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 | #include "misc/auxiliary.h" |
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12 | #include "clapsing.h" |
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13 | |
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14 | #include "factory/factory.h" |
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15 | #include "factory/cf_roots.h" |
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16 | |
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17 | #include "coeffs/numbers.h" |
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18 | #include "coeffs/coeffs.h" |
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19 | #include "coeffs/bigintmat.h" |
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20 | |
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21 | #include "monomials/ring.h" |
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22 | #include "simpleideals.h" |
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23 | #include "polys/flintconv.h" |
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24 | #include "polys/flint_mpoly.h" |
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25 | |
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26 | |
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27 | //#include "polys.h" |
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28 | #define TRANSEXT_PRIVATES |
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29 | |
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30 | #include "ext_fields/transext.h" |
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31 | |
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32 | |
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33 | #include "clapconv.h" |
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34 | |
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35 | #include "polys/monomials/p_polys.h" |
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36 | #include "polys/monomials/ring.h" |
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37 | #include "polys/simpleideals.h" |
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38 | #include "misc/intvec.h" |
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39 | #include "polys/matpol.h" |
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40 | #include "coeffs/bigintmat.h" |
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41 | |
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42 | |
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43 | void out_cf(const char *s1,const CanonicalForm &f,const char *s2); |
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44 | |
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45 | poly singclap_gcd_r ( poly f, poly g, const ring r ) |
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46 | { |
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47 | poly res=NULL; |
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48 | |
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49 | assume(f!=NULL); |
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50 | assume(g!=NULL); |
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51 | |
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52 | if(pNext(f)==NULL) |
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53 | { |
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54 | return p_GcdMon(f,g,r); |
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55 | } |
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56 | else if(pNext(g)==NULL) |
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57 | { |
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58 | return p_GcdMon(g,f,r); |
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59 | } |
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60 | #ifdef HAVE_FLINT |
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61 | #if __FLINT_RELEASE >= 20503 |
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62 | if (rField_is_Zp(r) && (r->cf->ch>10)) |
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63 | { |
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64 | nmod_mpoly_ctx_t ctx; |
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65 | if (!convSingRFlintR(ctx,r)) |
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66 | { |
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67 | // leading coef. 1 |
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68 | return Flint_GCD_MP(f,pLength(f),g,pLength(g),ctx,r); |
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69 | } |
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70 | } |
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71 | else |
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72 | if (rField_is_Q(r)) |
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73 | { |
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74 | fmpq_mpoly_ctx_t ctx; |
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75 | if (!convSingRFlintR(ctx,r)) |
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76 | { |
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77 | // leading coef. positive, all coeffs in Z |
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78 | poly res=Flint_GCD_MP(f,pLength(f),g,pLength(g),ctx,r); |
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79 | res=p_Cleardenom(res,r); |
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80 | return res; |
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81 | } |
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82 | } |
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83 | #endif |
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84 | #endif |
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85 | Off(SW_RATIONAL); |
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86 | if (rField_is_Q(r) || rField_is_Zp(r) || rField_is_Z(r) |
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87 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
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88 | { |
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89 | setCharacteristic( rChar(r) ); |
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90 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g, r ) ); |
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91 | res=convFactoryPSingP( gcd( F, G ) , r); |
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92 | if ( rField_is_Zp(r)) |
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93 | p_Norm(res,r); // leading coef. 1 |
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94 | else if (rField_is_Q(r) && (!n_GreaterZero(pGetCoeff(res),r->cf))) |
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95 | res = p_Neg(res,r); // leading coef. positive, all coeffs in Z |
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96 | } |
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97 | // and over Q(a) / Fp(a) |
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98 | else if ( r->cf->extRing!=NULL ) |
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99 | { |
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100 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
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101 | else setCharacteristic( rChar(r) ); |
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102 | if (r->cf->extRing->qideal!=NULL) |
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103 | { |
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104 | bool b1=isOn(SW_USE_QGCD); |
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105 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
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106 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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107 | r->cf->extRing); |
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108 | Variable a=rootOf(mipo); |
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109 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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110 | G( convSingAPFactoryAP( g,a,r ) ); |
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111 | res= convFactoryAPSingAP( gcd( F, G ),r ); |
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112 | prune (a); |
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113 | if (!b1) Off(SW_USE_QGCD); |
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114 | if ( rField_is_Zp_a(r)) p_Norm(res,r); // leading coef. 1 |
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115 | } |
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116 | else |
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117 | { |
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118 | convSingTrP(f,r); |
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119 | convSingTrP(g,r); |
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120 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
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121 | res= convFactoryPSingTrP( gcd( F, G ),r ); |
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122 | } |
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123 | } |
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124 | else if (r->cf->convSingNFactoryN==ndConvSingNFactoryN) |
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125 | WerrorS( feNotImplemented ); |
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126 | else |
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127 | { // handle user type coeffs: |
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128 | setCharacteristic( rChar(r) ); |
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129 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g, r ) ); |
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130 | res=convFactoryPSingP( gcd( F, G ) , r); |
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131 | } |
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132 | Off(SW_RATIONAL); |
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133 | return res; |
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134 | } |
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135 | |
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136 | poly singclap_gcd_and_divide ( poly& f, poly& g, const ring r) |
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137 | { |
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138 | poly res=NULL; |
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139 | |
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140 | if (g == NULL) |
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141 | { |
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142 | res= f; |
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143 | f=p_One (r); |
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144 | return res; |
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145 | } |
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146 | if (f==NULL) |
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147 | { |
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148 | res= g; |
