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 1997-04-02 15:07:21 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 "tok.h" |
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13 | #include "mmemory.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 "ipid.h" |
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21 | #include "longalg.h" |
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22 | #define FEHLER1 1 |
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23 | #define FEHLER2 1 |
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24 | #define FEHLER3 1 |
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25 | |
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26 | struct snaIdeal |
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27 | { |
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28 | int anz; |
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29 | alg *liste; |
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30 | }; |
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31 | typedef struct snaIdeal * naIdeal; |
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32 | |
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33 | naIdeal naI=NULL; |
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34 | |
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35 | //#define RECA_SIZE (sizeof(alg)+sizeof(number)) |
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36 | alg naMinimalPoly; |
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37 | int naNumbOfPar; |
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38 | char **naParNames; |
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39 | static int naIsChar0; |
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40 | static int naPrimeM; |
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41 | |
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42 | #ifdef LDEBUG |
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43 | #define naTest(a) naDBTest(a,__FILE__,__LINE__) |
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44 | BOOLEAN naDBTest(number a, char *f,int l); |
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45 | #else |
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46 | #define naTest(a) |
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47 | #endif |
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48 | |
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49 | number (*naMap)(number from); |
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50 | /* procedure variables */ |
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51 | static numberfunc |
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52 | nacMult, nacSub, nacAdd, nacDiv, nacGcd, nacLcm; |
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53 | #ifdef LDEBUG |
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54 | static void (*nacDBDelete)(number *a,char *f,int l); |
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55 | #define nacDelete(A) nacDBDelete(A,__FILE__,__LINE__) |
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56 | #else |
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57 | static void (*nacDelete)(number *a); |
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58 | #endif |
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59 | number (*nacInit)(int i); |
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60 | static int (*nacInt)(number &n); |
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61 | void (*nacNormalize)(number &a); |
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62 | static number (*nacNeg)(number a); |
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63 | static void (*nacWrite)(number &a); |
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64 | number (*nacCopy)(number a); |
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65 | static number (*nacInvers)(number a); |
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66 | BOOLEAN (*nacIsZero)(number a); |
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67 | static BOOLEAN (*nacIsOne)(number a); |
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68 | static BOOLEAN (*nacIsMOne)(number a); |
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69 | static BOOLEAN (*nacGreaterZero)(number a); |
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70 | static char * (*nacRead) (char *s, number *a); |
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71 | extern void napDelete(alg *p); |
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72 | static alg napRedp(alg q); |
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73 | static alg napTailred(alg q); |
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74 | static BOOLEAN napDivPoly(alg p, alg q); |
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75 | static int napExpi(int i, alg a, alg b); |
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76 | |
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77 | /*2 |
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78 | * sets the appropriate operators |
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79 | */ |
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80 | void naSetChar(int i, BOOLEAN complete, char ** param, int pars) |
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81 | { |
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82 | if (naI!=NULL) |
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83 | { |
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84 | int j; |
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85 | for (j=naI->anz-1; j>=0; j--) |
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86 | napDelete (&naI->liste[j]); |
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87 | Free((ADDRESS)naI->liste,naI->anz*sizeof(alg)); |
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88 | Free((ADDRESS)naI,sizeof(*naI)); |
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89 | naI=NULL; |
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90 | } |
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91 | naMap = naCopy; |
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92 | naMinimalPoly = NULL; |
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93 | naParNames=param; |
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94 | naNumbOfPar=pars; |
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95 | if (i == 1) |
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96 | { |
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97 | naIsChar0 = 1; |
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98 | #ifdef LDEBUG |
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99 | nacDBDelete = nlDBDelete; |
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100 | #else |
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101 | nacDelete = nlDelete; |
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102 | #endif |
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103 | if (complete) |
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104 | { |
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105 | nacInit = nlInit; |
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106 | nacInt = nlInt; |
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107 | nacCopy = nlCopy; |
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108 | nacAdd = nlAdd; |
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109 | nacSub = nlSub; |
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110 | nacMult = nlMult; |
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111 | nacDiv = nlDiv; |
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112 | nacInvers = nlInvers; |
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113 | nacNormalize = nlNormalize; |
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114 | nacNeg = nlNeg; |
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115 | nacIsZero = nlIsZero; |
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116 | nacRead = nlRead; |
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117 | nacWrite = nlWrite; |
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118 | nacGreaterZero = nlGreaterZero; |
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119 | nacIsOne = nlIsOne; |
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120 | nacIsMOne = nlIsMOne; |
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121 | nacGcd = nlGcd; |
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122 | nacLcm = nlLcm; |
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123 | } |
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124 | } |
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125 | else if (i < 0) |
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126 | { |
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127 | naIsChar0 = 0; |
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128 | #ifdef LDEBUG |
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129 | nacDBDelete = nDBDummy1; |
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130 | #else |
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131 | nacDelete = nDummy1; |
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132 | #endif |
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133 | if (complete) |
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134 | { |
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135 | npSetChar(-i); |
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136 | nacInit = npInit; |
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137 | nacInt = npInt; |
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138 | nacCopy = npCopy; |
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139 | nacAdd = npAdd; |
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140 | nacSub = npSub; |
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141 | nacMult = npMult; |
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142 | nacDiv = npDiv; |
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143 | nacInvers = npInvers; |
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144 | nacNormalize = nDummy2; |
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145 | nacNeg = npNeg; |
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146 | nacIsZero = npIsZero; |
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147 | nacRead = npRead; |
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148 | nacWrite = npWrite; |
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149 | nacGreaterZero = npGreaterZero; |
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150 | nacIsOne = npIsOne; |
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151 | nacIsMOne = npIsMOne; |
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152 | nacGcd = ndGcd; |
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153 | } |
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154 | } |
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155 | #ifdef TEST |
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156 | else |
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157 | { |
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158 | Print("hier ging was schief:c=%d compl=%d param=%d\n",i,complete,param); |
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159 | } |
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160 | #endif |
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161 | } |
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162 | |
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163 | /*============= procedure for polynomials: napXXXX =======================*/ |
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164 | |
