1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: longalg.cc,v 1.3 2004-04-29 15:04:22 Singular Exp $ */ |
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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 "clapsing.h" |
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23 | #endif |
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24 | #include "longalg.h" |
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25 | |
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26 | naIdeal naI=NULL; |
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27 | |
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28 | napoly naMinimalPoly; |
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29 | int naNumbOfPar; |
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30 | #ifndef LONGALGNEW |
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31 | int napMonomSize; |
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32 | char **naParNames; |
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33 | #else /* LONGALGNEW */ |
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34 | #define naParNames (currRing->parameter) |
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35 | #define napNormalize(p) p_Normalize(p,nacRing) |
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36 | #endif /* LONGALGNEW */ |
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37 | static int naIsChar0; |
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38 | static int naPrimeM; |
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39 | |
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40 | #ifdef LDEBUG |
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41 | #define naTest(a) naDBTest(a,__FILE__,__LINE__) |
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42 | BOOLEAN naDBTest(number a, char *f,int l); |
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43 | #else |
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44 | #define naTest(a) |
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45 | #endif |
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46 | |
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47 | number (*naMap)(number from); |
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48 | /* procedure variables */ |
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49 | static numberfunc |
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50 | nacMult, nacSub, nacAdd, nacDiv, nacIntDiv; |
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51 | static number (*nacGcd)(number a, number b, const ring r); |
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52 | static number (*nacLcm)(number a, number b, const ring r); |
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53 | static void (*nacDelete)(number *a, const ring r); |
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54 | number (*nacInit)(int i); |
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55 | static int (*nacInt)(number &n); |
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56 | void (*nacNormalize)(number &a); |
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57 | static number (*nacNeg)(number a); |
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58 | static void (*nacWrite)(number &a); |
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59 | number (*nacCopy)(number a); |
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60 | static number (*nacInvers)(number a); |
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61 | BOOLEAN (*nacIsZero)(number a); |
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62 | static BOOLEAN (*nacIsOne)(number a); |
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63 | static BOOLEAN (*nacIsMOne)(number a); |
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64 | static BOOLEAN (*nacGreaterZero)(number a); |
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65 | static char * (*nacRead) (char *s, number *a); |
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66 | #ifndef LONGALGNEW |
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67 | extern void napDelete(napoly *p); |
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68 | #endif /* not LONGALGNEW */ |
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69 | static napoly napRedp(napoly q); |
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70 | static napoly napTailred(napoly q); |
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71 | static BOOLEAN napDivPoly(napoly p, napoly q); |
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72 | static int napExpi(int i, napoly a, napoly b); |
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73 | static ring nacRing; |
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74 | |
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75 | static number nadGcd( number a, number b, const ring r) { return nacInit(1); } |
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76 | /*2 |
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77 | * sets the appropriate operators |
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78 | */ |
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79 | void naSetChar(int i, ring r) |
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80 | { |
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81 | if (naI!=NULL) |
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82 | { |
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83 | int j; |
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84 | for (j=naI->anz-1; j>=0; j--) |
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85 | napDelete (&naI->liste[j]); |
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86 | omFreeSize((ADDRESS)naI->liste,naI->anz*sizeof(napoly)); |
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87 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
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88 | naI=NULL; |
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89 | } |
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90 | naMap = naCopy; |
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91 | /*------------ set naMinimalPoly -----------------------------------*/ |
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92 | if (r->minpoly!=NULL) |
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93 | naMinimalPoly=((lnumber)r->minpoly)->z; |
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94 | else |
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95 | naMinimalPoly = NULL; |
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96 | naNumbOfPar=rPar(r); |
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97 | #ifndef LONGALGNEW |
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98 | naParNames=r->parameter; |
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99 | napMonomSize = RECA_SIZE + naNumbOfPar*SIZEOF_PARAMETER; |
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100 | #endif /* not LONGALGNEW */ |
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101 | if (i == 1) |
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102 | { |
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103 | naIsChar0 = 1; |
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104 | } |
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105 | else if (i < 0) |
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106 | { |
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107 | naIsChar0 = 0; |
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108 | npSetChar(-i, r->algring); // to be changed HS |
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109 | } |
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110 | #ifdef TEST |
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111 | else |
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112 | { |
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113 | Print("naSetChar:c=%d param=%d\n",i,rPar(r)); |
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114 | } |
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115 | #endif |
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116 | nacRing = r->algring; |
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117 | nacInit = nacRing->cf->nInit; |
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118 | nacInt = nacRing->cf->nInt; |
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119 | nacCopy = nacRing->cf->nCopy; |
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120 | nacAdd = nacRing->cf->nAdd; |
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121 | nacSub = nacRing->cf->nSub; |
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122 | nacNormalize = nacRing->cf->nNormalize; |
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123 | nacNeg = nacRing->cf->nNeg; |
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124 | nacIsZero = nacRing->cf->nIsZero; |
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125 | nacRead = nacRing->cf->nRead; |
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126 | nacWrite = nacRing->cf->nWrite; |
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127 | nacGreaterZero = nacRing->cf->nGreaterZero; |
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128 | nacIsOne = nacRing->cf->nIsOne; |
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129 | nacIsMOne = nacRing->cf->nIsMOne; |
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130 | nacGcd = nacRing->cf->nGcd; |
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131 | nacLcm = nacRing->cf->nLcm; |
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132 | nacDelete = nacRing->cf->cfDelete; |
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133 | nacMult = nacRing->cf->nMult; |
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134 | nacDiv = nacRing->cf->nDiv; |
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135 | nacIntDiv = nacRing->cf->nIntDiv; |
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136 | nacInvers = nacRing->cf->nInvers; |
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137 | } |
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138 | |
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139 | /*============= procedure for polynomials: napXXXX =======================*/ |
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140 | |
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141 | |
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142 | |
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143 | #ifdef LDEBUG |
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144 | static void napTest(napoly p) |
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145 | { |
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146 | while (p != NULL) |
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147 | { |
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148 | if (naIsChar0) |
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149 | nlDBTest(napGetCoeff(p), "", 0); |
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150 | napIter(p); |
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151 | } |
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152 | } |
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153 | #else |
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154 | #define napTest(p) ((void) 0) |
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155 | #endif |
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156 | |
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157 | #ifndef LONGALGNEW |
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158 | /*3 |
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159 | * creates an napoly poly |
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160 | */ |
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161 | static napoly napInit(int i) |
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162 | { |
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163 | napoly a = (napoly)omAlloc0(napMonomSize); |
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164 | |
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165 | a->ko = nacInit(i); |
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166 | if (!nacIsZero(a->ko)) |
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167 | { |
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168 | return a; |
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169 | } |
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170 | else |
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171 | { |
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172 | omFreeSize((ADDRESS)a, napMonomSize); |
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173 | return NULL; |
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174 | } |
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175 | } |
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176 | #define napMultCopy(p,q) napMult(napCopy(p),napCopy(q)) |
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177 | #define napIsConstant(p) (napDeg(p)==0) |
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178 | #define napSetCoeff(p,n) {nacDelete(&((p)->ko),nacRing);(p)->ko=n;} |
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179 | #else /* LONGALGNEW */ |
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180 | #define napInit(i) (napoly)p_ISet(i,nacRing) |
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181 | #define napSetCoeff(p,n) {nacDelete(&napGetCoeff(p),nacRing);napGetCoeff(p)=n;} |
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182 | #define napDelete1(p) p_LmDelete((poly *)p, nacRing) |
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183 | #define napCopy(p) (napoly)p_Copy((poly)p,nacRing) |
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184 | #define nap_Copy(p,r) (napoly)p_Copy((poly)p,r->algring) |
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185 | #define napComp(p,q) p_LmCmp((poly)p,(poly)q, nacRing) |
