1 | #include "config.h" |
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2 | |
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3 | #include "debug.h" |
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4 | |
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5 | #include "cf_algorithm.h" |
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6 | #include "templates/ftmpl_functions.h" |
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7 | #include "cf_primes.h" |
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8 | #include "cfGcdUtil.h" |
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9 | #include "cfUnivarGcd.h" |
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10 | |
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11 | #ifdef HAVE_NTL |
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12 | #include "NTLconvert.h" |
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13 | #endif |
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14 | |
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15 | #ifdef HAVE_FLINT |
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16 | #include "FLINTconvert.h" |
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17 | #endif |
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18 | |
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19 | #ifdef HAVE_NTL |
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20 | #ifndef HAVE_FLINT |
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21 | CanonicalForm |
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22 | gcd_univar_ntl0( const CanonicalForm & F, const CanonicalForm & G ) |
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23 | { |
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24 | ZZX F1=convertFacCF2NTLZZX(F); |
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25 | ZZX G1=convertFacCF2NTLZZX(G); |
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26 | ZZX R=GCD(F1,G1); |
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27 | return convertNTLZZX2CF(R,F.mvar()); |
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28 | } |
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29 | |
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30 | CanonicalForm |
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31 | gcd_univar_ntlp( const CanonicalForm & F, const CanonicalForm & G ) |
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32 | { |
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33 | if (fac_NTL_char!=getCharacteristic()) |
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34 | { |
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35 | fac_NTL_char=getCharacteristic(); |
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36 | zz_p::init(getCharacteristic()); |
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37 | } |
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38 | zz_pX F1=convertFacCF2NTLzzpX(F); |
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39 | zz_pX G1=convertFacCF2NTLzzpX(G); |
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40 | zz_pX R=GCD(F1,G1); |
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41 | return convertNTLzzpX2CF(R,F.mvar()); |
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42 | } |
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43 | #endif |
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44 | #endif |
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45 | |
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46 | #ifdef HAVE_FLINT |
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47 | CanonicalForm |
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48 | gcd_univar_flintp (const CanonicalForm& F, const CanonicalForm& G) |
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49 | { |
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50 | nmod_poly_t F1, G1; |
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51 | convertFacCF2nmod_poly_t (F1, F); |
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52 | convertFacCF2nmod_poly_t (G1, G); |
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53 | nmod_poly_gcd (F1, F1, G1); |
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54 | CanonicalForm result= convertnmod_poly_t2FacCF (F1, F.mvar()); |
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55 | nmod_poly_clear (F1); |
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56 | nmod_poly_clear (G1); |
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57 | return result; |
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58 | } |
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59 | |
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60 | CanonicalForm |
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61 | gcd_univar_flint0( const CanonicalForm & F, const CanonicalForm & G ) |
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62 | { |
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63 | fmpz_poly_t F1, G1; |
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64 | convertFacCF2Fmpz_poly_t(F1, F); |
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65 | convertFacCF2Fmpz_poly_t(G1, G); |
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66 | fmpz_poly_gcd (F1, F1, G1); |
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67 | CanonicalForm result= convertFmpz_poly_t2FacCF (F1, F.mvar()); |
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68 | fmpz_poly_clear (F1); |
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69 | fmpz_poly_clear (G1); |
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70 | return result; |
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71 | } |
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72 | #endif |
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73 | |
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74 | #ifndef HAVE_NTL |
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75 | CanonicalForm gcd_poly_univar0( const CanonicalForm & F, const CanonicalForm & G, bool primitive ) |
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76 | { |
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77 | CanonicalForm f, g, c, cg, cl, BB, B, M, q, Dp, newD, D, newq; |
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78 | int p, i; |
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79 | |
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80 | if ( primitive ) |
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81 | { |
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82 | f = F; |
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83 | g = G; |
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84 | c = 1; |
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85 | } |
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86 | else |
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87 | { |
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88 | CanonicalForm cF = content( F ), cG = content( G ); |
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89 | f = F / cF; |
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90 | g = G / cG; |
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91 | c = bgcd( cF, cG ); |
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92 | } |
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93 | cg = gcd( f.lc(), g.lc() ); |
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94 | cl = ( f.lc() / cg ) * g.lc(); |
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95 | // B = 2 * cg * tmin( |
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96 | // maxnorm(f)*power(CanonicalForm(2),f.degree())*isqrt(f.degree()+1), |
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97 | // maxnorm(g)*power(CanonicalForm(2),g.degree())*isqrt(g.degree()+1) |
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98 | // )+1; |
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99 | M = tmin( maxNorm(f), maxNorm(g) ); |
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100 | BB = power(CanonicalForm(2),tmin(f.degree(),g.degree()))*M; |
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101 | q = 0; |
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102 | i = cf_getNumSmallPrimes() - 1; |
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103 | while ( true ) |
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104 | { |
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105 | B = BB; |
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106 | while ( i >= 0 && q < B ) |
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107 | { |
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108 | p = cf_getSmallPrime( i ); |
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109 | i--; |
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110 | while ( i >= 0 && mod( cl, p ) == 0 ) |
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111 | { |
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112 | p = cf_getSmallPrime( i ); |
