1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: polys.cc,v 1.19 2007-05-23 07:47:30 wienand 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 | */ |
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9 | |
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10 | /* includes */ |
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11 | #include <stdio.h> |
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12 | #include <string.h> |
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13 | #include <ctype.h> |
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14 | #include "mod2.h" |
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15 | #include "structs.h" |
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16 | #include "omalloc.h" |
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17 | #include "febase.h" |
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18 | #include "numbers.h" |
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19 | #include "polys.h" |
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20 | #include "ring.h" |
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21 | |
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22 | #ifdef HAVE_PLURAL |
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23 | #include "gring.h" |
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24 | #endif |
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25 | |
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26 | /* ----------- global variables, set by pSetGlobals --------------------- */ |
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27 | /* computes length and maximal degree of a POLYnomial */ |
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28 | pLDegProc pLDeg; |
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29 | /* computes the degree of the initial term, used for std */ |
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30 | pFDegProc pFDeg; |
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31 | /* the monomial ordering of the head monomials a and b */ |
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32 | /* returns -1 if a comes before b, 0 if a=b, 1 otherwise */ |
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33 | |
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34 | int pVariables; // number of variables |
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35 | |
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36 | /* 1 for polynomial ring, -1 otherwise */ |
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37 | int pOrdSgn; |
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38 | // it is of type int, not BOOLEAN because it is also in ip |
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39 | /* TRUE if the monomial ordering is not compatible with pFDeg */ |
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40 | BOOLEAN pLexOrder; |
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41 | |
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42 | /* ----------- global variables, set by procedures from hecke/kstd1 ----- */ |
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43 | /* the highest monomial below pHEdge */ |
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44 | poly ppNoether = NULL; |
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45 | |
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46 | /* -------------------------------------------------------- */ |
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47 | /*2 |
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48 | * change all global variables to fit the description of the new ring |
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49 | */ |
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50 | |
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51 | |
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52 | void pSetGlobals(const ring r, BOOLEAN complete) |
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53 | { |
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54 | int i; |
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55 | if (ppNoether!=NULL) pDelete(&ppNoether); |
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56 | pVariables = r->N; |
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57 | pOrdSgn = r->OrdSgn; |
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58 | pFDeg=r->pFDeg; |
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59 | pLDeg=r->pLDeg; |
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60 | pLexOrder=r->LexOrder; |
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61 | |
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62 | if (complete) |
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63 | { |
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64 | test &= ~ TEST_RINGDEP_OPTS; |
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65 | test |= r->options; |
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66 | } |
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67 | } |
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68 | |
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69 | // resets the pFDeg and pLDeg: if pLDeg is not given, it is |
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70 | // set to currRing->pLDegOrig, i.e. to the respective LDegProc which |
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71 | // only uses pFDeg (and not pDeg, or pTotalDegree, etc) |
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72 | void pSetDegProcs(pFDegProc new_FDeg, pLDegProc new_lDeg) |
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73 | { |
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74 | assume(new_FDeg != NULL); |
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75 | pFDeg = new_FDeg; |
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76 | currRing->pFDeg = new_FDeg; |
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77 | |
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78 | if (new_lDeg == NULL) |
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79 | new_lDeg = currRing->pLDegOrig; |
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80 | |
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81 | pLDeg = new_lDeg; |
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82 | currRing->pLDeg = new_lDeg; |
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83 | } |
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84 | |
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85 | |
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86 | // restores pFDeg and pLDeg: |
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87 | extern void pRestoreDegProcs(pFDegProc old_FDeg, pLDegProc old_lDeg) |
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88 | { |
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89 | assume(old_FDeg != NULL && old_lDeg != NULL); |
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90 | pFDeg = old_FDeg; |
