1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: polys1.cc,v 1.13 1998-04-24 16:39:25 Singular Exp $ */ |
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5 | |
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6 | /* |
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7 | * ABSTRACT - all basic methods to manipulate polynomials: |
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8 | * independent of representation |
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9 | */ |
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10 | |
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11 | /* includes */ |
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12 | #include <string.h> |
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13 | #include "mod2.h" |
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14 | #include "structs.h" |
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15 | #include "tok.h" |
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16 | #include "numbers.h" |
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17 | #include "mmemory.h" |
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18 | #include "febase.h" |
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19 | #include "weight.h" |
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20 | #include "intvec.h" |
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21 | #include "longalg.h" |
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22 | #include "ring.h" |
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23 | #include "ideals.h" |
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24 | #include "polys.h" |
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25 | #include "ipid.h" |
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26 | #ifdef HAVE_FACTORY |
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27 | #include "clapsing.h" |
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28 | #endif |
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29 | |
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30 | /*-------- several access procedures to monomials -------------------- */ |
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31 | /*2 |
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32 | *test if the monomial is a constant |
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33 | */ |
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34 | BOOLEAN pIsConstant(poly p) |
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35 | { |
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36 | if (p!=NULL) |
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37 | { |
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38 | int i; |
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39 | for (i=pVariables;i;i--) |
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40 | { |
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41 | if (pGetExp(p,i)!=0) return FALSE; |
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42 | } |
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43 | if (pGetComp(p)) return FALSE; |
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44 | } |
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45 | return TRUE; |
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46 | } |
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47 | |
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48 | /*2 |
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49 | *test if the monomial is a constant as a vector component |
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50 | */ |
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51 | BOOLEAN pIsConstantComp(poly p) |
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52 | { |
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53 | int i; |
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54 | |
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55 | for (i=pVariables;i>0;i--) |
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56 | { |
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57 | if (pGetExp(p,i)!=0) return FALSE; |
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58 | } |
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59 | return TRUE; |
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60 | } |
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61 | |
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62 | /*2 |
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63 | *test if a monomial is a pure power |
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64 | */ |
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65 | int pIsPurePower(poly p) |
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66 | { |
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67 | pTest(p); |
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68 | int i,k=0; |
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69 | |
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70 | for (i=pVariables;i>0;i--) |
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71 | { |
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72 | if (pGetExp(p,i)!=0) |
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73 | { |
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74 | if(k!=0) return 0; |
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75 | k=i; |
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76 | } |
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77 | } |
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78 | return k; |
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79 | } |
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80 | |
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81 | /*-----------------------------------------------------------*/ |
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82 | /* |
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83 | * the module weights for std |
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84 | */ |
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85 | static pFDegProc pOldFDeg; |
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86 | static intvec * pModW; |
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87 | static BOOLEAN pOldLexOrder; |
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88 | |
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89 | static int pModDeg(poly p) |
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90 | { |
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91 | return pOldFDeg(p)+(*pModW)[pGetComp(p)-1]; |
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92 | } |
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93 | |
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94 | void pSetModDeg(intvec *w) |
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95 | { |
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96 | if (w!=NULL) |
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97 | { |
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98 | pModW = w; |
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99 | pOldFDeg = pFDeg; |
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100 | pOldLexOrder = pLexOrder; |
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101 | pFDeg = pModDeg; |
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102 | pLexOrder = TRUE; |
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103 | } |
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104 | else |
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105 | { |
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106 | pModW = NULL; |
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107 | pFDeg = pOldFDeg; |
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108 | pLexOrder = pOldLexOrder; |
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109 | } |
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110 | } |
