1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id$ */ |
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5 | /* |
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6 | * ABSTRACT: algebraic numbers |
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7 | */ |
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8 | |
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9 | #include <stdio.h> |
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10 | #include <string.h> |
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11 | #include "mod2.h" |
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12 | #include "structs.h" |
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13 | #include "omalloc.h" |
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14 | #include "febase.h" |
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15 | #include "longrat.h" |
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16 | #include "modulop.h" |
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17 | #include "numbers.h" |
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18 | #include "polys.h" |
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19 | #include "ideals.h" |
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20 | #include "ring.h" |
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21 | #ifdef HAVE_FACTORY |
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22 | #include "factory.h" |
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23 | #include "clapsing.h" |
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24 | #include "clapconv.h" |
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25 | #endif |
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26 | #include "longalg.h" |
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27 | |
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28 | struct snaIdeal |
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29 | { |
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30 | int anz; |
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31 | napoly *liste; |
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32 | }; |
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33 | typedef struct snaIdeal * naIdeal; |
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34 | |
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35 | naIdeal naI=NULL; |
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36 | |
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37 | omBin snaIdeal_bin = omGetSpecBin(sizeof(snaIdeal)); |
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38 | |
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39 | int naNumbOfPar; |
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40 | napoly naMinimalPoly; |
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41 | #define naParNames (currRing->parameter) |
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42 | static int naIsChar0; |
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43 | static ring naMapRing; |
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44 | |
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45 | #ifdef LDEBUG |
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46 | #define naTest(a) naDBTest(a,__FILE__,__LINE__) |
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47 | BOOLEAN naDBTest(number a, const char *f,const int l); |
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48 | #else |
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49 | #define naTest(a) |
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50 | #endif |
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51 | |
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52 | number (*naMap)(number from); |
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53 | /* procedure variables */ |
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54 | static numberfunc |
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55 | nacMult, nacSub, nacAdd, nacDiv, nacIntDiv; |
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56 | static number (*nacGcd)(number a, number b, const ring r); |
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57 | static number (*nacLcm)(number a, number b, const ring r); |
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58 | static number (*nacInit)(int i, const ring r); |
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59 | static int (*nacInt)(number &n, const ring r); |
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60 | static void (*nacDelete)(number *a, const ring r); |
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61 | #undef n_Delete |
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62 | #define n_Delete(A,R) nacDelete(A,R) |
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63 | void (*nacNormalize)(number &a); |
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64 | static number (*nacNeg)(number a); |
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65 | #define nacWrite(A) n_Write(A,nacRing) |
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66 | number (*nacCopy)(number a); |
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67 | static number (*nacInvers)(number a); |
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68 | BOOLEAN (*nacIsZero)(number a); |
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69 | static BOOLEAN (*nacIsOne)(number a); |
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70 | static BOOLEAN (*nacIsMOne)(number a); |
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71 | static BOOLEAN (*nacGreaterZero)(number a); |
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72 | static const char * (*nacRead) (const char *s, number *a); |
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73 | static napoly napRedp(napoly q); |
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74 | static napoly napTailred(napoly q); |
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75 | static BOOLEAN napDivPoly(napoly p, napoly q); |
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76 | static int napExpi(int i, napoly a, napoly b); |
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77 | ring nacRing; |
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78 | |
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79 | void naCoefNormalize(number pp); |
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80 | |
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81 | #define napCopy(p) p_Copy(p,nacRing) |
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82 | |
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83 | static number nadGcd( number a, number b, const ring r) { return nacInit(1,r); } |
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84 | /*2 |
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85 | * sets the appropriate operators |
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86 | */ |
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87 | void naSetChar(int i, ring r) |
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88 | { |
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89 | if (naI!=NULL) |
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90 | { |
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91 | int j; |
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92 | for (j=naI->anz-1; j>=0; j--) |
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93 | p_Delete (&naI->liste[j],nacRing); |
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94 | omFreeSize((ADDRESS)naI->liste,naI->anz*sizeof(napoly)); |
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95 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
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96 | naI=NULL; |
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97 | } |
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98 | naMap = naCopy; |
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99 | |
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100 | if (r->minpoly!=NULL) |
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101 | { |
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102 | naMinimalPoly=((lnumber)r->minpoly)->z; |
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103 | #ifdef LDEBUG |
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104 | omCheckAddr(naMinimalPoly); |
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105 | #endif |
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106 | } |
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107 | else |
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108 | naMinimalPoly = NULL; |
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109 | if (r->minideal!=NULL) |
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110 | { |
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111 | naI=(naIdeal)omAllocBin(snaIdeal_bin); |
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112 | naI->anz=IDELEMS(r->minideal); |
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113 | naI->liste=(napoly*)omAlloc(naI->anz*sizeof(napoly)); |
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114 | int j; |
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115 | for (j=naI->anz-1; j>=0; j--) |
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116 | { |
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117 | lnumber a = (lnumber)pGetCoeff(r->minideal->m[j]); |
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118 | naI->liste[j]=napCopy(a->z); |
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119 | } |
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120 | } |
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121 | |
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122 | naNumbOfPar=rPar(r); |
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123 | if (i == 1) |
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124 | { |
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125 | naIsChar0 = 1; |
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126 | } |
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127 | else if (i < 0) |
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128 | { |
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129 | naIsChar0 = 0; |
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130 | npSetChar(-i, r->algring); // to be changed HS |
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131 | } |
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132 | #ifdef TEST |
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133 | else |
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134 | { |
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135 | Print("naSetChar:c=%d param=%d\n",i,rPar(r)); |
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136 | } |
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137 | #endif |
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138 | nacRing = r->algring; |
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139 | nacInit = nacRing->cf->cfInit; |
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140 | nacInt = nacRing->cf->n_Int; |
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141 | nacCopy = nacRing->cf->nCopy; |
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142 | nacAdd = nacRing->cf->nAdd; |
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143 | nacSub = nacRing->cf->nSub; |
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144 | nacNormalize = nacRing->cf->nNormalize; |
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145 | nacNeg = nacRing->cf->nNeg; |
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146 | nacIsZero = nacRing->cf->nIsZero; |
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147 | nacRead = nacRing->cf->nRead; |
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148 | nacGreaterZero = nacRing->cf->nGreaterZero; |
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149 | nacIsOne = nacRing->cf->nIsOne; |
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150 | nacIsMOne = nacRing->cf->nIsMOne; |
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151 | nacGcd = nacRing->cf->nGcd; |
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152 | nacLcm = nacRing->cf->nLcm; |
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153 | nacMult = nacRing->cf->nMult; |
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154 | nacDiv = nacRing->cf->nDiv; |
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155 | nacIntDiv = nacRing->cf->nIntDiv; |
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156 | nacInvers = nacRing->cf->nInvers; |
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157 | nacDelete = nacRing->cf->cfDelete; |
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158 | } |
