[275ecc] | 1 | /**************************************** |
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| 2 | * Computer Algebra System SINGULAR * |
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| 3 | ****************************************/ |
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| 4 | /* |
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| 5 | * ABSTRACT: numbers modulo n |
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| 6 | */ |
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[f5f5c9] | 7 | #include "misc/auxiliary.h" |
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[f1c465f] | 8 | |
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[f5f5c9] | 9 | #include "misc/mylimits.h" |
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[417a91a] | 10 | #include "misc/prime.h" // IsPrime |
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[f5f5c9] | 11 | #include "reporter/reporter.h" |
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[2206753] | 12 | |
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[f5f5c9] | 13 | #include "coeffs/si_gmp.h" |
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| 14 | #include "coeffs/coeffs.h" |
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[acb07e] | 15 | #include "coeffs/modulop.h" |
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[4b5b36] | 16 | #include "coeffs/rintegers.h" |
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[f5f5c9] | 17 | #include "coeffs/numbers.h" |
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[2206753] | 18 | |
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[f5f5c9] | 19 | #include "coeffs/mpr_complex.h" |
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[2206753] | 20 | |
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[f5f5c9] | 21 | #include "coeffs/longrat.h" |
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| 22 | #include "coeffs/rmodulon.h" |
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[8d0331d] | 23 | |
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[f1c465f] | 24 | #include <string.h> |
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| 25 | |
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[2206753] | 26 | #ifdef HAVE_RINGS |
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| 27 | |
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[51a346] | 28 | void nrnWrite (number a, const coeffs); |
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[2206753] | 29 | #ifdef LDEBUG |
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| 30 | BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r); |
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| 31 | #endif |
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| 32 | |
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[a3f0fea] | 33 | EXTERN_VAR omBin gmp_nrz_bin; |
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[275ecc] | 34 | |
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[bcbdc40] | 35 | static void nrnCoeffWrite (const coeffs r, BOOLEAN /*details*/) |
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[7a8011] | 36 | { |
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[9b88e6] | 37 | size_t l = (size_t)mpz_sizeinbase(r->modBase, 10) + 2; |
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[7a8011] | 38 | char* s = (char*) omAlloc(l); |
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[0486a3] | 39 | s= mpz_get_str (s, 10, r->modBase); |
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[0b6a542] | 40 | |
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[417a91a] | 41 | #ifdef TEST_ZN_AS_ZP |
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| 42 | if (l<10) |
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| 43 | { |
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[1becad6] | 44 | if (nCoeff_is_Zn(r)) Print("ZZ/%s", s); |
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[417a91a] | 45 | else if (nCoeff_is_Ring_PtoM(r)) Print("ZZ/(%s^%lu)", s, r->modExponent); |
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| 46 | } |
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| 47 | else |
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| 48 | #endif |
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| 49 | { |
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[1becad6] | 50 | if (nCoeff_is_Zn(r)) Print("ZZ/bigint(%s)", s); |
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[417a91a] | 51 | else if (nCoeff_is_Ring_PtoM(r)) Print("ZZ/(bigint(%s)^%lu)", s, r->modExponent); |
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| 52 | } |
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[0b6a542] | 53 | |
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[7a8011] | 54 | omFreeSize((ADDRESS)s, l); |
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| 55 | } |
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| 56 | |
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[113a80] | 57 | coeffs nrnInitCfByName(char *s,n_coeffType n) |
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| 58 | { |
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[2443ced] | 59 | const char start[]="ZZ/bigint("; |
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| 60 | const int start_len=strlen(start); |
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| 61 | if (strncmp(s,start,start_len)==0) |
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[113a80] | 62 | { |
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| 63 | s+=start_len; |
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| 64 | mpz_t z; |
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| 65 | mpz_init(z); |
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| 66 | s=nEatLong(s,z); |
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| 67 | ZnmInfo info; |
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| 68 | info.base=z; |
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| 69 | info.exp= 1; |
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| 70 | while ((*s!='\0') && (*s!=')')) s++; |
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| 71 | // expect ")" or ")^exp" |
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| 72 | if (*s=='\0') { mpz_clear(z); return NULL; } |
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| 73 | if (((*s)==')') && (*(s+1)=='^')) |
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| 74 | { |
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| 75 | s=s+2; |
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| 76 | s=nEati(s,&(info.exp),0); |
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| 77 | return nInitChar(n_Znm,(void*) &info); |
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| 78 | } |
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| 79 | else |
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| 80 | return nInitChar(n_Zn,(void*) &info); |
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| 81 | } |
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| 82 | else return NULL; |
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| 83 | } |
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| 84 | |
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[a3f0fea] | 85 | STATIC_VAR char* nrnCoeffName_buff=NULL; |
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[3f7f11] | 86 | static char* nrnCoeffName(const coeffs r) |
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| 87 | { |
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[8d1432e] | 88 | if(nrnCoeffName_buff!=NULL) omFree(nrnCoeffName_buff); |
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[3f7f11] | 89 | size_t l = (size_t)mpz_sizeinbase(r->modBase, 10) + 2; |
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| 90 | char* s = (char*) omAlloc(l); |
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[4b5b36] | 91 | l+=22; |