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111 | |
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112 | /*-------------operations on polynomials:------------*/ |
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113 | /*2 |
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114 | * add p1 and p2, p1 and p2 are destroyed |
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115 | */ |
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116 | poly pAdd(poly p1, poly p2) |
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117 | { |
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118 | static poly a1, p, a2, a; |
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119 | int c; |
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120 | number t; |
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121 | |
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122 | if (p1==NULL) return p2; |
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123 | if (p2==NULL) return p1; |
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124 | a1 = p1; |
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125 | a2 = p2; |
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126 | a = p = pNew(); |
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127 | nNew(&(p->coef)); |
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128 | loop |
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129 | { |
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130 | /* a1 and a2 are non-NULL, so we may use pComp0 instead of pComp */ |
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131 | c = pComp0(a1, a2); |
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132 | if (c == 1) |
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133 | { |
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134 | a = pNext(a) = a1; |
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135 | pIter(a1); |
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136 | if (a1==NULL) |
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137 | { |
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138 | pNext(a) = a2; |
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139 | break; |
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140 | } |
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141 | } |
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142 | else if (c == -1) |
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143 | { |
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144 | a = pNext(a) = a2; |
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145 | pIter(a2); |
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146 | if (a2==NULL) |
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147 | { |
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148 | pNext(a) = a1; |
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149 | break; |
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150 | } |
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151 | } |
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152 | else |
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153 | { |
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154 | t=nAdd(a1->coef,a2->coef); |
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155 | pDelete1(&a2); |
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156 | if (nIsZero(t)) |
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157 | { |
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158 | nDelete(&t); |
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159 | pDelete1(&a1); |
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160 | } |
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161 | else |
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162 | { |
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163 | pSetCoeff(a1,t); |
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164 | a = pNext(a) = a1; |
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165 | pIter(a1); |
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166 | } |
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167 | if (a1==NULL) |
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168 | { |
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169 | pNext(a) = a2; |
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170 | break; |
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171 | } |
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172 | else if (a2==NULL) |
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173 | { |
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174 | pNext(a) = a1; |
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175 | break; |
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176 | } |
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177 | } |
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178 | } |
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179 | pDelete1(&p); |
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180 | return p; |
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181 | } |
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182 | |
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183 | /*2 |
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184 | * multiply a polynomial by -1 |
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185 | */ |
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186 | poly pNeg(poly p) |
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187 | { |
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188 | poly h = p; |
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189 | while (h!=NULL) |
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190 | { |
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191 | pGetCoeff(h)=nNeg(pGetCoeff(h)); |
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192 | pIter(h); |
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193 | } |
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194 | return p; |
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195 | } |
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196 | |
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197 | /*2 |
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198 | * subtract p2 from p1, p1 and p2 are destroyed |
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199 | * do not put attention on speed: the procedure is only used in the interpreter |
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200 | */ |
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201 | poly pSub(poly p1, poly p2) |
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202 | { |
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203 | return pAdd(p1, pNeg(p2)); |
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204 | } |
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205 | |
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206 | /*3 |
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207 | * create binomial coef. |
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208 | */ |
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209 | static number* pnBin(int exp) |
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210 | { |
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211 | int e, i, h; |
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212 | number x, y, *bin=NULL; |
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213 | |
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214 | x = nInit(exp); |
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215 | if (nIsZero(x)) |
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216 | { |
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217 | nDelete(&x); |
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218 | return bin; |
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219 | } |
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220 | h = (exp >> 1) + 1; |
