1 | // emacs edit mode for this file is -*- C++ -*- |
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2 | /**************************************** |
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3 | * Computer Algebra System SINGULAR * |
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4 | ****************************************/ |
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5 | /* |
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6 | * ABSTRACT: interface between Singular and factory |
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7 | */ |
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8 | |
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9 | //#define FACTORIZE2_DEBUG |
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10 | |
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11 | #ifdef HAVE_CONFIG_H |
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12 | #include "config.h" |
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13 | #endif /* HAVE_CONFIG_H */ |
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14 | |
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15 | #include <misc/auxiliary.h> |
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16 | |
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17 | #ifdef HAVE_FACTORY |
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18 | |
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19 | #define SI_DONT_HAVE_GLOBAL_VARS |
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20 | |
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21 | #include <misc/auxiliary.h> |
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22 | #include "clapsing.h" |
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23 | |
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24 | #include <factory/factory.h> |
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25 | |
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26 | #ifdef HAVE_LIBFAC |
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27 | # include <factory/libfac/libfac.h> |
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28 | #endif |
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29 | |
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30 | |
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31 | #include <omalloc/omalloc.h> |
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32 | #include <coeffs/numbers.h> |
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33 | #include <coeffs/coeffs.h> |
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34 | #include <coeffs/bigintmat.h> |
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35 | |
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36 | // #include <kernel/ffields.h> |
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37 | |
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38 | #include "monomials/ring.h" |
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39 | #include "simpleideals.h" |
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40 | |
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41 | |
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42 | //#include "polys.h" |
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43 | #define TRANSEXT_PRIVATES |
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44 | |
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45 | #include "ext_fields/transext.h" |
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46 | |
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47 | |
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48 | #include "clapconv.h" |
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49 | // #include <kernel/clapconv.h> |
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50 | |
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51 | #include <polys/monomials/p_polys.h> |
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52 | #include <polys/monomials/ring.h> |
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53 | #include <polys/simpleideals.h> |
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54 | #include <misc/intvec.h> |
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55 | #include <polys/matpol.h> |
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56 | #include <coeffs/bigintmat.h> |
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57 | |
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58 | |
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59 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
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60 | |
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61 | poly singclap_gcd_r ( poly f, poly g, const ring r ) |
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62 | { |
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63 | poly res=NULL; |
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64 | |
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65 | assume(f!=NULL); |
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66 | assume(g!=NULL); |
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67 | |
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68 | if(pNext(f)==NULL) |
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69 | { |
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70 | poly p=p_One(r); |
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71 | if (pNext(g)==NULL) |
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72 | { |
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73 | for(int i=rVar(r);i>0;i--) |
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74 | p_SetExp(p,i,si_min(p_GetExp(f,i,r),p_GetExp(g,i,r)),r); |
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75 | p_Setm(p,r); |
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76 | return p; |
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77 | } |
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78 | #if 0 |
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79 | else |
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80 | { |
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81 | poly h=g; |
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82 | for(int i=rVar(r);i>0;i--) |
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83 | p_SetExp(p,i,p_GetExp(f,i,r),r); |
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84 | while(h!=NULL) |
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85 | { |
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86 | for(int i=rVar(r);i>0;i--) |
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87 | p_SetExp(p,i,si_min(p_GetExp(p,i,r),p_GetExp(h,i,r)),r); |
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88 | pIter(h); |
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89 | } |
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90 | p_Setm(p,r); |
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91 | return p; |
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92 | } |
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93 | #endif |
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94 | } |
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95 | #if 0 |
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96 | else if (pNext(g)==NULL) |
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97 | { |
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98 | poly p=p_One(r); |
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99 | poly h=f; |
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100 | for(int i=rVar(r);i>0;i--) |
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101 | p_SetExp(p,i,p_GetExp(g,i,r),r); |
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102 | while(h!=NULL) |
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103 | { |
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104 | for(int i=rVar(r);i>0;i--) |
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105 | p_SetExp(p,i,si_min(p_GetExp(p,i,r),p_GetExp(h,i,r)),r); |
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106 | pIter(h); |
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107 | } |
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108 | p_Setm(p,r); |
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109 | return p; |
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110 | } |
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111 | #endif |
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112 | |
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113 | Off(SW_RATIONAL); |
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114 | if (rField_is_Q(r) || (rField_is_Zp(r))) |
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115 | { |
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116 | setCharacteristic( rChar(r) ); |
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117 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g, r ) ); |
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118 | res=convFactoryPSingP( gcd( F, G ) , r); |
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119 | } |
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120 | // and over Q(a) / Fp(a) |
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121 | else if ( rField_is_Extension(r)) |
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122 | { |
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123 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
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124 | else setCharacteristic( rChar(r) ); |
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125 | if (r->cf->extRing->qideal!=NULL) |
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126 | { |
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127 | bool b1=isOn(SW_USE_QGCD); |
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128 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