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159 | |
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160 | /*============= procedure for polynomials: napXXXX =======================*/ |
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161 | |
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162 | |
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163 | |
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164 | #ifdef LDEBUG |
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165 | static void napTest(napoly p) |
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166 | { |
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167 | while (p != NULL) |
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168 | { |
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169 | if (naIsChar0) |
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170 | nlDBTest(pGetCoeff(p), "", 0); |
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171 | pIter(p); |
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172 | } |
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173 | } |
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174 | #else |
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175 | #define napTest(p) ((void) 0) |
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176 | #endif |
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177 | |
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178 | #define napSetCoeff(p,n) {n_Delete(&pGetCoeff(p),nacRing);pGetCoeff(p)=n;} |
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179 | #define napComp(p,q) p_LmCmp((poly)p,(poly)q, nacRing) |
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180 | #define napMultT(A,E) A=(napoly)p_Mult_mm((poly)A,(poly)E,nacRing) |
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181 | #define napDeg(p) (int)p_ExpVectorQuerSum(p, nacRing) |
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182 | |
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183 | /*3 |
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184 | * creates an napoly |
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185 | */ |
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186 | napoly napInitz(number z) |
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187 | { |
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188 | napoly a = (napoly)p_Init(nacRing); |
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189 | pGetCoeff(a) = z; |
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190 | return a; |
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191 | } |
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192 | |
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193 | /*3 |
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194 | * copy a napoly. poly |
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195 | */ |
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196 | static napoly napCopyNeg(napoly p) |
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197 | { |
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198 | napoly r=napCopy(p); |
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199 | r=(napoly)p_Neg((poly)r, nacRing); |
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200 | return r; |
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201 | } |
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202 | |
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203 | /*3 |
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204 | * returns ph * z |
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205 | */ |
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206 | static void napMultN(napoly p, number z) |
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207 | { |
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208 | number t; |
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209 | |
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210 | while (p!=NULL) |
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211 | { |
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212 | t = nacMult(pGetCoeff(p), z); |
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213 | nacNormalize(t); |
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214 | n_Delete(&pGetCoeff(p),nacRing); |
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215 | pGetCoeff(p) = t; |
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216 | pIter(p); |
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217 | } |
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218 | } |
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219 | |
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220 | /*3 |
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221 | * division with rest; f = g*q + r, returns r and destroy f |
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222 | */ |
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223 | napoly napRemainder(napoly f, const napoly g) |
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224 | { |
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225 | napoly a, h, qq; |
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226 | |
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227 | qq = (napoly)p_Init(nacRing); |
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228 | pNext(qq) = NULL; |
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229 | p_Normalize(g, nacRing); |
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230 | p_Normalize(f, nacRing); |
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231 | a = f; |
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232 | do |
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233 | { |
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234 | napSetExp(qq,1, p_GetExp(a,1,nacRing) - p_GetExp(g,1,nacRing)); |
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235 | napSetm(qq); |
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236 | pGetCoeff(qq) = nacDiv(pGetCoeff(a), pGetCoeff(g)); |
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237 | pGetCoeff(qq) = nacNeg(pGetCoeff(qq)); |
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238 | nacNormalize(pGetCoeff(qq)); |
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239 | h = napCopy(g); |
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240 | napMultT(h, qq); |
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241 | p_Normalize(h,nacRing); |
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242 | n_Delete(&pGetCoeff(qq),nacRing); |
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243 | a = napAdd(a, h); |
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244 | } |
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245 | while ((a!=NULL) && (p_GetExp(a,1,nacRing) >= p_GetExp(g,1,nacRing))); |
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246 | omFreeBinAddr(qq); |
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247 | return a; |
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248 | } |
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249 | |
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250 | /*3 |
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251 | * division with rest; f = g*q + r, destroy f |
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252 | */ |
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253 | static void napDivMod(napoly f, napoly g, napoly *q, napoly *r) |
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254 | { |
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255 | napoly a, h, b, qq; |
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256 | |
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257 | qq = (napoly)p_Init(nacRing); |
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258 | pNext(qq) = b = NULL; |
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259 | p_Normalize(g,nacRing); |
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260 | p_Normalize(f,nacRing); |
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261 | a = f; |
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262 | do |
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263 | { |
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264 | napSetExp(qq,1, p_GetExp(a,1,nacRing) - p_GetExp(g,1,nacRing)); |
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265 | p_Setm(qq,nacRing); |
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266 | pGetCoeff(qq) = nacDiv(pGetCoeff(a), pGetCoeff(g)); |
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267 | nacNormalize(pGetCoeff(qq)); |
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268 | b = napAdd(b, napCopy(qq)); |
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269 | pGetCoeff(qq) = nacNeg(pGetCoeff(qq)); |
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270 | h = napCopy(g); |
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271 | napMultT(h, qq); |
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272 | p_Normalize(h,nacRing); |
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273 | n_Delete(&pGetCoeff(qq),nacRing); |
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274 | a = napAdd(a, h); |
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275 | } |
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276 | while ((a!=NULL) && (p_GetExp(a,1,nacRing) >= p_GetExp(g,1,nacRing))); |
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277 | omFreeBinAddr(qq); |
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278 | *q = b; |
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279 | *r = a; |
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280 | } |
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281 | |
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282 | /*3 |
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283 | * returns z with z*x mod c = 1 |
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284 | */ |
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285 | static napoly napInvers(napoly x, const napoly c) |
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286 | { |
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287 | napoly y, r, qa, qn, q; |
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288 | number t, h; |
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289 | |
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290 | if (p_GetExp(x,1,nacRing) >= p_GetExp(c,1,nacRing)) |
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291 | x = napRemainder(x, c); |
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292 | if (x==NULL) |
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293 | { |
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294 | goto zero_divisor; |
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295 | } |
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296 | if (p_GetExp(x,1,nacRing)==0) |
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297 | { |
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298 | if (!nacIsOne(pGetCoeff(x))) |
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299 | { |
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300 | nacNormalize(pGetCoeff(x)); |
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301 | t = nacInvers(pGetCoeff(x)); |
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302 | nacNormalize(t); |
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303 | n_Delete(&pGetCoeff(x),nacRing); |
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304 | pGetCoeff(x) = t; |
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305 | } |
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306 | return x; |
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307 | } |
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308 | y = napCopy(c); |
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309 | napDivMod(y, x, &qa, &r); |
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310 | if (r==NULL) |
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311 | { |
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312 | goto zero_divisor; |
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313 | } |
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314 | if (p_GetExp(r,1,nacRing)==0) |
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315 | { |
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316 | nacNormalize(pGetCoeff(r)); |
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317 | t = nacInvers(pGetCoeff(r)); |
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318 | nacNormalize(t); |
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319 | t = nacNeg(t); |
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320 | napMultN(qa, t); |