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221 | bin = (number *)Alloc0(h*sizeof(number)); |
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222 | bin[1] = x; |
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223 | if (exp < 4) |
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224 | return bin; |
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225 | i = exp - 1; |
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226 | for (e=2; e<h; e++) |
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227 | { |
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228 | // if(!nIsZero(bin[e-1])) |
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229 | // { |
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230 | x = nInit(i); |
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231 | i--; |
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232 | y = nMult(x,bin[e-1]); |
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233 | nDelete(&x); |
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234 | x = nInit(e); |
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235 | bin[e] = nIntDiv(y,x); |
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236 | nDelete(&x); |
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237 | nDelete(&y); |
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238 | // } |
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239 | // else |
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240 | // { |
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241 | // bin[e] = nInit(binom(exp,e)); |
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242 | // } |
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243 | } |
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244 | return bin; |
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245 | } |
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246 | |
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247 | static void pnFreeBin(number *bin, int exp) |
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248 | { |
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249 | int e, h = (exp >> 1) + 1; |
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250 | |
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251 | if (bin[1] != NULL) |
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252 | { |
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253 | for (e=1; e<h; e++) |
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254 | nDelete(&(bin[e])); |
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255 | } |
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256 | Free((ADDRESS)bin, h*sizeof(number)); |
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257 | } |
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258 | |
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259 | /*3 |
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260 | * compute for a monomial m |
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261 | * the power m^exp, exp > 1 |
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262 | * destroys p |
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263 | */ |
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264 | static poly pMonPower(poly p, int exp) |
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265 | { |
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266 | number x, y; |
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267 | int i; |
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268 | |
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269 | y = pGetCoeff(p); |
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270 | nPower(y,exp,&x); |
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271 | nDelete(&y); |
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272 | pSetCoeff0(p,x); |
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273 | for (i=pVariables; i!=0; i--) |
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274 | { |
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275 | pMultExp(p,i, exp); |
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276 | } |
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277 | #ifdef TEST_MAC_ORDER |
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278 | if (bNoAdd) |
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279 | pSetm(p); |
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280 | else |
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281 | #endif |
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282 | p->Order *= exp; |
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283 | return p; |
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284 | } |
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285 | |
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286 | /*3 |
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287 | * compute for monomials p*q |
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288 | * destroys p, keeps q |
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289 | */ |
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290 | static void pMonMult(poly p, poly q) |
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291 | { |
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292 | number x, y; |
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293 | int i; |
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294 | |
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295 | y = pGetCoeff(p); |
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296 | x = nMult(y,pGetCoeff(q)); |
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297 | nDelete(&y); |
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298 | pSetCoeff0(p,x); |
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299 | for (i=pVariables; i!=0; i--) |
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300 | { |
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301 | pAddExp(p,i, pGetExp(q,i)); |
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302 | } |
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303 | p->Order += q->Order; |
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304 | } |
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305 | |
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306 | /*3 |
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307 | * compute for monomials p*q |
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308 | * keeps p, q |
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309 | */ |
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310 | static poly pMonMultC(poly p, poly q) |
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311 | { |
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312 | number x; |
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313 | int i; |
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314 | poly r = pInit(); |
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315 | |
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316 | x = nMult(pGetCoeff(p),pGetCoeff(q)); |
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317 | pSetCoeff0(r,x); |
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318 | pSetComp(r, pGetComp(p)); |
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319 | for (i=pVariables; i!=0; i--) |
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320 | { |
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321 | pSetExp(r,i, pGetExp(p,i) + pGetExp(q,i)); |
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322 | } |
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323 | r->Order = p->Order + q->Order; |
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324 | return r; |
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325 | } |
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326 | |
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327 | /* |