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165 | /*3 |
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166 | * creates an alg poly |
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167 | */ |
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168 | static alg napInit(int i) |
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169 | { |
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170 | alg a = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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171 | |
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172 | a->ko = nacInit(i); |
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173 | if (!nacIsZero(a->ko)) |
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174 | { |
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175 | return a; |
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176 | } |
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177 | else |
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178 | { |
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179 | Free((ADDRESS)a, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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180 | return NULL; |
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181 | } |
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182 | } |
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183 | |
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184 | /*3 |
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185 | * creates an alg poly |
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186 | */ |
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187 | alg napInitz(number z) |
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188 | { |
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189 | alg a = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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190 | |
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191 | a->ko = z; |
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192 | return a; |
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193 | } |
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194 | |
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195 | /*3 |
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196 | * deletes head of an alg poly |
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197 | */ |
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198 | static void napDelete1(alg *p) |
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199 | { |
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200 | alg h = *p; |
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201 | |
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202 | if (h!=NULL) |
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203 | { |
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204 | *p = h->ne; |
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205 | nacDelete(&(h->ko)); |
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206 | Free((ADDRESS)h, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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207 | } |
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208 | } |
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209 | |
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210 | /*3 |
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211 | * delete an alg poly |
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212 | */ |
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213 | void napDelete(alg *p) |
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214 | { |
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215 | alg w, h = *p; |
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216 | |
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217 | while (h!=NULL) |
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218 | { |
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219 | w = h; |
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220 | h = h->ne; |
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221 | nacDelete(&(w->ko)); |
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222 | Free((ADDRESS)w, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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223 | } |
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224 | *p = NULL; |
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225 | } |
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226 | |
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227 | |
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228 | /*3 |
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229 | * copy a alg. poly |
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230 | */ |
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231 | static alg napCopy(alg p) |
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232 | { |
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233 | alg w, a; |
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234 | |
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235 | if (p==NULL) return NULL; |
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236 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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237 | a = w = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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238 | memcpy(w->e, p->e, naNumbOfPar * sizeof(int)); |
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239 | w->ko = nacCopy(p->ko); |
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240 | loop |
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241 | { |
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242 | p=p->ne; |
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243 | if (p==NULL) break; |
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244 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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245 | a->ne = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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246 | a = a->ne; |
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247 | memcpy(a->e, p->e, naNumbOfPar * sizeof(int)); |
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248 | a->ko = nacCopy(p->ko); |
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249 | } |
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250 | a->ne = NULL; |
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251 | return w; |
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252 | } |
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253 | |
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254 | /*3 |
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255 | * copy a alg. poly |
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256 | */ |
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257 | static alg napCopyNeg(alg p) |
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258 | { |
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259 | alg w, a; |
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260 | |
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261 | if (p==NULL) return NULL; |
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262 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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263 | a = w = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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264 | memcpy(w->e, p->e, naNumbOfPar * sizeof(int)); |
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265 | w->ko = nacNeg(nacCopy(p->ko)); |
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266 | loop |
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267 | { |
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268 | p=p->ne; |
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269 | if (p==NULL) break; |
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270 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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271 | a->ne = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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272 | a = a->ne; |
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273 | memcpy(a->e, p->e, naNumbOfPar * sizeof(int)); |
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274 | a->ko = nacNeg(nacCopy(p->ko)); |
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275 | } |
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276 | a->ne = NULL; |
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277 | return w; |
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278 | } |
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279 | |
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280 | /*3 |
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281 | * Compare exponents of p and q |
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282 | */ |
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283 | static int napComp(alg p, alg q) |
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284 | { |
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285 | int i = 0; |
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286 | |
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287 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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288 | mmTestP(q,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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289 | while (p->e[i] == q->e[i]) |
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290 | { |
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291 | i++; |
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292 | if (i >= naNumbOfPar) |
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293 | return 0; |
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294 | } |
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295 | if (p->e[i] > q->e[i]) |
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296 | return 1; |
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297 | else |
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298 | return - 1; |
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299 | } |
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300 | |
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301 | /*3 |
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302 | * addition of alg. polys |
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303 | */ |
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304 | alg napAdd(alg p1, alg p2) |
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305 | { |
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306 | alg a1, p, a2, a; |
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307 | int c; number t; |
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308 | |
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309 | if (p1==NULL) return p2; |
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310 | if (p2==NULL) return p1; |
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311 | mmTestP(p1,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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312 | mmTestP(p2,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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313 | a1 = p1; |
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314 | a2 = p2; |
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315 | a = p = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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316 | loop |
