1 | /***************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | *****************************************/ |
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4 | /* $Id: numbers.cc,v 1.5 2007-01-29 16:58:32 Singular Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT: interface to coefficient aritmetics |
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8 | */ |
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9 | |
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10 | #include <string.h> |
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11 | #include <stdlib.h> |
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12 | #include "mod2.h" |
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13 | #include "structs.h" |
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14 | #include "febase.h" |
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15 | #include "kstd1.h" |
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16 | #include "numbers.h" |
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17 | #include "longrat.h" |
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18 | #include "longalg.h" |
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19 | #include "modulop.h" |
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20 | #include "gnumpfl.h" |
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21 | #include "gnumpc.h" |
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22 | #include "ring.h" |
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23 | #include "ffields.h" |
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24 | #include "shortfl.h" |
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25 | #ifdef HAVE_RING2TOM |
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26 | #include "rmodulo2m.h" |
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27 | #endif |
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28 | |
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29 | //static int characteristic = 0; |
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30 | extern int IsPrime(int p); |
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31 | |
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32 | void (*nNew)(number *a); |
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33 | number (*nInit)(int i); |
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34 | number (*nPar)(int i); |
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35 | int (*nParDeg)(number n); |
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36 | int (*nSize)(number n); |
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37 | int (*nInt)(number &n); |
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38 | numberfunc nMult, nSub, nAdd, nDiv, nIntDiv, nIntMod, nExactDiv; |
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39 | number (*nNeg)(number a); |
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40 | number (*nInvers)(number a); |
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41 | void (*nNormalize)(number &a); |
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42 | number (*nCopy)(number a); |
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43 | number (*nRePart)(number a); |
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44 | number (*nImPart)(number a); |
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45 | BOOLEAN (*nGreater)(number a,number b); |
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46 | BOOLEAN (*nEqual)(number a,number b); |
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47 | BOOLEAN (*nIsZero)(number a); |
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48 | BOOLEAN (*nIsOne)(number a); |
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49 | BOOLEAN (*nIsMOne)(number a); |
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50 | BOOLEAN (*nGreaterZero)(number a); |
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51 | void (*nWrite)(number &a); |
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52 | char * (*nRead)(char *s,number *a); |
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53 | void (*nPower)(number a, int i, number * result); |
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54 | number (*nGcd)(number a, number b, const ring r); |
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55 | number (*nLcm)(number a, number b, const ring r); |
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56 | char * (*nName)(number n); |
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57 | void (*n__Delete)(number *a, const ring r); |
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58 | |
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59 | /*0 implementation*/ |
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60 | number nNULL; /* the 0 as constant */ |
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61 | |
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62 | |
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63 | n_Procs_s *cf_root=NULL; |
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64 | |
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65 | void nDummy1(number* d) { *d=NULL; } |
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66 | void ndDelete(number* d, const ring r) { *d=NULL; } |
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67 | void ndInpMult(number &a, number b, const ring r) |
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68 | { |
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69 | number n=n_Mult(a,b,r); |
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70 | n_Delete(&a,r); |
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71 | a=n; |
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72 | } |
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73 | |
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74 | #ifdef LDEBUG |
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75 | void nDBDummy1(number* d,char *f, int l) { *d=NULL; } |
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76 | #endif |
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77 | |
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78 | void nDummy2(number& d) { } |
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79 | |
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80 | char * ndName(number n) { return NULL; } |
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81 | |
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82 | number ndPar(int i) { return nInit(0); } |
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83 | |
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84 | number ndReturn0(number n) { return nInit(0); } |
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85 | |
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86 | int ndParDeg(number n) { return 0; } |
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87 | |
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88 | number ndGcd(number a, number b, const ring r) { return r->cf->nInit(1); } |
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89 | |
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90 | number ndIntMod(number a, number b) { return nInit(0); } |