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129 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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130 | r->cf->extRing); |
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131 | Variable a=rootOf(mipo); |
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132 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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133 | G( convSingAPFactoryAP( g,a,r ) ); |
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134 | res= convFactoryAPSingAP( gcd( F, G ),r ); |
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135 | if (!b1) Off(SW_USE_QGCD); |
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136 | } |
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137 | else |
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138 | { |
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139 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
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140 | res= convFactoryPSingTrP( gcd( F, G ),r ); |
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141 | } |
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142 | } |
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143 | else |
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144 | WerrorS( feNotImplemented ); |
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145 | Off(SW_RATIONAL); |
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146 | return res; |
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147 | } |
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148 | |
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149 | void singclap_gcd_and_divide ( poly& f, poly& g, const ring r) |
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150 | { |
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151 | poly res=NULL; |
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152 | |
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153 | if (f!=NULL) p_Cleardenom(f, r); |
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154 | if (g!=NULL) p_Cleardenom(g, r); |
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155 | else return; // g==0 => but do a p_Cleardenom(f) |
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156 | if (f==NULL) return; // f==0 => but do a p_Cleardenom(g) |
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157 | |
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158 | Off(SW_RATIONAL); |
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159 | CanonicalForm F,G,GCD; |
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160 | if (rField_is_Q(r) || (rField_is_Zp(r))) |
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161 | { |
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162 | bool b1=isOn(SW_USE_EZGCD_P); |
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163 | setCharacteristic( rChar(r) ); |
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164 | F=convSingPFactoryP( f,r ); |
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165 | G=convSingPFactoryP( g,r ); |
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166 | GCD=gcd(F,G); |
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167 | if (!GCD.isOne()) |
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168 | { |
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169 | p_Delete(&f,r); |
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170 | p_Delete(&g,r); |
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171 | f=convFactoryPSingP( F/GCD, r); |
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172 | g=convFactoryPSingP( G/GCD, r); |
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173 | } |
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174 | if (!b1) Off (SW_USE_EZGCD_P); |
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175 | } |
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176 | // and over Q(a) / Fp(a) |
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177 | else if ( rField_is_Extension(r)) |
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178 | { |
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179 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
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180 | else setCharacteristic( rChar(r) ); |
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181 | if (r->cf->extRing->qideal!=NULL) |
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182 | { |
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183 | bool b1=isOn(SW_USE_QGCD); |
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184 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
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185 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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186 | r->cf->extRing); |
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187 | Variable a=rootOf(mipo); |
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188 | F=( convSingAPFactoryAP( f,a,r ) ); |
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189 | G=( convSingAPFactoryAP( g,a,r ) ); |
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190 | GCD=gcd(F,G); |
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191 | if (!GCD.isOne()) |
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192 | { |
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193 | p_Delete(&f,r); |
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194 | p_Delete(&g,r); |
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195 | f= convFactoryAPSingAP( F/GCD,r ); |
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196 | g= convFactoryAPSingAP( G/GCD,r ); |
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197 | } |
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198 | if (!b1) Off(SW_USE_QGCD); |
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199 | } |
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200 | else |
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201 | { |
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202 | F=( convSingTrPFactoryP( f,r ) ); |
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203 | G=( convSingTrPFactoryP( g,r ) ); |
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204 | GCD=gcd(F,G); |
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205 | if (!GCD.isOne()) |
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206 | { |
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207 | p_Delete(&f,r); |
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208 | p_Delete(&g,r); |
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209 | f= convFactoryPSingTrP( F/GCD,r ); |
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210 | g= convFactoryPSingTrP( G/GCD,r ); |
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211 | } |
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212 | } |
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213 | } |
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214 | else |
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215 | WerrorS( feNotImplemented ); |
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216 | Off(SW_RATIONAL); |
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217 | } |
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218 | |
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219 | poly singclap_gcd ( poly f, poly g, const ring r) |
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220 | { |
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221 | poly res=NULL; |
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222 | |
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223 | if (f!=NULL) p_Cleardenom(f, r); |
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224 | if (g!=NULL) p_Cleardenom(g, r); |
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225 | else return f; // g==0 => gcd=f (but do a p_Cleardenom) |
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226 | if (f==NULL) return g; // f==0 => gcd=g (but do a p_Cleardenom) |
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227 | |
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228 | res=singclap_gcd_r(f,g,r); |
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229 | p_Delete(&f, r); |
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230 | p_Delete(&g, r); |
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231 | return res; |
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232 | } |
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233 | |
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234 | /*2 find the maximal exponent of var(i) in poly p*/ |
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235 | int pGetExp_Var(poly p, int i, const ring r) |
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236 | { |
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237 | int m=0; |
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238 | int mm; |
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239 | while (p!=NULL) |
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240 | { |
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241 | mm=p_GetExp(p,i,r); |
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242 | if (mm>m) m=mm; |
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243 | pIter(p); |
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244 | } |
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245 | return m; |
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246 | } |
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247 | |
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248 | // destroys f,g,x |
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249 | poly singclap_resultant ( poly f, poly g , poly x, const ring r) |
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250 | { |