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328 | * compute for a poly p = head+tail, tail is monomial |
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329 | * (head + tail)^exp, exp > 1 |
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330 | * with binomial coef. |
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331 | */ |
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332 | static poly pTwoMonPower(poly p, int exp) |
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333 | { |
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334 | int eh, e, al; |
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335 | poly *a; |
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336 | poly tail, b, res, h; |
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337 | number x; |
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338 | number *bin = pnBin(exp); |
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339 | |
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340 | tail = pNext(p); |
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341 | if (bin == NULL) |
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342 | { |
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343 | pMonPower(p,exp); |
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344 | pMonPower(tail,exp); |
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345 | #ifdef PDEBUG |
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346 | pTest(p); |
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347 | #endif |
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348 | return p; |
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349 | } |
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350 | eh = exp >> 1; |
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351 | al = (exp + 1) * sizeof(poly); |
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352 | a = (poly *)Alloc(al); |
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353 | a[1] = p; |
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354 | for (e=1; e<exp; e++) |
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355 | { |
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356 | a[e+1] = pMonMultC(a[e],p); |
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357 | } |
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358 | res = a[exp]; |
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359 | b = pHead(tail); |
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360 | for (e=exp-1; e>eh; e--) |
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361 | { |
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362 | h = a[e]; |
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363 | x = nMult(bin[exp-e],pGetCoeff(h)); |
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364 | pSetCoeff(h,x); |
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365 | pMonMult(h,b); |
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366 | res = pNext(res) = h; |
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367 | pMonMult(b,tail); |
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368 | } |
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369 | for (e=eh; e!=0; e--) |
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370 | { |
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371 | h = a[e]; |
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372 | x = nMult(bin[e],pGetCoeff(h)); |
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373 | pSetCoeff(h,x); |
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374 | pMonMult(h,b); |
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375 | res = pNext(res) = h; |
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376 | pMonMult(b,tail); |
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377 | } |
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378 | pDelete1(&tail); |
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379 | pNext(res) = b; |
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380 | pNext(b) = NULL; |
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381 | res = a[exp]; |
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382 | Free((ADDRESS)a, al); |
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383 | pnFreeBin(bin, exp); |
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384 | // tail=res; |
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385 | // while((tail!=NULL)&&(pNext(tail)!=NULL)) |
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386 | // { |
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387 | // if(nIsZero(pGetCoeff(pNext(tail)))) |
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388 | // { |
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389 | // pDelete1(&pNext(tail)); |
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390 | // } |
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391 | // else |
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392 | // pIter(tail); |
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393 | // } |
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394 | #ifdef PDEBUG |
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395 | pTest(res); |
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396 | #endif |
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397 | return res; |
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398 | } |
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399 | |
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400 | static poly pPow(poly p, int i) |
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401 | { |
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402 | poly rc = pCopy(p); |
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403 | i -= 2; |
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404 | do |
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405 | { |
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406 | rc = pMult(rc,pCopy(p)); |
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407 | i--; |
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408 | } |
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409 | while (i != 0); |
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410 | return pMult(rc,p); |
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411 | } |
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412 | |
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413 | /*2 |
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414 | * returns the i-th power of p |
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415 | * p will be destroyed |
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416 | */ |
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417 | poly pPower(poly p, int i) |
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418 | { |
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419 | if (i==0) |
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420 | return pOne(); |
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421 | |
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422 | poly rc=NULL; |
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423 | |
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424 | if(p!=NULL) |
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425 | { |
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426 | switch (i) |
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427 | { |
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428 | case 0: |
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429 | { |
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430 | rc=pOne(); |
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431 | #ifdef DRING |
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432 | if ((pDRING) && (pdDFlag(p)==1)) |
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433 | { |
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434 | pdDFlag(rc)=1; |