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186 | #define napMultT(A,E) A=(napoly)p_Mult_mm((poly)A,(poly)E,nacRing) |
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187 | #define napMult(A,B) (napoly)p_Mult_q((poly)A,(poly)B,nacRing) |
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188 | #define napMultCopy(A,B) (napoly)pp_Mult_qq((poly)A,(poly)B,nacRing) |
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189 | #define napIsConstant(p) p_LmIsConstant(p,nacRing) |
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190 | #define napDeg(p) (int)p_ExpVectorQuerSum(p, nacRing) |
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191 | #endif /* LONGALGNEW */ |
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192 | |
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193 | /*3 |
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194 | * creates an napoly |
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195 | */ |
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196 | napoly napInitz(number z) |
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197 | { |
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198 | #ifndef LONGALGNEW |
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199 | napoly a = (napoly)omAlloc0(napMonomSize); |
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200 | #else /* LONGALGNEW */ |
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201 | napoly a = (napoly)p_Init(nacRing); |
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202 | #endif /* LONGALGNEW */ |
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203 | napGetCoeff(a) = z; |
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204 | return a; |
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205 | } |
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206 | |
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207 | #ifndef LONGALGNEW |
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208 | /*3 |
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209 | * deletes head of an napoly poly |
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210 | */ |
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211 | static void napDelete1(napoly *p) |
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212 | { |
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213 | napoly h = *p; |
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214 | |
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215 | if (h!=NULL) |
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216 | { |
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217 | *p = h->ne; |
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218 | nacDelete(&(h->ko),nacRing); |
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219 | omFreeSize((ADDRESS)h, napMonomSize); |
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220 | } |
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221 | } |
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222 | |
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223 | /*3 |
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224 | * delete an napoly poly |
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225 | */ |
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226 | void napDelete(napoly *p) |
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227 | { |
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228 | napoly w, h = *p; |
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229 | |
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230 | while (h!=NULL) |
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231 | { |
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232 | w = h; |
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233 | h = h->ne; |
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234 | nacDelete(&(w->ko),nacRing); |
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235 | omFreeSize((ADDRESS)w, napMonomSize); |
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236 | } |
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237 | *p = NULL; |
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238 | } |
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239 | |
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240 | void nap_Delete(napoly *p, const ring r) |
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241 | { |
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242 | napoly w, h = *p; |
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243 | |
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244 | while (h!=NULL) |
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245 | { |
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246 | w = h; |
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247 | h = h->ne; |
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248 | n_Delete(&(w->ko),r->algring); |
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249 | omFree((ADDRESS)w); |
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250 | } |
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251 | *p = NULL; |
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252 | } |
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253 | |
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254 | |
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255 | /*3 |
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256 | * copy a napoly. poly |
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257 | */ |
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258 | static napoly napCopy(napoly p) |
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259 | { |
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260 | if (p==NULL) return NULL; |
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261 | |
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262 | napoly w, a; |
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263 | |
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264 | omCheckAddrSize(p,napMonomSize); |
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265 | a = w = (napoly)omAlloc(napMonomSize); |
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266 | memcpy4(w->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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267 | w->ko = nacCopy(p->ko); |
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268 | loop |
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269 | { |
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270 | p=p->ne; |
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271 | if (p==NULL) break; |
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272 | omCheckAddrSize(p,napMonomSize); |
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273 | a->ne = (napoly)omAlloc(napMonomSize); |
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274 | a = a->ne; |
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275 | memcpy4(a->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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276 | a->ko = nacCopy(p->ko); |
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277 | } |
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278 | a->ne = NULL; |
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279 | return w; |
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280 | } |
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281 | #endif /* not LONGALGNEW */ |
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282 | |
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283 | /*3 |
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284 | * copy a napoly. poly |
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285 | */ |
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286 | static napoly napCopyNeg(napoly p) |
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287 | { |
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288 | #ifndef LONGALGNEW |
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289 | napoly w, a; |
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290 | |
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291 | if (p==NULL) return NULL; |
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292 | omCheckAddrSize(p,napMonomSize); |
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293 | a = w = (napoly)omAlloc(napMonomSize); |
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294 | memcpy4(w->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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295 | w->ko = nacNeg(nacCopy(p->ko)); |
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296 | loop |
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297 | { |
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298 | p=p->ne; |
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299 | if (p==NULL) break; |
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300 | omCheckAddrSize(p,napMonomSize); |
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301 | a->ne = (napoly)omAlloc(napMonomSize); |
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302 | a = a->ne; |
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303 | memcpy4(a->e, p->e, naNumbOfPar * SIZEOF_PARAMETER); |
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304 | a->ko = nacNeg(nacCopy(p->ko)); |
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305 | } |
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306 | a->ne = NULL; |
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307 | return w; |
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308 | #else /* LONGALGNEW */ |
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309 | napoly r=napCopy(p); |
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310 | r=(napoly)p_Neg((poly)r, nacRing); |
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311 | return r; |
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312 | #endif /* LONGALGNEW */ |
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313 | } |
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314 | |
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315 | #ifndef LONGALGNEW |
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316 | /*3 |
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317 | * Compare exponents of p and q |
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318 | */ |
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319 | static int napComp(napoly p, napoly q) |
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320 | { |
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321 | int i = 0; |
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322 | |
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323 | omCheckAddrSize(p,napMonomSize); |
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324 | omCheckAddrSize(q,napMonomSize); |
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325 | while (p->e[i] == q->e[i]) |
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326 | { |
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327 | i++; |
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328 | if (i >= naNumbOfPar) |
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329 | return 0; |
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330 | } |
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331 | if (p->e[i] > q->e[i]) |
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332 | return 1; |
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333 | else |
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334 | return - 1; |
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335 | } |
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336 | |
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337 | /*3 |
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338 | * addition of napoly. polys |
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339 | */ |
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340 | napoly napAdd(napoly p1, napoly p2) |
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341 | { |
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342 | napoly a1, p, a2, a; |
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343 | int c; number t; |
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344 | |
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345 | if (p1==NULL) return p2; |
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346 | if (p2==NULL) return p1; |
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347 | omCheckAddrSize(p1,napMonomSize); |
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348 | omCheckAddrSize(p2,napMonomSize); |
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349 | a1 = p1; |
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350 | a2 = p2; |
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351 | a = p = (napoly)omAlloc(napMonomSize); |
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352 | loop |
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353 | { |
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354 | c = napComp(a1, a2); |
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355 | if (c == 1) |
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356 | { |
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357 | a = a->ne = a1; |
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358 | a1 = a1->ne; |
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359 | if (a1==NULL) |
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360 | { |
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361 | a->ne= a2; |
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362 | break; |
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363 | } |
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364 | omCheckAddrSize(a1,napMonomSize); |
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365 | } |
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366 | else if (c == -1) |
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367 | { |
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368 | a = a->ne = a2; |