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251 | poly res=NULL; |
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252 | int i=p_IsPurePower(x, r); |
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253 | if (i==0) |
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254 | { |
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255 | WerrorS("3rd argument must be a ring variable"); |
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256 | goto resultant_returns_res; |
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257 | } |
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258 | if ((f==NULL) || (g==NULL)) |
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259 | goto resultant_returns_res; |
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260 | // for now there is only the possibility to handle polynomials over |
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261 | // Q and Fp ... |
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262 | if (rField_is_Zp(r) || rField_is_Q(r)) |
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263 | { |
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264 | Variable X(i); |
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265 | setCharacteristic( rChar(r) ); |
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266 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
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267 | res=convFactoryPSingP( resultant( F, G, X),r ); |
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268 | Off(SW_RATIONAL); |
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269 | goto resultant_returns_res; |
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270 | } |
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271 | // and over Q(a) / Fp(a) |
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272 | else if (rField_is_Extension(r)) |
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273 | { |
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274 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
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275 | else setCharacteristic( rChar(r) ); |
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276 | Variable X(i+rPar(r)); |
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277 | if (r->cf->extRing->qideal!=NULL) |
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278 | { |
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279 | //Variable X(i); |
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280 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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281 | r->cf->extRing); |
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282 | Variable a=rootOf(mipo); |
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283 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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284 | G( convSingAPFactoryAP( g,a,r ) ); |
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285 | res= convFactoryAPSingAP( resultant( F, G, X ),r ); |
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286 | } |
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287 | else |
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288 | { |
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289 | //Variable X(i+rPar(currRing)); |
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290 | number nf,ng; |
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291 | p_Cleardenom_n(f,r,nf);p_Cleardenom_n(g,r,ng); |
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292 | int ef,eg; |
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293 | ef=pGetExp_Var(f,i,r); |
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294 | eg=pGetExp_Var(g,i,r); |
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295 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
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296 | res= convFactoryPSingTrP( resultant( F, G, X ),r ); |
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297 | if ((nf!=NULL)&&(!n_IsOne(nf,r->cf))) |
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298 | { |
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299 | number n=n_Invers(nf,r->cf); |
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300 | while(eg>0) |
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301 | { |
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302 | res=p_Mult_nn(res,n,r); |
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303 | eg--; |
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304 | } |
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305 | n_Delete(&n,r->cf); |
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306 | } |
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307 | n_Delete(&nf,r->cf); |
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308 | if ((ng!=NULL)&&(!n_IsOne(ng,r->cf))) |
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309 | { |
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310 | number n=n_Invers(ng,r->cf); |
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311 | while(ef>0) |
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312 | { |
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313 | res=p_Mult_nn(res,n,r); |
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314 | ef--; |
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315 | } |
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316 | n_Delete(&n,r->cf); |
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317 | } |
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318 | n_Delete(&ng,r->cf); |
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319 | } |
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320 | Off(SW_RATIONAL); |
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321 | goto resultant_returns_res; |
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322 | } |
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323 | else |
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324 | WerrorS( feNotImplemented ); |
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325 | resultant_returns_res: |
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326 | p_Delete(&f,r); |
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327 | p_Delete(&g,r); |
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328 | p_Delete(&x,r); |
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329 | return res; |
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330 | } |
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331 | //poly singclap_resultant ( poly f, poly g , poly x) |
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332 | //{ |
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333 | // int i=pVar(x); |
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334 | // if (i==0) |
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335 | // { |
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336 | // WerrorS("ringvar expected"); |
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337 | // return NULL; |
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338 | // } |
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339 | // ideal I=idInit(1,1); |
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340 | // |
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341 | // // get the coeffs von f wrt. x: |
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342 | // I->m[0]=pCopy(f); |
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343 | // matrix ffi=mpCoeffs(I,i); |
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344 | // ffi->rank=1; |
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345 | // ffi->ncols=ffi->nrows; |
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346 | // ffi->nrows=1; |
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347 | // ideal fi=(ideal)ffi; |
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348 | // |
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349 | // // get the coeffs von g wrt. x: |
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350 | // I->m[0]=pCopy(g); |
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351 | // matrix ggi=mpCoeffs(I,i); |
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352 | // ggi->rank=1; |
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353 | // ggi->ncols=ggi->nrows; |
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354 | // ggi->nrows=1; |
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355 | // ideal gi=(ideal)ggi; |
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356 | // |
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357 | // // contruct the matrix: |
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358 | // int fn=IDELEMS(fi); //= deg(f,x)+1 |
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359 | // int gn=IDELEMS(gi); //= deg(g,x)+1 |
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360 | // matrix m=mpNew(fn+gn-2,fn+gn-2); |
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361 | // if(m==NULL) |
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362 | // { |
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363 | // return NULL; |
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364 | // } |
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365 | // |
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366 | // // enter the coeffs into m: |
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367 | // int j; |
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368 | // for(i=0;i<gn-1;i++) |
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369 | // { |
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370 | // for(j=0;j<fn;j++) |
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371 | // { |
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372 | // MATELEM(m,i+1,fn-j+i)=pCopy(fi->m[j]); |