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| 92 | nrnCoeffName_buff=(char*)omAlloc(l); |
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[3f7f11] | 93 | s= mpz_get_str (s, 10, r->modBase); |
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[4b5b36] | 94 | int ll; |
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[1becad6] | 95 | if (nCoeff_is_Zn(r)) |
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[4b5b36] | 96 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/bigint(%s)",s); |
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[3f7f11] | 97 | else if (nCoeff_is_Ring_PtoM(r)) |
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[4b5b36] | 98 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/bigint(%s)^%lu",s,r->modExponent); |
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| 99 | assume(ll<(int)l); // otherwise nrnCoeffName_buff too small |
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| 100 | omFreeSize((ADDRESS)s, l-22); |
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[3f7f11] | 101 | return nrnCoeffName_buff; |
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| 102 | } |
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| 103 | |
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[417a91a] | 104 | static BOOLEAN nrnCoeffIsEqual(const coeffs r, n_coeffType n, void * parameter) |
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[b19ab84] | 105 | { |
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| 106 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
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[417a91a] | 107 | ZnmInfo *info=(ZnmInfo*)parameter; |
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| 108 | return (n==r->type) && (r->modExponent==info->exp) |
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| 109 | && (mpz_cmp(r->modBase,info->base)==0); |
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[b19ab84] | 110 | } |
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| 111 | |
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[45cc512] | 112 | static char* nrnCoeffString(const coeffs r) |
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| 113 | { |
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[9b88e6] | 114 | size_t l = (size_t)mpz_sizeinbase(r->modBase, 10) +2; |
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[0acf3e] | 115 | char* b = (char*) omAlloc(l); |
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| 116 | b= mpz_get_str (b, 10, r->modBase); |
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[f8735a] | 117 | char* s = (char*) omAlloc(15+l); |
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[1becad6] | 118 | if (nCoeff_is_Zn(r)) sprintf(s,"ZZ/%s",b); |
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[f8735a] | 119 | else /*if (nCoeff_is_Ring_PtoM(r))*/ sprintf(s,"ZZ/(bigint(%s)^%lu)",b,r->modExponent); |
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[0acf3e] | 120 | omFreeSize(b,l); |
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[45cc512] | 121 | return s; |
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| 122 | } |
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[b19ab84] | 123 | |
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[fea494] | 124 | static void nrnKillChar(coeffs r) |
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[fe99ed] | 125 | { |
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| 126 | mpz_clear(r->modNumber); |
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| 127 | mpz_clear(r->modBase); |
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| 128 | omFreeBin((void *) r->modBase, gmp_nrz_bin); |
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[fea494] | 129 | omFreeBin((void *) r->modNumber, gmp_nrz_bin); |
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[fe99ed] | 130 | } |
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| 131 | |
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[bcbdc40] | 132 | static coeffs nrnQuot1(number c, const coeffs r) |
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[2f864f] | 133 | { |
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| 134 | coeffs rr; |
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[777f8b] | 135 | long ch = r->cfInt(c, r); |
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[2f864f] | 136 | mpz_t a,b; |
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| 137 | mpz_init_set(a, r->modNumber); |
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| 138 | mpz_init_set_ui(b, ch); |
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[a0707f8] | 139 | mpz_t gcd; |
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[2f864f] | 140 | mpz_init(gcd); |
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| 141 | mpz_gcd(gcd, a,b); |
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| 142 | if(mpz_cmp_ui(gcd, 1) == 0) |
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[a0707f8] | 143 | { |
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| 144 | WerrorS("constant in q-ideal is coprime to modulus in ground ring"); |
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| 145 | WerrorS("Unable to create qring!"); |
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| 146 | return NULL; |
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| 147 | } |
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[2f864f] | 148 | if(r->modExponent == 1) |
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| 149 | { |
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[a0707f8] | 150 | ZnmInfo info; |
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| 151 | info.base = gcd; |
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| 152 | info.exp = (unsigned long) 1; |
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| 153 | rr = nInitChar(n_Zn, (void*)&info); |
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[2f864f] | 154 | } |
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| 155 | else |
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| 156 | { |
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[a0707f8] | 157 | ZnmInfo info; |
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| 158 | info.base = r->modBase; |
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| 159 | int kNew = 1; |
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| 160 | mpz_t baseTokNew; |
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| 161 | mpz_init(baseTokNew); |
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| 162 | mpz_set(baseTokNew, r->modBase); |
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| 163 | while(mpz_cmp(gcd, baseTokNew) > 0) |
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| 164 | { |
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| 165 | kNew++; |
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| 166 | mpz_mul(baseTokNew, baseTokNew, r->modBase); |
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| 167 | } |
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| 168 | //printf("\nkNew = %i\n",kNew); |
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| 169 | info.exp = kNew; |
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| 170 | mpz_clear(baseTokNew); |
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| 171 | rr = nInitChar(n_Znm, (void*)&info); |
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[2f864f] | 172 | } |
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[a0707f8] | 173 | mpz_clear(gcd); |
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[2f864f] | 174 | return(rr); |
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| 175 | } |
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| 176 | |
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[bcbdc40] | 177 | static number nrnCopy(number a, const coeffs) |
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[14b11bb] | 178 | { |