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321 | n_Delete(&t,nacRing); |
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322 | p_Normalize(qa,nacRing); |
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323 | p_Delete(&x,nacRing); |
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324 | p_Delete(&r,nacRing); |
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325 | return qa; |
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326 | } |
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327 | y = x; |
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328 | x = r; |
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329 | napDivMod(y, x, &q, &r); |
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330 | if (r==NULL) |
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331 | { |
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332 | goto zero_divisor; |
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333 | } |
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334 | if (p_GetExp(r,1,nacRing)==0) |
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335 | { |
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336 | q = p_Mult_q(q, qa,nacRing); |
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337 | q = napAdd(q, p_ISet(1,nacRing)); |
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338 | nacNormalize(pGetCoeff(r)); |
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339 | t = nacInvers(pGetCoeff(r)); |
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340 | napMultN(q, t); |
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341 | p_Normalize(q,nacRing); |
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342 | n_Delete(&t,nacRing); |
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343 | p_Delete(&x,nacRing); |
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344 | p_Delete(&r,nacRing); |
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345 | if (p_GetExp(q,1,nacRing) >= p_GetExp(c,1,nacRing)) |
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346 | q = napRemainder(q, c); |
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347 | return q; |
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348 | } |
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349 | q = p_Mult_q(q, napCopy(qa),nacRing); |
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350 | q = napAdd(q, p_ISet(1,nacRing)); |
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351 | qa = napNeg(qa); |
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352 | loop |
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353 | { |
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354 | y = x; |
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355 | x = r; |
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356 | napDivMod(y, x, &qn, &r); |
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357 | if (r==NULL) |
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358 | { |
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359 | break; |
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360 | } |
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361 | if (p_GetExp(r,1,nacRing)==0) |
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362 | { |
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363 | q = p_Mult_q(q, qn,nacRing); |
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364 | q = napNeg(q); |
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365 | q = napAdd(q, qa); |
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366 | nacNormalize(pGetCoeff(r)); |
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367 | t = nacInvers(pGetCoeff(r)); |
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368 | //nacNormalize(t); |
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369 | napMultN(q, t); |
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370 | p_Normalize(q,nacRing); |
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371 | n_Delete(&t,nacRing); |
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372 | p_Delete(&x,nacRing); |
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373 | p_Delete(&r,nacRing); |
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374 | if (p_GetExp(q,1,nacRing) >= p_GetExp(c,1,nacRing)) |
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375 | q = napRemainder(q, c); |
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376 | return q; |
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377 | } |
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378 | y = q; |
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379 | q = p_Mult_q(napCopy(q), qn, nacRing); |
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380 | q = napNeg(q); |
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381 | q = napAdd(q, qa); |
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382 | qa = y; |
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383 | } |
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384 | // zero divisor found: |
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385 | zero_divisor: |
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386 | Werror("zero divisor found - your minpoly is not irreducible"); |
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387 | return x; |
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388 | } |
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389 | |
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390 | /*3 |
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391 | * the max degree of an napoly poly (used for test of "simple" et al.) |
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392 | */ |
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393 | static int napMaxDeg(napoly p) |
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394 | { |
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395 | int d = 0; |
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396 | while(p!=NULL) |
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397 | { |
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398 | d=si_max(d,napDeg(p)); |
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399 | pIter(p); |
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400 | } |
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401 | return d; |
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402 | } |
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403 | |
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404 | /*3 |
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405 | * the max degree of an napoly poly (used for test of "simple" et al.) |
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406 | */ |
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407 | static int napMaxDegLen(napoly p, int &l) |
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408 | { |
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409 | int d = 0; |
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410 | int ll=0; |
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411 | while(p!=NULL) |
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412 | { |
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413 | d=si_max(d,napDeg(p)); |
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414 | pIter(p); |
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415 | ll++; |
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416 | } |
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417 | l=ll; |
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418 | return d; |
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419 | } |
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420 | |
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421 | |
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422 | /*3 |
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423 | *writes a polynomial number |
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424 | */ |
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425 | void napWrite(napoly p,const BOOLEAN has_denom, const ring r) |
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426 | { |
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427 | ring nacring=r->algring; |
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428 | if (p==NULL) |
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429 | StringAppendS("0"); |
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430 | else if (p_LmIsConstant(p,nacring)) |
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431 | { |
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432 | BOOLEAN kl=FALSE; |
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433 | if (has_denom) |
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434 | { |
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435 | number den=nacring->cf->cfGetDenom(pGetCoeff(p),nacring ); |
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436 | kl=!n_IsOne(den,nacring); |
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437 | n_Delete(&den, nacring); |
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438 | } |
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439 | if (kl) StringAppendS("("); |
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440 | //StringAppendS("-1"); |
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441 | n_Write(pGetCoeff(p),nacring); |
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442 | if (kl) StringAppendS(")"); |
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443 | } |
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444 | else |
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445 | { |
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446 | StringAppendS("("); |
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447 | loop |
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448 | { |
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449 | BOOLEAN wroteCoeff=FALSE; |
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450 | if ((p_LmIsConstant(p,nacring)) |
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451 | || ((!n_IsOne(pGetCoeff(p),nacring)) |
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452 | && (!n_IsMOne(pGetCoeff(p),nacring)))) |
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453 | { |
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454 | n_Write(pGetCoeff(p),nacring); |
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455 | wroteCoeff=(r->ShortOut==0); |
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456 | } |
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457 | else if (n_IsMOne(pGetCoeff(p),nacring)) |
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458 | { |
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459 | StringAppendS("-"); |
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460 | } |
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461 | int i; |
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462 | for (i = 0; i < r->P; i++) |
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463 | { |
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464 | int e=p_GetExp(p,i+1,nacring); |
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465 | if (e > 0) |
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466 | { |
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467 | if (wroteCoeff) |
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468 | StringAppendS("*"); |
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469 | else |
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470 | wroteCoeff=(r->ShortOut==0); |
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471 | StringAppendS(r->parameter[i]); |
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472 | if (e > 1) |
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473 | { |
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474 | if (r->ShortOut == 0) |
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475 | StringAppendS("^"); |
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476 | StringAppend("%d", e); |
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477 | } |
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478 | } |
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479 | } /*for*/ |
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480 | pIter(p); |
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481 | if (p==NULL) |
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482 | break; |
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483 | if (n_GreaterZero(pGetCoeff(p),nacring)) |
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484 | StringAppendS("+"); |
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485 | } |
