 1602 | */ |
---|
| 1603 | char * naName(number n) |
---|
| 1604 | { |
---|
| 1605 | lnumber ph = (lnumber)n; |
---|
| 1606 | if ((ph==NULL)||(ph->z==NULL)) |
---|
| 1607 | return NULL; |
---|
| 1608 | int i; |
---|
| 1609 | char *s=(char *)AllocL(4* naNumbOfPar); |
---|
| 1610 | char *t=(char *)Alloc(8); |
---|
| 1611 | s[0]='\0'; |
---|
| 1612 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
| 1613 | { |
---|
| 1614 | if (ph->z->e[i] > 0) |
---|
| 1615 | { |
---|
| 1616 | if (ph->z->e[i] >1) |
---|
| 1617 | { |
---|
| 1618 | sprintf(t,"%s%d",naParNames[i],ph->z->e[i]); |
---|
| 1619 | strcat(s,t); |
---|
| 1620 | } |
---|
| 1621 | else |
---|
| 1622 | { |
---|
| 1623 | strcat(s,naParNames[i]); |
---|
| 1624 | } |
---|
| 1625 | } |
---|
| 1626 | } |
---|
| 1627 | Free((ADDRESS)t,8); |
---|
| 1628 | if (s[0]=='\0') |
---|
| 1629 | { |
---|
| 1630 | FreeL((ADDRESS)s); |
---|
| 1631 | return NULL; |
---|
| 1632 | } |
---|
| 1633 | return s; |
---|
| 1634 | } |
---|
| 1635 | |
---|
| 1636 | /*2 |
---|
| 1637 | * writes a number |
---|
| 1638 | */ |
---|
| 1639 | void naWrite(number &phn) |
---|
| 1640 | { |
---|
| 1641 | lnumber ph = (lnumber)phn; |
---|
| 1642 | if ((ph==NULL)||(ph->z==NULL)) |
---|
| 1643 | StringAppendS("0"); |
---|
| 1644 | else |
---|
| 1645 | { |
---|
| 1646 | //phn->s = 0; |
---|
| 1647 | naNormalize(phn); |
---|
| 1648 | napWrite(ph->z); |
---|
| 1649 | if (ph->n!=NULL) |
---|
| 1650 | { |
---|
| 1651 | StringAppendS("/"); |
---|
| 1652 | napWrite(ph->n); |
---|
| 1653 | } |
---|
| 1654 | } |
---|
| 1655 | } |
---|
| 1656 | |
---|
| 1657 | /*2 |
---|
| 1658 | * za == 1 ? |
---|
| 1659 | */ |
---|
| 1660 | BOOLEAN naIsOne(number za) |
---|
| 1661 | { |
---|
| 1662 | lnumber a = (lnumber)za; |
---|
| 1663 | alg x, y; |
---|
| 1664 | number t; |
---|
| 1665 | if (a==NULL) return FALSE; |
---|
| 1666 | mmTestP(a,sizeof(rnumber)); |
---|
| 1667 | #ifdef TEST |
---|
| 1668 | if (a->z==NULL) WerrorS("internal zero error(4)"); |
---|
| 1669 | #endif |
---|
| 1670 | if (a->n==NULL) |
---|
| 1671 | { |
---|
| 1672 | if (napDeg(a->z)==0) return nacIsOne(a->z->ko); |
---|
| 1673 | else return FALSE; |
---|
| 1674 | } |
---|
| 1675 | x = a->z; |
---|
| 1676 | y = a->n; |
---|
| 1677 | do |
---|
| 1678 | { |
---|
| 1679 | if (napComp(x, y)) |
---|
| 1680 | return FALSE; |
---|
| 1681 | else |
---|
| 1682 | { |
---|
| 1683 | t = nacSub(x->ko, y->ko); |
---|
| 1684 | if (!nacIsZero(t)) |
---|
| 1685 | { |
---|
| 1686 | nacDelete(&t); |
---|
| 1687 | return FALSE; |
---|
| 1688 | } |
---|
| 1689 | else |
---|
| 1690 | nacDelete(&t); |
---|
| 1691 | } |
---|
| 1692 | x = x->ne; |
---|
| 1693 | y = y->ne; |
---|
| 1694 | } |
---|
| 1695 | while ((x!=NULL) && (y!=NULL)); |
---|
| 1696 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
| 1697 | napDelete(&a->z); |
---|
| 1698 | napDelete(&a->n); |
---|
| 1699 | a->z = napInit(1); |
---|
| 1700 | a->n = NULL; |
---|
| 1701 | a->s = 2; |
---|
| 1702 | return TRUE; |
---|
| 1703 | } |
---|
| 1704 | |
---|
| 1705 | /*2 |
---|