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373 | // } |
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374 | // } |
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375 | // for(i=0;i<fn-1;i++) |
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376 | // { |
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377 | // for(j=0;j<gn;j++) |
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378 | // { |
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379 | // MATELEM(m,gn+i,gn-j+i)=pCopy(gi->m[j]); |
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380 | // } |
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381 | // } |
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382 | // |
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383 | // poly r=mpDet(m); |
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384 | // |
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385 | // idDelete(&fi); |
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386 | // idDelete(&gi); |
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387 | // idDelete((ideal *)&m); |
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388 | // return r; |
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389 | //} |
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390 | |
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391 | BOOLEAN singclap_extgcd ( poly f, poly g, poly &res, poly &pa, poly &pb , const ring r) |
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392 | { |
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393 | // for now there is only the possibility to handle univariate |
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394 | // polynomials over |
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395 | // Q and Fp ... |
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396 | res=NULL;pa=NULL;pb=NULL; |
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397 | On(SW_SYMMETRIC_FF); |
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398 | if ( rField_is_Q(r) || rField_is_Zp(r) ) |
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399 | { |
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400 | setCharacteristic( rChar(r) ); |
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401 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r) ); |
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402 | CanonicalForm FpG=F+G; |
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403 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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404 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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405 | { |
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406 | Off(SW_RATIONAL); |
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407 | WerrorS("not univariate"); |
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408 | return TRUE; |
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409 | } |
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410 | CanonicalForm Fa,Gb; |
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411 | On(SW_RATIONAL); |
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412 | res=convFactoryPSingP( extgcd( F, G, Fa, Gb ),r ); |
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413 | pa=convFactoryPSingP(Fa,r); |
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414 | pb=convFactoryPSingP(Gb,r); |
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415 | Off(SW_RATIONAL); |
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416 | } |
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417 | // and over Q(a) / Fp(a) |
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418 | else if ( rField_is_Extension(r)) |
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419 | { |
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420 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
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421 | else setCharacteristic( rChar(r) ); |
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422 | CanonicalForm Fa,Gb; |
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423 | if (r->cf->extRing->qideal!=NULL) |
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424 | { |
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425 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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426 | r->cf->extRing); |
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427 | Variable a=rootOf(mipo); |
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428 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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429 | G( convSingAPFactoryAP( g,a,r ) ); |
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430 | CanonicalForm FpG=F+G; |
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431 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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432 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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433 | { |
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434 | WerrorS("not univariate"); |
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435 | return TRUE; |
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436 | } |
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437 | res= convFactoryAPSingAP( extgcd( F, G, Fa, Gb ),r ); |
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438 | pa=convFactoryAPSingAP(Fa,r); |
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439 | pb=convFactoryAPSingAP(Gb,r); |
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440 | } |
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441 | else |
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442 | { |
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443 | CanonicalForm F( convSingTrPFactoryP( f, r ) ), G( convSingTrPFactoryP( g, r ) ); |
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444 | CanonicalForm FpG=F+G; |
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445 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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446 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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447 | { |
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448 | Off(SW_RATIONAL); |
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449 | WerrorS("not univariate"); |
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450 | return TRUE; |
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451 | } |
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452 | res= convFactoryPSingTrP( extgcd( F, G, Fa, Gb ), r ); |
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453 | pa=convFactoryPSingTrP(Fa, r); |
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454 | pb=convFactoryPSingTrP(Gb, r); |
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455 | } |
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456 | Off(SW_RATIONAL); |
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457 | } |
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458 | else |
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459 | { |
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460 | WerrorS( feNotImplemented ); |
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461 | return TRUE; |
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462 | } |
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463 | #ifndef NDEBUG |
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464 | // checking the result of extgcd: |
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465 | poly dummy; |
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466 | dummy=p_Sub(p_Add_q(pp_Mult_qq(f,pa,r),pp_Mult_qq(g,pb,r),r),p_Copy(res,r),r); |
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467 | if (dummy!=NULL) |
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468 | { |
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469 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
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470 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
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471 | p_Delete(&dummy,r); |
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472 | } |
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473 | #endif |
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474 | return FALSE; |
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475 | } |
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476 | |
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477 | poly singclap_pdivide ( poly f, poly g, const ring r ) |
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478 | { |
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479 | poly res=NULL; |
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480 | On(SW_RATIONAL); |
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481 | if (rField_is_Zp(r) || rField_is_Q(r)) |
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482 | { |
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483 | setCharacteristic( rChar(r) ); |
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484 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
485 | res = convFactoryPSingP( F / G,r ); |
---|
486 | } |
---|
487 | else if (rField_is_Extension(r)) |
---|
488 | { |
---|
489 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
490 | else setCharacteristic( rChar(r) ); |
---|
491 | if (r->cf->extRing->qideal!=NULL) |
---|
492 | { |
---|
493 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
494 | r->cf->extRing); |
---|
495 | Variable a=rootOf(mipo); |
---|
496 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
497 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
498 | res= convFactoryAPSingAP( F / G, r ); |