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91 | currRing->pFDeg = old_FDeg; |
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92 | pLDeg = old_lDeg; |
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93 | currRing->pLDeg = old_lDeg; |
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94 | } |
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95 | |
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96 | /*2 |
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97 | * assumes that the head term of b is a multiple of the head term of a |
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98 | * and return the multiplicant *m |
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99 | */ |
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100 | poly pDivide(poly a, poly b) |
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101 | { |
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102 | int i; |
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103 | poly result = pInit(); |
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104 | |
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105 | for(i=(int)pVariables; i; i--) |
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106 | pSetExp(result,i, pGetExp(a,i)- pGetExp(b,i)); |
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107 | pSetComp(result, pGetComp(a) - pGetComp(b)); |
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108 | pSetm(result); |
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109 | return result; |
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110 | } |
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111 | |
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112 | #ifdef HAVE_RINGS //TODO Oliver |
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113 | #define pDiv_nn(p, n) p_Div_nn(p, n, currRing) |
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114 | |
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115 | poly p_Div_nn(poly p, const number n, const ring r) |
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116 | { |
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117 | pAssume(!n_IsZero(n,r)); |
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118 | p_Test(p, r); |
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119 | |
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120 | poly q = p; |
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121 | while (p != NULL) |
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122 | { |
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123 | number nc = pGetCoeff(p); |
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124 | pSetCoeff0(p, n_Div(nc, n, r)); |
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125 | n_Delete(&nc, r); |
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126 | pIter(p); |
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127 | } |
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128 | p_Test(q, r); |
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129 | return q; |
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130 | } |
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131 | #endif |
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132 | |
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133 | /*2 |
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134 | * divides a by the monomial b, ignores monomials which are not divisible |
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135 | * assumes that b is not NULL |
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136 | */ |
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137 | poly pDivideM(poly a, poly b) |
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138 | { |
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139 | if (a==NULL) return NULL; |
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140 | poly result=a; |
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141 | poly prev=NULL; |
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142 | int i; |
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143 | #ifdef HAVE_RINGS |
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144 | number inv=pGetCoeff(b); |
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145 | #else |
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146 | number inv=nInvers(pGetCoeff(b)); |
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147 | #endif |
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148 | |
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149 | while (a!=NULL) |
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150 | { |
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151 | if (pDivisibleBy(b,a)) |
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152 | { |
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153 | for(i=(int)pVariables; i; i--) |
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154 | pSubExp(a,i, pGetExp(b,i)); |
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155 | pSubComp(a, pGetComp(b)); |
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156 | pSetm(a); |
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157 | prev=a; |
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158 | pIter(a); |
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159 | } |
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160 | else |
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161 | { |
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162 | if (prev==NULL) |
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163 | { |
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164 | pDeleteLm(&result); |
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165 | a=result; |
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166 | } |
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167 | else |
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168 | { |
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169 | pDeleteLm(&pNext(prev)); |
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170 | a=pNext(prev); |
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171 | } |
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172 | } |
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173 | } |
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174 | #ifdef HAVE_RINGS |
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175 | pDiv_nn(result,inv); |
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176 | #else |
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177 | pMult_nn(result,inv); |
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178 | #endif |
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179 | nDelete(&inv); |
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180 | pDelete(&b); |
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181 | return result; |
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182 | } |