| 1706 | * za == -1 ? |
---|
| 1707 | */ |
---|
| 1708 | BOOLEAN naIsMOne(number za) |
---|
| 1709 | { |
---|
| 1710 | lnumber a = (lnumber)za; |
---|
| 1711 | alg x, y; |
---|
| 1712 | number t; |
---|
| 1713 | if (a==NULL) return FALSE; |
---|
| 1714 | mmTestP(a,sizeof(rnumber)); |
---|
| 1715 | #ifdef TEST |
---|
| 1716 | if (a->z==NULL) WerrorS("internal zero error(4)"); |
---|
| 1717 | #endif |
---|
| 1718 | if (a->n==NULL) |
---|
| 1719 | { |
---|
| 1720 | if (napDeg(a->z)==0) return nacIsMOne(a->z->ko); |
---|
| 1721 | else return FALSE; |
---|
| 1722 | } |
---|
| 1723 | x = a->z; |
---|
| 1724 | y = a->n; |
---|
| 1725 | do |
---|
| 1726 | { |
---|
| 1727 | t = nacAdd(x->ko, y->ko); |
---|
| 1728 | if (!nacIsZero(t)) |
---|
| 1729 | { |
---|
| 1730 | nacDelete(&t); |
---|
| 1731 | return FALSE; |
---|
| 1732 | } |
---|
| 1733 | else |
---|
| 1734 | nacDelete(&t); |
---|
| 1735 | x = x->ne; |
---|
| 1736 | y = y->ne; |
---|
| 1737 | } |
---|
| 1738 | while ((x!=NULL) && (y!=NULL)); |
---|
| 1739 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
| 1740 | napDelete(&a->z); |
---|
| 1741 | napDelete(&a->n); |
---|
| 1742 | a->z = napInit(-1); |
---|
| 1743 | a->n = NULL; |
---|
| 1744 | a->s = 2; |
---|
| 1745 | return TRUE; |
---|
| 1746 | } |
---|
| 1747 | |
---|
| 1748 | /*2 |
---|
| 1749 | * returns the i-th power of p (i>=0) |
---|
| 1750 | */ |
---|
| 1751 | void naPower(number p, int i, number *rc) |
---|
| 1752 | { |
---|
| 1753 | number x; |
---|
| 1754 | *rc = naInit(1); |
---|
| 1755 | for (; i > 0; i--) |
---|
| 1756 | { |
---|
| 1757 | x = naMult(*rc, p); |
---|
| 1758 | naDelete(rc); |
---|
| 1759 | *rc = x; |
---|
| 1760 | } |
---|
| 1761 | } |
---|
| 1762 | |
---|
| 1763 | /*2 |
---|
| 1764 | * result =gcd(a,b) |
---|
| 1765 | */ |
---|
| 1766 | number naGcd(number a, number b) |
---|
| 1767 | { |
---|
| 1768 | lnumber x, y; |
---|
| 1769 | lnumber result = (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 1770 | |
---|
| 1771 | x = (lnumber)a; |
---|
| 1772 | y = (lnumber)b; |
---|
| 1773 | if (naNumbOfPar == 1) |
---|
| 1774 | { |
---|
| 1775 | if (naMinimalPoly!=NULL) |
---|
| 1776 | { |
---|
| 1777 | if (x->z->ne!=NULL) |
---|
| 1778 | result->z = napCopy(x->z); |
---|
| 1779 | else |
---|
| 1780 | result->z = napGcd0(x->z, y->z); |
---|
| 1781 | } |
---|
| 1782 | else |
---|
| 1783 | result->z = napGcd(x->z, y->z); |
---|
| 1784 | } |
---|
| 1785 | else |
---|
| 1786 | result->z = napGcd0(x->z, y->z); |
---|
| 1787 | naTest((number)result); |
---|
| 1788 | return (number)result; |
---|
| 1789 | } |
---|
| 1790 | |
---|
| 1791 | /*2 |
---|
| 1792 | * naNumbOfPar = 1: |
---|
| 1793 | * clears denominator algebraic case; |
---|
| 1794 | * tries to simplify ratio transcendental case; |
---|
| 1795 | * |
---|
| 1796 | * cancels monomials |
---|
| 1797 | * occuring in denominator |
---|
| 1798 | * and enumerator ? naNumbOfPar != 1; |
---|
| 1799 | */ |
---|
| 1800 | void naNormalize(number &pp) |
---|
| 1801 | { |
---|
| 1802 | |
---|
| 1803 | int i,m; |
---|
| 1804 | number h, h1; |
