1 | #include <config.h> |
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2 | |
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3 | #include "cf_defs.h" |
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4 | #include "canonicalform.h" |
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5 | #include "fac_util.h" |
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6 | #include "cf_algorithm.h" |
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7 | #include "cf_reval.h" |
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8 | #include "cf_random.h" |
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9 | #include "cf_primes.h" |
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10 | #include "fac_distrib.h" |
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11 | #include "ftmpl_functions.h" |
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12 | #include "ffreval.h" |
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13 | #include "cf_binom.h" |
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14 | #include "fac_iterfor.h" |
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15 | #include "cf_iter.h" |
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16 | |
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17 | void FFREvaluation::nextpoint() |
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18 | { |
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19 | // enumerates the points stored in values |
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20 | int n = values.max(); |
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21 | int p = getCharacteristic(); |
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22 | for( int i=values.min(); i<=n; i++ ) |
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23 | { |
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24 | if( values[i] != p-1 ) |
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25 | { |
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26 | values[i] += 1; |
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27 | break; |
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28 | } |
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29 | values[i] += 1; // becomes 0 |
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30 | } |
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31 | } |
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32 | |
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33 | bool FFREvaluation::hasNext() |
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34 | { |
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35 | int n = values.max(); |
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36 | |
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37 | for( int i=values.min(); i<=n; i++ ) |
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38 | { |
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39 | if( values[i]!=start[i] ) |
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40 | return true; |
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41 | } |
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42 | return false; |
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43 | } |
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44 | |
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45 | FFREvaluation& FFREvaluation::operator= ( const FFREvaluation & e ) |
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46 | { |
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47 | if( this != &e ) |
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48 | { |
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49 | if( gen != NULL ) |
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50 | delete gen; |
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51 | values = e.values; |
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52 | start = e.start; |
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53 | if( e.gen == NULL ) |
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54 | gen = NULL; |
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55 | else |
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56 | gen = e.gen->clone(); |
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57 | } |
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58 | return *this; |
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59 | } |
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60 | |
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61 | /* ------------------------------------------------------------------------ */ |
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62 | /* forward declarations: fin_ezgcd stuff*/ |
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63 | static bool findeval_P( const CanonicalForm & F, const CanonicalForm & G, CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, REvaluation & b, int delta, int degF, int degG, int bound, int & counter ); |
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64 | static void solveF_P ( const CFArray & P, const CFArray & Q, const CFArray & S, const CFArray & T, const CanonicalForm & C, int r, CFArray & a ); |
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65 | static CanonicalForm derivAndEval_P ( const CanonicalForm & f, int n, const Variable & x, const CanonicalForm & a ); |
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66 | //static CanonicalForm checkCombination_P ( const CanonicalForm & W, const Evaluation & a, const IteratedFor & e, int k ); |
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67 | static CFArray findCorrCoeffs_P ( const CFArray & P, const CFArray & Q, const CFArray & P0, const CFArray & Q0, const CFArray & S, const CFArray & T, const CanonicalForm & C, const Evaluation & I, int r, int k, int h, int * n ); |
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68 | static bool liftStep_P ( CFArray & P, int k, int r, int t, const Evaluation & A, const CFArray & lcG, const CanonicalForm & Uk, int * n, int h ); |
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69 | static bool Hensel_P ( const CanonicalForm & U, CFArray & G, const CFArray & lcG, const Evaluation & A, const Variable & x ); |
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70 | static bool hasFirstAlgVar( const CanonicalForm & f, Variable & a ); |
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71 | |
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72 | CanonicalForm fin_ezgcd( const CanonicalForm & FF, const CanonicalForm & GG ) |
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73 | { |
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74 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, lcD; |
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75 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
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76 | int degF, degG, delta, count, maxeval; |
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77 | maxeval = getCharacteristic(); // bound on the number of eval. to use |
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78 | count = 0; // number of eval. used |
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79 | REvaluation b, bt; |
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80 | bool gcdfound = false; |