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486 | StringAppendS(")"); |
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487 | } |
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488 | } |
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489 | |
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490 | |
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491 | static const char *napHandleMons(const char *s, int i, napoly ex) |
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492 | { |
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493 | int j; |
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494 | if (strncmp(s,naParNames[i],strlen(naParNames[i]))==0) |
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495 | { |
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496 | s+=strlen(naParNames[i]); |
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497 | if ((*s >= '0') && (*s <= '9')) |
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498 | { |
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499 | s = eati(s, &j); |
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500 | napAddExp(ex,i+1,j); |
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501 | } |
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502 | else |
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503 | napAddExp(ex,i+1,1); |
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504 | } |
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505 | return s; |
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506 | } |
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507 | static const char *napHandlePars(const char *s, int i, napoly ex) |
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508 | { |
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509 | int j; |
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510 | if (strcmp(s,naParNames[i])==0) |
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511 | { |
---|
512 | s+=strlen(naParNames[i]); |
---|
513 | napSetExp(ex,i+1,1); |
---|
514 | } |
---|
515 | return s; |
---|
516 | } |
---|
517 | |
---|
518 | /*3 reads a monomial */ |
---|
519 | static const char *napRead(const char *s, napoly *b) |
---|
520 | { |
---|
521 | napoly a; |
---|
522 | int i; |
---|
523 | a = (napoly)p_Init(nacRing); |
---|
524 | if ((*s >= '0') && (*s <= '9')) |
---|
525 | { |
---|
526 | s = nacRead(s, &pGetCoeff(a)); |
---|
527 | if (nacIsZero(pGetCoeff(a))) |
---|
528 | { |
---|
529 | p_LmDelete(&a,nacRing); |
---|
530 | *b = NULL; |
---|
531 | return s; |
---|
532 | } |
---|
533 | } |
---|
534 | else |
---|
535 | pGetCoeff(a) = nacInit(1,nacRing); |
---|
536 | i = 0; |
---|
537 | const char *olds=s; |
---|
538 | loop |
---|
539 | { |
---|
540 | s = napHandlePars(s, i, a); |
---|
541 | if (olds == s) |
---|
542 | i++; |
---|
543 | else if (*s == '\0') |
---|
544 | { |
---|
545 | *b = a; |
---|
546 | return s; |
---|
547 | } |
---|
548 | if (i >= naNumbOfPar) |
---|
549 | break; |
---|
550 | } |
---|
551 | i=0; |
---|
552 | loop |
---|
553 | { |
---|
554 | olds = s; |
---|
555 | s = napHandleMons(s, i, a); |
---|
556 | if (olds == s) |
---|
557 | i++; |
---|
558 | else |
---|
559 | i = 0; |
---|
560 | if ((*s == '\0') || (i >= naNumbOfPar)) |
---|
561 | break; |
---|
562 | } |
---|
563 | *b = a; |
---|
564 | return s; |
---|
565 | } |
---|
566 | |
---|
567 | static int napExp(napoly a, napoly b) |
---|
568 | { |
---|
569 | while (pNext(a)!=NULL) pIter(a); |
---|
570 | int m = p_GetExp(a,1,nacRing); |
---|
571 | if (m==0) return 0; |
---|
572 | while (pNext(b)!=NULL) pIter(b); |
---|
573 | int mm=p_GetExp(b,1,nacRing); |
---|
574 | if (m > mm) m = mm; |
---|
575 | return m; |
---|
576 | } |
---|
577 | |
---|
578 | /* |
---|
579 | * finds the smallest i-th exponent in a and b |
---|
580 | * used to find it in a fraction |
---|
581 | */ |
---|
582 | static int napExpi(int i, napoly a, napoly b) |
---|
583 | { |
---|
584 | if (a==NULL || b==NULL) return 0; |
---|
585 | int m = p_GetExp(a,i+1,nacRing); |
---|
586 | if (m==0) return 0; |
---|
587 | while (pNext(a) != NULL) |
---|
588 | { |
---|
589 | pIter(a); |
---|
590 | if (m > p_GetExp(a,i+1,nacRing)) |
---|
591 | { |
---|
592 | m = p_GetExp(a,i+1,nacRing); |
---|
593 | if (m==0) return 0; |
---|
594 | } |
---|
595 | } |
---|
596 | do |
---|
597 | { |
---|
598 | if (m > p_GetExp(b,i+1,nacRing)) |
---|
599 | { |
---|
600 | m = p_GetExp(b,i+1,nacRing); |
---|
601 | if (m==0) return 0; |
---|
602 | } |
---|
603 | pIter(b); |
---|
604 | } |
---|
605 | while (b != NULL); |
---|
606 | return m; |
---|
607 | } |
---|
608 | |
---|
609 | static void napContent(napoly ph) |
---|
610 | { |
---|
611 | number h,d; |
---|
612 | napoly p; |
---|
613 | |
---|
614 | p = ph; |
---|
615 | if (nacIsOne(pGetCoeff(p))) |
---|
616 | return; |
---|
617 | h = nacCopy(pGetCoeff(p)); |
---|
618 | pIter(p); |
---|
619 | do |
---|
620 | { |
---|
621 | d=nacGcd(pGetCoeff(p), h, nacRing); |
---|
622 | if(nacIsOne(d)) |
---|
623 | { |
---|
624 | n_Delete(&h,nacRing); |
---|
625 | n_Delete(&d,nacRing); |
---|
626 | return; |
---|
627 | } |
---|
628 | n_Delete(&h,nacRing); |
---|
629 | h = d; |
---|
630 | pIter(p); |
---|
631 | } |
---|
632 | while (p!=NULL); |
---|
633 | h = nacInvers(d); |
---|
634 | n_Delete(&d,nacRing); |
---|
635 | p = ph; |
---|
636 | while (p!=NULL) |
---|
637 | { |
---|
638 | d = nacMult(pGetCoeff(p), h); |
---|
639 | n_Delete(&pGetCoeff(p),nacRing); |
---|
640 | pGetCoeff(p) = d; |
---|
641 | pIter(p); |
---|
642 | } |
---|
643 | n_Delete(&h,nacRing); |
---|
644 | } |
---|
645 | |
---|
646 | static void napCleardenom(napoly ph) |
---|
647 | { |
---|
648 | number d, h; |
---|
649 | napoly p; |
---|
650 | |
---|
651 | if (!naIsChar0) |
---|
652 | return; |
---|
653 | p = ph; |
---|
654 | h = nacInit(1,nacRing); |
---|
655 | while (p!=NULL) |
---|
656 | { |
---|
657 | d = nacLcm(h, pGetCoeff(p), nacRing); |
---|
658 | n_Delete(&h,nacRing); |
---|
659 | h = d; |
---|
660 | pIter(p); |
---|
661 | } |
---|
662 | if(!nacIsOne(h)) |
---|
663 | { |
---|
664 | p = ph; |
---|
665 | while (p!=NULL) |
---|
666 | { |
---|
667 | d=nacMult(h, pGetCoeff(p)); |
---|
668 | n_Delete(&pGetCoeff(p),nacRing); |
---|
669 | nacNormalize(d); |
---|
670 | pGetCoeff(p) = d; |
---|
671 | pIter(p); |
---|
672 | } |
---|
673 | n_Delete(&h,nacRing); |
---|
674 | } |
---|
675 | napContent(ph); |
---|
676 | } |
---|
677 | |
---|
678 | static napoly napGcd0(napoly a, napoly b) |
---|
679 | { |
---|
680 | number x, y; |
---|
681 | if (!naIsChar0) |
---|
682 | return p_ISet(1,nacRing); |
---|
683 | x = nacCopy(pGetCoeff(a)); |
---|
684 | if (nacIsOne(x)) |
---|
685 | return napInitz(x); |
---|
686 | while (pNext(a)!=NULL) |
---|
687 | { |
---|
688 | pIter(a); |
---|
689 | y = nacGcd(x, pGetCoeff(a), nacRing); |
---|
690 | n_Delete(&x,nacRing); |
---|
691 | x = y; |
---|
692 | if (nacIsOne(x)) |
---|
693 | return napInitz(x); |
---|
694 | } |
---|
695 | do |
---|
696 | { |
---|
697 | y = nacGcd(x, pGetCoeff(b), nacRing); |
---|
698 | n_Delete(&x,nacRing); |
---|
699 | x = y; |
---|
700 | if (nacIsOne(x)) |
---|
701 | return napInitz(x); |
---|
702 | pIter(b); |
---|
703 | } |
---|
704 | while (b!=NULL); |
---|
705 | return napInitz(x); |
---|
706 | } |
---|
707 | |
---|
708 | /*3 |
---|
709 | * result =gcd(a,b) |
---|
710 | */ |
---|
711 | static napoly napGcd(napoly a, napoly b) |
---|
712 | { |
---|
713 | int i; |
---|
714 | napoly g, x, y, h; |
---|
715 | if ((a==NULL) |
---|
716 | || ((pNext(a)==NULL)&&(nacIsZero(pGetCoeff(a))))) |
---|
717 | { |
---|
718 | if ((b==NULL) |
---|
719 | || ((pNext(b)==NULL)&&(nacIsZero(pGetCoeff(b))))) |
---|
720 | { |
---|
721 | return p_ISet(1,nacRing); |
---|
722 | } |
---|
723 | return napCopy(b); |
---|
724 | } |
---|
725 | else |
---|
726 | if ((b==NULL) |
---|
727 | || ((pNext(b)==NULL)&&(nacIsZero(pGetCoeff(b))))) |
---|
728 | { |
---|
729 | return napCopy(a); |
---|
730 | } |
---|
731 | if (naMinimalPoly != NULL) |
---|
732 | { |
---|
733 | if (p_GetExp(a,1,nacRing) >= p_GetExp(b,1,nacRing)) |
---|
734 | { |
---|
735 | x = a; |
---|
736 | y = b; |
---|
737 | } |
---|
738 | else |
---|
739 | { |
---|
740 | x = b; |
---|
741 | y = a; |
---|
742 | } |
---|
743 | if (!naIsChar0) g = p_ISet(1,nacRing); |
---|
744 | else g = napGcd0(x, y); |
---|
745 | if (pNext(y)==NULL) |
---|
746 | { |
---|
747 | napSetExp(g,1, napExp(x, y)); |
---|
748 | p_Setm(g,nacRing); |
---|
749 | return g; |
---|
750 | } |
---|
751 | x = napCopy(x); |
---|
752 | y = napCopy(y); |
---|
753 | loop |
---|
754 | { |
---|
755 | h = napRemainder(x, y); |
---|
756 | if (h==NULL) |
---|
757 | { |
---|
758 | napCleardenom(y); |
---|
759 | if (!nacIsOne(pGetCoeff(g))) |
---|
760 | napMultN(y, pGetCoeff(g)); |
---|
761 | p_LmDelete(&g,nacRing); |
---|
762 | return y; |
---|
763 | } |
---|
764 | else if (pNext(h)==NULL) |
---|
765 | break; |
---|
766 | x = y; |
---|
767 | y = h; |
---|
768 | } |
---|
769 | p_Delete(&y,nacRing); |
---|
770 | p_LmDelete(&h,nacRing); |
---|
771 | napSetExp(g,1, napExp(a, b)); |
---|
772 | p_Setm(g,nacRing); |
---|
773 | return g; |
---|
774 | } |
---|
775 | // Hmm ... this is a memory leak |
---|
776 | // x = (napoly)p_Init(nacRing); |
---|
777 | g=a; |
---|
778 | h=b; |
---|
779 | if (!naIsChar0) x = p_ISet(1,nacRing); |
---|
780 | else x = napGcd0(g,h); |
---|
781 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
782 | { |
---|
783 | napSetExp(x,i+1, napExpi(i,a,b)); |
---|
784 | p_Setm(x,nacRing); |
---|
785 | } |
---|
786 | return x; |
---|
787 | } |
---|
788 | |
---|
789 | |
---|
790 | number napLcm(napoly a) |
---|
791 | { |
---|
792 | number h = nacInit(1,nacRing); |
---|
793 | |
---|
794 | if (naIsChar0) |
---|
795 | { |
---|
796 | number d; |
---|
797 | napoly b = a; |
---|
798 | |
---|
799 | while (b!=NULL) |
---|
800 | { |
---|
801 | d = nacLcm(h, pGetCoeff(b), nacRing); |
---|
802 | n_Delete(&h,nacRing); |
---|
803 | h = d; |
---|
804 | pIter(b); |
---|
805 | } |
---|
806 | } |
---|
807 | return h; |
---|
808 | } |
---|
809 | |
---|
810 | |
---|
811 | /*2 |
---|
812 | * meins (for reduction in algebraic extension) |
---|
813 | * checks if head of p divides head of q |
---|
814 | * doesn't delete p and q |
---|
815 | */ |
---|
816 | static BOOLEAN napDivPoly (napoly p, napoly q) |
---|
817 | { |
---|
818 | int j=1; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
819 | |
---|
820 | while (p_GetExp(p,j,nacRing) <= p_GetExp(q,j,nacRing)) |
---|
821 | { |
---|
822 | j++; |
---|
823 | if (j > naNumbOfPar) |
---|
824 | return 1; |
---|
825 | } |
---|
826 | return 0; |
---|
827 | } |
---|
828 | |
---|
829 | |
---|
830 | /*2 |
---|
831 | * meins (for reduction in algebraic extension) |
---|
832 | * Normalform of poly with naI |
---|
833 | * changes q and returns it |
---|
834 | */ |
---|
835 | napoly napRedp (napoly q) |
---|
836 | { |
---|
837 | napoly h = (napoly)p_Init(nacRing); |
---|
838 | int i=0,j; |
---|
839 | |
---|
840 | loop |
---|
841 | { |
---|
842 | if (napDivPoly (naI->liste[i], q)) |
---|
843 | { |
---|
844 | /* h = lt(q)/lt(naI->liste[i])*/ |
---|
845 | pGetCoeff(h) = nacCopy(pGetCoeff(q)); |
---|
846 | for (j=naNumbOfPar; j>0; j--) |
---|
847 | napSetExp(h,j, p_GetExp(q,j,nacRing) - p_GetExp(naI->liste[i],j,nacRing)); |
---|
848 | p_Setm(h,nacRing); |
---|
849 | h = p_Mult_q(h, napCopy(naI->liste[i]),nacRing); |
---|
850 | h = napNeg (h); |
---|
851 | q = napAdd (q, napCopy(h)); |
---|
852 | p_Delete (&pNext(h),nacRing); |
---|
853 | if (q == NULL) |
---|
854 | { |
---|
855 | p_Delete(&h,nacRing); |
---|
856 | return q; |
---|
857 | } |
---|
858 | /* try to reduce further */ |
---|
859 | i = 0; |
---|
860 | } |
---|
861 | else |
---|
862 | { |
---|
863 | i++; |
---|
864 | if (i >= naI->anz) |
---|
865 | { |
---|
866 | p_Delete(&h,nacRing); |
---|
867 | return q; |
---|
868 | } |
---|
869 | } |
---|
870 | } |
---|
871 | } |
---|
872 | |
---|
873 | |
---|
874 | /*2 |
---|
875 | * meins (for reduction in algebraic extension) |
---|
876 | * reduces the tail of Poly q |
---|
877 | * needs q != NULL |
---|
878 | * changes q and returns it |
---|
879 | */ |
---|
880 | napoly napTailred (napoly q) |
---|
881 | { |
---|
882 | napoly h; |
---|
883 | |
---|
884 | h = pNext(q); |
---|
885 | while (h != NULL) |
---|
886 | { |
---|
887 | h = napRedp (h); |
---|
888 | if (h == NULL) |
---|
889 | return q; |
---|
890 | pIter(h); |
---|
891 | } |
---|
892 | return q; |
---|
893 | } |
---|
894 | |
---|
895 | |
---|
896 | /*================ procedure for rational functions: naXXXX =================*/ |
---|
897 | |
---|
898 | /*2 |
---|
899 | * z:= i |
---|
900 | */ |
---|
901 | number naInit(int i, const ring r) |
---|
902 | { |
---|
903 | if (i!=0) |
---|
904 | { |
---|
905 | number c=n_Init(i,r->algring); |
---|
906 | if (!n_IsZero(c,r->algring)) |
---|
907 | { |
---|
908 | poly z=p_Init(r->algring); |
---|