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369 | a2 = a2->ne; |
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370 | if (a2==NULL) |
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371 | { |
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372 | a->ne = a1; |
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373 | break; |
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374 | } |
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375 | omCheckAddrSize(a2,napMonomSize); |
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376 | } |
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377 | else |
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378 | { |
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379 | t = nacAdd(a1->ko, a2->ko); |
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380 | napDelete1(&a2); |
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381 | if (nacIsZero(t)) |
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382 | { |
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383 | nacDelete(&t,nacRing); |
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384 | napDelete1(&a1); |
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385 | } |
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386 | else |
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387 | { |
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388 | nacDelete(&(a1->ko),nacRing); |
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389 | a1->ko = t; |
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390 | a = a->ne = a1; |
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391 | a1 = a1->ne; |
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392 | } |
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393 | if (a1==NULL) |
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394 | { |
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395 | a->ne = a2; |
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396 | break; |
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397 | } |
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398 | else if (a2==NULL) |
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399 | { |
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400 | a->ne = a1; |
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401 | break; |
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402 | } |
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403 | omCheckAddrSize(a1,napMonomSize); |
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404 | omCheckAddrSize(a2,napMonomSize); |
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405 | } |
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406 | } |
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407 | a = p->ne; |
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408 | omFreeSize((ADDRESS)p, napMonomSize); |
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409 | return a; |
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410 | } |
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411 | |
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412 | |
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413 | /*3 |
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414 | * multiply a napoly. poly by -1 |
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415 | */ |
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416 | napoly napNeg(napoly a) |
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417 | { |
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418 | napoly p = a; |
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419 | |
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420 | while (p!=NULL) |
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421 | { |
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422 | omCheckAddrSize(p,napMonomSize); |
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423 | p->ko = nacNeg(p->ko); |
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424 | p = p->ne; |
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425 | } |
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426 | return a; |
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427 | } |
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428 | #endif /* not LONGALGNEW */ |
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429 | |
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430 | /*3 |
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431 | * returns ph * z |
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432 | */ |
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433 | static void napMultN(napoly p, number z) |
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434 | { |
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435 | number t; |
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436 | |
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437 | while (p!=NULL) |
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438 | { |
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439 | t = nacMult(napGetCoeff(p), z); |
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440 | nacNormalize(t); |
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441 | nacDelete(&napGetCoeff(p),nacRing); |
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442 | napGetCoeff(p) = t; |
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443 | napIter(p); |
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444 | } |
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445 | } |
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446 | |
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447 | #ifndef LONGALGNEW |
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448 | /*3 |
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449 | * update the polynomial a by multipying it by |
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450 | * the (number) coefficient |
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451 | * and the exponent vector (of) exp (a well initialized polynomial) |
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452 | */ |
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453 | static void napMultT(napoly a, napoly exp) |
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454 | { |
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455 | int i; |
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456 | number t, h; |
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457 | if (a==NULL) |
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458 | return; |
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459 | h = exp->ko; |
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460 | if (nacIsOne(h)) |
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461 | { |
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462 | do |
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463 | { |
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464 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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465 | a->e[i] += exp->e[i]; |
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466 | a = a->ne; |
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467 | } |
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468 | while (a!=NULL); |
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469 | } |
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470 | else |
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471 | { |
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472 | h = nacNeg(h); |
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473 | if (nacIsOne(h)) |
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474 | { |
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475 | h = nacNeg(h); |
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476 | do |
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477 | { |
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478 | a->ko = nacNeg(a->ko); |
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479 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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480 | a->e[i] += exp->e[i]; |
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481 | a = a->ne; |
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482 | } |
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483 | while (a!=NULL); |
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484 | } |
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485 | else |
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486 | { |
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487 | h = nacNeg(h); |
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488 | do |
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489 | { |
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490 | t = nacMult(a->ko, h); |
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491 | nacDelete(&(a->ko),nacRing); |
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492 | a->ko = t; |
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493 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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494 | a->e[i] += exp->e[i]; |
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495 | a = a->ne; |
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496 | } |
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497 | while (a!=NULL); |
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498 | } |
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499 | // need to do this, since nacNeg might have changed h |
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500 | exp->ko = h; |
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501 | } |
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502 | } |
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503 | #endif /* LONGALGNEW */ |
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504 | |
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505 | #ifndef LONGALGNEW |
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506 | /*3 |
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507 | * multiplication of napoly. polys |
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508 | * multiply p1 with p2, p1 and p2 are destroyed |
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509 | */ |
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510 | static napoly napMult(napoly p1, napoly p2) |
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511 | { |
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512 | napoly a1, a2, b, h; |
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513 | if (p1==NULL) |
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514 | { |
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515 | napDelete(&p2); |
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516 | return NULL; |
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517 | } |
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518 | if (p2==NULL) |
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519 | { |
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520 | napDelete(&p1); |
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521 | return NULL; |
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522 | } |
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523 | b = NULL; |
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524 | a1 = p1; |
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525 | a2 = p2; |
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526 | if (a2->ne!=NULL) |
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527 | { |
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528 | if (a1->ne!=NULL) |
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529 | { |
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530 | do |
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531 | { |
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532 | a1 = a1->ne; |
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533 | a2 = a2->ne; |
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534 | } |
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535 | while ((a1!=NULL) && (a2!=NULL)); |
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536 | if (a1!=NULL) |
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537 | { |
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538 | a1 = p1; |
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539 | a2 = p2; |
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540 | } |
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541 | else |
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542 | { |
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543 | a1 = p2; |
---|
544 | a2 = p1; |
---|
545 | } |
---|
546 | do |
---|
547 | { |
---|
548 | if (a2->ne!=NULL) |
---|
549 | h = napCopy(a1); |
---|
550 | else |
---|
551 | h = a1; |
---|
552 | napMultT(h, a2); |
---|
553 | b = napAdd(h, b); |
---|
554 | napDelete1(&a2); |
---|
555 | } |
---|
556 | while (a2!=NULL); |
---|
557 | } |
---|
558 | else |
---|
559 | { |
---|
560 | napMultT(a2, a1); |
---|
561 | b = napAdd(a2, b); |
---|
562 | napDelete1(&a1); |
---|
563 | } |
---|
564 | } |
---|
565 | else |
---|
566 | { |
---|
567 | napMultT(a1, a2); |
---|
568 | b = napAdd(a1, b); |
---|
569 | napDelete1(&a2); |
---|
570 | } |
---|
571 | return b; |
---|
572 | } |
---|
573 | #endif /* not LONGALGNEW */ |
---|
574 | |
---|
575 | /*3 |
---|
576 | * division with rest; f = g*q + r, returns r and destroy f |
---|
577 | */ |
---|
578 | static napoly napRemainder(napoly f, const napoly g) |
---|
579 | { |
---|
580 | napoly a, h, qq; |
---|
581 | |
---|
582 | #ifndef LONGALGNEW |
---|
583 | qq = (napoly)omAlloc(napMonomSize); |
---|
584 | #else /* LONGALGNEW */ |
---|
585 | qq = (napoly)p_Init(nacRing); |
---|
586 | #endif /* LONGALGNEW */ |
---|
587 | napNext(qq) = NULL; |
---|
588 | napNormalize(g); |
---|
589 | napNormalize(f); |
---|