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91 | |
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92 | number ndGetDenom(number &n, const ring r) { return n_Init(1,r); } |
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93 | |
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94 | int ndSize(number a) { return (int)nIsZero(a)==FALSE; } |
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95 | |
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96 | number ndCopy(number a) { return a; } |
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97 | number nd_Copy(number a,const ring r) { return r->cf->nCopy(a); } |
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98 | |
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99 | /*2 |
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100 | * init operations for characteristic c (complete==TRUE) |
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101 | * init nDelete for characteristic c (complete==FALSE) |
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102 | */ |
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103 | void nSetChar(ring r) |
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104 | { |
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105 | int c=rInternalChar(r); |
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106 | |
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107 | n__Delete= r->cf->cfDelete; |
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108 | if (rField_is_Extension(r)) |
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109 | { |
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110 | naSetChar(c,r); |
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111 | } |
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112 | #ifdef HAVE_RING2TOM |
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113 | /*----------------------ring Z / 2^m----------------*/ |
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114 | else if (rField_is_Ring_2toM(r)) |
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115 | { |
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116 | nr2mSetExp(c, r); |
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117 | } |
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118 | #endif |
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119 | else if (rField_is_Zp(r)) |
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120 | /*----------------------char. p----------------*/ |
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121 | { |
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122 | npSetChar(c, r); |
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123 | } |
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124 | /* -------------- GF(p^m) -----------------------*/ |
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125 | else if (rField_is_GF(r)) |
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126 | { |
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127 | nfSetChar(c,r->parameter); |
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128 | } |
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129 | /* -------------- R -----------------------*/ |
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130 | //if (c==(-1)) |
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131 | else if (rField_is_R(r)) |
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132 | { |
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133 | } |
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134 | /* -------------- long R -----------------------*/ |
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135 | /* -------------- long C -----------------------*/ |
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136 | else if ((rField_is_long_R(r)) |
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137 | || (rField_is_long_C(r))) |
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138 | { |
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139 | setGMPFloatDigits(r->float_len,r->float_len2); |
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140 | } |
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141 | #ifdef TEST |
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142 | /* -------------- R -----------------------*/ |
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143 | //if (c==(-1)) |
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144 | else if (!rField_is_R(r) && !rField_is_Q(r)) |
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145 | { |
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146 | WerrorS("unknown field"); |
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147 | } |
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148 | #endif |
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149 | nNew = r->cf->nNew; |
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150 | nNormalize=r->cf->nNormalize; |
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151 | nInit = r->cf->nInit; |
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152 | nPar = r->cf->nPar; |
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153 | nParDeg= r->cf->nParDeg; |
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154 | nInt = r->cf->nInt; |
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155 | nAdd = r->cf->nAdd; |
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156 | nSub = r->cf->nSub; |
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157 | nMult = r->cf->nMult; |
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158 | nDiv = r->cf->nDiv; |
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159 | nExactDiv= r->cf->nExactDiv; |
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160 | nIntDiv= r->cf->nIntDiv; |
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161 | nIntMod= r->cf->nIntMod; |
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162 | nNeg = r->cf->nNeg; |
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163 | nInvers= r->cf->nInvers; |
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164 | nCopy = r->cf->nCopy; |
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165 | nGreater = r->cf->nGreater; |
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166 | nEqual = r->cf->nEqual; |
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167 | nIsZero = r->cf->nIsZero; |
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168 | nIsOne = r->cf->nIsOne; |
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169 | nIsMOne = r->cf->nIsMOne; |
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170 | nGreaterZero = r->cf->nGreaterZero; |
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171 | nWrite = r->cf->nWrite; |
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172 | nRead = r->cf->nRead; |
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173 | nPower = r->cf->nPower; |
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174 | nGcd = r->cf->nGcd; |
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175 | nLcm = r->cf->nLcm; |
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176 | nName= r->cf->nName; |