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435 | } |
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436 | #endif |
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437 | pDelete(&p); |
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438 | break; |
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439 | } |
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440 | case 1: |
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441 | rc=p; |
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442 | break; |
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443 | case 2: |
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444 | rc=pMult(pCopy(p),p); |
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445 | break; |
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446 | default: |
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447 | if (i < 0) |
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448 | { |
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449 | #ifdef DRING |
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450 | if (pDRING) |
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451 | { |
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452 | int j,t; |
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453 | rc=p; |
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454 | while(p!=NULL) |
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455 | { |
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456 | for(j=1;j<=pdK;j++) |
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457 | { |
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458 | if(pGetExp(p,pdY(j))!=0) |
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459 | { |
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460 | pDelete(&rc); |
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461 | return NULL; |
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462 | } |
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463 | } |
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464 | for(j=1;j<=pdN;j++) |
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465 | { |
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466 | t=pGetExp(p,pdX(j)); |
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467 | pGetExp(p,pdX(j)]=pGetExp(p,pdIX(j)); |
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468 | pGetExp(p,pdIX(j))=t; |
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469 | } |
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470 | pIter(p); |
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471 | } |
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472 | return pPower(rc,-i); |
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473 | } |
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474 | else |
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475 | #endif |
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476 | { |
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477 | pDelete(&p); |
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478 | return NULL; |
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479 | } |
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480 | } |
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481 | #ifdef SDRING |
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482 | if(pSDRING) |
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483 | { |
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484 | return pPow(p,i); |
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485 | } |
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486 | else |
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487 | #endif |
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488 | { |
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489 | rc = pNext(p); |
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490 | if (rc != NULL) |
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491 | { |
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492 | int char_p=rChar(currRing); |
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493 | if ((pNext(rc) != NULL) |
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494 | || ((char_p>0) && (i>char_p))) |
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495 | { |
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496 | return pPow(p,i); |
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497 | } |
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498 | return pTwoMonPower(p,i); |
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499 | } |
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500 | return pMonPower(p,i); |
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501 | } |
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502 | /*end default:*/ |
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503 | } |
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504 | } |
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505 | return rc; |
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506 | } |
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507 | |
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508 | /*2 |
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509 | * returns the partial differentiate of a by the k-th variable |
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510 | * does not destroy the input |
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511 | */ |
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512 | poly pDiff(poly a, int k) |
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513 | { |
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514 | poly res, f, last; |
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515 | number t; |
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516 | |
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517 | last = res = NULL; |
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518 | while (a!=NULL) |
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519 | { |
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520 | if (pGetExp(a,k)!=0) |
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521 | { |
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522 | f = pNew(); |
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523 | pCopy2(f,a); |
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524 | pNext(f)=NULL; |
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525 | t = nInit(pGetExp(a,k)); |
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526 | pSetCoeff0(f,nMult(t,pGetCoeff(a))); |
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527 | nDelete(&t); |
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528 | if (nIsZero(pGetCoeff(f))) |
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529 | pDelete1(&f); |
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530 | else |
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531 | { |
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532 | pDecrExp(f,k); |
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533 | pSetm(f); |
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534 | if (res==NULL) |
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535 | { |
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536 | res=last=f; |
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537 | } |
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538 | else |
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539 | { |
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540 | pNext(last)=f; |
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541 | last=f; |
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542 | } |
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543 | //res = pAdd(res, f); |
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544 | } |
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545 | } |
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546 | pIter(a); |