590 | a = f; |
---|
591 | do |
---|
592 | { |
---|
593 | napSetExp(qq,1, napGetExp(a,1) - napGetExp(g,1)); |
---|
594 | p_Setm(qq,nacRing); |
---|
595 | napGetCoeff(qq) = nacDiv(napGetCoeff(a), napGetCoeff(g)); |
---|
596 | napGetCoeff(qq) = nacNeg(napGetCoeff(qq)); |
---|
597 | nacNormalize(napGetCoeff(qq)); |
---|
598 | h = napCopy(g); |
---|
599 | napMultT(h, qq); |
---|
600 | napNormalize(h); |
---|
601 | nacDelete(&napGetCoeff(qq),nacRing); |
---|
602 | a = napAdd(a, h); |
---|
603 | } |
---|
604 | while ((a!=NULL) && (napGetExp(a,1) >= napGetExp(g,1))); |
---|
605 | #ifndef LONGALGNEW |
---|
606 | omFreeSize((ADDRESS)qq, napMonomSize); |
---|
607 | #else /* LONGALGNEW */ |
---|
608 | omFreeBinAddr(qq); |
---|
609 | #endif /* LONGALGNEW */ |
---|
610 | return a; |
---|
611 | } |
---|
612 | |
---|
613 | /*3 |
---|
614 | * division with rest; f = g*q + r, destroy f |
---|
615 | */ |
---|
616 | static void napDivMod(napoly f, napoly g, napoly *q, napoly *r) |
---|
617 | { |
---|
618 | napoly a, h, b, qq; |
---|
619 | |
---|
620 | #ifndef LONGALGNEW |
---|
621 | qq = (napoly)omAlloc(napMonomSize); |
---|
622 | #else /* LONGALGNEW */ |
---|
623 | qq = (napoly)p_Init(nacRing); |
---|
624 | #endif /* LONGALGNEW */ |
---|
625 | napNext(qq) = b = NULL; |
---|
626 | napNormalize(g); |
---|
627 | napNormalize(f); |
---|
628 | a = f; |
---|
629 | do |
---|
630 | { |
---|
631 | napSetExp(qq,1, napGetExp(a,1) - napGetExp(g,1)); |
---|
632 | p_Setm(qq,nacRing); |
---|
633 | napGetCoeff(qq) = nacDiv(napGetCoeff(a), napGetCoeff(g)); |
---|
634 | nacNormalize(napGetCoeff(qq)); |
---|
635 | b = napAdd(b, napCopy(qq)); |
---|
636 | napGetCoeff(qq) = nacNeg(napGetCoeff(qq)); |
---|
637 | h = napCopy(g); |
---|
638 | napMultT(h, qq); |
---|
639 | napNormalize(h); |
---|
640 | nacDelete(&napGetCoeff(qq),nacRing); |
---|
641 | a = napAdd(a, h); |
---|
642 | } |
---|
643 | while ((a!=NULL) && (napGetExp(a,1) >= napGetExp(g,1))); |
---|
644 | #ifndef LONGALGNEW |
---|
645 | omFreeSize((ADDRESS)qq, napMonomSize); |
---|
646 | #else /* LONGALGNEW */ |
---|
647 | omFreeBinAddr(qq); |
---|
648 | #endif /* LONGALGNEW */ |
---|
649 | *q = b; |
---|
650 | *r = a; |
---|
651 | } |
---|
652 | |
---|
653 | /*3 |
---|
654 | * returns z with z*x mod c = 1 |
---|
655 | */ |
---|
656 | static napoly napInvers(napoly x, const napoly c) |
---|
657 | { |
---|
658 | napoly y, r, qa, qn, q; |
---|
659 | number t, h; |
---|
660 | |
---|
661 | if (napGetExp(x,1) >= napGetExp(c,1)) |
---|
662 | x = napRemainder(x, c); |
---|
663 | if (x==NULL) |
---|
664 | { |
---|
665 | goto zero_divisor; |
---|
666 | } |
---|
667 | if (napGetExp(x,1)==0) |
---|
668 | { |
---|
669 | if (!nacIsOne(napGetCoeff(x))) |
---|
670 | { |
---|
671 | nacNormalize(napGetCoeff(x)); |
---|
672 | t = nacInvers(napGetCoeff(x)); |
---|
673 | nacNormalize(t); |
---|
674 | nacDelete(&napGetCoeff(x),nacRing); |
---|
675 | napGetCoeff(x) = t; |
---|
676 | } |
---|
677 | return x; |
---|
678 | } |
---|
679 | y = napCopy(c); |
---|
680 | napDivMod(y, x, &qa, &r); |
---|
681 | if (r==NULL) |
---|
682 | { |
---|
683 | goto zero_divisor; |
---|
684 | } |
---|
685 | if (napGetExp(r,1)==0) |
---|
686 | { |
---|
687 | nacNormalize(napGetCoeff(r)); |
---|
688 | t = nacInvers(napGetCoeff(r)); |
---|
689 | nacNormalize(t); |
---|
690 | t = nacNeg(t); |
---|
691 | napMultN(qa, t); |
---|
692 | nacDelete(&t,nacRing); |
---|
693 | napNormalize(qa); |
---|
694 | napDelete(&x); |
---|
695 | napDelete(&r); |
---|
696 | return qa; |
---|
697 | } |
---|
698 | y = x; |
---|
699 | x = r; |
---|
700 | napDivMod(y, x, &q, &r); |
---|
701 | if (r==NULL) |
---|
702 | { |
---|
703 | goto zero_divisor; |
---|
704 | } |
---|
705 | if (napGetExp(r,1)==0) |
---|
706 | { |
---|
707 | q = napMult(q, qa); |
---|
708 | q = napAdd(q, napInit(1)); |
---|
709 | nacNormalize(napGetCoeff(r)); |
---|
710 | t = nacInvers(napGetCoeff(r)); |
---|
711 | napMultN(q, t); |
---|
712 | napNormalize(q); |
---|
713 | nacDelete(&t,nacRing); |
---|
714 | napDelete(&x); |
---|
715 | napDelete(&r); |
---|
716 | if (napGetExp(q,1) >= napGetExp(c,1)) |
---|
717 | q = napRemainder(q, c); |
---|
718 | return q; |
---|
719 | } |
---|
720 | q = napMult(q, napCopy(qa)); |
---|
721 | q = napAdd(q, napInit(1)); |
---|
722 | qa = napNeg(qa); |
---|
723 | loop |
---|
724 | { |
---|
725 | y = x; |
---|
726 | x = r; |
---|
727 | napDivMod(y, x, &qn, &r); |
---|
728 | if (r==NULL) |
---|
729 | { |
---|
730 | break; |
---|
731 | } |
---|
732 | if (napGetExp(r,1)==0) |
---|
733 | { |
---|
734 | q = napMult(q, qn); |
---|
735 | q = napNeg(q); |
---|
736 | q = napAdd(q, qa); |
---|
737 | nacNormalize(napGetCoeff(r)); |
---|
738 | t = nacInvers(napGetCoeff(r)); |
---|
739 | //nacNormalize(t); |
---|
740 | napMultN(q, t); |
---|
741 | napNormalize(q); |
---|
742 | nacDelete(&t,nacRing); |
---|
743 | napDelete(&x); |
---|
744 | napDelete(&r); |
---|
745 | if (napGetExp(q,1) >= napGetExp(c,1)) |
---|
746 | q = napRemainder(q, c); |
---|
747 | return q; |
---|
748 | } |
---|
749 | y = q; |
---|
750 | q = napMult(napCopy(q), qn); |
---|
751 | q = napNeg(q); |
---|
752 | q = napAdd(q, qa); |
---|
753 | qa = y; |
---|
754 | } |
---|
755 | // zero divisor found: |
---|
756 | zero_divisor: |
---|
757 | Werror("zero divisor found - your minpoly is not irreducible"); |
---|
758 | return x; |
---|
759 | } |
---|
760 | |
---|
761 | #ifndef LONGALGNEW |
---|
762 | /*3 |
---|
763 | * the degree of an napoly poly (used for test of "constant" et al.) |
---|
764 | */ |
---|
765 | static int napDeg(napoly p) |
---|
766 | { |
---|
767 | int d = 0, i; |
---|
768 | |
---|
769 | omCheckAddrSize(p,napMonomSize); |
---|
770 | for (i = naNumbOfPar-1; i>=0; i--) |
---|
771 | d += p->e[i]; |
---|
772 | return d; |
---|
773 | } |
---|
774 | #endif /* LONGALGNEW */ |
---|
775 | |
---|
776 | /*3 |
---|
777 | * the max degree of an napoly poly (used for test of "simple" et al.) |
---|
778 | */ |
---|
779 | static int napMaxDeg(napoly p) |
---|
780 | { |
---|
781 | int d = 0; |
---|
782 | while(p!=NULL) |
---|
783 | { |
---|
784 | d=si_max(d,napDeg(p)); |
---|
785 | napIter(p); |
---|
786 | } |
---|
787 | return d; |
---|
788 | } |
---|
789 | |
---|
790 | /*3 |
---|
791 | * the max degree of an napoly poly (used for test of "simple" et al.) |
---|
792 | */ |
---|
793 | static int napMaxDegLen(napoly p, int &l) |
---|
794 | { |
---|
795 | int d = 0; |
---|
796 | int ll=0; |
---|
797 | while(p!=NULL) |
---|
798 | { |
---|
799 | d=si_max(d,napDeg(p)); |
---|
800 | napIter(p); |
---|
801 | ll++; |
---|
802 | } |
---|
803 | l=ll; |
---|
804 | return d; |
---|
805 | } |
---|
806 | |
---|
807 | |
---|
808 | /*3 |
---|
809 | *writes a polynomial number |
---|
810 | */ |
---|
811 | void napWrite(napoly p,const BOOLEAN has_denom) |
---|
812 | { |
---|
813 | if (p==NULL) |
---|
814 | StringAppendS("0"); |
---|
815 | else if (napIsConstant(p)) |
---|
816 | { |
---|
817 | BOOLEAN kl=FALSE; |
---|
818 | if (has_denom) |
---|
819 | { |
---|
820 | number den=nacRing->cf->n_GetDenom(napGetCoeff(p), nacRing); |
---|
821 | kl=!n_IsOne(den,nacRing); |
---|
822 | n_Delete(&den, nacRing); |
---|
823 | } |
---|
824 | if (kl) StringAppendS("("); |
---|
825 | //StringAppendS("-1"); |
---|
826 | nacWrite(napGetCoeff(p)); |
---|
827 | if (kl) StringAppendS(")"); |
---|
828 | } |
---|
829 | else |
---|
830 | { |
---|
831 | StringAppendS("("); |
---|
832 | loop |
---|
833 | { |
---|
834 | BOOLEAN wroteCoeff=FALSE; |
---|
835 | if ((napIsConstant(p)) |
---|
836 | || ((!nacIsOne(napGetCoeff(p))) |
---|
837 | && (!nacIsMOne(napGetCoeff(p))))) |
---|
838 | { |
---|
839 | nacWrite(napGetCoeff(p)); |
---|
840 | wroteCoeff=(currRing->ShortOut==0); |
---|
841 | } |
---|
842 | else if (nacIsMOne(napGetCoeff(p))) |
---|
843 | { |
---|
844 | StringAppendS("-"); |
---|
845 | } |
---|
846 | int i; |
---|
847 | for (i = 0; i < naNumbOfPar; i++) |
---|
848 | { |
---|
849 | if (napGetExp(p,i+1) > 0) |
---|
850 | { |
---|
851 | if (wroteCoeff) |
---|
852 | StringAppendS("*"); |
---|
853 | else |
---|
854 | wroteCoeff=(currRing->ShortOut==0); |
---|
855 | StringAppendS(naParNames[i]); |
---|
856 | if (napGetExp(p,(i+1)) > 1) |
---|
857 | { |
---|
858 | if (currRing->ShortOut == 0) |
---|
859 | StringAppendS("^"); |
---|
860 | StringAppend("%d", napGetExp(p,i+1)); |
---|
861 | } |
---|
862 | } |
---|
863 | } /*for*/ |
---|
864 | napIter(p); |
---|
865 | if (p==NULL) |
---|
866 | break; |
---|
867 | if (nacGreaterZero(napGetCoeff(p))) |
---|
868 | StringAppendS("+"); |
---|
869 | } |
---|
870 | StringAppendS(")"); |
---|
871 | } |
---|
872 | } |
---|
873 | |
---|
874 | |
---|
875 | #ifndef LONGALGNEW |
---|
876 | static char *napHandleMons(char *s, int i, PARAMETER_TYPE *ex) |
---|
877 | #else /* LONGALGNEW */ |
---|
878 | static char *napHandleMons(char *s, int i, napoly ex) |
---|
879 | #endif /* LONGALGNEW */ |
---|
880 | { |
---|
881 | int j; |
---|
882 | if (strncmp(s,naParNames[i],strlen(naParNames[i]))==0) |
---|
883 | { |
---|
884 | s+=strlen(naParNames[i]); |
---|
885 | if ((*s >= '0') && (*s <= '9')) |
---|
886 | { |
---|
887 | s = eati(s, &j); |
---|
888 | #ifndef LONGALGNEW |
---|
889 | ex[i] += j; |
---|
890 | #else /* LONGALGNEW */ |
---|
891 | napAddExp(ex,i+1,j); |
---|
892 | #endif /* LONGALGNEW */ |
---|
893 | } |
---|
894 | else |
---|
895 | #ifndef LONGALGNEW |
---|
896 | ex[i]++; |
---|
897 | #else /* LONGALGNEW */ |
---|
898 | napAddExp(ex,i+1,1); |
---|
899 | #endif /* LONGALGNEW */ |
---|
900 | } |
---|
901 | return s; |
---|
902 | } |
---|
903 | |
---|
904 | /*3 reads a monomial */ |
---|
905 | static char *napRead(char *s, napoly *b) |
---|
906 | { |
---|
907 | napoly a; |
---|
908 | int i; |
---|
909 | #ifndef LONGALGNEW |
---|
910 | a = (napoly)omAlloc0(napMonomSize); |
---|
911 | #else /* LONGALGNEW */ |
---|
912 | a = (napoly)p_Init(nacRing); |
---|
913 | #endif /* LONGALGNEW */ |
---|
914 | if ((*s >= '0') && (*s <= '9')) |
---|
915 | { |
---|
916 | s = nacRead(s, &napGetCoeff(a)); |
---|
917 | if (nacIsZero(napGetCoeff(a))) |
---|
918 | { |
---|
919 | napDelete1(&a); |
---|
920 | *b = NULL; |
---|
921 | return s; |
---|
922 | } |
---|
923 | } |
---|
924 | else |
---|
925 | napGetCoeff(a) = nacInit(1); |
---|
926 | i = 0; |
---|
927 | char *olds; |
---|
928 | loop |
---|
929 | { |
---|
930 | olds = s; |
---|
931 | #ifndef LONGALGNEW |
---|
932 | s = napHandleMons(s, i, a->e); |
---|
933 | #else /* LONGALGNEW */ |
---|
934 | s = napHandleMons(s, i, a); |
---|
935 | #endif /* LONGALGNEW */ |
---|
936 | if (olds == s) |
---|
937 | i++; |
---|
938 | else |
---|
939 | i = 0; |
---|
940 | if ((*s == '\0') || (i >= naNumbOfPar)) |
---|
941 | break; |
---|
942 | } |
---|
943 | *b = a; |
---|
944 | return s; |
---|
945 | } |
---|
946 | |
---|
947 | static int napExp(napoly a, napoly b) |
---|
948 | { |
---|
949 | while (napNext(a)!=NULL) napIter(a); |
---|
950 | int m = napGetExp(a,1); |
---|
951 | if (m==0) return 0; |
---|
952 | while (napNext(b)!=NULL) napIter(b); |
---|
953 | int mm=napGetExp(b,1); |
---|
954 | if (m > mm) m = mm; |
---|
955 | return m; |
---|
956 | } |
---|
957 | |
---|
958 | /* |
---|
959 | * finds the smallest i-th exponent in a and b |
---|
960 | * used to find it in a fraction |
---|
961 | */ |
---|
962 | static int napExpi(int i, napoly a, napoly b) |
---|
963 | { |
---|
964 | if (a==NULL || b==NULL) return 0; |
---|
965 | int m = napGetExp(a,i+1); |
---|
966 | if (m==0) return 0; |
---|
967 | while (napNext(a) != NULL) |
---|
968 | { |
---|
969 | napIter(a); |
---|
970 | if (m > napGetExp(a,i+1)) |
---|
971 | { |
---|
972 | m = napGetExp(a,i+1); |
---|
973 | if (m==0) return 0; |
---|
974 | } |
---|
975 | } |
---|
976 | do |
---|
977 | { |
---|
978 | if (m > napGetExp(b,i+1)) |
---|
979 | { |
---|
980 | m = napGetExp(b,i+1); |
---|
981 | if (m==0) return 0; |
---|
982 | } |
---|
983 | napIter(b); |
---|
984 | } |
---|
985 | while (b != NULL); |
---|
986 | return m; |
---|
987 | } |
---|
988 | |
---|
989 | static void napContent(napoly ph) |
---|
990 | { |
---|
991 | number h,d; |
---|
992 | napoly p; |
---|
993 | |
---|
994 | p = ph; |
---|
995 | if (nacIsOne(napGetCoeff(p))) |
---|
996 | return; |
---|
997 | h = nacCopy(napGetCoeff(p)); |
---|
998 | napIter(p); |
---|
999 | do |
---|
1000 | { |
---|
1001 | d=nacGcd(napGetCoeff(p), h, nacRing); |
---|
1002 | if(nacIsOne(d)) |
---|
1003 | { |
---|
1004 | nacDelete(&h,nacRing); |
---|
1005 | nacDelete(&d,nacRing); |
---|
1006 | return; |
---|
1007 | } |
---|
1008 | nacDelete(&h,nacRing); |
---|
1009 | h = d; |
---|
1010 | napIter(p); |
---|
1011 | } |
---|
1012 | while (p!=NULL); |
---|
1013 | h = nacInvers(d); |
---|
1014 | nacDelete(&d,nacRing); |
---|
1015 | p = ph; |
---|
1016 | while (p!=NULL) |
---|
1017 | { |
---|
1018 | d = nacMult(napGetCoeff(p), h); |
---|
1019 | nacDelete(&napGetCoeff(p),nacRing); |
---|
1020 | napGetCoeff(p) = d; |
---|
1021 | napIter(p); |
---|
1022 | } |
---|
1023 | nacDelete(&h,nacRing); |
---|
1024 | } |
---|
1025 | |
---|
1026 | static void napCleardenom(napoly ph) |
---|
1027 | { |
---|
1028 | number d, h; |
---|
1029 | napoly p; |
---|
1030 | |
---|
1031 | if (!naIsChar0) |
---|
1032 | return; |
---|
1033 | p = ph; |
---|
1034 | h = nacInit(1); |
---|
1035 | while (p!=NULL) |
---|
1036 | { |
---|
1037 | d = nacLcm(h, napGetCoeff(p), nacRing); |
---|
1038 | nacDelete(&h,nacRing); |
---|
1039 | h = d; |
---|
1040 | napIter(p); |
---|
1041 | } |
---|
1042 | if(!nacIsOne(h)) |
---|
1043 | { |
---|
1044 | p = ph; |
---|
1045 | while (p!=NULL) |
---|
1046 | { |
---|
1047 | d=nacMult(h, napGetCoeff(p)); |
---|
1048 | nacDelete(&napGetCoeff(p),nacRing); |
---|
1049 | nacNormalize(d); |
---|
1050 | napGetCoeff(p) = d; |
---|
1051 | napIter(p); |
---|
1052 | } |
---|
1053 | nacDelete(&h,nacRing); |
---|
1054 | } |
---|
1055 | napContent(ph); |
---|
1056 | } |
---|
1057 | |
---|
1058 | static napoly napGcd0(napoly a, napoly b) |
---|
1059 | { |
---|
1060 | number x, y; |
---|
1061 | if (!naIsChar0) |
---|
1062 | return napInit(1); |
---|
1063 | x = nacCopy(napGetCoeff(a)); |
---|
1064 | if (nacIsOne(x)) |
---|
1065 | return napInitz(x); |
---|
1066 | while (napNext(a)!=NULL) |
---|