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183 | |
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184 | /*2 |
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185 | * returns the LCM of the head terms of a and b in *m |
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186 | */ |
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187 | void pLcm(poly a, poly b, poly m) |
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188 | { |
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189 | int i; |
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190 | for (i=pVariables; i; i--) |
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191 | { |
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192 | pSetExp(m,i, si_max( pGetExp(a,i), pGetExp(b,i))); |
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193 | } |
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194 | pSetComp(m, si_max(pGetComp(a), pGetComp(b))); |
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195 | /* Don't do a pSetm here, otherwise hres/lres chockes */ |
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196 | } |
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197 | |
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198 | /*2 |
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199 | * convert monomial given as string to poly, e.g. 1x3y5z |
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200 | */ |
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201 | char * p_Read(char *st, poly &rc, ring r) |
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202 | { |
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203 | if (r==NULL) { rc=NULL;return st;} |
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204 | int i,j; |
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205 | rc = p_Init(r); |
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206 | char *s = r->cf->nRead(st,&(rc->coef)); |
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207 | if (s==st) |
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208 | /* i.e. it does not start with a coeff: test if it is a ringvar*/ |
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209 | { |
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210 | j = r_IsRingVar(s,r); |
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211 | if (j >= 0) |
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212 | { |
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213 | p_IncrExp(rc,1+j,r); |
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214 | while (*s!='\0') s++; |
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215 | goto done; |
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216 | } |
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217 | } |
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218 | while (*s!='\0') |
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219 | { |
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220 | char ss[2]; |
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221 | ss[0] = *s++; |
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222 | ss[1] = '\0'; |
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223 | j = r_IsRingVar(ss,r); |
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224 | if (j >= 0) |
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225 | { |
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226 | char *s_save=s; |
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227 | s = eati(s,&i); |
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228 | if (((unsigned long)i) > r->bitmask) |
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229 | { |
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230 | return s_save; |
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231 | } |
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232 | p_AddExp(rc,1+j, (Exponent_t)i, r); |
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233 | } |
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234 | else |
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235 | { |
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236 | s--; |
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237 | return s; |
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238 | } |
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239 | } |
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240 | done: |
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241 | if (r->cf->nIsZero(pGetCoeff(rc))) p_DeleteLm(&rc,r); |
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242 | else |
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243 | { |
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244 | p_Setm(rc,r); |
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245 | } |
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246 | return s; |
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247 | } |
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248 | |
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249 | poly pmInit(char *st, BOOLEAN &ok) |
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250 | { |
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251 | poly p; |
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252 | char *s=p_Read(st,p,currRing); |
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253 | if (*s!='\0') |
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254 | { |
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255 | if ((s!=st)&&isdigit(st[0])) |
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256 | { |
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257 | errorreported=TRUE; |
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258 | } |
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259 | ok=FALSE; |
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260 | pDelete(&p); |
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261 | return NULL; |
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262 | } |
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263 | ok=!errorreported; |
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264 | return p; |
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265 | } |
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266 | |
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267 | /*2 |
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268 | *make p homogeneous by multiplying the monomials by powers of x_varnum |
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269 | */ |
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270 | poly pHomogen (poly p, int varnum) |
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271 | { |
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272 | poly q=NULL, qn; |
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273 | int o,ii; |
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274 | sBucket_pt bp; |
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275 | |