909 | pSetCoeff0(z,c); |
---|
910 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
911 | l->z = z; |
---|
912 | l->s = 2; |
---|
913 | l->n = NULL; |
---|
914 | return (number)l; |
---|
915 | } |
---|
916 | } |
---|
917 | /*else*/ |
---|
918 | return NULL; |
---|
919 | } |
---|
920 | |
---|
921 | number naPar(int i) |
---|
922 | { |
---|
923 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
924 | l->s = 2; |
---|
925 | l->z = p_ISet(1,nacRing); |
---|
926 | napSetExp(l->z,i,1); |
---|
927 | p_Setm(l->z,nacRing); |
---|
928 | l->n = NULL; |
---|
929 | return (number)l; |
---|
930 | } |
---|
931 | |
---|
932 | int naParDeg(number n) /* i := deg(n) */ |
---|
933 | { |
---|
934 | lnumber l = (lnumber)n; |
---|
935 | if (l==NULL) return -1; |
---|
936 | return napDeg(l->z); |
---|
937 | } |
---|
938 | |
---|
939 | //int naParDeg(number n) /* i := deg(n) */ |
---|
940 | //{ |
---|
941 | // lnumber l = (lnumber)n; |
---|
942 | // if (l==NULL) return -1; |
---|
943 | // return napMaxDeg(l->z)+napMaxDeg(l->n); |
---|
944 | //} |
---|
945 | |
---|
946 | int naSize(number n) /* size desc. */ |
---|
947 | { |
---|
948 | lnumber l = (lnumber)n; |
---|
949 | if (l==NULL) return -1; |
---|
950 | int len_z; |
---|
951 | int len_n; |
---|
952 | int o=napMaxDegLen(l->z,len_z)+napMaxDegLen(l->n,len_n); |
---|
953 | return (len_z+len_n)+o; |
---|
954 | } |
---|
955 | |
---|
956 | /*2 |
---|
957 | * convert a number to int (if possible) |
---|
958 | */ |
---|
959 | int naInt(number &n, const ring r) |
---|
960 | { |
---|
961 | lnumber l=(lnumber)n; |
---|
962 | if ((l!=NULL)&&(l->n==NULL)&&(p_IsConstant(l->z,r->algring))) |
---|
963 | { |
---|
964 | return nacInt(pGetCoeff(l->z),r->algring); |
---|
965 | } |
---|
966 | return 0; |
---|
967 | } |
---|
968 | |
---|
969 | /*2 |
---|
970 | * deletes p |
---|
971 | */ |
---|
972 | void naDelete(number *p, const ring r) |
---|
973 | { |
---|
974 | if ((*p)!=r->minpoly) |
---|
975 | { |
---|
976 | lnumber l = (lnumber) * p; |
---|
977 | if (l==NULL) return; |
---|
978 | p_Delete(&(l->z),r->algring); |
---|
979 | p_Delete(&(l->n),r->algring); |
---|
980 | omFreeBin((ADDRESS)l, rnumber_bin); |
---|
981 | } |
---|
982 | *p = NULL; |
---|
983 | } |
---|
984 | |
---|
985 | /*2 |
---|
986 | * copy p to erg |
---|
987 | */ |
---|
988 | number naCopy(number p) |
---|
989 | { |
---|
990 | if (p==NULL) return NULL; |
---|
991 | naTest(p); |
---|
992 | lnumber erg; |
---|
993 | lnumber src = (lnumber)p; |
---|
994 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
995 | erg->z = p_Copy(src->z, nacRing); |
---|
996 | erg->n = p_Copy(src->n, nacRing); |
---|
997 | erg->s = src->s; |
---|
998 | return (number)erg; |
---|
999 | } |
---|
1000 | number na_Copy(number p, const ring r) |
---|
1001 | { |
---|
1002 | if (p==NULL) return NULL; |
---|
1003 | lnumber erg; |
---|
1004 | lnumber src = (lnumber)p; |
---|
1005 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
1006 | erg->z = p_Copy(src->z,r->algring); |
---|
1007 | erg->n = p_Copy(src->n,r->algring); |
---|
1008 | erg->s = src->s; |
---|
1009 | return (number)erg; |
---|
1010 | } |
---|
1011 | |
---|
1012 | /*2 |
---|
1013 | * addition; lu:= la + lb |
---|
1014 | */ |
---|
1015 | number naAdd(number la, number lb) |
---|
1016 | { |
---|
1017 | if (la==NULL) return naCopy(lb); |
---|
1018 | if (lb==NULL) return naCopy(la); |
---|
1019 | |
---|
1020 | napoly x, y; |
---|
1021 | lnumber lu; |
---|
1022 | lnumber a = (lnumber)la; |
---|
1023 | lnumber b = (lnumber)lb; |
---|
1024 | #ifdef LDEBUG |
---|
1025 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1026 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1027 | #endif |
---|
1028 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
---|
1029 | else x = napCopy(a->z); |
---|
1030 | if (a->n!=NULL) y = pp_Mult_qq(b->z, a->n,nacRing); |
---|
1031 | else y = napCopy(b->z); |
---|
1032 | napoly res = napAdd(x, y); |
---|
1033 | if (res==NULL) |
---|
1034 | { |
---|
1035 | return (number)NULL; |
---|
1036 | } |
---|
1037 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
1038 | lu->z=res; |
---|
1039 | if (a->n!=NULL) |
---|
1040 | { |
---|
1041 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
---|
1042 | else x = napCopy(a->n); |
---|
1043 | } |
---|
1044 | else |
---|
1045 | { |
---|
1046 | if (b->n!=NULL) x = napCopy(b->n); |
---|
1047 | else x = NULL; |
---|
1048 | } |
---|
1049 | //if (x!=NULL) |
---|
1050 | //{ |
---|
1051 | // if (p_LmIsConstant(x,nacRing)) |
---|
1052 | // { |
---|
1053 | // number inv=nacInvers(pGetCoeff(x)); |
---|
1054 | // napMultN(lu->z,inv); |
---|
1055 | // n_Delete(&inv,nacRing); |
---|
1056 | // napDelete(&x); |
---|
1057 | // } |
---|
1058 | //} |
---|
1059 | lu->n = x; |
---|
1060 | lu->s = FALSE; |
---|
1061 | if (/*lu->n*/ x!=NULL) |
---|
1062 | { |
---|
1063 | number luu=(number)lu; |
---|
1064 | //if (p_IsConstant(lu->n,nacRing)) naCoefNormalize(luu); |
---|
1065 | //else |
---|
1066 | naNormalize(luu); |
---|
1067 | lu=(lnumber)luu; |
---|
1068 | } |
---|
1069 | //else lu->s=2; |
---|
1070 | naTest((number)lu); |
---|
1071 | return (number)lu; |
---|
1072 | } |
---|
1073 | |
---|
1074 | /*2 |
---|
1075 | * subtraction; r:= la - lb |
---|
1076 | */ |
---|
1077 | number naSub(number la, number lb) |
---|
1078 | { |
---|
1079 | lnumber lu; |
---|
1080 | |
---|
1081 | if (lb==NULL) return naCopy(la); |
---|
1082 | if (la==NULL) |
---|
1083 | { |
---|
1084 | lu = (lnumber)naCopy(lb); |
---|
1085 | lu->z = napNeg(lu->z); |
---|
1086 | return (number)lu; |
---|
1087 | } |
---|
1088 | |
---|
1089 | lnumber a = (lnumber)la; |
---|
1090 | lnumber b = (lnumber)lb; |
---|
1091 | |
---|
1092 | #ifdef LDEBUG |
---|
1093 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1094 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1095 | #endif |
---|
1096 | |
---|
1097 | napoly x, y; |
---|
1098 | if (b->n!=NULL) x = pp_Mult_qq(a->z, b->n,nacRing); |
---|
1099 | else x = napCopy(a->z); |
---|
1100 | if (a->n!=NULL) y = p_Mult_q(napCopy(b->z), napCopyNeg(a->n),nacRing); |
---|
1101 | else y = napCopyNeg(b->z); |
---|
1102 | napoly res = napAdd(x, y); |
---|
1103 | if (res==NULL) |
---|
1104 | { |
---|
1105 | return (number)NULL; |
---|
1106 | } |
---|
1107 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
1108 | lu->z=res; |
---|
1109 | if (a->n!=NULL) |
---|
1110 | { |
---|
1111 | if (b->n!=NULL) x = pp_Mult_qq(a->n, b->n,nacRing); |
---|
1112 | else x = napCopy(a->n); |
---|
1113 | } |
---|
1114 | else |
---|
1115 | { |
---|
1116 | if (b->n!=NULL) x = napCopy(b->n); |
---|
1117 | else x = NULL; |
---|
1118 | } |
---|
1119 | lu->n = x; |
---|
1120 | lu->s = FALSE; |
---|
1121 | if (/*lu->n*/ x!=NULL) |
---|
1122 | { |
---|
1123 | number luu=(number)lu; |
---|
1124 | //if (p_IsConstant(lu->n,nacRing)) naCoefNormalize(luu); |
---|
1125 | //else |
---|
1126 | naNormalize(luu); |
---|
1127 | lu=(lnumber)luu; |
---|
1128 | } |
---|
1129 | //else lu->s=2; |
---|
1130 | naTest((number)lu); |
---|
1131 | return (number)lu; |
---|
1132 | } |
---|
1133 | |
---|
1134 | /*2 |
---|
1135 | * multiplication; r:= la * lb |
---|
1136 | */ |
---|
1137 | number naMult(number la, number lb) |
---|
1138 | { |
---|
1139 | if ((la==NULL) || (lb==NULL)) |
---|
1140 | return NULL; |
---|
1141 | |
---|
1142 | lnumber a = (lnumber)la; |
---|
1143 | lnumber b = (lnumber)lb; |
---|
1144 | lnumber lo; |
---|
1145 | napoly x; |
---|
1146 | |
---|
1147 | #ifdef LDEBUG |
---|
1148 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1149 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1150 | #endif |
---|
1151 | naTest(la); |
---|
1152 | naTest(lb); |
---|
1153 | |
---|
1154 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
1155 | lo->z = pp_Mult_qq(a->z, b->z,nacRing); |
---|
1156 | |
---|
1157 | if (a->n==NULL) |
---|
1158 | { |
---|
1159 | if (b->n==NULL) |
---|
1160 | x = NULL; |
---|
1161 | else |
---|
1162 | x = napCopy(b->n); |
---|
1163 | } |
---|
1164 | else |
---|
1165 | { |
---|
1166 | if (b->n==NULL) |
---|
1167 | { |
---|
1168 | x = napCopy(a->n); |
---|
1169 | } |
---|
1170 | else |
---|
1171 | { |
---|
1172 | x = pp_Mult_qq(b->n, a->n, nacRing); |
---|
1173 | } |
---|
1174 | } |
---|
1175 | if (naMinimalPoly!=NULL) |
---|
1176 | { |
---|
1177 | if (p_GetExp(lo->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
1178 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
1179 | if ((x!=NULL) && (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing))) |
---|
1180 | x = napRemainder(x, naMinimalPoly); |
---|
1181 | } |
---|
1182 | if (naI!=NULL) |
---|
1183 | { |
---|
1184 | lo->z = napRedp (lo->z); |
---|
1185 | if (lo->z != NULL) |
---|
1186 | lo->z = napTailred (lo->z); |
---|
1187 | if (x!=NULL) |
---|
1188 | { |
---|
1189 | x = napRedp (x); |
---|
1190 | if (x!=NULL) |
---|
1191 | x = napTailred (x); |
---|
1192 | } |
---|
1193 | } |
---|
1194 | if ((x!=NULL) && (p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
1195 | p_Delete(&x,nacRing); |
---|
1196 | lo->n = x; |
---|
1197 | lo->s = 0; |
---|
1198 | if(lo->z==NULL) |
---|
1199 | { |
---|
1200 | omFreeBin((ADDRESS)lo, rnumber_bin); |
---|
1201 | lo=NULL; |
---|
1202 | } |
---|
1203 | else if (lo->n!=NULL) |
---|
1204 | { |
---|
1205 | number luu=(number)lo; |
---|
1206 | // if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
1207 | // else |
---|
1208 | naNormalize(luu); |
---|
1209 | lo=(lnumber)luu; |
---|
1210 | } |
---|
1211 | //if (naMinimalPoly==NULL) lo->s=2; |
---|
1212 | naTest((number)lo); |
---|
1213 | return (number)lo; |
---|
1214 | } |
---|
1215 | |
---|
1216 | number naIntDiv(number la, number lb) |
---|
1217 | { |
---|
1218 | lnumber res; |
---|
1219 | lnumber a = (lnumber)la; |
---|
1220 | lnumber b = (lnumber)lb; |
---|
1221 | if (a==NULL) |
---|
1222 | { |
---|
1223 | return NULL; |
---|
1224 | } |
---|
1225 | if (b==NULL) |
---|
1226 | { |
---|
1227 | WerrorS(nDivBy0); |
---|
1228 | return NULL; |
---|
1229 | } |
---|
1230 | assume(a->z!=NULL && b->z!=NULL); |
---|
1231 | assume(a->n==NULL && b->n==NULL); |
---|
1232 | res = (lnumber)omAllocBin(rnumber_bin); |
---|
1233 | res->z = napCopy(a->z); |
---|
1234 | res->n = napCopy(b->z); |
---|
1235 | res->s = 0; |
---|
1236 | number nres=(number)res; |
---|
1237 | naNormalize(nres); |
---|
1238 | |
---|
1239 | //napDelete(&res->n); |
---|
1240 | naTest(nres); |
---|
1241 | return nres; |
---|
1242 | } |
---|
1243 | |
---|
1244 | /*2 |
---|
1245 | * division; lo:= la / lb |
---|
1246 | */ |
---|
1247 | number naDiv(number la, number lb) |
---|
1248 | { |
---|
1249 | lnumber lo; |
---|
1250 | lnumber a = (lnumber)la; |
---|
1251 | lnumber b = (lnumber)lb; |
---|
1252 | napoly x; |
---|
1253 | |
---|
1254 | if (a==NULL) |
---|
1255 | return NULL; |
---|
1256 | |
---|
1257 | if (b==NULL) |
---|
1258 | { |
---|
1259 | WerrorS(nDivBy0); |
---|
1260 | return NULL; |
---|
1261 | } |
---|
1262 | #ifdef LDEBUG |
---|
1263 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1264 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1265 | #endif |
---|
1266 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
1267 | if (b->n!=NULL) |
---|
1268 | lo->z = pp_Mult_qq(a->z, b->n,nacRing); |
---|
1269 | else |
---|
1270 | lo->z = napCopy(a->z); |
---|
1271 | if (a->n!=NULL) |
---|
1272 | x = pp_Mult_qq(b->z, a->n, nacRing); |
---|
1273 | else |
---|
1274 | x = napCopy(b->z); |
---|
1275 | if (naMinimalPoly!=NULL) |
---|
1276 | { |
---|
1277 | if (p_GetExp(lo->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
1278 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
1279 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
1280 | x = napRemainder(x, naMinimalPoly); |
---|
1281 | } |
---|
1282 | if (naI!=NULL) |
---|
1283 | { |
---|
1284 | lo->z = napRedp (lo->z); |
---|
1285 | if (lo->z != NULL) |
---|
1286 | lo->z = napTailred (lo->z); |
---|
1287 | if (x!=NULL) |
---|
1288 | { |
---|
1289 | x = napRedp (x); |
---|
1290 | if (x!=NULL) |
---|
1291 | x = napTailred (x); |
---|
1292 | } |
---|
1293 | } |
---|
1294 | if ((p_LmIsConstant(x,nacRing)) && nacIsOne(pGetCoeff(x))) |
---|
1295 | p_Delete(&x,nacRing); |
---|
1296 | lo->n = x; |
---|
1297 | lo->s = 0; |
---|
1298 | if (lo->n!=NULL) |
---|
1299 | { |
---|
1300 | number luu=(number)lo; |
---|
1301 | //if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
1302 | //else |
---|
1303 | naNormalize(luu); |
---|
1304 | lo=(lnumber)luu; |
---|
1305 | } |
---|
1306 | //else lo->s=2; |
---|
1307 | naTest((number)lo); |
---|
1308 | return (number)lo; |
---|
1309 | } |
---|
1310 | |
---|
1311 | /*2 |
---|
1312 | * za:= - za, inplace |
---|
1313 | */ |
---|
1314 | number naNeg(number za) |
---|
1315 | { |
---|
1316 | if (za!=NULL) |
---|
1317 | { |
---|
1318 | lnumber e = (lnumber)za; |
---|
1319 | naTest(za); |
---|
1320 | e->z = napNeg(e->z); |
---|
1321 | } |
---|
1322 | return za; |
