1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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2 | /* $Id$ */ |
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3 | |
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4 | #include <config.h> |
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5 | |
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6 | #include "assert.h" |
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7 | #include "debug.h" |
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8 | |
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9 | #include "cf_defs.h" |
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10 | #include "canonicalform.h" |
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11 | #include "fac_util.h" |
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12 | #include "cf_algorithm.h" |
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13 | #include "cf_reval.h" |
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14 | #include "cf_random.h" |
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15 | #include "cf_primes.h" |
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16 | #include "fac_distrib.h" |
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17 | #include "templates/ftmpl_functions.h" |
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18 | |
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19 | static void findeval( const CanonicalForm & F, const CanonicalForm & G, CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, REvaluation & b, int delta, int degF, int degG ); |
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20 | |
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21 | static CanonicalForm ezgcd ( const CanonicalForm & FF, const CanonicalForm & GG, REvaluation & b, bool internal ); |
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22 | |
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23 | static CanonicalForm ezgcd_specialcase ( const CanonicalForm & F, const CanonicalForm & G, REvaluation & b, const modpk & bound ); |
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24 | |
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25 | static modpk findBound ( const CanonicalForm & F, const CanonicalForm & G, const CanonicalForm & lcF, const CanonicalForm & lcG, int degF, int degG ); |
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26 | |
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27 | static modpk enlargeBound ( const CanonicalForm & F, const CanonicalForm & Lb, const CanonicalForm & Db, const modpk & pk ); |
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28 | |
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29 | CanonicalForm |
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30 | ezgcd ( const CanonicalForm & FF, const CanonicalForm & GG ) |
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31 | { |
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32 | REvaluation b; |
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33 | return ezgcd( FF, GG, b, false ); |
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34 | } |
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35 | |
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36 | static CanonicalForm |
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37 | ezgcd ( const CanonicalForm & FF, const CanonicalForm & GG, REvaluation & b, bool internal ) |
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38 | { |
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39 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, lcD; |
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40 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
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41 | int degF, degG, delta, t; |
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42 | REvaluation bt; |
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43 | bool gcdfound = false; |
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44 | Variable x = Variable(1); |
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45 | modpk bound; |
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46 | |
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47 | DEBINCLEVEL( cerr, "ezgcd" ); |
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48 | DEBOUTLN( cerr, "FF = " << FF ); |
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49 | DEBOUTLN( cerr, "GG = " << GG ); |
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50 | f = content( FF, x ); g = content( GG, x ); d = gcd( f, g ); |
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51 | DEBOUTLN( cerr, "f = " << f ); |
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52 | DEBOUTLN( cerr, "g = " << g ); |
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53 | F = FF / f; G = GG / g; |
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54 | if ( F.isUnivariate() && G.isUnivariate() ) |
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55 | { |
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56 | DEBDECLEVEL( cerr, "ezgcd" ); |
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57 | if(F.mvar()==G.mvar()) |
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58 | d*=gcd(F,G); |
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59 | return d; |
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60 | } |
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61 | else if ( gcd_test_one( F, G, false ) ) |
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62 | { |
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63 | DEBDECLEVEL( cerr, "ezgcd" ); |
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64 | return d; |
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65 | } |
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66 | lcF = LC( F, x ); lcG = LC( G, x ); |
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67 | lcD = gcd( lcF, lcG ); |
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68 | delta = 0; |
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69 | degF = degree( F, x ); degG = degree( G, x ); |
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70 | t = tmax( F.level(), G.level() ); |
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71 | bound = findBound( F, G, lcF, lcG, degF, degG ); |