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317 | { |
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318 | c = napComp(a1, a2); |
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319 | if (c == 1) |
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320 | { |
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321 | a = a->ne = a1; |
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322 | a1 = a1->ne; |
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323 | if (!a1) |
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324 | { |
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325 | a->ne= a2; |
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326 | break; |
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327 | } |
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328 | mmTestP(a1,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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329 | } |
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330 | else if (c == -1) |
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331 | { |
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332 | a = a->ne = a2; |
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333 | a2 = a2->ne; |
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334 | if (!a2) |
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335 | { |
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336 | a->ne = a1; |
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337 | break; |
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338 | } |
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339 | mmTestP(a2,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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340 | } |
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341 | else |
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342 | { |
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343 | t = nacAdd(a1->ko, a2->ko); |
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344 | napDelete1(&a2); |
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345 | if (nacIsZero(t)) |
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346 | { |
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347 | nacDelete(&t); |
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348 | napDelete1(&a1); |
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349 | } |
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350 | else |
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351 | { |
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352 | nacDelete(&(a1->ko)); |
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353 | a1->ko = t; |
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354 | a = a->ne = a1; |
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355 | a1 = a1->ne; |
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356 | } |
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357 | if (a1==NULL) |
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358 | { |
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359 | a->ne = a2; |
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360 | break; |
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361 | } |
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362 | else if (a2==NULL) |
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363 | { |
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364 | a->ne = a1; |
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365 | break; |
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366 | } |
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367 | mmTestP(a1,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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368 | mmTestP(a2,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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369 | } |
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370 | } |
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371 | a = p->ne; |
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372 | Free((ADDRESS)p, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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373 | return a; |
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374 | } |
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375 | |
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376 | |
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377 | /*3 |
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378 | * multiply a alg. poly by -1 |
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379 | */ |
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380 | static alg napNeg(alg a) |
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381 | { |
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382 | alg p = a; |
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383 | |
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384 | while (p!=NULL) |
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385 | { |
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386 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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387 | p->ko = nacNeg(p->ko); |
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388 | p = p->ne; |
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389 | } |
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390 | return a; |
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391 | } |
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392 | |
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393 | /*3 |
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394 | * returns ph * z |
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395 | */ |
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396 | static void napMultN(alg p, number z) |
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397 | { |
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398 | number t; |
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399 | |
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400 | while (p!=NULL) |
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401 | { |
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402 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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403 | t = nacMult(p->ko, z); |
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404 | nacNormalize(t); |
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405 | nacDelete(&p->ko); |
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406 | p->ko = t; |
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407 | p = p->ne; |
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408 | } |
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409 | } |
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410 | |
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411 | /*3 |
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412 | * update the polynomial a by multipying it by |
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413 | * the (number) coefficient |
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414 | * and the exponent vector (of) exp (a well initialized polynomial) |
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415 | */ |
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416 | static void napMultT(alg a, alg exp) |
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417 | { |
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418 | int i; |
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419 | number t, h; |
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420 | if (a==NULL) |
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421 | return; |
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422 | h = exp->ko; |
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423 | if (nacIsOne(h)) |
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424 | { |
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425 | do |
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426 | { |
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427 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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428 | a->e[i] += exp->e[i]; |
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429 | a = a->ne; |
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430 | } |
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431 | while (a!=NULL); |
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432 | } |
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433 | else |
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434 | { |
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435 | h = nacNeg(h); |
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436 | if (nacIsOne(h)) |
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437 | { |
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438 | h = nacNeg(h); |
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439 | do |
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440 | { |
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441 | a->ko = nacNeg(a->ko); |
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442 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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443 | a->e[i] += exp->e[i]; |
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444 | a = a->ne; |
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445 | } |
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446 | while (a!=NULL); |
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447 | } |
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448 | else |
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449 | { |
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450 | h = nacNeg(h); |
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451 | do |
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452 | { |
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453 | t = nacMult(a->ko, h); |
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454 | nacDelete(&(a->ko)); |
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455 | a->ko = t; |
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456 | for (i = naNumbOfPar - 1; i >= 0; i--) |
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457 | a->e[i] += exp->e[i]; |
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458 | a = a->ne; |
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459 | } |
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460 | while (a!=NULL); |
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461 | } |
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462 | } |
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463 | } |
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464 | |
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465 | /*3 |
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466 | * multiplication of alg. polys |
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467 | * multiply p1 with p2, p1 and p2 are destroyed |
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468 | * do not put attention on speed: the procedure is only used in the interpreter |
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469 | */ |
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470 | static alg napMult(alg p1, alg p2) |
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471 | { |
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472 | alg a1, a2, b, h; |
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473 | if (p1==NULL) |