---|
1323 | } |
---|
1324 | |
---|
1325 | /*2 |
---|
1326 | * 1/a |
---|
1327 | */ |
---|
1328 | number naInvers(number a) |
---|
1329 | { |
---|
1330 | lnumber lo; |
---|
1331 | lnumber b = (lnumber)a; |
---|
1332 | napoly x; |
---|
1333 | |
---|
1334 | if (b==NULL) |
---|
1335 | { |
---|
1336 | WerrorS(nDivBy0); |
---|
1337 | return NULL; |
---|
1338 | } |
---|
1339 | #ifdef LDEBUG |
---|
1340 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1341 | #endif |
---|
1342 | lo = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
1343 | lo->s = b->s; |
---|
1344 | if (b->n!=NULL) |
---|
1345 | lo->z = napCopy(b->n); |
---|
1346 | else |
---|
1347 | lo->z = p_ISet(1,nacRing); |
---|
1348 | x = b->z; |
---|
1349 | if ((!p_LmIsConstant(x,nacRing)) || !nacIsOne(pGetCoeff(x))) |
---|
1350 | x = napCopy(x); |
---|
1351 | else |
---|
1352 | { |
---|
1353 | lo->n = NULL; |
---|
1354 | naTest((number)lo); |
---|
1355 | return (number)lo; |
---|
1356 | } |
---|
1357 | if (naMinimalPoly!=NULL) |
---|
1358 | { |
---|
1359 | x = napInvers(x, naMinimalPoly); |
---|
1360 | x = p_Mult_q(x, lo->z,nacRing); |
---|
1361 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
1362 | x = napRemainder(x, naMinimalPoly); |
---|
1363 | lo->z = x; |
---|
1364 | lo->n = NULL; |
---|
1365 | while (x!=NULL) |
---|
1366 | { |
---|
1367 | nacNormalize(pGetCoeff(x)); |
---|
1368 | pIter(x); |
---|
1369 | } |
---|
1370 | } |
---|
1371 | else |
---|
1372 | lo->n = x; |
---|
1373 | if (lo->n!=NULL) |
---|
1374 | { |
---|
1375 | number luu=(number)lo; |
---|
1376 | //if (p_IsConstant(lo->n,nacRing)) naCoefNormalize(luu); |
---|
1377 | //else |
---|
1378 | naNormalize(luu); |
---|
1379 | lo=(lnumber)luu; |
---|
1380 | } |
---|
1381 | naTest((number)lo); |
---|
1382 | return (number)lo; |
---|
1383 | } |
---|
1384 | |
---|
1385 | |
---|
1386 | BOOLEAN naIsZero(number za) |
---|
1387 | { |
---|
1388 | lnumber zb = (lnumber)za; |
---|
1389 | naTest(za); |
---|
1390 | #ifdef LDEBUG |
---|
1391 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
1392 | #endif |
---|
1393 | return (zb==NULL); |
---|
1394 | } |
---|
1395 | |
---|
1396 | |
---|
1397 | BOOLEAN naGreaterZero(number za) |
---|
1398 | { |
---|
1399 | lnumber zb = (lnumber)za; |
---|
1400 | #ifdef LDEBUG |
---|
1401 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
1402 | #endif |
---|
1403 | naTest(za); |
---|
1404 | if (zb!=NULL) |
---|
1405 | { |
---|
1406 | return (nacGreaterZero(pGetCoeff(zb->z))||(!p_LmIsConstant(zb->z,nacRing))); |
---|
1407 | } |
---|
1408 | /* else */ return FALSE; |
---|
1409 | } |
---|
1410 | |
---|
1411 | |
---|
1412 | /*2 |
---|
1413 | * a = b ? |
---|
1414 | */ |
---|
1415 | BOOLEAN naEqual (number a, number b) |
---|
1416 | { |
---|
1417 | if(a==b) return TRUE; |
---|
1418 | if((a==NULL)&&(b!=NULL)) return FALSE; |
---|
1419 | if((b==NULL)&&(a!=NULL)) return FALSE; |
---|
1420 | |
---|
1421 | lnumber aa=(lnumber)a; |
---|
1422 | lnumber bb=(lnumber)b; |
---|
1423 | |
---|
1424 | int an_deg=0; |
---|
1425 | if(aa->n!=NULL) |
---|
1426 | an_deg=napDeg(aa->n); |
---|
1427 | int bn_deg=0; |
---|
1428 | if(bb->n!=NULL) |
---|
1429 | bn_deg=napDeg(bb->n); |
---|
1430 | if(an_deg+napDeg(bb->z)!=bn_deg+napDeg(aa->z)) |
---|
1431 | return FALSE; |
---|
1432 | #if 0 |
---|
1433 | naNormalize(a); |
---|
1434 | aa=(lnumber)a; |
---|
1435 | naNormalize(b); |
---|
1436 | bb=(lnumber)b; |
---|
1437 | if((aa->n==NULL)&&(bb->n!=NULL)) return FALSE; |
---|
1438 | if((bb->n==NULL)&&(aa->n!=NULL)) return FALSE; |
---|
1439 | if(napComp(aa->z,bb->z)!=0) return FALSE; |
---|
1440 | if((aa->n!=NULL) && (napComp(aa->n,bb->n))) return FALSE; |
---|
1441 | #endif |
---|
1442 | number h = naSub(a, b); |
---|
1443 | BOOLEAN bo = naIsZero(h); |
---|
1444 | naDelete(&h,currRing); |
---|
1445 | return bo; |
---|
1446 | } |
---|
1447 | |
---|
1448 | |
---|
1449 | BOOLEAN naGreater (number a, number b) |
---|
1450 | { |
---|
1451 | if (naIsZero(a)) |
---|
1452 | return FALSE; |
---|
1453 | if (naIsZero(b)) |
---|
1454 | return TRUE; /* a!= 0)*/ |
---|
1455 | return napDeg(((lnumber)a)->z)>napDeg(((lnumber)b)->z); |
---|
1456 | } |
---|
1457 | |
---|
1458 | /*2 |
---|
1459 | * reads a number |
---|
1460 | */ |
---|
1461 | const char *naRead(const char *s, number *p) |
---|
1462 | { |
---|
1463 | napoly x; |
---|
1464 | lnumber a; |
---|
1465 | s = napRead(s, &x); |
---|
1466 | if (x==NULL) |
---|
1467 | { |
---|
1468 | *p = NULL; |
---|
1469 | return s; |
---|
1470 | } |
---|
1471 | *p = (number)omAlloc0Bin(rnumber_bin); |
---|
1472 | a = (lnumber)*p; |
---|
1473 | if ((naMinimalPoly!=NULL) |
---|
1474 | && (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing))) |
---|
1475 | a->z = napRemainder(x, naMinimalPoly); |
---|
1476 | else if (naI!=NULL) |
---|
1477 | { |
---|
1478 | a->z = napRedp(x); |
---|
1479 | if (a->z != NULL) |
---|
1480 | a->z = napTailred (a->z); |
---|
1481 | } |
---|
1482 | else |
---|
1483 | a->z = x; |
---|
1484 | if(a->z==NULL) |
---|
1485 | { |
---|
1486 | omFreeBin((ADDRESS)*p, rnumber_bin); |
---|
1487 | *p=NULL; |
---|
1488 | } |
---|
1489 | else |
---|
1490 | { |
---|
1491 | a->n = NULL; |
---|
1492 | a->s = 0; |
---|
1493 | naTest(*p); |
---|
1494 | } |
---|
1495 | return s; |
---|
1496 | } |
---|
1497 | |
---|
1498 | /*2 |
---|
1499 | * tries to convert a number to a name |
---|
1500 | */ |
---|
1501 | char * naName(number n) |
---|
1502 | { |
---|
1503 | lnumber ph = (lnumber)n; |
---|
1504 | if (ph==NULL) |
---|
1505 | return NULL; |
---|
1506 | int i; |
---|
1507 | char *s=(char *)omAlloc(4* naNumbOfPar); |
---|
1508 | char *t=(char *)omAlloc(8); |
---|
1509 | s[0]='\0'; |
---|
1510 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
1511 | { |
---|
1512 | int e=p_GetExp(ph->z,i+1,nacRing); |
---|
1513 | if (e > 0) |
---|
1514 | { |
---|
1515 | if (e >1) |
---|
1516 | { |
---|
1517 | sprintf(t,"%s%d",naParNames[i],e); |
---|
1518 | strcat(s,t); |
---|
1519 | } |
---|
1520 | else |
---|
1521 | { |
---|
1522 | strcat(s,naParNames[i]); |
---|
1523 | } |
---|
1524 | } |
---|
1525 | } |
---|
1526 | omFreeSize((ADDRESS)t,8); |
---|
1527 | if (s[0]=='\0') |
---|
1528 | { |
---|
1529 | omFree((ADDRESS)s); |
---|
1530 | return NULL; |
---|
1531 | } |
---|
1532 | return s; |
---|
1533 | } |
---|
1534 | |
---|
1535 | /*2 |
---|
1536 | * writes a number |
---|
1537 | */ |
---|
1538 | void naWrite(number &phn, const ring r) |
---|
1539 | { |
---|
1540 | lnumber ph = (lnumber)phn; |
---|
1541 | if (ph==NULL) |
---|
1542 | StringAppendS("0"); |
---|
1543 | else |
---|
1544 | { |
---|
1545 | phn->s = 0; |
---|
1546 | BOOLEAN has_denom=(ph->n!=NULL); |
---|
1547 | napWrite(ph->z,has_denom/*(ph->n!=NULL)*/,r); |
---|
1548 | if (has_denom/*(ph->n!=NULL)*/) |
---|
1549 | { |
---|
1550 | StringAppendS("/"); |
---|
1551 | napWrite(ph->n,TRUE,r); |
---|
1552 | } |
---|
1553 | } |
---|
1554 | } |
---|
1555 | |
---|
1556 | /*2 |
---|
1557 | * za == 1 ? |
---|
1558 | */ |
---|
1559 | BOOLEAN naIsOne(number za) |
---|
1560 | { |
---|
1561 | lnumber a = (lnumber)za; |
---|
1562 | napoly x, y; |
---|
1563 | number t; |
---|
1564 | if (a==NULL) return FALSE; |
---|
1565 | #ifdef LDEBUG |
---|
1566 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1567 | if (a->z==NULL) |
---|
1568 | { |
---|
1569 | WerrorS("internal zero error(4)"); |
---|
1570 | return FALSE; |
---|
1571 | } |
---|
1572 | #endif |
---|
1573 | if (a->n==NULL) |
---|
1574 | { |
---|
1575 | if (p_LmIsConstant(a->z,nacRing)) |
---|
1576 | { |
---|
1577 | return nacIsOne(pGetCoeff(a->z)); |
---|
1578 | } |
---|
1579 | else return FALSE; |
---|
1580 | } |
---|
1581 | #if 0 |
---|
1582 | x = a->z; |
---|
1583 | y = a->n; |
---|
1584 | do |
---|
1585 | { |
---|
1586 | if (napComp(x, y)) |
---|
1587 | return FALSE; |
---|
1588 | else |
---|
1589 | { |
---|
1590 | t = nacSub(pGetCoeff(x), pGetCoeff(y)); |
---|
1591 | if (!nacIsZero(t)) |
---|
1592 | { |
---|
1593 | n_Delete(&t,nacRing); |
---|
1594 | return FALSE; |
---|
1595 | } |
---|
1596 | else |
---|
1597 | n_Delete(&t,nacRing); |
---|
1598 | } |
---|
1599 | pIter(x); |
---|
1600 | pIter(y); |
---|
1601 | } |
---|
1602 | while ((x!=NULL) && (y!=NULL)); |
---|
1603 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
1604 | p_Delete(&a->z,nacRing); |
---|
1605 | p_Delete(&a->n,nacRing); |
---|
1606 | a->z = p_ISet(1,nacRing); |
---|
1607 | a->n = NULL; |
---|
1608 | return TRUE; |
---|
1609 | #else |
---|
1610 | return FALSE; |
---|
1611 | #endif |
---|
1612 | } |
---|
1613 | |
---|
1614 | /*2 |
---|
1615 | * za == -1 ? |
---|
1616 | */ |
---|
1617 | BOOLEAN naIsMOne(number za) |
---|
1618 | { |
---|
1619 | lnumber a = (lnumber)za; |
---|
1620 | napoly x, y; |
---|
1621 | number t; |
---|
1622 | if (a==NULL) return FALSE; |
---|
1623 | #ifdef LDEBUG |
---|
1624 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1625 | if (a->z==NULL) |
---|
1626 | { |
---|
1627 | WerrorS("internal zero error(5)"); |
---|
1628 | return FALSE; |
---|
1629 | } |
---|
1630 | #endif |
---|
1631 | if (a->n==NULL) |
---|
1632 | { |
---|
1633 | if (p_LmIsConstant(a->z,nacRing)) return nacIsMOne(pGetCoeff(a->z)); |
---|
1634 | /*else return FALSE;*/ |
---|
1635 | } |
---|
1636 | return FALSE; |
---|
1637 | } |
---|
1638 | |
---|
1639 | /*2 |
---|
1640 | * returns the i-th power of p (i>=0) |
---|
1641 | */ |
---|
1642 | void naPower(number p, int i, number *rc) |
---|
1643 | { |
---|
1644 | number x; |
---|
1645 | *rc = naInit(1,currRing); |
---|
1646 | for (; i > 0; i--) |
---|
1647 | { |
---|
1648 | x = naMult(*rc, p); |
---|
1649 | naDelete(rc,currRing); |
---|
1650 | *rc = x; |
---|
1651 | } |
---|
1652 | } |
---|
1653 | |
---|
1654 | /*2 |
---|
1655 | * result =gcd(a,b) |
---|
1656 | */ |
---|
1657 | number naGcd(number a, number b, const ring r) |
---|
1658 | { |
---|
1659 | if (a==NULL) return naCopy(b); |
---|
1660 | if (b==NULL) return naCopy(a); |
---|
1661 | |
---|
1662 | lnumber x, y; |
---|
1663 | lnumber result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
1664 | |
---|
1665 | x = (lnumber)a; |
---|
1666 | y = (lnumber)b; |
---|
1667 | if ((naNumbOfPar == 1) && (naMinimalPoly!=NULL)) |
---|
1668 | { |
---|
1669 | if (pNext(x->z)!=NULL) |
---|
1670 | result->z = p_Copy(x->z, r->algring); |
---|
1671 | else |
---|
1672 | result->z = napGcd0(x->z, y->z); |
---|
1673 | } |
---|
1674 | else |
---|
1675 | #ifndef HAVE_FACTORY |
---|
1676 | result->z = napGcd(x->z, y->z); // change from napGcd0 |
---|
1677 | #else |
---|
1678 | { |
---|
1679 | int c=ABS(nGetChar()); |
---|
1680 | if (c==1) c=0; |
---|
1681 | setCharacteristic( c ); |
---|
1682 | |
---|
1683 | napoly rz=napGcd(x->z, y->z); |
---|
1684 | CanonicalForm F, G, R; |
---|
1685 | R=convSingPFactoryP(rz,r->algring); |
---|
1686 | p_Normalize(x->z,nacRing); |
---|
1687 | F=convSingPFactoryP(x->z,r->algring)/R; |
---|
1688 | p_Normalize(y->z,nacRing); |
---|
1689 | G=convSingPFactoryP(y->z,r->algring)/R; |
---|
1690 | F = gcd( F, G ); |
---|
1691 | if (F.isOne()) |
---|
1692 | result->z= rz; |
---|
1693 | else |
---|
1694 | { |
---|
1695 | p_Delete(&rz,r->algring); |
---|
1696 | result->z=convFactoryPSingP( F*R,r->algring ); |
---|
1697 | p_Normalize(result->z,nacRing); |
---|
1698 | } |
---|
1699 | } |
---|
1700 | #endif |
---|
1701 | naTest((number)result); |
---|
1702 | return (number)result; |
---|
1703 | } |
---|
1704 | |
---|
1705 | |
---|
1706 | /*2 |
---|
1707 | * naNumbOfPar = 1: |
---|
1708 | * clears denominator algebraic case; |
---|
1709 | * tries to simplify ratio transcendental case; |
---|
1710 | * |
---|
1711 | * cancels monomials |
---|
1712 | * occuring in denominator |
---|
1713 | * and enumerator ? naNumbOfPar != 1; |
---|
1714 | * |
---|
1715 | * #defines for Factory: |
---|
1716 | * FACTORY_GCD_TEST: do not apply built in gcd for |
---|
1717 | * univariate polynomials, always use Factory |
---|
1718 | */ |
---|
1719 | //#define FACTORY_GCD_TEST |
---|
1720 | void naCoefNormalize(number pp) |
---|
1721 | { |
---|
1722 | if (pp==NULL) return; |
---|
1723 | lnumber p = (lnumber)pp; |
---|
1724 | number nz; // all denom. of the numerator |
---|
1725 | nz=p_GetAllDenom(p->z,nacRing); |
---|
1726 | BOOLEAN norm=FALSE; |
---|
1727 | if (!n_IsOne(nz,nacRing)) |
---|
1728 | { |
---|
1729 | norm=TRUE; |
---|
1730 | p->z=p_Mult_nn(p->z,nz,nacRing); |
---|
1731 | if (p->n==NULL) |
---|
1732 | { |
---|
1733 | p->n=p_NSet(nz,nacRing); |
---|
1734 | } |
---|
1735 | else |
---|
1736 | { |
---|
1737 | p->n=p_Mult_nn(p->n,nz,nacRing); |
---|
1738 | n_Delete(&nz, nacRing); |
---|
1739 | } |
---|
1740 | } |
---|
1741 | else |
---|
1742 | { |
---|
1743 | n_Delete(&nz, nacRing); |
---|
1744 | } |
---|
1745 | if (norm) |
---|
1746 | { |
---|
1747 | norm=FALSE; |
---|
1748 | p_Normalize(p->z,nacRing); |
---|
1749 | p_Normalize(p->n,nacRing); |
---|
1750 | } |
---|
1751 | number nn; |
---|
1752 | nn=p_GetAllDenom(p->n,nacRing); |