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149 | g=p_One (r); |
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150 | return res; |
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151 | } |
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152 | if (pNext(g)==NULL) |
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153 | { |
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154 | poly G=p_GcdMon(g,f,r); |
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155 | if (!n_IsOne(pGetCoeff(G),r->cf) |
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156 | || (!p_IsConstant(G,r))) |
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157 | { |
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158 | f=p_Div_mm(f,G,r); |
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159 | g=p_Div_mm(g,G,r); |
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160 | } |
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161 | return G; |
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162 | } |
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163 | else if (pNext(f)==NULL) |
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164 | { |
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165 | poly G=p_GcdMon(f,g,r); |
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166 | if (!n_IsOne(pGetCoeff(G),r->cf) |
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167 | || (!p_IsConstant(G,r))) |
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168 | { |
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169 | f=p_Div_mm(f,G,r); |
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170 | g=p_Div_mm(g,G,r); |
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171 | } |
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172 | return G; |
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173 | } |
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174 | |
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175 | Off(SW_RATIONAL); |
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176 | CanonicalForm F,G,GCD; |
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177 | if (rField_is_Q(r) || (rField_is_Zp(r)) |
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178 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
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179 | { |
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180 | bool b1=isOn(SW_USE_EZGCD_P); |
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181 | setCharacteristic( rChar(r) ); |
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182 | F=convSingPFactoryP( f,r ); |
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183 | G=convSingPFactoryP( g,r ); |
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184 | GCD=gcd(F,G); |
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185 | if (!GCD.isOne()) |
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186 | { |
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187 | p_Delete(&f,r); |
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188 | p_Delete(&g,r); |
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189 | if (getCharacteristic() == 0) |
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190 | On (SW_RATIONAL); |
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191 | F /= GCD; |
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192 | G /= GCD; |
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193 | if (getCharacteristic() == 0) |
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194 | { |
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195 | CanonicalForm denF= bCommonDen (F); |
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196 | CanonicalForm denG= bCommonDen (G); |
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197 | G *= denG; |
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198 | F *= denF; |
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199 | Off (SW_RATIONAL); |
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200 | CanonicalForm gcddenFdenG= gcd (denG, denF); |
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201 | denG /= gcddenFdenG; |
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202 | denF /= gcddenFdenG; |
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203 | On (SW_RATIONAL); |
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204 | G *= denF; |
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205 | F *= denG; |
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206 | } |
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207 | f=convFactoryPSingP( F, r); |
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208 | g=convFactoryPSingP( G, r); |
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209 | } |
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210 | res=convFactoryPSingP( GCD , r); |
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211 | if (!b1) Off (SW_USE_EZGCD_P); |
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212 | } |
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213 | // and over Q(a) / Fp(a) |
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214 | else if ( r->cf->extRing ) |
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215 | { |
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216 | if ( rField_is_Q_a(r)) setCharacteristic( 0 ); |
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217 | else setCharacteristic( rChar(r) ); |
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218 | if (r->cf->extRing->qideal!=NULL) |
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219 | { |
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220 | bool b1=isOn(SW_USE_QGCD); |
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221 | if ( rField_is_Q_a(r) ) On(SW_USE_QGCD); |
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222 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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223 | r->cf->extRing); |
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224 | Variable a=rootOf(mipo); |
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225 | F=( convSingAPFactoryAP( f,a,r ) ); |
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226 | G=( convSingAPFactoryAP( g,a,r ) ); |
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227 | GCD=gcd(F,G); |
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228 | if (!GCD.isOne()) |
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229 | { |
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230 | p_Delete(&f,r); |
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231 | p_Delete(&g,r); |
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232 | if (getCharacteristic() == 0) |
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233 | On (SW_RATIONAL); |
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234 | F /= GCD; |
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235 | G /= GCD; |
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236 | if (getCharacteristic() == 0) |
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237 | { |
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238 | CanonicalForm denF= bCommonDen (F); |
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239 | CanonicalForm denG= bCommonDen (G); |
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240 | G *= denG; |
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241 | F *= denF; |
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242 | Off (SW_RATIONAL); |
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243 | CanonicalForm gcddenFdenG= gcd (denG, denF); |
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244 | denG /= gcddenFdenG; |
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245 | denF /= gcddenFdenG; |
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246 | On (SW_RATIONAL); |
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247 | G *= denF; |
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248 | F *= denG; |
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249 | } |
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250 | f= convFactoryAPSingAP( F,r ); |
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251 | g= convFactoryAPSingAP( G,r ); |
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252 | } |
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253 | res= convFactoryAPSingAP( GCD,r ); |
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254 | prune (a); |
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255 | if (!b1) Off(SW_USE_QGCD); |
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256 | } |
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257 | else |
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258 | { |
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259 | F=( convSingTrPFactoryP( f,r ) ); |
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260 | G=( convSingTrPFactoryP( g,r ) ); |
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261 | GCD=gcd(F,G); |
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262 | if (!GCD.isOne()) |
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263 | { |
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264 | p_Delete(&f,r); |
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265 | p_Delete(&g,r); |
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266 | if (getCharacteristic() == 0) |
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267 | On (SW_RATIONAL); |
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268 | F /= GCD; |
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269 | G /= GCD; |
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270 | if (getCharacteristic() == 0) |
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271 | { |
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272 | CanonicalForm denF= bCommonDen (F); |
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273 | CanonicalForm denG= bCommonDen (G); |
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274 | G *= denG; |
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275 | F *= denF; |
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276 | Off (SW_RATIONAL); |
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277 | CanonicalForm gcddenFdenG= gcd (denG, denF); |
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278 | denG /= gcddenFdenG; |
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279 | denF /= gcddenFdenG; |
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280 | On (SW_RATIONAL); |
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281 | G *= denF; |
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282 | F *= denG; |
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283 | } |
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284 | f= convFactoryPSingTrP( F,r ); |
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285 | g= convFactoryPSingTrP( G,r ); |
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286 | } |
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287 | res= convFactoryPSingTrP( GCD,r ); |
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288 | } |
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289 | } |
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290 | else |