---|
| 1805 | alg x, y, r, x1, y1; |
---|
| 1806 | lnumber p = (lnumber)pp; |
---|
| 1807 | |
---|
| 1808 | if ((p==NULL) /*|| (p->s==2)*/) |
---|
| 1809 | return; |
---|
| 1810 | BOOLEAN normal_test=(p->s==2); |
---|
| 1811 | x = p->z; |
---|
| 1812 | y = p->n; |
---|
| 1813 | p->s = 2; |
---|
| 1814 | if ((y!=NULL) && (naMinimalPoly!=NULL)) |
---|
| 1815 | { |
---|
| 1816 | y = napInvers(y, naMinimalPoly); |
---|
| 1817 | x = napMult(x, y); |
---|
| 1818 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
| 1819 | x = napRemainder(x, naMinimalPoly); |
---|
| 1820 | p->z = x; |
---|
| 1821 | p->n = y = NULL; |
---|
| 1822 | } |
---|
| 1823 | if (y==NULL) |
---|
| 1824 | { |
---|
| 1825 | if (naIsChar0) |
---|
| 1826 | { |
---|
| 1827 | r = x; |
---|
| 1828 | while (r!=NULL) |
---|
| 1829 | { |
---|
| 1830 | nacNormalize(r->ko); |
---|
| 1831 | r = r->ne; |
---|
| 1832 | } |
---|
| 1833 | } |
---|
| 1834 | return; |
---|
| 1835 | } |
---|
| 1836 | // p->n !=NULL: |
---|
| 1837 | #if FEHLER1 |
---|
| 1838 | if (naMinimalPoly == NULL) |
---|
| 1839 | { |
---|
| 1840 | alg xx=x; |
---|
| 1841 | alg yy=y; |
---|
| 1842 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
| 1843 | { |
---|
| 1844 | m = napExpi(i, yy, xx); |
---|
| 1845 | if (m != 0) // in this case xx!=NULL!=yy |
---|
| 1846 | { |
---|
| 1847 | while (xx != NULL) |
---|
| 1848 | { |
---|
| 1849 | xx->e[i] -= m; |
---|
| 1850 | xx = xx->ne; |
---|
| 1851 | } |
---|
| 1852 | while (yy != NULL) |
---|
| 1853 | { |
---|
| 1854 | yy->e[i] -= m; |
---|
| 1855 | yy = yy->ne; |
---|
| 1856 | } |
---|
| 1857 | } |
---|
| 1858 | } |
---|
| 1859 | } |
---|
| 1860 | #endif |
---|
| 1861 | if (naIsChar0) |
---|
| 1862 | { |
---|
| 1863 | h1 = nacInvers(y->ko); |
---|
| 1864 | nacNormalize(h1); |
---|
| 1865 | napMultN(x, h1); |
---|
| 1866 | napMultN(y->ne, h1); |
---|
| 1867 | nacDelete(&y->ko); |
---|
| 1868 | y->ko = nacInit(1); |
---|
| 1869 | nacDelete(&h1); |
---|
| 1870 | } |
---|
| 1871 | if (napDeg(y)==0) |
---|
| 1872 | { |
---|
| 1873 | if (nacIsOne(y->ko)) |
---|
| 1874 | { |
---|
| 1875 | napDelete1(&y); |
---|
| 1876 | p->n = NULL; |
---|
| 1877 | return; |
---|
| 1878 | } |
---|
| 1879 | h = nacInit(1); |
---|
| 1880 | h1 = nacDiv(h, y->ko); |
---|
| 1881 | nacDelete(&h); |
---|
| 1882 | nacNormalize(h1); |
---|
| 1883 | napMultN(x, h1); |
---|
| 1884 | nacDelete(&h1); |
---|
| 1885 | napDelete1(&y); |
---|
| 1886 | p->n = NULL; |
---|
| 1887 | return; |
---|
| 1888 | } |
---|
| 1889 | if (naNumbOfPar != 1) |
---|
| 1890 | return; |
---|
| 1891 | i = napExp(x, y); |
---|
| 1892 | if (i!=0) |
---|
| 1893 | { |
---|
| 1894 | r = x; |
---|
| 1895 | while (r!=NULL) |
---|
| 1896 | { |
---|
| 1897 | r->e[0] -= i; |
---|
| 1898 | r = r->ne; |
---|
| 1899 | } |
---|
| 1900 | r = y; |
---|
| 1901 | while (r!=NULL) |
---|
| 1902 | { |
---|
| 1903 | r->e[0] -= i; |
---|
| 1904 | r = r->ne; |
---|
| 1905 | } |
---|
| 1906 | } |
---|
| 1907 | if (y->ne==NULL) |
---|
| 1908 | { |
---|
| 1909 | if (nacIsOne(y->ko)) |
---|
| 1910 | { |
