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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7 | #include "misc/auxiliary.h" |
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8 | |
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9 | #include "misc/mylimits.h" |
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10 | #include "misc/prime.h" // IsPrime |
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11 | #include "reporter/reporter.h" |
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12 | |
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13 | #include "coeffs/si_gmp.h" |
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14 | #include "coeffs/coeffs.h" |
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15 | #include "coeffs/modulop.h" |
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16 | #include "coeffs/rintegers.h" |
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17 | #include "coeffs/numbers.h" |
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18 | |
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19 | #include "coeffs/mpr_complex.h" |
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20 | |
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21 | #include "coeffs/longrat.h" |
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22 | #include "coeffs/rmodulon.h" |
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23 | |
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24 | #include <string.h> |
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25 | |
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26 | #ifdef HAVE_RINGS |
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27 | |
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28 | void nrnWrite (number a, const coeffs); |
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29 | #ifdef LDEBUG |
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30 | static 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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33 | EXTERN_VAR omBin gmp_nrz_bin; |
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34 | |
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35 | coeffs nrnInitCfByName(char *s,n_coeffType) |
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36 | { |
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37 | const char start[]="ZZ/bigint("; |
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38 | const int start_len=strlen(start); |
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39 | if (strncmp(s,start,start_len)==0) |
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40 | { |
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41 | s+=start_len; |
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42 | mpz_t z; |
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43 | mpz_init(z); |
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44 | s=nEatLong(s,z); |
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45 | ZnmInfo info; |
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46 | info.base=z; |
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47 | info.exp= 1; |
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48 | while ((*s!='\0') && (*s!=')')) s++; |
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49 | // expect ")" or ")^exp" |
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50 | if (*s=='\0') { mpz_clear(z); return NULL; } |
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51 | if (((*s)==')') && (*(s+1)=='^')) |
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52 | { |
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53 | s=s+2; |
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54 | int i; |
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55 | s=nEati(s,&i,0); |
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56 | info.exp=(unsigned long)i; |
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57 | return nInitChar(n_Znm,(void*) &info); |
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58 | } |
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59 | else |
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60 | return nInitChar(n_Zn,(void*) &info); |
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61 | } |
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62 | else return NULL; |
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63 | } |
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64 | |
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65 | STATIC_VAR char* nrnCoeffName_buff=NULL; |
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66 | static char* nrnCoeffName(const coeffs r) |
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67 | { |
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68 | if(nrnCoeffName_buff!=NULL) omFree(nrnCoeffName_buff); |
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69 | size_t l = (size_t)mpz_sizeinbase(r->modBase, 10) + 2; |
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70 | char* s = (char*) omAlloc(l); |
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71 | l+=24; |
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72 | nrnCoeffName_buff=(char*)omAlloc(l); |
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73 | s= mpz_get_str (s, 10, r->modBase); |
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74 | int ll=0; |
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75 | if (nCoeff_is_Zn(r)) |
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76 | { |
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77 | if (strlen(s)<10) |
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78 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/(%s)",s); |
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79 | else |
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80 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/bigint(%s)",s); |
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81 | } |
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82 | else if (nCoeff_is_Ring_PtoM(r)) |
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83 | ll=snprintf(nrnCoeffName_buff,l,"ZZ/(bigint(%s)^%lu)",s,r->modExponent); |
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84 | assume(ll<(int)l); // otherwise nrnCoeffName_buff too small |
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85 | omFreeSize((ADDRESS)s, l-22); |
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86 | return nrnCoeffName_buff; |
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87 | } |
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88 | |
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89 | static BOOLEAN nrnCoeffIsEqual(const coeffs r, n_coeffType n, void * parameter) |
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90 | { |
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91 | /* test, if r is an instance of nInitCoeffs(n,parameter) */ |
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92 | ZnmInfo *info=(ZnmInfo*)parameter; |
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93 | return (n==r->type) && (r->modExponent==info->exp) |
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94 | && (mpz_cmp(r->modBase,info->base)==0); |
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95 | } |
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96 | |
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97 | static void nrnKillChar(coeffs r) |
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98 | { |
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99 | mpz_clear(r->modNumber); |
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100 | mpz_clear(r->modBase); |
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101 | omFreeBin((void *) r->modBase, gmp_nrz_bin); |
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102 | omFreeBin((void *) r->modNumber, gmp_nrz_bin); |
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103 | } |
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104 | |
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105 | static coeffs nrnQuot1(number c, const coeffs r) |
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106 | { |
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107 | coeffs rr; |
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108 | long ch = r->cfInt(c, r); |
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109 | mpz_t a,b; |
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110 | mpz_init_set(a, r->modNumber); |