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[bcbdc40] | 179 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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| 180 | mpz_init_set(erg, (mpz_ptr) a); |
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| 181 | return (number) erg; |
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[14b11bb] | 182 | } |
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| 183 | |
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[8e1c4e] | 184 | /* |
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| 185 | * create a number from int |
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| 186 | */ |
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[bcbdc40] | 187 | static number nrnInit(long i, const coeffs r) |
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[8e1c4e] | 188 | { |
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[6a70f3] | 189 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 190 | mpz_init_set_si(erg, i); |
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[e90dfd6] | 191 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 192 | return (number) erg; |
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| 193 | } |
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| 194 | |
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[4b5b36] | 195 | /* |
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| 196 | * convert a number to int |
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| 197 | */ |
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| 198 | static long nrnInt(number &n, const coeffs) |
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| 199 | { |
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| 200 | return mpz_get_si((mpz_ptr) n); |
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| 201 | } |
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| 202 | |
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| 203 | #if SI_INTEGER_VARIANT==2 |
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| 204 | #define nrnDelete nrzDelete |
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| 205 | #define nrnSize nrzSize |
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| 206 | #else |
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[bcbdc40] | 207 | static void nrnDelete(number *a, const coeffs) |
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[8e1c4e] | 208 | { |
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[54bb6b] | 209 | if (*a != NULL) |
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| 210 | { |
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| 211 | mpz_clear((mpz_ptr) *a); |
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| 212 | omFreeBin((void *) *a, gmp_nrz_bin); |
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| 213 | *a = NULL; |
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| 214 | } |
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[bac8611] | 215 | } |
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[bcbdc40] | 216 | static int nrnSize(number a, const coeffs) |
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[bac8611] | 217 | { |
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[417a91a] | 218 | mpz_ptr p=(mpz_ptr)a; |
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| 219 | int s=p->_mp_alloc; |
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[54bb6b] | 220 | if (s==1) s=(mpz_cmp_ui(p,0)!=0); |
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[417a91a] | 221 | return s; |
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[8e1c4e] | 222 | } |
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[4b5b36] | 223 | #endif |
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[275ecc] | 224 | /* |
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| 225 | * Multiply two numbers |
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| 226 | */ |
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[bcbdc40] | 227 | static number nrnMult(number a, number b, const coeffs r) |
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[275ecc] | 228 | { |
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[6a70f3] | 229 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 230 | mpz_init(erg); |
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[6a70f3] | 231 | mpz_mul(erg, (mpz_ptr)a, (mpz_ptr) b); |
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[e90dfd6] | 232 | mpz_mod(erg, erg, r->modNumber); |
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[8e56ad] | 233 | return (number) erg; |
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[275ecc] | 234 | } |
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| 235 | |
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[bcbdc40] | 236 | static void nrnPower(number a, int i, number * result, const coeffs r) |
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[8e1c4e] | 237 | { |
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[6a70f3] | 238 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 239 | mpz_init(erg); |
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[6a70f3] | 240 | mpz_powm_ui(erg, (mpz_ptr)a, i, r->modNumber); |
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[8e1c4e] | 241 | *result = (number) erg; |
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| 242 | } |
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| 243 | |
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[bcbdc40] | 244 | static number nrnAdd(number a, number b, const coeffs r) |
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[8e1c4e] | 245 | { |
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[6a70f3] | 246 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 247 | mpz_init(erg); |
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[6a70f3] | 248 | mpz_add(erg, (mpz_ptr)a, (mpz_ptr) b); |
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[e90dfd6] | 249 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 250 | return (number) erg; |
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| 251 | } |
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| 252 | |
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[bcbdc40] | 253 | static number nrnSub(number a, number b, const coeffs r) |
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[8e1c4e] | 254 | { |
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[6a70f3] | 255 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 256 | mpz_init(erg); |
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[6a70f3] | 257 | mpz_sub(erg, (mpz_ptr)a, (mpz_ptr) b); |
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[e90dfd6] | 258 | mpz_mod(erg, erg, r->modNumber); |
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[8e1c4e] | 259 | return (number) erg; |
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| 260 | } |
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| 261 | |
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[bcbdc40] | 262 | static BOOLEAN nrnIsZero(number a, const coeffs) |
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| 263 | { |
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| 264 | return 0 == mpz_cmpabs_ui((mpz_ptr)a, 0); |
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| 265 | } |
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| 266 | |
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| 267 | static number nrnNeg(number c, const coeffs r) |
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[8e1c4e] | 268 | { |
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[0b7bf7] | 269 | if( !nrnIsZero(c, r) ) |
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| 270 | // Attention: This method operates in-place. |
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[6a70f3] | 271 | mpz_sub((mpz_ptr)c, r->modNumber, (mpz_ptr)c); |