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72 | if ( ! internal ) |
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73 | b = REvaluation( 2, t, IntRandom( 25 ) ); |
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74 | while ( ! gcdfound ) { |
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75 | /// ---> A2 |
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76 | DEBOUTLN( cerr, "search for evaluation, delta = " << delta ); |
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77 | DEBOUTLN( cerr, "F = " << F ); |
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78 | DEBOUTLN( cerr, "G = " << G ); |
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79 | findeval( F, G, Fb, Gb, Db, b, delta, degF, degG ); |
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80 | DEBOUTLN( cerr, "found evaluation b = " << b ); |
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81 | DEBOUTLN( cerr, "F(b) = " << Fb ); |
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82 | DEBOUTLN( cerr, "G(b) = " << Gb ); |
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83 | DEBOUTLN( cerr, "D(b) = " << Db ); |
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84 | delta = degree( Db ); |
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85 | /// ---> A3 |
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86 | if ( delta == 0 ) |
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87 | { |
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88 | DEBDECLEVEL( cerr, "ezgcd" ); |
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89 | return d; |
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90 | } |
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91 | /// ---> A4 |
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92 | //deltaold = delta; |
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93 | while ( 1 ) { |
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94 | bt = b; |
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95 | findeval( F, G, Fbt, Gbt, Dbt, bt, delta + 1, degF, degG ); |
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96 | int dd=degree( Dbt ); |
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97 | if ( dd /*degree( Dbt )*/ == 0 ) |
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98 | { |
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99 | DEBDECLEVEL( cerr, "ezgcd" ); |
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100 | return d; |
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101 | } |
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102 | if ( dd /*degree( Dbt )*/ == delta ) |
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103 | break; |
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104 | else if ( dd /*degree( Dbt )*/ < delta ) { |
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105 | delta = dd /*degree( Dbt )*/; |
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106 | b = bt; |
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107 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
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108 | } |
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109 | } |
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110 | DEBOUTLN( cerr, "now after A4, delta = " << delta ); |
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111 | /// ---> A5 |
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112 | if ( degF <= degG && delta == degF && fdivides( F, G ) ) |
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113 | { |
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114 | DEBDECLEVEL( cerr, "ezgcd" ); |
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115 | return d*F; |
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116 | } |
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117 | if ( degG < degF && delta == degG && fdivides( G, F ) ) |
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118 | { |
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119 | DEBDECLEVEL( cerr, "ezgcd" ); |
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120 | return d*G; |
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121 | } |
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122 | if ( delta != degF && delta != degG ) { |
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123 | bool B_is_F; |
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124 | /// ---> A6 |
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125 | CanonicalForm xxx; |
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126 | //if ( gcd( (DD[1] = Fb / Db), Db ) == 1 ) { |
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127 | DD[1] = Fb / Db; |
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128 | xxx= gcd( DD[1], Db ); |
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129 | DEBOUTLN( cerr, "gcd((Fb/Db),Db) = " << xxx ); |
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130 | DEBOUTLN( cerr, "Fb/Db = " << DD[1] ); |
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131 | DEBOUTLN( cerr, "Db = " << Db ); |
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132 | if (xxx.inCoeffDomain()) { |
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133 | B = F; |
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134 | DD[2] = Db; |
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135 | lcDD[1] = lcF; |
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136 | lcDD[2] = lcF; |
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137 | B *= lcF; |
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138 | B_is_F=true; |
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139 | } |
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140 | //else if ( gcd( (DD[1] = Gb / Db), Db ) == 1 ) { |
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141 | else |
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142 | { |
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143 | DD[1] = Gb / Db; |
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144 | xxx=gcd( DD[1], Db ); |
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145 | DEBOUTLN( cerr, "gcd((Gb/Db),Db) = " << xxx ); |
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146 | DEBOUTLN( cerr, "Gb/Db = " << DD[1] ); |