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474 | { |
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475 | napDelete(&p2); |
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476 | return NULL; |
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477 | } |
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478 | if (p2==NULL) |
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479 | { |
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480 | napDelete(&p1); |
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481 | return NULL; |
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482 | } |
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483 | b = NULL; |
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484 | a1 = p1; |
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485 | a2 = p2; |
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486 | if (a2->ne!=NULL) |
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487 | { |
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488 | if (a1->ne!=NULL) |
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489 | { |
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490 | do |
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491 | { |
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492 | a1 = a1->ne; |
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493 | a2 = a2->ne; |
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494 | } |
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495 | while ((a1!=NULL) && (a2!=NULL)); |
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496 | if (a1!=NULL) |
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497 | { |
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498 | a1 = p1; |
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499 | a2 = p2; |
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500 | } |
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501 | else |
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502 | { |
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503 | a1 = p2; |
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504 | a2 = p1; |
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505 | } |
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506 | do |
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507 | { |
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508 | if (a2->ne!=NULL) |
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509 | h = napCopy(a1); |
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510 | else |
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511 | h = a1; |
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512 | napMultT(h, a2); |
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513 | b = napAdd(h, b); |
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514 | napDelete1(&a2); |
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515 | } |
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516 | while (a2!=NULL); |
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517 | } |
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518 | else |
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519 | { |
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520 | napMultT(a2, a1); |
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521 | b = napAdd(a2, b); |
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522 | napDelete1(&a1); |
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523 | } |
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524 | } |
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525 | else |
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526 | { |
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527 | napMultT(a1, a2); |
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528 | b = napAdd(a1, b); |
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529 | napDelete1(&a2); |
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530 | } |
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531 | return b; |
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532 | } |
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533 | |
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534 | /*3 |
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535 | * division with rest; f = g*q + r, returns r and destroy f |
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536 | */ |
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537 | static alg napRemainder(alg f, const alg g) |
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538 | { |
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539 | alg a, h, qq; |
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540 | |
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541 | qq = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
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542 | qq->ne = NULL; |
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543 | a = f; |
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544 | do |
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545 | { |
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546 | mmTestP(a,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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547 | mmTestP(g,RECA_SIZE+naNumbOfPar*sizeof(int)); |
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548 | qq->e[0] = a->e[0] - g->e[0]; |
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549 | qq->ko = nacDiv(a->ko, g->ko); |
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550 | qq->ko = nacNeg(qq->ko); |
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551 | h = napCopy(g); |
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552 | napMultT(h, qq); |
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553 | nacDelete(&(qq->ko)); |
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554 | a = napAdd(a, h); |
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555 | } |
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556 | while ((a!=NULL) && (a->e[0] >= g->e[0])); |
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557 | Free((ADDRESS)qq, RECA_SIZE + naNumbOfPar * sizeof(int)); |
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558 | return a; |
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559 | } |
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560 | |
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561 | /*3 |
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562 | * division with rest; f = g*q + r, destroy f |
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563 | */ |
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564 | static void napDivMod(alg f, alg g, alg *q, alg *r) |
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565 | { |
---|
566 | alg a, h, b, qq; |
---|
567 | |
---|
568 | qq = (alg)Alloc(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
569 | qq->ne = b = NULL; |
---|
570 | a = f; |
---|
571 | do |
---|
572 | { |
---|
573 | mmTestP(a,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
574 | mmTestP(g,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
575 | qq->e[0] = a->e[0] - g->e[0]; |
---|
576 | qq->ko = nacDiv(a->ko, g->ko); |
---|
577 | b = napAdd(b, napCopy(qq)); |
---|
578 | qq->ko = nacNeg(qq->ko); |
---|
579 | h = napCopy(g); |
---|
580 | napMultT(h, qq); |
---|
581 | nacDelete(&(qq->ko)); |
---|
582 | a = napAdd(a, h); |
---|
583 | } |
---|
584 | while ((a!=NULL) && (a->e[0] >= g->e[0])); |
---|
585 | Free((ADDRESS)qq, RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
586 | *q = b; |
---|
587 | *r = a; |
---|
588 | } |
---|
589 | |
---|
590 | /*3 |
---|
591 | * returns z with z*x mod c = 1 |
---|
592 | */ |
---|
593 | static alg napInvers(alg x, const alg c) |
---|
594 | { |
---|
595 | alg y, r, qa, qn, q; |
---|
596 | number t, h; |
---|
597 | |
---|
598 | if (x->e[0] >= c->e[0]) |
---|
599 | x = napRemainder(x, c); |
---|
600 | if (x->e[0]==0) |
---|
601 | { |
---|
602 | if (!nacIsOne(x->ko)) |
---|
603 | { |
---|
604 | h = nacInit(1); |
---|
605 | t = nacDiv(h, x->ko); |
---|
606 | nacDelete(&(x->ko)); |
---|
607 | nacDelete(&h); |
---|
608 | x->ko = t; |
---|
609 | } |
---|
610 | return x; |
---|
611 | } |
---|
612 | y = napCopy(c); |
---|
613 | napDivMod(y, x, &qa, &r); |
---|
614 | if (r->e[0]==0) |
---|
615 | { |
---|
616 | h = nacInit(-1); |
---|
617 | t = nacDiv(h, r->ko); |
---|
618 | nacNormalize(t); |
---|
619 | napMultN(qa, t); |
---|
620 | nacDelete(&h); |
---|
621 | nacDelete(&t); |
---|
622 | napDelete(&x); |
---|
623 | napDelete(&r); |
---|
624 | return qa; |
---|
625 | } |
---|
626 | y = x; |
---|
627 | x = r; |
---|
628 | napDivMod(y, x, &q, &r); |
---|
629 | if (r->e[0]==0) |
---|
630 | { |
---|
631 | q = napMult(q, qa); |
---|
632 | q = napAdd(q, napInit(1)); |
---|
633 | h = nacInit(1); |
---|
634 | t = nacDiv(h, r->ko); |
---|
635 | napMultN(q, t); |
---|
636 | nacDelete(&h); |
---|
637 | nacDelete(&t); |
---|
638 | napDelete(&x); |
---|
639 | napDelete(&r); |
---|
640 | if (q->e[0] >= c->e[0]) |
---|
641 | q = napRemainder(q, c); |
---|
642 | return q; |
---|
643 | } |
---|
644 | q = napMult(q, napCopy(qa)); |
---|
645 | q = napAdd(q, napInit(1)); |
---|
646 | qa = napNeg(qa); |
---|
647 | loop |
---|
648 | { |
---|
649 | y = x; |
---|
650 | x = r; |
---|
651 | napDivMod(y, x, &qn, &r); |
---|
652 | if (r->e[0]==0) |
---|
653 | { |
---|
654 | q = napMult(q, qn); |
---|
655 | q = napNeg(q); |
---|
656 | q = napAdd(q, qa); |
---|
657 | h = nacInit(1); |
---|
658 | t = nacDiv(h, r->ko); |
---|
659 | napMultN(q, t); |
---|
660 | nacDelete(&h); |
---|
661 | nacDelete(&t); |
---|
662 | napDelete(&x); |
---|
663 | napDelete(&r); |
---|
664 | if (q->e[0] >= c->e[0]) |
---|
665 | q = napRemainder(q, c); |
---|
666 | return q; |
---|
667 | } |
---|
668 | y = q; |
---|
669 | q = napMult(napCopy(q), qn); |
---|
670 | q = napNeg(q); |
---|
671 | q = napAdd(q, qa); |
---|
672 | qa = y; |
---|
673 | } |
---|
674 | } |
---|
675 | |
---|
676 | /*3 |
---|
677 | * the degree of an alg poly (used for test of "constant" et al.) |
---|
678 | */ |
---|
679 | static int napDeg(alg p) |
---|
680 | { |
---|
681 | int d = 0, i; |
---|
682 | |
---|
683 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
684 | for (i = naNumbOfPar-1; i>=0; i--) |
---|
685 | d += p->e[i]; |
---|
686 | return d; |
---|
687 | } |
---|
688 | |
---|
689 | /*3 |
---|
690 | *writes a polynomial number |
---|
691 | */ |
---|
692 | static void napWrite(alg p) |
---|
693 | { |
---|
694 | int i; |
---|
695 | if (p==NULL) |
---|
696 | StringAppendS("0"); |
---|
697 | else |
---|
698 | { |
---|
699 | StringAppendS("("); |
---|
700 | loop |
---|
701 | { |
---|
702 | BOOLEAN wroteCoeff=FALSE; |
---|
703 | mmTestP(p,RECA_SIZE+naNumbOfPar*sizeof(int)); |
---|
704 | if ((napDeg(p)==0) |
---|
705 | || (!nacIsOne(p->ko))) |
---|
706 | { |
---|
707 | nacWrite(p->ko); |
---|
708 | wroteCoeff=(pShortOut==0); |
---|
709 | } |
---|
710 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
711 | { |
---|
712 | if (p->e[i] > 0) |
---|
713 | { |
---|
714 | if (wroteCoeff) |
---|
715 | StringAppendS("*"); |
---|
716 | else |
---|
717 | wroteCoeff=(pShortOut==0); |
---|
718 | StringAppend(naParNames[i]); |
---|
719 | if (p->e[i] > 1) |
---|
720 | { |
---|
721 | if (pShortOut == 0) |
---|
722 | StringAppendS("^"); |
---|
723 | StringAppend("%d", p->e[i]); |
---|
724 | } |
---|
725 | } |
---|
726 | } |
---|
727 | p = p->ne; |
---|
728 | if (p==NULL) |
---|
729 | break; |
---|
730 | if (nacGreaterZero(p->ko)) |
---|
731 | StringAppendS("+"); |
---|
732 | } |
---|
733 | StringAppendS(")"); |
---|
734 | } |
---|
735 | } |
---|
736 | |
---|
737 | |
---|