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291 | WerrorS( feNotImplemented ); |
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292 | Off(SW_RATIONAL); |
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293 | return res; |
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294 | } |
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295 | |
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296 | /*2 find the maximal exponent of var(i) in poly p*/ |
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297 | int pGetExp_Var(poly p, int i, const ring r) |
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298 | { |
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299 | int m=0; |
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300 | int mm; |
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301 | while (p!=NULL) |
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302 | { |
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303 | mm=p_GetExp(p,i,r); |
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304 | if (mm>m) m=mm; |
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305 | pIter(p); |
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306 | } |
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307 | return m; |
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308 | } |
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309 | |
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310 | // destroys f,g,x |
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311 | poly singclap_resultant ( poly f, poly g , poly x, const ring r) |
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312 | { |
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313 | poly res=NULL; |
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314 | int i=p_IsPurePower(x, r); |
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315 | if (i==0) |
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316 | { |
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317 | WerrorS("3rd argument must be a ring variable"); |
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318 | goto resultant_returns_res; |
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319 | } |
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320 | if ((f==NULL) || (g==NULL)) |
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321 | goto resultant_returns_res; |
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322 | // for now there is only the possibility to handle polynomials over |
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323 | // Q and Fp ... |
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324 | if (rField_is_Zp(r) || rField_is_Q(r) |
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325 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
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326 | { |
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327 | Variable X(i); |
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328 | setCharacteristic( rChar(r) ); |
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329 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
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330 | res=convFactoryPSingP( resultant( F, G, X),r ); |
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331 | Off(SW_RATIONAL); |
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332 | goto resultant_returns_res; |
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333 | } |
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334 | // and over Q(a) / Fp(a) |
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335 | else if (r->cf->extRing!=NULL) |
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336 | { |
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337 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
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338 | else setCharacteristic( rChar(r) ); |
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339 | Variable X(i+rPar(r)); |
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340 | if (r->cf->extRing->qideal!=NULL) |
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341 | { |
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342 | //Variable X(i); |
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343 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
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344 | r->cf->extRing); |
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345 | Variable a=rootOf(mipo); |
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346 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
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347 | G( convSingAPFactoryAP( g,a,r ) ); |
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348 | res= convFactoryAPSingAP( resultant( F, G, X ),r ); |
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349 | prune (a); |
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350 | } |
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351 | else |
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352 | { |
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353 | //Variable X(i+rPar(currRing)); |
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354 | number nf,ng; |
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355 | p_Cleardenom_n(f,r,nf);p_Cleardenom_n(g,r,ng); |
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356 | int ef,eg; |
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357 | ef=pGetExp_Var(f,i,r); |
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358 | eg=pGetExp_Var(g,i,r); |
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359 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
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360 | res= convFactoryPSingTrP( resultant( F, G, X ),r ); |
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361 | if ((nf!=NULL)&&(!n_IsOne(nf,r->cf))) |
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362 | { |
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363 | number n=n_Invers(nf,r->cf); |
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364 | while(eg>0) |
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365 | { |
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366 | res=__p_Mult_nn(res,n,r); |
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367 | eg--; |
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368 | } |
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369 | n_Delete(&n,r->cf); |
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370 | } |
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371 | n_Delete(&nf,r->cf); |
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372 | if ((ng!=NULL)&&(!n_IsOne(ng,r->cf))) |
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373 | { |
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374 | number n=n_Invers(ng,r->cf); |
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375 | while(ef>0) |
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376 | { |
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377 | res=__p_Mult_nn(res,n,r); |
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378 | ef--; |
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379 | } |
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380 | n_Delete(&n,r->cf); |
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381 | } |
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382 | n_Delete(&ng,r->cf); |
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383 | } |
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384 | Off(SW_RATIONAL); |
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385 | goto resultant_returns_res; |
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386 | } |
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387 | else |
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388 | WerrorS( feNotImplemented ); |
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389 | resultant_returns_res: |
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390 | p_Delete(&f,r); |
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391 | p_Delete(&g,r); |
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392 | p_Delete(&x,r); |
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393 | return res; |
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394 | } |
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395 | //poly singclap_resultant ( poly f, poly g , poly x) |
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396 | //{ |
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397 | // int i=pVar(x); |
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398 | // if (i==0) |
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399 | // { |
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400 | // WerrorS("ringvar expected"); |
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401 | // return NULL; |
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402 | // } |
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403 | // ideal I=idInit(1,1); |
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404 | // |
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405 | // // get the coeffs von f wrt. x: |
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406 | // I->m[0]=pCopy(f); |
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407 | // matrix ffi=mpCoeffs(I,i); |
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408 | // ffi->rank=1; |
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409 | // ffi->ncols=ffi->nrows; |
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410 | // ffi->nrows=1; |
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411 | // ideal fi=(ideal)ffi; |
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412 | // |
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413 | // // get the coeffs von g wrt. x: |
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414 | // I->m[0]=pCopy(g); |
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415 | // matrix ggi=mpCoeffs(I,i); |
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416 | // ggi->rank=1; |
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417 | // ggi->ncols=ggi->nrows; |
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418 | // ggi->nrows=1; |
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419 | // ideal gi=(ideal)ggi; |
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420 | // |
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421 | // // contruct the matrix: |
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422 | // int fn=IDELEMS(fi); //= deg(f,x)+1 |
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423 | // int gn=IDELEMS(gi); //= deg(g,x)+1 |
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424 | // matrix m=mpNew(fn+gn-2,fn+gn-2); |
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425 | // if(m==NULL) |
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426 | // { |
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427 | // return NULL; |
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428 | // } |