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113 | i--; |
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114 | } |
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115 | setCharacteristic( p ); |
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116 | Dp = gcd( mapinto( f ), mapinto( g ) ); |
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117 | Dp = ( Dp / Dp.lc() ) * mapinto( cg ); |
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118 | setCharacteristic( 0 ); |
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119 | if ( Dp.degree() == 0 ) |
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120 | return c; |
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121 | if ( q.isZero() ) |
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122 | { |
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123 | D = mapinto( Dp ); |
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124 | q = p; |
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125 | B = power(CanonicalForm(2),D.degree())*M+1; |
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126 | } |
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127 | else |
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128 | { |
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129 | if ( Dp.degree() == D.degree() ) |
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130 | { |
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131 | chineseRemainder( D, q, mapinto( Dp ), p, newD, newq ); |
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132 | q = newq; |
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133 | D = newD; |
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134 | } |
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135 | else if ( Dp.degree() < D.degree() ) |
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136 | { |
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137 | // all previous p's are bad primes |
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138 | q = p; |
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139 | D = mapinto( Dp ); |
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140 | B = power(CanonicalForm(2),D.degree())*M+1; |
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141 | } |
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142 | // else p is a bad prime |
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143 | } |
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144 | } |
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145 | if ( i >= 0 ) |
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146 | { |
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147 | // now balance D mod q |
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148 | D = pp( balance_p( D, q ) ); |
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149 | if ( fdivides( D, f ) && fdivides( D, g ) ) |
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150 | return D * c; |
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151 | else |
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152 | q = 0; |
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153 | } |
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154 | else |
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155 | return gcd_poly( F, G ); |
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156 | DEBOUTLN( cerr, "another try ..." ); |
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157 | } |
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158 | } |
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159 | #endif |
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160 | |
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161 | /** CanonicalForm extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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162 | * |
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163 | * extgcd() - returns polynomial extended gcd of f and g. |
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164 | * |
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165 | * Returns gcd(f, g) and a and b sucht that f*a+g*b=gcd(f, g). |
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166 | * The gcd is calculated using an extended euclidean polynomial |
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167 | * remainder sequence, so f and g should be polynomials over an |
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168 | * euclidean domain. Normalizes result. |
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169 | * |
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170 | * Note: be sure that f and g have the same level! |
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171 | * |
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172 | **/ |
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173 | CanonicalForm |
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174 | extgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
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175 | { |
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176 | if (f.isZero()) |
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177 | { |
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178 | a= 0; |
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179 | b= 1; |
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180 | return g; |
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181 | } |
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182 | else if (g.isZero()) |
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183 | { |
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184 | a= 1; |
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185 | b= 0; |
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186 | return f; |
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187 | } |
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188 | #ifdef HAVE_FLINT |
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189 | if (( getCharacteristic() > 0 ) && (CFFactory::gettype() != GaloisFieldDomain) |
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190 | && (f.level()==g.level()) && isPurePoly(f) && isPurePoly(g)) |
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191 | { |
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192 | nmod_poly_t F1, G1, A, B, R; |
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193 | convertFacCF2nmod_poly_t (F1, f); |
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194 | convertFacCF2nmod_poly_t (G1, g); |
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195 | nmod_poly_init (R, getCharacteristic()); |
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196 | nmod_poly_init (A, getCharacteristic()); |
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197 | nmod_poly_init (B, getCharacteristic()); |
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198 | nmod_poly_xgcd (R, A, B, F1, G1); |
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199 | a= convertnmod_poly_t2FacCF (A, f.mvar()); |
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200 | b= convertnmod_poly_t2FacCF (B, f.mvar()); |
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201 | CanonicalForm r= convertnmod_poly_t2FacCF (R, f.mvar()); |
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202 | nmod_poly_clear (F1); |
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203 | nmod_poly_clear (G1); |
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204 | nmod_poly_clear (A); |
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205 | nmod_poly_clear (B); |
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206 | nmod_poly_clear (R); |
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207 | return r; |
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208 | } |
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209 | #elif defined(HAVE_NTL) |
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210 | if (( getCharacteristic() > 0 ) && (CFFactory::gettype() != GaloisFieldDomain) |
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211 | && (f.level()==g.level()) && isPurePoly(f) && isPurePoly(g)) |
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212 | { |
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213 | if (fac_NTL_char!=getCharacteristic()) |
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214 | { |
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215 | fac_NTL_char=getCharacteristic(); |
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216 | zz_p::init(getCharacteristic()); |
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217 | } |
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218 | zz_pX F1=convertFacCF2NTLzzpX(f); |
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219 | zz_pX G1=convertFacCF2NTLzzpX(g); |
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220 | zz_pX R; |
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221 | zz_pX A,B; |