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81 | Variable x = Variable(1); |
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82 | f = content( FF, x ); g = content( GG, x ); d = gcd( f, g ); |
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83 | F = FF / f; G = GG / g; |
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84 | if( F.isUnivariate() && G.isUnivariate() ) |
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85 | { |
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86 | if( F.mvar() == G.mvar() ) |
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87 | d *= gcd( F, G ); |
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88 | return d; |
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89 | } |
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90 | if( gcd_test_one( F, G, false ) ) |
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91 | return d; |
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92 | |
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93 | lcF = LC( F, x ); lcG = LC( G, x ); |
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94 | lcD = gcd( lcF, lcG ); |
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95 | delta = 0; |
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96 | degF = degree( F, x ); degG = degree( G, x ); |
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97 | Variable a,bv; |
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98 | if(hasFirstAlgVar(F,a)) |
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99 | { |
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100 | if(hasFirstAlgVar(G,bv)) |
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101 | { |
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102 | if(bv.level() > a.level()) |
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103 | a = bv; |
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104 | } |
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105 | b = REvaluation( 2, tmax(F.level(), G.level()), AlgExtRandomF( a ) ); |
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106 | } |
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107 | else // F not in extension |
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108 | { |
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109 | if(hasFirstAlgVar(G,a)) |
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110 | b = REvaluation( 2, tmax(F.level(), G.level()), AlgExtRandomF( a ) ); |
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111 | else // both not in extension |
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112 | b = REvaluation( 2, tmax(F.level(), G.level()), FFRandom() ); |
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113 | } |
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114 | while( !gcdfound ) |
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115 | { |
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116 | if( !findeval_P( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count )) |
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117 | { // too many eval. used --> try another method |
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118 | Off( SW_USE_EZGCD_P ); |
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119 | d *= gcd( F, G ); |
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120 | On( SW_USE_EZGCD_P ); |
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121 | return d; |
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122 | } |
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123 | delta = degree( Db ); |
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124 | if( delta == 0 ) |
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125 | return d; |
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126 | while( true ) |
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127 | { |
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128 | bt = b; |
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129 | if( !findeval_P( F, G, Fbt, Gbt, Dbt, bt, delta+1, degF, degG, maxeval, count )) |
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130 | { // too many eval. used --> try another method |
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131 | Off( SW_USE_EZGCD_P ); |
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132 | d *= gcd( F, G ); |
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133 | On( SW_USE_EZGCD_P ); |
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134 | return d; |
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135 | } |
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136 | int dd = degree( Dbt ); |
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137 | if( dd == 0 ) |
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138 | return d; |
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139 | if( dd == delta ) |
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140 | break; |
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141 | if( dd < delta ) |
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142 | { |
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143 | delta = dd; |
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144 | b = bt; |
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145 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
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146 | } |
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147 | } |
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148 | if( degF <= degG && delta == degF && fdivides( F, G ) ) |
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149 | return d*F; |
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150 | if( degG < degF && delta == degG && fdivides( G, F ) ) |
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151 | return d*G; |
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152 | if( delta != degF && delta != degG ) |
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153 | { |
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154 | bool B_is_F; |
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155 | CanonicalForm xxx; |
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156 | DD[1] = Fb / Db; |
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157 | xxx = gcd( DD[1], Db ); |
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158 | if( xxx.inCoeffDomain() ) |
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159 | { |
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160 | B = F; |
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161 | DD[2] = Db; |
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162 | lcDD[1] = lcF; |
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163 | lcDD[2] = lcF; |
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164 | B *= lcF; |
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165 | B_is_F = true; |
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166 | } |
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167 | else |
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168 | { |
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169 | DD[1] = Gb / Db; |
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170 | xxx = gcd( DD[1], Db ); |