---|
| 1911 | if (y->e[0]==0) |
---|
| 1912 | { |
---|
| 1913 | napDelete1(&y); |
---|
| 1914 | p->n = NULL; |
---|
| 1915 | } |
---|
| 1916 | return; |
---|
| 1917 | } |
---|
| 1918 | h = nacInit(1); |
---|
| 1919 | h1 = nacDiv(h, y->ko); |
---|
| 1920 | if (y->e[0]!=0) |
---|
| 1921 | { |
---|
| 1922 | nacDelete(&y->ko); |
---|
| 1923 | y->ko = h; |
---|
| 1924 | } |
---|
| 1925 | else |
---|
| 1926 | { |
---|
| 1927 | napDelete1(&y); |
---|
| 1928 | nacDelete(&h); |
---|
| 1929 | p->n = NULL; |
---|
| 1930 | } |
---|
| 1931 | napMultN(x, h1); |
---|
| 1932 | nacDelete(&h1); |
---|
| 1933 | return; |
---|
| 1934 | } |
---|
| 1935 | if (x->e[0] >= y->e[0]) |
---|
| 1936 | { |
---|
| 1937 | x1 = napCopy(x); |
---|
| 1938 | y1 = napCopy(y); |
---|
| 1939 | } |
---|
| 1940 | else |
---|
| 1941 | { |
---|
| 1942 | x1 = napCopy(y); |
---|
| 1943 | y1 = napCopy(x); |
---|
| 1944 | } |
---|
| 1945 | loop |
---|
| 1946 | { |
---|
| 1947 | r = napRemainder(x1, y1); |
---|
| 1948 | if ((r==NULL) || (r->ne==NULL)) break; |
---|
| 1949 | x1 = y1; |
---|
| 1950 | y1 = r; |
---|
| 1951 | } |
---|
| 1952 | if (r!=NULL) |
---|
| 1953 | { |
---|
| 1954 | napDelete(&r); |
---|
| 1955 | napDelete(&y1); |
---|
| 1956 | } |
---|
| 1957 | else |
---|
| 1958 | { |
---|
| 1959 | napDivMod(x, y1, &(p->z), &r); |
---|
| 1960 | napDivMod(y, y1, &(p->n), &r); |
---|
| 1961 | napDelete(&y1); |
---|
| 1962 | } |
---|
| 1963 | x = p->z; |
---|
| 1964 | y = p->n; |
---|
| 1965 | if (y->ne==NULL) |
---|
| 1966 | { |
---|
| 1967 | if (nacIsOne(y->ko)) |
---|
| 1968 | { |
---|
| 1969 | if (y->e[0]==0) |
---|
| 1970 | { |
---|
| 1971 | napDelete1(&y); |
---|
| 1972 | p->n = NULL; |
---|
| 1973 | } |
---|
| 1974 | return; |
---|
| 1975 | } |
---|
| 1976 | h = nacInit(1); |
---|
| 1977 | h1 = nacDiv(h, y->ko); |
---|
| 1978 | if (y->e[0]!=0) |
---|
| 1979 | { |
---|
| 1980 | nacDelete(&(y->ko)); |
---|
| 1981 | y->ko = h; |
---|
| 1982 | } |
---|
| 1983 | else |
---|
| 1984 | { |
---|
| 1985 | napDelete1(&y); |
---|
| 1986 | nacDelete(&h); |
---|
| 1987 | p->n = NULL; |
---|
| 1988 | } |
---|
| 1989 | napMultN(x, h1); |
---|
| 1990 | nacDelete(&h1); |
---|
| 1991 | } |
---|
| 1992 | } |
---|
| 1993 | |
---|
| 1994 | /*2 |
---|
| 1995 | * returns in result->n 1 |
---|
| 1996 | * and in result->z the lcm(a->z,b->n) |
---|
| 1997 | */ |
---|
| 1998 | number naLcm(number la, number lb) |
---|
| 1999 | { |
---|
| 2000 | lnumber result; |
---|
| 2001 | lnumber a = (lnumber)la; |
---|
| 2002 | lnumber b = (lnumber)lb; |
---|
| 2003 | alg x; |
---|
| 2004 | number t, bt, r; |
---|
| 2005 | result = (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 2006 | if (((naMinimalPoly==NULL) && (naI==NULL)) || !naIsChar0) |
---|
| 2007 | { |
---|
| 2008 | result->z = napInit(1); |
---|
| 2009 | return (number)result; |
---|
| 2010 | } |
---|
| 2011 | naNormalize(lb); |
---|
| 2012 | x = napCopy(a->z); |
---|
| 2013 | t = napLcm(b->z); |
---|
| 2014 | if (!nacIsOne(t)) |
---|
| 2015 | { |
---|
| 2016 | bt = nacGcd(t, x->ko); |
---|