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222 | XGCD(R,A,B,F1,G1); |
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223 | a=convertNTLzzpX2CF(A,f.mvar()); |
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224 | b=convertNTLzzpX2CF(B,f.mvar()); |
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225 | return convertNTLzzpX2CF(R,f.mvar()); |
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226 | } |
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227 | #endif |
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228 | #ifdef HAVE_FLINT |
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229 | if (( getCharacteristic() ==0) && (f.level()==g.level()) |
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230 | && isPurePoly(f) && isPurePoly(g)) |
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231 | { |
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232 | fmpq_poly_t F1, G1; |
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233 | convertFacCF2Fmpq_poly_t (F1, f); |
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234 | convertFacCF2Fmpq_poly_t (G1, g); |
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235 | fmpq_poly_t R, A, B; |
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236 | fmpq_poly_init (R); |
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237 | fmpq_poly_init (A); |
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238 | fmpq_poly_init (B); |
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239 | fmpq_poly_xgcd (R, A, B, F1, G1); |
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240 | a= convertFmpq_poly_t2FacCF (A, f.mvar()); |
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241 | b= convertFmpq_poly_t2FacCF (B, f.mvar()); |
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242 | CanonicalForm r= convertFmpq_poly_t2FacCF (R, f.mvar()); |
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243 | fmpq_poly_clear (F1); |
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244 | fmpq_poly_clear (G1); |
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245 | fmpq_poly_clear (A); |
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246 | fmpq_poly_clear (B); |
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247 | fmpq_poly_clear (R); |
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248 | return r; |
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249 | } |
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250 | #elif defined(HAVE_NTL) |
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251 | if (( getCharacteristic() ==0) |
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252 | && (f.level()==g.level()) && isPurePoly(f) && isPurePoly(g)) |
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253 | { |
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254 | CanonicalForm fc=bCommonDen(f); |
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255 | CanonicalForm gc=bCommonDen(g); |
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256 | ZZX F1=convertFacCF2NTLZZX(f*fc); |
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257 | ZZX G1=convertFacCF2NTLZZX(g*gc); |
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258 | ZZX R=GCD(F1,G1); |
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259 | CanonicalForm r=convertNTLZZX2CF(R,f.mvar()); |
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260 | ZZ RR; |
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261 | ZZX A,B; |
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262 | if (r.inCoeffDomain()) |
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263 | { |
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264 | XGCD(RR,A,B,F1,G1,1); |
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265 | CanonicalForm rr=convertZZ2CF(RR); |
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266 | if(!rr.isZero()) |
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267 | { |
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268 | a=convertNTLZZX2CF(A,f.mvar())*fc/rr; |
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269 | b=convertNTLZZX2CF(B,f.mvar())*gc/rr; |
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270 | return CanonicalForm(1); |
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271 | } |
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272 | else |
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273 | { |
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274 | F1 /= R; |
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275 | G1 /= R; |
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276 | XGCD (RR, A,B,F1,G1,1); |
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277 | rr=convertZZ2CF(RR); |
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278 | a=convertNTLZZX2CF(A,f.mvar())*(fc/rr); |
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279 | b=convertNTLZZX2CF(B,f.mvar())*(gc/rr); |
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280 | } |
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281 | } |
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282 | else |
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283 | { |
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284 | XGCD(RR,A,B,F1,G1,1); |
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285 | CanonicalForm rr=convertZZ2CF(RR); |
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286 | if (!rr.isZero()) |
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287 | { |
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288 | a=convertNTLZZX2CF(A,f.mvar())*fc; |
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289 | b=convertNTLZZX2CF(B,f.mvar())*gc; |
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290 | } |
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291 | else |
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292 | { |
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293 | F1 /= R; |
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294 | G1 /= R; |
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295 | XGCD (RR, A,B,F1,G1,1); |
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296 | rr=convertZZ2CF(RR); |
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297 | a=convertNTLZZX2CF(A,f.mvar())*(fc/rr); |
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298 | b=convertNTLZZX2CF(B,f.mvar())*(gc/rr); |
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299 | } |
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300 | return r; |
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301 | } |
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302 | } |
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303 | #endif |
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304 | // may contain bug in the co-factors, see track 107 |
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305 | CanonicalForm contf = content( f ); |
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306 | CanonicalForm contg = content( g ); |
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307 | |
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308 | CanonicalForm p0 = f / contf, p1 = g / contg; |
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309 | CanonicalForm f0 = 1, f1 = 0, g0 = 0, g1 = 1, q, r; |
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310 | |
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311 | while ( ! p1.isZero() ) |
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312 | { |
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313 | divrem( p0, p1, q, r ); |
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314 | p0 = p1; p1 = r; |
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315 | r = g0 - g1 * q; |
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316 | g0 = g1; g1 = r; |
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317 | r = f0 - f1 * q; |
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318 | f0 = f1; f1 = r; |
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319 | } |
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320 | CanonicalForm contp0 = content( p0 ); |
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321 | a = f0 / ( contf * contp0 ); |
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322 | b = g0 / ( contg * contp0 ); |
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323 | p0 /= contp0; |
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324 | if ( p0.sign() < 0 ) |
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325 | { |
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326 | p0 = -p0; |
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327 | a = -a; |
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328 | b = -b; |
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329 | } |
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330 | return p0; |
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331 | } |
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