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177 | nSize = r->cf->nSize; |
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178 | nRePart = r->cf->nRePart; |
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179 | nImPart = r->cf->nImPart; |
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180 | nNULL=r->cf->nNULL; |
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181 | } |
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182 | |
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183 | /*2 |
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184 | * init operations for ring r |
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185 | */ |
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186 | void nInitChar(ring r) |
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187 | { |
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188 | int c=rInternalChar(r); |
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189 | n_coeffType t=rFieldType(r); |
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190 | |
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191 | if (rField_is_Extension(r)) |
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192 | { |
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193 | if (r->algring==NULL) |
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194 | { |
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195 | int ch=-c; |
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196 | if (c==1) ch=0; |
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197 | r->algring=(ring) rDefault(ch,r->P,r->parameter); |
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198 | //r->algring->ShortOut=r->ShortOut; |
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199 | // includes: nInitChar(r->algring); |
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200 | } |
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201 | } |
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202 | |
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203 | n_Procs_s *n=cf_root; |
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204 | while((n!=NULL) |
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205 | && ((n->nChar!=c) || (n->type!=t))) |
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206 | n=n->next; |
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207 | if (n==NULL) |
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208 | { |
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209 | n=(n_Procs_s*)omAlloc0(sizeof(n_Procs_s)); |
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210 | n->next=cf_root; |
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211 | n->ref=1; |
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212 | n->nChar=c; |
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213 | n->type=t; |
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214 | cf_root=n; |
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215 | } |
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216 | else if ((n->nChar==c) && (n->type==t)) |
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217 | { |
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218 | n->ref++; |
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219 | r->cf=n; |
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220 | return; |
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221 | } |
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222 | else |
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223 | { |
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224 | WerrorS("nInitChar failed"); |
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225 | return; |
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226 | } |
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227 | r->cf=n; |
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228 | n->nChar = c; |
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229 | n->nPar = ndPar; |
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230 | n->nParDeg=ndParDeg; |
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231 | n->nSize = ndSize; |
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232 | n->n_GetDenom= ndGetDenom; |
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233 | n->nName = ndName; |
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234 | n->nImPart=ndReturn0; |
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235 | n->cfDelete= ndDelete; |
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236 | n->nNew=nDummy1; |
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237 | n->nInpMult=ndInpMult; |
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238 | n->cfCopy=nd_Copy; |
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239 | n->nIntMod=ndIntMod; /* dummy !! */ |
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240 | n->nNormalize=nDummy2; |
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241 | n->nGcd = ndGcd; |
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242 | n->nLcm = ndGcd; /* tricky, isn't it ?*/ |
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243 | if (rField_is_Extension(r)) |
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244 | { |
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245 | //naInitChar(c,TRUE,r); |
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246 | n->cfDelete = naDelete; |
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247 | n-> nNew = naNew; |
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248 | n-> nNormalize = naNormalize; |
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249 | n->nInit = naInit; |
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250 | n->nPar = naPar; |
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251 | n->nParDeg = naParDeg; |
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252 | n->nInt = naInt; |
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253 | n->nAdd = naAdd; |
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254 | n->nSub = naSub; |
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255 | n->nMult = naMult; |
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256 | n->nDiv = naDiv; |
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257 | n->nExactDiv = naDiv; |
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258 | n->nIntDiv = naIntDiv; |
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259 | n->nNeg = naNeg; |
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260 | n->nInvers = naInvers; |
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261 | n->nCopy = naCopy; |
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262 | n->cfCopy = na_Copy; |
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263 | n->nGreater = naGreater; |
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264 | n->nEqual = naEqual; |
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265 | n->nIsZero = naIsZero; |
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266 | n->nIsOne = naIsOne; |
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267 | n->nIsMOne = naIsMOne; |
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268 | n->nGreaterZero= naGreaterZero; |