| 2017 | r = nacMult(t, x->ko); |
---|
| 2018 | nacDelete(&(x->ko)); |
---|
| 2019 | x->ko = nacDiv(r, bt); |
---|
| 2020 | nacNormalize(x->ko); |
---|
| 2021 | nacDelete(&bt); |
---|
| 2022 | nacDelete(&r); |
---|
| 2023 | } |
---|
| 2024 | nacDelete(&t); |
---|
| 2025 | result->z = x; |
---|
| 2026 | naTest((number)result); |
---|
| 2027 | return (number)result; |
---|
| 2028 | } |
---|
| 2029 | |
---|
| 2030 | /*2 |
---|
| 2031 | * input: a set of constant polynomials |
---|
| 2032 | * sets the global variable naI |
---|
| 2033 | */ |
---|
| 2034 | void naSetIdeal(ideal I) |
---|
| 2035 | { |
---|
| 2036 | int i; |
---|
| 2037 | |
---|
| 2038 | if (idIs0(I)) |
---|
| 2039 | { |
---|
| 2040 | for (i=naI->anz-1; i>=0; i--) |
---|
| 2041 | napDelete(&naI->liste[i]); |
---|
| 2042 | Free((ADDRESS)naI,sizeof(*naI)); |
---|
| 2043 | naI=NULL; |
---|
| 2044 | } |
---|
| 2045 | else |
---|
| 2046 | { |
---|
| 2047 | lnumber h; |
---|
| 2048 | number a; |
---|
| 2049 | alg x; |
---|
| 2050 | |
---|
| 2051 | naI=(naIdeal)Alloc(sizeof(*naI)); |
---|
| 2052 | naI->anz=IDELEMS(I); |
---|
| 2053 | naI->liste=(alg*)Alloc(naI->anz*sizeof(alg)); |
---|
| 2054 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
| 2055 | { |
---|
| 2056 | h=(lnumber)pGetCoeff(I->m[i]); |
---|
| 2057 | /* We only need the enumerator of h, as we expect it to be a polynomial */ |
---|
| 2058 | naI->liste[i]=napCopy(h->z); |
---|
| 2059 | /* If it isn't normalized (lc = 1) do this */ |
---|
| 2060 | if (!nacIsOne(naI->liste[i]->ko)) |
---|
| 2061 | { |
---|
| 2062 | x=naI->liste[i]; |
---|
| 2063 | a=nacCopy(x->ko); |
---|
| 2064 | a=nacDiv(nacInit(1),a); |
---|
| 2065 | napMultN(x,a); |
---|
| 2066 | nacDelete(&a); |
---|
| 2067 | } |
---|
| 2068 | } |
---|
| 2069 | } |
---|
| 2070 | } |
---|
| 2071 | |
---|
| 2072 | /*2 |
---|
| 2073 | * map Z/p -> Q(a) |
---|
| 2074 | */ |
---|
| 2075 | number naMapP0(number c) |
---|
| 2076 | { |
---|
| 2077 | if (npIsZero(c)) return NULL; |
---|
| 2078 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2079 | l->s=2; |
---|
| 2080 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 2081 | int i=(int)c; |
---|
| 2082 | if (i>(naPrimeM>>2)) i-=naPrimeM; |
---|
| 2083 | l->z->ko=nlInit(i); |
---|
| 2084 | l->n=NULL; |
---|
| 2085 | return (number)l; |
---|
| 2086 | } |
---|
| 2087 | |
---|
| 2088 | /*2 |
---|
| 2089 | * map Q -> Q(a) |
---|
| 2090 | */ |
---|
| 2091 | number naMap00(number c) |
---|
| 2092 | { |
---|
| 2093 | if (nlIsZero(c)) return NULL; |
---|
| 2094 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2095 | l->s=0; |
---|
| 2096 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 2097 | l->z->ko=nlCopy(c); |
---|
| 2098 | l->n=NULL; |
---|
| 2099 | return (number)l; |
---|
| 2100 | } |
---|
| 2101 | |
---|
| 2102 | /*2 |
---|
| 2103 | * map Z/p -> Z/p(a) |
---|
| 2104 | */ |
---|
| 2105 | number naMapPP(number c) |
---|
| 2106 | { |
---|
| 2107 | if (npIsZero(c)) return NULL; |
---|
| 2108 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2109 | l->s=2; |
---|