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276 | if (p!=NULL) |
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277 | { |
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278 | if ((varnum < 1) || (varnum > pVariables)) |
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279 | { |
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280 | return NULL; |
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281 | } |
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282 | o=pWTotaldegree(p); |
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283 | q=pNext(p); |
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284 | while (q != NULL) |
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285 | { |
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286 | ii=pWTotaldegree(q); |
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287 | if (ii>o) o=ii; |
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288 | pIter(q); |
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289 | } |
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290 | q = pCopy(p); |
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291 | bp = sBucketCreate(currRing); |
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292 | while (q != NULL) |
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293 | { |
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294 | ii = o-pWTotaldegree(q); |
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295 | if (ii!=0) |
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296 | { |
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297 | pAddExp(q,varnum, (Exponent_t)ii); |
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298 | pSetm(q); |
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299 | } |
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300 | qn = pNext(q); |
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301 | pNext(q) = NULL; |
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302 | sBucket_Add_p(bp, q, 1); |
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303 | q = qn; |
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304 | } |
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305 | sBucketDestroyAdd(bp, &q, &ii); |
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306 | } |
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307 | return q; |
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308 | } |
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309 | |
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310 | /*2 |
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311 | *replaces the maximal powers of the leading monomial of p2 in p1 by |
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312 | *the same powers of n, utility for dehomogenization |
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313 | */ |
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314 | poly pDehomogen (poly p1,poly p2,number n) |
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315 | { |
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316 | polyset P; |
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317 | int SizeOfSet=5; |
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318 | int i; |
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319 | poly p; |
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320 | number nn; |
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321 | |
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322 | P = (polyset)omAlloc0(5*sizeof(poly)); |
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323 | //for (i=0; i<5; i++) |
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324 | //{ |
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325 | // P[i] = NULL; |
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326 | //} |
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327 | pCancelPolyByMonom(p1,p2,&P,&SizeOfSet); |
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328 | p = P[0]; |
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329 | //P[0] = NULL ;// for safety, may be removed later |
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330 | for (i=1; i<SizeOfSet; i++) |
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331 | { |
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332 | if (P[i] != NULL) |
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333 | { |
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334 | nPower(n,i,&nn); |
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335 | pMult_nn(P[i],nn); |
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336 | p = pAdd(p,P[i]); |
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337 | //P[i] =NULL; // for safety, may be removed later |
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338 | nDelete(&nn); |
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339 | } |
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340 | } |
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341 | omFreeSize((ADDRESS)P,SizeOfSet*sizeof(poly)); |
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342 | return p; |
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343 | } |
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344 | |
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345 | /*4 |
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346 | *Returns the exponent of the maximal power of the leading monomial of |
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347 | *p2 in that of p1 |
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348 | */ |
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349 | static int pGetMaxPower (poly p1,poly p2) |
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350 | { |
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351 | int i,k,res = 32000; /*a very large integer*/ |
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352 | |
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353 | if (p1 == NULL) return 0; |
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354 | for (i=1; i<=pVariables; i++) |
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355 | { |
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356 | if ( pGetExp(p2,i) != 0) |
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357 | { |
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358 | k = pGetExp(p1,i) / pGetExp(p2,i); |
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359 | if (k < res) res = k; |
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360 | } |
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361 | } |
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362 | return res; |
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363 | } |
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364 | |
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365 | /*2 |
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366 | *Returns as i-th entry of P the coefficient of the (i-1) power of |