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111 | mpz_init_set_ui(b, ch); |
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112 | mpz_t gcd; |
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113 | mpz_init(gcd); |
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114 | mpz_gcd(gcd, a,b); |
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115 | if(mpz_cmp_ui(gcd, 1) == 0) |
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116 | { |
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117 | WerrorS("constant in q-ideal is coprime to modulus in ground ring"); |
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118 | WerrorS("Unable to create qring!"); |
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119 | return NULL; |
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120 | } |
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121 | if(r->modExponent == 1) |
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122 | { |
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123 | ZnmInfo info; |
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124 | info.base = gcd; |
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125 | info.exp = (unsigned long) 1; |
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126 | rr = nInitChar(n_Zn, (void*)&info); |
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127 | } |
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128 | else |
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129 | { |
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130 | ZnmInfo info; |
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131 | info.base = r->modBase; |
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132 | int kNew = 1; |
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133 | mpz_t baseTokNew; |
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134 | mpz_init(baseTokNew); |
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135 | mpz_set(baseTokNew, r->modBase); |
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136 | while(mpz_cmp(gcd, baseTokNew) > 0) |
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137 | { |
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138 | kNew++; |
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139 | mpz_mul(baseTokNew, baseTokNew, r->modBase); |
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140 | } |
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141 | //printf("\nkNew = %i\n",kNew); |
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142 | info.exp = kNew; |
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143 | mpz_clear(baseTokNew); |
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144 | rr = nInitChar(n_Znm, (void*)&info); |
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145 | } |
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146 | mpz_clear(gcd); |
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147 | return(rr); |
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148 | } |
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149 | |
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150 | static number nrnCopy(number a, const coeffs) |
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151 | { |
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152 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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153 | mpz_init_set(erg, (mpz_ptr) a); |
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154 | return (number) erg; |
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155 | } |
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156 | |
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157 | /* |
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158 | * create a number from int |
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159 | */ |
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160 | static number nrnInit(long i, const coeffs r) |
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161 | { |
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162 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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163 | mpz_init_set_si(erg, i); |
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164 | mpz_mod(erg, erg, r->modNumber); |
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165 | return (number) erg; |
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166 | } |
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167 | |
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168 | /* |
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169 | * convert a number to int |
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170 | */ |
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171 | static long nrnInt(number &n, const coeffs) |
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172 | { |
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173 | return mpz_get_si((mpz_ptr) n); |
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174 | } |
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175 | |
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176 | #if SI_INTEGER_VARIANT==2 |
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177 | #define nrnDelete nrzDelete |
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178 | #define nrnSize nrzSize |
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179 | #else |
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180 | static void nrnDelete(number *a, const coeffs) |
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181 | { |
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182 | if (*a != NULL) |
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183 | { |
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184 | mpz_clear((mpz_ptr) *a); |
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185 | omFreeBin((void *) *a, gmp_nrz_bin); |
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186 | *a = NULL; |
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187 | } |
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188 | } |
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189 | static int nrnSize(number a, const coeffs) |
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190 | { |
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191 | return mpz_size1((mpz_ptr)a); |
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192 | } |
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193 | #endif |
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194 | /* |
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195 | * Multiply two numbers |
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196 | */ |
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197 | static number nrnMult(number a, number b, const coeffs r) |
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198 | { |
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199 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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200 | mpz_init(erg); |
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201 | mpz_mul(erg, (mpz_ptr)a, (mpz_ptr) b); |
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202 | mpz_mod(erg, erg, r->modNumber); |
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203 | return (number) erg; |
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204 | } |
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205 | |
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206 | static void nrnInpMult(number &a, number b, const coeffs r) |
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207 | { |
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208 | mpz_mul((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b); |
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209 | mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber); |
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210 | } |
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211 | |
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212 | static void nrnPower(number a, int i, number * result, const coeffs r) |
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213 | { |
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214 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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215 | mpz_init(erg); |