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[a539ad] | 272 | return c; |
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[8e1c4e] | 273 | } |
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| 274 | |
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[bcbdc40] | 275 | static number nrnInvers(number c, const coeffs r) |
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[8e1c4e] | 276 | { |
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[6a70f3] | 277 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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[8e1c4e] | 278 | mpz_init(erg); |
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[6a70f3] | 279 | mpz_invert(erg, (mpz_ptr)c, r->modNumber); |
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[8e1c4e] | 280 | return (number) erg; |
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| 281 | } |
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| 282 | |
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[275ecc] | 283 | /* |
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[e90dfd6] | 284 | * Give the largest k, such that a = x * k, b = y * k has |
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[275ecc] | 285 | * a solution. |
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[54bb6b] | 286 | * a may be NULL, b not |
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[275ecc] | 287 | */ |
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[bcbdc40] | 288 | static number nrnGcd(number a, number b, const coeffs r) |
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[275ecc] | 289 | { |
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[6a70f3] | 290 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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[e90dfd6] | 291 | mpz_init_set(erg, r->modNumber); |
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[6a70f3] | 292 | if (a != NULL) mpz_gcd(erg, erg, (mpz_ptr)a); |
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[54bb6b] | 293 | mpz_gcd(erg, erg, (mpz_ptr)b); |
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[8d1432e] | 294 | if(mpz_cmp(erg,r->modNumber)==0) |
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| 295 | { |
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| 296 | mpz_clear(erg); |
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| 297 | omFreeBin((ADDRESS)erg,gmp_nrz_bin); |
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| 298 | return nrnInit(0,r); |
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| 299 | } |
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[e90dfd6] | 300 | return (number)erg; |
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[8e56ad] | 301 | } |
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| 302 | |
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[bcbdc40] | 303 | /* |
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| 304 | * Give the smallest k, such that a * x = k = b * y has a solution |
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| 305 | * TODO: lcm(gcd,gcd) better than gcd(lcm) ? |
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| 306 | */ |
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| 307 | static number nrnLcm(number a, number b, const coeffs r) |
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| 308 | { |
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| 309 | number erg = nrnGcd(NULL, a, r); |
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| 310 | number tmp = nrnGcd(NULL, b, r); |
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| 311 | mpz_lcm((mpz_ptr)erg, (mpz_ptr)erg, (mpz_ptr)tmp); |
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| 312 | nrnDelete(&tmp, r); |
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| 313 | return (number)erg; |
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| 314 | } |
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| 315 | |
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[8e1c4e] | 316 | /* Not needed any more, but may have room for improvement |
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[e90dfd6] | 317 | number nrnGcd3(number a,number b, number c,ring r) |
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[af378f7] | 318 | { |
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[6a70f3] | 319 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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[af378f7] | 320 | mpz_init(erg); |
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[e90dfd6] | 321 | if (a == NULL) a = (number)r->modNumber; |
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| 322 | if (b == NULL) b = (number)r->modNumber; |
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| 323 | if (c == NULL) c = (number)r->modNumber; |
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[6a70f3] | 324 | mpz_gcd(erg, (mpz_ptr)a, (mpz_ptr)b); |
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| 325 | mpz_gcd(erg, erg, (mpz_ptr)c); |
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[e90dfd6] | 326 | mpz_gcd(erg, erg, r->modNumber); |
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| 327 | return (number)erg; |
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[af378f7] | 328 | } |
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[8e1c4e] | 329 | */ |
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[af378f7] | 330 | |
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[8e56ad] | 331 | /* |
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[e90dfd6] | 332 | * Give the largest k, such that a = x * k, b = y * k has |
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[8e56ad] | 333 | * a solution and r, s, s.t. k = s*a + t*b |
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[fe99ed] | 334 | * CF: careful: ExtGcd is wrong as implemented (or at least may not |
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| 335 | * give you what you want: |
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| 336 | * ExtGcd(5, 10 modulo 12): |
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| 337 | * the gcdext will return 5 = 1*5 + 0*10 |
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| 338 | * however, mod 12, the gcd should be 1 |
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[8e56ad] | 339 | */ |
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[bcbdc40] | 340 | static number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r) |
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[8e56ad] | 341 | { |
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[6a70f3] | 342 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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| 343 | mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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| 344 | mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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[8e56ad] | 345 | mpz_init(erg); |
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| 346 | mpz_init(bs); |
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| 347 | mpz_init(bt); |
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[6a70f3] | 348 | mpz_gcdext(erg, bs, bt, (mpz_ptr)a, (mpz_ptr)b); |
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[e90dfd6] | 349 | mpz_mod(bs, bs, r->modNumber); |
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| 350 | mpz_mod(bt, bt, r->modNumber); |
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| 351 | *s = (number)bs; |
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| 352 | *t = (number)bt; |
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| 353 | return (number)erg; |
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[275ecc] | 354 | } |
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[bcbdc40] | 355 | |