---|
1753 | if (!n_IsOne(nn,nacRing)) |
---|
1754 | { |
---|
1755 | norm=TRUE; |
---|
1756 | p->n=p_Mult_nn(p->n,nn,nacRing); |
---|
1757 | p->z=p_Mult_nn(p->z,nn,nacRing); |
---|
1758 | n_Delete(&nn, nacRing); |
---|
1759 | } |
---|
1760 | else |
---|
1761 | { |
---|
1762 | n_Delete(&nn, nacRing); |
---|
1763 | } |
---|
1764 | if (norm) |
---|
1765 | { |
---|
1766 | p_Normalize(p->z,nacRing); |
---|
1767 | p_Normalize(p->n,nacRing); |
---|
1768 | } |
---|
1769 | // remove common factors in n, z: |
---|
1770 | if (p->n!=NULL) |
---|
1771 | { |
---|
1772 | poly pp=p->z; |
---|
1773 | nz=n_Copy(pGetCoeff(pp),nacRing); |
---|
1774 | pIter(pp); |
---|
1775 | while(pp!=NULL) |
---|
1776 | { |
---|
1777 | if (n_IsOne(nz,nacRing)) break; |
---|
1778 | number d=n_Gcd(nz,pGetCoeff(pp),nacRing); |
---|
1779 | n_Delete(&nz,nacRing); nz=d; |
---|
1780 | pIter(pp); |
---|
1781 | } |
---|
1782 | if (!n_IsOne(nz,nacRing)) |
---|
1783 | { |
---|
1784 | pp=p->n; |
---|
1785 | nn=n_Copy(pGetCoeff(pp),nacRing); |
---|
1786 | pIter(pp); |
---|
1787 | while(pp!=NULL) |
---|
1788 | { |
---|
1789 | if (n_IsOne(nn,nacRing)) break; |
---|
1790 | number d=n_Gcd(nn,pGetCoeff(pp),nacRing); |
---|
1791 | n_Delete(&nn,nacRing); nn=d; |
---|
1792 | pIter(pp); |
---|
1793 | } |
---|
1794 | number ng=n_Gcd(nz,nn,nacRing); |
---|
1795 | n_Delete(&nn,nacRing); |
---|
1796 | if (!n_IsOne(ng,nacRing)) |
---|
1797 | { |
---|
1798 | number ni=n_Invers(ng,nacRing); |
---|
1799 | p->z=p_Mult_nn(p->z,ni,nacRing); |
---|
1800 | p->n=p_Mult_nn(p->n,ni,nacRing); |
---|
1801 | p_Normalize(p->z,nacRing); |
---|
1802 | p_Normalize(p->n,nacRing); |
---|
1803 | n_Delete(&ni,nacRing); |
---|
1804 | } |
---|
1805 | n_Delete(&ng,nacRing); |
---|
1806 | } |
---|
1807 | n_Delete(&nz,nacRing); |
---|
1808 | } |
---|
1809 | if (p->n!=NULL) |
---|
1810 | { |
---|
1811 | if(!nacGreaterZero(pGetCoeff(p->n))) |
---|
1812 | { |
---|
1813 | p->z=napNeg(p->z); |
---|
1814 | p->n=napNeg(p->n); |
---|
1815 | } |
---|
1816 | |
---|
1817 | if (/*(p->n!=NULL) && */ |
---|
1818 | (p_IsConstant(p->n,nacRing)) |
---|
1819 | && (n_IsOne(pGetCoeff(p->n),nacRing))) |
---|
1820 | { |
---|
1821 | p_Delete(&(p->n), nacRing); |
---|
1822 | p->n = NULL; |
---|
1823 | } |
---|
1824 | } |
---|
1825 | } |
---|
1826 | |
---|
1827 | void naNormalize(number &pp) |
---|
1828 | { |
---|
1829 | |
---|
1830 | //naTest(pp); // input may not be "normal" |
---|
1831 | lnumber p = (lnumber)pp; |
---|
1832 | |
---|
1833 | if (p==NULL) |
---|
1834 | return; |
---|
1835 | naCoefNormalize(pp); |
---|
1836 | p->s = 2; |
---|
1837 | napoly x = p->z; |
---|
1838 | napoly y = p->n; |
---|
1839 | |
---|
1840 | BOOLEAN norm=FALSE; |
---|
1841 | |
---|
1842 | if ((y!=NULL) && (naMinimalPoly!=NULL)) |
---|
1843 | { |
---|
1844 | y = napInvers(y, naMinimalPoly); |
---|
1845 | x = p_Mult_q(x, y,nacRing); |
---|
1846 | if (p_GetExp(x,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
1847 | x = napRemainder(x, naMinimalPoly); |
---|
1848 | p->z = x; |
---|
1849 | p->n = y = NULL; |
---|
1850 | norm=naIsChar0; |
---|
1851 | } |
---|
1852 | |
---|
1853 | /* check for degree of x too high: */ |
---|
1854 | if ((x!=NULL) && (naMinimalPoly!=NULL) && (x!=naMinimalPoly) |
---|
1855 | && (p_GetExp(x,1,nacRing)>p_GetExp(naMinimalPoly,1,nacRing))) |
---|
1856 | // DO NOT REDUCE naMinimalPoly with itself |
---|
1857 | { |
---|
1858 | x = napRemainder(x, naMinimalPoly); |
---|
1859 | p->z = x; |
---|
1860 | norm=naIsChar0; |
---|
1861 | } |
---|
1862 | /* normalize all coefficients in n and z (if in Q) */ |
---|
1863 | if (norm) |
---|
1864 | { |
---|
1865 | naCoefNormalize(pp); |
---|
1866 | x = p->z; |
---|
1867 | y = p->n; |
---|
1868 | } |
---|
1869 | if (y==NULL) return; |
---|
1870 | |
---|
1871 | if ((naMinimalPoly == NULL) && (x!=NULL) && (y!=NULL)) |
---|
1872 | { |
---|
1873 | int i; |
---|
1874 | for (i=naNumbOfPar-1; i>=0; i--) |
---|
1875 | { |
---|
1876 | napoly xx=x; |
---|
1877 | napoly yy=y; |
---|
1878 | int m = napExpi(i, yy, xx); |
---|
1879 | if (m != 0) // in this case xx!=NULL!=yy |
---|
1880 | { |
---|
1881 | while (xx != NULL) |
---|
1882 | { |
---|
1883 | napAddExp(xx,i+1, -m); |
---|
1884 | pIter(xx); |
---|
1885 | } |
---|
1886 | while (yy != NULL) |
---|
1887 | { |
---|
1888 | napAddExp(yy,i+1, -m); |
---|
1889 | pIter(yy); |
---|
1890 | } |
---|
1891 | } |
---|
1892 | } |
---|
1893 | } |
---|
1894 | if (p_LmIsConstant(y,nacRing)) /* i.e. => simplify to (1/c)*z / monom */ |
---|
1895 | { |
---|
1896 | if (nacIsOne(pGetCoeff(y))) |
---|
1897 | { |
---|
1898 | p_LmDelete(&y,nacRing); |
---|
1899 | p->n = NULL; |
---|
1900 | naTest(pp); |
---|
1901 | return; |
---|
1902 | } |
---|
1903 | number h1 = nacInvers(pGetCoeff(y)); |
---|
1904 | nacNormalize(h1); |
---|
1905 | napMultN(x, h1); |
---|
1906 | n_Delete(&h1,nacRing); |
---|
1907 | p_LmDelete(&y,nacRing); |
---|
1908 | p->n = NULL; |
---|
1909 | naTest(pp); |
---|
1910 | return; |
---|
1911 | } |
---|
1912 | #ifndef FACTORY_GCD_TEST |
---|
1913 | if (naNumbOfPar == 1) /* apply built-in gcd */ |
---|
1914 | { |
---|
1915 | napoly x1,y1; |
---|
1916 | if (p_GetExp(x,1,nacRing) >= p_GetExp(y,1,nacRing)) |
---|
1917 | { |
---|
1918 | x1 = napCopy(x); |
---|
1919 | y1 = napCopy(y); |
---|
1920 | } |
---|
1921 | else |
---|
1922 | { |
---|
1923 | x1 = napCopy(y); |
---|
1924 | y1 = napCopy(x); |
---|
1925 | } |
---|
1926 | napoly r; |
---|
1927 | loop |
---|
1928 | { |
---|
1929 | r = napRemainder(x1, y1); |
---|
1930 | if ((r==NULL) || (pNext(r)==NULL)) break; |
---|
1931 | x1 = y1; |
---|
1932 | y1 = r; |
---|
1933 | } |
---|
1934 | if (r!=NULL) |
---|
1935 | { |
---|
1936 | p_Delete(&r,nacRing); |
---|
1937 | p_Delete(&y1,nacRing); |
---|
1938 | } |
---|
1939 | else |
---|
1940 | { |
---|
1941 | napDivMod(x, y1, &(p->z), &r); |
---|
1942 | napDivMod(y, y1, &(p->n), &r); |
---|
1943 | p_Delete(&y1,nacRing); |
---|
1944 | } |
---|
1945 | x = p->z; |
---|
1946 | y = p->n; |
---|
1947 | /* collect all denoms from y and multiply x and y by it */ |
---|
1948 | if (naIsChar0) |
---|
1949 | { |
---|
1950 | number n=napLcm(y); |
---|
1951 | napMultN(x,n); |
---|
1952 | napMultN(y,n); |
---|
1953 | n_Delete(&n,nacRing); |
---|
1954 | while(x!=NULL) |
---|
1955 | { |
---|
1956 | nacNormalize(pGetCoeff(x)); |
---|
1957 | pIter(x); |
---|
1958 | } |
---|
1959 | x = p->z; |
---|
1960 | while(y!=NULL) |
---|
1961 | { |
---|
1962 | nacNormalize(pGetCoeff(y)); |
---|
1963 | pIter(y); |
---|
1964 | } |
---|
1965 | y = p->n; |
---|
1966 | } |
---|
1967 | if (pNext(y)==NULL) |
---|
1968 | { |
---|
1969 | if (nacIsOne(pGetCoeff(y))) |
---|
1970 | { |
---|
1971 | if (p_GetExp(y,1,nacRing)==0) |
---|
1972 | { |
---|
1973 | p_LmDelete(&y,nacRing); |
---|
1974 | p->n = NULL; |
---|
1975 | } |
---|
1976 | naTest(pp); |
---|
1977 | return; |
---|
1978 | } |
---|
1979 | } |
---|
1980 | } |
---|
1981 | #endif /* FACTORY_GCD_TEST */ |
---|
1982 | #ifdef HAVE_FACTORY |
---|
1983 | #ifndef FACTORY_GCD_TEST |
---|
1984 | else |
---|
1985 | #endif |
---|
1986 | { |
---|
1987 | napoly xx,yy; |
---|
1988 | singclap_algdividecontent(x,y,xx,yy); |
---|
1989 | if (xx!=NULL) |
---|
1990 | { |
---|
1991 | p->z=xx; |
---|
1992 | p->n=yy; |
---|
1993 | p_Delete(&x,nacRing); |
---|
1994 | p_Delete(&y,nacRing); |
---|
1995 | } |
---|
1996 | } |
---|
1997 | #endif |
---|
1998 | /* remove common factors from z and n */ |
---|
1999 | x=p->z; |
---|
2000 | y=p->n; |
---|
2001 | if(!nacGreaterZero(pGetCoeff(y))) |
---|
2002 | { |
---|
2003 | x=napNeg(x); |
---|
2004 | y=napNeg(y); |
---|
2005 | } |
---|
2006 | number g=nacCopy(pGetCoeff(x)); |
---|
2007 | pIter(x); |
---|
2008 | while (x!=NULL) |
---|
2009 | { |
---|
2010 | number d=nacGcd(g,pGetCoeff(x), nacRing); |
---|
2011 | if(nacIsOne(d)) |
---|
2012 | { |
---|
2013 | n_Delete(&g,nacRing); |
---|
2014 | n_Delete(&d,nacRing); |
---|
2015 | naTest(pp); |
---|
2016 | return; |
---|
2017 | } |
---|
2018 | n_Delete(&g,nacRing); |
---|
2019 | g = d; |
---|
2020 | pIter(x); |
---|
2021 | } |
---|
2022 | while (y!=NULL) |
---|
2023 | { |
---|
2024 | number d=nacGcd(g,pGetCoeff(y), nacRing); |
---|
2025 | if(nacIsOne(d)) |
---|
2026 | { |
---|
2027 | n_Delete(&g,nacRing); |
---|
2028 | n_Delete(&d,nacRing); |
---|
2029 | naTest(pp); |
---|
2030 | return; |
---|
2031 | } |
---|
2032 | n_Delete(&g,nacRing); |
---|
2033 | g = d; |
---|
2034 | pIter(y); |
---|
2035 | } |
---|
2036 | x=p->z; |
---|
2037 | y=p->n; |
---|
2038 | while (x!=NULL) |
---|
2039 | { |
---|
2040 | number d = nacIntDiv(pGetCoeff(x),g); |
---|
2041 | napSetCoeff(x,d); |
---|
2042 | pIter(x); |
---|
2043 | } |
---|
2044 | while (y!=NULL) |
---|
2045 | { |
---|
2046 | number d = nacIntDiv(pGetCoeff(y),g); |
---|
2047 | napSetCoeff(y,d); |
---|
2048 | pIter(y); |
---|
2049 | } |
---|
2050 | n_Delete(&g,nacRing); |
---|
2051 | naTest(pp); |
---|
2052 | } |
---|
2053 | |
---|
2054 | /*2 |
---|
2055 | * returns in result->n 1 |
---|
2056 | * and in result->z the lcm(a->z,b->n) |
---|
2057 | */ |
---|
2058 | number naLcm(number la, number lb, const ring r) |
---|
2059 | { |
---|
2060 | lnumber result; |
---|
2061 | lnumber a = (lnumber)la; |
---|
2062 | lnumber b = (lnumber)lb; |
---|
2063 | result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
2064 | //if (((naMinimalPoly==NULL) && (naI==NULL)) || !naIsChar0) |
---|
2065 | //{ |
---|
2066 | // result->z = p_ISet(1,nacRing); |
---|
2067 | // return (number)result; |
---|
2068 | //} |
---|
2069 | //naNormalize(lb); |
---|
2070 | naTest(la); |
---|
2071 | naTest(lb); |
---|
2072 | napoly x = p_Copy(a->z, r->algring); |
---|
2073 | number t = napLcm(b->z); // get all denom of b->z |
---|
2074 | if (!nacIsOne(t)) |
---|
2075 | { |
---|
2076 | number bt, rr; |
---|
2077 | napoly xx=x; |
---|
2078 | while (xx!=NULL) |
---|
2079 | { |
---|
2080 | bt = nacGcd(t, pGetCoeff(xx), r->algring); |
---|
2081 | rr = nacMult(t, pGetCoeff(xx)); |
---|
2082 | n_Delete(&pGetCoeff(xx),r->algring); |
---|
2083 | pGetCoeff(xx) = nacDiv(rr, bt); |
---|
2084 | nacNormalize(pGetCoeff(xx)); |
---|
2085 | n_Delete(&bt,r->algring); |
---|
2086 | n_Delete(&rr,r->algring); |
---|
2087 | pIter(xx); |
---|
2088 | } |
---|
2089 | } |
---|
2090 | n_Delete(&t,r->algring); |
---|
2091 | result->z = x; |
---|
2092 | #ifdef HAVE_FACTORY |
---|
2093 | if (b->n!=NULL) |
---|
2094 | { |
---|
2095 | result->z=singclap_alglcm(result->z,b->n); |
---|
2096 | p_Delete(&x,r->algring); |
---|
2097 | } |
---|
2098 | #endif |
---|
2099 | naTest(la); |
---|
2100 | naTest(lb); |
---|
2101 | naTest((number)result); |
---|
2102 | return ((number)result); |
---|
2103 | } |
---|
2104 | |
---|
2105 | /*2 |
---|
2106 | * input: a set of constant polynomials |
---|
2107 | * sets the global variable naI |
---|
2108 | */ |
---|
2109 | void naSetIdeal(ideal I) |
---|
2110 | { |
---|
2111 | int i; |
---|
2112 | |
---|
2113 | if (idIs0(I)) |
---|
2114 | { |
---|
2115 | for (i=naI->anz-1; i>=0; i--) |
---|
2116 | p_Delete(&naI->liste[i],nacRing); |
---|
2117 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
---|
2118 | naI=NULL; |
---|
2119 | } |
---|
2120 | else |
---|
2121 | { |
---|
2122 | lnumber h; |
---|
2123 | number a; |
---|
2124 | napoly x; |
---|
2125 | |
---|
2126 | naI=(naIdeal)omAllocBin(snaIdeal_bin); |
---|
2127 | naI->anz=IDELEMS(I); |
---|
2128 | naI->liste=(napoly*)omAlloc(naI->anz*sizeof(napoly)); |
---|
2129 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
2130 | { |
---|
2131 | h=(lnumber)pGetCoeff(I->m[i]); |
---|
2132 | /* We only need the enumerator of h, as we expect it to be a polynomial */ |
---|
2133 | naI->liste[i]=napCopy(h->z); |
---|
2134 | /* If it isn't normalized (lc = 1) do this */ |
---|
2135 | if (!nacIsOne(pGetCoeff(naI->liste[i]))) |
---|
2136 | { |
---|
2137 | x=naI->liste[i]; |
---|
2138 | nacNormalize(pGetCoeff(x)); |
---|
2139 | a=nacCopy(pGetCoeff(x)); |
---|
2140 | number aa=nacInvers(a); |
---|
2141 | n_Delete(&a,nacRing); |
---|
2142 | napMultN(x,aa); |
---|
2143 | n_Delete(&aa,nacRing); |
---|
2144 | } |
---|
2145 | } |
---|
2146 | } |
---|
2147 | } |
---|
2148 | |
---|
2149 | /*2 |
---|
2150 | * map Z/p -> Q(a) |
---|
2151 | */ |
---|
2152 | number naMapP0(number c) |
---|
2153 | { |
---|
2154 | if (npIsZero(c)) return NULL; |
---|
2155 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2156 | l->s=2; |
---|
2157 | l->z=(napoly)p_Init(nacRing); |
---|
2158 | int i=(int)((long)c); |
---|
2159 | if (i>((long)naMapRing->ch>>2)) i-=(long)naMapRing->ch; |
---|
2160 | pGetCoeff(l->z)=nlInit(i, nacRing); |
---|
2161 | l->n=NULL; |
---|
2162 | return (number)l; |
---|
2163 | } |
---|
2164 | |
---|
2165 | /*2 |
---|
2166 | * map Q -> Q(a) |
---|
2167 | */ |
---|
2168 | number naMap00(number c) |
---|
2169 | { |
---|
2170 | if (nlIsZero(c)) return NULL; |
---|
2171 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2172 | l->s=0; |