1067 | { |
---|
1068 | napIter(a); |
---|
1069 | y = nacGcd(x, napGetCoeff(a), nacRing); |
---|
1070 | nacDelete(&x,nacRing); |
---|
1071 | x = y; |
---|
1072 | if (nacIsOne(x)) |
---|
1073 | return napInitz(x); |
---|
1074 | } |
---|
1075 | do |
---|
1076 | { |
---|
1077 | y = nacGcd(x, napGetCoeff(b), nacRing); |
---|
1078 | nacDelete(&x,nacRing); |
---|
1079 | x = y; |
---|
1080 | if (nacIsOne(x)) |
---|
1081 | return napInitz(x); |
---|
1082 | napIter(b); |
---|
1083 | } |
---|
1084 | while (b!=NULL); |
---|
1085 | return napInitz(x); |
---|
1086 | } |
---|
1087 | |
---|
1088 | /*3 |
---|
1089 | * result =gcd(a,b) |
---|
1090 | */ |
---|
1091 | static napoly napGcd(napoly a, napoly b) |
---|
1092 | { |
---|
1093 | int i; |
---|
1094 | napoly g, x, y, h; |
---|
1095 | if ((a==NULL) |
---|
1096 | || ((napNext(a)==NULL)&&(nacIsZero(napGetCoeff(a))))) |
---|
1097 | { |
---|
1098 | if ((b==NULL) |
---|
1099 | || ((napNext(b)==NULL)&&(nacIsZero(napGetCoeff(b))))) |
---|
1100 | { |
---|
1101 | return napInit(1); |
---|
1102 | } |
---|
1103 | return napCopy(b); |
---|
1104 | } |
---|
1105 | else |
---|
1106 | if ((b==NULL) |
---|
1107 | || ((napNext(b)==NULL)&&(nacIsZero(napGetCoeff(b))))) |
---|
1108 | { |
---|
1109 | return napCopy(a); |
---|
1110 | } |
---|
1111 | if (naMinimalPoly != NULL) |
---|
1112 | { |
---|
1113 | if (napGetExp(a,1) >= napGetExp(b,1)) |
---|
1114 | { |
---|
1115 | x = a; |
---|
1116 | y = b; |
---|
1117 | } |
---|
1118 | else |
---|
1119 | { |
---|
1120 | x = b; |
---|
1121 | y = a; |
---|
1122 | } |
---|
1123 | if (!naIsChar0) g = napInit(1); |
---|
1124 | else g = napGcd0(x, y); |
---|
1125 | if (napNext(y)==NULL) |
---|
1126 | { |
---|
1127 | napSetExp(g,1, napExp(x, y)); |
---|
1128 | p_Setm(g,nacRing); |
---|
1129 | return g; |
---|
1130 | } |
---|
1131 | x = napCopy(x); |
---|
1132 | y = napCopy(y); |
---|
1133 | loop |
---|
1134 | { |
---|
1135 | h = napRemainder(x, y); |
---|
1136 | if (h==NULL) |
---|
1137 | { |
---|
1138 | napCleardenom(y); |
---|
1139 | if (!nacIsOne(napGetCoeff(g))) |
---|
1140 | napMultN(y, napGetCoeff(g)); |
---|
1141 | napDelete1(&g); |
---|
1142 | return y; |
---|
1143 | } |
---|
1144 | else if (napNext(h)==NULL) |
---|
1145 | break; |
---|
1146 | x = y; |
---|
1147 | y = h; |
---|
1148 | } |
---|
1149 | napDelete(&y); |
---|
1150 | napDelete1(&h); |
---|
1151 | napSetExp(g,1, napExp(a, b)); |
---|
1152 | p_Setm(g,nacRing); |
---|
1153 | return g; |
---|
1154 | } |
---|
1155 | // Hmm ... this is a memory leak |
---|
1156 | #ifndef LONGALGNEW |
---|
1157 | // x = (napoly)omAlloc0(napMonomSize); |
---|
1158 | #else /* LONGALGNEW */ |
---|
1159 | // x = (napoly)p_Init(nacRing); |
---|
1160 | #endif /* LONGALGNEW */ |
---|
1161 | g=a; |
---|
1162 | h=b; |
---|
1163 | if (!naIsChar0) x = napInit(1); |
---|
1164 | else x = napGcd0(g,h); |
---|
1165 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
1166 | { |
---|
1167 | napSetExp(x,i+1, napExpi(i,a,b)); |
---|
1168 | p_Setm(x,nacRing); |
---|
1169 | } |
---|
1170 | return x; |
---|
1171 | } |
---|
1172 | |
---|
1173 | |
---|
1174 | number napLcm(napoly a) |
---|
1175 | { |
---|
1176 | number h = nacInit(1); |
---|
1177 | |
---|
1178 | if (naIsChar0) |
---|
1179 | { |
---|
1180 | number d; |
---|
1181 | napoly b = a; |
---|
1182 | |
---|
1183 | while (b!=NULL) |
---|
1184 | { |
---|
1185 | d = nacLcm(h, napGetCoeff(b), nacRing); |
---|
1186 | nacDelete(&h,nacRing); |
---|
1187 | h = d; |
---|
1188 | napIter(b); |
---|
1189 | } |
---|
1190 | } |
---|
1191 | return h; |
---|
1192 | } |
---|
1193 | |
---|
1194 | |
---|
1195 | /*2 |
---|
1196 | * meins (for reduction in algebraic extension) |
---|
1197 | * checks if head of p divides head of q |
---|
1198 | * doesn't delete p and q |
---|
1199 | */ |
---|
1200 | static BOOLEAN napDivPoly (napoly p, napoly q) |
---|
1201 | { |
---|
1202 | #ifndef LONGALGNEW |
---|
1203 | int j=0; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
1204 | #else /* LONGALGNEW */ |
---|
1205 | int j=1; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
1206 | #endif /* LONGALGNEW */ |
---|
1207 | |
---|
1208 | #ifndef LONGALGNEW |
---|
1209 | while (p->e[j] <= q->e[j]) |
---|
1210 | #else /* LONGALGNEW */ |
---|
1211 | while (napGetExp(p,j) <= napGetExp(q,j)) |
---|
1212 | #endif /* LONGALGNEW */ |
---|
1213 | { |
---|
1214 | j++; |
---|
1215 | #ifndef LONGALGNEW |
---|
1216 | if (j >= naNumbOfPar) |
---|
1217 | #else /* LONGALGNEW */ |
---|
1218 | if (j > naNumbOfPar) |
---|
1219 | #endif /* LONGALGNEW */ |
---|
1220 | return 1; |
---|
1221 | } |
---|
1222 | return 0; |
---|
1223 | } |
---|
1224 | |
---|
1225 | |
---|
1226 | /*2 |
---|
1227 | * meins (for reduction in algebraic extension) |
---|
1228 | * Normalform of poly with naI |
---|
1229 | * changes q and returns it |
---|
1230 | */ |
---|
1231 | napoly napRedp (napoly q) |
---|
1232 | { |
---|
1233 | #ifndef LONGALGNEW |
---|
1234 | napoly h = (napoly)omAlloc0(napMonomSize); |
---|
1235 | #else /* LONGALGNEW */ |
---|
1236 | napoly h = (napoly)p_Init(nacRing); |
---|
1237 | #endif /* LONGALGNEW */ |
---|
1238 | int i=0,j; |
---|
1239 | |
---|
1240 | loop |
---|
1241 | { |
---|
1242 | if (napDivPoly (naI->liste[i], q)) |
---|
1243 | { |
---|
1244 | /* h = lt(q)/lt(naI->liste[i])*/ |
---|
1245 | napGetCoeff(h) = nacCopy(napGetCoeff(q)); |
---|
1246 | for (j=naNumbOfPar; j>0; j--) |
---|
1247 | napSetExp(h,j, napGetExp(q,j) - napGetExp(naI->liste[i],j)); |
---|
1248 | p_Setm(h,nacRing); |
---|
1249 | h = napMult (h, napCopy(naI->liste[i])); |
---|
1250 | h = napNeg (h); |
---|
1251 | q = napAdd (q, napCopy(h)); |
---|
1252 | napDelete (&napNext(h)); |
---|
1253 | if (q == NULL) |
---|
1254 | { |
---|
1255 | napDelete(&h); |
---|
1256 | return q; |
---|
1257 | } |
---|
1258 | /* try to reduce further */ |
---|
1259 | i = 0; |
---|
1260 | } |
---|
1261 | else |
---|
1262 | { |
---|
1263 | i++; |
---|
1264 | if (i >= naI->anz) |
---|
1265 | { |
---|
1266 | napDelete(&h); |
---|
1267 | return q; |
---|
1268 | } |
---|
1269 | } |
---|
1270 | } |
---|
1271 | } |
---|
1272 | |
---|
1273 | |
---|
1274 | /*2 |
---|
1275 | * meins (for reduction in algebraic extension) |
---|
1276 | * reduces the tail of Poly q |
---|
1277 | * needs q != NULL |
---|
1278 | * changes q and returns it |
---|
1279 | */ |
---|
1280 | napoly napTailred (napoly q) |
---|
1281 | { |
---|
1282 | napoly h; |
---|
1283 | |
---|
1284 | h = napNext(q); |
---|
1285 | while (h != NULL) |
---|
1286 | { |
---|
1287 | h = napRedp (h); |
---|
1288 | if (h == NULL) |
---|
1289 | return q; |
---|
1290 | napIter(h); |
---|
1291 | } |
---|
1292 | return q; |
---|
1293 | } |
---|
1294 | |
---|
1295 | |
---|
1296 | /*================ procedure for rational functions: naXXXX =================*/ |
---|
1297 | |
---|
1298 | /*2 |
---|
1299 | * z:= i |
---|
1300 | */ |
---|
1301 | number naInit(int i) |
---|
1302 | { |
---|
1303 | if (i!=0) |
---|
1304 | { |
---|
1305 | #ifndef LONGALGNEW |
---|
1306 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
1307 | l->z = napInit(i); |
---|
1308 | if (l->z==NULL) |
---|
1309 | { |
---|
1310 | omFreeBin((ADDRESS)l, rnumber_bin); |
---|
1311 | return NULL; |
---|
1312 | } |
---|
1313 | l->s = 2; |
---|
1314 | l->n = NULL; |
---|
1315 | return (number)l; |
---|
1316 | #else /* LONGALGNEW */ |
---|
1317 | napoly z=napInit(i); |
---|
1318 | if (z!=NULL) |
---|
1319 | { |
---|
1320 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
1321 | l->z = z; |
---|
1322 | l->s = 2; |
---|
1323 | l->n = NULL; |
---|
1324 | return (number)l; |
---|
1325 | } |
---|
1326 | #endif /* LONGALGNEW */ |
---|
1327 | } |
---|
1328 | /*else*/ |
---|
1329 | return NULL; |
---|
1330 | } |
---|
1331 | |
---|
1332 | number naPar(int i) |
---|
1333 | { |
---|
1334 | lnumber l = (lnumber)omAllocBin(rnumber_bin); |
---|
1335 | l->s = 2; |
---|
1336 | l->z = napInit(1); |
---|
1337 | napSetExp(l->z,i,1); |
---|
1338 | p_Setm(l->z,nacRing); |
---|
1339 | l->n = NULL; |
---|
1340 | return (number)l; |
---|
1341 | } |
---|
1342 | |
---|
1343 | int naParDeg(number n) /* i := deg(n) */ |
---|
1344 | { |
---|
1345 | lnumber l = (lnumber)n; |
---|
1346 | if (l==NULL) return -1; |
---|
1347 | return napDeg(l->z); |
---|
1348 | } |
---|
1349 | |
---|
1350 | //int naParDeg(number n) /* i := deg(n) */ |
---|
1351 | //{ |
---|
1352 | // lnumber l = (lnumber)n; |
---|
1353 | // if (l==NULL) return -1; |
---|
1354 | // return napMaxDeg(l->z)+napMaxDeg(l->n); |
---|
1355 | //} |
---|
1356 | |
---|
1357 | int naSize(number n) /* size desc. */ |
---|
1358 | { |
---|
1359 | lnumber l = (lnumber)n; |
---|
1360 | if (l==NULL) return -1; |
---|
1361 | int len_z; |
---|
1362 | int len_n; |
---|
1363 | int o=napMaxDegLen(l->z,len_z)+napMaxDegLen(l->n,len_n); |
---|
1364 | return (len_z+len_n)+o; |
---|
1365 | } |
---|
1366 | |
---|
1367 | /*2 |
---|
1368 | * convert a number to int (if possible) |
---|
1369 | */ |
---|
1370 | int naInt(number &n) |
---|
1371 | { |
---|
1372 | lnumber l=(lnumber)n; |
---|
1373 | if ((l!=NULL)&&(l->n==NULL)&&(napIsConstant(l->z))) |
---|
1374 | { |
---|
1375 | return nacInt(napGetCoeff(l->z)); |
---|
1376 | } |
---|
1377 | return 0; |
---|
1378 | } |
---|
1379 | |
---|
1380 | /*2 |
---|
1381 | * deletes p |
---|
1382 | */ |
---|
1383 | void naDelete(number *p, const ring r) |
---|
1384 | { |
---|
1385 | lnumber l = (lnumber) * p; |
---|
1386 | if (l==NULL) return; |
---|
1387 | nap_Delete(&(l->z),r); |
---|
1388 | nap_Delete(&(l->n),r); |
---|
1389 | omFreeBin((ADDRESS)l, rnumber_bin); |
---|
1390 | *p = NULL; |
---|
1391 | } |
---|
1392 | |
---|
1393 | /*2 |
---|
1394 | * copy p to erg |
---|
1395 | */ |
---|
1396 | number naCopy(number p) |
---|
1397 | { |
---|
1398 | if (p==NULL) return NULL; |
---|
1399 | naTest(p); |
---|
1400 | lnumber erg; |
---|
1401 | lnumber src = (lnumber)p; |
---|
1402 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
1403 | erg->z = napCopy(src->z); |
---|
1404 | erg->n = napCopy(src->n); |
---|
1405 | erg->s = src->s; |
---|
1406 | return (number)erg; |
---|
1407 | } |
---|
1408 | number na_Copy(number p, const ring r) |
---|
1409 | { |
---|
1410 | if (p==NULL) return NULL; |
---|
1411 | lnumber erg; |
---|
1412 | lnumber src = (lnumber)p; |
---|
1413 | erg = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
1414 | erg->z = nap_Copy(src->z,r); |
---|
1415 | erg->n = nap_Copy(src->n,r); |
---|
1416 | erg->s = src->s; |
---|
1417 | return (number)erg; |
---|
1418 | } |
---|
1419 | |
---|
1420 | /*2 |
---|
1421 | * a dummy number: 0 |
---|
1422 | */ |
---|
1423 | void naNew(number *z) |
---|
1424 | { |
---|
1425 | *z = NULL; |
---|
1426 | } |
---|
1427 | |
---|
1428 | /*2 |
---|
1429 | * addition; lu:= la + lb |
---|
1430 | */ |
---|
1431 | number naAdd(number la, number lb) |
---|
1432 | { |
---|
1433 | napoly x, y; |
---|
1434 | lnumber lu; |
---|
1435 | lnumber a = (lnumber)la; |
---|
1436 | lnumber b = (lnumber)lb; |
---|
1437 | if (a==NULL) return naCopy(lb); |
---|
1438 | if (b==NULL) return naCopy(la); |
---|
1439 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1440 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1441 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
1442 | if (b->n!=NULL) x = napMultCopy(a->z, b->n); |
---|
1443 | else x = napCopy(a->z); |
---|
1444 | if (a->n!=NULL) y = napMultCopy(b->z, a->n); |
---|
1445 | else y = napCopy(b->z); |
---|
1446 | lu->z = napAdd(x, y); |
---|
1447 | if (lu->z==NULL) |
---|
1448 | { |
---|
1449 | omFreeBin((ADDRESS)lu, rnumber_bin); |
---|
1450 | return (number)NULL; |
---|
1451 | } |
---|
1452 | if (a->n!=NULL) |
---|
1453 | { |
---|
1454 | if (b->n!=NULL) x = napMultCopy(a->n, b->n); |
---|
1455 | else x = napCopy(a->n); |
---|
1456 | } |
---|
1457 | else |
---|
1458 | { |
---|
1459 | if (b->n!=NULL) x = napCopy(b->n); |
---|
1460 | else x = NULL; |
---|
1461 | } |
---|
1462 | #ifndef LONGALGNEW |
---|
1463 | if ((x!=NULL) && (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
1464 | napDelete(&x); |
---|
1465 | #else /* LONGALGNEW */ |
---|
1466 | if (x!=NULL) |
---|
1467 | { |
---|
1468 | assume(!napIsConstant(x)); |
---|
1469 | } |
---|
1470 | #endif /* LONGALGNEW */ |
---|
1471 | lu->n = x; |
---|
1472 | lu->s = 0; |
---|
1473 | #ifdef LONGALGNEW |
---|
1474 | if (lu->n!=NULL) |
---|
1475 | { |
---|
1476 | number luu=(number)lu; |
---|
1477 | naNormalize(luu); |
---|
1478 | lu=(lnumber)luu; |
---|
1479 | } |
---|
1480 | #endif /* LONGALGNEW */ |
---|
1481 | naTest((number)lu); |
---|
1482 | return (number)lu; |
---|
1483 | } |
---|
1484 | |
---|
1485 | /*2 |
---|
1486 | * subtraction; r:= la - lb |
---|
1487 | */ |
---|
1488 | number naSub(number la, number lb) |
---|
1489 | { |
---|
1490 | lnumber lu; |
---|
1491 | |
---|
1492 | if (lb==NULL) return naCopy(la); |
---|
1493 | if (la==NULL) |
---|
1494 | { |
---|
1495 | lu = (lnumber)naCopy(lb); |
---|
1496 | lu->z = napNeg(lu->z); |
---|
1497 | return (number)lu; |
---|
1498 | } |
---|
1499 | |
---|
1500 | napoly x, y; |
---|
1501 | lnumber a = (lnumber)la; |
---|
1502 | lnumber b = (lnumber)lb; |
---|
1503 | |
---|
1504 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1505 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1506 | lu = (lnumber)omAllocBin(rnumber_bin); |
---|
1507 | if (b->n!=NULL) x = napMultCopy(a->z, b->n); |
---|
1508 | else x = napCopy(a->z); |
---|
1509 | if (a->n!=NULL) y = napMult(napCopy(b->z), napCopyNeg(a->n)); |
---|
1510 | else y = napCopyNeg(b->z); |
---|
1511 | lu->z = napAdd(x, y); |
---|
1512 | if (lu->z==NULL) |
---|
1513 | { |
---|
1514 | omFreeBin((ADDRESS)lu, rnumber_bin); |
---|
1515 | return (number)NULL; |
---|
1516 | } |
---|
1517 | if (a->n!=NULL) |
---|
1518 | { |
---|
1519 | if (b->n!=NULL) x = napMultCopy(a->n, b->n); |
---|
1520 | else x = napCopy(a->n); |
---|
1521 | } |
---|
1522 | else |
---|
1523 | { |
---|
1524 | if (b->n!=NULL) x = napCopy(b->n); |
---|
1525 | else x = NULL; |
---|
1526 | } |
---|
1527 | #ifndef LONGALGNEW |
---|
1528 | if ((x!=NULL)&& (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
1529 | napDelete(&x); |
---|
1530 | #else /* LONGALGNEW */ |
---|
1531 | if (x!=NULL) |
---|