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547 | } |
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548 | return res; |
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549 | } |
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550 | |
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551 | static poly pDiffOpM(poly a, poly b,BOOLEAN multiply) |
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552 | { |
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553 | int i,j,s; |
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554 | number n,h,hh; |
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555 | poly p=pOne(); |
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556 | n=nMult(pGetCoeff(a),pGetCoeff(b)); |
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557 | for(i=pVariables;i>0;i--) |
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558 | { |
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559 | s=pGetExp(b,i); |
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560 | if (s<pGetExp(a,i)) |
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561 | { |
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562 | nDelete(&n); |
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563 | pDelete1(&p); |
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564 | return NULL; |
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565 | } |
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566 | if (multiply) |
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567 | { |
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568 | for(j=pGetExp(a,i); j>0;j--) |
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569 | { |
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570 | h = nInit(s); |
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571 | hh=nMult(n,h); |
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572 | nDelete(&h); |
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573 | nDelete(&n); |
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574 | n=hh; |
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575 | s--; |
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576 | } |
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577 | pSetExp(p,i,s); |
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578 | } |
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579 | else |
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580 | { |
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581 | pSetExp(p,i,s-pGetExp(a,i)); |
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582 | } |
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583 | } |
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584 | pSetm(p); |
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585 | /*if (multiply)*/ pSetCoeff(p,n); |
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586 | return p; |
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587 | } |
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588 | |
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589 | poly pDiffOp(poly a, poly b,BOOLEAN multiply) |
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590 | { |
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591 | poly result=NULL; |
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592 | poly h; |
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593 | for(;a!=NULL;pIter(a)) |
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594 | { |
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595 | for(h=b;h!=NULL;pIter(h)) |
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596 | { |
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597 | result=pAdd(result,pDiffOpM(a,h,multiply)); |
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598 | } |
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599 | } |
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600 | return result; |
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601 | } |
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602 | |
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603 | /*2 |
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604 | * returns the length of a (numbers of monomials) |
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605 | */ |
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606 | int pLength(poly a) |
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607 | { |
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608 | int l = 0; |
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609 | |
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610 | while (a!=NULL) |
---|
611 | { |
---|
612 | pIter(a); |
---|
613 | l++; |
---|
614 | } |
---|
615 | return l; |
---|
616 | } |
---|
617 | |
---|
618 | |
---|
619 | void pSplit(poly p, poly *h) |
---|
620 | { |
---|
621 | *h=pNext(p); |
---|
622 | pNext(p)=NULL; |
---|
623 | } |
---|
624 | |
---|
625 | /*2 |
---|
626 | * returns maximal column number in the modul element a (or 0) |
---|
627 | */ |
---|
628 | int pMaxComp(poly p) |
---|
629 | { |
---|
630 | int result,i; |
---|
631 | |
---|
632 | if(p==NULL) return 0; |
---|
633 | result = pGetComp(p); |
---|
634 | while (pNext(p)!=NULL) |
---|
635 | { |
---|
636 | pIter(p); |
---|
637 | i = pGetComp(p); |
---|
638 | if (i>result) result = i; |
---|
639 | } |
---|
640 | return result; |
---|
641 | } |
---|
642 | |
---|
643 | /*2 |
---|
644 | * returns minimal column number in the modul element a (or 0) |
---|
645 | */ |
---|
646 | int pMinComp(poly p) |
---|
647 | { |
---|
648 | int result,i; |
---|
649 | |
---|
650 | if(p==NULL) return 0; |
---|
651 | result = pGetComp(p); |
---|
652 | while (pNext(p)!=NULL) |
---|
653 | { |
---|
654 | pIter(p); |
---|
655 | i = pGetComp(p); |
---|
656 | if (i<result) result = i; |
---|
657 | } |
---|
658 | return result; |
---|
659 | } |
---|
660 | |
---|
661 | /*2 |
---|
662 | * multiplies the polynomial a by the column generator with number i |
---|
663 | */ |
---|
664 | void pSetCompP(poly p, int i) |
---|
665 | { |
---|
666 | |
---|
667 | if ((p!=NULL) && (pGetComp(p)==0)) |
---|
668 | { |
---|
669 | do |
---|
670 | { |
---|
671 | pSetComp(p, (Exponent_t)i); |
---|
672 | pIter(p); |
---|
673 | } while (p!=NULL); |
---|
674 | } |
---|
675 | } |
---|
676 | |
---|
677 | /*2 |
---|
678 | * handle memory request for sets of polynomials (ideals) |
---|
679 | * l is the length of *p, increment is the difference (may be negative) |
---|
680 | */ |
---|
681 | void pEnlargeSet(polyset *p, int l, int increment) |
---|
682 | { |
---|
683 | int i; |
---|
684 | polyset h; |
---|
685 | |
---|
686 | h=(polyset)ReAlloc((poly*)*p,l*sizeof(poly),(l+increment)*sizeof(poly)); |
---|
687 | if (increment>0) |
---|
688 | { |
---|
689 | for (i=l; i<l+increment; i++) |
---|
690 | h[i]=NULL; |
---|
691 | } |
---|
692 | *p=h; |
---|
693 | } |
---|
694 | |
---|
695 | /*2 |
---|
696 | * returns a polynomial representing the integer i |
---|
697 | */ |
---|
698 | poly pISet(int i) |
---|
699 | { |
---|
700 | poly rc = NULL; |
---|
701 | if (i!=0) |
---|
702 | { |
---|
703 | rc = pInit(); |
---|
704 | pSetCoeff0(rc,nInit(i)); |
---|
705 | if (nIsZero(pGetCoeff(rc))) |
---|
706 | pDelete1(&rc); |
---|
707 | #ifdef TEST_MAC_ORDER |
---|
708 | else if (bNoAdd) |
---|
709 | pSetm(rc); |
---|
710 | #endif |
---|
711 | } |
---|
712 | return rc; |
---|
713 | } |
---|
714 | |
---|
715 | // /*2 |
---|
716 | // * create a new polynomial and init it as 1 |
---|
717 | // */ |
---|
718 | // poly pOne(void) |
---|
719 | // { |
---|
720 | // poly p=pInit(); |
---|
721 | // pSetCoeff0(p,nInit(1)); |
---|
722 | // #ifdef TEST_MAC_ORDER |
---|
723 | // pSetm(p); |
---|
724 | // #endif |
---|
725 | // return p; |
---|
726 | // } |
---|
727 | |
---|
728 | void pContent(poly ph) |
---|
729 | { |
---|
730 | number h,d; |
---|
731 | poly p; |
---|
732 | |
---|
733 | p = ph; |
---|
734 | if(pNext(p)==NULL) |
---|
735 | { |
---|
736 | pSetCoeff(p,nInit(1)); |