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367 | *the leading monomial of p2 in p1 |
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368 | */ |
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369 | void pCancelPolyByMonom (poly p1,poly p2,polyset * P,int * SizeOfSet) |
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370 | { |
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371 | int maxPow; |
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372 | poly p,qp,Coeff; |
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373 | |
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374 | if (*P == NULL) |
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375 | { |
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376 | *P = (polyset) omAlloc(5*sizeof(poly)); |
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377 | *SizeOfSet = 5; |
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378 | } |
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379 | p = pCopy(p1); |
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380 | while (p != NULL) |
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381 | { |
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382 | qp = p->next; |
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383 | p->next = NULL; |
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384 | maxPow = pGetMaxPower(p,p2); |
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385 | Coeff = pDivByMonom(p,p2); |
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386 | if (maxPow > *SizeOfSet) |
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387 | { |
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388 | pEnlargeSet(P,*SizeOfSet,maxPow+1-*SizeOfSet); |
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389 | *SizeOfSet = maxPow+1; |
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390 | } |
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391 | (*P)[maxPow] = pAdd((*P)[maxPow],Coeff); |
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392 | pDelete(&p); |
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393 | p = qp; |
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394 | } |
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395 | } |
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396 | |
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397 | /*2 |
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398 | *returns the leading monomial of p1 divided by the maximal power of that |
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399 | *of p2 |
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400 | */ |
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401 | poly pDivByMonom (poly p1,poly p2) |
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402 | { |
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403 | int k, i; |
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404 | |
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405 | if (p1 == NULL) return NULL; |
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406 | k = pGetMaxPower(p1,p2); |
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407 | if (k == 0) |
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408 | return pHead(p1); |
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409 | else |
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410 | { |
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411 | number n; |
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412 | poly p = pInit(); |
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413 | |
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414 | p->next = NULL; |
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415 | for (i=1; i<=pVariables; i++) |
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416 | { |
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417 | pSetExp(p,i, pGetExp(p1,i)-k* pGetExp(p2,i)); |
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418 | } |
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419 | nPower(p2->coef,k,&n); |
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420 | pSetCoeff0(p,nDiv(p1->coef,n)); |
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421 | nDelete(&n); |
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422 | pSetm(p); |
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423 | return p; |
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424 | } |
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425 | } |
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426 | /*----------utilities for syzygies--------------*/ |
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427 | poly pTakeOutComp(poly * p, int k) |
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428 | { |
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429 | poly q = *p,qq=NULL,result = NULL; |
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430 | |
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431 | if (q==NULL) return NULL; |
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432 | if (pGetComp(q)==k) |
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433 | { |
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434 | result = q; |
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435 | do |
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436 | { |
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437 | pSetComp(q,0); |
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438 | pSetmComp(q); |
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439 | qq = q; |
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440 | pIter(q); |
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441 | } |
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442 | while ((q!=NULL) && (pGetComp(q)==k)); |
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443 | *p = q; |
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444 | pNext(qq) = NULL; |
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445 | } |
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446 | if (q==NULL) return result; |
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447 | if (pGetComp(q) > k) |
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448 | { |
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449 | pDecrComp(q); |
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450 | pSetmComp(q); |
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451 | } |
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452 | poly pNext_q; |
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453 | while ((pNext_q=pNext(q))!=NULL) |
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454 | { |
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455 | if (pGetComp(pNext_q)==k) |
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456 | { |
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457 | if (result==NULL) |