1532 | { |
---|
1533 | assume(!napIsConstant(x)); |
---|
1534 | } |
---|
1535 | #endif /* LONGALGNEW */ |
---|
1536 | lu->n = x; |
---|
1537 | lu->s = 0; |
---|
1538 | #ifdef LONGALGNEW |
---|
1539 | if (lu->n!=NULL) |
---|
1540 | { |
---|
1541 | number luu=(number)lu; |
---|
1542 | naNormalize(luu); |
---|
1543 | lu=(lnumber)luu; |
---|
1544 | } |
---|
1545 | #endif /* LONGALGNEW */ |
---|
1546 | naTest((number)lu); |
---|
1547 | return (number)lu; |
---|
1548 | } |
---|
1549 | |
---|
1550 | /*2 |
---|
1551 | * multiplication; r:= la * lb |
---|
1552 | */ |
---|
1553 | number naMult(number la, number lb) |
---|
1554 | { |
---|
1555 | if ((la==NULL) || (lb==NULL)) |
---|
1556 | return NULL; |
---|
1557 | |
---|
1558 | lnumber a = (lnumber)la; |
---|
1559 | lnumber b = (lnumber)lb; |
---|
1560 | lnumber lo; |
---|
1561 | napoly x; |
---|
1562 | |
---|
1563 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1564 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1565 | naTest(la); |
---|
1566 | naTest(lb); |
---|
1567 | |
---|
1568 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
1569 | lo->z = napMultCopy(a->z, b->z); |
---|
1570 | |
---|
1571 | if (a->n==NULL) |
---|
1572 | { |
---|
1573 | if (b->n==NULL) |
---|
1574 | x = NULL; |
---|
1575 | else |
---|
1576 | x = napCopy(b->n); |
---|
1577 | } |
---|
1578 | else |
---|
1579 | { |
---|
1580 | if (b->n==NULL) |
---|
1581 | { |
---|
1582 | x = napCopy(a->n); |
---|
1583 | } |
---|
1584 | else |
---|
1585 | { |
---|
1586 | x = napMultCopy(b->n, a->n); |
---|
1587 | } |
---|
1588 | } |
---|
1589 | if (naMinimalPoly!=NULL) |
---|
1590 | { |
---|
1591 | if (napGetExp(lo->z,1) >= napGetExp(naMinimalPoly,1)) |
---|
1592 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
1593 | if ((x!=NULL) && (napGetExp(x,1) >= napGetExp(naMinimalPoly,1))) |
---|
1594 | x = napRemainder(x, naMinimalPoly); |
---|
1595 | } |
---|
1596 | if (naI!=NULL) |
---|
1597 | { |
---|
1598 | lo->z = napRedp (lo->z); |
---|
1599 | if (lo->z != NULL) |
---|
1600 | lo->z = napTailred (lo->z); |
---|
1601 | if (x!=NULL) |
---|
1602 | { |
---|
1603 | x = napRedp (x); |
---|
1604 | if (x!=NULL) |
---|
1605 | x = napTailred (x); |
---|
1606 | } |
---|
1607 | } |
---|
1608 | if ((x!=NULL) && (napIsConstant(x)) && nacIsOne(napGetCoeff(x))) |
---|
1609 | napDelete(&x); |
---|
1610 | lo->n = x; |
---|
1611 | lo->s = 0; |
---|
1612 | if(lo->z==NULL) |
---|
1613 | { |
---|
1614 | omFreeBin((ADDRESS)lo, rnumber_bin); |
---|
1615 | lo=NULL; |
---|
1616 | } |
---|
1617 | #if 0 |
---|
1618 | if (lo->n!=NULL) |
---|
1619 | { |
---|
1620 | number luu=(number)lo; |
---|
1621 | naNormalize(luu); |
---|
1622 | lo=(lnumber)luu; |
---|
1623 | } |
---|
1624 | #endif |
---|
1625 | naTest((number)lo); |
---|
1626 | return (number)lo; |
---|
1627 | } |
---|
1628 | |
---|
1629 | number naIntDiv(number la, number lb) |
---|
1630 | { |
---|
1631 | lnumber res; |
---|
1632 | lnumber a = (lnumber)la; |
---|
1633 | lnumber b = (lnumber)lb; |
---|
1634 | #ifndef LONGALGNEW |
---|
1635 | if ((a==NULL) || (a->z==NULL)) |
---|
1636 | #else /* LONGALGNEW */ |
---|
1637 | if (a==NULL) |
---|
1638 | { |
---|
1639 | assume(a->z!=NULL); |
---|
1640 | #endif /* LONGALGNEW */ |
---|
1641 | return NULL; |
---|
1642 | #ifndef LONGALGNEW |
---|
1643 | if ((b==NULL) || (b->z==NULL)) |
---|
1644 | #else /* LONGALGNEW */ |
---|
1645 | } |
---|
1646 | if (b==NULL) |
---|
1647 | #endif /* LONGALGNEW */ |
---|
1648 | { |
---|
1649 | #ifdef LONGALGNEW |
---|
1650 | assume(b->z!=NULL); |
---|
1651 | #endif /* LONGALGNEW */ |
---|
1652 | WerrorS("div. by 0"); |
---|
1653 | return NULL; |
---|
1654 | } |
---|
1655 | assume(a->z!=NULL && b->z!=NULL); |
---|
1656 | assume(a->n==NULL && b->n==NULL); |
---|
1657 | res = (lnumber)omAllocBin(rnumber_bin); |
---|
1658 | res->z = napCopy(a->z); |
---|
1659 | res->n = napCopy(b->z); |
---|
1660 | res->s = 0; |
---|
1661 | number nres=(number)res; |
---|
1662 | naNormalize(nres); |
---|
1663 | |
---|
1664 | //napDelete(&res->n); |
---|
1665 | naTest(nres); |
---|
1666 | return nres; |
---|
1667 | } |
---|
1668 | |
---|
1669 | /*2 |
---|
1670 | * division; lo:= la / lb |
---|
1671 | */ |
---|
1672 | number naDiv(number la, number lb) |
---|
1673 | { |
---|
1674 | lnumber lo; |
---|
1675 | lnumber a = (lnumber)la; |
---|
1676 | lnumber b = (lnumber)lb; |
---|
1677 | napoly x; |
---|
1678 | |
---|
1679 | if ((a==NULL) || (a->z==NULL)) |
---|
1680 | return NULL; |
---|
1681 | |
---|
1682 | if ((b==NULL) || (b->z==NULL)) |
---|
1683 | { |
---|
1684 | WerrorS("div. by 0"); |
---|
1685 | return NULL; |
---|
1686 | } |
---|
1687 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1688 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1689 | lo = (lnumber)omAllocBin(rnumber_bin); |
---|
1690 | if (b->n!=NULL) |
---|
1691 | lo->z = napMultCopy(a->z, b->n); |
---|
1692 | else |
---|
1693 | lo->z = napCopy(a->z); |
---|
1694 | if (a->n!=NULL) |
---|
1695 | x = napMultCopy(b->z, a->n); |
---|
1696 | else |
---|
1697 | x = napCopy(b->z); |
---|
1698 | if (naMinimalPoly!=NULL) |
---|
1699 | { |
---|
1700 | if (napGetExp(lo->z,1) >= napGetExp(naMinimalPoly,1)) |
---|
1701 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
1702 | if (napGetExp(x,1) >= napGetExp(naMinimalPoly,1)) |
---|
1703 | x = napRemainder(x, naMinimalPoly); |
---|
1704 | } |
---|
1705 | if (naI!=NULL) |
---|
1706 | { |
---|
1707 | lo->z = napRedp (lo->z); |
---|
1708 | if (lo->z != NULL) |
---|
1709 | lo->z = napTailred (lo->z); |
---|
1710 | if (x!=NULL) |
---|
1711 | { |
---|
1712 | x = napRedp (x); |
---|
1713 | if (x!=NULL) |
---|
1714 | x = napTailred (x); |
---|
1715 | } |
---|
1716 | } |
---|
1717 | if ((napIsConstant(x)) && nacIsOne(napGetCoeff(x))) |
---|
1718 | napDelete(&x); |
---|
1719 | lo->s = 0; |
---|
1720 | lo->n = x; |
---|
1721 | #ifdef LONGALGNEW |
---|
1722 | if (lo->n!=NULL) |
---|
1723 | { |
---|
1724 | number luu=(number)lo; |
---|
1725 | naNormalize(luu); |
---|
1726 | lo=(lnumber)luu; |
---|
1727 | } |
---|
1728 | #endif /* LONGALGNEW */ |
---|
1729 | naTest((number)lo); |
---|
1730 | return (number)lo; |
---|
1731 | } |
---|
1732 | |
---|
1733 | /*2 |
---|
1734 | * za:= - za |
---|
1735 | */ |
---|
1736 | number naNeg(number za) |
---|
1737 | { |
---|
1738 | if (za!=NULL) |
---|
1739 | { |
---|
1740 | lnumber e = (lnumber)za; |
---|
1741 | naTest(za); |
---|
1742 | e->z = napNeg(e->z); |
---|
1743 | } |
---|
1744 | return za; |
---|
1745 | } |
---|
1746 | |
---|
1747 | /*2 |
---|
1748 | * 1/a |
---|
1749 | */ |
---|
1750 | number naInvers(number a) |
---|
1751 | { |
---|
1752 | lnumber lo; |
---|
1753 | lnumber b = (lnumber)a; |
---|
1754 | napoly x; |
---|
1755 | |
---|
1756 | if (b==NULL) |
---|
1757 | { |
---|
1758 | WerrorS("div. by 0"); |
---|
1759 | return NULL; |
---|
1760 | } |
---|
1761 | omCheckAddrSize(b,sizeof(snumber)); |
---|
1762 | lo = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
1763 | lo->s = b->s; |
---|
1764 | if (b->n!=NULL) |
---|
1765 | lo->z = napCopy(b->n); |
---|
1766 | else |
---|
1767 | lo->z = napInit(1); |
---|
1768 | x = b->z; |
---|
1769 | if ((!napIsConstant(x)) || !nacIsOne(napGetCoeff(x))) |
---|
1770 | x = napCopy(x); |
---|
1771 | else |
---|
1772 | { |
---|
1773 | lo->n = NULL; |
---|
1774 | naTest((number)lo); |
---|
1775 | return (number)lo; |
---|
1776 | } |
---|
1777 | if (naMinimalPoly!=NULL) |
---|
1778 | { |
---|
1779 | x = napInvers(x, naMinimalPoly); |
---|
1780 | x = napMult(x, lo->z); |
---|
1781 | if (napGetExp(x,1) >= napGetExp(naMinimalPoly,1)) |
---|
1782 | x = napRemainder(x, naMinimalPoly); |
---|
1783 | lo->z = x; |
---|
1784 | lo->n = NULL; |
---|
1785 | lo->s = 2; |
---|
1786 | while (x!=NULL) |
---|
1787 | { |
---|
1788 | nacNormalize(napGetCoeff(x)); |
---|
1789 | napIter(x); |
---|
1790 | } |
---|
1791 | } |
---|
1792 | else |
---|
1793 | lo->n = x; |
---|
1794 | #ifdef LONGALGNEW |
---|
1795 | if (lo->n!=NULL) |
---|
1796 | { |
---|
1797 | number luu=(number)lo; |
---|
1798 | naNormalize(luu); |
---|
1799 | lo=(lnumber)luu; |
---|
1800 | } |
---|
1801 | #endif /* LONGALGNEW */ |
---|
1802 | naTest((number)lo); |
---|
1803 | return (number)lo; |
---|
1804 | } |
---|
1805 | |
---|
1806 | |
---|
1807 | BOOLEAN naIsZero(number za) |
---|
1808 | { |
---|
1809 | lnumber zb = (lnumber)za; |
---|
1810 | naTest(za); |
---|
1811 | #ifdef LDEBUG |
---|
1812 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
1813 | #endif |
---|
1814 | return ((zb==NULL) || (zb->z==NULL)); |
---|
1815 | } |
---|
1816 | |
---|
1817 | |
---|
1818 | BOOLEAN naGreaterZero(number za) |
---|
1819 | { |
---|
1820 | lnumber zb = (lnumber)za; |
---|
1821 | #ifdef LDEBUG |
---|
1822 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
1823 | #endif |
---|
1824 | naTest(za); |
---|
1825 | if ((zb!=NULL) && (zb->z!=NULL)) |
---|
1826 | { |
---|
1827 | if (zb->n!=NULL) |
---|
1828 | { |
---|
1829 | if ((napIsConstant(zb->z)) && !nacGreaterZero(napGetCoeff(zb->z))) |
---|
1830 | return FALSE; |
---|
1831 | return TRUE; |
---|
1832 | } |
---|
1833 | if ((napIsConstant(zb->z)) && !nacGreaterZero(napGetCoeff(zb->z))) |
---|
1834 | return FALSE; |
---|
1835 | } |
---|
1836 | return TRUE; |
---|
1837 | } |
---|
1838 | |
---|
1839 | |
---|
1840 | /*2 |
---|
1841 | * a = b ? |
---|
1842 | */ |
---|
1843 | BOOLEAN naEqual (number a, number b) |
---|
1844 | { |
---|
1845 | if(a==b) return TRUE; |
---|
1846 | if((a==NULL)&&(b!=NULL)) return FALSE; |
---|
1847 | if((b==NULL)&&(a!=NULL)) return FALSE; |
---|
1848 | |
---|
1849 | lnumber aa=(lnumber)a; |
---|
1850 | lnumber bb=(lnumber)b; |
---|
1851 | |
---|
1852 | int an_deg=0; |
---|
1853 | if(aa->n!=NULL) |
---|
1854 | an_deg=napDeg(aa->n); |
---|
1855 | int bn_deg=0; |
---|
1856 | if(bb->n!=NULL) |
---|
1857 | bn_deg=napDeg(bb->n); |
---|
1858 | if(an_deg+napDeg(bb->z)!=bn_deg+napDeg(aa->z)) |
---|
1859 | return FALSE; |
---|
1860 | #if 0 |
---|
1861 | naNormalize(a); |
---|
1862 | aa=(lnumber)a; |
---|
1863 | naNormalize(b); |
---|
1864 | bb=(lnumber)b; |
---|
1865 | if((aa->n==NULL)&&(bb->n!=NULL)) return FALSE; |
---|
1866 | if((bb->n==NULL)&&(aa->n!=NULL)) return FALSE; |
---|
1867 | if(napComp(aa->z,bb->z)!=0) return FALSE; |
---|
1868 | if((aa->n!=NULL) && (napComp(aa->n,bb->n))) return FALSE; |
---|
1869 | #endif |
---|
1870 | number h = naSub(a, b); |
---|
1871 | BOOLEAN bo = naIsZero(h); |
---|
1872 | naDelete(&h,currRing); |
---|
1873 | return bo; |
---|
1874 | } |
---|
1875 | |
---|
1876 | |
---|
1877 | BOOLEAN naGreater (number a, number b) |
---|
1878 | { |
---|
1879 | if (naIsZero(a)) |
---|
1880 | return FALSE; |
---|
1881 | if (naIsZero(b)) |
---|
1882 | return TRUE; /* a!= 0)*/ |
---|
1883 | return napDeg(((lnumber)a)->z)>napDeg(((lnumber)b)->z); |
---|
1884 | } |
---|
1885 | |
---|
1886 | /*2 |
---|
1887 | * reads a number |
---|
1888 | */ |
---|
1889 | char *naRead(char *s, number *p) |
---|
1890 | { |
---|
1891 | napoly x; |
---|
1892 | lnumber a; |
---|
1893 | s = napRead(s, &x); |
---|
1894 | if (x==NULL) |
---|
1895 | { |
---|
1896 | *p = NULL; |
---|
1897 | return s; |
---|
1898 | } |
---|
1899 | *p = (number)omAlloc0Bin(rnumber_bin); |
---|
1900 | a = (lnumber)*p; |
---|
1901 | if ((naMinimalPoly!=NULL) |
---|
1902 | && (napGetExp(x,1) >= napGetExp(naMinimalPoly,1))) |
---|
1903 | a->z = napRemainder(x, naMinimalPoly); |
---|
1904 | else if (naI!=NULL) |
---|
1905 | { |
---|
1906 | a->z = napRedp(x); |
---|
1907 | if (a->z != NULL) |
---|
1908 | a->z = napTailred (a->z); |
---|
1909 | } |
---|
1910 | else |
---|
1911 | a->z = x; |
---|
1912 | if(a->z==NULL) |
---|
1913 | { |
---|
1914 | omFreeBin((ADDRESS)*p, rnumber_bin); |
---|
1915 | *p=NULL; |
---|
1916 | } |
---|
1917 | else |
---|
1918 | { |
---|
1919 | a->n = NULL; |
---|
1920 | a->s = 0; |
---|
1921 | naTest(*p); |
---|
1922 | } |
---|
1923 | return s; |
---|
1924 | } |
---|
1925 | |
---|
1926 | /*2 |
---|
1927 | * tries to convert a number to a name |
---|
1928 | */ |
---|
1929 | char * naName(number n) |
---|
1930 | { |
---|
1931 | lnumber ph = (lnumber)n; |
---|
1932 | if ((ph==NULL)||(ph->z==NULL)) |
---|
1933 | return NULL; |
---|
1934 | int i; |
---|
1935 | char *s=(char *)omAlloc(4* naNumbOfPar); |
---|
1936 | char *t=(char *)omAlloc(8); |
---|
1937 | s[0]='\0'; |
---|
1938 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
1939 | { |
---|
1940 | if (napGetExp(ph->z,i+1) > 0) |
---|
1941 | { |
---|
1942 | if (napGetExp(ph->z,i+1) >1) |
---|
1943 | { |
---|
1944 | sprintf(t,"%s%d",naParNames[i],(int)napGetExp(ph->z,i+1)); |
---|
1945 | strcat(s,t); |
---|
1946 | } |
---|
1947 | else |
---|
1948 | { |
---|
1949 | strcat(s,naParNames[i]); |
---|
1950 | } |
---|
1951 | } |
---|
1952 | } |
---|
1953 | omFreeSize((ADDRESS)t,8); |
---|
1954 | if (s[0]=='\0') |
---|
1955 | { |
---|
1956 | omFree((ADDRESS)s); |
---|
1957 | return NULL; |
---|
1958 | } |
---|
1959 | return s; |
---|
1960 | } |
---|
1961 | |
---|
1962 | /*2 |
---|
1963 | * writes a number |
---|
1964 | */ |
---|
1965 | void naWrite(number &phn) |
---|
1966 | { |
---|
1967 | lnumber ph = (lnumber)phn; |
---|
1968 | if ((ph==NULL)||(ph->z==NULL)) |
---|
1969 | StringAppendS("0"); |
---|
1970 | else |
---|
1971 | { |
---|
1972 | phn->s = 0; |
---|
1973 | naNormalize(phn); |
---|
1974 | BOOLEAN has_denom=(ph->n!=NULL); |
---|
1975 | napWrite(ph->z,has_denom/*(ph->n!=NULL)*/); |
---|
1976 | if (has_denom/*(ph->n!=NULL)*/) |
---|
1977 | { |
---|
1978 | StringAppendS("/"); |
---|
1979 | napWrite(ph->n,TRUE); |
---|
1980 | } |
---|
1981 | } |
---|
1982 | } |
---|
1983 | |
---|
1984 | /*2 |
---|
1985 | * za == 1 ? |
---|
1986 | */ |
---|
1987 | BOOLEAN naIsOne(number za) |
---|
1988 | { |
---|
1989 | lnumber a = (lnumber)za; |
---|
1990 | napoly x, y; |
---|
1991 | number t; |
---|
1992 | if (a==NULL) return FALSE; |
---|
1993 | omCheckAddrSize(a,sizeof(snumber)); |
---|
1994 | #ifdef LDEBUG |
---|
1995 | if (a->z==NULL) WerrorS("internal zero error(4)"); |
---|
1996 | #endif |
---|
1997 | if (a->n==NULL) |
---|
1998 | { |
---|
1999 | if (napIsConstant(a->z)) return nacIsOne(napGetCoeff(a->z)); |
---|
2000 | else return FALSE; |
---|
2001 | } |
---|
2002 | x = a->z; |