---|
499 | } |
---|
500 | else |
---|
501 | { |
---|
502 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
503 | res= convFactoryPSingTrP( F / G,r ); |
---|
504 | } |
---|
505 | } |
---|
506 | #if 0 // not yet working |
---|
507 | else if (rField_is_GF()) |
---|
508 | { |
---|
509 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
510 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
511 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
512 | res = convFactoryGFSingGF( F / G ); |
---|
513 | } |
---|
514 | #endif |
---|
515 | else |
---|
516 | WerrorS( feNotImplemented ); |
---|
517 | Off(SW_RATIONAL); |
---|
518 | return res; |
---|
519 | } |
---|
520 | |
---|
521 | void singclap_divide_content ( poly f, const ring r ) |
---|
522 | { |
---|
523 | if ( f==NULL ) |
---|
524 | { |
---|
525 | return; |
---|
526 | } |
---|
527 | else if ( pNext( f ) == NULL ) |
---|
528 | { |
---|
529 | p_SetCoeff( f, n_Init( 1, r->cf ), r ); |
---|
530 | return; |
---|
531 | } |
---|
532 | else |
---|
533 | { |
---|
534 | if ( rField_is_Q_a(r) ) |
---|
535 | setCharacteristic( 0 ); |
---|
536 | else if ( rField_is_Zp_a(r) ) |
---|
537 | setCharacteristic( -rChar(r) ); |
---|
538 | else |
---|
539 | return; /* not implemented*/ |
---|
540 | |
---|
541 | CFList L; |
---|
542 | CanonicalForm g, h; |
---|
543 | poly p = pNext(f); |
---|
544 | |
---|
545 | // first attemp: find 2 smallest g: |
---|
546 | |
---|
547 | number g1=pGetCoeff(f); |
---|
548 | number g2=pGetCoeff(p); // p==pNext(f); |
---|
549 | pIter(p); |
---|
550 | int sz1=n_Size(g1, r->cf); |
---|
551 | int sz2=n_Size(g2, r->cf); |
---|
552 | if (sz1>sz2) |
---|
553 | { |
---|
554 | number gg=g1; |
---|
555 | g1=g2; g2=gg; |
---|
556 | int sz=sz1; |
---|
557 | sz1=sz2; sz2=sz; |
---|
558 | } |
---|
559 | while (p!=NULL) |
---|
560 | { |
---|
561 | int n_sz=n_Size(pGetCoeff(p),r->cf); |
---|
562 | if (n_sz<sz1) |
---|
563 | { |
---|
564 | sz2=sz1; |
---|
565 | g2=g1; |
---|
566 | g1=pGetCoeff(p); |
---|
567 | sz1=n_sz; |
---|
568 | if (sz1<=3) break; |
---|
569 | } |
---|
570 | else if(n_sz<sz2) |
---|
571 | { |
---|
572 | sz2=n_sz; |
---|
573 | g2=pGetCoeff(p); |
---|
574 | sz2=n_sz; |
---|
575 | } |
---|
576 | pIter(p); |
---|
577 | } |
---|
578 | g = convSingPFactoryP( NUM(((fraction)g1)), r->cf->extRing ); |
---|
579 | g = gcd( g, convSingPFactoryP( NUM(((fraction)g2)) , r->cf->extRing)); |
---|
580 | |
---|
581 | // second run: gcd's |
---|
582 | |
---|
583 | p = f; |
---|
584 | while ( (p != NULL) && (g != 1) && ( g != 0)) |
---|
585 | { |
---|
586 | h = convSingPFactoryP( NUM(((fraction)pGetCoeff(p))), r->cf->extRing ); |
---|
587 | pIter( p ); |
---|
588 | |
---|
589 | g = gcd( g, h ); |
---|
590 | |
---|
591 | L.append( h ); |
---|
592 | } |
---|
593 | if (( g == 1 ) || (g == 0)) |
---|
594 | { |
---|
595 | // pTest(f); |
---|
596 | return; |
---|
597 | } |
---|
598 | else |
---|
599 | { |
---|
600 | CFListIterator i; |
---|
601 | for ( i = L, p = f; i.hasItem(); i++, p=pNext(p) ) |
---|
602 | { |
---|
603 | fraction c=(fraction)pGetCoeff(p); |
---|
604 | p_Delete(&(NUM(c)),r->cf->extRing); // 2nd arg used to be nacRing |
---|
605 | NUM(c)=convFactoryPSingP( i.getItem() / g, r->cf->extRing ); |
---|
606 | //nTest((number)c); |
---|
607 | //#ifdef LDEBUG |
---|
608 | //number cn=(number)c; |
---|
609 | //StringSetS(""); nWrite(nt); StringAppend(" ==> "); |
---|
610 | //nWrite(cn);PrintS(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
611 | //#endif |
---|
612 | } |
---|
613 | } |
---|
614 | // pTest(f); |
---|
615 | } |
---|
616 | } |
---|
617 | |
---|
618 | BOOLEAN count_Factors(ideal I, intvec *v,int j, poly &f, poly fac, const ring r) |
---|
619 | { |
---|
620 | p_Test(f,r); |
---|
621 | p_Test(fac,r); |
---|
622 | int e=0; |
---|
623 | if (!p_IsConstantPoly(fac,r)) |
---|
624 | { |
---|
625 | #ifdef FACTORIZE2_DEBUG |
---|
626 | printf("start count_Factors(%d), Fdeg=%d, factor deg=%d\n",j,p_Totaldegree(f,r),p_Totaldegree(fac,r)); |
---|
627 | p_wrp(fac,r);PrintLn(); |
---|
628 | #endif |
---|
629 | On(SW_RATIONAL); |
---|
630 | CanonicalForm F, FAC,Q,R; |
---|
631 | Variable a; |
---|
632 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
633 | { |
---|
634 | F=convSingPFactoryP( f,r ); |
---|
635 | FAC=convSingPFactoryP( fac,r ); |
---|
636 | } |
---|
637 | else if (rField_is_Extension(r)) |
---|
638 | { |
---|
639 | if (r->cf->extRing->qideal!=NULL) |
---|
640 | { |
---|
641 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
642 | r->cf->extRing); |
---|
643 | a=rootOf(mipo); |
---|
644 | F=convSingAPFactoryAP( f,a,r ); |
---|
645 | FAC=convSingAPFactoryAP( fac,a,r ); |
---|
646 | } |
---|
647 | else |
---|
648 | { |
---|
649 | F=convSingTrPFactoryP( f,r ); |
---|
650 | FAC=convSingTrPFactoryP( fac,r ); |
---|
651 | } |
---|
652 | } |
---|
653 | else |
---|
654 | WerrorS( feNotImplemented ); |
---|
655 | |
---|
656 | poly q; |
---|
657 | loop |
---|
658 | { |
---|
659 | Q=F; |
---|
660 | Q/=FAC; |
---|
661 | R=Q; |
---|
662 | R*=FAC; |
---|
663 | R-=F; |
---|
664 | if (R.isZero()) |
---|
665 | { |
---|
666 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
667 | { |
---|
668 | q = convFactoryPSingP( Q,r ); |
---|
669 | } |
---|
670 | else if (rField_is_Extension(r)) |
---|
671 | { |
---|
672 | if (r->cf->extRing->qideal!=NULL) |
---|
673 | { |
---|
674 | q= convFactoryAPSingAP( Q,r ); |
---|
675 | } |
---|
676 | else |
---|
677 | { |
---|
678 | q= convFactoryPSingTrP( Q,r ); |
---|
679 | } |
---|
680 | } |
---|
681 | e++; p_Delete(&f,r); f=q; q=NULL; F=Q; |
---|
682 | } |
---|
683 | else |
---|
684 | { |
---|
685 | break; |
---|
686 | } |
---|
687 | } |
---|
688 | if (e==0) |
---|
689 | { |
---|
690 | Off(SW_RATIONAL); |
---|
691 | return FALSE; |
---|
692 | } |
---|
693 | } |
---|
694 | else e=1; |
---|
695 | I->m[j]=fac; |
---|
696 | if (v!=NULL) (*v)[j]=e; |
---|
697 | Off(SW_RATIONAL); |
---|
698 | return TRUE; |
---|
699 | } |
---|
700 | |
---|
701 | #ifdef HAVE_FACTORY |
---|
702 | int singclap_factorize_retry; |
---|
703 | # ifdef HAVE_LIBFAC |
---|
704 | extern int libfac_interruptflag; |
---|
705 | # endif |
---|
706 | #endif |
---|
707 | |
---|
708 | ideal singclap_factorize ( poly f, intvec ** v , int with_exps, const ring r) |
---|
709 | /* destroys f, sets *v */ |
---|
710 | { |
---|
711 | p_Test(f,r); |
---|
712 | #ifdef FACTORIZE2_DEBUG |
---|
713 | printf("singclap_factorize, degree %ld\n",p_Totaldegree(f,r)); |
---|
714 | #endif |
---|
715 | // with_exps: 3,1 return only true factors, no exponents |
---|
716 | // 2 return true factors and exponents |
---|
717 | // 0 return coeff, factors and exponents |
---|
718 | BOOLEAN save_errorreported=errorreported; |
---|
719 | |
---|
720 | ideal res=NULL; |
---|
721 | |
---|
722 | // handle factorize(0) ========================================= |
---|
723 | if (f==NULL) |
---|
724 | { |
---|
725 | res=idInit(1,1); |
---|
726 | if (with_exps!=1) |
---|
727 | { |
---|
728 | (*v)=new intvec(1); |
---|
729 | (**v)[0]=1; |
---|
730 | } |
---|
731 | return res; |
---|
732 | } |
---|
733 | // handle factorize(mon) ========================================= |
---|
734 | if (pNext(f)==NULL) |
---|
735 | { |
---|
736 | int i=0; |
---|
737 | int n=0; |
---|
738 | int e; |
---|
739 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
740 | if (with_exps==0) n++; // with coeff |
---|
741 | res=idInit(si_max(n,1),1); |
---|
742 | switch(with_exps) |
---|
743 | { |
---|
744 | case 0: // with coef & exp. |
---|
745 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
746 | // no break |
---|
747 | case 2: // with exp. |
---|
748 | (*v)=new intvec(si_max(1,n)); |
---|
749 | (**v)[0]=1; |
---|
750 | // no break |
---|
751 | case 1: ; |
---|
752 | #ifdef TEST |
---|
753 | default: ; |
---|
754 | #endif |
---|
755 | } |
---|
756 | if (n==0) |
---|
757 | { |
---|
758 | res->m[0]=p_One(r); |
---|
759 | // (**v)[0]=1; is already done |
---|
760 | } |
---|
761 | else |
---|
762 | { |
---|
763 | for(i=rVar(r);i>0;i--) |
---|
764 | { |
---|
765 | e=p_GetExp(f,i,r); |
---|
766 | if(e!=0) |
---|
767 | { |
---|
768 | n--; |
---|
769 | poly p=p_One(r); |
---|
770 | p_SetExp(p,i,1,r); |
---|
771 | p_Setm(p,r); |
---|
772 | res->m[n]=p; |
---|
773 | if (with_exps!=1) (**v)[n]=e; |
---|
774 | } |
---|
775 | } |
---|
776 | } |
---|
777 | p_Delete(&f,r); |
---|
778 | return res; |
---|
779 | } |
---|
780 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
781 | // use factory/libfac in general ============================== |
---|
782 | Off(SW_RATIONAL); |
---|
783 | On(SW_SYMMETRIC_FF); |
---|
784 | #ifdef HAVE_NTL |
---|
785 | extern int prime_number; |
---|
786 | if(rField_is_Q(r)) prime_number=0; |
---|
787 | #endif |
---|
788 | CFFList L; |
---|
789 | number N=NULL; |
---|
790 | number NN=NULL; |
---|
791 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
792 | |
---|
793 | if (!rField_is_Zp(r) && !rField_is_Zp_a(r)) /* Q, Q(a) */ |
---|
794 | { |
---|
795 | //if (f!=NULL) // already tested at start of routine |
---|
796 | { |
---|
797 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
798 | if (with_exps==0) |
---|
799 | N=n_Copy(n0,r->cf); |
---|
800 | p_Cleardenom(f, r); |
---|
801 | //after here f should not have a denominator!! |
---|
802 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
803 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
804 | n_Delete(&n0,r->cf); |
---|
805 | if (with_exps==0) |
---|
806 | { |
---|
807 | n_Delete(&N,r->cf); |
---|
808 | N=n_Copy(NN,r->cf); |
---|
809 | } |
---|
810 | } |
---|
811 | } |
---|
812 | else if (rField_is_Zp_a(r)) |
---|
813 | { |
---|
814 | //if (f!=NULL) // already tested at start of routine |
---|
815 | if (singclap_factorize_retry==0) |
---|
816 | { |
---|
817 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
818 | if (with_exps==0) |
---|
819 | N=n_Copy(n0,r->cf); |
---|
820 | p_Norm(f,r); |
---|
821 | p_Cleardenom(f, r); |
---|
822 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