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458 | { |
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459 | result = pNext_q; |
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460 | qq = result; |
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461 | } |
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462 | else |
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463 | { |
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464 | pNext(qq) = pNext_q; |
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465 | pIter(qq); |
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466 | } |
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467 | pNext(q) = pNext(pNext_q); |
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468 | pNext(qq) =NULL; |
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469 | pSetComp(qq,0); |
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470 | pSetmComp(qq); |
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471 | } |
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472 | else |
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473 | { |
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474 | /*pIter(q);*/ q=pNext_q; |
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475 | if (pGetComp(q) > k) |
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476 | { |
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477 | pDecrComp(q); |
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478 | pSetmComp(q); |
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479 | } |
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480 | } |
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481 | } |
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482 | return result; |
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483 | } |
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484 | |
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485 | // Splits *p into two polys: *q which consists of all monoms with |
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486 | // component == comp and *p of all other monoms *lq == pLength(*q) |
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487 | void pTakeOutComp(poly *r_p, Exponent_t comp, poly *r_q, int *lq) |
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488 | { |
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489 | spolyrec pp, qq; |
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490 | poly p, q, p_prev; |
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491 | int l = 0; |
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492 | |
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493 | #ifdef HAVE_ASSUME |
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494 | int lp = pLength(*r_p); |
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495 | #endif |
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496 | |
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497 | pNext(&pp) = *r_p; |
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498 | p = *r_p; |
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499 | p_prev = &pp; |
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500 | q = &qq; |
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501 | |
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502 | while(p != NULL) |
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503 | { |
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504 | while (pGetComp(p) == comp) |
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505 | { |
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506 | pNext(q) = p; |
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507 | pIter(q); |
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508 | pSetComp(p, 0); |
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509 | pSetmComp(p); |
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510 | pIter(p); |
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511 | l++; |
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512 | if (p == NULL) |
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513 | { |
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514 | pNext(p_prev) = NULL; |
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515 | goto Finish; |
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516 | } |
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517 | } |
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518 | pNext(p_prev) = p; |
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519 | p_prev = p; |
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520 | pIter(p); |
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521 | } |
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522 | |
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523 | Finish: |
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524 | pNext(q) = NULL; |
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525 | *r_p = pNext(&pp); |
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526 | *r_q = pNext(&qq); |
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527 | *lq = l; |
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528 | #ifdef HAVE_ASSUME |
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529 | assume(pLength(*r_p) + pLength(*r_q) == lp); |
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530 | #endif |
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531 | pTest(*r_p); |
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532 | pTest(*r_q); |
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533 | } |
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534 | |
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535 | void pDecrOrdTakeOutComp(poly *r_p, Exponent_t comp, Order_t order, |
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536 | poly *r_q, int *lq) |
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537 | { |
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538 | spolyrec pp, qq; |
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539 | poly p, q, p_prev; |
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540 | int l = 0; |
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541 | |
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542 | pNext(&pp) = *r_p; |
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543 | p = *r_p; |
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544 | p_prev = &pp; |
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545 | q = &qq; |
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546 | |
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547 | #ifdef HAVE_ASSUME |
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548 | if (p != NULL) |
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549 | { |
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550 | while (pNext(p) != NULL) |
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551 | { |
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552 | assume(pGetOrder(p) >= pGetOrder(pNext(p))); |