| 2110 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 2111 | l->z->ko=c; /* omit npCopy, because npCopy is a no-op */ |
---|
| 2112 | l->n=NULL; |
---|
| 2113 | return (number)l; |
---|
| 2114 | } |
---|
| 2115 | |
---|
| 2116 | /*2 |
---|
| 2117 | * map Z/p' -> Z/p(a) |
---|
| 2118 | */ |
---|
| 2119 | number naMapPP1(number c) |
---|
| 2120 | { |
---|
| 2121 | if (npIsZero(c)) return NULL; |
---|
| 2122 | int i=(int)c; |
---|
| 2123 | if (i>naPrimeM) i-=naPrimeM; |
---|
| 2124 | number n=npInit(i); |
---|
| 2125 | if (npIsZero(n)) return NULL; |
---|
| 2126 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2127 | l->s=2; |
---|
| 2128 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 2129 | l->z->ko=n; |
---|
| 2130 | l->n=NULL; |
---|
| 2131 | return (number)l; |
---|
| 2132 | } |
---|
| 2133 | |
---|
| 2134 | /*2 |
---|
| 2135 | * map Q -> Z/p(a) |
---|
| 2136 | */ |
---|
| 2137 | number naMap0P(number c) |
---|
| 2138 | { |
---|
| 2139 | if (nlIsZero(c)) return NULL; |
---|
| 2140 | number n=npInit(nlInt(c)); |
---|
| 2141 | if (npIsZero(n)) return NULL; |
---|
| 2142 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
| 2143 | l->s=2; |
---|
| 2144 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 2145 | l->z->ko=n; |
---|
| 2146 | l->n=NULL; |
---|
| 2147 | return (number)l; |
---|
| 2148 | } |
---|
| 2149 | |
---|
| 2150 | static number (*nacMap)(number); |
---|
| 2151 | static int naParsToCopy; |
---|
| 2152 | static alg napMap(alg p) |
---|
| 2153 | { |
---|
| 2154 | alg w, a; |
---|
| 2155 | |
---|
| 2156 | if (p==NULL) return NULL; |
---|
| 2157 | a = w = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 2158 | memcpy(a->e, p->e, naParsToCopy * sizeof(int)); |
---|
| 2159 | w->ko = nacMap(p->ko); |
---|
| 2160 | loop |
---|
| 2161 | { |
---|
| 2162 | p=p->ne; |
---|
| 2163 | if (p==NULL) break; |
---|
| 2164 | a->ne = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
| 2165 | a = a->ne; |
---|
| 2166 | memcpy(a->e, p->e, naParsToCopy * sizeof(int)); |
---|
| 2167 | a->ko = nacMap(p->ko); |
---|
| 2168 | } |
---|
| 2169 | a->ne = NULL; |
---|
| 2170 | return w; |
---|
| 2171 | } |
---|
| 2172 | |
---|
| 2173 | /*2 |
---|
| 2174 | * map _(a) -> _(b) |
---|
| 2175 | */ |
---|
| 2176 | number naMapQaQb(number c) |
---|
| 2177 | { |
---|
| 2178 | if (c==NULL) return NULL; |
---|
| 2179 | lnumber erg= (lnumber)Alloc0(sizeof(rnumber)); |
---|
| 2180 | lnumber src =(lnumber)c; |
---|
| 2181 | erg->s=src->s; |
---|
| 2182 | erg->z=napMap(src->z); |
---|
| 2183 | erg->n=napMap(src->n); |
---|
| 2184 | return (number)erg; |
---|
| 2185 | } |
---|
| 2186 | |
---|
| 2187 | BOOLEAN naSetMap(int c, char ** par, int nop, number minpol) |
---|
| 2188 | { |
---|
| 2189 | if (currRing->ch==1) /* -> Q(a) */ |
---|
| 2190 | { |
---|
| 2191 | if (c == 0) |
---|
| 2192 | { |
---|
| 2193 | nMap = naMap00; /*Q -> Q(a)*/ |
---|
| 2194 | return TRUE; |
---|
| 2195 | } |
---|
| 2196 | if (c>1) |
---|
| 2197 | { |
---|
| 2198 | if (par==NULL) |
---|
| 2199 | { |
---|
| 2200 | naPrimeM = c; |