---|
2003 | y = a->n; |
---|
2004 | do |
---|
2005 | { |
---|
2006 | if (napComp(x, y)) |
---|
2007 | return FALSE; |
---|
2008 | else |
---|
2009 | { |
---|
2010 | t = nacSub(napGetCoeff(x), napGetCoeff(y)); |
---|
2011 | if (!nacIsZero(t)) |
---|
2012 | { |
---|
2013 | nacDelete(&t,nacRing); |
---|
2014 | return FALSE; |
---|
2015 | } |
---|
2016 | else |
---|
2017 | nacDelete(&t,nacRing); |
---|
2018 | } |
---|
2019 | napIter(x); |
---|
2020 | napIter(y); |
---|
2021 | } |
---|
2022 | while ((x!=NULL) && (y!=NULL)); |
---|
2023 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
2024 | napDelete(&a->z); |
---|
2025 | napDelete(&a->n); |
---|
2026 | a->z = napInit(1); |
---|
2027 | a->n = NULL; |
---|
2028 | a->s = 2; |
---|
2029 | return TRUE; |
---|
2030 | } |
---|
2031 | |
---|
2032 | /*2 |
---|
2033 | * za == -1 ? |
---|
2034 | */ |
---|
2035 | BOOLEAN naIsMOne(number za) |
---|
2036 | { |
---|
2037 | lnumber a = (lnumber)za; |
---|
2038 | napoly x, y; |
---|
2039 | number t; |
---|
2040 | if (a==NULL) return FALSE; |
---|
2041 | omCheckAddrSize(a,sizeof(snumber)); |
---|
2042 | #ifdef LDEBUG |
---|
2043 | if (a->z==NULL) |
---|
2044 | { |
---|
2045 | WerrorS("internal zero error(5)"); |
---|
2046 | return FALSE; |
---|
2047 | } |
---|
2048 | #endif |
---|
2049 | if (a->n==NULL) |
---|
2050 | { |
---|
2051 | if (napIsConstant(a->z)) return nacIsMOne(napGetCoeff(a->z)); |
---|
2052 | /*else return FALSE;*/ |
---|
2053 | } |
---|
2054 | return FALSE; |
---|
2055 | } |
---|
2056 | |
---|
2057 | /*2 |
---|
2058 | * returns the i-th power of p (i>=0) |
---|
2059 | */ |
---|
2060 | void naPower(number p, int i, number *rc) |
---|
2061 | { |
---|
2062 | number x; |
---|
2063 | *rc = naInit(1); |
---|
2064 | for (; i > 0; i--) |
---|
2065 | { |
---|
2066 | x = naMult(*rc, p); |
---|
2067 | naDelete(rc,currRing); |
---|
2068 | *rc = x; |
---|
2069 | } |
---|
2070 | } |
---|
2071 | |
---|
2072 | /*2 |
---|
2073 | * result =gcd(a,b) |
---|
2074 | */ |
---|
2075 | number naGcd(number a, number b, const ring r) |
---|
2076 | { |
---|
2077 | lnumber x, y; |
---|
2078 | lnumber result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
2079 | |
---|
2080 | x = (lnumber)a; |
---|
2081 | y = (lnumber)b; |
---|
2082 | if (naNumbOfPar == 1) |
---|
2083 | { |
---|
2084 | if (naMinimalPoly!=NULL) |
---|
2085 | { |
---|
2086 | if (napNext(x->z)!=NULL) |
---|
2087 | result->z = napCopy(x->z); |
---|
2088 | else |
---|
2089 | result->z = napGcd0(x->z, y->z); |
---|
2090 | } |
---|
2091 | else |
---|
2092 | result->z = napGcd(x->z, y->z); |
---|
2093 | } |
---|
2094 | else |
---|
2095 | result->z = napGcd(x->z, y->z); // change from napGcd0 |
---|
2096 | naTest((number)result); |
---|
2097 | return (number)result; |
---|
2098 | } |
---|
2099 | |
---|
2100 | /*2 |
---|
2101 | * naNumbOfPar = 1: |
---|
2102 | * clears denominator algebraic case; |
---|
2103 | * tries to simplify ratio transcendental case; |
---|
2104 | * |
---|
2105 | * cancels monomials |
---|
2106 | * occuring in denominator |
---|
2107 | * and enumerator ? naNumbOfPar != 1; |
---|
2108 | * |
---|
2109 | * #defines for Factory: |
---|
2110 | * FACTORY_GCD_TEST: do not apply built in gcd for |
---|
2111 | * univariate polynomials, always use Factory |
---|
2112 | */ |
---|
2113 | void naNormalize(number &pp) |
---|
2114 | { |
---|
2115 | |
---|
2116 | //naTest(pp); // input may not be "normal" |
---|
2117 | lnumber p = (lnumber)pp; |
---|
2118 | |
---|
2119 | if ((p==NULL) /*|| (p->s==2)*/) |
---|
2120 | return; |
---|
2121 | p->s = 2; |
---|
2122 | napoly x = p->z; |
---|
2123 | napoly y = p->n; |
---|
2124 | if ((y!=NULL) && (naMinimalPoly!=NULL)) |
---|
2125 | { |
---|
2126 | y = napInvers(y, naMinimalPoly); |
---|
2127 | x = napMult(x, y); |
---|
2128 | if (napGetExp(x,1) >= napGetExp(naMinimalPoly,1)) |
---|
2129 | x = napRemainder(x, naMinimalPoly); |
---|
2130 | p->z = x; |
---|
2131 | p->n = y = NULL; |
---|
2132 | } |
---|
2133 | /* check for degree of x too high: */ |
---|
2134 | if ((x!=NULL) && (naMinimalPoly!=NULL) && (x!=naMinimalPoly) |
---|
2135 | && (napGetExp(x,1)>napGetExp(naMinimalPoly,1))) |
---|
2136 | // DO NOT REDUCE naMinimalPoly with itself |
---|
2137 | { |
---|
2138 | x = napRemainder(x, naMinimalPoly); |
---|
2139 | p->z = x; |
---|
2140 | } |
---|
2141 | /* normalize all coefficients in n and z (if in Q) */ |
---|
2142 | if (naIsChar0) |
---|
2143 | { |
---|
2144 | while(x!=NULL) |
---|
2145 | { |
---|
2146 | nacNormalize(napGetCoeff(x)); |
---|
2147 | napIter(x); |
---|
2148 | } |
---|
2149 | x = p->z; |
---|
2150 | } |
---|
2151 | if (y==NULL) return; |
---|
2152 | if (naIsChar0) |
---|
2153 | { |
---|
2154 | while(y!=NULL) |
---|
2155 | { |
---|
2156 | nacNormalize(napGetCoeff(y)); |
---|
2157 | napIter(y); |
---|
2158 | } |
---|
2159 | y = p->n; |
---|
2160 | } |
---|
2161 | // p->n !=NULL: |
---|
2162 | /* collect all denoms from y and multiply x and y by it */ |
---|
2163 | if (naIsChar0) |
---|
2164 | { |
---|
2165 | number n=napLcm(y); |
---|
2166 | napMultN(x,n); |
---|
2167 | napMultN(y,n); |
---|
2168 | nacDelete(&n,nacRing); |
---|
2169 | while(x!=NULL) |
---|
2170 | { |
---|
2171 | nacNormalize(napGetCoeff(x)); |
---|
2172 | napIter(x); |
---|
2173 | } |
---|
2174 | x = p->z; |
---|
2175 | while(y!=NULL) |
---|
2176 | { |
---|
2177 | nacNormalize(napGetCoeff(y)); |
---|
2178 | napIter(y); |
---|
2179 | } |
---|
2180 | y = p->n; |
---|
2181 | } |
---|
2182 | if (naMinimalPoly == NULL) |
---|
2183 | { |
---|
2184 | int i; |
---|
2185 | for (i=naNumbOfPar-1; i>=0; i--) |
---|
2186 | { |
---|
2187 | napoly xx=x; |
---|
2188 | napoly yy=y; |
---|
2189 | int m = napExpi(i, yy, xx); |
---|
2190 | if (m != 0) // in this case xx!=NULL!=yy |
---|
2191 | { |
---|
2192 | while (xx != NULL) |
---|
2193 | { |
---|
2194 | napAddExp(xx,i+1, -m); |
---|
2195 | napIter(xx); |
---|
2196 | } |
---|
2197 | while (yy != NULL) |
---|
2198 | { |
---|
2199 | napAddExp(yy,i+1, -m); |
---|
2200 | napIter(yy); |
---|
2201 | } |
---|
2202 | } |
---|
2203 | } |
---|
2204 | } |
---|
2205 | if (napIsConstant(y)) /* i.e. => simplify to (1/c)*z / monom */ |
---|
2206 | { |
---|
2207 | if (nacIsOne(napGetCoeff(y))) |
---|
2208 | { |
---|
2209 | napDelete1(&y); |
---|
2210 | p->n = NULL; |
---|
2211 | naTest(pp); |
---|
2212 | return; |
---|
2213 | } |
---|
2214 | number h1 = nacInvers(napGetCoeff(y)); |
---|
2215 | nacNormalize(h1); |
---|
2216 | napMultN(x, h1); |
---|
2217 | nacDelete(&h1,nacRing); |
---|
2218 | napDelete1(&y); |
---|
2219 | p->n = NULL; |
---|
2220 | naTest(pp); |
---|
2221 | return; |
---|
2222 | } |
---|
2223 | #ifndef FACTORY_GCD_TEST |
---|
2224 | if (naNumbOfPar == 1) /* apply built-in gcd */ |
---|
2225 | { |
---|
2226 | napoly x1,y1; |
---|
2227 | if (napGetExp(x,1) >= napGetExp(y,1)) |
---|
2228 | { |
---|
2229 | x1 = napCopy(x); |
---|
2230 | y1 = napCopy(y); |
---|
2231 | } |
---|
2232 | else |
---|
2233 | { |
---|
2234 | x1 = napCopy(y); |
---|
2235 | y1 = napCopy(x); |
---|
2236 | } |
---|
2237 | napoly r; |
---|
2238 | loop |
---|
2239 | { |
---|
2240 | r = napRemainder(x1, y1); |
---|
2241 | if ((r==NULL) || (napNext(r)==NULL)) break; |
---|
2242 | x1 = y1; |
---|
2243 | y1 = r; |
---|
2244 | } |
---|
2245 | if (r!=NULL) |
---|
2246 | { |
---|
2247 | napDelete(&r); |
---|
2248 | napDelete(&y1); |
---|
2249 | } |
---|
2250 | else |
---|
2251 | { |
---|
2252 | napDivMod(x, y1, &(p->z), &r); |
---|
2253 | napDivMod(y, y1, &(p->n), &r); |
---|
2254 | napDelete(&y1); |
---|
2255 | } |
---|
2256 | x = p->z; |
---|
2257 | y = p->n; |
---|
2258 | /* collect all denoms from y and multiply x and y by it */ |
---|
2259 | if (naIsChar0) |
---|
2260 | { |
---|
2261 | number n=napLcm(y); |
---|
2262 | napMultN(x,n); |
---|
2263 | napMultN(y,n); |
---|
2264 | nacDelete(&n,nacRing); |
---|
2265 | while(x!=NULL) |
---|
2266 | { |
---|
2267 | nacNormalize(napGetCoeff(x)); |
---|
2268 | napIter(x); |
---|
2269 | } |
---|
2270 | x = p->z; |
---|
2271 | while(y!=NULL) |
---|
2272 | { |
---|
2273 | nacNormalize(napGetCoeff(y)); |
---|
2274 | napIter(y); |
---|
2275 | } |
---|
2276 | y = p->n; |
---|
2277 | } |
---|
2278 | if (napNext(y)==NULL) |
---|
2279 | { |
---|
2280 | if (nacIsOne(napGetCoeff(y))) |
---|
2281 | { |
---|
2282 | if (napGetExp(y,1)==0) |
---|
2283 | { |
---|
2284 | napDelete1(&y); |
---|
2285 | p->n = NULL; |
---|
2286 | } |
---|
2287 | naTest(pp); |
---|
2288 | return; |
---|
2289 | } |
---|
2290 | } |
---|
2291 | } |
---|
2292 | #endif /* FACTORY_GCD_TEST */ |
---|
2293 | #ifdef HAVE_FACTORY |
---|
2294 | #ifndef FACTORY_GCD_TEST |
---|
2295 | else |
---|
2296 | #endif |
---|
2297 | { |
---|
2298 | napoly xx,yy; |
---|
2299 | singclap_algdividecontent(x,y,xx,yy); |
---|
2300 | if (xx!=NULL) |
---|
2301 | { |
---|
2302 | p->z=xx; |
---|
2303 | p->n=yy; |
---|
2304 | napDelete(&x); |
---|
2305 | napDelete(&y); |
---|
2306 | } |
---|
2307 | } |
---|
2308 | #endif |
---|
2309 | /* remove common factors from z and n */ |
---|
2310 | x=p->z; |
---|
2311 | y=p->n; |
---|
2312 | if(!nacGreaterZero(napGetCoeff(y))) |
---|
2313 | { |
---|
2314 | x=napNeg(x); |
---|
2315 | y=napNeg(y); |
---|
2316 | } |
---|
2317 | number g=nacCopy(napGetCoeff(x)); |
---|
2318 | napIter(x); |
---|
2319 | while (x!=NULL) |
---|
2320 | { |
---|
2321 | number d=nacGcd(g,napGetCoeff(x), nacRing); |
---|
2322 | if(nacIsOne(d)) |
---|
2323 | { |
---|
2324 | nacDelete(&g,nacRing); |
---|
2325 | nacDelete(&d,nacRing); |
---|
2326 | naTest(pp); |
---|
2327 | return; |
---|
2328 | } |
---|
2329 | nacDelete(&g,nacRing); |
---|
2330 | g = d; |
---|
2331 | napIter(x); |
---|
2332 | } |
---|
2333 | while (y!=NULL) |
---|
2334 | { |
---|
2335 | number d=nacGcd(g,napGetCoeff(y), nacRing); |
---|
2336 | if(nacIsOne(d)) |
---|
2337 | { |
---|
2338 | nacDelete(&g,nacRing); |
---|
2339 | nacDelete(&d,nacRing); |
---|
2340 | naTest(pp); |
---|
2341 | return; |
---|
2342 | } |
---|
2343 | nacDelete(&g,nacRing); |
---|
2344 | g = d; |
---|
2345 | napIter(y); |
---|
2346 | } |
---|
2347 | x=p->z; |
---|
2348 | y=p->n; |
---|
2349 | while (x!=NULL) |
---|
2350 | { |
---|
2351 | number d = nacIntDiv(napGetCoeff(x),g); |
---|
2352 | napSetCoeff(x,d); |
---|
2353 | napIter(x); |
---|
2354 | } |
---|
2355 | while (y!=NULL) |
---|
2356 | { |
---|
2357 | number d = nacIntDiv(napGetCoeff(y),g); |
---|
2358 | napSetCoeff(y,d); |
---|
2359 | napIter(y); |
---|
2360 | } |
---|
2361 | nacDelete(&g,nacRing); |
---|
2362 | naTest(pp); |
---|
2363 | } |
---|
2364 | |
---|
2365 | /*2 |
---|
2366 | * returns in result->n 1 |
---|
2367 | * and in result->z the lcm(a->z,b->n) |
---|
2368 | */ |
---|
2369 | number naLcm(number la, number lb, const ring r) |
---|
2370 | { |
---|
2371 | lnumber result; |
---|
2372 | lnumber a = (lnumber)la; |
---|
2373 | lnumber b = (lnumber)lb; |
---|
2374 | result = (lnumber)omAlloc0Bin(rnumber_bin); |
---|
2375 | //if (((naMinimalPoly==NULL) && (naI==NULL)) || !naIsChar0) |
---|
2376 | //{ |
---|
2377 | // result->z = napInit(1); |
---|
2378 | // return (number)result; |
---|
2379 | //} |
---|
2380 | naNormalize(lb); |
---|
2381 | naTest(la); |
---|
2382 | naTest(lb); |
---|
2383 | napoly x = napCopy(a->z); |
---|
2384 | number t = napLcm(b->z); // get all denom of b->z |
---|
2385 | if (!nacIsOne(t)) |
---|
2386 | { |
---|
2387 | number bt, r; |
---|
2388 | napoly xx=x; |
---|
2389 | while (xx!=NULL) |
---|
2390 | { |
---|
2391 | bt = nacGcd(t, napGetCoeff(xx), nacRing); |
---|
2392 | r = nacMult(t, napGetCoeff(xx)); |
---|
2393 | nacDelete(&napGetCoeff(xx),nacRing); |
---|
2394 | napGetCoeff(xx) = nacDiv(r, bt); |
---|
2395 | nacNormalize(napGetCoeff(xx)); |
---|
2396 | nacDelete(&bt,nacRing); |
---|
2397 | nacDelete(&r,nacRing); |
---|
2398 | napIter(xx); |
---|
2399 | } |
---|
2400 | } |
---|
2401 | nacDelete(&t,nacRing); |
---|
2402 | result->z = x; |
---|
2403 | #ifdef HAVE_FACTORY |
---|
2404 | if (b->n!=NULL) |
---|
2405 | { |
---|
2406 | result->z=singclap_alglcm(result->z,b->n); |
---|
2407 | napDelete(&x); |
---|
2408 | } |
---|
2409 | #endif |
---|
2410 | naTest(la); |
---|
2411 | naTest(lb); |
---|
2412 | naTest((number)result); |
---|
2413 | return ((number)result); |
---|
2414 | } |
---|
2415 | |
---|
2416 | /*2 |
---|
2417 | * input: a set of constant polynomials |
---|
2418 | * sets the global variable naI |
---|
2419 | */ |
---|
2420 | void naSetIdeal(ideal I) |
---|
2421 | { |
---|
2422 | int i; |
---|
2423 | |
---|
2424 | if (idIs0(I)) |
---|
2425 | { |
---|
2426 | for (i=naI->anz-1; i>=0; i--) |
---|
2427 | napDelete(&naI->liste[i]); |
---|
2428 | omFreeBin((ADDRESS)naI, snaIdeal_bin); |
---|
2429 | naI=NULL; |
---|
2430 | } |
---|
2431 | else |
---|
2432 | { |
---|
2433 | lnumber h; |
---|
2434 | number a; |
---|
2435 | napoly x; |
---|
2436 | |
---|
2437 | naI=(naIdeal)omAllocBin(snaIdeal_bin); |
---|
2438 | naI->anz=IDELEMS(I); |
---|
2439 | naI->liste=(napoly*)omAlloc(naI->anz*sizeof(napoly)); |
---|
2440 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
2441 | { |
---|
2442 | h=(lnumber)pGetCoeff(I->m[i]); |
---|
2443 | /* We only need the enumerator of h, as we expect it to be a polynomial */ |
---|
2444 | naI->liste[i]=napCopy(h->z); |
---|
2445 | /* If it isn't normalized (lc = 1) do this */ |
---|
2446 | if (!nacIsOne(napGetCoeff(naI->liste[i]))) |
---|
2447 | { |
---|
2448 | x=naI->liste[i]; |
---|
2449 | nacNormalize(napGetCoeff(x)); |
---|
2450 | a=nacCopy(napGetCoeff(x)); |
---|
2451 | number aa=nacInvers(a); |
---|
2452 | nacDelete(&a,nacRing); |
---|
2453 | napMultN(x,aa); |
---|
2454 | nacDelete(&aa,nacRing); |
---|
2455 | } |
---|
2456 | } |
---|
2457 | } |
---|
2458 | } |
---|
2459 | |
---|
2460 | /*2 |
---|
2461 | * map Z/p -> Q(a) |
---|
2462 | */ |
---|
2463 | number naMapP0(number c) |
---|
2464 | { |
---|
2465 | if (npIsZero(c)) return NULL; |
---|
2466 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2467 | l->s=2; |
---|
2468 | #ifndef LONGALGNEW |
---|
2469 | l->z=(napoly)omAlloc0(napMonomSize); |
---|
2470 | #else /* LONGALGNEW */ |
---|
2471 | l->z=(napoly)p_Init(nacRing); |
---|
2472 | #endif /* LONGALGNEW */ |
---|
2473 | int i=(int)c; |
---|