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429 | // |
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430 | // // enter the coeffs into m: |
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431 | // int j; |
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432 | // for(i=0;i<gn-1;i++) |
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433 | // { |
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434 | // for(j=0;j<fn;j++) |
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435 | // { |
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436 | // MATELEM(m,i+1,fn-j+i)=pCopy(fi->m[j]); |
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437 | // } |
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438 | // } |
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439 | // for(i=0;i<fn-1;i++) |
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440 | // { |
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441 | // for(j=0;j<gn;j++) |
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442 | // { |
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443 | // MATELEM(m,gn+i,gn-j+i)=pCopy(gi->m[j]); |
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444 | // } |
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445 | // } |
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446 | // |
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447 | // poly r=mpDet(m); |
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448 | // |
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449 | // idDelete(&fi); |
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450 | // idDelete(&gi); |
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451 | // idDelete((ideal *)&m); |
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452 | // return r; |
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453 | //} |
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454 | |
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455 | BOOLEAN singclap_extgcd ( poly f, poly g, poly &res, poly &pa, poly &pb , const ring r) |
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456 | { |
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457 | // for now there is only the possibility to handle univariate |
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458 | // polynomials over |
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459 | // Q and Fp ... |
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460 | res=NULL;pa=NULL;pb=NULL; |
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461 | On(SW_SYMMETRIC_FF); |
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462 | if ( rField_is_Q(r) || rField_is_Zp(r) |
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463 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
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464 | { |
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465 | setCharacteristic( rChar(r) ); |
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466 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r) ); |
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467 | CanonicalForm FpG=F+G; |
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468 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
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469 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
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470 | { |
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471 | Off(SW_RATIONAL); |
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472 | WerrorS("not univariate"); |
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473 | return TRUE; |
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474 | } |
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475 | CanonicalForm Fa,Gb; |
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476 | On(SW_RATIONAL); |
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477 | res=convFactoryPSingP( extgcd( F, G, Fa, Gb ),r ); |
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478 | pa=convFactoryPSingP(Fa,r); |
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479 | pb=convFactoryPSingP(Gb,r); |
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480 | Off(SW_RATIONAL); |
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481 | } |
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482 | // and over Q(a) / Fp(a) |
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483 | else if ( r->cf->extRing!=NULL ) |
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484 | { |
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485 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
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486 | else setCharacteristic( rChar(r) ); |
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487 | CanonicalForm Fa,Gb; |
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488 | if (r->cf->extRing->qideal!=NULL) |
---|
489 | { |
---|
490 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
491 | r->cf->extRing); |
---|
492 | Variable a=rootOf(mipo); |
---|
493 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
494 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
495 | CanonicalForm FpG=F+G; |
---|
496 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
---|
497 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
---|
498 | { |
---|
499 | WerrorS("not univariate"); |
---|
500 | return TRUE; |
---|
501 | } |
---|
502 | res= convFactoryAPSingAP( extgcd( F, G, Fa, Gb ),r ); |
---|
503 | pa=convFactoryAPSingAP(Fa,r); |
---|
504 | pb=convFactoryAPSingAP(Gb,r); |
---|
505 | prune (a); |
---|
506 | } |
---|
507 | else |
---|
508 | { |
---|
509 | CanonicalForm F( convSingTrPFactoryP( f, r ) ), G( convSingTrPFactoryP( g, r ) ); |
---|
510 | CanonicalForm FpG=F+G; |
---|
511 | if (!(FpG.isUnivariate()|| FpG.inCoeffDomain())) |
---|
512 | //if (!F.isUnivariate() || !G.isUnivariate() || F.mvar()!=G.mvar()) |
---|
513 | { |
---|
514 | Off(SW_RATIONAL); |
---|
515 | WerrorS("not univariate"); |
---|
516 | return TRUE; |
---|
517 | } |
---|
518 | res= convFactoryPSingTrP( extgcd( F, G, Fa, Gb ), r ); |
---|
519 | pa=convFactoryPSingTrP(Fa, r); |
---|
520 | pb=convFactoryPSingTrP(Gb, r); |
---|
521 | } |
---|
522 | Off(SW_RATIONAL); |
---|
523 | } |
---|
524 | else |
---|
525 | { |
---|
526 | WerrorS( feNotImplemented ); |
---|
527 | return TRUE; |
---|
528 | } |
---|
529 | #ifndef SING_NDEBUG |
---|
530 | // checking the result of extgcd: |
---|
531 | poly dummy; |
---|
532 | dummy=p_Sub(p_Add_q(pp_Mult_qq(f,pa,r),pp_Mult_qq(g,pb,r),r),p_Copy(res,r),r); |
---|
533 | if (dummy!=NULL) |
---|
534 | { |
---|
535 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
---|
536 | PrintS("extgcd( ");p_Write(f,r);p_Write0(g,r);PrintS(" )\n"); |
---|
537 | p_Delete(&dummy,r); |
---|
538 | } |
---|
539 | #endif |
---|
540 | return FALSE; |
---|
541 | } |
---|
542 | |
---|
543 | poly singclap_pmult ( poly f, poly g, const ring r ) |
---|
544 | { |
---|
545 | poly res=NULL; |
---|
546 | On(SW_RATIONAL); |
---|
547 | if (rField_is_Zp(r) || rField_is_Q(r) || rField_is_Z(r) |
---|
548 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
549 | { |
---|
550 | if (rField_is_Z(r)) Off(SW_RATIONAL); |
---|
551 | setCharacteristic( rChar(r) ); |
---|
552 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
553 | res = convFactoryPSingP( F * G,r ); |
---|
554 | } |
---|
555 | else if (r->cf->extRing!=NULL) |
---|
556 | { |
---|
557 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
558 | else setCharacteristic( rChar(r) ); |
---|
559 | if (r->cf->extRing->qideal!=NULL) |
---|
560 | { |
---|
561 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
562 | r->cf->extRing); |
---|
563 | Variable a=rootOf(mipo); |
---|
564 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
565 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
566 | res= convFactoryAPSingAP( F * G, r ); |
---|
567 | prune (a); |
---|
568 | } |
---|
569 | else |
---|
570 | { |
---|
571 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
572 | res= convFactoryPSingTrP( F * G,r ); |
---|
573 | } |
---|
574 | } |
---|
575 | #if 0 // not yet working |
---|
576 | else if (rField_is_GF()) |
---|
577 | { |
---|
578 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
579 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
580 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
581 | res = convFactoryGFSingGF( F * G ); |
---|
582 | } |
---|
583 | #endif |
---|
584 | else |
---|
585 | WerrorS( feNotImplemented ); |
---|
586 | Off(SW_RATIONAL); |
---|
587 | return res; |
---|
588 | } |
---|
589 | |
---|
590 | poly singclap_pdivide ( poly f, poly g, const ring r ) |
---|
591 | { |
---|
592 | poly res=NULL; |
---|
593 | |
---|
594 | #ifdef HAVE_FLINT |
---|
595 | #if __FLINT_RELEASE >= 20503 |
---|
596 | /* |
---|
597 | If the division is not exact, control will pass to factory where the |
---|
598 | polynomials can be divided using the ordering that factory chooses. |
---|
599 | */ |
---|
600 | if (rField_is_Zp(r)) |
---|
601 | { |
---|
602 | nmod_mpoly_ctx_t ctx; |
---|
603 | if (!convSingRFlintR(ctx,r)) |
---|
604 | { |
---|
605 | res = Flint_Divide_MP(f,0,g,0,ctx,r); |
---|
606 | if (res != NULL) |
---|
607 | return res; |
---|
608 | } |
---|
609 | } |
---|
610 | else |
---|
611 | if (rField_is_Q(r)) |
---|
612 | { |
---|
613 | fmpq_mpoly_ctx_t ctx; |
---|
614 | if (!convSingRFlintR(ctx,r)) |
---|
615 | { |
---|
616 | res = Flint_Divide_MP(f,0,g,0,ctx,r); |
---|
617 | if (res != NULL) |
---|
618 | return res; |
---|
619 | } |
---|
620 | } |
---|
621 | #endif |
---|
622 | #endif |
---|
623 | |
---|
624 | On(SW_RATIONAL); |
---|
625 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
626 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
627 | { |
---|
628 | setCharacteristic( rChar(r) ); |
---|
629 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
630 | res = convFactoryPSingP( F / G,r ); |
---|
631 | } |
---|
632 | // div is not implemented for ZZ coeffs in factory |
---|
633 | else if (r->cf->extRing!=NULL) |
---|
634 | { |
---|
635 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
636 | else setCharacteristic( rChar(r) ); |
---|
637 | if (r->cf->extRing->qideal!=NULL) |
---|
638 | { |
---|
639 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
640 | r->cf->extRing); |
---|
641 | Variable a=rootOf(mipo); |
---|
642 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
643 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
644 | res= convFactoryAPSingAP( F / G, r ); |
---|
645 | prune (a); |
---|
646 | } |
---|
647 | else |
---|
648 | { |
---|
649 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
650 | res= convFactoryPSingTrP( F / G,r ); |
---|
651 | } |
---|
652 | } |
---|
653 | #if 0 // not yet working |
---|
654 | else if (rField_is_GF()) |
---|
655 | { |
---|
656 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
657 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
658 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
659 | res = convFactoryGFSingGF( F / G ); |
---|
660 | } |
---|
661 | #endif |
---|
662 | else |
---|
663 | WerrorS( feNotImplemented ); |
---|
664 | Off(SW_RATIONAL); |
---|
665 | return res; |
---|
666 | } |