---|
| 2201 | nMap = naMapP0; /* Z/p -> Q(a)*/ |
---|
| 2202 | return TRUE; |
---|
| 2203 | } |
---|
| 2204 | else |
---|
| 2205 | { |
---|
| 2206 | return FALSE; /* GF(q) -> Q(a) */ |
---|
| 2207 | } |
---|
| 2208 | } |
---|
| 2209 | if (c<0) |
---|
| 2210 | { |
---|
| 2211 | return FALSE; /* Z/p(a) -> Q(b)*/ |
---|
| 2212 | } |
---|
| 2213 | if (c==1) |
---|
| 2214 | { |
---|
| 2215 | int i; |
---|
| 2216 | naParsToCopy=0; |
---|
| 2217 | for(i=0;i<nop;i++) |
---|
| 2218 | { |
---|
| 2219 | if ((i>=currRing->P) |
---|
| 2220 | ||(strcmp(par[i],currRing->parameter[i])!=0)) |
---|
| 2221 | return FALSE; |
---|
| 2222 | naParsToCopy++; |
---|
| 2223 | } |
---|
| 2224 | nacMap=nacCopy; |
---|
| 2225 | nMap=naMapQaQb; |
---|
| 2226 | return TRUE; /* Q(a) -> Q(a) */ |
---|
| 2227 | } |
---|
| 2228 | } |
---|
| 2229 | /*-----------------------------------------------------*/ |
---|
| 2230 | if (currRing->ch<0) /* -> Z/p(a) */ |
---|
| 2231 | { |
---|
| 2232 | if (c == 0) |
---|
| 2233 | { |
---|
| 2234 | nMap = naMap0P; /*Q -> Z/p(a)*/ |
---|
| 2235 | return TRUE; |
---|
| 2236 | } |
---|
| 2237 | if (c>1) |
---|
| 2238 | { |
---|
| 2239 | if (par==NULL) |
---|
| 2240 | { |
---|
| 2241 | if (c==npPrimeM) |
---|
| 2242 | { |
---|
| 2243 | nMap = naMapPP; /* Z/p -> Z/p(a)*/ |
---|
| 2244 | return TRUE; |
---|
| 2245 | } |
---|
| 2246 | else |
---|
| 2247 | { |
---|
| 2248 | naPrimeM = c; |
---|
| 2249 | nMap = naMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
| 2250 | return TRUE; |
---|
| 2251 | } |
---|
| 2252 | } |
---|
| 2253 | else |
---|
| 2254 | { |
---|
| 2255 | return FALSE; /* GF(q) ->Z/p(a) */ |
---|
| 2256 | } |
---|
| 2257 | } |
---|
| 2258 | if (c<0) |
---|
| 2259 | { |
---|
| 2260 | if (c==currRing->ch) |
---|
| 2261 | { |
---|
| 2262 | nacMap=nacCopy; |
---|
| 2263 | } |
---|
| 2264 | else |
---|
| 2265 | { |
---|
| 2266 | npMapPrime=-c; |
---|
| 2267 | nacMap = npMapP; |
---|
| 2268 | } |
---|
| 2269 | int i; |
---|
| 2270 | naParsToCopy=0; |
---|
| 2271 | for(i=0;i<nop;i++) |
---|
| 2272 | { |
---|
| 2273 | if ((i>=currRing->P) |
---|
| 2274 | ||(strcmp(par[i],currRing->parameter[i])!=0)) |
---|
| 2275 | return FALSE; |
---|
| 2276 | naParsToCopy++; |
---|
| 2277 | } |
---|
| 2278 | nMap=naMapQaQb; |
---|
| 2279 | return TRUE; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
| 2280 | } |
---|
| 2281 | if (c==1) |
---|
| 2282 | { |
---|
| 2283 | return FALSE; /* Q(a) -> Z/p(b) */ |
---|
| 2284 | } |
---|
| 2285 | } |
---|
| 2286 | return FALSE; /* default */ |
---|
| 2287 | } |
---|
| 2288 | |
---|
| 2289 | /*2 |
---|
| 2290 | * convert a alg number into a poly |
---|
| 2291 | */ |
---|
| 2292 | poly naPermNumber(number z, int * par_perm, int P) |
---|
| 2293 | { |
---|
| 2294 | if (z==NULL) return NULL; |
---|
| 2295 | poly res=NULL; |
---|
| 2296 | poly p; |
---|
| 2297 | napoly za=((lnumber)z)->z; |
---|
| 2298 | do |
---|
| 2299 | { |
---|
| 2300 | p=pNew(); |
---|
| 2301 | pNext(p)=NULL; |
---|
| 2302 | nNew(&pGetCoeff(p)); |
---|
| 2303 | int i; |
---|