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269 | n->nWrite = naWrite; |
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270 | n->nRead = naRead; |
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271 | n->nPower = naPower; |
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272 | n->nGcd = naGcd; |
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273 | n->nLcm = naLcm; |
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274 | n->cfSetMap = naSetMap; |
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275 | n->nName = naName; |
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276 | n->nSize = naSize; |
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277 | n->n_GetDenom = naGetDenom; |
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278 | #ifdef LDEBUG |
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279 | //n->nDBTest = naDBTest; |
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280 | #endif |
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281 | } |
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282 | #ifdef HAVE_RING2TOM |
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283 | /* -------------- Z/2^m ----------------------- */ |
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284 | else if (rField_is_Ring_2toM(r)) |
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285 | { |
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286 | nr2mInitExp(c,r); |
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287 | n->nInit = nr2mInit; |
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288 | n->nCopy = ndCopy; |
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289 | n->nInt = nr2mInt; |
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290 | n->nAdd = nr2mAdd; |
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291 | n->nSub = nr2mSub; |
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292 | n->nMult = nr2mMult; |
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293 | n->nDiv = nr2mDiv; |
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294 | n->nIntDiv = nr2mIntDiv; |
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295 | n->nExactDiv= nr2mDiv; |
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296 | n->nNeg = nr2mNeg; |
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297 | n->nInvers= nr2mInvers; |
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298 | n->nGreater = nr2mGreater; |
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299 | n->nEqual = nr2mEqual; |
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300 | n->nIsZero = nr2mIsZero; |
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301 | n->nIsOne = nr2mIsOne; |
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302 | n->nIsMOne = nr2mIsMOne; |
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303 | n->nGreaterZero = nr2mGreaterZero; |
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304 | n->nWrite = nr2mWrite; |
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305 | n->nRead = nr2mRead; |
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306 | n->nPower = nr2mPower; |
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307 | n->cfSetMap = nr2mSetMap; |
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308 | n->nNormalize = nDummy2; |
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309 | n->nLcm = nr2mLcm; |
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310 | n->nGcd = nr2mGcd; |
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311 | // n->nGetUnit = nr2mGetUnit; //TODO OLIVER |
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312 | n->nName= ndName; |
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313 | #ifdef LDEBUG |
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314 | // n->nDBTest=nr2mDBTest; |
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315 | #endif |
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316 | } |
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317 | #endif |
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318 | else if (rField_is_Q(r)) |
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319 | { |
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320 | n->cfDelete= nlDelete; |
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321 | n->nNew = nlNew; |
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322 | n->nNormalize=nlNormalize; |
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323 | n->nInit = nlInit; |
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324 | n->nInt = nlInt; |
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325 | n->nAdd = nlAdd; |
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326 | n->nSub = nlSub; |
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327 | n->nMult = nlMult; |
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328 | n->nInpMult=nlInpMult; |
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329 | n->nDiv = nlDiv; |
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330 | n->nExactDiv= nlExactDiv; |
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331 | n->nIntDiv= nlIntDiv; |
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332 | n->nIntMod= nlIntMod; |
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333 | n->nNeg = nlNeg; |
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334 | n->nInvers= nlInvers; |
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335 | n->nCopy = nlCopy; |
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336 | n->nGreater = nlGreater; |
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337 | n->nEqual = nlEqual; |
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338 | n->nIsZero = nlIsZero; |
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339 | n->nIsOne = nlIsOne; |
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340 | n->nIsMOne = nlIsMOne; |
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341 | n->nGreaterZero = nlGreaterZero; |
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342 | n->nWrite = nlWrite; |
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343 | n->nRead = nlRead; |
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344 | n->nPower = nlPower; |
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345 | n->nGcd = nlGcd; |
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346 | n->nLcm = nlLcm; |
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347 | n->cfSetMap = nlSetMap; |
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348 | n->nSize = nlSize; |
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349 | n->n_GetDenom = nlGetDenom; |
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350 | #ifdef LDEBUG |
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351 | //n->nDBTest=nlDBTest; |
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352 | #endif |
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353 | } |
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354 | else if (rField_is_Zp(r)) |
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355 | /*----------------------char. p----------------*/ |
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356 | { |