---|
667 | |
---|
668 | poly singclap_pmod ( poly f, poly g, const ring r ) |
---|
669 | { |
---|
670 | poly res=NULL; |
---|
671 | On(SW_RATIONAL); |
---|
672 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
673 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
674 | { |
---|
675 | setCharacteristic( rChar(r) ); |
---|
676 | CanonicalForm F( convSingPFactoryP( f,r ) ), G( convSingPFactoryP( g,r ) ); |
---|
677 | CanonicalForm Q,R; |
---|
678 | divrem(F,G,Q,R); |
---|
679 | res = convFactoryPSingP(R,r); |
---|
680 | //res = convFactoryPSingP( F-(F/G)*G,r ); |
---|
681 | } |
---|
682 | // mod is not implemented for ZZ coeffs in factory |
---|
683 | else if (r->cf->extRing!=NULL) |
---|
684 | { |
---|
685 | if (rField_is_Q_a(r)) setCharacteristic( 0 ); |
---|
686 | else setCharacteristic( rChar(r) ); |
---|
687 | if (r->cf->extRing->qideal!=NULL) |
---|
688 | { |
---|
689 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
690 | r->cf->extRing); |
---|
691 | Variable a=rootOf(mipo); |
---|
692 | CanonicalForm F( convSingAPFactoryAP( f,a,r ) ), |
---|
693 | G( convSingAPFactoryAP( g,a,r ) ); |
---|
694 | CanonicalForm Q,R; |
---|
695 | divrem(F,G,Q,R); |
---|
696 | res = convFactoryAPSingAP(R,r); |
---|
697 | //res= convFactoryAPSingAP( F-(F/G)*G, r ); |
---|
698 | prune (a); |
---|
699 | } |
---|
700 | else |
---|
701 | { |
---|
702 | CanonicalForm F( convSingTrPFactoryP( f,r ) ), G( convSingTrPFactoryP( g,r ) ); |
---|
703 | CanonicalForm Q,R; |
---|
704 | divrem(F,G,Q,R); |
---|
705 | res = convFactoryPSingTrP(R,r); |
---|
706 | //res= convFactoryPSingTrP( F-(F/G)*G,r ); |
---|
707 | } |
---|
708 | } |
---|
709 | #if 0 // not yet working |
---|
710 | else if (rField_is_GF()) |
---|
711 | { |
---|
712 | //Print("GF(%d^%d)\n",nfCharP,nfMinPoly[0]); |
---|
713 | setCharacteristic( nfCharP,nfMinPoly[0], currRing->parameter[0][0] ); |
---|
714 | CanonicalForm F( convSingGFFactoryGF( f ) ), G( convSingGFFactoryGF( g ) ); |
---|
715 | res = convFactoryGFSingGF( F / G ); |
---|
716 | } |
---|
717 | #endif |
---|
718 | else |
---|
719 | WerrorS( feNotImplemented ); |
---|
720 | Off(SW_RATIONAL); |
---|
721 | return res; |
---|
722 | } |
---|
723 | |
---|
724 | #if 0 |
---|
725 | // unused |
---|
726 | void singclap_divide_content ( poly f, const ring r ) |
---|
727 | { |
---|
728 | if ( f==NULL ) |
---|
729 | { |
---|
730 | return; |
---|
731 | } |
---|
732 | else if ( pNext( f ) == NULL ) |
---|
733 | { |
---|
734 | p_SetCoeff( f, n_Init( 1, r->cf ), r ); |
---|
735 | return; |
---|
736 | } |
---|
737 | else |
---|
738 | { |
---|
739 | if ( rField_is_Q_a(r) ) |
---|
740 | setCharacteristic( 0 ); |
---|
741 | else if ( rField_is_Zp_a(r) ) |
---|
742 | setCharacteristic( -rChar(r) ); |
---|
743 | else |
---|
744 | return; /* not implemented*/ |
---|
745 | |
---|
746 | CFList L; |
---|
747 | CanonicalForm g, h; |
---|
748 | poly p = pNext(f); |
---|
749 | |
---|
750 | // first attemp: find 2 smallest g: |
---|
751 | |
---|
752 | number g1=pGetCoeff(f); |
---|
753 | number g2=pGetCoeff(p); // p==pNext(f); |
---|
754 | pIter(p); |
---|
755 | int sz1=n_Size(g1, r->cf); |
---|
756 | int sz2=n_Size(g2, r->cf); |
---|
757 | if (sz1>sz2) |
---|
758 | { |
---|
759 | number gg=g1; |
---|
760 | g1=g2; g2=gg; |
---|
761 | int sz=sz1; |
---|
762 | sz1=sz2; sz2=sz; |
---|
763 | } |
---|
764 | while (p!=NULL) |
---|
765 | { |
---|
766 | int n_sz=n_Size(pGetCoeff(p),r->cf); |
---|
767 | if (n_sz<sz1) |
---|
768 | { |
---|
769 | sz2=sz1; |
---|
770 | g2=g1; |
---|
771 | g1=pGetCoeff(p); |
---|
772 | sz1=n_sz; |
---|
773 | if (sz1<=3) break; |
---|
774 | } |
---|
775 | else if(n_sz<sz2) |
---|
776 | { |
---|
777 | sz2=n_sz; |
---|
778 | g2=pGetCoeff(p); |
---|
779 | sz2=n_sz; |
---|
780 | } |
---|
781 | pIter(p); |
---|
782 | } |
---|
783 | g = convSingPFactoryP( NUM(((fraction)g1)), r->cf->extRing ); |
---|
784 | g = gcd( g, convSingPFactoryP( NUM(((fraction)g2)) , r->cf->extRing)); |
---|
785 | |
---|
786 | // second run: gcd's |
---|
787 | |
---|
788 | p = f; |
---|
789 | while ( (p != NULL) && (g != 1) && ( g != 0)) |
---|
790 | { |
---|
791 | h = convSingPFactoryP( NUM(((fraction)pGetCoeff(p))), r->cf->extRing ); |
---|
792 | pIter( p ); |
---|
793 | |
---|
794 | g = gcd( g, h ); |
---|
795 | |
---|
796 | L.append( h ); |
---|
797 | } |
---|
798 | if (( g == 1 ) || (g == 0)) |
---|
799 | { |
---|
800 | // pTest(f); |
---|
801 | return; |
---|
802 | } |
---|
803 | else |
---|
804 | { |
---|
805 | CFListIterator i; |
---|
806 | for ( i = L, p = f; i.hasItem(); i++, p=pNext(p) ) |
---|
807 | { |
---|
808 | fraction c=(fraction)pGetCoeff(p); |
---|
809 | p_Delete(&(NUM(c)),r->cf->extRing); // 2nd arg used to be nacRing |
---|
810 | NUM(c)=convFactoryPSingP( i.getItem() / g, r->cf->extRing ); |
---|
811 | //nTest((number)c); |
---|
812 | //#ifdef LDEBUG |
---|
813 | //number cn=(number)c; |
---|
814 | //StringSetS(""); nWrite(nt); StringAppend(" ==> "); |
---|
815 | //nWrite(cn);PrintS(StringEndS("\n")); // NOTE/TODO: use StringAppendS("\n"); omFree(s); |
---|
816 | //#endif |
---|
817 | } |
---|
818 | } |
---|
819 | // pTest(f); |
---|
820 | } |
---|
821 | } |
---|
822 | #endif |
---|
823 | |
---|
824 | BOOLEAN count_Factors(ideal I, intvec *v,int j, poly &f, poly fac, const ring r) |
---|
825 | { |
---|
826 | p_Test(f,r); |
---|
827 | p_Test(fac,r); |
---|
828 | int e=0; |
---|
829 | if (!p_IsConstant(fac,r)) |
---|
830 | { |
---|
831 | #ifdef FACTORIZE2_DEBUG |
---|
832 | printf("start count_Factors(%d), Fdeg=%d, factor deg=%d\n",j,p_Totaldegree(f,r),p_Totaldegree(fac,r)); |
---|
833 | p_wrp(fac,r);PrintLn(); |
---|
834 | #endif |
---|
835 | On(SW_RATIONAL); |
---|
836 | CanonicalForm F, FAC,Q,R; |
---|
837 | Variable a; |
---|
838 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
839 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
840 | { |
---|
841 | F=convSingPFactoryP( f,r ); |
---|
842 | FAC=convSingPFactoryP( fac,r ); |
---|
843 | } |
---|
844 | else if (r->cf->extRing!=NULL) |
---|
845 | { |
---|
846 | if (r->cf->extRing->qideal!=NULL) |
---|
847 | { |
---|
848 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
849 | r->cf->extRing); |
---|
850 | a=rootOf(mipo); |
---|
851 | F=convSingAPFactoryAP( f,a,r ); |
---|
852 | FAC=convSingAPFactoryAP( fac,a,r ); |
---|
853 | } |
---|
854 | else |
---|
855 | { |
---|
856 | F=convSingTrPFactoryP( f,r ); |
---|
857 | FAC=convSingTrPFactoryP( fac,r ); |
---|
858 | } |
---|
859 | } |
---|
860 | else |
---|
861 | WerrorS( feNotImplemented ); |
---|
862 | |
---|
863 | poly q; |
---|
864 | loop |
---|
865 | { |
---|
866 | Q=F; |
---|
867 | Q/=FAC; |
---|
868 | R=Q; |
---|
869 | R*=FAC; |
---|
870 | R-=F; |
---|
871 | if (R.isZero()) |
---|
872 | { |
---|
873 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
874 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
875 | { |
---|
876 | q = convFactoryPSingP( Q,r ); |
---|
877 | } |
---|
878 | else if (r->cf->extRing!=NULL) |
---|
879 | { |
---|
880 | if (r->cf->extRing->qideal!=NULL) |
---|
881 | { |
---|
882 | q= convFactoryAPSingAP( Q,r ); |
---|
883 | } |
---|
884 | else |
---|
885 | { |
---|
886 | q= convFactoryPSingTrP( Q,r ); |
---|
887 | } |
---|
888 | } |
---|
889 | e++; p_Delete(&f,r); f=q; q=NULL; F=Q; |
---|
890 | } |
---|
891 | else |
---|
892 | { |
---|
893 | break; |
---|
894 | } |
---|
895 | } |
---|
896 | if (r->cf->extRing!=NULL) |
---|
897 | if (r->cf->extRing->qideal!=NULL) |
---|
898 | prune (a); |
---|
899 | if (e==0) |
---|
900 | { |
---|
901 | Off(SW_RATIONAL); |
---|
902 | return FALSE; |
---|
903 | } |
---|
904 | } |
---|
905 | else e=1; |
---|
906 | I->m[j]=fac; |
---|
907 | if (v!=NULL) (*v)[j]=e; |
---|
908 | Off(SW_RATIONAL); |
---|
909 | return TRUE; |
---|
910 | } |
---|
911 | |
---|
912 | VAR int singclap_factorize_retry; |
---|
913 | |
---|
914 | ideal singclap_factorize ( poly f, intvec ** v , int with_exps, const ring r) |
---|
915 | /* destroys f, sets *v */ |
---|
916 | { |
---|
917 | p_Test(f,r); |
---|
918 | #ifdef FACTORIZE2_DEBUG |
---|
919 | printf("singclap_factorize, degree %ld\n",p_Totaldegree(f,r)); |
---|
920 | #endif |
---|
921 | // with_exps: 3,1 return only true factors, no exponents |
---|
922 | // 2 return true factors and exponents |
---|
923 | // 0 return coeff, factors and exponents |
---|
924 | BOOLEAN save_errorreported=errorreported; |
---|
925 | |
---|
926 | ideal res=NULL; |
---|
927 | |
---|
928 | // handle factorize(0) ========================================= |
---|
929 | if (f==NULL) |
---|
930 | { |
---|
931 | res=idInit(1,1); |
---|
932 | if (with_exps!=1) |
---|
933 | { |
---|
934 | (*v)=new intvec(1); |
---|
935 | (**v)[0]=1; |
---|
936 | } |
---|
937 | return res; |
---|
938 | } |
---|
939 | // handle factorize(mon) ========================================= |
---|
940 | if (pNext(f)==NULL) |
---|
941 | { |
---|
942 | int i=0; |
---|
943 | int n=0; |
---|
944 | int e; |
---|
945 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
946 | if (with_exps==0) n++; // with coeff |
---|
947 | res=idInit(si_max(n,1),1); |
---|
948 | switch(with_exps) |
---|
949 | { |
---|
950 | case 0: // with coef & exp. |
---|
951 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
952 | // no break |
---|
953 | case 2: // with exp. |
---|
954 | (*v)=new intvec(si_max(1,n)); |
---|
955 | (**v)[0]=1; |
---|
956 | // no break |
---|
957 | case 1: ; |
---|
958 | #ifdef TEST |
---|
959 | default: ; |
---|
960 | #endif |
---|
961 | } |
---|
962 | if (n==0) |
---|
963 | { |
---|
964 | if (res->m[0]==NULL) res->m[0]=p_One(r); |
---|
965 | // (**v)[0]=1; is already done |
---|
966 | } |
---|
967 | else |
---|
968 | { |
---|
969 | for(i=rVar(r);i>0;i--) |
---|
970 | { |
---|
971 | e=p_GetExp(f,i,r); |
---|
972 | if(e!=0) |
---|
973 | { |
---|
974 | n--; |
---|
975 | poly p=p_One(r); |
---|
976 | p_SetExp(p,i,1,r); |
---|
977 | p_Setm(p,r); |
---|
978 | res->m[n]=p; |
---|
979 | if (with_exps!=1) (**v)[n]=e; |
---|
980 | } |
---|
981 | } |
---|
982 | } |
---|
983 | p_Delete(&f,r); |
---|
984 | return res; |
---|
985 | } |
---|
986 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
987 | // use factory/libfac in general ============================== |
---|
988 | Variable dummy(-1); prune(dummy); // remove all (tmp.) extensions |
---|
989 | Off(SW_RATIONAL); |
---|
990 | On(SW_SYMMETRIC_FF); |
---|
991 | CFFList L; |
---|
992 | number N=NULL; |
---|
993 | number NN=NULL; |
---|
994 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
995 | |
---|
996 | Variable a; |
---|
997 | if (r->cf->convSingNFactoryN!=ndConvSingNFactoryN) |
---|
998 | { |
---|
999 | if (rField_is_Q(r) || rField_is_Q_a(r) || rField_is_Z(r)) /* Q, Q(a), Z */ |
---|
1000 | { |
---|
1001 | //if (f!=NULL) // already tested at start of routine |
---|
1002 | { |
---|
1003 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
1004 | if (with_exps==0) |
---|
1005 | N=n_Copy(n0,r->cf); |
---|
1006 | if (rField_is_Z(r)) p_Content(f, r); |
---|
1007 | else p_Cleardenom(f, r); |
---|
1008 | //after here f should not have a denominator!! and no content |
---|
1009 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
1010 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1011 | n_Delete(&n0,r->cf); |
---|
1012 | if (with_exps==0) |
---|
1013 | { |
---|
1014 | n_Delete(&N,r->cf); |