738 | static char *napHandleMons(char *s, int i, int *ex) |
---|
739 | { |
---|
740 | int j; |
---|
741 | if (strncmp(s,naParNames[i],strlen(naParNames[i]))==0) |
---|
742 | { |
---|
743 | s+=strlen(naParNames[i]); |
---|
744 | if ((*s >= '0') && (*s <= '9')) |
---|
745 | { |
---|
746 | s = eati(s, &j); |
---|
747 | ex[i] += j; |
---|
748 | } |
---|
749 | else |
---|
750 | ex[i]++; |
---|
751 | } |
---|
752 | return s; |
---|
753 | } |
---|
754 | |
---|
755 | /*3 reads a monomial */ |
---|
756 | static char *napRead(char *s, alg *b) |
---|
757 | { |
---|
758 | alg a; |
---|
759 | int i; |
---|
760 | a = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
761 | if ((*s >= '0') && (*s <= '9')) |
---|
762 | { |
---|
763 | s = nacRead(s, &(a->ko)); |
---|
764 | if (nacIsZero(a->ko)) |
---|
765 | { |
---|
766 | napDelete1(&a); |
---|
767 | *b = NULL; |
---|
768 | return s; |
---|
769 | } |
---|
770 | } |
---|
771 | else |
---|
772 | a->ko = nacInit(1); |
---|
773 | i = 0; |
---|
774 | char *olds; |
---|
775 | loop |
---|
776 | { |
---|
777 | olds = s; |
---|
778 | s = napHandleMons(s, i, a->e); |
---|
779 | if (olds == s) |
---|
780 | i++; |
---|
781 | else |
---|
782 | i = 0; |
---|
783 | if ((*s == '\0') || (i >= naNumbOfPar)) |
---|
784 | break; |
---|
785 | } |
---|
786 | *b = a; |
---|
787 | return s; |
---|
788 | } |
---|
789 | |
---|
790 | static int napExp(alg a, alg b) |
---|
791 | { |
---|
792 | while (a->ne!=NULL) a = a->ne; |
---|
793 | int m = a->e[0]; |
---|
794 | if (m==0) return m; |
---|
795 | while (b->ne!=NULL) b = b->ne; |
---|
796 | if (m > b->e[0]) m = b->e[0]; |
---|
797 | return m; |
---|
798 | } |
---|
799 | |
---|
800 | #if FEHLER2 |
---|
801 | /*meins |
---|
802 | * finds the smallest i-th exponent in a and b |
---|
803 | * used to find it in a fraction |
---|
804 | */ |
---|
805 | static int napExpi(int i, alg a, alg b) |
---|
806 | { |
---|
807 | if (a==NULL || b==NULL) return 0; |
---|
808 | int m = a->e[i]; |
---|
809 | if (m==0) return 0; |
---|
810 | while (a->ne != NULL) |
---|
811 | { |
---|
812 | a = a->ne; |
---|
813 | if (m > a->e[i]) |
---|
814 | { |
---|
815 | m = a->e[i]; |
---|
816 | if (m==0) return 0; |
---|
817 | } |
---|
818 | } |
---|
819 | do |
---|
820 | { |
---|
821 | if (m > b->e[i]) |
---|
822 | { |
---|
823 | m = b->e[i]; |
---|
824 | if (m==0) return 0; |
---|
825 | } |
---|
826 | b = b->ne; |
---|
827 | } |
---|
828 | while (b != NULL); |
---|
829 | return m; |
---|
830 | } |
---|
831 | #endif |
---|
832 | |
---|
833 | static void napContent(alg ph) |
---|
834 | { |
---|
835 | number h,d; |
---|
836 | alg p; |
---|
837 | |
---|
838 | p = ph; |
---|
839 | if (nacIsOne(p->ko)) |
---|
840 | return; |
---|
841 | h = nacCopy(p->ko); |
---|
842 | p = p->ne; |
---|
843 | do |
---|
844 | { |
---|
845 | d=nacGcd(p->ko, h); |
---|
846 | if(nacIsOne(d)) |
---|
847 | { |
---|
848 | nacDelete(&h); |
---|
849 | nacDelete(&d); |
---|
850 | return; |
---|
851 | } |
---|
852 | nacDelete(&h); |
---|
853 | h = d; |
---|
854 | p = p->ne; |
---|
855 | } |
---|
856 | while (p!=NULL); |
---|
857 | h = nacInvers(d); |
---|
858 | nacDelete(&d); |
---|
859 | p = ph; |
---|
860 | while (p!=NULL) |
---|
861 | { |
---|
862 | d = nacMult(p->ko, h); |
---|
863 | nacDelete(&(p->ko)); |
---|
864 | p->ko = d; |
---|
865 | p = p->ne; |
---|
866 | } |
---|
867 | nacDelete(&h); |
---|
868 | } |
---|
869 | |
---|
870 | static void napCleardenom(alg ph) |
---|
871 | { |
---|
872 | number d, h; |
---|
873 | alg p; |
---|
874 | |
---|
875 | if (!naIsChar0) |
---|
876 | return; |
---|
877 | p = ph; |
---|
878 | h = nacInit(1); |
---|
879 | while (p!=NULL) |
---|
880 | { |
---|
881 | d = nacLcm(h, p->ko); |
---|
882 | nacDelete(&h); |
---|
883 | h = d; |
---|
884 | p = p->ne; |
---|
885 | } |
---|
886 | if(!nacIsOne(h)) |
---|
887 | { |
---|
888 | p = ph; |
---|
889 | while (p!=NULL) |
---|
890 | { |
---|
891 | d=nacMult(h, p->ko); |
---|
892 | nacDelete(&(p->ko)); |
---|
893 | p->ko = d; |
---|
894 | p = p->ne; |
---|
895 | } |
---|
896 | nacDelete(&h); |
---|
897 | } |
---|
898 | napContent(ph); |
---|
899 | } |
---|
900 | |
---|
901 | static alg napGcd0(alg a, alg b) |
---|
902 | { |
---|
903 | number x, y; |
---|
904 | if (!naIsChar0) |
---|
905 | return napInit(1); |
---|
906 | x = nacCopy(a->ko); |
---|
907 | if (nacIsOne(x)) |
---|
908 | return napInitz(x); |
---|
909 | while (a->ne!=NULL) |
---|
910 | { |
---|
911 | a = a->ne; |
---|
912 | y = nacGcd(x, a->ko); |
---|
913 | nacDelete(&x); |
---|
914 | x = y; |
---|
915 | if (nacIsOne(x)) |
---|
916 | return napInitz(x); |
---|
917 | } |
---|
918 | do |
---|
919 | { |
---|
920 | y = nacGcd(x, b->ko); |
---|
921 | nacDelete(&x); |
---|
922 | x = y; |
---|
923 | if (nacIsOne(x)) |
---|
924 | return napInitz(x); |
---|
925 | b = b->ne; |
---|
926 | } |
---|
927 | while (b!=NULL); |
---|
928 | return napInitz(x); |
---|
929 | } |
---|
930 | |
---|
931 | /*3 |
---|
932 | * result =gcd(a,b) |
---|
933 | */ |
---|
934 | static alg napGcd(alg a, alg b) |
---|
935 | { |
---|
936 | int i; |
---|
937 | alg g, x, y, h; |
---|
938 | if ((a==NULL) |
---|
939 | || ((a->ne==NULL)&&(nacIsZero(a->ko)))) |
---|
940 | { |
---|
941 | if ((b==NULL) |
---|
942 | || ((b->ne==NULL)&&(nacIsZero(b->ko)))) |
---|
943 | { |
---|
944 | return napInit(1); |
---|
945 | } |
---|
946 | return napCopy(b); |
---|
947 | } |
---|
948 | if (naMinimalPoly != NULL) |
---|
949 | { |
---|
950 | if (a->e[0] >= b->e[0]) |
---|
951 | { |
---|
952 | x = a; |
---|
953 | y = b; |
---|
954 | } |
---|
955 | else |
---|
956 | { |
---|
957 | x = b; |
---|
958 | y = a; |
---|
959 | } |
---|
960 | g = napGcd0(x, y); |
---|
961 | if (y->ne==NULL) |
---|
962 | { |
---|
963 | g->e[0] = napExp(x, y); |
---|
964 | return g; |
---|
965 | } |
---|
966 | x = napCopy(x); |
---|
967 | y = napCopy(y); |
---|
968 | loop |
---|
969 | { |
---|
970 | h = napRemainder(x, y); |
---|
971 | if (h==NULL) |
---|
972 | { |
---|
973 | napCleardenom(y); |
---|
974 | if (!nacIsOne(g->ko)) napMultN(y, g->ko); |
---|
975 | napDelete1(&g); |
---|
976 | return y; |
---|
977 | } |
---|
978 | else if (h->ne==NULL) |
---|
979 | break; |
---|
980 | x = y; |
---|
981 | y = h; |
---|
982 | } |
---|
983 | napDelete(&y); |
---|
984 | napDelete1(&h); |
---|
985 | g->e[0] = napExp(a, b); |
---|
986 | return g; |
---|
987 | } |
---|
988 | x = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
989 | g=a; |
---|
990 | h=b; |
---|
991 | x = napGcd0(g,h); |
---|
992 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
993 | x->e[i] = napExpi(i,a,b); |
---|
994 | return x; |
---|
995 | } |
---|
996 | |
---|
997 | |
---|
998 | number napLcm(alg a) |
---|
999 | { |
---|
1000 | number d, h; |
---|
1001 | alg b; |
---|
1002 | |
---|
1003 | h = nacInit(1); |
---|
1004 | b = a; |
---|
1005 | while (b!=NULL) |
---|
1006 | { |
---|
1007 | d = nacLcm(h, b->ko); |
---|
1008 | nacDelete(&h); |
---|
1009 | h = d; |
---|
1010 | b = b->ne; |
---|
1011 | } |
---|
1012 | return h; |
---|
1013 | } |
---|
1014 | |
---|
1015 | |
---|
1016 | /*2 |
---|
1017 | * meins (for reduction in algebraic extension) |
---|
1018 | * checks if head of p divides head of q |
---|
1019 | * doesn't delete p and q |
---|
1020 | */ |
---|
1021 | BOOLEAN napDivPoly (alg p, alg q) |
---|
1022 | { |
---|
1023 | int j=0; /* evtl. von naNumber.. -1 abwaerts zaehlen */ |
---|
1024 | |
---|
1025 | while (p->e[j] <= q->e[j]) |
---|
1026 | { |
---|
1027 | j++; |
---|
1028 | if (j >= naNumbOfPar) |
---|
1029 | return 1; |
---|
1030 | } |
---|
1031 | return 0; |
---|
1032 | } |
---|
1033 | |
---|
1034 | |
---|
1035 | /*2 |
---|
1036 | * meins (for reduction in algebraic extension) |
---|
1037 | * Normalform of poly with naI |
---|
1038 | * changes q and returns it |
---|
1039 | */ |
---|
1040 | alg napRedp (alg q) |
---|
1041 | { |
---|
1042 | alg h = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
1043 | int i=0,j; |
---|
1044 | |
---|
1045 | loop |
---|
1046 | { |
---|
1047 | if (napDivPoly (naI->liste[i], q)) |
---|
1048 | { |
---|
1049 | mmTestP((ADDRESS)q,RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
1050 | StringSetS(""); |
---|
1051 | napWrite(q); |
---|
1052 | napWrite(naI->liste[i]); |
---|
1053 | Print(StringAppendS("\n")); |
---|
1054 | /* h = lt(q)/lt(naI->liste[i])*/ |
---|
1055 | h->ko = nacCopy(q->ko); |
---|
1056 | for (j=naNumbOfPar-1; j>=0; j--) |
---|
1057 | h->e[j] = q->e[j] - naI->liste[i]->e[j]; |
---|
1058 | h = napMult (h, napCopy(naI->liste[i])); |
---|
1059 | h = napNeg (h); |
---|
1060 | q = napAdd (q, napCopy(h)); |
---|
1061 | napDelete (&(h->ne)); |
---|
1062 | if (q == NULL) |
---|
1063 | { |
---|
1064 | napDelete(&h); |
---|
1065 | return q; |
---|
1066 | } |
---|
1067 | /* try to reduce further */ |
---|
1068 | i = 0; |
---|
1069 | } |
---|
1070 | else |
---|
1071 | { |
---|
1072 | i++; |
---|
1073 | if (i >= naI->anz) |
---|
1074 | { |
---|
1075 | napDelete(&h); |
---|
1076 | return q; |
---|
1077 | } |
---|
1078 | } |
---|
1079 | } |
---|
1080 | } |
---|
1081 | |
---|
1082 | |
---|
1083 | /*2 |
---|
1084 | * meins (for reduction in algebraic extension) |
---|
1085 | * reduces the tail of Poly q |
---|
1086 | * needs q != NULL |
---|
1087 | * changes q and returns it |
---|
1088 | */ |
---|
1089 | alg napTailred (alg q) |
---|
1090 | { |
---|
1091 | alg h; |
---|
1092 | |
---|
1093 | h = q->ne; |
---|
1094 | while (h != NULL) |
---|
1095 | { |
---|
1096 | h = napRedp (h); |
---|
1097 | if (h == NULL) |
---|
1098 | return q; |
---|
1099 | h = h->ne; |
---|
1100 | } |
---|
1101 | return q; |
---|
1102 | } |
---|
1103 | |
---|
1104 | |
---|
1105 | /*================ procedure for rational functions: naXXXX =================*/ |
---|
1106 | |
---|
1107 | /*2 |
---|
1108 | * z:= i |
---|
1109 | */ |
---|
1110 | number naInit(int i) |
---|
1111 | { |
---|
1112 | if (i!=0) |
---|
1113 | { |
---|
1114 | lnumber l = (lnumber)Alloc(sizeof(rnumber)); |
---|
1115 | l->z = napInit(i); |
---|
1116 | if (l->z==NULL) |
---|
1117 | { |
---|
1118 | Free((ADDRESS)l, sizeof(rnumber)); |
---|
1119 | return NULL; |
---|
1120 | } |
---|
1121 | l->s = 2; |
---|
1122 | l->n = NULL; |
---|
1123 | return (number)l; |
---|
1124 | } |
---|
1125 | /*else*/ |
---|
1126 | return NULL; |
---|
1127 | } |
---|
1128 | |
---|
1129 | number naPar(int i) |
---|
1130 | { |
---|
1131 | lnumber l = (lnumber)Alloc(sizeof(rnumber)); |
---|
1132 | l->s = 2; |
---|
1133 | l->z = napInit(1); |
---|
1134 | l->z->e[i-1]=1; |
---|
1135 | l->n = NULL; |
---|
1136 | return (number)l; |
---|
1137 | } |
---|
1138 | |
---|
1139 | int naParDeg(number n) /* i := deg(n) */ |
---|
1140 | { |
---|
1141 | lnumber l = (lnumber)n; |
---|
1142 | if (l==NULL) return -1; |
---|
1143 | return napDeg(l->z); |
---|
1144 | } |
---|
1145 | |
---|
1146 | /*2 |
---|
1147 | * convert a number to int (if possible) |
---|
1148 | */ |
---|
1149 | int naInt(number &n) |
---|
1150 | { |
---|
1151 | lnumber l=(lnumber)n; |
---|
1152 | if ((l!=NULL)&&(l->n==NULL)&&(napDeg(l->z)==0)) |
---|
1153 | { |
---|
1154 | return nacInt(l->z->ko); |
---|
1155 | } |
---|
1156 | return 0; |
---|
1157 | } |
---|
1158 | |
---|
1159 | /*2 |
---|
1160 | * deletes p |
---|
1161 | */ |
---|
1162 | #ifdef LDEBUG |
---|
1163 | void naDBDelete(number *p,char *f, int lno) |
---|
1164 | #else |
---|
1165 | void naDelete(number *p) |
---|
1166 | #endif |
---|
1167 | { |
---|
1168 | lnumber l = (lnumber) * p; |
---|
1169 | if (l==NULL) return; |
---|
1170 | napDelete(&(l->z)); |
---|
1171 | napDelete(&(l->n)); |
---|
1172 | #if defined(MDEBUG) && defined(LDEBUG) |
---|
1173 | mmDBFreeBlock((ADDRESS)l, sizeof(rnumber),f,lno); |
---|
1174 | #else |
---|
1175 | Free((ADDRESS)l, sizeof(rnumber)); |
---|
1176 | #endif |
---|
1177 | *p = NULL; |
---|
1178 | } |
---|
1179 | |
---|
1180 | /*2 |
---|
1181 | * copy p to erg |
---|