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553 | pIter(p); |
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554 | } |
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555 | } |
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556 | p = *r_p; |
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557 | #endif |
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558 | |
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559 | while (p != NULL && pGetOrder(p) > order) pIter(p); |
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560 | |
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561 | while(p != NULL && pGetOrder(p) == order) |
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562 | { |
---|
563 | while (pGetComp(p) == comp) |
---|
564 | { |
---|
565 | pNext(q) = p; |
---|
566 | pIter(q); |
---|
567 | pIter(p); |
---|
568 | pSetComp(p, 0); |
---|
569 | pSetmComp(p); |
---|
570 | l++; |
---|
571 | if (p == NULL || pGetOrder(p) != order) |
---|
572 | { |
---|
573 | pNext(p_prev) = p; |
---|
574 | goto Finish; |
---|
575 | } |
---|
576 | } |
---|
577 | pNext(p_prev) = p; |
---|
578 | p_prev = p; |
---|
579 | pIter(p); |
---|
580 | } |
---|
581 | |
---|
582 | Finish: |
---|
583 | pNext(q) = NULL; |
---|
584 | *r_p = pNext(&pp); |
---|
585 | *r_q = pNext(&qq); |
---|
586 | *lq = l; |
---|
587 | } |
---|
588 | |
---|
589 | #if 1 |
---|
590 | poly pTakeOutComp1(poly * p, int k) |
---|
591 | { |
---|
592 | poly q = *p; |
---|
593 | |
---|
594 | if (q==NULL) return NULL; |
---|
595 | |
---|
596 | poly qq=NULL,result = NULL; |
---|
597 | |
---|
598 | if (pGetComp(q)==k) |
---|
599 | { |
---|
600 | result = q; /* *p */ |
---|
601 | while ((q!=NULL) && (pGetComp(q)==k)) |
---|
602 | { |
---|
603 | pSetComp(q,0); |
---|
604 | pSetmComp(q); |
---|
605 | qq = q; |
---|
606 | pIter(q); |
---|
607 | } |
---|
608 | *p = q; |
---|
609 | pNext(qq) = NULL; |
---|
610 | } |
---|
611 | if (q==NULL) return result; |
---|
612 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
613 | while (pNext(q)!=NULL) |
---|
614 | { |
---|
615 | if (pGetComp(pNext(q))==k) |
---|
616 | { |
---|
617 | if (result==NULL) |
---|
618 | { |
---|
619 | result = pNext(q); |
---|
620 | qq = result; |
---|
621 | } |
---|
622 | else |
---|
623 | { |
---|
624 | pNext(qq) = pNext(q); |
---|
625 | pIter(qq); |
---|
626 | } |
---|
627 | pNext(q) = pNext(pNext(q)); |
---|
628 | pNext(qq) =NULL; |
---|
629 | pSetComp(qq,0); |
---|
630 | pSetmComp(qq); |
---|
631 | } |
---|
632 | else |
---|
633 | { |
---|
634 | pIter(q); |
---|
635 | // if (pGetComp(q) > k) pGetComp(q)--; |
---|
636 | } |
---|
637 | } |
---|
638 | return result; |
---|
639 | } |
---|
640 | #endif |
---|
641 | |
---|
642 | void pDeleteComp(poly * p,int k) |
---|
643 | { |
---|
644 | poly q; |
---|
645 | |
---|
646 | while ((*p!=NULL) && (pGetComp(*p)==k)) pDeleteLm(p); |
---|
647 | if (*p==NULL) return; |
---|
648 | q = *p; |
---|
649 | if (pGetComp(q)>k) |
---|
650 | { |
---|
651 | pDecrComp(q); |
---|
652 | pSetmComp(q); |
---|
653 | } |
---|
654 | while (pNext(q)!=NULL) |
---|
655 | { |
---|
656 | if (pGetComp(pNext(q))==k) |
---|
657 | pDeleteLm(&(pNext(q))); |
---|
658 | else |
---|
659 | { |
---|
660 | pIter(q); |
---|
661 | if (pGetComp(q)>k) |
---|
662 | { |
---|
663 | pDecrComp(q); |
---|
664 | pSetmComp(q); |
---|
665 | } |
---|
666 | } |
---|
667 | } |
---|
668 | } |
---|
669 | /*----------end of utilities for syzygies--------------*/ |
---|
670 | |
---|
671 | /*2 |
---|
672 | * pair has no common factor ? or is no polynomial |
---|
673 | */ |
---|
674 | BOOLEAN pHasNotCF(poly p1, poly p2) |
---|
675 | { |
---|
676 | |
---|
677 | if (!TEST_OPT_IDLIFT) |
---|
678 | { |
---|
679 | if (pGetComp(p1) > 0 || pGetComp(p2) > 0) |
---|
680 | return FALSE; |
---|
681 | } |
---|
682 | int i = 1; |
---|
683 | loop |
---|
684 | { |
---|
685 | if ((pGetExp(p1, i) > 0) && (pGetExp(p2, i) > 0)) return FALSE; |
---|
686 | if (i == pVariables) return TRUE; |
---|
687 | i++; |
---|
688 | } |
---|
689 | } |
---|
690 | |
---|
691 | #ifdef HAVE_RINGS //HACK TODO Oliver |
---|
692 | number nGetUnit(number k) { |
---|
693 | number unit = nIntDiv(k, nGcd(k, 0, currRing)); |
---|
694 | number gcd = nGcd(unit, 0, currRing); |
---|
695 | if (!nIsOne(gcd)) |
---|
696 | { |
---|
697 | number tmp = nMult(unit, unit); |
---|
698 | number gcd_new = nGcd(tmp, 0, currRing); |
---|
699 | while (gcd_new != gcd) |
---|
700 | { |
---|
701 | gcd = gcd_new; |
---|
702 | tmp = nMult(tmp, unit); |
---|
703 | gcd_new = nGcd(tmp, 0, currRing); |
---|
704 | } |
---|
705 | unit = nAdd(unit, nIntDiv(0, gcd_new)); |
---|
706 | } |
---|
707 | // Print("k = %d ; unit = %d ; gcd = %d", k, unit, gcd); |
---|
708 | return unit; |
---|
709 | } |
---|
710 | #endif |
---|
711 | |
---|
712 | /*2 |
---|
713 | *divides p1 by its leading coefficient |
---|
714 | */ |
---|
715 | void pNorm(poly p1) |
---|
716 | { |
---|
717 | poly h; |
---|
718 | number k, c; |
---|
719 | #ifdef HAVE_RINGS |
---|
720 | if (rField_is_Ring(currRing)) |
---|
721 | { |
---|
722 | if (p1!=NULL) |
---|
723 | { |
---|
724 | k = nGetUnit(pGetCoeff(p1)); |
---|
725 | if (!nIsOne(k)) |
---|
726 | { |
---|
727 | c = nDiv(pGetCoeff(p1), k); |
---|
728 | pSetCoeff0(p1, c); |
---|
729 | h = pNext(p1); |
---|
730 | while (h != NULL) |
---|
731 | { |
---|
732 | c = nDiv(pGetCoeff(h), k); |
---|
733 | pSetCoeff(h, c); |
---|
734 | pIter(h); |
---|
735 | } |
---|
736 | nDelete(&k); |
---|
737 | } |
---|
738 | return; |
---|
739 | } |
---|
740 | } |
---|
741 | else |
---|
742 | #endif |
---|
743 | if (p1!=NULL) |
---|
744 | { |
---|
745 | if (pNext(p1)==NULL) |
---|
746 | { |
---|
747 | pSetCoeff(p1,nInit(1)); |
---|
748 | return; |
---|
749 | } |
---|
750 | if (!nIsOne(pGetCoeff(p1))) |
---|
751 | { |
---|
752 | nNormalize(pGetCoeff(p1)); |
---|
753 | k = pGetCoeff(p1); |
---|
754 | c = nInit(1); |
---|
755 | pSetCoeff0(p1,c); |
---|
756 | h = pNext(p1); |
---|
757 | while (h!=NULL) |
---|
758 | { |
---|
759 | c=nDiv(pGetCoeff(h),k); |
---|
760 | if (!nIsOne(c)) nNormalize(c); |
---|
761 | pSetCoeff(h,c); |
---|
762 | pIter(h); |
---|
763 | } |
---|
764 | nDelete(&k); |
---|
765 | } |
---|
766 | else |
---|
767 | { |
---|
768 | if (nNormalize != nDummy2) |
---|
769 | { |
---|
770 | h = pNext(p1); |
---|
771 | while (h!=NULL) |
---|
772 | { |
---|
773 | nNormalize(pGetCoeff(h)); |
---|
774 | pIter(h); |
---|
775 | } |
---|
776 | } |
---|
777 | } |
---|
778 | } |
---|
779 | } |
---|
780 | |
---|
781 | /*2 |
---|
782 | *normalize all coefficients |
---|
783 | */ |
---|
784 | void p_Normalize(poly p, ring r) |
---|
785 | { |
---|
786 | if (rField_has_simple_inverse(r)) return; /* Z/p, GF(p,n), R, long R/C */ |
---|
787 | while (p!=NULL) |
---|
788 | { |
---|
789 | if (currRing==r) {nTest(pGetCoeff(p));} |
---|
790 | n_Normalize(pGetCoeff(p),r); |
---|
791 | pIter(p); |
---|
792 | } |
---|
793 | } |
---|
794 | |
---|
795 | // splits p into polys with Exp(n) == 0 and Exp(n) != 0 |
---|