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216 | mpz_powm_ui(erg, (mpz_ptr)a, i, r->modNumber); |
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217 | *result = (number) erg; |
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218 | } |
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219 | |
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220 | static number nrnAdd(number a, number b, const coeffs r) |
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221 | { |
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222 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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223 | mpz_init(erg); |
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224 | mpz_add(erg, (mpz_ptr)a, (mpz_ptr) b); |
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225 | mpz_mod(erg, erg, r->modNumber); |
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226 | return (number) erg; |
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227 | } |
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228 | |
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229 | static void nrnInpAdd(number &a, number b, const coeffs r) |
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230 | { |
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231 | mpz_add((mpz_ptr)a, (mpz_ptr)a, (mpz_ptr) b); |
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232 | mpz_mod((mpz_ptr)a, (mpz_ptr)a, r->modNumber); |
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233 | } |
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234 | |
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235 | static number nrnSub(number a, number b, const coeffs r) |
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236 | { |
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237 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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238 | mpz_init(erg); |
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239 | mpz_sub(erg, (mpz_ptr)a, (mpz_ptr) b); |
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240 | mpz_mod(erg, erg, r->modNumber); |
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241 | return (number) erg; |
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242 | } |
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243 | |
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244 | static BOOLEAN nrnIsZero(number a, const coeffs) |
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245 | { |
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246 | return 0 == mpz_sgn1((mpz_ptr)a); |
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247 | } |
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248 | |
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249 | static number nrnNeg(number c, const coeffs r) |
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250 | { |
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251 | if( !nrnIsZero(c, r) ) |
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252 | // Attention: This method operates in-place. |
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253 | mpz_sub((mpz_ptr)c, r->modNumber, (mpz_ptr)c); |
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254 | return c; |
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255 | } |
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256 | |
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257 | static number nrnInvers(number c, const coeffs r) |
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258 | { |
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259 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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260 | mpz_init(erg); |
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261 | if (nrnIsZero(c,r)) |
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262 | { |
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263 | WerrorS(nDivBy0); |
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264 | } |
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265 | else |
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266 | { |
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267 | mpz_invert(erg, (mpz_ptr)c, r->modNumber); |
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268 | } |
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269 | return (number) erg; |
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270 | } |
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271 | |
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272 | /* |
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273 | * Give the largest k, such that a = x * k, b = y * k has |
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274 | * a solution. |
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275 | * a may be NULL, b not |
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276 | */ |
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277 | static number nrnGcd(number a, number b, const coeffs r) |
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278 | { |
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279 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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280 | mpz_init_set(erg, r->modNumber); |
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281 | if (a != NULL) mpz_gcd(erg, erg, (mpz_ptr)a); |
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282 | mpz_gcd(erg, erg, (mpz_ptr)b); |
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283 | if(mpz_cmp(erg,r->modNumber)==0) |
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284 | { |
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285 | mpz_clear(erg); |
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286 | omFreeBin((ADDRESS)erg,gmp_nrz_bin); |
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287 | return nrnInit(0,r); |
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288 | } |
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289 | return (number)erg; |
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290 | } |
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291 | |
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292 | /* |
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293 | * Give the smallest k, such that a * x = k = b * y has a solution |
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294 | * TODO: lcm(gcd,gcd) better than gcd(lcm) ? |
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295 | */ |
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296 | static number nrnLcm(number a, number b, const coeffs r) |
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297 | { |
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298 | number erg = nrnGcd(NULL, a, r); |
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299 | number tmp = nrnGcd(NULL, b, r); |
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300 | mpz_lcm((mpz_ptr)erg, (mpz_ptr)erg, (mpz_ptr)tmp); |
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301 | nrnDelete(&tmp, r); |
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302 | return (number)erg; |
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303 | } |
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304 | |
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305 | /* Not needed any more, but may have room for improvement |
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306 | number nrnGcd3(number a,number b, number c,ring r) |
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307 | { |
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308 | mpz_ptr erg = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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309 | mpz_init(erg); |
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310 | if (a == NULL) a = (number)r->modNumber; |
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311 | if (b == NULL) b = (number)r->modNumber; |
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312 | if (c == NULL) c = (number)r->modNumber; |
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313 | mpz_gcd(erg, (mpz_ptr)a, (mpz_ptr)b); |
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314 | mpz_gcd(erg, erg, (mpz_ptr)c); |
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315 | mpz_gcd(erg, erg, r->modNumber); |
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316 | return (number)erg; |