1182 | */ |
---|
1183 | number naCopy(number p) |
---|
1184 | { |
---|
1185 | if (p==NULL) return NULL; |
---|
1186 | naTest(p); |
---|
1187 | lnumber erg; |
---|
1188 | lnumber src = (lnumber)p; |
---|
1189 | erg = (lnumber)Alloc0(sizeof(rnumber)); |
---|
1190 | erg->z = napCopy(src->z); |
---|
1191 | erg->n = napCopy(src->n); |
---|
1192 | erg->s = src->s; |
---|
1193 | return (number)erg; |
---|
1194 | } |
---|
1195 | |
---|
1196 | /*2 |
---|
1197 | * a dummy number: 0 |
---|
1198 | */ |
---|
1199 | void naNew(number *z) |
---|
1200 | { |
---|
1201 | *z = NULL; |
---|
1202 | } |
---|
1203 | |
---|
1204 | /*2 |
---|
1205 | * addition; lu:= la + lb |
---|
1206 | */ |
---|
1207 | number naAdd(number la, number lb) |
---|
1208 | { |
---|
1209 | alg x, y; |
---|
1210 | lnumber lu; |
---|
1211 | lnumber a = (lnumber)la; |
---|
1212 | lnumber b = (lnumber)lb; |
---|
1213 | if (a==NULL) return naCopy(lb); |
---|
1214 | if (b==NULL) return naCopy(la); |
---|
1215 | mmTestP(a,sizeof(rnumber)); |
---|
1216 | mmTestP(b,sizeof(rnumber)); |
---|
1217 | lu = (lnumber)Alloc(sizeof(rnumber)); |
---|
1218 | if (b->n!=NULL) x = napMult(napCopy(a->z), napCopy(b->n)); |
---|
1219 | else x = napCopy(a->z); |
---|
1220 | if (a->n!=NULL) y = napMult(napCopy(b->z), napCopy(a->n)); |
---|
1221 | else y = napCopy(b->z); |
---|
1222 | lu->z = napAdd(x, y); |
---|
1223 | if (lu->z==NULL) |
---|
1224 | { |
---|
1225 | Free((ADDRESS)lu, sizeof(rnumber)); |
---|
1226 | return (number)NULL; |
---|
1227 | } |
---|
1228 | if (a->n!=NULL) |
---|
1229 | { |
---|
1230 | if (b->n!=NULL) x = napMult(napCopy(a->n), napCopy(b->n)); |
---|
1231 | else x = napCopy(a->n); |
---|
1232 | } |
---|
1233 | else |
---|
1234 | { |
---|
1235 | if (b->n!=NULL) x = napCopy(b->n); |
---|
1236 | else x = NULL; |
---|
1237 | } |
---|
1238 | if ((x!=NULL) && (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
1239 | napDelete(&x); |
---|
1240 | lu->n = x; |
---|
1241 | lu->s = 0; |
---|
1242 | naTest((number)lu); |
---|
1243 | return (number)lu; |
---|
1244 | } |
---|
1245 | |
---|
1246 | /*2 |
---|
1247 | * subtraction; r:= la - lb |
---|
1248 | */ |
---|
1249 | number naSub(number la, number lb) |
---|
1250 | { |
---|
1251 | lnumber lu; |
---|
1252 | |
---|
1253 | if (lb==NULL) return naCopy(la); |
---|
1254 | if (la==NULL) |
---|
1255 | { |
---|
1256 | //if (lb!=NULL) |
---|
1257 | //{ |
---|
1258 | lu = (lnumber)naCopy(lb); |
---|
1259 | lu->z = napNeg(lu->z); |
---|
1260 | return (number)lu; |
---|
1261 | //} |
---|
1262 | //else |
---|
1263 | // return NULL; |
---|
1264 | } |
---|
1265 | |
---|
1266 | alg x, y; |
---|
1267 | lnumber a = (lnumber)la; |
---|
1268 | lnumber b = (lnumber)lb; |
---|
1269 | |
---|
1270 | mmTestP(a,sizeof(rnumber)); |
---|
1271 | mmTestP(b,sizeof(rnumber)); |
---|
1272 | lu = (lnumber)Alloc(sizeof(rnumber)); |
---|
1273 | if (b->n!=NULL) x = napMult(napCopy(a->z), napCopy(b->n)); |
---|
1274 | else x = napCopy(a->z); |
---|
1275 | if (a->n!=NULL) y = napMult(napCopy(b->z), napCopyNeg(a->n)); |
---|
1276 | else y = napCopyNeg(b->z); |
---|
1277 | lu->z = napAdd(x, y); |
---|
1278 | if (lu->z==NULL) |
---|
1279 | { |
---|
1280 | Free((ADDRESS)lu, sizeof(rnumber)); |
---|
1281 | return (number)NULL; |
---|
1282 | } |
---|
1283 | if (a->n!=NULL) |
---|
1284 | { |
---|
1285 | if (b->n!=NULL) x = napMult(napCopy(a->n), napCopy(b->n)); |
---|
1286 | else x = napCopy(a->n); |
---|
1287 | } |
---|
1288 | else |
---|
1289 | { |
---|
1290 | if (b->n!=NULL) x = napCopy(b->n); |
---|
1291 | else x = NULL; |
---|
1292 | } |
---|
1293 | if ((x!=NULL)&& (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
1294 | napDelete(&x); |
---|
1295 | lu->n = x; |
---|
1296 | lu->s = 0; |
---|
1297 | naTest((number)lu); |
---|
1298 | return (number)lu; |
---|
1299 | } |
---|
1300 | |
---|
1301 | /*2 |
---|
1302 | * multiplication; r:= la * lb |
---|
1303 | */ |
---|
1304 | number naMult(number la, number lb) |
---|
1305 | { |
---|
1306 | if ((la==NULL) || (lb==NULL)) |
---|
1307 | return NULL; |
---|
1308 | |
---|
1309 | lnumber a = (lnumber)la; |
---|
1310 | lnumber b = (lnumber)lb; |
---|
1311 | lnumber lo; |
---|
1312 | alg x; |
---|
1313 | |
---|
1314 | mmTestP(a,sizeof(rnumber)); |
---|
1315 | mmTestP(b,sizeof(rnumber)); |
---|
1316 | lo = (lnumber)Alloc(sizeof(rnumber)); |
---|
1317 | lo->z = napMult(napCopy(a->z), napCopy(b->z)); |
---|
1318 | if (a->n==NULL) |
---|
1319 | { |
---|
1320 | if (b->n==NULL) |
---|
1321 | x = NULL; |
---|
1322 | else |
---|
1323 | x = napCopy(b->n); |
---|
1324 | } |
---|
1325 | else |
---|
1326 | { |
---|
1327 | if (b->n==NULL) |
---|
1328 | x = napCopy(a->n); |
---|
1329 | else |
---|
1330 | x = napMult(napCopy(b->n), napCopy(a->n)); |
---|
1331 | } |
---|
1332 | if (naMinimalPoly!=NULL) |
---|
1333 | { |
---|
1334 | if (lo->z->e[0] >= naMinimalPoly->e[0]) |
---|
1335 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
1336 | if ((x!=NULL) && (x->e[0] >= naMinimalPoly->e[0])) |
---|
1337 | x = napRemainder(x, naMinimalPoly); |
---|
1338 | } |
---|
1339 | #if FEHLER1 |
---|
1340 | if (naI!=NULL) |
---|
1341 | { |
---|
1342 | lo->z = napRedp (lo->z); |
---|
1343 | if (lo->z != NULL) |
---|
1344 | lo->z = napTailred (lo->z); |
---|
1345 | if (x!=NULL) |
---|
1346 | { |
---|
1347 | x = napRedp (x); |
---|
1348 | if (x!=NULL) |
---|
1349 | x = napTailred (x); |
---|
1350 | } |
---|
1351 | } |
---|
1352 | #endif |
---|
1353 | if ((x!=NULL) && (napDeg(x)==0) && nacIsOne(x->ko)) |
---|
1354 | napDelete(&x); |
---|
1355 | lo->n = x; |
---|
1356 | lo->s = 0; |
---|
1357 | if(lo->z==NULL) |
---|
1358 | { |
---|
1359 | Free((ADDRESS)lo,sizeof(rnumber)); |
---|
1360 | lo=NULL; |
---|
1361 | } |
---|
1362 | naTest((number)lo); |
---|
1363 | return (number)lo; |
---|
1364 | } |
---|
1365 | |
---|
1366 | number naIntDiv(number la, number lb) |
---|
1367 | { |
---|
1368 | lnumber res; |
---|
1369 | lnumber a = (lnumber)la; |
---|
1370 | lnumber b = (lnumber)lb; |
---|
1371 | if ((a==NULL) || (a->z==NULL)) |
---|
1372 | return NULL; |
---|
1373 | if ((b==NULL) || (b->z==NULL)) |
---|
1374 | { |
---|
1375 | WerrorS("div. by 0"); |
---|
1376 | return NULL; |
---|
1377 | } |
---|
1378 | res = (lnumber)Alloc(sizeof(rnumber)); |
---|
1379 | res->z = napCopy(a->z); |
---|
1380 | res->n = napCopy(b->z); |
---|
1381 | res->s = 0; |
---|
1382 | number nres=(number)res; |
---|
1383 | naNormalize(nres); |
---|
1384 | |
---|
1385 | //napDelete(&res->n); |
---|
1386 | naTest(nres); |
---|
1387 | return nres; |
---|
1388 | } |
---|
1389 | |
---|
1390 | /*2 |
---|
1391 | * division; lo:= la / lb |
---|
1392 | */ |
---|
1393 | number naDiv(number la, number lb) |
---|
1394 | { |
---|
1395 | lnumber lo; |
---|
1396 | lnumber a = (lnumber)la; |
---|
1397 | lnumber b = (lnumber)lb; |
---|
1398 | alg x; |
---|
1399 | |
---|
1400 | if ((a==NULL) || (a->z==NULL)) |
---|
1401 | return NULL; |
---|
1402 | |
---|
1403 | if ((b==NULL) || (b->z==NULL)) |
---|
1404 | { |
---|
1405 | WerrorS("div. by 0"); |
---|
1406 | return NULL; |
---|
1407 | } |
---|
1408 | mmTestP(a,sizeof(rnumber)); |
---|
1409 | mmTestP(b,sizeof(rnumber)); |
---|
1410 | lo = (lnumber)Alloc(sizeof(rnumber)); |
---|
1411 | if (b->n!=NULL) |
---|
1412 | lo->z = napMult(napCopy(a->z), napCopy(b->n)); |
---|
1413 | else |
---|
1414 | lo->z = napCopy(a->z); |
---|
1415 | if (a->n!=NULL) |
---|
1416 | x = napMult(napCopy(b->z), napCopy(a->n)); |
---|
1417 | else |
---|
1418 | x = napCopy(b->z); |
---|
1419 | if (naMinimalPoly!=NULL) |
---|
1420 | { |
---|
1421 | if (lo->z->e[0] >= naMinimalPoly->e[0]) |
---|
1422 | lo->z = napRemainder(lo->z, naMinimalPoly); |
---|
1423 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
1424 | x = napRemainder(x, naMinimalPoly); |
---|
1425 | } |
---|
1426 | #if FEHLER1 |
---|
1427 | if (naI!=NULL) |
---|
1428 | { |
---|
1429 | lo->z = napRedp (lo->z); |
---|
1430 | if (lo->z != NULL) |
---|
1431 | lo->z = napTailred (lo->z); |
---|
1432 | if (x!=NULL) |
---|
1433 | { |
---|
1434 | x = napRedp (x); |
---|
1435 | if (x!=NULL) |
---|
1436 | x = napTailred (x); |
---|
1437 | } |
---|
1438 | } |
---|
1439 | #endif |
---|
1440 | if ((napDeg(x)==0) && nacIsOne(x->ko)) |
---|
1441 | napDelete(&x); |
---|
1442 | lo->s = 0; |
---|
1443 | lo->n = x; |
---|
1444 | naTest((number)lo); |
---|
1445 | return (number)lo; |
---|
1446 | } |
---|
1447 | |
---|
1448 | /*2 |
---|
1449 | * za:= - za |
---|
1450 | */ |
---|
1451 | number naNeg(number za) |
---|
1452 | { |
---|
1453 | if (za!=NULL) |
---|
1454 | { |
---|
1455 | lnumber e = (lnumber)za; |
---|
1456 | naTest(za); |
---|
1457 | e->z = napNeg(e->z); |
---|
1458 | } |
---|
1459 | return za; |
---|
1460 | } |
---|
1461 | |
---|
1462 | /*2 |
---|
1463 | * 1/a |
---|
1464 | */ |
---|
1465 | number naInvers(number a) |
---|
1466 | { |
---|
1467 | lnumber lo; |
---|
1468 | lnumber b = (lnumber)a; |
---|
1469 | alg x; |
---|
1470 | |
---|
1471 | if (b==NULL) |
---|
1472 | { |
---|
1473 | WerrorS("div. by 0"); |
---|
1474 | return NULL; |
---|
1475 | } |
---|
1476 | mmTestP(b,sizeof(rnumber)); |
---|
1477 | lo = (lnumber)Alloc0(sizeof(rnumber)); |
---|
1478 | lo->s = b->s; |
---|
1479 | if (b->n!=NULL) |
---|
1480 | lo->z = napCopy(b->n); |
---|
1481 | else |
---|
1482 | lo->z = napInit(1); |
---|
1483 | x = b->z; |
---|
1484 | if ((napDeg(x)!=0) || !nacIsOne(x->ko)) |
---|
1485 | x = napCopy(x); |
---|
1486 | else |
---|
1487 | { |
---|
1488 | lo->n = NULL; |
---|
1489 | naTest((number)lo); |
---|
1490 | return (number)lo; |
---|
1491 | } |
---|
1492 | if (naMinimalPoly!=NULL) |
---|
1493 | { |
---|
1494 | x = napInvers(x, naMinimalPoly); |
---|
1495 | x = napMult(x, lo->z); |
---|
1496 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
1497 | x = napRemainder(x, naMinimalPoly); |
---|
1498 | lo->z = x; |
---|
1499 | lo->n = NULL; |
---|
1500 | lo->s = 2; |
---|
1501 | while (x!=NULL) |
---|
1502 | { |
---|
1503 | nacNormalize(x->ko); |
---|
1504 | x = x->ne; |
---|
1505 | } |
---|
1506 | } |
---|
1507 | else |
---|
1508 | lo->n = x; |
---|
1509 | naTest((number)lo); |
---|
1510 | return (number)lo; |
---|
1511 | } |
---|
1512 | |
---|
1513 | |
---|
1514 | BOOLEAN naIsZero(number za) |
---|
1515 | { |
---|
1516 | lnumber zb = (lnumber)za; |
---|
1517 | naTest(za); |
---|
1518 | #ifdef TEST |
---|
1519 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(2)"); |
---|
1520 | #endif |
---|
1521 | return ((zb==NULL) || (zb->z==NULL)); |
---|
1522 | } |
---|
1523 | |
---|
1524 | |
---|
1525 | BOOLEAN naGreaterZero(number za) |
---|
1526 | { |
---|
1527 | lnumber zb = (lnumber)za; |
---|
1528 | #ifdef TEST |
---|
1529 | if ((zb!=NULL) && (zb->z==NULL)) WerrorS("internal zero error(3)"); |
---|
1530 | #endif |
---|
1531 | naTest(za); |
---|
1532 | return ((zb!=NULL) && (zb->z!=NULL)); |
---|
1533 | } |
---|
1534 | |
---|
1535 | |
---|
1536 | /*2 |
---|
1537 | * a = b ? |
---|
1538 | */ |
---|
1539 | BOOLEAN naEqual (number a, number b) |
---|
1540 | { |
---|
1541 | number h; |
---|
1542 | BOOLEAN bo; |
---|
1543 | h = naSub(a, b); |
---|
1544 | bo = naIsZero(h); |
---|
1545 | naDelete(&h); |
---|
1546 | return bo; |
---|
1547 | } |
---|
1548 | |
---|
1549 | |
---|
1550 | BOOLEAN naGreater (number a, number b) |
---|
1551 | { |
---|
1552 | if (naIsZero(a)) |
---|
1553 | return FALSE; |
---|
1554 | if (naIsZero(b)) |
---|
1555 | return TRUE; /* a!= 0)*/ |
---|
1556 | return napDeg(((lnumber)a)->n)>napDeg(((lnumber)b)->n); |
---|
1557 | } |
---|
1558 | |
---|
1559 | /*2 |
---|
1560 | * reads a number |
---|
1561 | */ |
---|
1562 | char *naRead(char *s, number *p) |
---|
1563 | { |
---|
1564 | alg x; |
---|
1565 | lnumber a; |
---|
1566 | s = napRead(s, &x); |
---|
1567 | if (x==NULL) |
---|
1568 | { |
---|
1569 | *p = NULL; |
---|
1570 | return s; |
---|
1571 | } |
---|