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147 | DEBOUTLN( cerr, "Db = " << Db ); |
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148 | if (xxx.inCoeffDomain()) |
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149 | { |
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150 | B = G; |
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151 | DD[2] = Db; |
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152 | lcDD[1] = lcG; |
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153 | lcDD[2] = lcG; |
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154 | B *= lcG; |
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155 | B_is_F=false; |
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156 | } |
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157 | else |
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158 | { |
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159 | #ifdef DEBUGOUTPUT |
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160 | CanonicalForm dummyres = d * ezgcd_specialcase( F, G, b, bound ); |
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161 | DEBDECLEVEL( cerr, "ezgcd" ); |
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162 | return dummyres; |
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163 | #else |
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164 | return d * ezgcd_specialcase( F, G, b, bound ); |
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165 | #endif |
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166 | } |
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167 | } |
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168 | /// ---> A7 |
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169 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
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170 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
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171 | bound = enlargeBound( B, DD[2], DD[1], bound ); |
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172 | DEBOUTLN( cerr, "(hensel) B = " << B ); |
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173 | DEBOUTLN( cerr, "(hensel) lcB = " << LC( B, Variable(1) ) ); |
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174 | DEBOUTLN( cerr, "(hensel) b(B) = " << b(B) ); |
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175 | DEBOUTLN( cerr, "(hensel) DD = " << DD ); |
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176 | DEBOUTLN( cerr, "(hensel) lcDD = " << lcDD ); |
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177 | gcdfound = Hensel( B, DD, lcDD, b, bound, x ); |
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178 | DEBOUTLN( cerr, "(hensel finished) DD = " << DD ); |
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179 | |
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180 | if (gcdfound) |
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181 | { |
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182 | CanonicalForm xxx=content(DD[2],Variable(1)); |
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183 | CanonicalForm cand=DD[2] / xxx; //content(DD[2],Variable(1)); |
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184 | #if 0 |
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185 | gcdfound= fdivides(cand,G) && fdivides(cand,F); |
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186 | #else |
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187 | if (B_is_F /*B==F*lcF*/) |
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188 | { |
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189 | DEBOUTLN( cerr, "(test) G: "<<G<<" % gcd:"<<cand<<" -> " << G%cand ); |
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190 | gcdfound= fdivides(cand,G); |
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191 | } |
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192 | else |
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193 | { |
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194 | DEBOUTLN( cerr, "(test) F: "<<F<<" % gcd:"<<cand<<" -> " << F%cand); |
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195 | gcdfound= fdivides(cand,F); |
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196 | } |
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197 | #endif |
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198 | } |
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199 | /// ---> A8 (gcdfound) |
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200 | } |
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201 | delta++; |
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202 | } |
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203 | /// ---> A9 |
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204 | DEBDECLEVEL( cerr, "ezgcd" ); |
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205 | return d * DD[2] / content(DD[2],Variable(1)); |
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206 | } |
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207 | |
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208 | static CanonicalForm |
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209 | ezgcd_specialcase ( const CanonicalForm & F, const CanonicalForm & G, REvaluation & b, const modpk & bound ) |
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210 | { |
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211 | CanonicalForm d; |
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212 | #if 1 |
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213 | Off(SW_USE_EZGCD); |
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214 | //bool ntl0=isOn(SW_USE_NTL_GCD_0); |
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215 | //Off(SW_USE_NTL_GCD_0); |
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216 | //bool ntlp=isOn(SW_USE_NTL_GCD_P); |
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217 | //Off(SW_USE_NTL_GCD_P); |
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218 | d=gcd( F, G ); |
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219 | //if (ntl0) On(SW_USE_NTL_GCD_0); |
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220 | //if (ntlp) On(SW_USE_NTL_GCD_P); |
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221 | On(SW_USE_EZGCD); |