2474 | if (i>(naPrimeM>>2)) i-=naPrimeM; |
---|
2475 | napGetCoeff(l->z)=nlInit(i); |
---|
2476 | l->n=NULL; |
---|
2477 | return (number)l; |
---|
2478 | } |
---|
2479 | |
---|
2480 | /*2 |
---|
2481 | * map Q -> Q(a) |
---|
2482 | */ |
---|
2483 | number naMap00(number c) |
---|
2484 | { |
---|
2485 | if (nlIsZero(c)) return NULL; |
---|
2486 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2487 | l->s=0; |
---|
2488 | #ifndef LONGALGNEW |
---|
2489 | l->z=(napoly)omAlloc0(napMonomSize); |
---|
2490 | #else /* LONGALGNEW */ |
---|
2491 | l->z=(napoly)p_Init(nacRing); |
---|
2492 | #endif /* LONGALGNEW */ |
---|
2493 | napGetCoeff(l->z)=nlCopy(c); |
---|
2494 | l->n=NULL; |
---|
2495 | return (number)l; |
---|
2496 | } |
---|
2497 | |
---|
2498 | /*2 |
---|
2499 | * map Z/p -> Z/p(a) |
---|
2500 | */ |
---|
2501 | number naMapPP(number c) |
---|
2502 | { |
---|
2503 | if (npIsZero(c)) return NULL; |
---|
2504 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2505 | l->s=2; |
---|
2506 | #ifndef LONGALGNEW |
---|
2507 | l->z=(napoly)omAlloc0(napMonomSize); |
---|
2508 | #else /* LONGALGNEW */ |
---|
2509 | l->z=(napoly)p_Init(nacRing); |
---|
2510 | #endif /* LONGALGNEW */ |
---|
2511 | napGetCoeff(l->z)=c; /* omit npCopy, because npCopy is a no-op */ |
---|
2512 | l->n=NULL; |
---|
2513 | return (number)l; |
---|
2514 | } |
---|
2515 | |
---|
2516 | /*2 |
---|
2517 | * map Z/p' -> Z/p(a) |
---|
2518 | */ |
---|
2519 | number naMapPP1(number c) |
---|
2520 | { |
---|
2521 | if (npIsZero(c)) return NULL; |
---|
2522 | int i=(int)c; |
---|
2523 | if (i>naPrimeM) i-=naPrimeM; |
---|
2524 | number n=npInit(i); |
---|
2525 | if (npIsZero(n)) return NULL; |
---|
2526 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2527 | l->s=2; |
---|
2528 | #ifndef LONGALGNEW |
---|
2529 | l->z=(napoly)omAlloc0(napMonomSize); |
---|
2530 | #else /* LONGALGNEW */ |
---|
2531 | l->z=(napoly)p_Init(nacRing); |
---|
2532 | #endif /* LONGALGNEW */ |
---|
2533 | napGetCoeff(l->z)=n; |
---|
2534 | l->n=NULL; |
---|
2535 | return (number)l; |
---|
2536 | } |
---|
2537 | |
---|
2538 | /*2 |
---|
2539 | * map Q -> Z/p(a) |
---|
2540 | */ |
---|
2541 | number naMap0P(number c) |
---|
2542 | { |
---|
2543 | if (nlIsZero(c)) return NULL; |
---|
2544 | number n=npInit(nlInt(c)); |
---|
2545 | if (npIsZero(n)) return NULL; |
---|
2546 | lnumber l=(lnumber)omAllocBin(rnumber_bin); |
---|
2547 | l->s=2; |
---|
2548 | #ifndef LONGALGNEW |
---|
2549 | l->z=(napoly)omAlloc0(napMonomSize); |
---|
2550 | #else /* LONGALGNEW */ |
---|
2551 | l->z=(napoly)p_Init(nacRing); |
---|
2552 | #endif /* LONGALGNEW */ |
---|
2553 | napGetCoeff(l->z)=n; |
---|
2554 | l->n=NULL; |
---|
2555 | return (number)l; |
---|
2556 | } |
---|
2557 | |
---|
2558 | static number (*nacMap)(number); |
---|
2559 | static int naParsToCopy; |
---|
2560 | #ifdef LONGALGNEW |
---|
2561 | static ring napMapRing; |
---|
2562 | #endif /* LONGALGNEW */ |
---|
2563 | static napoly napMap(napoly p) |
---|
2564 | { |
---|
2565 | napoly w, a; |
---|
2566 | |
---|
2567 | if (p==NULL) return NULL; |
---|
2568 | #ifndef LONGALGNEW |
---|
2569 | a = w = (napoly)omAlloc0(napMonomSize); |
---|
2570 | memcpy4(a->e, p->e, naParsToCopy * SIZEOF_PARAMETER); |
---|
2571 | w->ko = nacMap(p->ko); |
---|
2572 | #else /* LONGALGNEW */ |
---|
2573 | a = w = (napoly)p_Init(nacRing); |
---|
2574 | int i; |
---|
2575 | for(i=1;i<=naParsToCopy;i++) |
---|
2576 | napSetExp(a,i,napGetExpFrom(p,i,napMapRing)); |
---|
2577 | p_Setm(a,nacRing); |
---|
2578 | napGetCoeff(w) = nacMap(napGetCoeff(p)); |
---|
2579 | #endif /* LONGALGNEW */ |
---|
2580 | loop |
---|
2581 | { |
---|
2582 | napIter(p); |
---|
2583 | if (p==NULL) break; |
---|
2584 | #ifndef LONGALGNEW |
---|
2585 | a->ne = (napoly)omAlloc0(napMonomSize); |
---|
2586 | a = a->ne; |
---|
2587 | memcpy4(a->e, p->e, naParsToCopy * SIZEOF_PARAMETER); |
---|
2588 | #else /* LONGALGNEW */ |
---|
2589 | napNext(a) = (napoly)p_Init(nacRing); |
---|
2590 | napIter(a); |
---|
2591 | for(i=1;i<=naParsToCopy;i++) |
---|
2592 | napSetExp(a,i,napGetExpFrom(p,i,napMapRing)); |
---|
2593 | p_Setm(a,nacRing); |
---|
2594 | #endif /* LONGALGNEW */ |
---|
2595 | napGetCoeff(a) = nacMap(napGetCoeff(p)); |
---|
2596 | } |
---|
2597 | napNext(a) = NULL; |
---|
2598 | return w; |
---|
2599 | } |
---|
2600 | |
---|
2601 | static napoly napPerm(napoly p,const int *par_perm,const ring src_ring,const nMapFunc nMap) |
---|
2602 | { |
---|
2603 | napoly w, a; |
---|
2604 | |
---|
2605 | if (p==NULL) return NULL; |
---|
2606 | w = (napoly)p_Init(nacRing); |
---|
2607 | int i; |
---|
2608 | BOOLEAN not_null=TRUE; |
---|
2609 | loop |
---|
2610 | { |
---|
2611 | for(i=1;i<=rPar(src_ring);i++) |
---|
2612 | { |
---|
2613 | int e; |
---|
2614 | if (par_perm!=NULL) e=par_perm[i-1]; |
---|
2615 | else e=-i; |
---|
2616 | int ee=napGetExpFrom(p,i,src_ring); |
---|
2617 | if (e<0) |
---|
2618 | napSetExp(w,-e,ee); |
---|
2619 | else if (ee>0) |
---|
2620 | not_null=FALSE; |
---|
2621 | } |
---|
2622 | napGetCoeff(w) = nMap(napGetCoeff(p)); |
---|
2623 | p_Setm(w,nacRing); |
---|
2624 | napIter(p); |
---|
2625 | if (!not_null) |
---|
2626 | { |
---|
2627 | if (p==NULL) |
---|
2628 | { |
---|
2629 | napDelete(&w); |
---|
2630 | return NULL; |
---|
2631 | } |
---|
2632 | /* else continue*/ |
---|
2633 | nacDelete(&(napGetCoeff(w)),nacRing); |
---|
2634 | } |
---|
2635 | else |
---|
2636 | { |
---|
2637 | if (p==NULL) return w; |
---|
2638 | else |
---|
2639 | { |
---|
2640 | napNext(w)=napPerm(p,par_perm,src_ring,nMap); |
---|
2641 | return w; |
---|
2642 | } |
---|
2643 | } |
---|
2644 | } |
---|
2645 | } |
---|
2646 | |
---|
2647 | /*2 |
---|
2648 | * map _(a) -> _(b) |
---|
2649 | */ |
---|
2650 | number naMapQaQb(number c) |
---|
2651 | { |
---|
2652 | if (c==NULL) return NULL; |
---|
2653 | lnumber erg= (lnumber)omAlloc0Bin(rnumber_bin); |
---|
2654 | lnumber src =(lnumber)c; |
---|
2655 | erg->s=src->s; |
---|
2656 | erg->z=napMap(src->z); |
---|
2657 | erg->n=napMap(src->n); |
---|
2658 | if (naMinimalPoly!=NULL) |
---|
2659 | { |
---|
2660 | if (napGetExp(erg->z,1) >= napGetExp(naMinimalPoly,1)) |
---|
2661 | { |
---|
2662 | erg->z = napRemainder(erg->z, naMinimalPoly); |
---|
2663 | if (erg->z==NULL) |
---|
2664 | { |
---|
2665 | number t_erg=(number)erg; |
---|
2666 | naDelete(&t_erg,currRing); |
---|
2667 | return (number)NULL; |
---|
2668 | } |
---|
2669 | } |
---|
2670 | if (erg->n!=NULL) |
---|
2671 | { |
---|
2672 | if (napGetExp(erg->n,1) >= napGetExp(naMinimalPoly,1)) |
---|
2673 | erg->n = napRemainder(erg->n, naMinimalPoly); |
---|
2674 | #ifndef LONGALGNEW |
---|
2675 | if ((napDeg(erg->n)==0) && nacIsOne(erg->n->ko)) |
---|
2676 | #else /* LONGALGNEW */ |
---|
2677 | if ((napIsConstant(erg->n)) && nacIsOne(napGetCoeff(erg->n))) |
---|
2678 | #endif /* LONGALGNEW */ |
---|
2679 | napDelete(&(erg->n)); |
---|
2680 | } |
---|
2681 | } |
---|
2682 | return (number)erg; |
---|
2683 | } |
---|
2684 | |
---|
2685 | nMapFunc naSetMap(ring src, ring dst) |
---|
2686 | { |
---|
2687 | if (rField_is_Q_a(dst)) /* -> Q(a) */ |
---|
2688 | { |
---|
2689 | if (rField_is_Q(src)) |
---|
2690 | { |
---|
2691 | return naMap00; /*Q -> Q(a)*/ |
---|
2692 | } |
---|
2693 | if (rField_is_Zp(src)) |
---|
2694 | { |
---|
2695 | naPrimeM = rChar(src); |
---|
2696 | return naMapP0; /* Z/p -> Q(a)*/ |
---|
2697 | } |
---|
2698 | if (rField_is_Q_a(src)) |
---|
2699 | { |
---|
2700 | int i; |
---|
2701 | naParsToCopy=0; |
---|
2702 | for(i=0;i<rPar(src);i++) |
---|
2703 | { |
---|
2704 | if ((i>=rPar(dst)) |
---|
2705 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
2706 | return NULL; |
---|
2707 | naParsToCopy++; |
---|
2708 | } |
---|
2709 | #ifdef LONGALGNEW |
---|
2710 | napMapRing=src; |
---|
2711 | #endif /* LONGALGNEW */ |
---|
2712 | nacMap=nacCopy; |
---|
2713 | return naMapQaQb; /* Q(a) -> Q(a) */ |
---|
2714 | } |
---|
2715 | } |
---|
2716 | /*-----------------------------------------------------*/ |
---|
2717 | if (rField_is_Zp_a(dst)) /* -> Z/p(a) */ |
---|
2718 | { |
---|
2719 | if (rField_is_Q(src)) |
---|
2720 | { |
---|
2721 | return naMap0P; /*Q -> Z/p(a)*/ |
---|
2722 | } |
---|
2723 | if (rField_is_Zp(src)) |
---|
2724 | { |
---|
2725 | int c=rChar(src); |
---|
2726 | if (c==npPrimeM) |
---|
2727 | { |
---|
2728 | return naMapPP; /* Z/p -> Z/p(a)*/ |
---|
2729 | } |
---|
2730 | else |
---|
2731 | { |
---|
2732 | naPrimeM = c; |
---|
2733 | return naMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
2734 | } |
---|
2735 | } |
---|
2736 | if (rField_is_Zp_a(src)) |
---|
2737 | { |
---|
2738 | if (rChar(src)==rChar(dst)) |
---|
2739 | { |
---|
2740 | nacMap=nacCopy; |
---|
2741 | } |
---|
2742 | else |
---|
2743 | { |
---|
2744 | npMapPrime=rChar(src); |
---|
2745 | nacMap = npMapP; |
---|
2746 | } |
---|
2747 | int i; |
---|
2748 | naParsToCopy=0; |
---|
2749 | for(i=0;i<rPar(src);i++) |
---|
2750 | { |
---|
2751 | if ((i>=rPar(dst)) |
---|
2752 | ||(strcmp(src->parameter[i],dst->parameter[i])!=0)) |
---|
2753 | return NULL; |
---|
2754 | naParsToCopy++; |
---|
2755 | } |
---|
2756 | #ifdef LONGALGNEW |
---|
2757 | napMapRing=src; |
---|
2758 | #endif /* LONGALGNEW */ |
---|
2759 | return naMapQaQb; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
2760 | } |
---|
2761 | } |
---|
2762 | return NULL; /* default */ |
---|
2763 | } |
---|
2764 | |
---|
2765 | /*2 |
---|
2766 | * convert a napoly number into a poly |
---|
2767 | */ |
---|
2768 | poly naPermNumber(number z, int * par_perm, int P, ring r) |
---|
2769 | { |
---|
2770 | if (z==NULL) return NULL; |
---|
2771 | poly res=NULL; |
---|
2772 | poly p; |
---|
2773 | napoly za=((lnumber)z)->z; |
---|
2774 | napoly zb=((lnumber)z)->n; |
---|
2775 | nMapFunc nMap=naSetMap(r,currRing); |
---|
2776 | if (currRing->parameter!=NULL) |
---|
2777 | nMap=currRing->algring->cf->cfSetMap(r->algring, nacRing); |
---|
2778 | else |
---|
2779 | nMap=currRing->cf->cfSetMap(r->algring, currRing); |
---|
2780 | if (nMap==NULL) return NULL; /* emergency exit only */ |
---|
2781 | do |
---|
2782 | { |
---|
2783 | p = pInit(); |
---|
2784 | pNext(p)=NULL; |
---|
2785 | nNew(&pGetCoeff(p)); |
---|
2786 | int i; |
---|
2787 | for(i=pVariables;i;i--) |
---|
2788 | pSetExp(p,i, 0); |
---|
2789 | pSetComp(p, 0); |
---|
2790 | napoly pa=NULL; |
---|
2791 | lnumber pan; |
---|
2792 | if (currRing->parameter!=NULL) |
---|
2793 | { |
---|
2794 | assume(r->algring!=NULL); |
---|
2795 | pGetCoeff(p)=(number)omAlloc0Bin(rnumber_bin); |
---|
2796 | pan=(lnumber)pGetCoeff(p); |
---|
2797 | pan->s=2; |
---|
2798 | pan->z=napInitz(nMap(napGetCoeff(za))); |
---|
2799 | pa=pan->z; |
---|
2800 | } |
---|
2801 | else |
---|
2802 | { |
---|
2803 | pGetCoeff(p)=nMap(napGetCoeff(za)); |
---|
2804 | } |
---|
2805 | for(i=0;i<P;i++) |
---|
2806 | { |
---|
2807 | if(napGetExpFrom(za,i+1,r)!=0) |
---|
2808 | { |
---|
2809 | if(par_perm==NULL) |
---|
2810 | { |
---|
2811 | if ((rPar(currRing)>=i) && (pa!=NULL)) |
---|
2812 | { |
---|
2813 | napSetExp(pa,i+1,napGetExpFrom(za,i+1,r)); |
---|
2814 | p_Setm(pa,nacRing); |
---|
2815 | } |
---|
2816 | else |
---|
2817 | { |
---|
2818 | pDelete(&p); |
---|
2819 | break; |
---|
2820 | } |
---|
2821 | } |
---|
2822 | else if(par_perm[i]>0) |
---|
2823 | pSetExp(p,par_perm[i],napGetExpFrom(za,i+1,r)); |
---|
2824 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
2825 | { |
---|
2826 | napSetExp(pa,-par_perm[i], napGetExpFrom(za,i+1,r)); |
---|
2827 | p_Setm(pa,nacRing); |
---|
2828 | } |
---|
2829 | else |
---|
2830 | { |
---|
2831 | pDelete(&p); |
---|
2832 | break; |
---|
2833 | } |
---|
2834 | } |
---|
2835 | } |
---|
2836 | if (p!=NULL) |
---|
2837 | { |
---|
2838 | pSetm(p); |
---|
2839 | if (zb!=NULL) |
---|
2840 | { |
---|
2841 | pan->n=napPerm(zb,par_perm,r,nMap); |
---|
2842 | if(pan->n==NULL) /* error in mapping or mapping to variable */ |
---|
2843 | pDelete(&p); |
---|
2844 | } |
---|
2845 | pTest(p); |
---|
2846 | res=pAdd(res,p); |
---|
2847 | } |
---|
2848 | napIter(za); |
---|
2849 | } |
---|
2850 | while (za!=NULL); |
---|
2851 | pTest(res); |
---|
2852 | return res; |
---|
2853 | } |
---|
2854 | |
---|
2855 | number naGetDenom(number &n, const ring r) |
---|
2856 | { |
---|
2857 | if (r==currRing) naNormalize(n); |
---|
2858 | lnumber x=(lnumber)n; |
---|
2859 | if (x->n!=NULL) |
---|
2860 | { |
---|
2861 | lnumber rr=(lnumber)omAlloc0Bin(rnumber_bin); |
---|
2862 | rr->z=nap_Copy(naGetDenom0(x),r); |
---|
2863 | rr->s = 2; |
---|
2864 | return (number)rr; |
---|
2865 | } |
---|
2866 | return r->cf->nInit(1); |
---|
2867 | } |
---|
2868 | |
---|
2869 | #ifdef LDEBUG |
---|
2870 | BOOLEAN naDBTest(number a, char *f,int l) |
---|
2871 | { |
---|
2872 | lnumber x=(lnumber)a; |
---|
2873 | if (x == NULL) |
---|
2874 | return TRUE; |
---|
2875 | omCheckAddrSize(a, sizeof(snumber)); |
---|
2876 | napoly p = x->z; |
---|
2877 | if (p==NULL) |
---|
2878 | { |
---|
2879 | Print("0/* in %s:%d\n",f,l); |
---|
2880 | return FALSE; |
---|
2881 | } |
---|
2882 | while(p!=NULL) |
---|
2883 | { |
---|
2884 | if ((naIsChar0 && nlIsZero(napGetCoeff(p))) |
---|
2885 | || ((!naIsChar0) && npIsZero(napGetCoeff(p)))) |
---|
2886 | { |
---|
2887 | Print("coeff 0 in %s:%d\n",f,l); |
---|
2888 | return FALSE; |
---|
2889 | } |
---|
2890 | if((naMinimalPoly!=NULL)&&(napGetExp(p,1)>napGetExp(naMinimalPoly,1)) |
---|
2891 | &&(p!=naMinimalPoly)) |
---|
2892 | { |
---|
2893 | Print("deg>minpoly in %s:%d\n",f,l); |
---|
2894 | return FALSE; |
---|
2895 | } |
---|
2896 | //if (naIsChar0 && (((int)p->ko &3) == 0) && (p->ko->s==0) && (x->s==2)) |
---|
2897 | //{ |
---|
2898 | // Print("normalized with non-normal coeffs in %s:%d\n",f,l); |
---|
2899 | // return FALSE; |
---|
2900 | //} |
---|
2901 | if (naIsChar0 && !(nlDBTest(napGetCoeff(p),f,l))) |
---|
2902 | return FALSE; |
---|
2903 | napIter(p); |
---|
2904 | } |
---|
2905 | p = naGetDenom0(x); |
---|
2906 | while(p!=NULL) |
---|
2907 | { |
---|
2908 | if (naIsChar0 && !(nlDBTest(napGetCoeff(p),f,l))) |
---|
2909 | return FALSE; |
---|
2910 | napIter(p); |
---|
2911 | } |
---|
2912 | return TRUE; |
---|
2913 | } |
---|
2914 | #endif |
---|
2915 | |
---|