---|
1015 | N=n_Copy(NN,r->cf); |
---|
1016 | } |
---|
1017 | } |
---|
1018 | } |
---|
1019 | else if (rField_is_Zp_a(r)) |
---|
1020 | { |
---|
1021 | //if (f!=NULL) // already tested at start of routine |
---|
1022 | if (singclap_factorize_retry==0) |
---|
1023 | { |
---|
1024 | number n0=n_Copy(pGetCoeff(f),r->cf); |
---|
1025 | if (with_exps==0) |
---|
1026 | N=n_Copy(n0,r->cf); |
---|
1027 | p_Norm(f,r); |
---|
1028 | p_Cleardenom(f, r); |
---|
1029 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1030 | n_Delete(&n0,r->cf); |
---|
1031 | if (with_exps==0) |
---|
1032 | { |
---|
1033 | n_Delete(&N,r->cf); |
---|
1034 | N=n_Copy(NN,r->cf); |
---|
1035 | } |
---|
1036 | } |
---|
1037 | } |
---|
1038 | if (rField_is_Q(r) || rField_is_Zp(r) || rField_is_Z(r) || rField_is_Zn(r)) |
---|
1039 | { |
---|
1040 | setCharacteristic( rChar(r) ); |
---|
1041 | if (errorreported) goto notImpl; // char too large |
---|
1042 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
1043 | L = factorize( F ); |
---|
1044 | } |
---|
1045 | // and over Q(a) / Fp(a) |
---|
1046 | else if (r->cf->extRing!=NULL) |
---|
1047 | { |
---|
1048 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
1049 | else setCharacteristic( rChar(r) ); |
---|
1050 | if (errorreported) goto notImpl; // char too large |
---|
1051 | if (r->cf->extRing->qideal!=NULL) /*algebraic extension */ |
---|
1052 | { |
---|
1053 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
1054 | r->cf->extRing); |
---|
1055 | a=rootOf(mipo); |
---|
1056 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
1057 | L = factorize( F, a ); |
---|
1058 | prune(a); |
---|
1059 | } |
---|
1060 | else /* rational functions */ |
---|
1061 | { |
---|
1062 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
1063 | L = factorize( F ); |
---|
1064 | } |
---|
1065 | } |
---|
1066 | else |
---|
1067 | { |
---|
1068 | goto notImpl; |
---|
1069 | } |
---|
1070 | } |
---|
1071 | else |
---|
1072 | { |
---|
1073 | goto notImpl; |
---|
1074 | } |
---|
1075 | if (errorreported) |
---|
1076 | { |
---|
1077 | errorreported=FALSE; |
---|
1078 | } |
---|
1079 | { |
---|
1080 | poly ff=p_Copy(f,r); // a copy for the retry stuff |
---|
1081 | // the first factor should be a constant |
---|
1082 | if ( ! L.getFirst().factor().inCoeffDomain() ) |
---|
1083 | L.insert(CFFactor(1,1)); |
---|
1084 | // convert into ideal |
---|
1085 | int n = L.length(); |
---|
1086 | if (n==0) n=1; |
---|
1087 | CFFListIterator J=L; |
---|
1088 | int j=0; |
---|
1089 | if (with_exps!=1) |
---|
1090 | { |
---|
1091 | if ((with_exps==2)&&(n>1)) |
---|
1092 | { |
---|
1093 | n--; |
---|
1094 | J++; |
---|
1095 | } |
---|
1096 | *v = new intvec( n ); |
---|
1097 | } |
---|
1098 | res = idInit( n ,1); |
---|
1099 | for ( ; J.hasItem(); J++, j++ ) |
---|
1100 | { |
---|
1101 | if (with_exps!=1) (**v)[j] = J.getItem().exp(); |
---|
1102 | if (rField_is_Zp(r) || rField_is_Q(r)|| rField_is_Z(r) |
---|
1103 | || rField_is_Zn(r)) /* Q, Fp, Z */ |
---|
1104 | { |
---|
1105 | //count_Factors(res,*v,f, j, convFactoryPSingP( J.getItem().factor() ); |
---|
1106 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
1107 | } |
---|
1108 | #if 0 |
---|
1109 | else if (rField_is_GF()) |
---|
1110 | res->m[j] = convFactoryGFSingGF( J.getItem().factor() ); |
---|
1111 | #endif |
---|
1112 | else if (r->cf->extRing!=NULL) /* Q(a), Fp(a) */ |
---|
1113 | { |
---|
1114 | #ifndef SING_NDEBUG |
---|
1115 | intvec *w=NULL; |
---|
1116 | if (v!=NULL) w=*v; |
---|
1117 | #endif |
---|
1118 | if (r->cf->extRing->qideal==NULL) |
---|
1119 | { |
---|
1120 | #ifdef SING_NDEBUG |
---|
1121 | res->m[j]= convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
1122 | #else |
---|
1123 | if(!count_Factors(res,w,j,ff,convFactoryPSingTrP( J.getItem().factor(),r ),r)) |
---|
1124 | { |
---|
1125 | if (w!=NULL) |
---|
1126 | (*w)[j]=1; |
---|
1127 | res->m[j]=p_One(r); |
---|
1128 | } |
---|
1129 | #endif |
---|
1130 | } |
---|
1131 | else |
---|
1132 | { |
---|
1133 | #ifdef SING_NDEBUG |
---|
1134 | res->m[j]= convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
1135 | #else |
---|
1136 | if (!count_Factors(res,w,j,ff,convFactoryAPSingAP( J.getItem().factor(),r ),r)) |
---|
1137 | { |
---|
1138 | if (w!=NULL) |
---|
1139 | (*w)[j]=1; |
---|
1140 | res->m[j]=p_One(r); |
---|
1141 | } |
---|
1142 | #endif |
---|
1143 | } |
---|
1144 | } |
---|
1145 | } |
---|
1146 | if (r->cf->extRing!=NULL) |
---|
1147 | if (r->cf->extRing->qideal!=NULL) |
---|
1148 | prune (a); |
---|
1149 | #ifndef SING_NDEBUG |
---|
1150 | if ((r->cf->extRing!=NULL) && (!p_IsConstant(ff,r))) |
---|
1151 | { |
---|
1152 | singclap_factorize_retry++; |
---|
1153 | if (singclap_factorize_retry<3) |
---|
1154 | { |
---|
1155 | int jj; |
---|
1156 | #ifdef FACTORIZE2_DEBUG |
---|
1157 | printf("factorize_retry\n"); |
---|
1158 | #endif |
---|
1159 | intvec *ww=NULL; |
---|
1160 | id_Test(res,r); |
---|
1161 | ideal h=singclap_factorize ( ff, &ww , with_exps, r ); |
---|
1162 | id_Test(h,r); |
---|
1163 | int l=(*v)->length(); |
---|
1164 | (*v)->resize(l+ww->length()); |
---|
1165 | for(jj=0;jj<ww->length();jj++) |
---|
1166 | (**v)[jj+l]=(*ww)[jj]; |
---|
1167 | delete ww; |
---|
1168 | ideal hh=idInit(IDELEMS(res)+IDELEMS(h),1); |
---|
1169 | for(jj=IDELEMS(res)-1;jj>=0;jj--) |
---|
1170 | { |
---|
1171 | hh->m[jj]=res->m[jj]; |
---|
1172 | res->m[jj]=NULL; |
---|
1173 | } |
---|
1174 | for(jj=IDELEMS(h)-1;jj>=0;jj--) |
---|
1175 | { |
---|
1176 | hh->m[jj+IDELEMS(res)]=h->m[jj]; |
---|
1177 | h->m[jj]=NULL; |
---|
1178 | } |
---|
1179 | id_Delete(&res,r); |
---|
1180 | id_Delete(&h,r); |
---|
1181 | res=hh; |
---|
1182 | id_Test(res,r); |
---|
1183 | ff=NULL; |
---|
1184 | } |
---|
1185 | else |
---|
1186 | { |
---|
1187 | WarnS("problem with factorize"); |
---|
1188 | #if 0 |
---|
1189 | pWrite(ff); |
---|
1190 | idShow(res); |
---|
1191 | #endif |
---|
1192 | id_Delete(&res,r); |
---|
1193 | res=idInit(2,1); |
---|
1194 | res->m[0]=p_One(r); |
---|
1195 | res->m[1]=ff; ff=NULL; |
---|
1196 | } |
---|
1197 | } |
---|
1198 | #endif |
---|
1199 | p_Delete(&ff,r); |
---|
1200 | if (N!=NULL) |
---|
1201 | { |
---|
1202 | __p_Mult_nn(res->m[0],N,r); |
---|
1203 | n_Delete(&N,r->cf); |
---|
1204 | N=NULL; |
---|
1205 | } |
---|
1206 | // delete constants |
---|
1207 | if (res!=NULL) |
---|
1208 | { |
---|
1209 | int i=IDELEMS(res)-1; |
---|
1210 | int j=0; |
---|
1211 | for(;i>=0;i--) |
---|
1212 | { |
---|
1213 | if ((res->m[i]!=NULL) |
---|
1214 | && (pNext(res->m[i])==NULL) |
---|
1215 | && (p_IsConstant(res->m[i],r))) |
---|
1216 | { |
---|
1217 | if (with_exps!=0) |
---|
1218 | { |
---|
1219 | p_Delete(&(res->m[i]),r); |
---|
1220 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1221 | (**v)[i]=0; |
---|
1222 | j++; |
---|
1223 | } |
---|
1224 | else if (i!=0) |
---|
1225 | { |
---|
1226 | while ((v!=NULL) && ((*v)!=NULL) && ((**v)[i]>1)) |
---|
1227 | { |
---|
1228 | res->m[0]=p_Mult_q(res->m[0],p_Copy(res->m[i],r),r); |
---|
1229 | (**v)[i]--; |
---|
1230 | } |
---|
1231 | res->m[0]=p_Mult_q(res->m[0],res->m[i],r); |
---|
1232 | res->m[i]=NULL; |
---|
1233 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1234 | (**v)[i]=1; |
---|
1235 | j++; |
---|
1236 | } |
---|
1237 | } |
---|
1238 | } |
---|
1239 | if (j>0) |
---|
1240 | { |
---|
1241 | idSkipZeroes(res); |
---|
1242 | if ((v!=NULL) && ((*v)!=NULL)) |
---|
1243 | { |
---|
1244 | intvec *w=*v; |
---|
1245 | int len=IDELEMS(res); |
---|
1246 | *v = new intvec( len ); |
---|
1247 | for (i=0,j=0;i<si_min(w->length(),len);i++) |
---|
1248 | { |
---|
1249 | if((*w)[i]!=0) |
---|
1250 | { |
---|
1251 | (**v)[j]=(*w)[i]; j++; |
---|
1252 | } |
---|
1253 | } |
---|
1254 | delete w; |
---|
1255 | } |
---|
1256 | } |
---|
1257 | if (res->m[0]==NULL) |
---|
1258 | { |
---|
1259 | res->m[0]=p_One(r); |
---|
1260 | } |
---|
1261 | } |
---|
1262 | } |
---|
1263 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
1264 | { |
---|
1265 | int i=IDELEMS(res)-1; |
---|
1266 | int stop=1; |
---|
1267 | if (with_exps!=0) stop=0; |
---|
1268 | for(;i>=stop;i--) |
---|
1269 | { |
---|
1270 | p_Norm(res->m[i],r); |
---|
1271 | } |
---|
1272 | if (with_exps==0) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
1273 | else n_Delete(&old_lead_coeff,r->cf); |
---|
1274 | } |
---|
1275 | else |
---|
1276 | n_Delete(&old_lead_coeff,r->cf); |
---|
1277 | errorreported=save_errorreported; |
---|
1278 | notImpl: |
---|
1279 | prune(a); |
---|
1280 | if (res==NULL) |
---|
1281 | WerrorS( feNotImplemented ); |
---|
1282 | if (NN!=NULL) |
---|
1283 | { |
---|
1284 | n_Delete(&NN,r->cf); |
---|
1285 | } |
---|
1286 | if (N!=NULL) |
---|
1287 | { |
---|
1288 | n_Delete(&N,r->cf); |
---|
1289 | } |
---|
1290 | if (f!=NULL) p_Delete(&f,r); |
---|
1291 | //PrintS("......S\n"); |
---|
1292 | return res; |
---|
1293 | } |
---|
1294 | |
---|
1295 | ideal singclap_sqrfree ( poly f, intvec ** v , int with_exps, const ring r) |
---|
1296 | { |
---|
1297 | p_Test(f,r); |
---|
1298 | #ifdef FACTORIZE2_DEBUG |
---|
1299 | printf("singclap_sqrfree, degree %d\n",pTotaldegree(f)); |
---|
1300 | #endif |
---|
1301 | // with_exps: 3,1 return only true factors, no exponents |
---|
1302 | // 2 return true factors and exponents |
---|
1303 | // 0 return coeff, factors and exponents |
---|
1304 | BOOLEAN save_errorreported=errorreported; |
---|
1305 | |
---|
1306 | ideal res=NULL; |
---|
1307 | |
---|
1308 | // handle factorize(0) ========================================= |
---|
1309 | if (f==NULL) |
---|
1310 | { |
---|
1311 | res=idInit(1,1); |
---|
1312 | if (with_exps!=1 && with_exps!=3) |
---|
1313 | { |
---|
1314 | (*v)=new intvec(1); |
---|
1315 | (**v)[0]=1; |
---|
1316 | } |
---|
1317 | return res; |
---|
1318 | } |
---|
1319 | // handle factorize(mon) ========================================= |
---|
1320 | if (pNext(f)==NULL) |
---|
1321 | { |
---|
1322 | int i=0; |
---|
1323 | int n=0; |
---|
1324 | int e; |
---|
1325 | for(i=rVar(r);i>0;i--) if(p_GetExp(f,i,r)!=0) n++; |
---|
1326 | if (with_exps==0 || with_exps==3) n++; // with coeff |
---|
1327 | res=idInit(si_max(n,1),1); |
---|
1328 | if(with_exps!=1) |
---|
1329 | { |
---|
1330 | (*v)=new intvec(si_max(1,n)); |
---|
1331 | (**v)[0]=1; |
---|
1332 | } |
---|
1333 | res->m[0]=p_NSet(n_Copy(pGetCoeff(f),r->cf),r); |
---|
1334 | if (n==0) |
---|
1335 | { |
---|
1336 | res->m[0]=p_One(r); |
---|
1337 | // (**v)[0]=1; is already done |
---|
1338 | } |
---|
1339 | else |
---|
1340 | { |
---|
1341 | for(i=rVar(r);i>0;i--) |
---|
1342 | { |
---|
1343 | e=p_GetExp(f,i,r); |
---|
1344 | if(e!=0) |
---|
1345 | { |
---|
1346 | n--; |
---|
1347 | poly p=p_One(r); |
---|
1348 | p_SetExp(p,i,1,r); |
---|
1349 | p_Setm(p,r); |
---|
1350 | res->m[n]=p; |
---|
1351 | if (with_exps!=1) (**v)[n]=e; |
---|
1352 | } |
---|
1353 | } |
---|
1354 | } |
---|
1355 | p_Delete(&f,r); |
---|
1356 | return res; |
---|
1357 | } |
---|
1358 | //PrintS("S:");pWrite(f);PrintLn(); |
---|
1359 | // use factory/libfac in general ============================== |
---|
1360 | Off(SW_RATIONAL); |
---|
1361 | On(SW_SYMMETRIC_FF); |
---|
1362 | CFFList L; |
---|
1363 | number N=NULL; |
---|
1364 | number NN=NULL; |
---|
1365 | number old_lead_coeff=n_Copy(pGetCoeff(f), r->cf); |