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317 | } |
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318 | */ |
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319 | |
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320 | /* |
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321 | * Give the largest k, such that a = x * k, b = y * k has |
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322 | * a solution and r, s, s.t. k = s*a + t*b |
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323 | * CF: careful: ExtGcd is wrong as implemented (or at least may not |
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324 | * give you what you want: |
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325 | * ExtGcd(5, 10 modulo 12): |
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326 | * the gcdext will return 5 = 1*5 + 0*10 |
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327 | * however, mod 12, the gcd should be 1 |
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328 | */ |
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329 | static number nrnExtGcd(number a, number b, number *s, number *t, const coeffs r) |
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330 | { |
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331 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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332 | mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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333 | mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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334 | mpz_init(erg); |
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335 | mpz_init(bs); |
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336 | mpz_init(bt); |
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337 | mpz_gcdext(erg, bs, bt, (mpz_ptr)a, (mpz_ptr)b); |
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338 | mpz_mod(bs, bs, r->modNumber); |
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339 | mpz_mod(bt, bt, r->modNumber); |
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340 | *s = (number)bs; |
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341 | *t = (number)bt; |
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342 | return (number)erg; |
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343 | } |
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344 | |
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345 | static BOOLEAN nrnIsOne(number a, const coeffs) |
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346 | { |
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347 | return 0 == mpz_cmp_si((mpz_ptr)a, 1); |
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348 | } |
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349 | |
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350 | static BOOLEAN nrnEqual(number a, number b, const coeffs) |
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351 | { |
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352 | return 0 == mpz_cmp((mpz_ptr)a, (mpz_ptr)b); |
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353 | } |
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354 | |
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355 | static number nrnGetUnit(number k, const coeffs r) |
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356 | { |
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357 | if (mpz_divisible_p(r->modNumber, (mpz_ptr)k)) return nrnInit(1,r); |
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358 | |
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359 | mpz_ptr unit = (mpz_ptr)nrnGcd(NULL, k, r); |
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360 | mpz_tdiv_q(unit, (mpz_ptr)k, unit); |
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361 | mpz_ptr gcd = (mpz_ptr)nrnGcd(NULL, (number)unit, r); |
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362 | if (!nrnIsOne((number)gcd,r)) |
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363 | { |
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364 | mpz_ptr ctmp; |
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365 | // tmp := unit^2 |
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366 | mpz_ptr tmp = (mpz_ptr) nrnMult((number) unit,(number) unit,r); |
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367 | // gcd_new := gcd(tmp, 0) |
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368 | mpz_ptr gcd_new = (mpz_ptr) nrnGcd(NULL, (number) tmp, r); |
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369 | while (!nrnEqual((number) gcd_new,(number) gcd,r)) |
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370 | { |
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371 | // gcd := gcd_new |
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372 | ctmp = gcd; |
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373 | gcd = gcd_new; |
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374 | gcd_new = ctmp; |
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375 | // tmp := tmp * unit |
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376 | mpz_mul(tmp, tmp, unit); |
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377 | mpz_mod(tmp, tmp, r->modNumber); |
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378 | // gcd_new := gcd(tmp, 0) |
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379 | mpz_gcd(gcd_new, tmp, r->modNumber); |
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380 | } |
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381 | // unit := unit + modNumber / gcd_new |
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382 | mpz_tdiv_q(tmp, r->modNumber, gcd_new); |
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383 | mpz_add(unit, unit, tmp); |
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384 | mpz_mod(unit, unit, r->modNumber); |
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385 | nrnDelete((number*) &gcd_new, r); |
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386 | nrnDelete((number*) &tmp, r); |
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387 | } |
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388 | nrnDelete((number*) &gcd, r); |
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389 | return (number)unit; |
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390 | } |
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391 | |
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392 | /* XExtGcd returns a unimodular matrix ((s,t)(u,v)) sth. |
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393 | * (a,b)^t ((st)(uv)) = (g,0)^t |
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394 | * Beware, the ExtGcd will not necessaairly do this. |
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395 | * Problem: if g = as+bt then (in Z/nZ) it follows NOT that |
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396 | * 1 = (a/g)s + (b/g) t |
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397 | * due to the zero divisors. |
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398 | */ |
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399 | |
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400 | //#define CF_DEB; |
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401 | static number nrnXExtGcd(number a, number b, number *s, number *t, number *u, number *v, const coeffs r) |
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402 | { |
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403 | number xx; |
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404 | #ifdef CF_DEB |
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405 | StringSetS("XExtGcd of "); |
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406 | nrnWrite(a, r); |
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407 | StringAppendS("\t"); |
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408 | nrnWrite(b, r); |
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409 | StringAppendS(" modulo "); |
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410 | nrnWrite(xx = (number)r->modNumber, r); |
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411 | Print("%s\n", StringEndS()); |
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412 | #endif |
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413 | |