1572 | *p = (number)Alloc0(sizeof(rnumber)); |
---|
1573 | a = (lnumber)*p; |
---|
1574 | if ((naMinimalPoly!=NULL) && (x->e[0] >= naMinimalPoly->e[0])) |
---|
1575 | a->z = napRemainder(x, naMinimalPoly); |
---|
1576 | #if FEHLER3 |
---|
1577 | else if (naI!=NULL) |
---|
1578 | { |
---|
1579 | a->z = napRedp(x); |
---|
1580 | if (a->z != NULL) |
---|
1581 | a->z = napTailred (a->z); |
---|
1582 | } |
---|
1583 | #endif |
---|
1584 | else |
---|
1585 | a->z = x; |
---|
1586 | if(a->z==NULL) |
---|
1587 | { |
---|
1588 | Free((ADDRESS)*p,sizeof(rnumber)); |
---|
1589 | *p=NULL; |
---|
1590 | } |
---|
1591 | else |
---|
1592 | { |
---|
1593 | a->n = NULL; |
---|
1594 | a->s = 0; |
---|
1595 | naTest(*p); |
---|
1596 | } |
---|
1597 | return s; |
---|
1598 | } |
---|
1599 | |
---|
1600 | /*2 |
---|
1601 | * tries to convert a number to a name |
---|
1602 | */ |
---|
1603 | char * naName(number n) |
---|
1604 | { |
---|
1605 | lnumber ph = (lnumber)n; |
---|
1606 | if ((ph==NULL)||(ph->z==NULL)) |
---|
1607 | return NULL; |
---|
1608 | int i; |
---|
1609 | char *s=(char *)AllocL(4* naNumbOfPar); |
---|
1610 | char *t=(char *)Alloc(8); |
---|
1611 | s[0]='\0'; |
---|
1612 | for (i = 0; i <= naNumbOfPar - 1; i++) |
---|
1613 | { |
---|
1614 | if (ph->z->e[i] > 0) |
---|
1615 | { |
---|
1616 | if (ph->z->e[i] >1) |
---|
1617 | { |
---|
1618 | sprintf(t,"%s%d",naParNames[i],ph->z->e[i]); |
---|
1619 | strcat(s,t); |
---|
1620 | } |
---|
1621 | else |
---|
1622 | { |
---|
1623 | strcat(s,naParNames[i]); |
---|
1624 | } |
---|
1625 | } |
---|
1626 | } |
---|
1627 | Free((ADDRESS)t,8); |
---|
1628 | if (s[0]=='\0') |
---|
1629 | { |
---|
1630 | FreeL((ADDRESS)s); |
---|
1631 | return NULL; |
---|
1632 | } |
---|
1633 | return s; |
---|
1634 | } |
---|
1635 | |
---|
1636 | /*2 |
---|
1637 | * writes a number |
---|
1638 | */ |
---|
1639 | void naWrite(number &phn) |
---|
1640 | { |
---|
1641 | lnumber ph = (lnumber)phn; |
---|
1642 | if ((ph==NULL)||(ph->z==NULL)) |
---|
1643 | StringAppendS("0"); |
---|
1644 | else |
---|
1645 | { |
---|
1646 | //phn->s = 0; |
---|
1647 | naNormalize(phn); |
---|
1648 | napWrite(ph->z); |
---|
1649 | if (ph->n!=NULL) |
---|
1650 | { |
---|
1651 | StringAppendS("/"); |
---|
1652 | napWrite(ph->n); |
---|
1653 | } |
---|
1654 | } |
---|
1655 | } |
---|
1656 | |
---|
1657 | /*2 |
---|
1658 | * za == 1 ? |
---|
1659 | */ |
---|
1660 | BOOLEAN naIsOne(number za) |
---|
1661 | { |
---|
1662 | lnumber a = (lnumber)za; |
---|
1663 | alg x, y; |
---|
1664 | number t; |
---|
1665 | if (a==NULL) return FALSE; |
---|
1666 | mmTestP(a,sizeof(rnumber)); |
---|
1667 | #ifdef TEST |
---|
1668 | if (a->z==NULL) WerrorS("internal zero error(4)"); |
---|
1669 | #endif |
---|
1670 | if (a->n==NULL) |
---|
1671 | { |
---|
1672 | if (napDeg(a->z)==0) return nacIsOne(a->z->ko); |
---|
1673 | else return FALSE; |
---|
1674 | } |
---|
1675 | x = a->z; |
---|
1676 | y = a->n; |
---|
1677 | do |
---|
1678 | { |
---|
1679 | if (napComp(x, y)) |
---|
1680 | return FALSE; |
---|
1681 | else |
---|
1682 | { |
---|
1683 | t = nacSub(x->ko, y->ko); |
---|
1684 | if (!nacIsZero(t)) |
---|
1685 | { |
---|
1686 | nacDelete(&t); |
---|
1687 | return FALSE; |
---|
1688 | } |
---|
1689 | else |
---|
1690 | nacDelete(&t); |
---|
1691 | } |
---|
1692 | x = x->ne; |
---|
1693 | y = y->ne; |
---|
1694 | } |
---|
1695 | while ((x!=NULL) && (y!=NULL)); |
---|
1696 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
1697 | napDelete(&a->z); |
---|
1698 | napDelete(&a->n); |
---|
1699 | a->z = napInit(1); |
---|
1700 | a->n = NULL; |
---|
1701 | a->s = 2; |
---|
1702 | return TRUE; |
---|
1703 | } |
---|
1704 | |
---|
1705 | /*2 |
---|
1706 | * za == -1 ? |
---|
1707 | */ |
---|
1708 | BOOLEAN naIsMOne(number za) |
---|
1709 | { |
---|
1710 | lnumber a = (lnumber)za; |
---|
1711 | alg x, y; |
---|
1712 | number t; |
---|
1713 | if (a==NULL) return FALSE; |
---|
1714 | mmTestP(a,sizeof(rnumber)); |
---|
1715 | #ifdef TEST |
---|
1716 | if (a->z==NULL) WerrorS("internal zero error(4)"); |
---|
1717 | #endif |
---|
1718 | if (a->n==NULL) |
---|
1719 | { |
---|
1720 | if (napDeg(a->z)==0) return nacIsMOne(a->z->ko); |
---|
1721 | else return FALSE; |
---|
1722 | } |
---|
1723 | x = a->z; |
---|
1724 | y = a->n; |
---|
1725 | do |
---|
1726 | { |
---|
1727 | t = nacAdd(x->ko, y->ko); |
---|
1728 | if (!nacIsZero(t)) |
---|
1729 | { |
---|
1730 | nacDelete(&t); |
---|
1731 | return FALSE; |
---|
1732 | } |
---|
1733 | else |
---|
1734 | nacDelete(&t); |
---|
1735 | x = x->ne; |
---|
1736 | y = y->ne; |
---|
1737 | } |
---|
1738 | while ((x!=NULL) && (y!=NULL)); |
---|
1739 | if ((x!=NULL) || (y!=NULL)) return FALSE; |
---|
1740 | napDelete(&a->z); |
---|
1741 | napDelete(&a->n); |
---|
1742 | a->z = napInit(-1); |
---|
1743 | a->n = NULL; |
---|
1744 | a->s = 2; |
---|
1745 | return TRUE; |
---|
1746 | } |
---|
1747 | |
---|
1748 | /*2 |
---|
1749 | * returns the i-th power of p (i>=0) |
---|
1750 | */ |
---|
1751 | void naPower(number p, int i, number *rc) |
---|
1752 | { |
---|
1753 | number x; |
---|
1754 | *rc = naInit(1); |
---|
1755 | for (; i > 0; i--) |
---|
1756 | { |
---|
1757 | x = naMult(*rc, p); |
---|
1758 | naDelete(rc); |
---|
1759 | *rc = x; |
---|
1760 | } |
---|
1761 | } |
---|
1762 | |
---|
1763 | /*2 |
---|
1764 | * result =gcd(a,b) |
---|
1765 | */ |
---|
1766 | number naGcd(number a, number b) |
---|
1767 | { |
---|
1768 | lnumber x, y; |
---|
1769 | lnumber result = (lnumber)Alloc0(sizeof(rnumber)); |
---|
1770 | |
---|
1771 | x = (lnumber)a; |
---|
1772 | y = (lnumber)b; |
---|
1773 | if (naNumbOfPar == 1) |
---|
1774 | { |
---|
1775 | if (naMinimalPoly!=NULL) |
---|
1776 | { |
---|
1777 | if (x->z->ne!=NULL) |
---|
1778 | result->z = napCopy(x->z); |
---|
1779 | else |
---|
1780 | result->z = napGcd0(x->z, y->z); |
---|
1781 | } |
---|
1782 | else |
---|
1783 | result->z = napGcd(x->z, y->z); |
---|
1784 | } |
---|
1785 | else |
---|
1786 | result->z = napGcd0(x->z, y->z); |
---|
1787 | naTest((number)result); |
---|
1788 | return (number)result; |
---|
1789 | } |
---|
1790 | |
---|
1791 | /*2 |
---|
1792 | * naNumbOfPar = 1: |
---|
1793 | * clears denominator algebraic case; |
---|
1794 | * tries to simplify ratio transcendental case; |
---|
1795 | * |
---|
1796 | * cancels monomials |
---|
1797 | * occuring in denominator |
---|
1798 | * and enumerator ? naNumbOfPar != 1; |
---|
1799 | */ |
---|
1800 | void naNormalize(number &pp) |
---|
1801 | { |
---|
1802 | |
---|
1803 | int i,m; |
---|
1804 | number h, h1; |
---|
1805 | alg x, y, r, x1, y1; |
---|
1806 | lnumber p = (lnumber)pp; |
---|
1807 | |
---|
1808 | if ((p==NULL) /*|| (p->s==2)*/) |
---|
1809 | return; |
---|
1810 | BOOLEAN normal_test=(p->s==2); |
---|
1811 | x = p->z; |
---|
1812 | y = p->n; |
---|
1813 | p->s = 2; |
---|
1814 | if ((y!=NULL) && (naMinimalPoly!=NULL)) |
---|
1815 | { |
---|
1816 | y = napInvers(y, naMinimalPoly); |
---|
1817 | x = napMult(x, y); |
---|
1818 | if (x->e[0] >= naMinimalPoly->e[0]) |
---|
1819 | x = napRemainder(x, naMinimalPoly); |
---|
1820 | p->z = x; |
---|
1821 | p->n = y = NULL; |
---|
1822 | } |
---|
1823 | if (y==NULL) |
---|
1824 | { |
---|
1825 | if (naIsChar0) |
---|
1826 | { |
---|
1827 | r = x; |
---|
1828 | while (r!=NULL) |
---|
1829 | { |
---|
1830 | nacNormalize(r->ko); |
---|
1831 | r = r->ne; |
---|
1832 | } |
---|
1833 | } |
---|
1834 | return; |
---|
1835 | } |
---|
1836 | // p->n !=NULL: |
---|
1837 | #if FEHLER1 |
---|
1838 | if (naMinimalPoly == NULL) |
---|
1839 | { |
---|
1840 | alg xx=x; |
---|
1841 | alg yy=y; |
---|
1842 | for (i=(naNumbOfPar-1); i>=0; i--) |
---|
1843 | { |
---|
1844 | m = napExpi(i, yy, xx); |
---|
1845 | if (m != 0) // in this case xx!=NULL!=yy |
---|
1846 | { |
---|
1847 | while (xx != NULL) |
---|
1848 | { |
---|
1849 | xx->e[i] -= m; |
---|
1850 | xx = xx->ne; |
---|
1851 | } |
---|
1852 | while (yy != NULL) |
---|
1853 | { |
---|
1854 | yy->e[i] -= m; |
---|
1855 | yy = yy->ne; |
---|
1856 | } |
---|
1857 | } |
---|
1858 | } |
---|
1859 | } |
---|
1860 | #endif |
---|
1861 | if (naIsChar0) |
---|
1862 | { |
---|
1863 | h1 = nacInvers(y->ko); |
---|
1864 | nacNormalize(h1); |
---|
1865 | napMultN(x, h1); |
---|
1866 | napMultN(y->ne, h1); |
---|
1867 | nacDelete(&y->ko); |
---|
1868 | y->ko = nacInit(1); |
---|
1869 | nacDelete(&h1); |
---|
1870 | } |
---|
1871 | if (napDeg(y)==0) |
---|
1872 | { |
---|
1873 | if (nacIsOne(y->ko)) |
---|
1874 | { |
---|
1875 | napDelete1(&y); |
---|
1876 | p->n = NULL; |
---|
1877 | return; |
---|
1878 | } |
---|
1879 | h = nacInit(1); |
---|
1880 | h1 = nacDiv(h, y->ko); |
---|
1881 | nacDelete(&h); |
---|
1882 | nacNormalize(h1); |
---|
1883 | napMultN(x, h1); |
---|
1884 | nacDelete(&h1); |
---|
1885 | napDelete1(&y); |
---|
1886 | p->n = NULL; |
---|
1887 | return; |
---|
1888 | } |
---|
1889 | if (naNumbOfPar != 1) |
---|
1890 | return; |
---|
1891 | i = napExp(x, y); |
---|
1892 | if (i!=0) |
---|
1893 | { |
---|
1894 | r = x; |
---|
1895 | while (r!=NULL) |
---|
1896 | { |
---|
1897 | r->e[0] -= i; |
---|
1898 | r = r->ne; |
---|
1899 | } |
---|
1900 | r = y; |
---|
1901 | while (r!=NULL) |
---|
1902 | { |
---|
1903 | r->e[0] -= i; |
---|
1904 | r = r->ne; |
---|
1905 | } |
---|
1906 | } |
---|
1907 | if (y->ne==NULL) |
---|
1908 | { |
---|
1909 | if (nacIsOne(y->ko)) |
---|
1910 | { |
---|
1911 | if (y->e[0]==0) |
---|
1912 | { |
---|
1913 | napDelete1(&y); |
---|
1914 | p->n = NULL; |
---|
1915 | } |
---|
1916 | return; |
---|
1917 | } |
---|
1918 | h = nacInit(1); |
---|
1919 | h1 = nacDiv(h, y->ko); |
---|
1920 | if (y->e[0]!=0) |
---|
1921 | { |
---|
1922 | nacDelete(&y->ko); |
---|
1923 | y->ko = h; |
---|
1924 | } |
---|
1925 | else |
---|
1926 | { |
---|
1927 | napDelete1(&y); |
---|
1928 | nacDelete(&h); |
---|
1929 | p->n = NULL; |
---|
1930 | } |
---|
1931 | napMultN(x, h1); |
---|
1932 | nacDelete(&h1); |
---|
1933 | return; |
---|
1934 | } |
---|
1935 | if (x->e[0] >= y->e[0]) |
---|
1936 | { |
---|
1937 | x1 = napCopy(x); |
---|
1938 | y1 = napCopy(y); |
---|
1939 | } |
---|
1940 | else |
---|
1941 | { |
---|
1942 | x1 = napCopy(y); |
---|
1943 | y1 = napCopy(x); |
---|
1944 | } |
---|
1945 | loop |
---|
1946 | { |
---|
1947 | r = napRemainder(x1, y1); |
---|
1948 | if ((r==NULL) || (r->ne==NULL)) break; |
---|
1949 | x1 = y1; |
---|
1950 | y1 = r; |
---|
1951 | } |
---|
1952 | if (r!=NULL) |
---|
1953 | { |
---|
1954 | napDelete(&r); |
---|
1955 | napDelete(&y1); |
---|
1956 | } |
---|
1957 | else |
---|
1958 | { |
---|
1959 | napDivMod(x, y1, &(p->z), &r); |
---|
1960 | napDivMod(y, y1, &(p->n), &r); |
---|
1961 | napDelete(&y1); |
---|
1962 | } |
---|
1963 | x = p->z; |
---|
1964 | y = p->n; |
---|
1965 | if (y->ne==NULL) |
---|
1966 | { |
---|
1967 | if (nacIsOne(y->ko)) |
---|
1968 | { |
---|
1969 | if (y->e[0]==0) |
---|
1970 | { |
---|
1971 | napDelete1(&y); |
---|
1972 | p->n = NULL; |
---|
1973 | } |
---|
1974 | return; |
---|
1975 | } |
---|
1976 | h = nacInit(1); |
---|
1977 | h1 = nacDiv(h, y->ko); |
---|
1978 | if (y->e[0]!=0) |
---|
1979 | { |
---|
1980 | nacDelete(&(y->ko)); |
---|
1981 | y->ko = h; |
---|
1982 | } |
---|
1983 | else |
---|
1984 | { |
---|
1985 | napDelete1(&y); |
---|
1986 | nacDelete(&h); |
---|
1987 | p->n = NULL; |
---|
1988 | } |
---|
1989 | napMultN(x, h1); |
---|
1990 | nacDelete(&h1); |
---|
1991 | } |
---|
1992 | } |
---|
1993 | |
---|
1994 | /*2 |
---|
1995 | * returns in result->n 1 |
---|
1996 | * and in result->z the lcm(a->z,b->n) |
---|
1997 | */ |
---|
1998 | number naLcm(number la, number lb) |
---|
1999 | { |
---|
2000 | lnumber result; |
---|
2001 | lnumber a = (lnumber)la; |
---|
2002 | lnumber b = (lnumber)lb; |
---|
2003 | alg x; |
---|
2004 | number t, bt, r; |
---|
2005 | result = (lnumber)Alloc0(sizeof(rnumber)); |