---|
1366 | Variable a; |
---|
1367 | |
---|
1368 | if (!rField_is_Zp(r) && !rField_is_Zp_a(r)) /* Q, Q(a) */ |
---|
1369 | { |
---|
1370 | //if (f!=NULL) // already tested at start of routine |
---|
1371 | number n0=n_Copy(old_lead_coeff,r->cf); |
---|
1372 | if (with_exps==0 || with_exps==3) |
---|
1373 | N=n_Copy(n0,r->cf); |
---|
1374 | p_Cleardenom(f, r); |
---|
1375 | //after here f should not have a denominator!! |
---|
1376 | //PrintS("S:");p_Write(f,r);PrintLn(); |
---|
1377 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1378 | n_Delete(&n0,r->cf); |
---|
1379 | if (with_exps==0 || with_exps==3) |
---|
1380 | { |
---|
1381 | n_Delete(&N,r->cf); |
---|
1382 | N=n_Copy(NN,r->cf); |
---|
1383 | } |
---|
1384 | } |
---|
1385 | else if (rField_is_Zp_a(r)) |
---|
1386 | { |
---|
1387 | //if (f!=NULL) // already tested at start of routine |
---|
1388 | if (singclap_factorize_retry==0) |
---|
1389 | { |
---|
1390 | number n0=n_Copy(old_lead_coeff,r->cf); |
---|
1391 | if (with_exps==0 || with_exps==3) |
---|
1392 | N=n_Copy(n0,r->cf); |
---|
1393 | p_Norm(f,r); |
---|
1394 | p_Cleardenom(f, r); |
---|
1395 | NN=n_Div(n0,pGetCoeff(f),r->cf); |
---|
1396 | n_Delete(&n0,r->cf); |
---|
1397 | if (with_exps==0 || with_exps==3) |
---|
1398 | { |
---|
1399 | n_Delete(&N,r->cf); |
---|
1400 | N=n_Copy(NN,r->cf); |
---|
1401 | } |
---|
1402 | } |
---|
1403 | } |
---|
1404 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1405 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1406 | { |
---|
1407 | setCharacteristic( rChar(r) ); |
---|
1408 | CanonicalForm F( convSingPFactoryP( f,r ) ); |
---|
1409 | L = sqrFree( F ); |
---|
1410 | } |
---|
1411 | else if (r->cf->extRing!=NULL) |
---|
1412 | { |
---|
1413 | if (rField_is_Q_a (r)) setCharacteristic (0); |
---|
1414 | else setCharacteristic( rChar(r) ); |
---|
1415 | if (r->cf->extRing->qideal!=NULL) |
---|
1416 | { |
---|
1417 | CanonicalForm mipo=convSingPFactoryP(r->cf->extRing->qideal->m[0], |
---|
1418 | r->cf->extRing); |
---|
1419 | a=rootOf(mipo); |
---|
1420 | CanonicalForm F( convSingAPFactoryAP( f, a, r ) ); |
---|
1421 | L= sqrFree (F); |
---|
1422 | } |
---|
1423 | else |
---|
1424 | { |
---|
1425 | CanonicalForm F( convSingTrPFactoryP( f,r ) ); |
---|
1426 | L = sqrFree( F ); |
---|
1427 | } |
---|
1428 | } |
---|
1429 | #if 0 |
---|
1430 | else if (rField_is_GF()) |
---|
1431 | { |
---|
1432 | int c=rChar(r); |
---|
1433 | setCharacteristic( c, primepower(c) ); |
---|
1434 | CanonicalForm F( convSingGFFactoryGF( f ) ); |
---|
1435 | if (F.isUnivariate()) |
---|
1436 | { |
---|
1437 | L = factorize( F ); |
---|
1438 | } |
---|
1439 | else |
---|
1440 | { |
---|
1441 | goto notImpl; |
---|
1442 | } |
---|
1443 | } |
---|
1444 | #endif |
---|
1445 | else |
---|
1446 | { |
---|
1447 | goto notImpl; |
---|
1448 | } |
---|
1449 | { |
---|
1450 | // convert into ideal |
---|
1451 | int n = L.length(); |
---|
1452 | if (n==0) n=1; |
---|
1453 | CFFListIterator J=L; |
---|
1454 | int j=0; |
---|
1455 | if (with_exps!=1) |
---|
1456 | { |
---|
1457 | if ((with_exps==2)&&(n>1)) |
---|
1458 | { |
---|
1459 | n--; |
---|
1460 | J++; |
---|
1461 | } |
---|
1462 | *v = new intvec( n ); |
---|
1463 | } |
---|
1464 | else if (L.getFirst().factor().inCoeffDomain() && with_exps!=3) |
---|
1465 | { |
---|
1466 | n--; |
---|
1467 | J++; |
---|
1468 | } |
---|
1469 | res = idInit( n ,1); |
---|
1470 | for ( ; J.hasItem(); J++, j++ ) |
---|
1471 | { |
---|
1472 | if (with_exps!=1 && with_exps!=3) (**v)[j] = J.getItem().exp(); |
---|
1473 | if (rField_is_Zp(r) || rField_is_Q(r) |
---|
1474 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1475 | res->m[j] = convFactoryPSingP( J.getItem().factor(),r ); |
---|
1476 | else if (r->cf->extRing!=NULL) /* Q(a), Fp(a) */ |
---|
1477 | { |
---|
1478 | if (r->cf->extRing->qideal==NULL) |
---|
1479 | res->m[j]=convFactoryPSingTrP( J.getItem().factor(),r ); |
---|
1480 | else |
---|
1481 | res->m[j]=convFactoryAPSingAP( J.getItem().factor(),r ); |
---|
1482 | } |
---|
1483 | } |
---|
1484 | if (res->m[0]==NULL) |
---|
1485 | { |
---|
1486 | res->m[0]=p_One(r); |
---|
1487 | } |
---|
1488 | if (N!=NULL) |
---|
1489 | { |
---|
1490 | __p_Mult_nn(res->m[0],N,r); |
---|
1491 | n_Delete(&N,r->cf); |
---|
1492 | N=NULL; |
---|
1493 | } |
---|
1494 | } |
---|
1495 | if (r->cf->extRing!=NULL) |
---|
1496 | if (r->cf->extRing->qideal!=NULL) |
---|
1497 | prune (a); |
---|
1498 | if (rField_is_Q_a(r) && (r->cf->extRing->qideal!=NULL)) |
---|
1499 | { |
---|
1500 | int i=IDELEMS(res)-1; |
---|
1501 | int stop=1; |
---|
1502 | if (with_exps!=0 || with_exps==3) stop=0; |
---|
1503 | for(;i>=stop;i--) |
---|
1504 | { |
---|
1505 | p_Norm(res->m[i],r); |
---|
1506 | } |
---|
1507 | if (with_exps==0 || with_exps==3) p_SetCoeff(res->m[0],old_lead_coeff,r); |
---|
1508 | else n_Delete(&old_lead_coeff,r->cf); |
---|
1509 | } |
---|
1510 | else |
---|
1511 | n_Delete(&old_lead_coeff,r->cf); |
---|
1512 | p_Delete(&f,r); |
---|
1513 | errorreported=save_errorreported; |
---|
1514 | notImpl: |
---|
1515 | if (res==NULL) |
---|
1516 | WerrorS( feNotImplemented ); |
---|
1517 | if (NN!=NULL) |
---|
1518 | { |
---|
1519 | n_Delete(&NN,r->cf); |
---|
1520 | } |
---|
1521 | if (N!=NULL) |
---|
1522 | { |
---|
1523 | n_Delete(&N,r->cf); |
---|
1524 | } |
---|
1525 | return res; |
---|
1526 | } |
---|
1527 | |
---|
1528 | matrix singclap_irrCharSeries ( ideal I, const ring r) |
---|
1529 | { |
---|
1530 | if (idIs0(I)) return mpNew(1,1); |
---|
1531 | |
---|
1532 | // for now there is only the possibility to handle polynomials over |
---|
1533 | // Q and Fp ... |
---|
1534 | matrix res=NULL; |
---|
1535 | int i; |
---|
1536 | Off(SW_RATIONAL); |
---|
1537 | On(SW_SYMMETRIC_FF); |
---|
1538 | CFList L; |
---|
1539 | ListCFList LL; |
---|
1540 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1541 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1542 | { |
---|
1543 | setCharacteristic( rChar(r) ); |
---|
1544 | for(i=0;i<IDELEMS(I);i++) |
---|
1545 | { |
---|
1546 | poly p=I->m[i]; |
---|
1547 | if (p!=NULL) |
---|
1548 | { |
---|
1549 | p=p_Copy(p,r); |
---|
1550 | p_Cleardenom(p, r); |
---|
1551 | L.append(convSingPFactoryP(p,r)); |
---|
1552 | p_Delete(&p,r); |
---|
1553 | } |
---|
1554 | } |
---|
1555 | } |
---|
1556 | // and over Q(a) / Fp(a) |
---|
1557 | else if (nCoeff_is_transExt (r->cf)) |
---|
1558 | { |
---|
1559 | setCharacteristic( rChar(r) ); |
---|
1560 | for(i=0;i<IDELEMS(I);i++) |
---|
1561 | { |
---|
1562 | poly p=I->m[i]; |
---|
1563 | if (p!=NULL) |
---|
1564 | { |
---|
1565 | p=p_Copy(p,r); |
---|
1566 | p_Cleardenom(p, r); |
---|
1567 | L.append(convSingTrPFactoryP(p,r)); |
---|
1568 | p_Delete(&p,r); |
---|
1569 | } |
---|
1570 | } |
---|
1571 | } |
---|
1572 | else |
---|
1573 | { |
---|
1574 | WerrorS( feNotImplemented ); |
---|
1575 | return res; |
---|
1576 | } |
---|
1577 | |
---|
1578 | // a very bad work-around --- FIX IT in libfac |
---|
1579 | // should be fixed as of 2001/6/27 |
---|
1580 | int tries=0; |
---|
1581 | int m,n; |
---|
1582 | ListIterator<CFList> LLi; |
---|
1583 | loop |
---|
1584 | { |
---|
1585 | LL=irrCharSeries(L); |
---|
1586 | m= LL.length(); // Anzahl Zeilen |
---|
1587 | n=0; |
---|
1588 | for ( LLi = LL; LLi.hasItem(); LLi++ ) |
---|
1589 | { |
---|
1590 | n = si_max(LLi.getItem().length(),n); |
---|
1591 | } |
---|
1592 | if ((m!=0) && (n!=0)) break; |
---|
1593 | tries++; |
---|
1594 | if (tries>=5) break; |
---|
1595 | } |
---|
1596 | if ((m==0) || (n==0)) |
---|
1597 | { |
---|
1598 | Warn("char_series returns %d x %d matrix from %d input polys (%d)", |
---|
1599 | m,n,IDELEMS(I)+1,LL.length()); |
---|
1600 | iiWriteMatrix((matrix)I,"I",2,r,0); |
---|
1601 | m=si_max(m,1); |
---|
1602 | n=si_max(n,1); |
---|
1603 | } |
---|
1604 | res=mpNew(m,n); |
---|
1605 | CFListIterator Li; |
---|
1606 | for ( m=1, LLi = LL; LLi.hasItem(); LLi++, m++ ) |
---|
1607 | { |
---|
1608 | for (n=1, Li = LLi.getItem(); Li.hasItem(); Li++, n++) |
---|
1609 | { |
---|
1610 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1611 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1612 | MATELEM(res,m,n)=convFactoryPSingP(Li.getItem(),r); |
---|
1613 | else |
---|
1614 | MATELEM(res,m,n)=convFactoryPSingTrP(Li.getItem(),r); |
---|
1615 | } |
---|
1616 | } |
---|
1617 | Off(SW_RATIONAL); |
---|
1618 | return res; |
---|
1619 | } |
---|
1620 | |
---|
1621 | char* singclap_neworder ( ideal I, const ring r) |
---|
1622 | { |
---|
1623 | int i; |
---|
1624 | Off(SW_RATIONAL); |
---|
1625 | On(SW_SYMMETRIC_FF); |
---|
1626 | CFList L; |
---|
1627 | if (rField_is_Q(r) || rField_is_Zp(r) |
---|
1628 | || (rField_is_Zn(r)&&(r->cf->convSingNFactoryN!=ndConvSingNFactoryN))) |
---|
1629 | { |
---|
1630 | setCharacteristic( rChar(r) ); |
---|
1631 | for(i=0;i<IDELEMS(I);i++) |
---|
1632 | { |
---|
1633 | poly p=I->m[i]; |
---|
1634 | if (p!=NULL) |
---|
1635 | { |
---|
1636 | p=p_Copy(p,r); |
---|
1637 | p_Cleardenom(p, r); |
---|
1638 | L.append(convSingPFactoryP(p,r)); |
---|
1639 | } |
---|
1640 | } |
---|
1641 | } |
---|
1642 | // and over Q(a) / Fp(a) |
---|
1643 | else if (nCoeff_is_transExt (r->cf)) |
---|
1644 | { |
---|
1645 | setCharacteristic( rChar(r) ); |
---|
1646 | for(i=0;i<IDELEMS(I);i++) |
---|
1647 | { |
---|
1648 | poly p=I->m[i]; |
---|
1649 | if (p!=NULL) |
---|
1650 | { |
---|
1651 | p=p_Copy(p,r); |
---|
1652 | p_Cleardenom(p, r); |
---|
1653 | L.append(convSingTrPFactoryP(p,r)); |
---|
1654 | } |
---|
1655 | } |
---|
1656 | } |
---|
1657 | else |
---|
1658 | { |
---|
1659 | WerrorS( feNotImplemented ); |
---|
1660 | return NULL; |
---|
1661 | } |
---|
1662 | |
---|
1663 | List<int> IL=neworderint(L); |
---|
1664 | ListIterator<int> Li; |
---|
1665 | StringSetS(""); |
---|
1666 | Li = IL; |
---|
1667 | int offs=rPar(r); |
---|
1668 | int* mark=(int*)omAlloc0((rVar(r)+offs)*sizeof(int)); |
---|
1669 | int cnt=rVar(r)+offs; |
---|
1670 | loop |
---|
1671 | { |
---|
1672 | if(! Li.hasItem()) break; |
---|
1673 | BOOLEAN done=TRUE; |
---|
1674 | i=Li.getItem()-1; |
---|
1675 | mark[i]=1; |
---|
1676 | if (i<offs) |
---|
1677 | { |
---|
1678 | done=FALSE; |
---|
1679 | //StringAppendS(r->parameter[i]); |
---|
1680 | } |
---|
1681 | else |
---|
1682 | { |
---|
1683 | StringAppendS(r->names[i-offs]); |
---|
1684 | } |
---|
1685 | Li++; |
---|
1686 | cnt--; |
---|
1687 | if(cnt==0) break; |
---|
1688 | if (done) StringAppendS(","); |
---|
1689 | } |
---|
1690 | for(i=0;i<rVar(r)+offs;i++) |
---|
1691 | { |
---|
1692 | BOOLEAN done=TRUE; |
---|
1693 | if(mark[i]==0) |
---|
1694 | { |
---|
1695 | if (i<offs) |
---|
1696 | { |
---|
1697 | done=FALSE; |
---|
1698 | //StringAppendS(r->parameter[i]); |
---|
1699 | } |
---|
1700 | else |
---|
1701 | { |
---|
1702 | StringAppendS(r->names[i-offs]); |
---|
1703 | } |
---|
1704 | cnt--; |
---|
1705 | if(cnt==0) break; |
---|
1706 | if (done) StringAppendS(","); |
---|
1707 | } |
---|
1708 | } |
---|
1709 | char * s=StringEndS(); |
---|
1710 | if (s[strlen(s)-1]==',') s[strlen(s)-1]='\0'; |
---|
1711 | return s; |
---|
1712 | } |
---|
1713 | |
---|
1714 | poly singclap_det( const matrix m, const ring s ) |
---|
1715 | { |
---|
1716 | int r=m->rows(); |
---|
1717 | if (r!=m->cols()) |
---|
1718 | { |
---|