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171 | if( xxx.inCoeffDomain() ) |
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172 | { |
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173 | B = G; |
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174 | DD[2] = Db; |
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175 | lcDD[1] = lcG; |
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176 | lcDD[2] = lcG; |
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177 | B *= lcG; |
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178 | B_is_F = false; |
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179 | } |
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180 | else // special case handling |
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181 | { |
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182 | Off( SW_USE_EZGCD_P ); |
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183 | d *= gcd( F, G ); // try another method |
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184 | On( SW_USE_EZGCD_P ); |
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185 | return d; |
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186 | } |
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187 | } |
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188 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
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189 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
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190 | |
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191 | gcdfound = Hensel_P( B, DD, lcDD, b, x ); |
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192 | |
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193 | if( gcdfound ) |
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194 | { |
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195 | CanonicalForm cand = DD[2] / content( DD[2], Variable(1) ); |
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196 | if( B_is_F ) |
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197 | gcdfound = fdivides( cand, G ); |
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198 | else |
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199 | gcdfound = fdivides( cand, F ); |
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200 | } |
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201 | } |
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202 | delta++; |
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203 | } |
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204 | return d * DD[2] / content( DD[2],Variable(1) ); |
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205 | } |
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206 | |
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207 | |
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208 | static bool hasFirstAlgVar( const CanonicalForm & f, Variable & a ) |
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209 | { |
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210 | if( f.inBaseDomain() ) // f has NO alg. variable |
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211 | return false; |
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212 | if( f.level()<0 ) // f has only alg. vars, so take the first one |
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213 | { |
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214 | a = f.mvar(); |
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215 | return true; |
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216 | } |
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217 | for(CFIterator i=f; i.hasTerms(); i++) |
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218 | if( hasFirstAlgVar( i.coeff(), a )) |
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219 | return true; // 'a' is already set |
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220 | return false; |
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221 | } |
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222 | |
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223 | |
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224 | static bool findeval_P( const CanonicalForm & F, const CanonicalForm & G, CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, REvaluation & b, int delta, int degF, int degG, int maxeval, int & count ) |
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225 | { |
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226 | if( delta != 0 ) |
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227 | { |
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228 | b.nextpoint(); |
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229 | if( count++ > maxeval ) |
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230 | return false; // too many eval. used |
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231 | } |
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232 | while( true ) |
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233 | { |
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234 | Fb = b( F ); |
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235 | if( degree( Fb ) == degF ) |
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236 | { |
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237 | Gb = b( G ); |
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238 | if( degree( Gb ) == degG ) |
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239 | { |
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240 | Db = gcd( Fb, Gb ); |
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241 | if( delta > 0 ) |
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242 | { |
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243 | if( degree( Db ) < delta ) |
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244 | return true; |
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245 | } |
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246 | else |
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247 | return true; |
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248 | } |
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249 | } |
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250 | b.nextpoint(); |
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251 | if( count++ > maxeval ) // too many eval. used |
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252 | return false; |
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253 | } |
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254 | } |
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255 | |
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256 | |
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257 | static void solveF_P ( const CFArray & P, const CFArray & Q, const CFArray & S, const CFArray & T, const CanonicalForm & C, int r, CFArray & a ) |
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258 | { |
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259 | CanonicalForm bb, b = C; |
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260 | for ( int j = 1; j < r; j++ ) |
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261 | { |