---|
2006 | if (((naMinimalPoly==NULL) && (naI==NULL)) || !naIsChar0) |
---|
2007 | { |
---|
2008 | result->z = napInit(1); |
---|
2009 | return (number)result; |
---|
2010 | } |
---|
2011 | naNormalize(lb); |
---|
2012 | x = napCopy(a->z); |
---|
2013 | t = napLcm(b->z); |
---|
2014 | if (!nacIsOne(t)) |
---|
2015 | { |
---|
2016 | bt = nacGcd(t, x->ko); |
---|
2017 | r = nacMult(t, x->ko); |
---|
2018 | nacDelete(&(x->ko)); |
---|
2019 | x->ko = nacDiv(r, bt); |
---|
2020 | nacNormalize(x->ko); |
---|
2021 | nacDelete(&bt); |
---|
2022 | nacDelete(&r); |
---|
2023 | } |
---|
2024 | nacDelete(&t); |
---|
2025 | result->z = x; |
---|
2026 | naTest((number)result); |
---|
2027 | return (number)result; |
---|
2028 | } |
---|
2029 | |
---|
2030 | /*2 |
---|
2031 | * input: a set of constant polynomials |
---|
2032 | * sets the global variable naI |
---|
2033 | */ |
---|
2034 | void naSetIdeal(ideal I) |
---|
2035 | { |
---|
2036 | int i; |
---|
2037 | |
---|
2038 | if (idIs0(I)) |
---|
2039 | { |
---|
2040 | for (i=naI->anz-1; i>=0; i--) |
---|
2041 | napDelete(&naI->liste[i]); |
---|
2042 | Free((ADDRESS)naI,sizeof(*naI)); |
---|
2043 | naI=NULL; |
---|
2044 | } |
---|
2045 | else |
---|
2046 | { |
---|
2047 | lnumber h; |
---|
2048 | number a; |
---|
2049 | alg x; |
---|
2050 | |
---|
2051 | naI=(naIdeal)Alloc(sizeof(*naI)); |
---|
2052 | naI->anz=IDELEMS(I); |
---|
2053 | naI->liste=(alg*)Alloc(naI->anz*sizeof(alg)); |
---|
2054 | for (i=IDELEMS(I)-1; i>=0; i--) |
---|
2055 | { |
---|
2056 | h=(lnumber)pGetCoeff(I->m[i]); |
---|
2057 | /* We only need the enumerator of h, as we expect it to be a polynomial */ |
---|
2058 | naI->liste[i]=napCopy(h->z); |
---|
2059 | /* If it isn't normalized (lc = 1) do this */ |
---|
2060 | if (!nacIsOne(naI->liste[i]->ko)) |
---|
2061 | { |
---|
2062 | x=naI->liste[i]; |
---|
2063 | a=nacCopy(x->ko); |
---|
2064 | a=nacDiv(nacInit(1),a); |
---|
2065 | napMultN(x,a); |
---|
2066 | nacDelete(&a); |
---|
2067 | } |
---|
2068 | } |
---|
2069 | } |
---|
2070 | } |
---|
2071 | |
---|
2072 | /*2 |
---|
2073 | * map Z/p -> Q(a) |
---|
2074 | */ |
---|
2075 | number naMapP0(number c) |
---|
2076 | { |
---|
2077 | if (npIsZero(c)) return NULL; |
---|
2078 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
2079 | l->s=2; |
---|
2080 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
2081 | int i=(int)c; |
---|
2082 | if (i>(naPrimeM>>2)) i-=naPrimeM; |
---|
2083 | l->z->ko=nlInit(i); |
---|
2084 | l->n=NULL; |
---|
2085 | return (number)l; |
---|
2086 | } |
---|
2087 | |
---|
2088 | /*2 |
---|
2089 | * map Q -> Q(a) |
---|
2090 | */ |
---|
2091 | number naMap00(number c) |
---|
2092 | { |
---|
2093 | if (nlIsZero(c)) return NULL; |
---|
2094 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
2095 | l->s=0; |
---|
2096 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
2097 | l->z->ko=nlCopy(c); |
---|
2098 | l->n=NULL; |
---|
2099 | return (number)l; |
---|
2100 | } |
---|
2101 | |
---|
2102 | /*2 |
---|
2103 | * map Z/p -> Z/p(a) |
---|
2104 | */ |
---|
2105 | number naMapPP(number c) |
---|
2106 | { |
---|
2107 | if (npIsZero(c)) return NULL; |
---|
2108 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
2109 | l->s=2; |
---|
2110 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
2111 | l->z->ko=c; /* omit npCopy, because npCopy is a no-op */ |
---|
2112 | l->n=NULL; |
---|
2113 | return (number)l; |
---|
2114 | } |
---|
2115 | |
---|
2116 | /*2 |
---|
2117 | * map Z/p' -> Z/p(a) |
---|
2118 | */ |
---|
2119 | number naMapPP1(number c) |
---|
2120 | { |
---|
2121 | if (npIsZero(c)) return NULL; |
---|
2122 | int i=(int)c; |
---|
2123 | if (i>naPrimeM) i-=naPrimeM; |
---|
2124 | number n=npInit(i); |
---|
2125 | if (npIsZero(n)) return NULL; |
---|
2126 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
2127 | l->s=2; |
---|
2128 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
2129 | l->z->ko=n; |
---|
2130 | l->n=NULL; |
---|
2131 | return (number)l; |
---|
2132 | } |
---|
2133 | |
---|
2134 | /*2 |
---|
2135 | * map Q -> Z/p(a) |
---|
2136 | */ |
---|
2137 | number naMap0P(number c) |
---|
2138 | { |
---|
2139 | if (nlIsZero(c)) return NULL; |
---|
2140 | number n=npInit(nlInt(c)); |
---|
2141 | if (npIsZero(n)) return NULL; |
---|
2142 | lnumber l=(lnumber)Alloc(sizeof(rnumber)); |
---|
2143 | l->s=2; |
---|
2144 | l->z=(alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
2145 | l->z->ko=n; |
---|
2146 | l->n=NULL; |
---|
2147 | return (number)l; |
---|
2148 | } |
---|
2149 | |
---|
2150 | static number (*nacMap)(number); |
---|
2151 | static int naParsToCopy; |
---|
2152 | static alg napMap(alg p) |
---|
2153 | { |
---|
2154 | alg w, a; |
---|
2155 | |
---|
2156 | if (p==NULL) return NULL; |
---|
2157 | a = w = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
2158 | memcpy(a->e, p->e, naParsToCopy * sizeof(int)); |
---|
2159 | w->ko = nacMap(p->ko); |
---|
2160 | loop |
---|
2161 | { |
---|
2162 | p=p->ne; |
---|
2163 | if (p==NULL) break; |
---|
2164 | a->ne = (alg)Alloc0(RECA_SIZE + naNumbOfPar * sizeof(int)); |
---|
2165 | a = a->ne; |
---|
2166 | memcpy(a->e, p->e, naParsToCopy * sizeof(int)); |
---|
2167 | a->ko = nacMap(p->ko); |
---|
2168 | } |
---|
2169 | a->ne = NULL; |
---|
2170 | return w; |
---|
2171 | } |
---|
2172 | |
---|
2173 | /*2 |
---|
2174 | * map _(a) -> _(b) |
---|
2175 | */ |
---|
2176 | number naMapQaQb(number c) |
---|
2177 | { |
---|
2178 | if (c==NULL) return NULL; |
---|
2179 | lnumber erg= (lnumber)Alloc0(sizeof(rnumber)); |
---|
2180 | lnumber src =(lnumber)c; |
---|
2181 | erg->s=src->s; |
---|
2182 | erg->z=napMap(src->z); |
---|
2183 | erg->n=napMap(src->n); |
---|
2184 | return (number)erg; |
---|
2185 | } |
---|
2186 | |
---|
2187 | BOOLEAN naSetMap(int c, char ** par, int nop, number minpol) |
---|
2188 | { |
---|
2189 | if (currRing->ch==1) /* -> Q(a) */ |
---|
2190 | { |
---|
2191 | if (c == 0) |
---|
2192 | { |
---|
2193 | nMap = naMap00; /*Q -> Q(a)*/ |
---|
2194 | return TRUE; |
---|
2195 | } |
---|
2196 | if (c>1) |
---|
2197 | { |
---|
2198 | if (par==NULL) |
---|
2199 | { |
---|
2200 | naPrimeM = c; |
---|
2201 | nMap = naMapP0; /* Z/p -> Q(a)*/ |
---|
2202 | return TRUE; |
---|
2203 | } |
---|
2204 | else |
---|
2205 | { |
---|
2206 | return FALSE; /* GF(q) -> Q(a) */ |
---|
2207 | } |
---|
2208 | } |
---|
2209 | if (c<0) |
---|
2210 | { |
---|
2211 | return FALSE; /* Z/p(a) -> Q(b)*/ |
---|
2212 | } |
---|
2213 | if (c==1) |
---|
2214 | { |
---|
2215 | int i; |
---|
2216 | naParsToCopy=0; |
---|
2217 | for(i=0;i<nop;i++) |
---|
2218 | { |
---|
2219 | if ((i>=currRing->P) |
---|
2220 | ||(strcmp(par[i],currRing->parameter[i])!=0)) |
---|
2221 | return FALSE; |
---|
2222 | naParsToCopy++; |
---|
2223 | } |
---|
2224 | nacMap=nacCopy; |
---|
2225 | nMap=naMapQaQb; |
---|
2226 | return TRUE; /* Q(a) -> Q(a) */ |
---|
2227 | } |
---|
2228 | } |
---|
2229 | /*-----------------------------------------------------*/ |
---|
2230 | if (currRing->ch<0) /* -> Z/p(a) */ |
---|
2231 | { |
---|
2232 | if (c == 0) |
---|
2233 | { |
---|
2234 | nMap = naMap0P; /*Q -> Z/p(a)*/ |
---|
2235 | return TRUE; |
---|
2236 | } |
---|
2237 | if (c>1) |
---|
2238 | { |
---|
2239 | if (par==NULL) |
---|
2240 | { |
---|
2241 | if (c==npPrimeM) |
---|
2242 | { |
---|
2243 | nMap = naMapPP; /* Z/p -> Z/p(a)*/ |
---|
2244 | return TRUE; |
---|
2245 | } |
---|
2246 | else |
---|
2247 | { |
---|
2248 | naPrimeM = c; |
---|
2249 | nMap = naMapPP1; /* Z/p' -> Z/p(a)*/ |
---|
2250 | return TRUE; |
---|
2251 | } |
---|
2252 | } |
---|
2253 | else |
---|
2254 | { |
---|
2255 | return FALSE; /* GF(q) ->Z/p(a) */ |
---|
2256 | } |
---|
2257 | } |
---|
2258 | if (c<0) |
---|
2259 | { |
---|
2260 | if (c==currRing->ch) |
---|
2261 | { |
---|
2262 | nacMap=nacCopy; |
---|
2263 | } |
---|
2264 | else |
---|
2265 | { |
---|
2266 | npMapPrime=-c; |
---|
2267 | nacMap = npMapP; |
---|
2268 | } |
---|
2269 | int i; |
---|
2270 | naParsToCopy=0; |
---|
2271 | for(i=0;i<nop;i++) |
---|
2272 | { |
---|
2273 | if ((i>=currRing->P) |
---|
2274 | ||(strcmp(par[i],currRing->parameter[i])!=0)) |
---|
2275 | return FALSE; |
---|
2276 | naParsToCopy++; |
---|
2277 | } |
---|
2278 | nMap=naMapQaQb; |
---|
2279 | return TRUE; /* Z/p(a),Z/p'(a) -> Z/p(b)*/ |
---|
2280 | } |
---|
2281 | if (c==1) |
---|
2282 | { |
---|
2283 | return FALSE; /* Q(a) -> Z/p(b) */ |
---|
2284 | } |
---|
2285 | } |
---|
2286 | return FALSE; /* default */ |
---|
2287 | } |
---|
2288 | |
---|
2289 | /*2 |
---|
2290 | * convert a alg number into a poly |
---|
2291 | */ |
---|
2292 | poly naPermNumber(number z, int * par_perm, int P) |
---|
2293 | { |
---|
2294 | if (z==NULL) return NULL; |
---|
2295 | poly res=NULL; |
---|
2296 | poly p; |
---|
2297 | napoly za=((lnumber)z)->z; |
---|
2298 | do |
---|
2299 | { |
---|
2300 | p=pNew(); |
---|
2301 | pNext(p)=NULL; |
---|
2302 | nNew(&pGetCoeff(p)); |
---|
2303 | int i; |
---|
2304 | for(i=pVariables;i>=0;i--) |
---|
2305 | pGetExp(p,i)=0; |
---|
2306 | napoly pa=NULL; |
---|
2307 | if (currRing->parameter!=NULL) |
---|
2308 | { |
---|
2309 | pGetCoeff(p)=(number)Alloc0(sizeof(rnumber)); |
---|
2310 | ((lnumber)pGetCoeff(p))->s=2; |
---|
2311 | ((lnumber)pGetCoeff(p))->z=napInitz(nacCopy(napGetCoeff(za))); |
---|
2312 | pa=((lnumber)pGetCoeff(p))->z; |
---|
2313 | } |
---|
2314 | else |
---|
2315 | { |
---|
2316 | pGetCoeff(p)=nCopy(napGetCoeff(za)); |
---|
2317 | } |
---|
2318 | for(i=0;i<P;i++) |
---|
2319 | { |
---|
2320 | if(za->e[i]!=0) |
---|
2321 | { |
---|
2322 | if(par_perm[i]>0) |
---|
2323 | pGetExp(p,par_perm[i])=za->e[i]; |
---|
2324 | else if((par_perm[i]<0)&&(pa!=NULL)) |
---|
2325 | pa->e[-par_perm[i]-1]=za->e[i]; |
---|
2326 | else |
---|
2327 | { |
---|
2328 | pDelete(&p); |
---|
2329 | break; |
---|
2330 | } |
---|
2331 | } |
---|
2332 | } |
---|
2333 | if (p!=NULL) |
---|
2334 | { |
---|
2335 | pSetm(p); |
---|
2336 | pTest(p); |
---|
2337 | res=pAdd(res,p); |
---|
2338 | } |
---|
2339 | za=za->ne; |
---|
2340 | } |
---|
2341 | while (za!=NULL); |
---|
2342 | pTest(res); |
---|
2343 | return res; |
---|
2344 | } |
---|
2345 | |
---|
2346 | #ifdef LDEBUG |
---|
2347 | BOOLEAN naDBTest(number a, char *f,int l) |
---|
2348 | { |
---|
2349 | lnumber x=(lnumber)a; |
---|
2350 | if (x == NULL) |
---|
2351 | return TRUE; |
---|
2352 | #ifdef MDEBUG |
---|
2353 | if (!mmDBTestBlock(a,sizeof(rnumber),f,l)) |
---|
2354 | return FALSE; |
---|
2355 | #endif |
---|
2356 | alg p = x->z; |
---|
2357 | if (p==NULL) |
---|
2358 | { |
---|
2359 | Print("0/* in %s:%d\n",f,l); |
---|
2360 | return FALSE; |
---|
2361 | } |
---|
2362 | while(p!=NULL) |
---|
2363 | { |
---|
2364 | if((naMinimalPoly!=NULL)&&(p->e[0]>naMinimalPoly->e[0]) |
---|
2365 | &&(p!=naMinimalPoly)) |
---|
2366 | { |
---|
2367 | Print("deg>minpoly in %s:%d\n",f,l); |
---|
2368 | return FALSE; |
---|
2369 | } |
---|
2370 | //if (naIsChar0 && (((int)p->ko &3) == 0) && (p->ko->s==0) && (x->s==2)) |
---|
2371 | //{ |
---|
2372 | // Print("normalized with non-normal coeffs in %s:%d\n",f,l); |
---|
2373 | // return FALSE; |
---|
2374 | //} |
---|
2375 | if (naIsChar0 && nlDBTest(p->ko,f,l)) |
---|
2376 | return FALSE; |
---|
2377 | #ifdef MDEBUG |
---|
2378 | if (!mmDBTestBlock(p,RECA_SIZE+naNumbOfPar*sizeof(int),f,l)) |
---|
2379 | return FALSE; |
---|
2380 | #endif |
---|
2381 | p = p->ne; |
---|
2382 | } |
---|
2383 | p = x->n; |
---|
2384 | while(p!=NULL) |
---|
2385 | { |
---|
2386 | if (naIsChar0 && nlDBTest(p->ko,f,l)) |
---|
2387 | return FALSE; |
---|
2388 | #ifdef MDEBUG |
---|
2389 | if (!mmDBTestBlock(p,RECA_SIZE+naNumbOfPar*sizeof(int),f,l)) |
---|
2390 | return FALSE; |
---|
2391 | #endif |
---|
2392 | p = p->ne; |
---|
2393 | } |
---|
2394 | return TRUE; |
---|
2395 | } |
---|
2396 | #endif |
---|
2397 | |
---|