1719 | Werror("det of %d x %d matrix",r,m->cols()); |
---|
1720 | return NULL; |
---|
1721 | } |
---|
1722 | poly res=NULL; |
---|
1723 | CFMatrix M(r,r); |
---|
1724 | int i,j; |
---|
1725 | for(i=r;i>0;i--) |
---|
1726 | { |
---|
1727 | for(j=r;j>0;j--) |
---|
1728 | { |
---|
1729 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
1730 | } |
---|
1731 | } |
---|
1732 | res= convFactoryPSingP( determinant(M,r),s ) ; |
---|
1733 | Off(SW_RATIONAL); |
---|
1734 | return res; |
---|
1735 | } |
---|
1736 | |
---|
1737 | int singclap_det_i( intvec * m, const ring /*r*/) |
---|
1738 | { |
---|
1739 | // assume( r == currRing ); // Anything else is not guaranted to work! |
---|
1740 | |
---|
1741 | setCharacteristic( 0 ); // ? |
---|
1742 | CFMatrix M(m->rows(),m->cols()); |
---|
1743 | int i,j; |
---|
1744 | for(i=m->rows();i>0;i--) |
---|
1745 | { |
---|
1746 | for(j=m->cols();j>0;j--) |
---|
1747 | { |
---|
1748 | M(i,j)=IMATELEM(*m,i,j); |
---|
1749 | } |
---|
1750 | } |
---|
1751 | int res= convFactoryISingI( determinant(M,m->rows()) ) ; |
---|
1752 | return res; |
---|
1753 | } |
---|
1754 | |
---|
1755 | number singclap_det_bi( bigintmat * m, const coeffs cf) |
---|
1756 | { |
---|
1757 | assume(m->basecoeffs()==cf); |
---|
1758 | CFMatrix M(m->rows(),m->cols()); |
---|
1759 | int i,j; |
---|
1760 | BOOLEAN setchar=TRUE; |
---|
1761 | for(i=m->rows();i>0;i--) |
---|
1762 | { |
---|
1763 | for(j=m->cols();j>0;j--) |
---|
1764 | { |
---|
1765 | M(i,j)=n_convSingNFactoryN(BIMATELEM(*m,i,j),setchar,cf); |
---|
1766 | setchar=FALSE; |
---|
1767 | } |
---|
1768 | } |
---|
1769 | number res=n_convFactoryNSingN( determinant(M,m->rows()),cf ) ; |
---|
1770 | return res; |
---|
1771 | } |
---|
1772 | |
---|
1773 | #if defined(HAVE_NTL) || defined(AHVE_FLINT) |
---|
1774 | matrix singntl_HNF(matrix m, const ring s ) |
---|
1775 | { |
---|
1776 | int r=m->rows(); |
---|
1777 | if (r!=m->cols()) |
---|
1778 | { |
---|
1779 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
1780 | return NULL; |
---|
1781 | } |
---|
1782 | |
---|
1783 | matrix res=mpNew(r,r); |
---|
1784 | |
---|
1785 | if (rField_is_Q(s)) |
---|
1786 | { |
---|
1787 | |
---|
1788 | CFMatrix M(r,r); |
---|
1789 | int i,j; |
---|
1790 | for(i=r;i>0;i--) |
---|
1791 | { |
---|
1792 | for(j=r;j>0;j--) |
---|
1793 | { |
---|
1794 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s ); |
---|
1795 | } |
---|
1796 | } |
---|
1797 | CFMatrix *MM=cf_HNF(M); |
---|
1798 | for(i=r;i>0;i--) |
---|
1799 | { |
---|
1800 | for(j=r;j>0;j--) |
---|
1801 | { |
---|
1802 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
1803 | } |
---|
1804 | } |
---|
1805 | delete MM; |
---|
1806 | } |
---|
1807 | return res; |
---|
1808 | } |
---|
1809 | |
---|
1810 | intvec* singntl_HNF(intvec* m) |
---|
1811 | { |
---|
1812 | int r=m->rows(); |
---|
1813 | if (r!=m->cols()) |
---|
1814 | { |
---|
1815 | Werror("HNF of %d x %d matrix",r,m->cols()); |
---|
1816 | return NULL; |
---|
1817 | } |
---|
1818 | setCharacteristic( 0 ); |
---|
1819 | CFMatrix M(r,r); |
---|
1820 | int i,j; |
---|
1821 | for(i=r;i>0;i--) |
---|
1822 | { |
---|
1823 | for(j=r;j>0;j--) |
---|
1824 | { |
---|
1825 | M(i,j)=IMATELEM(*m,i,j); |
---|
1826 | } |
---|
1827 | } |
---|
1828 | CFMatrix *MM=cf_HNF(M); |
---|
1829 | intvec *mm=ivCopy(m); |
---|
1830 | for(i=r;i>0;i--) |
---|
1831 | { |
---|
1832 | for(j=r;j>0;j--) |
---|
1833 | { |
---|
1834 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
1835 | } |
---|
1836 | } |
---|
1837 | delete MM; |
---|
1838 | return mm; |
---|
1839 | } |
---|
1840 | |
---|
1841 | bigintmat* singntl_HNF(bigintmat* b) |
---|
1842 | { |
---|
1843 | int r=b->rows(); |
---|
1844 | if (r!=b->cols()) |
---|
1845 | { |
---|
1846 | Werror("HNF of %d x %d matrix",r,b->cols()); |
---|
1847 | return NULL; |
---|
1848 | } |
---|
1849 | setCharacteristic( 0 ); |
---|
1850 | CFMatrix M(r,r); |
---|
1851 | int i,j; |
---|
1852 | for(i=r;i>0;i--) |
---|
1853 | { |
---|
1854 | for(j=r;j>0;j--) |
---|
1855 | { |
---|
1856 | M(i,j)=n_convSingNFactoryN(BIMATELEM(*b,i,j),FALSE,b->basecoeffs()); |
---|
1857 | } |
---|
1858 | } |
---|
1859 | CFMatrix *MM=cf_HNF(M); |
---|
1860 | bigintmat *mm=bimCopy(b); |
---|
1861 | for(i=r;i>0;i--) |
---|
1862 | { |
---|
1863 | for(j=r;j>0;j--) |
---|
1864 | { |
---|
1865 | BIMATELEM(*mm,i,j)=n_convFactoryNSingN((*MM)(i,j),b->basecoeffs()); |
---|
1866 | } |
---|
1867 | } |
---|
1868 | delete MM; |
---|
1869 | return mm; |
---|
1870 | } |
---|
1871 | |
---|
1872 | matrix singntl_LLL(matrix m, const ring s ) |
---|
1873 | { |
---|
1874 | int r=m->rows(); |
---|
1875 | int c=m->cols(); |
---|
1876 | matrix res=mpNew(r,c); |
---|
1877 | if (rField_is_Q(s)) |
---|
1878 | { |
---|
1879 | CFMatrix M(r,c); |
---|
1880 | int i,j; |
---|
1881 | for(i=r;i>0;i--) |
---|
1882 | { |
---|
1883 | for(j=c;j>0;j--) |
---|
1884 | { |
---|
1885 | M(i,j)=convSingPFactoryP(MATELEM(m,i,j),s); |
---|
1886 | } |
---|
1887 | } |
---|
1888 | CFMatrix *MM=cf_LLL(M); |
---|
1889 | for(i=r;i>0;i--) |
---|
1890 | { |
---|
1891 | for(j=c;j>0;j--) |
---|
1892 | { |
---|
1893 | MATELEM(res,i,j)=convFactoryPSingP((*MM)(i,j),s); |
---|
1894 | } |
---|
1895 | } |
---|
1896 | delete MM; |
---|
1897 | } |
---|
1898 | return res; |
---|
1899 | } |
---|
1900 | |
---|
1901 | intvec* singntl_LLL(intvec* m) |
---|
1902 | { |
---|
1903 | int r=m->rows(); |
---|
1904 | int c=m->cols(); |
---|
1905 | setCharacteristic( 0 ); |
---|
1906 | CFMatrix M(r,c); |
---|
1907 | int i,j; |
---|
1908 | for(i=r;i>0;i--) |
---|
1909 | { |
---|
1910 | for(j=c;j>0;j--) |
---|
1911 | { |
---|
1912 | M(i,j)=IMATELEM(*m,i,j); |
---|
1913 | } |
---|
1914 | } |
---|
1915 | CFMatrix *MM=cf_LLL(M); |
---|
1916 | intvec *mm=ivCopy(m); |
---|
1917 | for(i=r;i>0;i--) |
---|
1918 | { |
---|
1919 | for(j=c;j>0;j--) |
---|
1920 | { |
---|
1921 | IMATELEM(*mm,i,j)=convFactoryISingI((*MM)(i,j)); |
---|
1922 | } |
---|
1923 | } |
---|
1924 | delete MM; |
---|
1925 | return mm; |
---|
1926 | } |
---|
1927 | #else |
---|
1928 | matrix singntl_HNF(matrix m, const ring s ) |
---|
1929 | { |
---|
1930 | WerrorS("NTL/FLINT missing"); |
---|
1931 | return NULL; |
---|
1932 | } |
---|
1933 | |
---|
1934 | intvec* singntl_HNF(intvec* m) |
---|
1935 | { |
---|
1936 | WerrorS("NTL/FLINT missing"); |
---|
1937 | return NULL; |
---|
1938 | } |
---|
1939 | |
---|
1940 | matrix singntl_LLL(matrix m, const ring s ) |
---|
1941 | { |
---|
1942 | WerrorS("NTL/FLINT missing"); |
---|
1943 | return NULL; |
---|
1944 | } |
---|
1945 | |
---|
1946 | intvec* singntl_LLL(intvec* m) |
---|
1947 | { |
---|
1948 | WerrorS("NTL/FLINT missing"); |
---|
1949 | return NULL; |
---|
1950 | } |
---|
1951 | #endif |
---|
1952 | |
---|
1953 | #ifdef HAVE_NTL |
---|
1954 | ideal singclap_absFactorize ( poly f, ideal & mipos, intvec ** exps, int & numFactors, const ring r) |
---|
1955 | { |
---|
1956 | p_Test(f, r); |
---|
1957 | |
---|
1958 | ideal res=NULL; |
---|
1959 | |
---|
1960 | int offs = rPar(r); |
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1961 | if (f==NULL) |
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1962 | { |
---|
1963 | res= idInit (1, 1); |
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1964 | mipos= idInit (1, 1); |
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1965 | mipos->m[0]= convFactoryPSingTrP (Variable (offs), r); //overkill |
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1966 | (*exps)=new intvec (1); |
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1967 | (**exps)[0]= 1; |
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1968 | numFactors= 0; |
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1969 | return res; |
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1970 | } |
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1971 | CanonicalForm F( convSingTrPFactoryP( f, r) ); |
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1972 | |
---|
1973 | bool isRat= isOn (SW_RATIONAL); |
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1974 | if (!isRat) |
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1975 | On (SW_RATIONAL); |
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1976 | |
---|
1977 | CFAFList absFactors= absFactorize (F); |
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1978 | |
---|
1979 | int n= absFactors.length(); |
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1980 | *exps=new intvec (n); |
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1981 | |
---|
1982 | res= idInit (n, 1); |
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1983 | |
---|
1984 | mipos= idInit (n, 1); |
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1985 | |
---|
1986 | Variable x= Variable (offs); |
---|
1987 | Variable alpha; |
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1988 | int i= 0; |
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1989 | numFactors= 0; |
---|
1990 | int count; |
---|
1991 | CFAFListIterator iter= absFactors; |
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1992 | CanonicalForm lead= iter.getItem().factor(); |
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1993 | if (iter.getItem().factor().inCoeffDomain()) |
---|
1994 | { |
---|
1995 | i++; |
---|
1996 | iter++; |
---|
1997 | } |
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1998 | for (; iter.hasItem(); iter++, i++) |
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1999 | { |
---|
2000 | (**exps)[i]= iter.getItem().exp(); |
---|
2001 | alpha= iter.getItem().minpoly().mvar(); |
---|
2002 | if (iter.getItem().minpoly().isOne()) |
---|
2003 | lead /= power (bCommonDen (iter.getItem().factor()), iter.getItem().exp()); |
---|
2004 | else |
---|
2005 | lead /= power (power (bCommonDen (iter.getItem().factor()), degree (iter.getItem().minpoly())), iter.getItem().exp()); |
---|
2006 | res->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().factor()*bCommonDen (iter.getItem().factor()), alpha, x), r); |
---|
2007 | if (iter.getItem().minpoly().isOne()) |
---|
2008 | { |
---|
2009 | count= iter.getItem().exp(); |
---|
2010 | mipos->m[i]= convFactoryPSingTrP (x,r); |
---|
2011 | } |
---|
2012 | else |
---|
2013 | { |
---|
2014 | count= iter.getItem().exp()*degree (iter.getItem().minpoly()); |
---|
2015 | mipos->m[i]= convFactoryPSingTrP (replacevar (iter.getItem().minpoly(), alpha, x), r); |
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2016 | } |
---|
2017 | if (!iter.getItem().minpoly().isOne()) |
---|
2018 | prune (alpha); |
---|
2019 | numFactors += count; |
---|
2020 | } |
---|
2021 | if (!isRat) |
---|
2022 | Off (SW_RATIONAL); |
---|
2023 | |
---|
2024 | (**exps)[0]= 1; |
---|
2025 | res->m[0]= convFactoryPSingTrP (lead, r); |
---|
2026 | mipos->m[0]= convFactoryPSingTrP (x, r); |
---|
2027 | return res; |
---|
2028 | } |
---|
2029 | |
---|
2030 | #else |
---|
2031 | ideal singclap_absFactorize ( poly f, ideal & mipos, intvec ** exps, int & numFactors, const ring r) |
---|
2032 | { |
---|
2033 | WerrorS("NTL missing"); |
---|
2034 | return NULL; |
---|
2035 | } |
---|
2036 | |
---|
2037 | #endif /* HAVE_NTL */ |
---|
2038 | |
---|
2039 | int * Zp_roots(poly p, const ring r) |
---|
2040 | { |
---|
2041 | CanonicalForm pp=convSingPFactoryP(p,r); |
---|
2042 | return Zp_roots(pp); |
---|
2043 | } |
---|