823 | n_Delete(&n0,r->cf); |
---|
824 | if (with_exps==0) |
---|
825 | { |
---|
826 | n_Delete(&N,r->cf); |
---|
827 | N=n_Copy(NN,r->cf); |
---|
828 | } |
---|
829 | } |
---|
830 | } |
---|
831 | if (rField_is_Q(r) || rField_is_Zp(r)) |
---|
832 | { |
---|
833 | setCharacteristic( rChar(r) ); |
---|
834 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
835 | L = factorize( F ); |
---|
836 | } |
---|
837 | // and over Q(a) / Fp(a) |
---|
838 | else if (rField_is_Extension(r)) |
---|
839 | { |
---|
840 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
841 | else setCharacteristic( rChar(r) ); |
---|
842 | if (r->cf->extRing->qideal!=NULL) |
---|
843 | { |
---|
844 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
845 | r->cf->extRing); |
---|
846 | Variable a=rootOf(mipo); |
---|
847 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
848 | if (rField_is_Zp_a(r)) |
---|
849 | { |
---|
850 | L = factorize( F, a ); |
---|
851 | } |
---|
852 | else |
---|
853 | { |
---|
854 | // over Q(a) |
---|
855 | L= factorize (F, a); |
---|
856 | } |
---|
857 | } |
---|
858 | else |
---|
859 | { |
---|
860 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
861 | L = factorize( F ); |
---|
862 | } |
---|
863 | } |
---|
864 | else |
---|
865 | { |
---|
866 | goto notImpl; |
---|
867 | } |
---|
868 | { |
---|
869 | poly ff=p_Copy(f,r); // a copy for the retry stuff |
---|
870 | // the first factor should be a constant |
---|
871 | if ( ! L.getFirst().factor().inCoeffDomain() ) |
---|
872 | L.insert(CFFactor(1,1)); |
---|
873 | // convert into ideal |
---|
874 | int n = L.length(); |
---|
875 | if (n==0) n=1; |
---|
876 | CFFListIterator J=L; |
---|
877 | int j=0; |
---|
878 | if (with_exps!=1) |
---|
879 | { |
---|
880 | if ((with_exps==2)&&(n>1)) |
---|
881 | { |
---|
882 | n--; |
---|
883 | J++; |
---|
884 | } |
---|
885 | *v = new intvec( n ); |
---|
886 | } |
---|
887 | res = idInit( n ,1); |
---|
888 | for ( ; J.hasItem(); J++, j++ ) |
---|
889 | { |
---|
890 | if (with_exps!=1) (**v)[j] = J.getItem().exp(); |
---|
891 | if (rField_is_Zp(r) || rField_is_Q(r)) /* Q, Fp */ |
---|
892 | { |
---|
893 | //count_Factors(res,*v,f, j, convFactoryPSingP( J.getItem().factor() ); |
---|
894 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
895 | } |
---|
896 | #if 0 |
---|
897 | else if (rField_is_GF()) |
---|
898 | res->m[j] = convFactoryGFSingGF( J.getItem().factor() ); |
---|
899 | #endif |
---|
900 | else if (rField_is_Extension(r)) /* Q(a), Fp(a) */ |
---|
901 | { |
---|
902 | #ifndef NDEBUG |
---|
903 | intvec *w=NULL; |
---|
904 | if (v!=NULL) w=*v; |
---|
905 | #endif |
---|
906 | if (r->cf->extRing->qideal==NULL) |
---|
907 | { |
---|
908 | #ifdef NDEBUG |
---|
909 | res->m[j]= convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
910 | #else |
---|
911 | if(!count_Factors(res,w,j,ff,convFactoryPSingTrP( J.getItem().factor(),r ),r)) |
---|
912 | { |
---|
913 | if (w!=NULL) |
---|
914 | (*w)[j]=1; |
---|
915 | res->m[j]=p_One(r); |
---|
916 | } |
---|
917 | #endif |
---|
918 | } |
---|
919 | else |
---|
920 | { |
---|
921 | #ifdef NDEBUG |
---|
922 | res->m[j]= convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
923 | #else |
---|
924 | if (!count_Factors(res,w,j,ff,convFactoryAPSingAP( J.getItem().factor(),r ),r)) |
---|
925 | { |
---|
926 | if (w!=NULL) |
---|
927 | (*w)[j]=1; |
---|
928 | res->m[j]=p_One(r); |
---|
929 | } |
---|
930 | #endif |
---|
931 | } |
---|
932 | } |
---|
933 | } |
---|
934 | #ifndef NDEBUG |
---|
935 | if (rField_is_Extension(r) && (!p_IsConstantPoly(ff,r))) |
---|
936 | { |
---|
937 | singclap_factorize_retry++; |
---|
938 | if (singclap_factorize_retry<3) |
---|
939 | { |
---|
940 | int jj; |
---|
941 | #ifdef FACTORIZE2_DEBUG |
---|
942 | printf("factorize_retry\n"); |
---|
943 | #endif |
---|
944 | intvec *ww=NULL; |
---|
945 | id_Test(res,r); |
---|
946 | ideal h=singclap_factorize ( ff, &ww , with_exps, r ); |
---|
947 | id_Test(h,r); |
---|
948 | int l=(*v)->length(); |
---|
949 | (*v)->resize(l+ww->length()); |
---|
950 | for(jj=0;jj<ww->length();jj++) |
---|
951 | (**v)[jj+l]=(*ww)[jj]; |
---|
952 | delete ww; |
---|
953 | ideal hh=idInit(IDELEMS(res)+IDELEMS(h),1); |
---|
954 | for(jj=IDELEMS(res)-1;jj>=0;jj--) |
---|
955 | { |
---|
956 | hh->m[jj]=res->m[jj]; |
---|
957 | res->m[jj]=NULL; |
---|
958 | } |
---|
959 | for(jj=IDELEMS(h)-1;jj>=0;jj--) |
---|
960 | { |
---|
961 | hh->m[jj+IDELEMS(res)]=h->m[jj]; |
---|
962 | h->m[jj]=NULL; |
---|
963 | } |
---|
964 | id_Delete(&res,r); |
---|
965 | id_Delete(&h,r); |
---|
966 | res=hh; |
---|
967 | id_Test(res,r); |
---|
968 | ff=NULL; |
---|
969 | } |
---|
970 | else |
---|
971 | { |
---|
972 | WarnS("problem with factorize"); |
---|
973 | #if 0 |
---|
974 | pWrite(ff); |
---|
975 | idShow(res); |
---|
976 | #endif |
---|
977 | id_Delete(&res,r); |
---|
978 | res=idInit(2,1); |
---|
979 | res->m[0]=p_One(r); |
---|
980 | res->m[1]=ff; ff=NULL; |
---|
981 | } |
---|
982 | } |
---|
983 | #endif |
---|
984 | p_Delete(&ff,r); |
---|
985 | if (N!=NULL) |
---|
986 | { |
---|
987 | p_Mult_nn(res->m[0],N,r); |
---|
988 | n_Delete(&N,r->cf); |
---|
989 | N=NULL; |
---|
990 | } |
---|
991 | // delete constants |
---|
992 | if (res!=NULL) |
---|
993 | { |
---|
994 | int i=IDELEMS(res)-1; |
---|
995 | int j=0; |
---|
996 | for(;i>=0;i--) |
---|
997 | { |
---|
998 | if ((res->m[i]!=NULL) |
---|
999 | && (pNext(res->m[i])==NULL) |
---|
1000 | && (p_IsConstant(res->m[i],r))) |
---|
1001 | { |
---|
1002 | if (with_exps!=0) |
---|
1003 | { |
---|
1004 | p_Delete(&(res->m[i]),r); |
---|
1005 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1006 | (**v)[i]=0; |
---|
1007 | j++; |
---|
1008 | } |
---|
1009 | else if (i!=0) |
---|
1010 | { |
---|
1011 | while ((v!=NULL) && ((*v)!=NULL) && ((**v)[i]>1)) |
---|
1012 | { |
---|
1013 | res->m[0]=p_Mult_q(res->m[0],p_Copy(res->m[i],r),r); |
---|
1014 | (**v)[i]--; |
---|
1015 | } |
---|
1016 | res->m[0]=p_Mult_q(res->m[0],res->m[i],r); |
---|
1017 | res->m[i]=NULL; |
---|
1018 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1019 | (**v)[i]=1; |
---|
1020 | j++; |
---|
1021 | } |
---|
1022 | } |
---|
1023 | } |
---|
1024 | if (j>0) |
---|
1025 | { |
---|
1026 | idSkipZeroes(res); |
---|
1027 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1028 | { |
---|
1029 | intvec *w=*v; |
---|
1030 | int len=IDELEMS(res); |
---|
1031 | *v = new intvec( len ); |
---|
1032 | for (i=0,j=0;i<si_min(w->length(),len);i++) |
---|
1033 | { |
---|
1034 | if((*w)[i]!=0) |
---|
1035 | { |
---|
1036 | (**v)[j]=(*w)[i]; j++; |
---|
1037 | } |
---|
1038 | } |
---|
1039 | delete w; |
---|
1040 | } |
---|
1041 | } |
---|
1042 | if (res->m[0]==NULL) |
---|
1043 | { |
---|
1044 | res->m[0]=p_One(r); |
---|
1045 | } |
---|
1046 | } |
---|
1047 | } |
---|
1048 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
1049 | { |
---|
1050 | int i=IDELEMS(res)-1; |
---|
1051 | int stop=1; |
---|
1052 | if (with_exps!=0) stop=0; |
---|
1053 | for(;i>=stop;i--) |
---|
1054 | { |
---|
1055 | p_Norm(res->m[i],r); |
---|
1056 | } |
---|
1057 | if (with_exps==0) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
1058 | else n_Delete(&old_lead_coeff,r->cf); |
---|
1059 | } |
---|
1060 | else |
---|
1061 | n_Delete(&old_lead_coeff,r->cf); |
---|
1062 | errorreported=save_errorreported; |
---|
1063 | notImpl: |
---|
1064 | if (res==NULL) |
---|
1065 | WerrorS( feNotImplemented ); |
---|
1066 | if (NN!=NULL) |
---|
1067 | { |
---|
1068 | n_Delete(&NN,r->cf); |
---|
1069 | } |
---|
1070 | if (N!=NULL) |
---|
1071 | { |
---|
1072 | n_Delete(&N,r->cf); |
---|
1073 | } |
---|
1074 | if (f!=NULL) p_Delete(&f,r); |
---|
1075 | //PrintS("......S\n"); |
---|
1076 | return res; |
---|
1077 | } |
---|
1078 | |
---|
1079 | ideal singclap_sqrfree ( poly f, intvec ** v , int with_exps, const ring r) |
---|
1080 | { |
---|
1081 | p_Test(f,r); |
---|
1082 | #ifdef FACTORIZE2_DEBUG |
---|
1083 | printf("singclap_sqrfree, degree %d\n",pTotaldegree(f)); |
---|
1084 | #endif |
---|
1085 | // with_exps: 3,1 return only true factors, no exponents |
---|
1086 | // 2 return true factors and exponents |
---|
1087 | // 0 return coeff, factors and exponents |
---|
1088 | BOOLEAN save_errorreported=errorreported; |
---|
1089 | |
---|
1090 | ideal res=NULL; |
---|
1091 | |
---|
1092 | // handle factorize(0) ========================================= |
---|
1093 | if (f==NULL) |
---|
1094 | { |
---|
1095 | res=idInit(1,1); |
---|
1096 | if (with_exps!=1 && with_exps!=3) |
---|
1097 | { |
---|
1098 | (*v)=new intvec(1); |
---|
1099 | (**v)[0]=1; |
---|
1100 | } |
---|
1101 | return res; |
---|
1102 | } |
---|
1103 | // handle factorize(mon) ========================================= |
---|
1104 | if (pNext(f)==NULL) |
---|
1105 | { |
---|
1106 | int i=0; |
---|
1107 | int n=0; |
---|
1108 | int e; |
---|
1109 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
1110 | if (with_exps==0 || with_exps==3) n++; // with coeff |
---|
1111 | res=idInit(si_max(n,1),1); |
---|
1112 | switch(with_exps) |
---|
1113 | { |
---|
1114 | case 0: // with coef & exp. |
---|
1115 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
1116 | // no break |
---|
1117 | case 3: // with coef & exp. |
---|
1118 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
1119 | // no break |
---|
1120 | case 2: // with exp. |
---|
1121 | (*v)=new intvec(si_max(1,n)); |
---|
1122 | (**v)[0]=1; |
---|
1123 | // no break |
---|
1124 | case 1: ; |
---|
1125 | #ifdef TEST |
---|
1126 | default: ; |
---|
1127 | #endif |
---|
1128 | } |
---|
1129 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
1130 | if (n==0) |
---|
1131 | { |
---|
1132 | res->m[0]=p_One(r); |
---|
1133 | // (**v)[0]=1; is already done |
---|
1134 | } |
---|
1135 | else |
---|
1136 | { |
---|
1137 | for(i=rVar(r);i>0;i--) |
---|
1138 | { |
---|
1139 | e=p_GetExp(f,i,r); |
---|
1140 | if(e!=0) |
---|
1141 | { |
---|
1142 | n--; |
---|
1143 | poly p=p_One(r); |
---|