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262 | divrem( S[j] * b, Q[j], a[j], bb ); |
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263 | a[j] = T[j] * b + a[j] * P[j]; |
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264 | b = bb; |
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265 | } |
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266 | a[r] = b; |
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267 | } |
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268 | |
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269 | |
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270 | static CanonicalForm derivAndEval_P ( const CanonicalForm & f, int n, const Variable & x, const CanonicalForm & a ) |
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271 | { |
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272 | if ( n == 0 ) |
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273 | return f( a, x ); |
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274 | if ( f.degree( x ) < n ) |
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275 | return 0; |
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276 | CFIterator i; |
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277 | CanonicalForm sum = 0, fact; |
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278 | int min, j; |
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279 | Variable v = Variable( f.level() + 1 ); |
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280 | for ( i = swapvar( f, x, v); i.hasTerms() && i.exp() >= n; i++ ) |
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281 | { |
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282 | fact = 1; |
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283 | min = i.exp() - n; |
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284 | for ( j = i.exp(); j > min; j-- ) |
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285 | fact *= j; |
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286 | sum += fact * i.coeff() * power( v, min ); |
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287 | } |
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288 | return sum( a, v ); |
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289 | } |
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290 | |
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291 | |
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292 | static CFArray findCorrCoeffs_P ( const CFArray & P, const CFArray & Q, const CFArray & P0, const CFArray & Q0, const CFArray & S, const CFArray & T, const CanonicalForm & C, const Evaluation & I, int r, int k, int h, int * n ) |
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293 | { |
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294 | bool what; |
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295 | int i, j, m; |
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296 | CFArray A(1,r), a(1,r); |
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297 | CanonicalForm C0, Dm, g, prodcomb; |
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298 | C0 = I( C, 2, k-1 ); |
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299 | solveF_P( P0, Q0, S, T, 1, r, a ); |
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300 | for ( i = 1; i <= r; i++ ) |
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301 | A[i] = (a[i] * C0) % P0[i]; |
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302 | for ( m = 0; m <= h && ( m == 0 || Dm != 0 ); m++ ) |
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303 | { |
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304 | Dm = -C; |
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305 | prodcomb = 1; |
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306 | for ( i = 1; i <= r; i++ ) |
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307 | { |
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308 | Dm += prodcomb * A[i] * Q[i]; |
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309 | prodcomb *= P[i]; |
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310 | } |
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311 | if ( Dm != 0 ) |
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312 | { |
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313 | if ( k == 2 ) |
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314 | { |
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315 | solveF_P( P0, Q0, S, T, Dm, r, a ); |
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316 | for ( i = 1; i <= r; i++ ) |
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317 | A[i] -= a[i]; |
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318 | } |
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319 | else |
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320 | { |
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321 | IteratedFor e( 2, k-1, m+1 ); |
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322 | while ( e.iterations_left() ) |
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323 | { |
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324 | j = 0; |
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325 | what = true; |
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326 | for ( i = 2; i < k; i++ ) |
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327 | { |
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328 | j += e[i]; |
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329 | if ( e[i] > n[i] ) |
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330 | { |
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331 | what = false; |
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332 | break; |
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333 | } |
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334 | } |
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335 | if ( what && j == m+1 ) |
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336 | { |
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337 | g = Dm; |
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338 | for ( i = k-1; i >= 2 && ! g.isZero(); i-- ) |
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339 | g = derivAndEval_P( g, e[i], Variable( i ), I[i] ); |
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340 | if ( ! g.isZero() ) |
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341 | { |
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342 | prodcomb = 1; |
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343 | for ( i = 2; i < k; i++ ) |
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344 | for ( j = 2; j <= e[i]; j++ ) |
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345 | prodcomb *= j; |
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346 | g /= prodcomb; |
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347 | if( ! (g.mvar() > Variable(1)) ) |
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348 | { |
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349 | prodcomb = 1; |
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350 | for ( i = k-1; i > 1; i-- ) |
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351 | prodcomb *= binomialpower( Variable(i), -I[i], e[i] ); |