| 2304 | for(i=pVariables;i>=0;i--) |
---|
| 2305 | pGetExp(p,i)=0; |
---|
| 2306 | napoly pa=NULL; |
---|
| 2307 | if (currRing->parameter!=NULL) |
---|
| 2308 | { |
---|
| 2309 | pGetCoeff(p)=(number)Alloc0(sizeof(rnumber)); |
---|
| 2310 | ((lnumber)pGetCoeff(p))->s=2; |
---|
| 2311 | ((lnumber)pGetCoeff(p))->z=napInitz(nacCopy(napGetCoeff(za))); |
---|
| 2312 | pa=((lnumber)pGetCoeff(p))->z; |
---|
| 2313 | } |
---|
| 2314 | else |
---|
| 2315 | { |
---|
| 2316 | pGetCoeff(p)=nCopy(napGetCoeff(za)); |
---|
| 2317 | } |
---|
| 2318 | for(i=0;i<P;i++) |
---|
| 2319 | { |
---|
| 2320 | if(za->e[i]!=0) |
---|
| 2321 | { |
---|
| 2322 | if(par_perm[i]>0) |
---|
| 2323 | pGetExp(p,par_perm[i])=za->e[i]; |
---|
| 2324 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
| 2325 | pa->e[-par_perm[i]-1]=za->e[i]; |
---|
| 2326 | else |
---|
| 2327 | { |
---|
| 2328 | pDelete(&p); |
---|
| 2329 | break; |
---|
| 2330 | } |
---|
| 2331 | } |
---|
| 2332 | } |
---|
| 2333 | if (p!=NULL) |
---|
| 2334 | { |
---|
| 2335 | pSetm(p); |
---|
| 2336 | pTest(p); |
---|
| 2337 | res=pAdd(res,p); |
---|
| 2338 | } |
---|
| 2339 | za=za->ne; |
---|
| 2340 | } |
---|
| 2341 | while (za!=NULL); |
---|
| 2342 | pTest(res); |
---|
| 2343 | return res; |
---|
| 2344 | } |
---|
| 2345 | |
---|
| 2346 | #ifdef LDEBUG |
---|
| 2347 | BOOLEAN naDBTest(number a, char *f,int l) |
---|
| 2348 | { |
---|
| 2349 | lnumber x=(lnumber)a; |
---|
| 2350 | if (x == NULL) |
---|
| 2351 | return TRUE; |
---|
| 2352 | #ifdef MDEBUG |
---|
| 2353 | if (!mmDBTestBlock(a,sizeof(rnumber),f,l)) |
---|
| 2354 | return FALSE; |
---|
| 2355 | #endif |
---|
| 2356 | alg p = x->z; |
---|
| 2357 | if (p==NULL) |
---|
| 2358 | { |
---|
| 2359 | Print("0/* in %s:%d\n",f,l); |
---|
| 2360 | return FALSE; |
---|
| 2361 | } |
---|
| 2362 | while(p!=NULL) |
---|
| 2363 | { |
---|
| 2364 | if((naMinimalPoly!=NULL)&&(p->e[0]>naMinimalPoly->e[0]) |
---|
| 2365 | &&(p!=naMinimalPoly)) |
---|
| 2366 | { |
---|
| 2367 | Print("deg>minpoly in %s:%d\n",f,l); |
---|
| 2368 | return FALSE; |
---|
| 2369 | } |
---|
| 2370 | //if (naIsChar0 && (((int)p->ko &3) == 0) && (p->ko->s==0) && (x->s==2)) |
---|
| 2371 | //{ |
---|
| 2372 | // Print("normalized with non-normal coeffs in %s:%d\n",f,l); |
---|
| 2373 | // return FALSE; |
---|
| 2374 | //} |
---|
| 2375 | if (naIsChar0 && nlDBTest(p->ko,f,l)) |
---|
| 2376 | return FALSE; |
---|
| 2377 | #ifdef MDEBUG |
---|
| 2378 | if (!mmDBTestBlock(p,RECA_SIZE+naNumbOfPar*sizeof(int),f,l)) |
---|
| 2379 | return FALSE; |
---|
| 2380 | #endif |
---|
| 2381 | p = p->ne; |
---|
| 2382 | } |
---|
| 2383 | p = x->n; |
---|
| 2384 | while(p!=NULL) |
---|
| 2385 | { |
---|
| 2386 | if (naIsChar0 && nlDBTest(p->ko,f,l)) |
---|
| 2387 | return FALSE; |
---|
| 2388 | #ifdef MDEBUG |
---|
| 2389 | if (!mmDBTestBlock(p,RECA_SIZE+naNumbOfPar*sizeof(int),f,l)) |
---|
| 2390 | return FALSE; |
---|
| 2391 | #endif |
---|
| 2392 | p = p->ne; |
---|
| 2393 | } |
---|
| 2394 | return TRUE; |
---|
| 2395 | } |
---|
| 2396 | #endif |
---|
| 2397 | |
---|