---|
737 | } |
---|
738 | else |
---|
739 | { |
---|
740 | #ifdef PDEBUG |
---|
741 | if (!pTest(p)) return; |
---|
742 | #endif |
---|
743 | nNormalize(pGetCoeff(p)); |
---|
744 | if(!nGreaterZero(pGetCoeff(ph))) |
---|
745 | ph = pNeg(ph); |
---|
746 | h=nCopy(pGetCoeff(p)); |
---|
747 | pIter(p); |
---|
748 | while (p!=NULL) |
---|
749 | { |
---|
750 | nNormalize(pGetCoeff(p)); |
---|
751 | d=nGcd(h,pGetCoeff(p)); |
---|
752 | nDelete(&h); |
---|
753 | h = d; |
---|
754 | if(nIsOne(h)) |
---|
755 | { |
---|
756 | break; |
---|
757 | } |
---|
758 | pIter(p); |
---|
759 | } |
---|
760 | p = ph; |
---|
761 | //number tmp; |
---|
762 | if(!nIsOne(h)) |
---|
763 | { |
---|
764 | while (p!=NULL) |
---|
765 | { |
---|
766 | //d = nDiv(pGetCoeff(p),h); |
---|
767 | //tmp = nIntDiv(pGetCoeff(p),h); |
---|
768 | //if (!nEqual(d,tmp)) |
---|
769 | //{ |
---|
770 | // StringSetS("** div0:");nWrite(pGetCoeff(p));StringAppendS("/"); |
---|
771 | // nWrite(h);StringAppendS("=");nWrite(d);StringAppendS(" int:"); |
---|
772 | // nWrite(tmp);Print(StringAppendS("\n")); |
---|
773 | //} |
---|
774 | //nDelete(&tmp); |
---|
775 | d = nIntDiv(pGetCoeff(p),h); |
---|
776 | pSetCoeff(p,d); |
---|
777 | pIter(p); |
---|
778 | } |
---|
779 | } |
---|
780 | nDelete(&h); |
---|
781 | #ifdef HAVE_FACTORY |
---|
782 | if ( (nGetChar() == 1) || (nGetChar() < 0) ) /* Q[a],Q(a),Zp[a],Z/p(a) */ |
---|
783 | { |
---|
784 | pTest(ph); |
---|
785 | singclap_divide_content(ph); |
---|
786 | pTest(ph); |
---|
787 | } |
---|
788 | #endif |
---|
789 | } |
---|
790 | } |
---|
791 | |
---|
792 | void pCleardenom(poly ph) |
---|
793 | { |
---|
794 | number d, h; |
---|
795 | poly p; |
---|
796 | |
---|
797 | p = ph; |
---|
798 | if(pNext(p)==NULL) |
---|
799 | { |
---|
800 | pSetCoeff(p,nInit(1)); |
---|
801 | } |
---|
802 | else |
---|
803 | { |
---|
804 | h = nInit(1); |
---|
805 | while (p!=NULL) |
---|
806 | { |
---|
807 | nNormalize(pGetCoeff(p)); |
---|
808 | d=nLcm(h,pGetCoeff(p)); |
---|
809 | nDelete(&h); |
---|
810 | h=d; |
---|
811 | pIter(p); |
---|
812 | } |
---|
813 | /* contains the 1/lcm of all denominators */ |
---|
814 | if(!nIsOne(h)) |
---|
815 | { |
---|
816 | p = ph; |
---|
817 | while (p!=NULL) |
---|
818 | { |
---|
819 | /* should be: |
---|
820 | * number hh; |
---|
821 | * nGetDenom(p->coef,&hh); |
---|
822 | * nMult(&h,&hh,&d); |
---|
823 | * nNormalize(d); |
---|
824 | * nDelete(&hh); |
---|
825 | * nMult(d,p->coef,&hh); |
---|
826 | * nDelete(&d); |
---|
827 | * nDelete(&(p->coef)); |
---|
828 | * p->coef =hh; |
---|
829 | */ |
---|
830 | d=nMult(h,pGetCoeff(p)); |
---|
831 | nNormalize(d); |
---|
832 | pSetCoeff(p,d); |
---|
833 | pIter(p); |
---|
834 | } |
---|
835 | nDelete(&h); |
---|
836 | if (nGetChar()==1) |
---|
837 | { |
---|
838 | h = nInit(1); |
---|
839 | p=ph; |
---|
840 | while (p!=NULL) |
---|
841 | { |
---|
842 | d=nLcm(h,pGetCoeff(p)); |
---|
843 | nDelete(&h); |
---|
844 | h=d; |
---|
845 | pIter(p); |
---|
846 | } |
---|
847 | /* contains the 1/lcm of all denominators */ |
---|
848 | if(!nIsOne(h)) |
---|
849 | { |
---|
850 | p = ph; |
---|
851 | while (p!=NULL) |
---|
852 | { |
---|
853 | /* should be: |
---|
854 | * number hh; |
---|
855 | * nGetDenom(p->coef,&hh); |
---|
856 | * nMult(&h,&hh,&d); |
---|
857 | * nNormalize(d); |
---|
858 | * nDelete(&hh); |
---|
859 | * nMult(d,p->coef,&hh); |
---|
860 | * nDelete(&d); |
---|
861 | * nDelete(&(p->coef)); |
---|
862 | * p->coef =hh; |
---|
863 | */ |
---|
864 | d=nMult(h,pGetCoeff(p)); |
---|
865 | nNormalize(d); |
---|
866 | pSetCoeff(p,d); |
---|
867 | pIter(p); |
---|
868 | } |
---|
869 | nDelete(&h); |
---|
870 | } |
---|
871 | } |
---|
872 | } |
---|
873 | pContent(ph); |
---|
874 | } |
---|
875 | } |
---|
876 | |
---|
877 | /*2 |
---|
878 | *tests if p is homogeneous with respect to the actual weigths |
---|
879 | */ |
---|
880 | BOOLEAN pIsHomogeneous (poly p) |
---|
881 | { |
---|
882 | poly qp=p; |
---|
883 | int o; |
---|
884 | |
---|
885 | if ((p == NULL) || (pNext(p) == NULL)) return TRUE; |
---|
886 | pFDegProc d=(pLexOrder ? pTotaldegree : pFDeg ); |
---|
887 | o = d(p); |
---|
888 | do |
---|
889 | { |
---|
890 | if (d(qp) != o) return FALSE; |
---|
891 | pIter(qp); |
---|
892 | } |
---|
893 | while (qp != NULL); |
---|
894 | return TRUE; |
---|
895 | } |
---|
896 | |
---|
897 | // orders monoms of poly using merge sort (ususally faster than |
---|
898 | // insertion sort). ASSUMES that pSetm was performed on monoms |
---|
899 | // (i.e. that Order field is set correctly) |
---|
900 | poly pOrdPolyMerge(poly p) |
---|
901 | { |
---|
902 | poly qq,pp,result=NULL; |
---|
903 | |
---|
904 | if (p == NULL) return NULL; |
---|
905 | |
---|
906 | for (;;) |
---|
907 | { |
---|
908 | qq = p; |
---|
909 | for (;;) |
---|
910 | { |
---|
911 | if (pNext(p) == NULL) return pAdd(result, qq); |
---|
912 | if (pComp(p,pNext(p)) != 1) |
---|
913 | { |
---|
914 | pp = p; |
---|
915 | pIter(p); |
---|
916 | pNext(pp) = NULL; |
---|
917 | result = pAdd(result, qq); |
---|
918 | break; |
---|
919 | } |
---|
920 | pIter(p); |
---|
921 | } |
---|
922 | } |
---|
923 | } |
---|
924 | |
---|
925 | // orders monoms of poly using insertion sort, performs pSetm on each |
---|
926 | // monom (i.e. sets Order field) |
---|
927 | poly pOrdPolyInsertSetm(poly p) |
---|
928 | { |
---|
929 | poly qq,result = NULL; |
---|
930 | |
---|
931 | while (p != NULL) |
---|
932 | { |
---|
933 | qq = p; |
---|
934 | pIter(p); |
---|
935 | qq->next = NULL; |
---|
936 | pSetm(qq); |
---|
937 | result = pAdd(result,qq); |
---|
938 | pTest(result); |
---|
939 | } |
---|
940 | return result; |
---|
941 | } |
---|
942 | |
---|
943 | /*2 |
---|
944 | *returns a re-ordered copy of a polynomial, with permutation of the variables |
---|
945 | */ |
---|
946 | poly pPermPoly (poly p, int * perm, ring oldRing, |
---|
947 | int *par_perm, int OldPar) |
---|
948 | { |
---|
949 | int OldpVariables = oldRing->N; |
---|
950 | poly result = NULL; |
---|
951 | poly aq=NULL; |
---|
952 | poly qq; |
---|
953 | int i; |
---|
954 | |
---|
955 | while (p != NULL) |
---|
956 | { |
---|
957 | if (OldPar==0) |
---|
958 | { |
---|
959 | qq = pInit(); |
---|
960 | pGetCoeff(qq)=nMap(pGetCoeff(p)); |
---|
961 | } |
---|
962 | else |
---|
963 | { |
---|
964 | qq=pOne(); |
---|
965 | aq=naPermNumber(pGetCoeff(p),par_perm,OldPar); |
---|
966 | pTest(aq); |
---|
967 | } |
---|
968 | pSetComp(qq, pRingGetComp(oldRing,p)); |
---|
969 | if (nIsZero(pGetCoeff(qq))) |
---|
970 | { |
---|
971 | pDelete1(&qq); |
---|
972 | } |
---|
973 | else |
---|
974 | { |
---|
975 | for(i=1; i<=OldpVariables; i++) |
---|
976 | { |
---|
977 | if (pRingGetExp(oldRing,p,i)!=0) |
---|
978 | { |
---|
979 | if (perm==NULL) |
---|
980 | { |
---|
981 | pSetExp(qq,i, pRingGetExp(oldRing,p,i)); |
---|
982 | } |
---|
983 | else if (perm[i]>0) |
---|
984 | pAddExp(qq,perm[i], pRingGetExp(oldRing, p,i)); |
---|
985 | else if (perm[i]<0) |
---|
986 | { |
---|
987 | lnumber c=(lnumber)pGetCoeff(qq); |
---|
988 | c->z->e[-perm[i]-1]+=pRingGetExp(oldRing, p,i); |
---|
989 | } |
---|
990 | else |
---|
991 | { |
---|
992 | /* this variable maps to 0 !*/ |
---|
993 | pDelete1(&qq); |
---|
994 | break; |
---|
995 | } |
---|
996 | } |
---|
997 | } |
---|
998 | } |
---|
999 | pIter(p); |
---|
1000 | if (qq!=NULL) |
---|
1001 | { |
---|
1002 | pSetm(qq); |
---|
1003 | pTest(qq); |
---|
1004 | pTest(aq); |
---|
1005 | if (aq!=NULL) |
---|
1006 | { |
---|
1007 | qq=pMult(aq,qq); |
---|
1008 | aq=NULL; |
---|
1009 | } |
---|
1010 | result = pAdd(result,qq); |
---|
1011 | pTest(result); |
---|
1012 | } |
---|
1013 | else if (aq!=NULL) |
---|
1014 | { |
---|
1015 | pDelete(&aq); |
---|
1016 | } |
---|
1017 | } |
---|
1018 | return result; |
---|
1019 | } |
---|
1020 | |
---|
1021 | poly pJet(poly p, int m) |
---|
1022 | { |
---|
1023 | poly r=NULL; |
---|
1024 | poly t=NULL; |
---|
1025 | |
---|
1026 | while (p!=NULL) |
---|
1027 | { |
---|
1028 | if (pTotaldegree(p)<=m) |
---|
1029 | { |
---|
1030 | if (r==NULL) |