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352 | solveF_P( P0, Q0, S, T, g, r, a ); |
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353 | for ( i = 1; i <= r; i++ ) |
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354 | A[i] -= a[i] * prodcomb; |
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355 | } |
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356 | } |
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357 | } |
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358 | e++; |
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359 | } |
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360 | } |
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361 | } |
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362 | } |
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363 | return A; |
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364 | } |
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365 | |
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366 | |
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367 | static bool liftStep_P ( CFArray & P, int k, int r, int t, const Evaluation & A, const CFArray & lcG, const CanonicalForm & Uk, int * n, int h ) |
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368 | { |
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369 | CFArray K( 1, r ), Q( 1, r ), Q0( 1, r ), P0( 1, r ), S( 1, r ), T( 1, r ), alpha( 1, r ); |
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370 | CanonicalForm Rm, C, D, xa = Variable(k) - A[k]; |
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371 | CanonicalForm xa1 = xa, xa2 = xa*xa; |
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372 | int i, m; |
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373 | for ( i = 1; i <= r; i++ ) |
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374 | { |
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375 | Variable vm = Variable( t + 1 ); |
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376 | Variable v1 = Variable(1); |
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377 | K[i] = swapvar( replaceLc( swapvar( P[i], v1, vm ), swapvar( A( lcG[i], k+1, t ), v1, vm ) ), v1, vm ); |
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378 | P[i] = A( K[i], k, t ); |
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379 | } |
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380 | Q[r] = 1; |
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381 | for ( i = r; i > 1; i-- ) |
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382 | { |
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383 | Q[i-1] = Q[i] * P[i]; |
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384 | P0[i] = A( P[i], 2, k-1 ); |
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385 | Q0[i] = A( Q[i], 2, k-1 ); |
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386 | (void) extgcd( P0[i], Q0[i], S[i], T[i] ); |
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387 | } |
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388 | P0[1] = A( P[1], 2, k-1 ); |
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389 | Q0[1] = A( Q[1], 2, k-1 ); |
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390 | (void) extgcd( P0[1], Q0[1], S[1], T[1] ); |
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391 | for ( m = 1; m <= n[k]+1; m++ ) |
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392 | { |
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393 | Rm = prod( K ) - Uk; |
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394 | for ( i = 2; i < k; i++ ) |
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395 | Rm.mod( binomialpower( Variable(i), -A[i], n[i]+1 ) ); |
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396 | if ( mod( Rm, xa2 ) != 0 ) |
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397 | { |
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398 | C = derivAndEval_P( Rm, m, Variable( k ), A[k] ); |
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399 | D = 1; |
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400 | for ( i = 2; i <= m; i++ ) |
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401 | D *= i; |
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402 | C /= D; |
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403 | alpha = findCorrCoeffs_P( P, Q, P0, Q0, S, T, C, A, r, k, h, n ); |
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404 | for ( i = 1; i <= r; i++ ) |
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405 | K[i] -= alpha[i] * xa1; |
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406 | } |
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407 | xa1 = xa2; |
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408 | xa2 *= xa; |
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409 | } |
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410 | for ( i = 1; i <= r; i++ ) |
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411 | P[i] = K[i]; |
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412 | return prod( K ) - Uk == 0; |
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413 | } |
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414 | |
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415 | |
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416 | static bool Hensel_P ( const CanonicalForm & U, CFArray & G, const CFArray & lcG, const Evaluation & A, const Variable & x ) |
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417 | { |
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418 | int k, i, h, t = A.max(); |
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419 | bool goodeval = true; |
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420 | CFArray Uk( A.min(), A.max() ); |
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421 | int * n = new int[t+1]; |
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422 | Uk[t] = U; |
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423 | for ( k = t-1; k > 1; k-- ) |
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424 | { |
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425 | Uk[k] = Uk[k+1]( A[k+1], Variable( k+1 ) ); |
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426 | n[k] = degree( Uk[k], Variable( k ) ); |
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427 | } |
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428 | for ( k = A.min(); goodeval && (k <= t); k++ ) |
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429 | { |
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430 | h = totaldegree( Uk[k], Variable(A.min()), Variable(k-1) ); |
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431 | for ( i = A.min(); i <= k; i++ ) |
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432 | n[i] = degree( Uk[k], Variable(i) ); |
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433 | goodeval = liftStep_P( G, k, G.max(), t, A, lcG, Uk[k], n, h ); |
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434 | } |
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435 | delete[] n; |
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436 | return goodeval; |
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437 | } |
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