796 | // Poly with Exp(n) != 0 is reversed |
---|
797 | static void pSplitAndReversePoly(poly p, int n, poly *non_zero, poly *zero) |
---|
798 | { |
---|
799 | if (p == NULL) |
---|
800 | { |
---|
801 | *non_zero = NULL; |
---|
802 | *zero = NULL; |
---|
803 | return; |
---|
804 | } |
---|
805 | spolyrec sz; |
---|
806 | poly z, n_z, next; |
---|
807 | z = &sz; |
---|
808 | n_z = NULL; |
---|
809 | |
---|
810 | while(p != NULL) |
---|
811 | { |
---|
812 | next = pNext(p); |
---|
813 | if (pGetExp(p, n) == 0) |
---|
814 | { |
---|
815 | pNext(z) = p; |
---|
816 | pIter(z); |
---|
817 | } |
---|
818 | else |
---|
819 | { |
---|
820 | pNext(p) = n_z; |
---|
821 | n_z = p; |
---|
822 | } |
---|
823 | p = next; |
---|
824 | } |
---|
825 | pNext(z) = NULL; |
---|
826 | *zero = pNext(&sz); |
---|
827 | *non_zero = n_z; |
---|
828 | return; |
---|
829 | } |
---|
830 | |
---|
831 | /*3 |
---|
832 | * substitute the n-th variable by 1 in p |
---|
833 | * destroy p |
---|
834 | */ |
---|
835 | static poly pSubst1 (poly p,int n) |
---|
836 | { |
---|
837 | poly qq=NULL, result = NULL; |
---|
838 | poly zero=NULL, non_zero=NULL; |
---|
839 | |
---|
840 | // reverse, so that add is likely to be linear |
---|
841 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
842 | |
---|
843 | while (non_zero != NULL) |
---|
844 | { |
---|
845 | assume(pGetExp(non_zero, n) != 0); |
---|
846 | qq = non_zero; |
---|
847 | pIter(non_zero); |
---|
848 | qq->next = NULL; |
---|
849 | pSetExp(qq,n,0); |
---|
850 | pSetm(qq); |
---|
851 | result = pAdd(result,qq); |
---|
852 | } |
---|
853 | p = pAdd(result, zero); |
---|
854 | pTest(p); |
---|
855 | return p; |
---|
856 | } |
---|
857 | |
---|
858 | /*3 |
---|
859 | * substitute the n-th variable by number e in p |
---|
860 | * destroy p |
---|
861 | */ |
---|
862 | static poly pSubst2 (poly p,int n, number e) |
---|
863 | { |
---|
864 | assume( ! nIsZero(e) ); |
---|
865 | poly qq,result = NULL; |
---|
866 | number nn, nm; |
---|
867 | poly zero, non_zero; |
---|
868 | |
---|
869 | // reverse, so that add is likely to be linear |
---|
870 | pSplitAndReversePoly(p, n, &non_zero, &zero); |
---|
871 | |
---|
872 | while (non_zero != NULL) |
---|
873 | { |
---|
874 | assume(pGetExp(non_zero, n) != 0); |
---|
875 | qq = non_zero; |
---|
876 | pIter(non_zero); |
---|
877 | qq->next = NULL; |
---|
878 | nPower(e, pGetExp(qq, n), &nn); |
---|
879 | nm = nMult(nn, pGetCoeff(qq)); |
---|
880 | pSetCoeff(qq, nm); |
---|
881 | nDelete(&nn); |
---|
882 | pSetExp(qq, n, 0); |
---|
883 | pSetm(qq); |
---|
884 | result = pAdd(result,qq); |
---|
885 | } |
---|
886 | p = pAdd(result, zero); |
---|
887 | pTest(p); |
---|
888 | return p; |
---|
889 | } |
---|
890 | |
---|
891 | |
---|
892 | /* delete monoms whose n-th exponent is different from zero */ |
---|
893 | poly pSubst0(poly p, int n) |
---|
894 | { |
---|
895 | spolyrec res; |
---|
896 | poly h = &res; |
---|
897 | pNext(h) = p; |
---|
898 | |
---|
899 | while (pNext(h)!=NULL) |
---|
900 | { |
---|
901 | if (pGetExp(pNext(h),n)!=0) |
---|
902 | { |
---|
903 | pDeleteLm(&pNext(h)); |
---|
904 | } |
---|
905 | else |
---|
906 | { |
---|
907 | pIter(h); |
---|
908 | } |
---|
909 | } |
---|
910 | pTest(pNext(&res)); |
---|
911 | return pNext(&res); |
---|
912 | } |
---|
913 | |
---|
914 | /*2 |
---|
915 | * substitute the n-th variable by e in p |
---|
916 | * destroy p |
---|
917 | */ |
---|
918 | poly pSubst(poly p, int n, poly e) |
---|
919 | { |
---|
920 | if (e == NULL) return pSubst0(p, n); |
---|
921 | |
---|
922 | if (pIsConstant(e)) |
---|
923 | { |
---|
924 | if (nIsOne(pGetCoeff(e))) return pSubst1(p,n); |
---|
925 | else return pSubst2(p, n, pGetCoeff(e)); |
---|
926 | } |
---|
927 | |
---|
928 | #ifdef HAVE_PLURAL |
---|
929 | if (rIsPluralRing(currRing)) |
---|
930 | { |
---|
931 | return nc_pSubst(p,n,e); |
---|
932 | } |
---|
933 | #endif |
---|
934 | |
---|
935 | int exponent,i; |
---|
936 | poly h, res, m; |
---|
937 | int *me,*ee; |
---|
938 | number nu,nu1; |
---|
939 | |
---|
940 | me=(int *)omAlloc((pVariables+1)*sizeof(int)); |
---|
941 | ee=(int *)omAlloc((pVariables+1)*sizeof(int)); |
---|
942 | if (e!=NULL) pGetExpV(e,ee); |
---|
943 | res=NULL; |
---|
944 | h=p; |
---|
945 | while (h!=NULL) |
---|
946 | { |
---|
947 | if ((e!=NULL) || (pGetExp(h,n)==0)) |
---|
948 | { |
---|
949 | m=pHead(h); |
---|
950 | pGetExpV(m,me); |
---|
951 | exponent=me[n]; |
---|
952 | me[n]=0; |
---|
953 | for(i=pVariables;i>0;i--) |
---|
954 | me[i]+=exponent*ee[i]; |
---|
955 | pSetExpV(m,me); |
---|
956 | if (e!=NULL) |
---|
957 | { |
---|
958 | nPower(pGetCoeff(e),exponent,&nu); |
---|
959 | nu1=nMult(pGetCoeff(m),nu); |
---|
960 | nDelete(&nu); |
---|
961 | pSetCoeff(m,nu1); |
---|
962 | } |
---|
963 | res=pAdd(res,m); |
---|
964 | } |
---|
965 | pDeleteLm(&h); |
---|
966 | } |
---|
967 | omFreeSize((ADDRESS)me,(pVariables+1)*sizeof(int)); |
---|
968 | omFreeSize((ADDRESS)ee,(pVariables+1)*sizeof(int)); |
---|
969 | return res; |
---|
970 | } |
---|
971 | |
---|
972 | /* Returns TRUE if |
---|
973 | * LM(p) | LM(lcm) |
---|
974 | * LC(p) | LC(lcm) only if ring |
---|
975 | * Exists i, j: |
---|
976 | * LE(p, i) != LE(lcm, i) |
---|
977 | * LE(p1, i) != LE(lcm, i) ==> LCM(p1, p) != lcm |
---|
978 | * LE(p, j) != LE(lcm, j) |
---|
979 | * LE(p2, j) != LE(lcm, j) ==> LCM(p2, p) != lcm |
---|
980 | */ |
---|
981 | BOOLEAN pCompareChain (poly p,poly p1,poly p2,poly lcm) |
---|
982 | { |
---|
983 | int k, j; |
---|
984 | |
---|
985 | if (lcm==NULL) return FALSE; |
---|
986 | |
---|
987 | for (j=pVariables; j; j--) |
---|
988 | if ( pGetExp(p,j) > pGetExp(lcm,j)) return FALSE; |
---|
989 | if ( pGetComp(p) != pGetComp(lcm)) return FALSE; |
---|
990 | for (j=pVariables; j; j--) |
---|
991 | { |
---|
992 | if (pGetExp(p1,j)!=pGetExp(lcm,j)) |
---|
993 | { |
---|
994 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
995 | { |
---|
996 | for (k=pVariables; k>j; k--) |
---|
997 | { |
---|
998 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
999 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
1000 | return TRUE; |
---|
1001 | } |
---|
1002 | for (k=j-1; k; k--) |
---|
1003 | { |
---|
1004 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1005 | && (pGetExp(p2,k)!=pGetExp(lcm,k))) |
---|
1006 | return TRUE; |
---|
1007 | } |
---|
1008 | return FALSE; |
---|
1009 | } |
---|
1010 | } |
---|
1011 | else if (pGetExp(p2,j)!=pGetExp(lcm,j)) |
---|
1012 | { |
---|
1013 | if (pGetExp(p,j)!=pGetExp(lcm,j)) |
---|
1014 | { |
---|
1015 | for (k=pVariables; k>j; k--) |
---|
1016 | { |
---|
1017 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1018 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
1019 | return TRUE; |
---|
1020 | } |
---|
1021 | for (k=j-1; k!=0 ; k--) |
---|
1022 | { |
---|
1023 | if ((pGetExp(p,k)!=pGetExp(lcm,k)) |
---|
1024 | && (pGetExp(p1,k)!=pGetExp(lcm,k))) |
---|
1025 | return TRUE; |
---|
1026 | } |
---|
1027 | return FALSE; |
---|
1028 | } |
---|
1029 | } |
---|
1030 | } |
---|
1031 | return FALSE; |
---|
1032 | } |
---|