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| 356 | static BOOLEAN nrnIsOne(number a, const coeffs) |
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| 357 | { |
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| 358 | return 0 == mpz_cmp_si((mpz_ptr)a, 1); |
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| 359 | } |
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| 360 | |
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| 361 | static BOOLEAN nrnEqual(number a, number b, const coeffs) |
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| 362 | { |
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| 363 | return 0 == mpz_cmp((mpz_ptr)a, (mpz_ptr)b); |
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| 364 | } |
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| 365 | |
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| 366 | static number nrnGetUnit(number k, const coeffs r) |
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| 367 | { |
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| 368 | if (mpz_divisible_p(r->modNumber, (mpz_ptr)k)) return nrnInit(1,r); |
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| 369 | |
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[54bb6b] | 370 | mpz_ptr unit = (mpz_ptr)nrnGcd(NULL, k, r); |
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[bcbdc40] | 371 | mpz_tdiv_q(unit, (mpz_ptr)k, unit); |
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[54bb6b] | 372 | mpz_ptr gcd = (mpz_ptr)nrnGcd(NULL, (number)unit, r); |
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[bcbdc40] | 373 | if (!nrnIsOne((number)gcd,r)) |
---|
| 374 | { |
---|
| 375 | mpz_ptr ctmp; |
---|
| 376 | // tmp := unit^2 |
---|
| 377 | mpz_ptr tmp = (mpz_ptr) nrnMult((number) unit,(number) unit,r); |
---|
| 378 | // gcd_new := gcd(tmp, 0) |
---|
[54bb6b] | 379 | mpz_ptr gcd_new = (mpz_ptr) nrnGcd(NULL, (number) tmp, r); |
---|
[bcbdc40] | 380 | while (!nrnEqual((number) gcd_new,(number) gcd,r)) |
---|
| 381 | { |
---|
| 382 | // gcd := gcd_new |
---|
| 383 | ctmp = gcd; |
---|
| 384 | gcd = gcd_new; |
---|
| 385 | gcd_new = ctmp; |
---|
| 386 | // tmp := tmp * unit |
---|
| 387 | mpz_mul(tmp, tmp, unit); |
---|
| 388 | mpz_mod(tmp, tmp, r->modNumber); |
---|
| 389 | // gcd_new := gcd(tmp, 0) |
---|
| 390 | mpz_gcd(gcd_new, tmp, r->modNumber); |
---|
| 391 | } |
---|
| 392 | // unit := unit + modNumber / gcd_new |
---|
| 393 | mpz_tdiv_q(tmp, r->modNumber, gcd_new); |
---|
| 394 | mpz_add(unit, unit, tmp); |
---|
| 395 | mpz_mod(unit, unit, r->modNumber); |
---|
[54bb6b] | 396 | nrnDelete((number*) &gcd_new, r); |
---|
| 397 | nrnDelete((number*) &tmp, r); |
---|
[bcbdc40] | 398 | } |
---|
[54bb6b] | 399 | nrnDelete((number*) &gcd, r); |
---|
[bcbdc40] | 400 | return (number)unit; |
---|
| 401 | } |
---|
| 402 | |
---|
[fe99ed] | 403 | /* XExtGcd returns a unimodular matrix ((s,t)(u,v)) sth. |
---|
| 404 | * (a,b)^t ((st)(uv)) = (g,0)^t |
---|
| 405 | * Beware, the ExtGcd will not necessaairly do this. |
---|
| 406 | * Problem: if g = as+bt then (in Z/nZ) it follows NOT that |
---|
| 407 | * 1 = (a/g)s + (b/g) t |
---|
| 408 | * due to the zero divisors. |
---|
| 409 | */ |
---|
| 410 | |
---|
| 411 | //#define CF_DEB; |
---|
[bcbdc40] | 412 | static number nrnXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r) |
---|
[fe99ed] | 413 | { |
---|
| 414 | number xx; |
---|
| 415 | #ifdef CF_DEB |
---|
| 416 | StringSetS("XExtGcd of "); |
---|
| 417 | nrnWrite(a, r); |
---|
| 418 | StringAppendS("\t"); |
---|
| 419 | nrnWrite(b, r); |
---|
| 420 | StringAppendS(" modulo "); |
---|
| 421 | nrnWrite(xx = (number)r->modNumber, r); |
---|
| 422 | Print("%s\n", StringEndS()); |
---|
| 423 | #endif |
---|
| 424 | |
---|
[6a70f3] | 425 | mpz_ptr one = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 426 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 427 | mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 428 | mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 429 | mpz_ptr bu = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 430 | mpz_ptr bv = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[fe99ed] | 431 | mpz_init(erg); |
---|
| 432 | mpz_init(one); |
---|
[6a70f3] | 433 | mpz_init_set(bs, (mpz_ptr) a); |
---|
| 434 | mpz_init_set(bt, (mpz_ptr) b); |
---|
[fe99ed] | 435 | mpz_init(bu); |
---|
| 436 | mpz_init(bv); |
---|
| 437 | mpz_gcd(erg, bs, bt); |
---|
| 438 | |
---|
| 439 | #ifdef CF_DEB |
---|
| 440 | StringSetS("1st gcd:"); |
---|
| 441 | nrnWrite(xx= (number)erg, r); |
---|
| 442 | #endif |
---|
| 443 | |
---|
| 444 | mpz_gcd(erg, erg, r->modNumber); |
---|
| 445 | |
---|
| 446 | mpz_div(bs, bs, erg); |
---|
| 447 | mpz_div(bt, bt, erg); |
---|
| 448 | |
---|
| 449 | #ifdef CF_DEB |
---|
| 450 | Print("%s\n", StringEndS()); |
---|
| 451 | StringSetS("xgcd: "); |
---|
| 452 | #endif |
---|
| 453 | |
---|
| 454 | mpz_gcdext(one, bu, bv, bs, bt); |
---|
| 455 | number ui = nrnGetUnit(xx = (number) one, r); |
---|
| 456 | #ifdef CF_DEB |
---|
| 457 | n_Write(xx, r); |
---|
| 458 | StringAppendS("\t"); |
---|
| 459 | n_Write(ui, r); |
---|
| 460 | Print("%s\n", StringEndS()); |
---|
| 461 | #endif |
---|
| 462 | nrnDelete(&xx, r); |
---|
[f9b0bd] | 463 | if (!nrnIsOne(ui, r)) |
---|
| 464 | { |
---|
[fe99ed] | 465 | #ifdef CF_DEB |
---|
[f9b0bd] | 466 | PrintS("Scaling\n"); |
---|
[fe99ed] | 467 | #endif |
---|
| 468 | number uii = nrnInvers(ui, r); |
---|
| 469 | nrnDelete(&ui, r); |
---|
| 470 | ui = uii; |
---|
[6a70f3] | 471 | mpz_ptr uu = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 472 | mpz_init_set(uu, (mpz_ptr)ui); |
---|
[fe99ed] | 473 | mpz_mul(bu, bu, uu); |
---|
| 474 | mpz_mul(bv, bv, uu); |
---|
| 475 | mpz_clear(uu); |
---|
| 476 | omFreeBin(uu, gmp_nrz_bin); |
---|
[fea494] | 477 | } |
---|
[fe99ed] | 478 | nrnDelete(&ui, r); |
---|
| 479 | #ifdef CF_DEB |
---|
| 480 | StringSetS("xgcd"); |
---|
| 481 | nrnWrite(xx= (number)bs, r); |
---|
| 482 | StringAppendS("*"); |
---|
| 483 | nrnWrite(xx= (number)bu, r); |
---|
| 484 | StringAppendS(" + "); |
---|
| 485 | nrnWrite(xx= (number)bt, r); |
---|
| 486 | StringAppendS("*"); |
---|
| 487 | nrnWrite(xx= (number)bv, r); |
---|
| 488 | Print("%s\n", StringEndS()); |
---|
| 489 | #endif |
---|
| 490 | |
---|
| 491 | mpz_mod(bs, bs, r->modNumber); |
---|
| 492 | mpz_mod(bt, bt, r->modNumber); |
---|
| 493 | mpz_mod(bu, bu, r->modNumber); |
---|
| 494 | mpz_mod(bv, bv, r->modNumber); |
---|
| 495 | *s = (number)bu; |
---|
| 496 | *t = (number)bv; |
---|
| 497 | *u = (number)bt; |
---|
| 498 | *u = nrnNeg(*u, r); |
---|
| 499 | *v = (number)bs; |
---|
| 500 | return (number)erg; |
---|
| 501 | } |
---|
| 502 | |
---|
[bcbdc40] | 503 | static BOOLEAN nrnIsMOne(number a, const coeffs r) |
---|
[8e56ad] | 504 | { |
---|
[417a91a] | 505 | if((r->ch==2) && (nrnIsOne(a,r))) return FALSE; |
---|
[6a70f3] | 506 | mpz_t t; mpz_init_set(t, (mpz_ptr)a); |
---|
[e90dfd6] | 507 | mpz_add_ui(t, t, 1); |
---|
| 508 | bool erg = (0 == mpz_cmp(t, r->modNumber)); |
---|
| 509 | mpz_clear(t); |
---|
| 510 | return erg; |
---|
[275ecc] | 511 | } |
---|
| 512 | |
---|
[bcbdc40] | 513 | static BOOLEAN nrnGreater(number a, number b, const coeffs) |
---|
[275ecc] | 514 | { |
---|
[6a70f3] | 515 | return 0 < mpz_cmp((mpz_ptr)a, (mpz_ptr)b); |
---|
[275ecc] | 516 | } |
---|
| 517 | |
---|
[417a91a] | 518 | static BOOLEAN nrnGreaterZero(number k, const coeffs cf) |
---|
[275ecc] | 519 | { |
---|
[417a91a] | 520 | if (cf->is_field) |
---|
| 521 | { |
---|
| 522 | if (mpz_cmp_ui(cf->modBase,2)==0) |
---|
| 523 | { |
---|
| 524 | return TRUE; |
---|
| 525 | } |
---|
| 526 | mpz_t ch2; mpz_init_set(ch2, cf->modBase); |
---|
| 527 | mpz_sub_ui(ch2,ch2,1); |
---|
| 528 | mpz_divexact_ui(ch2,ch2,2); |
---|
| 529 | if (mpz_cmp(ch2,(mpz_ptr)k)<0) |
---|
| 530 | return FALSE; |
---|
| 531 | mpz_clear(ch2); |
---|
| 532 | } |
---|
[52f3e2] | 533 | return 0 < mpz_sgn1((mpz_ptr)k); |
---|