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414 | mpz_ptr one = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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415 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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416 | mpz_ptr bs = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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417 | mpz_ptr bt = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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418 | mpz_ptr bu = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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419 | mpz_ptr bv = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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420 | mpz_init(erg); |
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421 | mpz_init(one); |
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422 | mpz_init_set(bs, (mpz_ptr) a); |
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423 | mpz_init_set(bt, (mpz_ptr) b); |
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424 | mpz_init(bu); |
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425 | mpz_init(bv); |
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426 | mpz_gcd(erg, bs, bt); |
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427 | |
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428 | #ifdef CF_DEB |
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429 | StringSetS("1st gcd:"); |
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430 | nrnWrite(xx= (number)erg, r); |
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431 | #endif |
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432 | |
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433 | mpz_gcd(erg, erg, r->modNumber); |
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434 | |
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435 | mpz_div(bs, bs, erg); |
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436 | mpz_div(bt, bt, erg); |
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437 | |
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438 | #ifdef CF_DEB |
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439 | Print("%s\n", StringEndS()); |
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440 | StringSetS("xgcd: "); |
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441 | #endif |
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442 | |
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443 | mpz_gcdext(one, bu, bv, bs, bt); |
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444 | number ui = nrnGetUnit(xx = (number) one, r); |
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445 | #ifdef CF_DEB |
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446 | n_Write(xx, r); |
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447 | StringAppendS("\t"); |
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448 | n_Write(ui, r); |
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449 | Print("%s\n", StringEndS()); |
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450 | #endif |
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451 | nrnDelete(&xx, r); |
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452 | if (!nrnIsOne(ui, r)) |
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453 | { |
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454 | #ifdef CF_DEB |
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455 | PrintS("Scaling\n"); |
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456 | #endif |
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457 | number uii = nrnInvers(ui, r); |
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458 | nrnDelete(&ui, r); |
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459 | ui = uii; |
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460 | mpz_ptr uu = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
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461 | mpz_init_set(uu, (mpz_ptr)ui); |
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462 | mpz_mul(bu, bu, uu); |
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463 | mpz_mul(bv, bv, uu); |
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464 | mpz_clear(uu); |
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465 | omFreeBin(uu, gmp_nrz_bin); |
---|
466 | } |
---|
467 | nrnDelete(&ui, r); |
---|
468 | #ifdef CF_DEB |
---|
469 | StringSetS("xgcd"); |
---|
470 | nrnWrite(xx= (number)bs, r); |
---|
471 | StringAppendS("*"); |
---|
472 | nrnWrite(xx= (number)bu, r); |
---|
473 | StringAppendS(" + "); |
---|
474 | nrnWrite(xx= (number)bt, r); |
---|
475 | StringAppendS("*"); |
---|
476 | nrnWrite(xx= (number)bv, r); |
---|
477 | Print("%s\n", StringEndS()); |
---|
478 | #endif |
---|
479 | |
---|
480 | mpz_mod(bs, bs, r->modNumber); |
---|
481 | mpz_mod(bt, bt, r->modNumber); |
---|
482 | mpz_mod(bu, bu, r->modNumber); |
---|
483 | mpz_mod(bv, bv, r->modNumber); |
---|
484 | *s = (number)bu; |
---|
485 | *t = (number)bv; |
---|
486 | *u = (number)bt; |
---|
487 | *u = nrnNeg(*u, r); |
---|
488 | *v = (number)bs; |
---|
489 | return (number)erg; |
---|
490 | } |
---|
491 | |
---|
492 | static BOOLEAN nrnIsMOne(number a, const coeffs r) |
---|
493 | { |
---|
494 | if((r->ch==2) && (nrnIsOne(a,r))) return FALSE; |
---|
495 | mpz_t t; mpz_init_set(t, (mpz_ptr)a); |
---|
496 | mpz_add_ui(t, t, 1); |
---|
497 | bool erg = (0 == mpz_cmp(t, r->modNumber)); |
---|
498 | mpz_clear(t); |
---|
499 | return erg; |
---|
500 | } |
---|
501 | |
---|
502 | static BOOLEAN nrnGreater(number a, number b, const coeffs) |
---|
503 | { |
---|
504 | return 0 < mpz_cmp((mpz_ptr)a, (mpz_ptr)b); |
---|
505 | } |
---|
506 | |
---|
507 | static BOOLEAN nrnGreaterZero(number k, const coeffs cf) |
---|
508 | { |
---|
509 | if (cf->is_field) |
---|
510 | { |
---|
511 | if (mpz_cmp_ui(cf->modBase,2)==0) |
---|
512 | { |
---|
513 | return TRUE; |
---|
514 | } |
---|
515 | #if 0 |
---|
516 | mpz_t ch2; mpz_init_set(ch2, cf->modBase); |
---|
517 | mpz_sub_ui(ch2,ch2,1); //cf->modBase is odd |
---|
518 | mpz_divexact_ui(ch2,ch2,2); |
---|
519 | if (mpz_cmp(ch2,(mpz_ptr)k)<0) |
---|
520 | { |
---|
521 | mpz_clear(ch2); |
---|
522 | return FALSE; |
---|
523 | } |
---|
524 | mpz_clear(ch2); |
---|
525 | #endif |
---|
526 | } |
---|
527 | #if 0 |
---|
528 | else |
---|
529 | { |
---|
530 | mpz_t ch2; mpz_init_set(ch2, cf->modBase); |
---|
531 | mpz_tdiv_q_ui(ch2,ch2,2); |
---|
532 | if (mpz_cmp(ch2,(mpz_ptr)k)<0) |
---|
533 | { |
---|
534 | mpz_clear(ch2); |
---|
535 | return FALSE; |
---|
536 | } |
---|
537 | mpz_clear(ch2); |
---|
538 | } |
---|
539 | #endif |
---|
540 | return 0 < mpz_sgn1((mpz_ptr)k); |
---|
541 | } |
---|
542 | |
---|
543 | static BOOLEAN nrnIsUnit(number a, const coeffs r) |
---|
544 | { |
---|
545 | number tmp = nrnGcd(a, (number)r->modNumber, r); |
---|
546 | bool res = nrnIsOne(tmp, r); |
---|
547 | nrnDelete(&tmp, r); |
---|
548 | return res; |
---|
549 | } |
---|
550 | |
---|
551 | static number nrnAnn(number k, const coeffs r) |
---|
552 | { |
---|
553 | mpz_ptr tmp = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
554 | mpz_init(tmp); |
---|
555 | mpz_gcd(tmp, (mpz_ptr) k, r->modNumber); |
---|
556 | if (mpz_cmp_si(tmp, 1)==0) |
---|
557 | { |
---|
558 | mpz_set_ui(tmp, 0); |
---|
559 | return (number) tmp; |
---|
560 | } |
---|
561 | mpz_divexact(tmp, r->modNumber, tmp); |
---|
562 | return (number) tmp; |
---|
563 | } |
---|
564 | |
---|
565 | static BOOLEAN nrnDivBy(number a, number b, const coeffs r) |
---|
566 | { |
---|
567 | /* b divides a iff b/gcd(a, b) is a unit in the given ring: */ |
---|
568 | number n = nrnGcd(a, b, r); |
---|
569 | mpz_tdiv_q((mpz_ptr)n, (mpz_ptr)b, (mpz_ptr)n); |
---|
570 | bool result = nrnIsUnit(n, r); |
---|
571 | nrnDelete(&n, NULL); |
---|
572 | return result; |
---|
573 | } |
---|
574 | |
---|
575 | static int nrnDivComp(number a, number b, const coeffs r) |
---|
576 | { |
---|
577 | if (nrnEqual(a, b,r)) return 2; |
---|
578 | if (mpz_divisible_p((mpz_ptr) a, (mpz_ptr) b)) return -1; |
---|
579 | if (mpz_divisible_p((mpz_ptr) b, (mpz_ptr) a)) return 1; |
---|
580 | return 0; |
---|
581 | } |
---|
582 | |
---|
583 | static number nrnDiv(number a, number b, const coeffs r) |
---|
584 | { |
---|
585 | if (nrnIsZero(b,r)) |
---|
586 | { |
---|
587 | WerrorS(nDivBy0); |
---|
588 | return nrnInit(0,r); |
---|
589 | } |
---|
590 | else if (r->is_field) |
---|
591 | { |
---|
592 | number inv=nrnInvers(b,r); |
---|