1144 | p_SetExp(p,i,1,r); |
---|
1145 | p_Setm(p,r); |
---|
1146 | res->m[n]=p; |
---|
1147 | if (with_exps!=1) (**v)[n]=e; |
---|
1148 | } |
---|
1149 | } |
---|
1150 | } |
---|
1151 | p_Delete(&f,r); |
---|
1152 | return res; |
---|
1153 | } |
---|
1154 | //PrintS("S:");pWrite(f);PrintLn(); |
---|
1155 | // use factory/libfac in general ============================== |
---|
1156 | Off(SW_RATIONAL); |
---|
1157 | On(SW_SYMMETRIC_FF); |
---|
1158 | #ifdef HAVE_NTL |
---|
1159 | extern int prime_number; |
---|
1160 | if(rField_is_Q(r)) prime_number=0; |
---|
1161 | #endif |
---|
1162 | CFFList L; |
---|
1163 | number N=NULL; |
---|
1164 | number NN=NULL; |
---|
1165 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
1166 | |
---|
1167 | if (!rField_is_Zp(r) && !rField_is_Zp_a(r)) /* Q, Q(a) */ |
---|
1168 | { |
---|
1169 | //if (f!=NULL) // already tested at start of routine |
---|
1170 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
1171 | if (with_exps==0 || with_exps==3) |
---|
1172 | N=n_Copy(n0,r->cf); |
---|
1173 | p_Cleardenom(f, r); |
---|
1174 | //after here f should not have a denominator!! |
---|
1175 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
1176 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1177 | n_Delete(&n0,r->cf); |
---|
1178 | if (with_exps==0 || with_exps==3) |
---|
1179 | { |
---|
1180 | n_Delete(&N,r->cf); |
---|
1181 | N=n_Copy(NN,r->cf); |
---|
1182 | } |
---|
1183 | } |
---|
1184 | else if (rField_is_Zp_a(r)) |
---|
1185 | { |
---|
1186 | //if (f!=NULL) // already tested at start of routine |
---|
1187 | if (singclap_factorize_retry==0) |
---|
1188 | { |
---|
1189 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
1190 | if (with_exps==0 || with_exps==3) |
---|
1191 | N=n_Copy(n0,r->cf); |
---|
1192 | p_Norm(f,r); |
---|
1193 | p_Cleardenom(f, r); |
---|
1194 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1195 | n_Delete(&n0,r->cf); |
---|
1196 | if (with_exps==0 || with_exps==3) |
---|
1197 | { |
---|
1198 | n_Delete(&N,r->cf); |
---|
1199 | N=n_Copy(NN,r->cf); |
---|
1200 | } |
---|
1201 | } |
---|
1202 | } |
---|
1203 | if (rField_is_Q(r) || rField_is_Zp(r)) |
---|
1204 | { |
---|
1205 | setCharacteristic( rChar(r) ); |
---|
1206 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
1207 | L = sqrFree( F ); |
---|
1208 | } |
---|
1209 | else if (rField_is_Extension(r)) |
---|
1210 | { |
---|
1211 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
1212 | else setCharacteristic( rChar(r) ); |
---|
1213 | if (r->cf->extRing->qideal!=NULL) |
---|
1214 | { |
---|
1215 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
1216 | r->cf->extRing); |
---|
1217 | Variable a=rootOf(mipo); |
---|
1218 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
1219 | L= sqrFree (F); |
---|
1220 | } |
---|
1221 | else |
---|
1222 | { |
---|
1223 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
1224 | L = sqrFree( F ); |
---|
1225 | } |
---|
1226 | } |
---|
1227 | #if 0 |
---|
1228 | else if (rField_is_GF()) |
---|
1229 | { |
---|
1230 | int c=rChar(r); |
---|
1231 | setCharacteristic( c, primepower(c) ); |
---|
1232 | CanonicalForm F( convSingGFFactoryGF( f ) ); |
---|
1233 | if (F.isUnivariate()) |
---|
1234 | { |
---|
1235 | L = factorize( F ); |
---|
1236 | } |
---|
1237 | else |
---|
1238 | { |
---|
1239 | goto notImpl; |
---|
1240 | } |
---|
1241 | } |
---|
1242 | #endif |
---|
1243 | else |
---|
1244 | { |
---|
1245 | goto notImpl; |
---|
1246 | } |
---|
1247 | { |
---|
1248 | // convert into ideal |
---|
1249 | int n = L.length(); |
---|
1250 | if (n==0) n=1; |
---|
1251 | CFFListIterator J=L; |
---|
1252 | int j=0; |
---|
1253 | if (with_exps!=1) |
---|
1254 | { |
---|
1255 | if ((with_exps==2)&&(n>1)) |
---|
1256 | { |
---|
1257 | n--; |
---|
1258 | J++; |
---|
1259 | } |
---|
1260 | *v = new intvec( n ); |
---|
1261 | } |
---|
1262 | else if (L.getFirst().factor().inCoeffDomain() && with_exps!=3) |
---|
1263 | { |
---|
1264 | n--; |
---|
1265 | J++; |
---|
1266 | } |
---|
1267 | res = idInit( n ,1); |
---|
1268 | for ( ; J.hasItem(); J++, j++ ) |
---|
1269 | { |
---|
1270 | if (with_exps!=1 && with_exps!=3) (**v)[j] = J.getItem().exp(); |
---|
1271 | if (rField_is_Zp(r) || rField_is_Q(r)) |
---|
1272 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
1273 | else if (rField_is_Extension(r)) /* Q(a), Fp(a) */ |
---|
1274 | { |
---|
1275 | if (r->cf->extRing->qideal==NULL) |
---|
1276 | res->m[j]=convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
1277 | else |
---|
1278 | res->m[j]=convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
1279 | } |
---|
1280 | } |
---|
1281 | if (res->m[0]==NULL) |
---|
1282 | { |
---|
1283 | res->m[0]=p_One(r); |
---|
1284 | } |
---|
1285 | if (N!=NULL) |
---|
1286 | { |
---|
1287 | p_Mult_nn(res->m[0],N,r); |
---|
1288 | n_Delete(&N,r->cf); |
---|
1289 | N=NULL; |
---|
1290 | } |
---|
1291 | } |
---|
1292 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
1293 | { |
---|
1294 | int i=IDELEMS(res)-1; |
---|
1295 | int stop=1; |
---|
1296 | if (with_exps!=0 || with_exps==3) stop=0; |
---|
1297 | for(;i>=stop;i--) |
---|
1298 | { |
---|
1299 | p_Norm(res->m[i],r); |
---|
1300 | } |
---|
1301 | if (with_exps==0 || with_exps==3) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
1302 | else n_Delete(&old_lead_coeff,r->cf); |
---|
1303 | } |
---|
1304 | else |
---|
1305 | n_Delete(&old_lead_coeff,r->cf); |
---|
1306 | p_Delete(&f,r); |
---|
1307 | errorreported=save_errorreported; |
---|
1308 | notImpl: |
---|
1309 | if (res==NULL) |
---|
1310 | WerrorS( feNotImplemented ); |
---|
1311 | if (NN!=NULL) |
---|
1312 | { |
---|
1313 | n_Delete(&NN,r->cf); |
---|
1314 | } |
---|
1315 | if (N!=NULL) |
---|
1316 | { |
---|
1317 | n_Delete(&N,r->cf); |
---|
1318 | } |
---|
1319 | return res; |
---|
1320 | } |
---|
1321 | |
---|
1322 | #ifdef HAVE_LIBFAC |
---|
1323 | matrix singclap_irrCharSeries ( ideal I, const ring r) |
---|
1324 | { |
---|
1325 | if (idIs0(I)) return mpNew(1,1); |
---|
1326 | |
---|
1327 | // for now there is only the possibility to handle polynomials over |
---|
1328 | // Q and Fp ... |
---|
1329 | matrix res=NULL; |
---|
1330 | int i; |
---|
1331 | Off(SW_RATIONAL); |
---|
1332 | On(SW_SYMMETRIC_FF); |
---|
1333 | CFList L; |
---|
1334 | ListCFList LL; |
---|
1335 | if (((rChar(r) == 0) || (rChar(r) > 1) ) |
---|
1336 | && (rPar(r)==0)) |
---|
1337 | { |
---|
1338 | setCharacteristic( rChar(r) ); |
---|
1339 | for(i=0;i<IDELEMS(I);i++) |
---|
1340 | { |
---|
1341 | poly p=I->m[i]; |
---|
1342 | if (p!=NULL) |
---|
1343 | { |
---|
1344 | p=p_Copy(p,r); |
---|
1345 | p_Cleardenom(p, r); |
---|
1346 | L.append(convSingPFactoryP(p,r)); |
---|
1347 | } |
---|
1348 | } |
---|
1349 | } |
---|
1350 | // and over Q(a) / Fp(a) |
---|
1351 | else if (( rChar(r)==1 ) // Q(a) |
---|
1352 | || (rChar(r) <-1)) // Fp(a) |
---|
1353 | { |
---|
1354 | if (rChar(r)==1) setCharacteristic( 0 ); |
---|
1355 | else setCharacteristic( -rChar(r) ); |
---|
1356 | for(i=0;i<IDELEMS(I);i++) |
---|
1357 | { |
---|
1358 | poly p=I->m[i]; |
---|
1359 | if (p!=NULL) |
---|
1360 | { |
---|
1361 | p=p_Copy(p,r); |
---|
1362 | p_Cleardenom(p, r); |
---|
1363 | L.append(convSingTrPFactoryP(p,r)); |
---|
1364 | } |
---|
1365 | } |
---|
1366 | } |
---|
1367 | else |
---|
1368 | { |
---|
1369 | WerrorS( feNotImplemented ); |
---|
1370 | return res; |
---|
1371 | } |
---|
1372 | |
---|
1373 | // a very bad work-around --- FIX IT in libfac |
---|
1374 | // should be fixed as of 2001/6/27 |
---|
1375 | int tries=0; |
---|
1376 | int m,n; |
---|
1377 | ListIterator<CFList> LLi; |
---|
1378 | loop |
---|
1379 | { |
---|
1380 | LL=IrrCharSeries(L); |
---|
1381 | m= LL.length(); // Anzahl Zeilen |
---|
1382 | n=0; |
---|
1383 | for ( LLi = LL; LLi.hasItem(); LLi++ ) |
---|
1384 | { |
---|
1385 | n = si_max(LLi.getItem().length(),n); |
---|
1386 | } |
---|
1387 | if ((m!=0) && (n!=0)) break; |
---|
1388 | tries++; |
---|
1389 | if (tries>=5) break; |
---|
1390 | } |
---|
1391 | if ((m==0) || (n==0)) |
---|
1392 | { |
---|
1393 | Warn("char_series returns %d x %d matrix from %d input polys (%d)", |
---|
1394 | m,n,IDELEMS(I)+1,LL.length()); |
---|
1395 | iiWriteMatrix((matrix)I,"I",2,r,0); |
---|
1396 | m=si_max(m,1); |
---|
1397 | n=si_max(n,1); |
---|
1398 | } |
---|
1399 | res=mpNew(m,n); |
---|
1400 | CFListIterator Li; |
---|
1401 | for ( m=1, LLi = LL; LLi.hasItem(); LLi++, m++ ) |
---|
1402 | { |
---|
1403 | for (n=1, Li = LLi.getItem(); Li.hasItem(); Li++, n++) |
---|
1404 | { |
---|
1405 | if ( (rChar(r) == 0) || (rChar(r) > 1) ) |
---|
1406 | MATELEM(res,m,n)=convFactoryPSingP(Li.getItem(),r); |
---|
1407 | else |
---|
1408 | MATELEM(res,m,n)=convFactoryPSingTrP(Li.getItem(),r); |
---|
1409 | } |
---|
1410 | } |
---|
1411 | Off(SW_RATIONAL); |
---|
1412 | return res; |
---|
1413 | } |
---|
1414 | |
---|
1415 | char* singclap_neworder ( ideal I, const ring r) |
---|
1416 | { |
---|
1417 | int i; |
---|
1418 | Off(SW_RATIONAL); |
---|
1419 | On(SW_SYMMETRIC_FF); |
---|
1420 | CFList L; |
---|
1421 | if (((rChar(r) == 0) || (rChar(r) > 1) ) |
---|
1422 | && (rPar(r)==0)) |
---|
1423 | { |
---|
1424 | setCharacteristic( rChar(r) ); |
---|
1425 | for(i=0;i<IDELEMS(I);i++) |
---|
1426 | { |
---|
1427 | L.append(convSingPFactoryP(I->m[i],r)); |
---|
1428 | } |
---|
1429 | } |
---|
1430 | // and over Q(a) / Fp(a) |
---|
1431 | else if (( rChar(r)==1 ) // Q(a) |
---|
1432 | || (rChar(r) <-1)) // Fp(a) |
---|
1433 | { |
---|
1434 | if (rChar(r)==1) setCharacteristic( 0 ); |
---|
1435 | else setCharacteristic( -rChar(r) ); |
---|
1436 | for(i=0;i<IDELEMS(I);i++) |
---|
1437 | { |
---|
1438 | L.append(convSingTrPFactoryP(I->m[i],r)); |
---|
1439 | } |
---|
1440 | } |
---|
1441 | else |
---|
1442 | { |
---|
1443 | WerrorS( feNotImplemented ); |
---|
1444 | return NULL; |
---|
1445 | } |
---|
1446 | |
---|
1447 | List<int> IL=neworderint(L); |
---|
1448 | ListIterator<int> Li; |
---|
1449 | StringSetS(""); |
---|
1450 | Li = IL; |