---|
1031 | r=pHead(p); |
---|
1032 | else |
---|
1033 | if (t==NULL) |
---|
1034 | { |
---|
1035 | pNext(r)=pHead(p); |
---|
1036 | t=pNext(r); |
---|
1037 | } |
---|
1038 | else |
---|
1039 | { |
---|
1040 | pNext(t)=pHead(p); |
---|
1041 | pIter(t); |
---|
1042 | } |
---|
1043 | } |
---|
1044 | pIter(p); |
---|
1045 | } |
---|
1046 | return r; |
---|
1047 | } |
---|
1048 | |
---|
1049 | poly pJetW(poly p, int m, short *w) |
---|
1050 | { |
---|
1051 | poly r=NULL; |
---|
1052 | poly t=NULL; |
---|
1053 | short *wsave=ecartWeights; |
---|
1054 | |
---|
1055 | ecartWeights=w; |
---|
1056 | |
---|
1057 | while (p!=NULL) |
---|
1058 | { |
---|
1059 | if (totaldegreeWecart(p)<=m) |
---|
1060 | { |
---|
1061 | if (r==NULL) |
---|
1062 | r=pHead(p); |
---|
1063 | else |
---|
1064 | if (t==NULL) |
---|
1065 | { |
---|
1066 | pNext(r)=pHead(p); |
---|
1067 | t=pNext(r); |
---|
1068 | } |
---|
1069 | else |
---|
1070 | { |
---|
1071 | pNext(t)=pHead(p); |
---|
1072 | pIter(t); |
---|
1073 | } |
---|
1074 | } |
---|
1075 | pIter(p); |
---|
1076 | } |
---|
1077 | ecartWeights=wsave; |
---|
1078 | return r; |
---|
1079 | } |
---|
1080 | |
---|
1081 | int pDegW(poly p, short *w) |
---|
1082 | { |
---|
1083 | int r=0; |
---|
1084 | short *wsave=ecartWeights; |
---|
1085 | |
---|
1086 | ecartWeights=w; |
---|
1087 | |
---|
1088 | while (p!=NULL) |
---|
1089 | { |
---|
1090 | r=max(r, totaldegreeWecart(p)); |
---|
1091 | pIter(p); |
---|
1092 | } |
---|
1093 | ecartWeights=wsave; |
---|
1094 | return r; |
---|
1095 | } |
---|
1096 | |
---|
1097 | /*-----------type conversions ----------------------------*/ |
---|
1098 | /*2 |
---|
1099 | * input: a set of polys (len elements: p[0]..p[len-1]) |
---|
1100 | * output: a vector |
---|
1101 | * p will not be changed |
---|
1102 | */ |
---|
1103 | poly pPolys2Vec(polyset p, int len) |
---|
1104 | { |
---|
1105 | poly v=NULL; |
---|
1106 | poly h; |
---|
1107 | int i; |
---|
1108 | |
---|
1109 | for (i=len-1; i>=0; i--) |
---|
1110 | { |
---|
1111 | if (p[i]) |
---|
1112 | { |
---|
1113 | h=pCopy(p[i]); |
---|
1114 | pSetCompP(h,i+1); |
---|
1115 | v=pAdd(v,h); |
---|
1116 | } |
---|
1117 | } |
---|
1118 | return v; |
---|
1119 | } |
---|
1120 | |
---|
1121 | /*2 |
---|
1122 | * convert a vector to a set of polys, |
---|
1123 | * allocates the polyset, (entries 0..(*len)-1) |
---|
1124 | * the vector will not be changed |
---|
1125 | */ |
---|
1126 | void pVec2Polys(poly v, polyset *p, int *len) |
---|
1127 | { |
---|
1128 | poly h; |
---|
1129 | int k; |
---|
1130 | |
---|
1131 | *len=pMaxComp(v); |
---|
1132 | if (*len==0) *len=1; |
---|
1133 | *p=(polyset)Alloc0((*len)*sizeof(poly)); |
---|
1134 | while (v!=NULL) |
---|
1135 | { |
---|
1136 | h=pHead(v); |
---|
1137 | k=pGetComp(h); |
---|
1138 | pSetComp(h,0); |
---|
1139 | (*p)[k-1]=pAdd((*p)[k-1],h); |
---|
1140 | pIter(v); |
---|
1141 | } |
---|
1142 | } |
---|
1143 | |
---|
1144 | int pVar(poly m) |
---|
1145 | { |
---|
1146 | if (m==NULL) return 0; |
---|
1147 | if (pNext(m)!=NULL) return 0; |
---|
1148 | int i,e=0; |
---|
1149 | for (i=pVariables; i>0; i--) |
---|
1150 | { |
---|
1151 | if (pGetExp(m,i)==1) |
---|
1152 | { |
---|
1153 | if (e==0) e=i; |
---|
1154 | else return 0; |
---|
1155 | } |
---|
1156 | } |
---|
1157 | return e; |
---|
1158 | } |
---|
1159 | |
---|
1160 | /*----------utilities for syzygies--------------*/ |
---|
1161 | //BOOLEAN pVectorHasUnitM(poly p, int * k) |
---|
1162 | //{ |
---|
1163 | // while (p!=NULL) |
---|
1164 | // { |
---|
1165 | // if (pIsConstantComp(p)) |
---|
1166 | // { |
---|
1167 | // *k = pGetComp(p); |
---|
1168 | // return TRUE; |
---|
1169 | // } |
---|
1170 | // else pIter(p); |
---|
1171 | // } |
---|
1172 | // return FALSE; |
---|
1173 | //} |
---|
1174 | |
---|
1175 | BOOLEAN pVectorHasUnitB(poly p, int * k) |
---|
1176 | { |
---|
1177 | poly q=p,qq; |
---|
1178 | int i; |
---|
1179 | |
---|
1180 | while (q!=NULL) |
---|
1181 | { |
---|
1182 | if (pIsConstantComp(q)) |
---|
1183 | { |
---|
1184 | i = pGetComp(q); |
---|
1185 | qq = p; |
---|
1186 | while ((qq != q) && (pGetComp(qq) != i)) pIter(qq); |
---|
1187 | if (qq == q) |
---|
1188 | { |
---|
1189 | *k = i; |
---|
1190 | return TRUE; |
---|
1191 | } |
---|
1192 | else |
---|
1193 | pIter(q); |
---|
1194 | } |
---|
1195 | else pIter(q); |
---|
1196 | } |
---|
1197 | return FALSE; |
---|
1198 | } |
---|
1199 | |
---|
1200 | void pVectorHasUnit(poly p, int * k, int * len) |
---|
1201 | { |
---|
1202 | poly q=p,qq; |
---|
1203 | int i,j=0; |
---|
1204 | |
---|
1205 | *len = 0; |
---|
1206 | while (q!=NULL) |
---|
1207 | { |
---|
1208 | if (pIsConstantComp(q)) |
---|
1209 | { |
---|
1210 | i = pGetComp(q); |
---|
1211 | qq = p; |
---|
1212 | while ((qq != q) && (pGetComp(qq) != i)) pIter(qq); |
---|
1213 | if (qq == q) |
---|
1214 | { |
---|
1215 | j = 0; |
---|
1216 | while (qq!=NULL) |
---|
1217 | { |
---|
1218 | if (pGetComp(qq)==i) j++; |
---|
1219 | pIter(qq); |
---|
1220 | } |
---|
1221 | if ((*len == 0) || (j<*len)) |
---|
1222 | { |
---|
1223 | *len = j; |
---|
1224 | *k = i; |
---|
1225 | } |
---|
1226 | } |
---|
1227 | } |
---|
1228 | pIter(q); |
---|
1229 | } |
---|
1230 | } |
---|
1231 | |
---|
1232 | /*2 |
---|
1233 | * returns TRUE if p1 = p2 |
---|
1234 | */ |
---|
1235 | BOOLEAN pEqualPolys(poly p1,poly p2) |
---|
1236 | { |
---|
1237 | while ((p1 != NULL) && (p2 != NULL)) |
---|
1238 | { |
---|
1239 | /* p1 and p2 are non-NULL, so we may use pComp0 instead of pComp */ |
---|
1240 | if (pComp0(p1,p2) != 0) |
---|
1241 | { |
---|
1242 | return FALSE; |
---|
1243 | } |
---|
1244 | if (nEqual(pGetCoeff(p1),pGetCoeff(p2)) == FALSE) |
---|
1245 | { |
---|
1246 | return FALSE; |
---|
1247 | } |
---|
1248 | pIter(p1); |
---|
1249 | pIter(p2); |
---|
1250 | } |
---|
1251 | return (p1==p2); |
---|
1252 | } |
---|
1253 | |
---|
1254 | /*2 |
---|
1255 | *returns TRUE if p1 is a skalar multiple of p2 |
---|
1256 | *assume p1 != NULL and p2 != NULL |
---|
1257 | */ |
---|
1258 | BOOLEAN pComparePolys(poly p1,poly p2) |
---|
1259 | { |
---|
1260 | number n,nn; |
---|
1261 | int i; |
---|
1262 | |
---|
1263 | if (pLength(p1) != pLength(p2)) |
---|
1264 | return FALSE; |
---|
1265 | n=nDiv(pGetCoeff(p1),pGetCoeff(p2)); |
---|
1266 | while ((p1 != NULL) /*&& (p2 != NULL)*/) |
---|
1267 | { |
---|
1268 | for (i=1; i<=pVariables; i++) |
---|
1269 | { |
---|
1270 | if (pGetExp(p1,i)!=pGetExp(p2,i)) |
---|
1271 | { |
---|
1272 | nDelete(&n); |
---|
1273 | return FALSE; |
---|
1274 | } |
---|
1275 | } |
---|
1276 | if (pGetComp(p1) != pGetComp(p2)) |
---|
1277 | { |
---|
1278 | nDelete(&n); |
---|
1279 | return FALSE; |
---|
1280 | } |
---|
1281 | if (!nEqual(pGetCoeff(p1),nn=nMult(pGetCoeff(p2),n))) |
---|
1282 | { |
---|
1283 | nDelete(&n); |
---|
1284 | nDelete(&nn); |
---|
1285 | return FALSE; |
---|
1286 | } |
---|
1287 | nDelete(&nn); |
---|
1288 | pIter(p1); |
---|
1289 | pIter(p2); |
---|
1290 | } |
---|
1291 | nDelete(&n); |
---|
1292 | return TRUE; |
---|
1293 | } |
---|
1294 | //{ |
---|
1295 | // number m=NULL,n=NULL; |
---|
1296 | // |
---|
1297 | // while ((p1 != NULL) && (p2 != NULL)) |
---|
1298 | // { |
---|
1299 | // if (pComp(p1,p2) != 0) |
---|
1300 | // { |
---|
1301 | // if (n!=NULL) nDelete(&n); |
---|
1302 | // return FALSE; |
---|
1303 | // } |
---|
1304 | // if (n == NULL) |
---|
1305 | // { |
---|
1306 | // n=nDiv(pGetCoeff(p1),pGetCoeff(p2)); |
---|
1307 | // } |
---|
1308 | // else |
---|
1309 | // { |
---|
1310 | // m=nDiv(pGetCoeff(p1),pGetCoeff(p2)); |
---|
1311 | // if (! nEqual(m,n)) |
---|
1312 | // { |
---|
1313 | // nDelete(&n); |
---|
1314 | // nDelete(&m); |
---|
1315 | // return FALSE; |
---|
1316 | // } |
---|
1317 | // nDelete(&m); |
---|
1318 | // } |
---|
1319 | // p1=pNext(p1); |
---|
1320 | // p2=pNext(p2); |
---|
1321 | // } |
---|
1322 | // nDelete(&n); |
---|
1323 | // //if (p1 != p2) |
---|
1324 | // // return FALSE; |
---|
1325 | // //else |
---|
1326 | // // return TRUE; |
---|
1327 | // return (p1==p2); |
---|
1328 | //} |
---|