593 | number erg=nrnMult(a,inv,r); |
---|
594 | nrnDelete(&inv,r); |
---|
595 | return erg; |
---|
596 | } |
---|
597 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
598 | mpz_init(erg); |
---|
599 | if (mpz_divisible_p((mpz_ptr)a, (mpz_ptr)b)) |
---|
600 | { |
---|
601 | mpz_divexact(erg, (mpz_ptr)a, (mpz_ptr)b); |
---|
602 | return (number)erg; |
---|
603 | } |
---|
604 | else |
---|
605 | { |
---|
606 | mpz_ptr gcd = (mpz_ptr)nrnGcd(a, b, r); |
---|
607 | mpz_divexact(erg, (mpz_ptr)b, gcd); |
---|
608 | if (!nrnIsUnit((number)erg, r)) |
---|
609 | { |
---|
610 | WerrorS("Division not possible, even by cancelling zero divisors."); |
---|
611 | nrnDelete((number*) &gcd, r); |
---|
612 | nrnDelete((number*) &erg, r); |
---|
613 | return (number)NULL; |
---|
614 | } |
---|
615 | // a / gcd(a,b) * [b / gcd (a,b)]^(-1) |
---|
616 | mpz_ptr tmp = (mpz_ptr)nrnInvers((number) erg,r); |
---|
617 | mpz_divexact(erg, (mpz_ptr)a, gcd); |
---|
618 | mpz_mul(erg, erg, tmp); |
---|
619 | nrnDelete((number*) &gcd, r); |
---|
620 | nrnDelete((number*) &tmp, r); |
---|
621 | mpz_mod(erg, erg, r->modNumber); |
---|
622 | return (number)erg; |
---|
623 | } |
---|
624 | } |
---|
625 | |
---|
626 | static number nrnMod(number a, number b, const coeffs r) |
---|
627 | { |
---|
628 | /* |
---|
629 | We need to return the number rr which is uniquely determined by the |
---|
630 | following two properties: |
---|
631 | (1) 0 <= rr < |b| (with respect to '<' and '<=' performed in Z x Z) |
---|
632 | (2) There exists some k in the integers Z such that a = k * b + rr. |
---|
633 | Consider g := gcd(n, |b|). Note that then |b|/g is a unit in Z/n. |
---|
634 | Now, there are three cases: |
---|
635 | (a) g = 1 |
---|
636 | Then |b| is a unit in Z/n, i.e. |b| (and also b) divides a. |
---|
637 | Thus rr = 0. |
---|
638 | (b) g <> 1 and g divides a |
---|
639 | Then a = (a/g) * (|b|/g)^(-1) * b (up to sign), i.e. again rr = 0. |
---|
640 | (c) g <> 1 and g does not divide a |
---|
641 | Then denote the division with remainder of a by g as this: |
---|
642 | a = s * g + t. Then t = a - s * g = a - s * (|b|/g)^(-1) * |b| |
---|
643 | fulfills (1) and (2), i.e. rr := t is the correct result. Hence |
---|
644 | in this third case, rr is the remainder of division of a by g in Z. |
---|
645 | Remark: according to mpz_mod: a,b are always non-negative |
---|
646 | */ |
---|
647 | mpz_ptr g = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
648 | mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
649 | mpz_init(g); |
---|
650 | mpz_init_set_ui(rr, 0); |
---|
651 | mpz_gcd(g, (mpz_ptr)r->modNumber, (mpz_ptr)b); // g is now as above |
---|
652 | if (mpz_cmp_si(g, 1L) != 0) mpz_mod(rr, (mpz_ptr)a, g); // the case g <> 1 |
---|
653 | mpz_clear(g); |
---|
654 | omFreeBin(g, gmp_nrz_bin); |
---|
655 | return (number)rr; |
---|
656 | } |
---|
657 | |
---|
658 | /* CF: note that Z/nZ has (at least) two distinct euclidean structures |
---|
659 | * 1st phi(a) := (a mod n) which is just the structure directly |
---|
660 | * inherited from Z |
---|
661 | * 2nd phi(a) := gcd(a, n) |
---|
662 | * The 1st version is probably faster as everything just comes from Z, |
---|
663 | * but the 2nd version behaves nicely wrt. to quotient operations |
---|
664 | * and HNF and such. In agreement with nrnMod we imlement the 2nd here |
---|
665 | * |
---|
666 | * For quotrem note that if b exactly divides a, then |
---|
667 | * min(v_p(a), v_p(n)) >= min(v_p(b), v_p(n)) |
---|
668 | * so if we divide a and b by g:= gcd(a,b,n), then b becomes a |
---|
669 | * unit mod n/g. |
---|
670 | * Thus we 1st compute the remainder (similar to nrnMod) and then |
---|
671 | * the exact quotient. |
---|
672 | */ |
---|
673 | static number nrnQuotRem(number a, number b, number * rem, const coeffs r) |
---|
674 | { |
---|
675 | mpz_t g, aa, bb; |
---|
676 | mpz_ptr qq = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
677 | mpz_ptr rr = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
678 | mpz_init(qq); |
---|
679 | mpz_init(rr); |
---|
680 | mpz_init(g); |
---|
681 | mpz_init_set(aa, (mpz_ptr)a); |
---|
682 | mpz_init_set(bb, (mpz_ptr)b); |
---|
683 | |
---|
684 | mpz_gcd(g, bb, r->modNumber); |
---|
685 | mpz_mod(rr, aa, g); |
---|
686 | mpz_sub(aa, aa, rr); |
---|
687 | mpz_gcd(g, aa, g); |
---|
688 | mpz_div(aa, aa, g); |
---|
689 | mpz_div(bb, bb, g); |
---|
690 | mpz_div(g, r->modNumber, g); |
---|
691 | mpz_invert(g, bb, g); |
---|
692 | mpz_mul(qq, aa, g); |
---|
693 | if (rem) |
---|
694 | *rem = (number)rr; |
---|
695 | else { |
---|
696 | mpz_clear(rr); |
---|
697 | omFreeBin(rr, gmp_nrz_bin); |
---|
698 | } |
---|
699 | mpz_clear(g); |
---|
700 | mpz_clear(aa); |
---|
701 | mpz_clear(bb); |
---|
702 | return (number) qq; |
---|
703 | } |
---|
704 | |
---|
705 | /* |
---|
706 | * Helper function for computing the module |
---|
707 | */ |
---|
708 | |
---|
709 | STATIC_VAR mpz_ptr nrnMapCoef = NULL; |
---|
710 | |
---|
711 | static number nrnMapModN(number from, const coeffs /*src*/, const coeffs dst) |
---|
712 | { |
---|
713 | return nrnMult(from, (number) nrnMapCoef, dst); |
---|
714 | } |
---|
715 | |
---|
716 | static number nrnMap2toM(number from, const coeffs /*src*/, const coeffs dst) |
---|
717 | { |
---|
718 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
719 | mpz_init(erg); |
---|
720 | mpz_mul_ui(erg, nrnMapCoef, (unsigned long)from); |
---|
721 | mpz_mod(erg, erg, dst->modNumber); |
---|
722 | return (number)erg; |
---|
723 | } |
---|
724 | |
---|
725 | static number nrnMapZp(number from, const coeffs /*src*/, const coeffs dst) |
---|
726 | { |
---|
727 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
728 | mpz_init(erg); |
---|
729 | // TODO: use npInt(...) |
---|
730 | mpz_mul_si(erg, nrnMapCoef, (unsigned long)from); |
---|
731 | mpz_mod(erg, erg, dst->modNumber); |
---|
732 | return (number)erg; |
---|
733 | } |
---|
734 | |
---|
735 | number nrnMapGMP(number from, const coeffs /*src*/, const coeffs dst) |
---|
736 | { |
---|
737 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
738 | mpz_init(erg); |
---|
739 | mpz_mod(erg, (mpz_ptr)from, dst->modNumber); |
---|
740 | return (number)erg; |
---|
741 | } |
---|
742 | |
---|
743 | static number nrnMapQ(number from, const coeffs src, const coeffs dst) |
---|
744 | { |
---|
745 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
746 | nlMPZ(erg, from, src); |
---|
747 | mpz_mod(erg, erg, dst->modNumber); |
---|
748 | return (number)erg; |
---|
749 | } |
---|
750 | |
---|
751 | #if SI_INTEGER_VARIANT==3 |
---|
752 | static number nrnMapZ(number from, const coeffs /*src*/, const coeffs dst) |
---|
753 | { |
---|
754 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
755 | if (n_Z_IS_SMALL(from)) |
---|
756 | mpz_init_set_si(erg, SR_TO_INT(from)); |
---|
757 | else |
---|
758 | mpz_init_set(erg, (mpz_ptr) from); |
---|
759 | mpz_mod(erg, erg, dst->modNumber); |
---|
760 | return (number)erg; |
---|
761 | } |
---|
762 | #elif SI_INTEGER_VARIANT==2 |
---|
763 | |
---|
764 | static number nrnMapZ(number from, const coeffs src, const coeffs dst) |
---|
765 | { |
---|
766 | if (SR_HDL(from) & SR_INT) |
---|
767 | { |
---|
768 | long f_i=SR_TO_INT(from); |
---|
769 | return nrnInit(f_i,dst); |
---|
770 | } |
---|
771 | return nrnMapGMP(from,src,dst); |
---|
772 | } |
---|
773 | #elif SI_INTEGER_VARIANT==1 |
---|
774 | static number nrnMapZ(number from, const coeffs src, const coeffs dst) |
---|
775 | { |
---|
776 | return nrnMapQ(from,src,dst); |
---|
777 | } |
---|
778 | #endif |
---|
779 | void nrnWrite (number a, const coeffs /*cf*/) |
---|
780 | { |
---|
781 | char *s,*z; |
---|
782 | if (a==NULL) |
---|
783 | { |
---|
784 | StringAppendS("o"); |
---|
785 | } |
---|
786 | else |
---|
787 | { |
---|
788 | int l=mpz_sizeinbase((mpz_ptr) a, 10) + 2; |
---|
789 | s=(char*)omAlloc(l); |
---|
790 | z=mpz_get_str(s,10,(mpz_ptr) a); |
---|
791 | StringAppendS(z); |
---|
792 | omFreeSize((ADDRESS)s,l); |
---|
793 | } |
---|
794 | } |
---|
795 | |
---|
796 | nMapFunc nrnSetMap(const coeffs src, const coeffs dst) |
---|
797 | { |
---|
798 | /* dst = nrn */ |
---|
799 | if ((src->rep==n_rep_gmp) && nCoeff_is_Z(src)) |
---|
800 | { |
---|
801 | return nrnMapZ; |
---|
802 | } |
---|
803 | if ((src->rep==n_rep_gap_gmp) /*&& nCoeff_is_Z(src)*/) |
---|
804 | { |
---|
805 | return nrnMapZ; |
---|
806 | } |
---|
807 | if (src->rep==n_rep_gap_rat) /*&& nCoeff_is_Q(src)) or Z*/ |
---|
808 | { |
---|
809 | return nrnMapQ; |
---|
810 | } |
---|