---|
2173 | l->z=(napoly)p_Init(nacRing); |
---|
2174 | pGetCoeff(l->z)=nlCopy(c); |
---|
2175 | l->n=NULL; |
---|
2176 | return (number)l; |
---|
2177 | } |
---|
2178 | |
---|
2179 | /*2 |
---|
2180 | * map Z/p -> Z/p(a) |
---|
2181 | */ |
---|
2182 | number naMapPP(number c) |
---|
2183 | { |
---|
2184 | if (npIsZero(c)) return NULL; |
---|
2185 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2186 | l->s=2; |
---|
2187 | l->z=(napoly)p_Init(nacRing); |
---|
2188 | pGetCoeff(l->z)=c; /* omit npCopy, because npCopy is a no-op */ |
---|
2189 | l->n=NULL; |
---|
2190 | return (number)l; |
---|
2191 | } |
---|
2192 | |
---|
2193 | /*2 |
---|
2194 | * map Z/p' -> Z/p(a) |
---|
2195 | */ |
---|
2196 | number naMapPP1(number c) |
---|
2197 | { |
---|
2198 | if (npIsZero(c)) return NULL; |
---|
2199 | int i=(int)((long)c); |
---|
2200 | if (i>(long)naMapRing->ch) i-=(long)naMapRing->ch; |
---|
2201 | number n=npInit(i,naMapRing); |
---|
2202 | if (npIsZero(n)) return NULL; |
---|
2203 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2204 | l->s=2; |
---|
2205 | l->z=(napoly)p_Init(nacRing); |
---|
2206 | pGetCoeff(l->z)=n; |
---|
2207 | l->n=NULL; |
---|
2208 | return (number)l; |
---|
2209 | } |
---|
2210 | |
---|
2211 | /*2 |
---|
2212 | * map Q -> Z/p(a) |
---|
2213 | */ |
---|
2214 | number naMap0P(number c) |
---|
2215 | { |
---|
2216 | if (nlIsZero(c)) return NULL; |
---|
2217 | number n=npInit(nlModP(c,npPrimeM),nacRing); |
---|
2218 | if (npIsZero(n)) return NULL; |
---|
2219 | npTest(n); |
---|
2220 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2221 | l->s=2; |
---|
2222 | l->z=(napoly)p_Init(nacRing); |
---|
2223 | pGetCoeff(l->z)=n; |
---|
2224 | l->n=NULL; |
---|
2225 | return (number)l; |
---|
2226 | } |
---|
2227 | |
---|
2228 | static number (*nacMap)(number); |
---|
2229 | static int naParsToCopy; |
---|
2230 | static napoly napMap(napoly p) |
---|
2231 | { |
---|
2232 | napoly w, a; |
---|
2233 | |
---|
2234 | if (p==NULL) return NULL; |
---|
2235 | a = w = (napoly)p_Init(nacRing); |
---|
2236 | int i; |
---|
2237 | for(i=1;i<=naParsToCopy;i++) |
---|
2238 | napSetExp(a,i,napGetExpFrom(p,i,naMapRing)); |
---|
2239 | p_Setm(a,nacRing); |
---|
2240 | pGetCoeff(w) = nacMap(pGetCoeff(p)); |
---|
2241 | loop |
---|
2242 | { |
---|
2243 | pIter(p); |
---|
2244 | if (p==NULL) break; |
---|
2245 | pNext(a) = (napoly)p_Init(nacRing); |
---|
2246 | pIter(a); |
---|
2247 | for(i=1;i<=naParsToCopy;i++) |
---|
2248 | napSetExp(a,i,napGetExpFrom(p,i,naMapRing)); |
---|
2249 | p_Setm(a,nacRing); |
---|
2250 | pGetCoeff(a) = nacMap(pGetCoeff(p)); |
---|
2251 | } |
---|
2252 | pNext(a) = NULL; |
---|
2253 | return w; |
---|
2254 | } |
---|
2255 | |
---|
2256 | static napoly napPerm(napoly p,const int *par_perm,const ring src_ring,const nMapFunc nMap) |
---|
2257 | { |
---|
2258 | napoly w, a; |
---|
2259 | |
---|
2260 | if (p==NULL) return NULL; |
---|
2261 | w = (napoly)p_Init(nacRing); |
---|
2262 | int i; |
---|
2263 | BOOLEAN not_null=TRUE; |
---|
2264 | loop |
---|
2265 | { |
---|
2266 | for(i=1;i<=rPar(src_ring);i++) |
---|
2267 | { |
---|
2268 | int e; |
---|
2269 | if (par_perm!=NULL) e=par_perm[i-1]; |
---|
2270 | else e=-i; |
---|
2271 | int ee=napGetExpFrom(p,i,src_ring); |
---|
2272 | if (e<0) |
---|
2273 | napSetExp(w,-e,ee); |
---|
2274 | else if (ee>0) |
---|
2275 | not_null=FALSE; |
---|
2276 | } |
---|
2277 | pGetCoeff(w) = nMap(pGetCoeff(p)); |
---|
2278 | p_Setm(w,nacRing); |
---|
2279 | pIter(p); |
---|
2280 | if (!not_null) |
---|
2281 | { |
---|
2282 | if (p==NULL) |
---|
2283 | { |
---|
2284 | p_Delete(&w,nacRing); |
---|
2285 | return NULL; |
---|
2286 | } |
---|
2287 | /* else continue*/ |
---|
2288 | n_Delete(&(pGetCoeff(w)),nacRing); |
---|
2289 | } |
---|
2290 | else |
---|
2291 | { |
---|
2292 | if (p==NULL) return w; |
---|
2293 | else |
---|
2294 | { |
---|
2295 | pNext(w)=napPerm(p,par_perm,src_ring,nMap); |
---|
2296 | return w; |
---|
2297 | } |
---|
2298 | } |
---|
2299 | } |
---|
2300 | } |
---|
2301 | |
---|
2302 | /*2 |
---|
2303 | * map _(a) -> _(b) |
---|
2304 | */ |
---|
2305 | number naMapQaQb(number c) |
---|
2306 | { |
---|
2307 | if (c==NULL) return NULL; |
---|
2308 | lnumber erg= (lnumber)omAlloc0Bin(rnumber_bin); |
---|
2309 | lnumber src =(lnumber)c; |
---|
2310 | erg->s=src->s; |
---|
2311 | erg->z=napMap(src->z); |
---|
2312 | erg->n=napMap(src->n); |
---|
2313 | if (naMinimalPoly!=NULL) |
---|
2314 | { |
---|
2315 | if (p_GetExp(erg->z,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
2316 | { |
---|
2317 | erg->z = napRemainder(erg->z, naMinimalPoly); |
---|
2318 | if (erg->z==NULL) |
---|
2319 | { |
---|
2320 | number t_erg=(number)erg; |
---|
2321 | naDelete(&t_erg,currRing); |
---|
2322 | return (number)NULL; |
---|
2323 | } |
---|
2324 | } |
---|
2325 | if (erg->n!=NULL) |
---|
2326 | { |
---|
2327 | if (p_GetExp(erg->n,1,nacRing) >= p_GetExp(naMinimalPoly,1,nacRing)) |
---|
2328 | erg->n = napRemainder(erg->n, naMinimalPoly); |
---|
2329 | if ((p_IsConstant(erg->n,nacRing)) && nacIsOne(pGetCoeff(erg->n))) |
---|
2330 | p_Delete(&(erg->n),nacRing); |
---|
2331 | } |
---|
2332 | } |
---|
2333 | return (number)erg; |
---|
2334 | } |
---|
2335 | |
---|
2336 | nMapFunc naSetMap(const ring src, const ring dst) |
---|
2337 | { |
---|
2338 | naMapRing=src; |
---|
2339 | if (rField_is_Q_a(dst)) /* -> Q(a) */ |
---|
2340 | { |
---|
2341 | if (rField_is_Q(src)) |
---|
2342 | { |
---|
2343 | return naMap00; /*Q -> Q(a)*/ |
---|
2344 | } |
---|
2345 | if (rField_is_Zp(src)) |
---|
2346 | { |
---|
2347 | return naMapP0; /* Z/p -> Q(a)*/ |
---|
2348 | } |
---|
2349 | if (rField_is_Q_a(src)) |
---|
2350 | { |
---|
2351 | int i; |
---|
2352 | naParsToCopy=0; |
---|
2353 | for(i=0;i<rPar(src);i++) |
---|
2354 | { |
---|
2355 | if ((i>=rPar(dst)) |
---|
2356 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
2357 | return NULL; |
---|
2358 | naParsToCopy++; |
---|
2359 | } |
---|
2360 | nacMap=nacCopy; |
---|
2361 | if ((naParsToCopy==rPar(dst))&&(naParsToCopy==rPar(src))) |
---|
2362 | return naCopy; /* Q(a) -> Q(a) */ |
---|
2363 | return naMapQaQb; /* Q(a..) -> Q(a..) */ |
---|
2364 | } |
---|
2365 | } |
---|
2366 | /*-----------------------------------------------------*/ |
---|
2367 | if (rField_is_Zp_a(dst)) /* -> Z/p(a) */ |
---|
2368 | { |
---|
2369 | if (rField_is_Q(src)) |
---|
2370 | { |
---|
2371 | return naMap0P; /*Q -> Z/p(a)*/ |
---|
2372 | } |
---|
2373 | if (rField_is_Zp(src)) |
---|
2374 | { |
---|
2375 | if (src->ch==dst->ch) |
---|
2376 | { |
---|
2377 | return naMapPP; /* Z/p -> Z/p(a)*/ |
---|
2378 | } |
---|
2379 | else |
---|
2380 | { |
---|
2381 | return naMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
2382 | } |
---|
2383 | } |
---|
2384 | if (rField_is_Zp_a(src)) |
---|
2385 | { |
---|
2386 | if (rChar(src)==rChar(dst)) |
---|
2387 | { |
---|
2388 | nacMap=nacCopy; |
---|
2389 | } |
---|
2390 | else |
---|
2391 | { |
---|
2392 | nacMap = npMapP; |
---|
2393 | } |
---|
2394 | int i; |
---|
2395 | naParsToCopy=0; |
---|
2396 | for(i=0;i<rPar(src);i++) |
---|
2397 | { |
---|
2398 | if ((i>=rPar(dst)) |
---|
2399 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
2400 | return NULL; |
---|
2401 | naParsToCopy++; |
---|
2402 | } |
---|
2403 | if ((naParsToCopy==rPar(dst))&&(naParsToCopy==rPar(src)) |
---|
2404 | && (nacMap==nacCopy)) |
---|
2405 | return naCopy; /* Z/p(a) -> Z/p(a) */ |
---|
2406 | return naMapQaQb; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
2407 | } |
---|
2408 | } |
---|
2409 | return NULL; /* default */ |
---|
2410 | } |
---|
2411 | |
---|
2412 | /*2 |
---|
2413 | * convert a napoly number into a poly |
---|
2414 | */ |
---|
2415 | poly naPermNumber(number z, int * par_perm, int P, ring oldRing) |
---|
2416 | { |
---|
2417 | if (z==NULL) return NULL; |
---|
2418 | poly res=NULL; |
---|
2419 | poly p; |
---|
2420 | napoly za=((lnumber)z)->z; |
---|
2421 | napoly zb=((lnumber)z)->n; |
---|
2422 | nMapFunc nMap=naSetMap(oldRing,currRing); |
---|
2423 | if (currRing->parameter!=NULL) |
---|
2424 | nMap=currRing->algring->cf->cfSetMap(oldRing->algring, nacRing); |
---|
2425 | else |
---|
2426 | nMap=currRing->cf->cfSetMap(oldRing->algring, currRing); |
---|
2427 | if (nMap==NULL) return NULL; /* emergency exit only */ |
---|
2428 | do |
---|
2429 | { |
---|
2430 | p = pInit(); |
---|
2431 | pNext(p)=NULL; |
---|
2432 | nNew(&pGetCoeff(p)); |
---|
2433 | int i; |
---|
2434 | for(i=pVariables;i;i--) |
---|
2435 | pSetExp(p,i, 0); |
---|
2436 | pSetComp(p, 0); |
---|
2437 | napoly pa=NULL; |
---|
2438 | lnumber pan; |
---|
2439 | if (currRing->parameter!=NULL) |
---|
2440 | { |
---|
2441 | assume(oldRing->algring!=NULL); |
---|
2442 | pGetCoeff(p)=(number)omAlloc0Bin(rnumber_bin); |
---|
2443 | pan=(lnumber)pGetCoeff(p); |
---|
2444 | pan->s=2; |
---|
2445 | pan->z=napInitz(nMap(pGetCoeff(za))); |
---|
2446 | pa=pan->z; |
---|
2447 | } |
---|
2448 | else |
---|
2449 | { |
---|
2450 | pGetCoeff(p)=nMap(pGetCoeff(za)); |
---|
2451 | } |
---|
2452 | for(i=0;i<P;i++) |
---|
2453 | { |
---|
2454 | if(napGetExpFrom(za,i+1,oldRing)!=0) |
---|
2455 | { |
---|
2456 | if(par_perm==NULL) |
---|
2457 | { |
---|
2458 | if ((rPar(currRing)>=i) && (pa!=NULL)) |
---|
2459 | { |
---|
2460 | napSetExp(pa,i+1,napGetExpFrom(za,i+1,oldRing)); |
---|
2461 | p_Setm(pa,nacRing); |
---|
2462 | } |
---|
2463 | else |
---|
2464 | { |
---|
2465 | pDelete(&p); |
---|
2466 | break; |
---|
2467 | } |
---|
2468 | } |
---|
2469 | else if(par_perm[i]>0) |
---|
2470 | pSetExp(p,par_perm[i],napGetExpFrom(za,i+1,oldRing)); |
---|
2471 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
2472 | { |
---|
2473 | napSetExp(pa,-par_perm[i], napGetExpFrom(za,i+1,oldRing)); |
---|
2474 | p_Setm(pa,nacRing); |
---|
2475 | } |
---|
2476 | else |
---|
2477 | { |
---|
2478 | pDelete(&p); |
---|
2479 | break; |
---|
2480 | } |
---|
2481 | } |
---|
2482 | } |
---|
2483 | if (p!=NULL) |
---|
2484 | { |
---|
2485 | pSetm(p); |
---|
2486 | if (zb!=NULL) |
---|
2487 | { |
---|
2488 | if (currRing->P>0) |
---|
2489 | { |
---|
2490 | pan->n=napPerm(zb,par_perm,oldRing,nMap); |
---|
2491 | if(pan->n==NULL) /* error in mapping or mapping to variable */ |
---|
2492 | pDelete(&p); |
---|
2493 | } |
---|
2494 | else |
---|
2495 | pDelete(&p); |
---|
2496 | } |
---|
2497 | pTest(p); |
---|
2498 | res=pAdd(res,p); |
---|
2499 | } |
---|
2500 | pIter(za); |
---|
2501 | } |
---|
2502 | while (za!=NULL); |
---|
2503 | pTest(res); |
---|
2504 | return res; |
---|
2505 | } |
---|
2506 | |
---|
2507 | number naGetDenom(number &n, const ring r) |
---|
2508 | { |
---|
2509 | lnumber x=(lnumber)n; |
---|
2510 | if (x->n!=NULL) |
---|
2511 | { |
---|
2512 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
2513 | rr->z=p_Copy(x->n,r->algring); |
---|
2514 | rr->s = 2; |
---|
2515 | return (number)rr; |
---|
2516 | } |
---|
2517 | return n_Init(1,r); |
---|
2518 | } |
---|
2519 | |
---|
2520 | number naGetNumerator(number &n, const ring r) |
---|
2521 | { |
---|
2522 | lnumber x=(lnumber)n; |
---|
2523 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
2524 | rr->z=p_Copy(x->z,r->algring); |
---|
2525 | rr->s = 2; |
---|
2526 | return (number)rr; |
---|
2527 | } |
---|
2528 | |
---|
2529 | #ifdef LDEBUG |
---|
2530 | BOOLEAN naDBTest(number a, const char *f,const int l) |
---|
2531 | { |
---|
2532 | lnumber x=(lnumber)a; |
---|
2533 | if (x == NULL) |
---|
2534 | return TRUE; |
---|
2535 | #ifdef LDEBUG |
---|
2536 | omCheckAddrSize(a, sizeof(snumber)); |
---|
2537 | #endif |
---|
2538 | napoly p = x->z; |
---|
2539 | if (p==NULL) |
---|
2540 | { |
---|
2541 | Print("0/* in %s:%d\n",f,l); |
---|
2542 | return FALSE; |
---|
2543 | } |
---|
2544 | while(p!=NULL) |
---|
2545 | { |
---|
2546 | if ((naIsChar0 && nlIsZero(pGetCoeff(p))) |
---|
2547 | || ((!naIsChar0) && npIsZero(pGetCoeff(p)))) |
---|
2548 | { |
---|
2549 | Print("coeff 0 in %s:%d\n",f,l); |
---|
2550 | return FALSE; |
---|
2551 | } |
---|
2552 | if((naMinimalPoly!=NULL) |
---|
2553 | &&(p_GetExp(p,1,nacRing)>p_GetExp(naMinimalPoly,1,nacRing)) |
---|
2554 | &&(p!=naMinimalPoly)) |
---|
2555 | { |
---|
2556 | Print("deg>minpoly in %s:%d\n",f,l); |
---|
2557 | return FALSE; |
---|
2558 | } |
---|
2559 | //if (naIsChar0 && (((int)p->ko &3) == 0) && (p->ko->s==0) && (x->s==2)) |
---|
2560 | //{ |
---|
2561 | // Print("normalized with non-normal coeffs in %s:%d\n",f,l); |
---|
2562 | // return FALSE; |
---|
2563 | //} |
---|
2564 | if (naIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
2565 | return FALSE; |
---|
2566 | pIter(p); |
---|
2567 | } |
---|
2568 | p = x->n; |
---|
2569 | while(p!=NULL) |
---|
2570 | { |
---|
2571 | if (naIsChar0 && !(nlDBTest(pGetCoeff(p),f,l))) |
---|
2572 | return FALSE; |
---|
2573 | pIter(p); |
---|
2574 | } |
---|
2575 | return TRUE; |
---|
2576 | } |
---|
2577 | #endif |
---|