---|
1451 | int offs=rPar(r); |
---|
1452 | int* mark=(int*)omAlloc0((rVar(r)+offs)*sizeof(int)); |
---|
1453 | int cnt=rVar(r)+offs; |
---|
1454 | loop |
---|
1455 | { |
---|
1456 | if(! Li.hasItem()) break; |
---|
1457 | BOOLEAN done=TRUE; |
---|
1458 | i=Li.getItem()-1; |
---|
1459 | mark[i]=1; |
---|
1460 | if (i<offs) |
---|
1461 | { |
---|
1462 | done=FALSE; |
---|
1463 | //StringAppendS(r->parameter[i]); |
---|
1464 | } |
---|
1465 | else |
---|
1466 | { |
---|
1467 | StringAppendS(r->names[i-offs]); |
---|
1468 | } |
---|
1469 | Li++; |
---|
1470 | cnt--; |
---|
1471 | if(cnt==0) break; |
---|
1472 | if (done) StringAppendS(","); |
---|
1473 | } |
---|
1474 | for(i=0;i<rVar(r)+offs;i++) |
---|
1475 | { |
---|
1476 | BOOLEAN done=TRUE; |
---|
1477 | if(mark[i]==0) |
---|
1478 | { |
---|
1479 | if (i<offs) |
---|
1480 | { |
---|
1481 | done=FALSE; |
---|
1482 | //StringAppendS(r->parameter[i]); |
---|
1483 | } |
---|
1484 | else |
---|
1485 | { |
---|
1486 | StringAppendS(r->names[i-offs]); |
---|
1487 | } |
---|
1488 | cnt--; |
---|
1489 | if(cnt==0) break; |
---|
1490 | if (done) StringAppendS(","); |
---|
1491 | } |
---|
1492 | } |
---|
1493 | char * s=StringEndS(); |
---|
1494 | if (s[strlen(s)-1]==',') s[strlen(s)-1]='\0'; |
---|
1495 | return s; |
---|
1496 | } |
---|
1497 | #endif /*HAVE_LIBFAC*/ |
---|
1498 | |
---|
1499 | BOOLEAN singclap_isSqrFree(poly f, const ring r) |
---|
1500 | { |
---|
1501 | BOOLEAN b=FALSE; |
---|
1502 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
1503 | if((r->cf->type==n_Zp)&&(!F.isUnivariate())) |
---|
1504 | goto err; |
---|
1505 | b=(BOOLEAN)isSqrFree(F); |
---|
1506 | Off(SW_RATIONAL); |
---|
1507 | return b; |
---|
1508 | err: |
---|
1509 | WerrorS( feNotImplemented ); |
---|
1510 | return 0; |
---|
1511 | } |
---|
1512 | |
---|
1513 | poly singclap_det( const matrix m, const ring s ) |
---|
1514 | { |
---|
1515 | int r=m->rows(); |
---|
1516 | if (r!=m->cols()) |
---|
1517 | { |
---|
1518 | Werror("det of %d x %d matrix",r,m->cols()); |
---|
1519 | return NULL; |
---|
1520 | } |
---|
1521 | poly res=NULL; |
---|
1522 | CFMatrix M(r,r); |
---|
1523 | int i,j; |
---|
1524 | for(i=r;i>0;i--) |
---|
1525 | { |
---|
1526 | for(j=r;j>0;j--) |
---|
1527 | { |
---|
1528 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
1529 | } |
---|
1530 | } |
---|
1531 | res= convFactoryPSingP( determinant(M,r),s ) ; |
---|
1532 | Off(SW_RATIONAL); |
---|
1533 | return res; |
---|
1534 | } |
---|
1535 | |
---|
1536 | int singclap_det_i( intvec * m, const ring /*r*/) |
---|
1537 | { |
---|
1538 | // assume( r == currRing ); // Anything else is not guaranted to work! |
---|
1539 | |
---|
1540 | setCharacteristic( 0 ); // ? |
---|
1541 | CFMatrix M(m->rows(),m->cols()); |
---|
1542 | int i,j; |
---|
1543 | for(i=m->rows();i>0;i--) |
---|
1544 | { |
---|
1545 | for(j=m->cols();j>0;j--) |
---|
1546 | { |
---|
1547 | M(i,j)=IMATELEM(*m,i,j); |
---|
1548 | } |
---|
1549 | } |
---|
1550 | int res= convFactoryISingI( determinant(M,m->rows()) ) ; |
---|
1551 | return res; |
---|
1552 | } |
---|
1553 | |
---|
1554 | number singclap_det_bi( bigintmat * m, const coeffs cf) |
---|
1555 | { |
---|
1556 | assume(m->basecoeffs()==cf); |
---|
1557 | CFMatrix M(m->rows(),m->cols()); |
---|
1558 | int i,j; |
---|
1559 | BOOLEAN setchar=TRUE; |
---|
1560 | for(i=m->rows();i>0;i--) |
---|
1561 | { |
---|
1562 | for(j=m->cols();j>0;j--) |
---|
1563 | { |
---|
1564 | M(i,j)=cf->convSingNFactoryN(BIMATELEM(*m,i,j),setchar,cf); |
---|
1565 | setchar=FALSE; |
---|
1566 | } |
---|
1567 | } |
---|
1568 | number res= cf->convFactoryNSingN( determinant(M,m->rows()),cf ) ; |
---|
1569 | return res; |
---|
1570 | } |
---|
1571 | |
---|
1572 | #ifdef HAVE_NTL |
---|
1573 | #if 1 |
---|
1574 | matrix singntl_HNF(matrix m, const ring s ) |
---|
1575 | { |
---|
1576 | int r=m->rows(); |
---|
1577 | if (r!=m->cols()) |
---|
1578 | { |
---|
1579 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
1580 | return NULL; |
---|
1581 | } |
---|
1582 | |
---|
1583 | matrix res=mp_New(r,r); |
---|
1584 | |
---|
1585 | if (rField_is_Q(s)) |
---|
1586 | { |
---|
1587 | |
---|
1588 | CFMatrix M(r,r); |
---|
1589 | int i,j; |
---|
1590 | for(i=r;i>0;i--) |
---|
1591 | { |
---|
1592 | for(j=r;j>0;j--) |
---|
1593 | { |
---|
1594 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s ); |
---|
1595 | } |
---|
1596 | } |
---|
1597 | CFMatrix *MM=cf_HNF(M); |
---|
1598 | for(i=r;i>0;i--) |
---|
1599 | { |
---|
1600 | for(j=r;j>0;j--) |
---|
1601 | { |
---|
1602 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
1603 | } |
---|
1604 | } |
---|
1605 | delete MM; |
---|
1606 | } |
---|
1607 | return res; |
---|
1608 | } |
---|
1609 | |
---|
1610 | intvec* singntl_HNF(intvec* m, const ring) |
---|
1611 | { |
---|
1612 | int r=m->rows(); |
---|
1613 | if (r!=m->cols()) |
---|
1614 | { |
---|
1615 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
1616 | return NULL; |
---|
1617 | } |
---|
1618 | setCharacteristic( 0 ); |
---|
1619 | CFMatrix M(r,r); |
---|
1620 | int i,j; |
---|
1621 | for(i=r;i>0;i--) |
---|
1622 | { |
---|
1623 | for(j=r;j>0;j--) |
---|
1624 | { |
---|
1625 | M(i,j)=IMATELEM(*m,i,j); |
---|
1626 | } |
---|
1627 | } |
---|
1628 | CFMatrix *MM=cf_HNF(M); |
---|
1629 | intvec *mm=ivCopy(m); |
---|
1630 | for(i=r;i>0;i--) |
---|
1631 | { |
---|
1632 | for(j=r;j>0;j--) |
---|
1633 | { |
---|
1634 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
1635 | } |
---|
1636 | } |
---|
1637 | delete MM; |
---|
1638 | return mm; |
---|
1639 | } |
---|
1640 | |
---|
1641 | matrix singntl_LLL(matrix m, const ring s ) |
---|
1642 | { |
---|
1643 | int r=m->rows(); |
---|
1644 | int c=m->cols(); |
---|
1645 | matrix res=mp_New(r,c); |
---|
1646 | if (rField_is_Q(s)) |
---|
1647 | { |
---|
1648 | CFMatrix M(r,c); |
---|
1649 | int i,j; |
---|
1650 | for(i=r;i>0;i--) |
---|
1651 | { |
---|
1652 | for(j=c;j>0;j--) |
---|
1653 | { |
---|
1654 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
1655 | } |
---|
1656 | } |
---|
1657 | CFMatrix *MM=cf_LLL(M); |
---|
1658 | for(i=r;i>0;i--) |
---|
1659 | { |
---|
1660 | for(j=c;j>0;j--) |
---|
1661 | { |
---|
1662 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
1663 | } |
---|
1664 | } |
---|
1665 | delete MM; |
---|
1666 | } |
---|
1667 | return res; |
---|
1668 | } |
---|
1669 | |
---|
1670 | intvec* singntl_LLL(intvec* m, const ring) |
---|
1671 | { |
---|
1672 | int r=m->rows(); |
---|
1673 | int c=m->cols(); |
---|
1674 | setCharacteristic( 0 ); |
---|
1675 | CFMatrix M(r,c); |
---|
1676 | int i,j; |
---|
1677 | for(i=r;i>0;i--) |
---|
1678 | { |
---|
1679 | for(j=r;j>0;j--) |
---|
1680 | { |
---|
1681 | M(i,j)=IMATELEM(*m,i,j); |
---|
1682 | } |
---|
1683 | } |
---|
1684 | CFMatrix *MM=cf_LLL(M); |
---|
1685 | intvec *mm=ivCopy(m); |
---|
1686 | for(i=r;i>0;i--) |
---|
1687 | { |
---|
1688 | for(j=c;j>0;j--) |
---|
1689 | { |
---|
1690 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
1691 | } |
---|
1692 | } |
---|
1693 | delete MM; |
---|
1694 | return mm; |
---|
1695 | } |
---|
1696 | |
---|
1697 | ideal singclap_absBiFactorize ( poly f, ideal & mipos, intvec ** exps, int & numFactors, const ring r) |
---|
1698 | { |
---|
1699 | p_Test(f, r); |
---|
1700 | |
---|
1701 | ideal res=NULL; |
---|
1702 | |
---|
1703 | int offs = rPar(r); |
---|
1704 | if (f==NULL) |
---|
1705 | { |
---|
1706 | res= idInit (1, 1); |
---|
1707 | mipos= idInit (1, 1); |
---|
1708 | mipos->m[0]= convFactoryPSingTrP (Variable (offs), r); //overkill |
---|
1709 | (*exps)=new intvec (1); |
---|
1710 | (**exps)[0]= 1; |
---|
1711 | numFactors= 0; |
---|
1712 | return res; |
---|
1713 | } |
---|
1714 | CanonicalForm F( convSingTrPFactoryP( f, r) ); |
---|
1715 | |
---|
1716 | bool isRat= isOn (SW_RATIONAL); |
---|
1717 | if (!isRat) |
---|
1718 | On (SW_RATIONAL); |
---|
1719 | |
---|
1720 | CFAFList absFactors= absFactorize (F); |
---|
1721 | |
---|
1722 | int n= absFactors.length(); |
---|
1723 | *exps=new intvec (n); |
---|
1724 | |
---|
1725 | res= idInit (n, 1); |
---|
1726 | |
---|
1727 | mipos= idInit (n, 1); |
---|
1728 | |
---|
1729 | Variable x= Variable (offs); |
---|
1730 | Variable alpha; |
---|
1731 | int i= 0; |
---|
1732 | numFactors= 0; |
---|
1733 | int count; |
---|
1734 | CFAFListIterator iter= absFactors; |
---|
1735 | CanonicalForm lead= iter.getItem().factor(); |
---|
1736 | if (iter.getItem().factor().inCoeffDomain()) |
---|
1737 | { |
---|
1738 | i++; |
---|
1739 | iter++; |
---|
1740 | } |
---|
1741 | for (; iter.hasItem(); iter++, i++) |
---|
1742 | { |
---|
1743 | (**exps)[i]= iter.getItem().exp(); |
---|
1744 | alpha= iter.getItem().minpoly().mvar(); |
---|
1745 | if (iter.getItem().minpoly().isOne()) |
---|
1746 | lead /= power (bCommonDen (iter.getItem().factor()), iter.getItem().exp()); |
---|
1747 | else |
---|
1748 | lead /= power (power (bCommonDen (iter.getItem().factor()), degree (iter.getItem().minpoly())), iter.getItem().exp()); |
---|
1749 | res->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().factor()*bCommonDen (iter.getItem().factor()), alpha, x), r); |
---|
1750 | if (iter.getItem().minpoly().isOne()) |
---|
1751 | { |
---|
1752 | count= iter.getItem().exp(); |
---|
1753 | mipos->m[i]= convFactoryPSingTrP (x,r); |
---|
1754 | } |
---|
1755 | else |
---|
1756 | { |
---|
1757 | count= iter.getItem().exp()*degree (iter.getItem().minpoly()); |
---|
1758 | mipos->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().minpoly(), alpha, x), r); |
---|
1759 | } |
---|
1760 | numFactors += count; |
---|
1761 | } |
---|
1762 | if (!isRat) |
---|
1763 | Off (SW_RATIONAL); |
---|
1764 | |
---|
1765 | (**exps)[0]= 1; |
---|
1766 | res->m[0]= convFactoryPSingTrP (lead, r); |
---|
1767 | mipos->m[0]= convFactoryPSingTrP (x, r); |
---|
1768 | return res; |
---|
1769 | } |
---|
1770 | |
---|
1771 | #endif |
---|
1772 | #endif /* HAVE_NTL */ |
---|
1773 | |
---|
1774 | |
---|
1775 | #endif /* HAVE_FACTORY */ |
---|