811 | // Some type of Z/n ring / field |
---|
812 | if (nCoeff_is_Zn(src) || nCoeff_is_Ring_PtoM(src) || |
---|
813 | nCoeff_is_Ring_2toM(src) || nCoeff_is_Zp(src)) |
---|
814 | { |
---|
815 | if ( (!nCoeff_is_Zp(src)) |
---|
816 | && (mpz_cmp(src->modBase, dst->modBase) == 0) |
---|
817 | && (src->modExponent == dst->modExponent)) return ndCopyMap; |
---|
818 | else |
---|
819 | { |
---|
820 | mpz_ptr nrnMapModul = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
821 | // Computing the n of Z/n |
---|
822 | if (nCoeff_is_Zp(src)) |
---|
823 | { |
---|
824 | mpz_init_set_si(nrnMapModul, src->ch); |
---|
825 | } |
---|
826 | else |
---|
827 | { |
---|
828 | mpz_init(nrnMapModul); |
---|
829 | mpz_set(nrnMapModul, src->modNumber); |
---|
830 | } |
---|
831 | // nrnMapCoef = 1 in dst if dst is a subring of src |
---|
832 | // nrnMapCoef = 0 in dst / src if src is a subring of dst |
---|
833 | if (nrnMapCoef == NULL) |
---|
834 | { |
---|
835 | nrnMapCoef = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
---|
836 | mpz_init(nrnMapCoef); |
---|
837 | } |
---|
838 | if (mpz_divisible_p(nrnMapModul, dst->modNumber)) |
---|
839 | { |
---|
840 | mpz_set_ui(nrnMapCoef, 1); |
---|
841 | } |
---|
842 | else |
---|
843 | if (mpz_divisible_p(dst->modNumber,nrnMapModul)) |
---|
844 | { |
---|
845 | mpz_divexact(nrnMapCoef, dst->modNumber, nrnMapModul); |
---|
846 | mpz_ptr tmp = dst->modNumber; |
---|
847 | dst->modNumber = nrnMapModul; |
---|
848 | if (!nrnIsUnit((number) nrnMapCoef,dst)) |
---|
849 | { |
---|
850 | dst->modNumber = tmp; |
---|
851 | nrnDelete((number*) &nrnMapModul, dst); |
---|
852 | return NULL; |
---|
853 | } |
---|
854 | mpz_ptr inv = (mpz_ptr) nrnInvers((number) nrnMapCoef,dst); |
---|
855 | dst->modNumber = tmp; |
---|
856 | mpz_mul(nrnMapCoef, nrnMapCoef, inv); |
---|
857 | mpz_mod(nrnMapCoef, nrnMapCoef, dst->modNumber); |
---|
858 | nrnDelete((number*) &inv, dst); |
---|
859 | } |
---|
860 | else |
---|
861 | { |
---|
862 | nrnDelete((number*) &nrnMapModul, dst); |
---|
863 | return NULL; |
---|
864 | } |
---|
865 | nrnDelete((number*) &nrnMapModul, dst); |
---|
866 | if (nCoeff_is_Ring_2toM(src)) |
---|
867 | return nrnMap2toM; |
---|
868 | else if (nCoeff_is_Zp(src)) |
---|
869 | return nrnMapZp; |
---|
870 | else |
---|
871 | return nrnMapModN; |
---|
872 | } |
---|
873 | } |
---|
874 | return NULL; // default |
---|
875 | } |
---|
876 | |
---|
877 | static number nrnInitMPZ(mpz_t m, const coeffs r) |
---|
878 | { |
---|
879 | mpz_ptr erg = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
880 | mpz_init_set(erg,m); |
---|
881 | mpz_mod(erg, erg, r->modNumber); |
---|
882 | return (number) erg; |
---|
883 | } |
---|
884 | |
---|
885 | static void nrnMPZ(mpz_t m, number &n, const coeffs) |
---|
886 | { |
---|
887 | mpz_init_set(m, (mpz_ptr)n); |
---|
888 | } |
---|
889 | |
---|
890 | /* |
---|
891 | * set the exponent (allocate and init tables) (TODO) |
---|
892 | */ |
---|
893 | |
---|
894 | static void nrnSetExp(unsigned long m, coeffs r) |
---|
895 | { |
---|
896 | /* clean up former stuff */ |
---|
897 | if (r->modNumber != NULL) mpz_clear(r->modNumber); |
---|
898 | |
---|
899 | r->modExponent= m; |
---|
900 | r->modNumber = (mpz_ptr)omAllocBin(gmp_nrz_bin); |
---|
901 | mpz_init_set (r->modNumber, r->modBase); |
---|
902 | mpz_pow_ui (r->modNumber, r->modNumber, m); |
---|
903 | } |
---|
904 | |
---|
905 | /* We expect this ring to be Z/n^m for some m > 0 and for some n > 2 which is not a prime. */ |
---|
906 | static void nrnInitExp(unsigned long m, coeffs r) |
---|
907 | { |
---|
908 | nrnSetExp(m, r); |
---|
909 | assume (r->modNumber != NULL); |
---|
910 | //CF: in general, the modulus is computed somewhere. I don't want to |
---|
911 | // check it's size before I construct the best ring. |
---|
912 | // if (mpz_cmp_ui(r->modNumber,2) <= 0) |
---|
913 | // WarnS("nrnInitExp failed (m in Z/m too small)"); |
---|
914 | } |
---|
915 | |
---|
916 | #ifdef LDEBUG |
---|
917 | static BOOLEAN nrnDBTest (number a, const char *f, const int l, const coeffs r) |
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918 | { |
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919 | if ( (mpz_sgn1((mpz_ptr) a) < 0) || (mpz_cmp((mpz_ptr) a, r->modNumber) > 0) ) |
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920 | { |
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921 | Warn("mod-n: out of range at %s:%d\n",f,l); |
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922 | return FALSE; |
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923 | } |
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924 | return TRUE; |
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925 | } |
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926 | #endif |
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927 | |
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928 | /*2 |
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929 | * extracts a long integer from s, returns the rest (COPY FROM longrat0.cc) |
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930 | */ |
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931 | static const char * nlCPEatLongC(char *s, mpz_ptr i) |
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932 | { |
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933 | const char * start=s; |
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934 | if (!(*s >= '0' && *s <= '9')) |
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935 | { |
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936 | mpz_init_set_ui(i, 1); |
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937 | return s; |
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938 | } |
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939 | mpz_init(i); |
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940 | while (*s >= '0' && *s <= '9') s++; |
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941 | if (*s=='\0') |
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942 | { |
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943 | mpz_set_str(i,start,10); |
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944 | } |
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945 | else |
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946 | { |
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947 | char c=*s; |
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948 | *s='\0'; |
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949 | mpz_set_str(i,start,10); |
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950 | *s=c; |
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951 | } |
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952 | return s; |
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953 | } |
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954 | |
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955 | static const char * nrnRead (const char *s, number *a, const coeffs r) |
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956 | { |
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957 | mpz_ptr z = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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958 | { |
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959 | s = nlCPEatLongC((char *)s, z); |
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960 | } |
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961 | mpz_mod(z, z, r->modNumber); |
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962 | if ((*s)=='/') |
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963 | { |
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964 | mpz_ptr n = (mpz_ptr) omAllocBin(gmp_nrz_bin); |
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965 | s++; |
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966 | s=nlCPEatLongC((char*)s,n); |
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967 | if (!nrnIsOne((number)n,r)) |
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968 | { |
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969 | *a=nrnDiv((number)z,(number)n,r); |
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970 | mpz_clear(z); |
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971 | omFreeBin((void *)z, gmp_nrz_bin); |
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972 | mpz_clear(n); |
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973 | omFreeBin((void *)n, gmp_nrz_bin); |