[8e1c4e] | 534 | } |
---|
| 535 | |
---|
[bcbdc40] | 536 | static BOOLEAN nrnIsUnit(number a, const coeffs r) |
---|
[8e1c4e] | 537 | { |
---|
[e90dfd6] | 538 | number tmp = nrnGcd(a, (number)r->modNumber, r); |
---|
| 539 | bool res = nrnIsOne(tmp, r); |
---|
[54bb6b] | 540 | nrnDelete(&tmp, r); |
---|
[8e1c4e] | 541 | return res; |
---|
[275ecc] | 542 | } |
---|
| 543 | |
---|
[bcbdc40] | 544 | static number nrnAnn(number k, const coeffs r) |
---|
[fe99ed] | 545 | { |
---|
[6a70f3] | 546 | mpz_ptr tmp = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
[fe99ed] | 547 | mpz_init(tmp); |
---|
[6a70f3] | 548 | mpz_gcd(tmp, (mpz_ptr) k, r->modNumber); |
---|
[54bb6b] | 549 | if (mpz_cmp_si(tmp, 1)==0) |
---|
| 550 | { |
---|
[5a0d2ae] | 551 | mpz_set_ui(tmp, 0); |
---|
[fe99ed] | 552 | return (number) tmp; |
---|
| 553 | } |
---|
| 554 | mpz_divexact(tmp, r->modNumber, tmp); |
---|
| 555 | return (number) tmp; |
---|
| 556 | } |
---|
| 557 | |
---|
[bcbdc40] | 558 | static BOOLEAN nrnDivBy(number a, number b, const coeffs r) |
---|
[275ecc] | 559 | { |
---|
[54bb6b] | 560 | /* b divides a iff b/gcd(a, b) is a unit in the given ring: */ |
---|
| 561 | number n = nrnGcd(a, b, r); |
---|
| 562 | mpz_tdiv_q((mpz_ptr)n, (mpz_ptr)b, (mpz_ptr)n); |
---|
| 563 | bool result = nrnIsUnit(n, r); |
---|
| 564 | nrnDelete(&n, NULL); |
---|
| 565 | return result; |
---|
[275ecc] | 566 | } |
---|
| 567 | |
---|
[bcbdc40] | 568 | static int nrnDivComp(number a, number b, const coeffs r) |
---|
[275ecc] | 569 | { |
---|
[4d1ae5] | 570 | if (nrnEqual(a, b,r)) return 2; |
---|
[6a70f3] | 571 | if (mpz_divisible_p((mpz_ptr) a, (mpz_ptr) b)) return -1; |
---|
| 572 | if (mpz_divisible_p((mpz_ptr) b, (mpz_ptr) a)) return 1; |
---|
[e90dfd6] | 573 | return 0; |
---|
[275ecc] | 574 | } |
---|
| 575 | |
---|
[bcbdc40] | 576 | static number nrnDiv(number a, number b, const coeffs r) |
---|
[275ecc] | 577 | { |
---|
[417a91a] | 578 | if (r->is_field) |
---|
| 579 | { |
---|
| 580 | number inv=nrnInvers(b,r); |
---|
| 581 | number erg=nrnMult(a,inv,r); |
---|
| 582 | nrnDelete(&inv,r); |
---|
| 583 | return erg; |
---|
| 584 | } |
---|
[6a70f3] | 585 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[8e56ad] | 586 | mpz_init(erg); |
---|
[6a70f3] | 587 | if (mpz_divisible_p((mpz_ptr)a, (mpz_ptr)b)) |
---|
[275ecc] | 588 | { |
---|
[6a70f3] | 589 | mpz_divexact(erg, (mpz_ptr)a, (mpz_ptr)b); |
---|
[e90dfd6] | 590 | return (number)erg; |
---|
[275ecc] | 591 | } |
---|
| 592 | else |
---|
| 593 | { |
---|
[6a70f3] | 594 | mpz_ptr gcd = (mpz_ptr)nrnGcd(a, b, r); |
---|
| 595 | mpz_divexact(erg, (mpz_ptr)b, gcd); |
---|
[e90dfd6] | 596 | if (!nrnIsUnit((number)erg, r)) |
---|
[8e56ad] | 597 | { |
---|
[bca575c] | 598 | WerrorS("Division not possible, even by cancelling zero divisors."); |
---|
[54bb6b] | 599 | nrnDelete((number*) &gcd, r); |
---|
| 600 | nrnDelete((number*) &erg, r); |
---|
| 601 | return (number)NULL; |
---|
[8e56ad] | 602 | } |
---|
[31e857] | 603 | // a / gcd(a,b) * [b / gcd (a,b)]^(-1) |
---|
[6a70f3] | 604 | mpz_ptr tmp = (mpz_ptr)nrnInvers((number) erg,r); |
---|
| 605 | mpz_divexact(erg, (mpz_ptr)a, gcd); |
---|
[12ea9d] | 606 | mpz_mul(erg, erg, tmp); |
---|
[54bb6b] | 607 | nrnDelete((number*) &gcd, r); |
---|
| 608 | nrnDelete((number*) &tmp, r); |
---|
[e90dfd6] | 609 | mpz_mod(erg, erg, r->modNumber); |
---|
| 610 | return (number)erg; |
---|
[275ecc] | 611 | } |
---|
| 612 | } |
---|
| 613 | |
---|
[bcbdc40] | 614 | static number nrnMod(number a, number b, const coeffs r) |
---|
[6ea941] | 615 | { |
---|
| 616 | /* |
---|
[e90dfd6] | 617 | We need to return the number rr which is uniquely determined by the |
---|
[6ea941] | 618 | following two properties: |
---|
[e90dfd6] | 619 | (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z) |
---|
| 620 | (2) There exists some k in the integers Z such that a = k * b + rr. |
---|
[6ea941] | 621 | Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n. |
---|
| 622 | Now, there are three cases: |
---|
| 623 | (a) g = 1 |
---|
| 624 | Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a. |
---|
[e90dfd6] | 625 | Thus rr = 0. |
---|
[6ea941] | 626 | (b) g <> 1 and g divides a |
---|
[e90dfd6] | 627 | Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0. |
---|
[6ea941] | 628 | (c) g <> 1 and g does not divide a |
---|
| 629 | Then denote the division with remainder of a by g as this: |
---|
| 630 | a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b| |
---|
[e90dfd6] | 631 | fulfills (1) and (2), i.e. rr := t is the correct result. Hence |
---|
| 632 | in this third case, rr is the remainder of division of a by g in Z. |
---|
[e1634d] | 633 | Remark: according to mpz_mod: a,b are always non-negative |
---|
[6ea941] | 634 | */ |
---|
[6a70f3] | 635 | mpz_ptr g = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 636 | mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[6ea941] | 637 | mpz_init(g); |
---|
[5a0d2ae] | 638 | mpz_init_set_ui(rr, 0); |
---|
[6a70f3] | 639 | mpz_gcd(g, (mpz_ptr)r->modNumber, (mpz_ptr)b); // g is now as above |
---|
[9b88e6] | 640 | if (mpz_cmp_si(g, 1L) != 0) mpz_mod(rr, (mpz_ptr)a, g); // the case g <> 1 |
---|
[6ea941] | 641 | mpz_clear(g); |
---|
[3c3880b] | 642 | omFreeBin(g, gmp_nrz_bin); |
---|
[e90dfd6] | 643 | return (number)rr; |
---|
[6ea941] | 644 | } |
---|
| 645 | |
---|
[bcbdc40] | 646 | static number nrnIntDiv(number a, number b, const coeffs r) |
---|
[275ecc] | 647 | { |
---|
[6a70f3] | 648 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[8e56ad] | 649 | mpz_init(erg); |
---|
[6a70f3] | 650 | mpz_tdiv_q(erg, (mpz_ptr)a, (mpz_ptr)b); |
---|
[e90dfd6] | 651 | return (number)erg; |
---|
[275ecc] | 652 | } |
---|
| 653 | |
---|
[fe99ed] | 654 | /* CF: note that Z/nZ has (at least) two distinct euclidean structures |
---|
| 655 | * 1st phi(a) := (a mod n) which is just the structure directly |
---|
[fea494] | 656 | * inherited from Z |
---|
[fe99ed] | 657 | * 2nd phi(a) := gcd(a, n) |
---|
| 658 | * The 1st version is probably faster as everything just comes from Z, |
---|
| 659 | * but the 2nd version behaves nicely wrt. to quotient operations |
---|
| 660 | * and HNF and such. In agreement with nrnMod we imlement the 2nd here |
---|
| 661 | * |
---|
[fea494] | 662 | * For quotrem note that if b exactly divides a, then |
---|
[fe99ed] | 663 | * min(v_p(a), v_p(n)) >= min(v_p(b), v_p(n)) |
---|
[fea494] | 664 | * so if we divide a and b by g:= gcd(a,b,n), then b becomes a |
---|
[fe99ed] | 665 | * unit mod n/g. |
---|
| 666 | * Thus we 1st compute the remainder (similar to nrnMod) and then |
---|
| 667 | * the exact quotient. |
---|
| 668 | */ |
---|
[bcbdc40] | 669 | static number nrnQuotRem(number a, number b, number * rem, const coeffs r) |
---|
[ed371e] | 670 | { |
---|
[fe99ed] | 671 | mpz_t g, aa, bb; |
---|
[6a70f3] | 672 | mpz_ptr qq = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 673 | mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[fe99ed] | 674 | mpz_init(qq); |
---|
| 675 | mpz_init(rr); |
---|
| 676 | mpz_init(g); |
---|
[6a70f3] | 677 | mpz_init_set(aa, (mpz_ptr)a); |
---|
| 678 | mpz_init_set(bb, (mpz_ptr)b); |
---|
[fe99ed] | 679 | |
---|
| 680 | mpz_gcd(g, bb, r->modNumber); |
---|
| 681 | mpz_mod(rr, aa, g); |
---|
| 682 | mpz_sub(aa, aa, rr); |
---|
| 683 | mpz_gcd(g, aa, g); |
---|
| 684 | mpz_div(aa, aa, g); |
---|
| 685 | mpz_div(bb, bb, g); |
---|
| 686 | mpz_div(g, r->modNumber, g); |
---|
| 687 | mpz_invert(g, bb, g); |
---|
| 688 | mpz_mul(qq, aa, g); |
---|
| 689 | if (rem) |
---|
| 690 | *rem = (number)rr; |
---|
| 691 | else { |
---|
| 692 | mpz_clear(rr); |
---|
| 693 | omFreeBin(rr, gmp_nrz_bin); |
---|
| 694 | } |
---|
| 695 | mpz_clear(g); |
---|
| 696 | mpz_clear(aa); |
---|
| 697 | mpz_clear(bb); |
---|
| 698 | return (number) qq; |
---|
[ed371e] | 699 | } |
---|
| 700 | |
---|
[d351d8] | 701 | /* |
---|
[d9301a] | 702 | * Helper function for computing the module |