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357 | npInitChar(c,r); |
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358 | n->nInit = npInit; |
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359 | n->nInt = npInt; |
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360 | n->nAdd = npAdd; |
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361 | n->nSub = npSub; |
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362 | n->nMult = npMult; |
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363 | n->nDiv = npDiv; |
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364 | n->nExactDiv= npDiv; |
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365 | n->nNeg = npNeg; |
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366 | n->nInvers= npInvers; |
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367 | n->nCopy = ndCopy; |
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368 | n->nGreater = npGreater; |
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369 | n->nEqual = npEqual; |
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370 | n->nIsZero = npIsZero; |
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371 | n->nIsOne = npIsOne; |
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372 | n->nIsMOne = npIsMOne; |
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373 | n->nGreaterZero = npGreaterZero; |
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374 | n->nWrite = npWrite; |
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375 | n->nRead = npRead; |
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376 | n->nPower = npPower; |
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377 | n->cfSetMap = npSetMap; |
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378 | /* nName= ndName; */ |
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379 | /*nSize = ndSize;*/ |
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380 | #ifdef LDEBUG |
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381 | //n->nDBTest=npDBTest; |
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382 | #endif |
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383 | #ifdef NV_OPS |
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384 | if (c>NV_MAX_PRIME) |
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385 | { |
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386 | n->nMult = nvMult; |
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387 | n->nDiv = nvDiv; |
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388 | n->nExactDiv= nvDiv; |
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389 | n->nInvers= nvInvers; |
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390 | } |
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391 | #endif |
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392 | } |
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393 | /* -------------- GF(p^m) -----------------------*/ |
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394 | else if (rField_is_GF(r)) |
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395 | { |
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396 | //nfSetChar(c,r->parameter); |
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397 | n->nInit = nfInit; |
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398 | n->nPar = nfPar; |
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399 | n->nParDeg= nfParDeg; |
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400 | n->nInt = nfInt; |
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401 | n->nAdd = nfAdd; |
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402 | n->nSub = nfSub; |
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403 | n->nMult = nfMult; |
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404 | n->nDiv = nfDiv; |
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405 | n->nExactDiv= nfDiv; |
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406 | n->nNeg = nfNeg; |
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407 | n->nInvers= nfInvers; |
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408 | n->nCopy = ndCopy; |
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409 | n->nGreater = nfGreater; |
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410 | n->nEqual = nfEqual; |
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411 | n->nIsZero = nfIsZero; |
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412 | n->nIsOne = nfIsOne; |
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413 | n->nIsMOne = nfIsMOne; |
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414 | n->nGreaterZero = nfGreaterZero; |
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415 | n->nWrite = nfWrite; |
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416 | n->nRead = nfRead; |
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417 | n->nPower = nfPower; |
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418 | n->cfSetMap = nfSetMap; |
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419 | n->nName= nfName; |
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420 | /*nSize = ndSize;*/ |
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421 | #ifdef LDEBUG |
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422 | //n->nDBTest=nfDBTest; |
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423 | #endif |
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424 | } |
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425 | /* -------------- R -----------------------*/ |
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426 | //if (c==(-1)) |
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427 | else if (rField_is_R(r)) |
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428 | { |
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429 | n->nInit = nrInit; |
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430 | n->nInt = nrInt; |
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431 | n->nAdd = nrAdd; |
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432 | n->nSub = nrSub; |
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433 | n->nMult = nrMult; |
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434 | n->nDiv = nrDiv; |
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435 | n->nExactDiv= nrDiv; |
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436 | n->nNeg = nrNeg; |
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437 | n->nInvers= nrInvers; |
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438 | n->nCopy = ndCopy; |
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439 | n->nGreater = nrGreater; |
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440 | n->nEqual = nrEqual; |
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441 | n->nIsZero = nrIsZero; |
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442 | n->nIsOne = nrIsOne; |
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443 | n->nIsMOne = nrIsMOne; |
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444 | n->nGreaterZero = nrGreaterZero; |
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445 | n->nWrite = nrWrite; |
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446 | n->nRead = nrRead; |