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974 | } |
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975 | } |
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976 | else |
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977 | *a = (number) z; |
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978 | return s; |
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979 | } |
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980 | |
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981 | static number nrnConvFactoryNSingN( const CanonicalForm n, const coeffs r) |
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982 | { |
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983 | return nrnInit(n.intval(),r); |
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984 | } |
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985 | |
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986 | static CanonicalForm nrnConvSingNFactoryN( number n, BOOLEAN setChar, const coeffs r ) |
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987 | { |
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988 | if (setChar) setCharacteristic( r->ch ); |
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989 | return CanonicalForm(nrnInt( n,r )); |
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990 | } |
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991 | |
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992 | /* for initializing function pointers */ |
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993 | BOOLEAN nrnInitChar (coeffs r, void* p) |
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994 | { |
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995 | assume( (getCoeffType(r) == n_Zn) || (getCoeffType (r) == n_Znm) ); |
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996 | ZnmInfo * info= (ZnmInfo *) p; |
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997 | r->modBase= (mpz_ptr)nrnCopy((number)info->base, r); //this circumvents the problem |
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998 | //in bigintmat.cc where we cannot create a "legal" nrn that can be freed. |
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999 | //If we take a copy, we can do whatever we want. |
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1000 | |
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1001 | nrnInitExp (info->exp, r); |
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1002 | |
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1003 | /* next computation may yield wrong characteristic as r->modNumber |
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1004 | is a GMP number */ |
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1005 | r->ch = mpz_get_ui(r->modNumber); |
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1006 | |
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1007 | r->is_field=FALSE; |
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1008 | r->is_domain=FALSE; |
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1009 | r->rep=n_rep_gmp; |
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1010 | |
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1011 | r->cfInit = nrnInit; |
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1012 | r->cfDelete = nrnDelete; |
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1013 | r->cfCopy = nrnCopy; |
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1014 | r->cfSize = nrnSize; |
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1015 | r->cfInt = nrnInt; |
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1016 | r->cfAdd = nrnAdd; |
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1017 | r->cfInpAdd = nrnInpAdd; |
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1018 | r->cfSub = nrnSub; |
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1019 | r->cfMult = nrnMult; |
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1020 | r->cfInpMult = nrnInpMult; |
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1021 | r->cfDiv = nrnDiv; |
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1022 | r->cfAnn = nrnAnn; |
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1023 | r->cfIntMod = nrnMod; |
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1024 | r->cfExactDiv = nrnDiv; |
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1025 | r->cfInpNeg = nrnNeg; |
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1026 | r->cfInvers = nrnInvers; |
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1027 | r->cfDivBy = nrnDivBy; |
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1028 | r->cfDivComp = nrnDivComp; |
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1029 | r->cfGreater = nrnGreater; |
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1030 | r->cfEqual = nrnEqual; |
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1031 | r->cfIsZero = nrnIsZero; |
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1032 | r->cfIsOne = nrnIsOne; |
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1033 | r->cfIsMOne = nrnIsMOne; |
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1034 | r->cfGreaterZero = nrnGreaterZero; |
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1035 | r->cfWriteLong = nrnWrite; |
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1036 | r->cfRead = nrnRead; |
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1037 | r->cfPower = nrnPower; |
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1038 | r->cfSetMap = nrnSetMap; |
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1039 | //r->cfNormalize = ndNormalize; |
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1040 | r->cfLcm = nrnLcm; |
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1041 | r->cfGcd = nrnGcd; |
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1042 | r->cfIsUnit = nrnIsUnit; |
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1043 | r->cfGetUnit = nrnGetUnit; |
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1044 | r->cfExtGcd = nrnExtGcd; |
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1045 | r->cfXExtGcd = nrnXExtGcd; |
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1046 | r->cfQuotRem = nrnQuotRem; |
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1047 | r->cfCoeffName = nrnCoeffName; |
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1048 | r->nCoeffIsEqual = nrnCoeffIsEqual; |
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1049 | r->cfKillChar = nrnKillChar; |
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1050 | r->cfQuot1 = nrnQuot1; |
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1051 | r->cfInitMPZ = nrnInitMPZ; |
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1052 | r->cfMPZ = nrnMPZ; |
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1053 | #if SI_INTEGER_VARIANT==2 |
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1054 | r->cfWriteFd = nrzWriteFd; |
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1055 | r->cfReadFd = nrzReadFd; |
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1056 | #endif |
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1057 | |
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1058 | #ifdef LDEBUG |
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1059 | r->cfDBTest = nrnDBTest; |
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1060 | #endif |
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1061 | if ((r->modExponent==1)&&(mpz_size1(r->modBase)==1)) |
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1062 | { |
---|
1063 | long p=mpz_get_si(r->modBase); |
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1064 | if ((p<=FACTORY_MAX_PRIME)&&(p==IsPrime(p))) /*factory limit: <2^29*/ |
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1065 | { |
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1066 | r->convFactoryNSingN=nrnConvFactoryNSingN; |
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1067 | r->convSingNFactoryN=nrnConvSingNFactoryN; |
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1068 | } |
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1069 | } |
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1070 | return FALSE; |
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1071 | } |
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1072 | |
---|
1073 | #endif |
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1074 | /* #ifdef HAVE_RINGS */ |
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