---|
| 703 | */ |
---|
| 704 | |
---|
[a3f0fea] | 705 | STATIC_VAR mpz_ptr nrnMapCoef = NULL; |
---|
[d9301a] | 706 | |
---|
[bcbdc40] | 707 | static number nrnMapModN(number from, const coeffs /*src*/, const coeffs dst) |
---|
[d351d8] | 708 | { |
---|
[4d1ae5] | 709 | return nrnMult(from, (number) nrnMapCoef, dst); |
---|
[d351d8] | 710 | } |
---|
[d9301a] | 711 | |
---|
[bcbdc40] | 712 | static number nrnMap2toM(number from, const coeffs /*src*/, const coeffs dst) |
---|
[d9301a] | 713 | { |
---|
[6a70f3] | 714 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 715 | mpz_init(erg); |
---|
[6a70f3] | 716 | mpz_mul_ui(erg, nrnMapCoef, (unsigned long)from); |
---|
[e90dfd6] | 717 | mpz_mod(erg, erg, dst->modNumber); |
---|
| 718 | return (number)erg; |
---|
[d9301a] | 719 | } |
---|
| 720 | |
---|
[bcbdc40] | 721 | static number nrnMapZp(number from, const coeffs /*src*/, const coeffs dst) |
---|
[894f5b1] | 722 | { |
---|
[6a70f3] | 723 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 724 | mpz_init(erg); |
---|
[4d1ae5] | 725 | // TODO: use npInt(...) |
---|
[6a70f3] | 726 | mpz_mul_si(erg, nrnMapCoef, (unsigned long)from); |
---|
[e90dfd6] | 727 | mpz_mod(erg, erg, dst->modNumber); |
---|
| 728 | return (number)erg; |
---|
[894f5b1] | 729 | } |
---|
| 730 | |
---|
[9bb5457] | 731 | number nrnMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
[d9301a] | 732 | { |
---|
[6a70f3] | 733 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 734 | mpz_init(erg); |
---|
[6a70f3] | 735 | mpz_mod(erg, (mpz_ptr)from, dst->modNumber); |
---|
[e90dfd6] | 736 | return (number)erg; |
---|
[d9301a] | 737 | } |
---|
| 738 | |
---|
[d22092f] | 739 | static number nrnMapQ(number from, const coeffs src, const coeffs dst) |
---|
| 740 | { |
---|
| 741 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
| 742 | mpz_init(erg); |
---|
[a0707f8] | 743 | nlGMP(from, erg, src); // FIXME? TODO? // extern void nlGMP(number &i, number n, const coeffs r); // to be replaced with n_MPZ(erg, from, src); // ? |
---|
[d22092f] | 744 | mpz_mod(erg, erg, dst->modNumber); |
---|
| 745 | return (number)erg; |
---|
| 746 | } |
---|
| 747 | |
---|
[fe99ed] | 748 | #if SI_INTEGER_VARIANT==3 |
---|
[bcbdc40] | 749 | static number nrnMapZ(number from, const coeffs /*src*/, const coeffs dst) |
---|
[fe99ed] | 750 | { |
---|
[6a70f3] | 751 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[fe99ed] | 752 | if (n_Z_IS_SMALL(from)) |
---|
| 753 | mpz_init_set_si(erg, SR_TO_INT(from)); |
---|
| 754 | else |
---|
[6a70f3] | 755 | mpz_init_set(erg, (mpz_ptr) from); |
---|
[fe99ed] | 756 | mpz_mod(erg, erg, dst->modNumber); |
---|
| 757 | return (number)erg; |
---|
| 758 | } |
---|
| 759 | #elif SI_INTEGER_VARIANT==2 |
---|
| 760 | |
---|
[bcbdc40] | 761 | static number nrnMapZ(number from, const coeffs src, const coeffs dst) |
---|
[6a1aa7] | 762 | { |
---|
| 763 | if (SR_HDL(from) & SR_INT) |
---|
| 764 | { |
---|
| 765 | long f_i=SR_TO_INT(from); |
---|
| 766 | return nrnInit(f_i,dst); |
---|
| 767 | } |
---|
| 768 | return nrnMapGMP(from,src,dst); |
---|
| 769 | } |
---|
[f3e64d2] | 770 | #elif SI_INTEGER_VARIANT==1 |
---|
[bcbdc40] | 771 | static number nrnMapZ(number from, const coeffs src, const coeffs dst) |
---|
[f3e64d2] | 772 | { |
---|
| 773 | return nrnMapQ(from,src,dst); |
---|
| 774 | } |
---|
| 775 | #endif |
---|
[417a91a] | 776 | void nrnWrite (number a, const coeffs cf) |
---|
[f3e64d2] | 777 | { |
---|
| 778 | char *s,*z; |
---|
| 779 | if (a==NULL) |
---|
| 780 | { |
---|
| 781 | StringAppendS("o"); |
---|
| 782 | } |
---|
| 783 | else |
---|
| 784 | { |
---|
[6a70f3] | 785 | int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2; |
---|
[f3e64d2] | 786 | s=(char*)omAlloc(l); |
---|
[417a91a] | 787 | if (cf->is_field) |
---|
| 788 | { |
---|
| 789 | mpz_t ch2; mpz_init_set(ch2, cf->modBase); |
---|
| 790 | mpz_sub_ui(ch2,ch2,1); |
---|
| 791 | mpz_divexact_ui(ch2,ch2,2); |
---|
| 792 | if ((mpz_cmp_ui(cf->modBase,2)!=0) && (mpz_cmp(ch2,(mpz_ptr)a)<0)) |
---|
| 793 | { |
---|
| 794 | mpz_sub(ch2,(mpz_ptr)a,cf->modBase); |
---|
| 795 | z=mpz_get_str(s,10,ch2); |
---|
| 796 | StringAppendS(z); |
---|
| 797 | } |
---|
| 798 | else |
---|
| 799 | { |
---|
| 800 | z=mpz_get_str(s,10,(mpz_ptr) a); |
---|
| 801 | StringAppendS(z); |
---|
| 802 | } |
---|
| 803 | mpz_clear(ch2); |
---|
| 804 | } |
---|
| 805 | else |
---|
| 806 | { |
---|
| 807 | z=mpz_get_str(s,10,(mpz_ptr) a); |
---|
| 808 | StringAppendS(z); |
---|
| 809 | } |
---|
[f3e64d2] | 810 | omFreeSize((ADDRESS)s,l); |
---|
| 811 | } |
---|
| 812 | } |
---|
[6a1aa7] | 813 | |
---|
[4d1ae5] | 814 | nMapFunc nrnSetMap(const coeffs src, const coeffs dst) |
---|
[275ecc] | 815 | { |
---|
[6a1aa7] | 816 | /* dst = nrn */ |
---|
[353a42] | 817 | if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src)) |
---|
[d351d8] | 818 | { |
---|
[fe99ed] | 819 | return nrnMapZ; |
---|
[894f5b1] | 820 | } |
---|
[353a42] | 821 | if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/) |
---|
[6a1aa7] | 822 | { |
---|
| 823 | return nrnMapZ; |
---|
| 824 | } |
---|
[f3e64d2] | 825 | if (src->rep==n_rep_gap_rat) /*&& nCoeff_is_Q(src)) or Z*/ |
---|
[894f5b1] | 826 | { |
---|
| 827 | return nrnMapQ; |
---|
[d9301a] | 828 | } |
---|
[894f5b1] | 829 | // Some type of Z/n ring / field |
---|
[1becad6] | 830 | if (nCoeff_is_Zn(src) || nCoeff_is_Ring_PtoM(src) || |
---|
[f0797c] | 831 | nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src)) |
---|
[d9301a] | 832 | { |
---|
[66ce6d] | 833 | if ( (!nCoeff_is_Zp(src)) |
---|
[e90dfd6] | 834 | && (mpz_cmp(src->modBase, dst->modBase) == 0) |
---|
[417a91a] | 835 | && (src->modExponent == dst->modExponent)) return ndCopyMap; |
---|
[d351d8] | 836 | else |
---|
| 837 | { |
---|
[6a70f3] | 838 | mpz_ptr nrnMapModul = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
[894f5b1] | 839 | // Computing the n of Z/n |
---|
[1cce47] | 840 | if (nCoeff_is_Zp(src)) |
---|
[894f5b1] | 841 | { |
---|
| 842 | mpz_init_set_si(nrnMapModul, src->ch); |
---|
| 843 | } |
---|
| 844 | else |
---|
| 845 | { |
---|
| 846 | mpz_init(nrnMapModul); |
---|
[e90dfd6] | 847 | mpz_set(nrnMapModul, src->modNumber); |
---|
[894f5b1] | 848 | } |
---|
| 849 | // nrnMapCoef = 1 in dst if dst is a subring of src |
---|
| 850 | // nrnMapCoef = 0 in dst / src if src is a subring of dst |
---|
[d9301a] | 851 | if (nrnMapCoef == NULL) |
---|
[d351d8] | 852 | { |
---|
[6a70f3] | 853 | nrnMapCoef = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
[d9301a] | 854 | mpz_init(nrnMapCoef); |
---|
| 855 | } |
---|
[e90dfd6] | 856 | if (mpz_divisible_p(nrnMapModul, dst->modNumber)) |
---|
[894f5b1] | 857 | { |
---|
[5a0d2ae] | 858 | mpz_set_ui(nrnMapCoef, 1); |
---|
[894f5b1] | 859 | } |
---|
| 860 | else |
---|
[54bb6b] | 861 | if (mpz_divisible_p(dst->modNumber,nrnMapModul)) |
---|
[d9301a] | 862 | { |
---|
[e90dfd6] | 863 | mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul); |
---|
[6a70f3] | 864 | mpz_ptr tmp = dst->modNumber; |
---|
[e90dfd6] | 865 | dst->modNumber = nrnMapModul; |
---|
[4d1ae5] | 866 | if (!nrnIsUnit((number) nrnMapCoef,dst)) |
---|
[0959dc] | 867 | { |
---|
[e90dfd6] | 868 | dst->modNumber = tmp; |
---|
[4d1ae5] | 869 | nrnDelete((number*) &nrnMapModul, dst); |
---|
[0959dc] | 870 | return NULL; |
---|
| 871 | } |
---|
[6a70f3] | 872 | mpz_ptr inv = (mpz_ptr) nrnInvers((number) nrnMapCoef,dst); |
---|
[e90dfd6] | 873 | dst->modNumber = tmp; |
---|
[d9301a] | 874 | mpz_mul(nrnMapCoef, nrnMapCoef, inv); |
---|
[e90dfd6] | 875 | mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber); |
---|
[4d1ae5] | 876 | nrnDelete((number*) &inv, dst); |
---|
[d9301a] | 877 | } |
---|
| 878 | else |
---|
| 879 | { |
---|
[4d1ae5] | 880 | nrnDelete((number*) &nrnMapModul, dst); |
---|
[d9301a] | 881 | return NULL; |
---|
[d351d8] | 882 | } |
---|
[4d1ae5] | 883 | nrnDelete((number*) &nrnMapModul, dst); |
---|