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447 | n->nPower = nrPower; |
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448 | n->cfSetMap=nrSetMap; |
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449 | /* nName= ndName; */ |
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450 | /*nSize = ndSize;*/ |
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451 | #ifdef LDEBUG |
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452 | //n->nDBTest=nrDBTest; |
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453 | #endif |
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454 | } |
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455 | /* -------------- long R -----------------------*/ |
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456 | else if (rField_is_long_R(r)) |
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457 | { |
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458 | n->cfDelete= ngfDelete; |
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459 | n->nNew=ngfNew; |
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460 | n->nInit = ngfInit; |
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461 | n->nInt = ngfInt; |
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462 | n->nAdd = ngfAdd; |
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463 | n->nSub = ngfSub; |
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464 | n->nMult = ngfMult; |
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465 | n->nDiv = ngfDiv; |
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466 | n->nExactDiv= ngfDiv; |
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467 | n->nNeg = ngfNeg; |
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468 | n->nInvers= ngfInvers; |
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469 | n->nCopy = ngfCopy; |
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470 | n->nGreater = ngfGreater; |
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471 | n->nEqual = ngfEqual; |
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472 | n->nIsZero = ngfIsZero; |
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473 | n->nIsOne = ngfIsOne; |
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474 | n->nIsMOne = ngfIsMOne; |
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475 | n->nGreaterZero = ngfGreaterZero; |
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476 | n->nWrite = ngfWrite; |
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477 | n->nRead = ngfRead; |
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478 | n->nPower = ngfPower; |
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479 | n->cfSetMap=ngfSetMap; |
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480 | n->nName= ndName; |
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481 | n->nSize = ndSize; |
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482 | #ifdef LDEBUG |
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483 | //n->nDBTest=ngfDBTest; |
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484 | #endif |
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485 | } |
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486 | /* -------------- long C -----------------------*/ |
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487 | else if (rField_is_long_C(r)) |
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488 | { |
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489 | n->cfDelete= ngcDelete; |
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490 | n->nNew=ngcNew; |
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491 | n->nNormalize=nDummy2; |
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492 | n->nInit = ngcInit; |
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493 | n->nInt = ngcInt; |
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494 | n->nAdd = ngcAdd; |
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495 | n->nSub = ngcSub; |
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496 | n->nMult = ngcMult; |
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497 | n->nDiv = ngcDiv; |
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498 | n->nExactDiv= ngcDiv; |
---|
499 | n->nNeg = ngcNeg; |
---|
500 | n->nInvers= ngcInvers; |
---|
501 | n->nCopy = ngcCopy; |
---|
502 | n->nGreater = ngcGreater; |
---|
503 | n->nEqual = ngcEqual; |
---|
504 | n->nIsZero = ngcIsZero; |
---|
505 | n->nIsOne = ngcIsOne; |
---|
506 | n->nIsMOne = ngcIsMOne; |
---|
507 | n->nGreaterZero = ngcGreaterZero; |
---|
508 | n->nWrite = ngcWrite; |
---|
509 | n->nRead = ngcRead; |
---|
510 | n->nPower = ngcPower; |
---|
511 | n->cfSetMap=ngcSetMap; |
---|
512 | n->nPar=ngcPar; |
---|
513 | n->nRePart=ngcRePart; |
---|
514 | n->nImPart=ngcImPart; |
---|
515 | /*nSize = ndSize;*/ |
---|
516 | #ifdef LDEBUG |
---|
517 | //n->nDBTest=ngcDBTest; |
---|
518 | #endif |
---|
519 | } |
---|
520 | #ifdef TEST |
---|
521 | else |
---|
522 | { |
---|
523 | WerrorS("unknown field"); |
---|
524 | } |
---|
525 | #endif |
---|
526 | if (!errorreported) |
---|
527 | { |
---|
528 | n->nNULL=n->nInit(0); |
---|
529 | if (n->nRePart==NULL) |
---|
530 | n->nRePart=n->nCopy; |
---|
531 | if (n->nIntDiv==NULL) |
---|
532 | n->nIntDiv=n->nDiv; |
---|
533 | } |
---|
534 | } |
---|
535 | |
---|
536 | void nKillChar(ring r) |
---|
537 | { |
---|
538 | if (r!=NULL) |
---|
539 | { |
---|
540 | if (r->cf!=NULL) |
---|
541 | { |
---|
542 | r->cf->ref--; |
---|
543 | if (r->cf->ref<=0) |
---|
544 | { |
---|
545 | n_Procs_s tmp; |
---|
546 | n_Procs_s* n=&tmp; |
---|
547 | tmp.next=cf_root; |
---|
548 | while((n->next!=NULL) && (n->next!=r->cf)) n=n->next; |
---|
549 | if (n->next==r->cf) |
---|
550 | { |
---|
551 | n->next=n->next->next; |
---|
552 | if (cf_root==r->cf) cf_root=n->next; |
---|
553 | r->cf->cfDelete(&(r->cf->nNULL),r); |
---|
554 | switch(r->cf->type) |
---|
555 | { |
---|
556 | case n_Zp: |
---|
557 | #ifdef HAVE_DIV_MOD |
---|
558 | if (r->cf->npInvTable!=NULL) |
---|
559 | omFreeSize( (ADDRESS)r->cf->npInvTable, |
---|
560 | r->cf->npPrimeM*sizeof(CARDINAL) ); |
---|
561 | #else |
---|
562 | if (r->cf->npExpTable!=NULL) |
---|
563 | { |
---|
564 | omFreeSize( (ADDRESS)r->cf->npExpTable, |
---|
565 | r->cf->npPrimeM*sizeof(CARDINAL) ); |
---|
566 | omFreeSize( (ADDRESS)r->cf->npLogTable, |
---|
567 | r->cf->npPrimeM*sizeof(CARDINAL) ); |
---|
568 | } |
---|
569 | #endif |
---|
570 | break; |
---|
571 | case n_Zp_a: |
---|
572 | case n_Q_a: |
---|
573 | { |
---|
574 | number n=r->minpoly; |
---|
575 | if (n!=NULL) |
---|
576 | { |
---|
577 | r->minpoly=NULL; |
---|
578 | if (r==currRing) naMinimalPoly=NULL; |
---|
579 | naDelete(&n,r); |
---|
580 | } |
---|
581 | } |
---|
582 | break; |
---|
583 | |
---|
584 | default: |
---|
585 | break; |
---|
586 | } |
---|
587 | omFreeSize((ADDRESS)r->cf, sizeof(n_Procs_s)); |
---|
588 | r->cf=NULL; |
---|
589 | } |
---|
590 | else |
---|
591 | { |
---|
592 | WarnS("cf_root list destroyed"); |
---|
593 | } |
---|
594 | } |
---|
595 | } |
---|
596 | if (r->algring!=NULL) |
---|
597 | { |
---|
598 | rKill(r->algring); |
---|
599 | r->algring=NULL; |
---|
600 | } |
---|
601 | } |
---|
602 | } |
---|