[1cce47] | 884 | if (nCoeff_is_Ring_2toM(src)) |
---|
[d9301a] | 885 | return nrnMap2toM; |
---|
[1cce47] | 886 | else if (nCoeff_is_Zp(src)) |
---|
[894f5b1] | 887 | return nrnMapZp; |
---|
[d351d8] | 888 | else |
---|
[d9301a] | 889 | return nrnMapModN; |
---|
[d351d8] | 890 | } |
---|
| 891 | } |
---|
| 892 | return NULL; // default |
---|
[275ecc] | 893 | } |
---|
| 894 | |
---|
| 895 | /* |
---|
| 896 | * set the exponent (allocate and init tables) (TODO) |
---|
| 897 | */ |
---|
| 898 | |
---|
[bcbdc40] | 899 | static void nrnSetExp(unsigned long m, coeffs r) |
---|
[275ecc] | 900 | { |
---|
[e90dfd6] | 901 | /* clean up former stuff */ |
---|
| 902 | if (r->modNumber != NULL) mpz_clear(r->modNumber); |
---|
[20704f] | 903 | |
---|
[0486a3] | 904 | r->modExponent= m; |
---|
[6a70f3] | 905 | r->modNumber = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
[0486a3] | 906 | mpz_init_set (r->modNumber, r->modBase); |
---|
| 907 | mpz_pow_ui (r->modNumber, r->modNumber, m); |
---|
[275ecc] | 908 | } |
---|
| 909 | |
---|
[0486a3] | 910 | /* We expect this ring to be Z/n^m for some m > 0 and for some n > 2 which is not a prime. */ |
---|
[bcbdc40] | 911 | static void nrnInitExp(unsigned long m, coeffs r) |
---|
[275ecc] | 912 | { |
---|
[12ea9d] | 913 | nrnSetExp(m, r); |
---|
[0486a3] | 914 | assume (r->modNumber != NULL); |
---|
[4d5437] | 915 | //CF: in general, the modulus is computed somewhere. I don't want to |
---|
[fe99ed] | 916 | // check it's size before I construct the best ring. |
---|
| 917 | // if (mpz_cmp_ui(r->modNumber,2) <= 0) |
---|
| 918 | // WarnS("nrnInitExp failed (m in Z/m too small)"); |
---|
[275ecc] | 919 | } |
---|
| 920 | |
---|
| 921 | #ifdef LDEBUG |
---|
[52f3e2] | 922 | BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r) |
---|
[275ecc] | 923 | { |
---|
[52f3e2] | 924 | if ( (mpz_sgn1((mpz_ptr) a) < 0) || (mpz_cmp((mpz_ptr) a, r->modNumber) > 0) ) |
---|
[275ecc] | 925 | { |
---|
[52f3e2] | 926 | Warn("mod-n: out of range at %s:%d\n",f,l); |
---|
[275ecc] | 927 | return FALSE; |
---|
| 928 | } |
---|
| 929 | return TRUE; |
---|
| 930 | } |
---|
| 931 | #endif |
---|
| 932 | |
---|
[8e56ad] | 933 | /*2 |
---|
| 934 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
---|
| 935 | */ |
---|
[a604c3] | 936 | static const char * nlCPEatLongC(char *s, mpz_ptr i) |
---|
[275ecc] | 937 | { |
---|
[85e68dd] | 938 | const char * start=s; |
---|
[af378f7] | 939 | if (!(*s >= '0' && *s <= '9')) |
---|
| 940 | { |
---|
[5a0d2ae] | 941 | mpz_init_set_ui(i, 1); |
---|
[af378f7] | 942 | return s; |
---|
| 943 | } |
---|
| 944 | mpz_init(i); |
---|
[8e56ad] | 945 | while (*s >= '0' && *s <= '9') s++; |
---|
| 946 | if (*s=='\0') |
---|
[275ecc] | 947 | { |
---|
[8e56ad] | 948 | mpz_set_str(i,start,10); |
---|
| 949 | } |
---|
| 950 | else |
---|
| 951 | { |
---|
| 952 | char c=*s; |
---|
| 953 | *s='\0'; |
---|
| 954 | mpz_set_str(i,start,10); |
---|
| 955 | *s=c; |
---|
[275ecc] | 956 | } |
---|
| 957 | return s; |
---|
| 958 | } |
---|
| 959 | |
---|
[bcbdc40] | 960 | static const char * nrnRead (const char *s, number *a, const coeffs r) |
---|
[275ecc] | 961 | { |
---|
[6a70f3] | 962 | mpz_ptr z = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
[275ecc] | 963 | { |
---|
[85e68dd] | 964 | s = nlCPEatLongC((char *)s, z); |
---|
[275ecc] | 965 | } |
---|
[e90dfd6] | 966 | mpz_mod(z, z, r->modNumber); |
---|
[417a91a] | 967 | if ((*s)=='/') |
---|
| 968 | { |
---|
| 969 | mpz_ptr n = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
| 970 | s++; |
---|
| 971 | s=nlCPEatLongC((char*)s,n); |
---|
| 972 | if (!nrnIsOne((number)n,r)) |
---|
| 973 | { |
---|
| 974 | *a=nrnDiv((number)z,(number)n,r); |
---|
| 975 | mpz_clear(z); |
---|
| 976 | omFreeBin((void *)z, gmp_nrz_bin); |
---|
| 977 | mpz_clear(n); |
---|
| 978 | omFreeBin((void *)n, gmp_nrz_bin); |
---|
| 979 | } |
---|
| 980 | } |
---|
| 981 | else |
---|
| 982 | *a = (number) z; |
---|
[275ecc] | 983 | return s; |
---|
| 984 | } |
---|
[bcbdc40] | 985 | |
---|
[417a91a] | 986 | static number nrnConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
---|
| 987 | { |
---|
| 988 | return nrnInit(n.intval(),r); |
---|
| 989 | } |
---|
| 990 | |
---|
| 991 | static CanonicalForm nrnConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r ) |
---|
| 992 | { |
---|
| 993 | if (setChar) setCharacteristic( r->ch ); |
---|
| 994 | return CanonicalForm(nrnInt( n,r )); |
---|
| 995 | } |
---|
| 996 | |
---|
[bcbdc40] | 997 | /* for initializing function pointers */ |
---|
| 998 | BOOLEAN nrnInitChar (coeffs r, void* p) |
---|
| 999 | { |
---|
| 1000 | assume( (getCoeffType(r) == n_Zn) || (getCoeffType (r) == n_Znm) ); |
---|
| 1001 | ZnmInfo * info= (ZnmInfo *) p; |
---|
| 1002 | r->modBase= (mpz_ptr)nrnCopy((number)info->base, r); //this circumvents the problem |
---|
| 1003 | //in bigintmat.cc where we cannot create a "legal" nrn that can be freed. |
---|
| 1004 | //If we take a copy, we can do whatever we want. |
---|
| 1005 | |
---|
| 1006 | nrnInitExp (info->exp, r); |
---|
| 1007 | |
---|
| 1008 | /* next computation may yield wrong characteristic as r->modNumber |
---|
| 1009 | is a GMP number */ |
---|
| 1010 | r->ch = mpz_get_ui(r->modNumber); |
---|
| 1011 | |
---|
| 1012 | r->is_field=FALSE; |
---|
| 1013 | r->is_domain=FALSE; |
---|
| 1014 | r->rep=n_rep_gmp; |
---|
| 1015 | |
---|
| 1016 | |
---|
| 1017 | r->cfCoeffString = nrnCoeffString; |
---|
| 1018 | |
---|
| 1019 | r->cfInit = nrnInit; |
---|
| 1020 | r->cfDelete = nrnDelete; |
---|
| 1021 | r->cfCopy = nrnCopy; |
---|
| 1022 | r->cfSize = nrnSize; |
---|
| 1023 | r->cfInt = nrnInt; |
---|
| 1024 | r->cfAdd = nrnAdd; |
---|
| 1025 | r->cfSub = nrnSub; |
---|
| 1026 | r->cfMult = nrnMult; |
---|
| 1027 | r->cfDiv = nrnDiv; |
---|
| 1028 | r->cfAnn = nrnAnn; |
---|
| 1029 | r->cfIntMod = nrnMod; |
---|
| 1030 | r->cfExactDiv = nrnDiv; |
---|
[a0707f8] | 1031 | r->cfInpNeg = nrnNeg; |
---|
[bcbdc40] | 1032 | r->cfInvers = nrnInvers; |
---|
| 1033 | r->cfDivBy = nrnDivBy; |
---|
| 1034 | r->cfDivComp = nrnDivComp; |
---|
| 1035 | r->cfGreater = nrnGreater; |
---|
| 1036 | r->cfEqual = nrnEqual; |
---|
| 1037 | r->cfIsZero = nrnIsZero; |
---|
| 1038 | r->cfIsOne = nrnIsOne; |
---|
| 1039 | r->cfIsMOne = nrnIsMOne; |
---|
| 1040 | r->cfGreaterZero = nrnGreaterZero; |
---|
| 1041 | r->cfWriteLong = nrnWrite; |
---|
| 1042 | r->cfRead = nrnRead; |
---|
| 1043 | r->cfPower = nrnPower; |
---|
| 1044 | r->cfSetMap = nrnSetMap; |
---|
| 1045 | //r->cfNormalize = ndNormalize; |
---|
| 1046 | r->cfLcm = nrnLcm; |
---|
| 1047 | r->cfGcd = nrnGcd; |
---|
| 1048 | r->cfIsUnit = nrnIsUnit; |
---|
| 1049 | r->cfGetUnit = nrnGetUnit; |
---|
| 1050 | r->cfExtGcd = nrnExtGcd; |
---|
| 1051 | r->cfXExtGcd = nrnXExtGcd; |
---|
| 1052 | r->cfQuotRem = nrnQuotRem; |
---|
| 1053 | r->cfCoeffName = nrnCoeffName; |
---|
| 1054 | r->cfCoeffWrite = nrnCoeffWrite; |
---|
[417a91a] | 1055 | r->nCoeffIsEqual = nrnCoeffIsEqual; |
---|
[bcbdc40] | 1056 | r->cfKillChar = nrnKillChar; |
---|
| 1057 | r->cfQuot1 = nrnQuot1; |
---|
[4b5b36] | 1058 | #if SI_INTEGER_VARIANT==2 |
---|
| 1059 | r->cfWriteFd = nrzWriteFd; |
---|
| 1060 | r->cfReadFd = nrzReadFd; |
---|
| 1061 | #endif |
---|
| 1062 | |
---|
[bcbdc40] | 1063 | #ifdef LDEBUG |
---|
| 1064 | r->cfDBTest = nrnDBTest; |
---|
| 1065 | #endif |
---|
[417a91a] | 1066 | if ((r->modExponent==1)&&(mpz_size1(r->modBase)==1)) |
---|
| 1067 | { |
---|
| 1068 | long p=mpz_get_si(r->modBase); |
---|
[acb07e] | 1069 | if ((p<=FACTORY_MAX_PRIME)&&(p==IsPrime(p))) /*factory limit: <2^29*/ |
---|
[417a91a] | 1070 | { |
---|
| 1071 | r->convFactoryNSingN=nrnConvFactoryNSingN; |
---|
| 1072 | r->convSingNFactoryN=nrnConvSingNFactoryN; |
---|
| 1073 | } |
---|
| 1074 | } |
---|
[bcbdc40] | 1075 | return FALSE; |
---|
| 1076 | } |
---|
| 1077 | |
---|
[275ecc] | 1078 | #endif |
---|
[8d0331d] | 1079 | /* #ifdef HAVE_RINGS */ |
---|