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222 | return d; |
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223 | #else |
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224 | DEBOUTLN( cerr, "ezgcd: special case" ); |
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225 | CanonicalForm Ft, Gt, L, LL, Fb, Gb, Db, Lb, D, Ds, Dt; |
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226 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
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227 | Variable x = Variable( 1 ); |
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228 | bool gcdfound; |
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229 | |
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230 | Dt = 1; |
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231 | /// ---> S1 |
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232 | DEBOUTLN( cerr, "ezgcdspec: (S1)" ); |
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233 | Ft = ezgcd( F, F.deriv( x ) ); |
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234 | if ( Ft.isOne() ) |
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235 | { |
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236 | // In this case F is squarefree and we came here by bad chance |
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237 | // (means: bad evaluation point). Try again with another |
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238 | // evaluation point. Bug fix (?) by JS. The bad example was |
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239 | // gcd.debug -ocr /+USE_EZGCD/@12/CB \ |
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240 | // '(16*B^8-208*B^6*C+927*B^4*C^2-1512*B^2*C^3+432*C^4)' \ |
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241 | // '(4*B^7*C^2-50*B^5*C^3+208*B^3*C^4-288*B*C^5)' |
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242 | b.nextpoint(); |
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243 | return ezgcd( F, G, b, true ); |
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244 | } |
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245 | |
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246 | DEBOUTLN( cerr, "ezgcdspec: (S1) done, Ft = " << Ft ); |
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247 | L = F / Ft; |
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248 | /// ---> S2 |
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249 | DEBOUTLN( cerr, "ezgcdspec: (S2)" ); |
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250 | |
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251 | L = ezgcd( L, G, b, true ); |
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252 | DEBOUTLN( cerr, "ezgcdspec: (S2) done, Ds = " << Ds ); |
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253 | Gt = G / L; |
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254 | Ds = L; Dt = L; |
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255 | Lb = b( L ); Gb = b( Gt ); Fb = b( Ft ); |
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256 | d = gcd( LC( L, x ), gcd( LC( Ft, x ), LC( Gt, x ) ) ); |
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257 | while ( true ) { |
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258 | /// ---> S3 |
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259 | DEBOUTLN( cerr, "ezgcdspec: (S3)" ); |
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260 | DEBOUTLN( cerr, "ezgcdspec: Fb = " << Fb ); |
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261 | DEBOUTLN( cerr, "ezgcdspec: Gb = " << Gb ); |
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262 | DD[1] = gcd( Lb, gcd( Fb, Gb ) ); |
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263 | /// ---> S4 |
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264 | DEBOUTLN( cerr, "ezgcdspec: (S4)" ); |
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265 | if ( degree( DD[1] ) == 0 ) |
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266 | return Ds; |
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267 | /// ---> S5 |
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268 | DEBOUTLN( cerr, "ezgcdspec: (S5)" ); |
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269 | DEBOUTLN( cerr, "ezgcdspec: Lb = " << Lb ); |
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270 | DEBOUTLN( cerr, "ezgcdspec: Db = " << DD[1] ); |
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271 | Db = DD[1]; |
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272 | if ( ! (DD[2] = Lb/DD[1]).isOne() ) { |
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273 | DEBOUTLN( cerr, "ezgcdspec: (S55)" ); |
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274 | lcDD[2] = LC( L, x ); |
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275 | lcDD[1] = d; |
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276 | DD[1] = ( DD[1] * b( d ) ) / lc( DD[1] ); |
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277 | DD[2] = ( DD[2] * b( lcDD[2] ) ) / lc( DD[2] ); |
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278 | LL = L * d; |
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279 | modpk newbound = enlargeBound( LL, DD[2], DD[1], bound ); |
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280 | DEBOUTLN( cerr, "ezgcdspec: begin with lift." ); |
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281 | DEBOUTLN( cerr, "ezgcdspec: B = " << LL ); |
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282 | DEBOUTLN( cerr, "ezgcdspec: DD = " << DD ); |
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283 | DEBOUTLN( cerr, "ezgcdspec: lcDD = " << lcDD ); |
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284 | DEBOUTLN( cerr, "ezgcdspec: b = " << b ); |
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285 | DEBOUTLN( cerr, "ezgcdspec: bound = " << bound.getpk() ); |
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286 | DEBOUTLN( cerr, "ezgcdspec: lc(B) = " << LC( LL, x ) ); |
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287 | DEBOUTLN( cerr, "ezgcdspec: test = " << b( LL ) - DD[1] * DD[2] ); |
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288 | gcdfound = Hensel( LL, DD, lcDD, b, newbound, x ); |
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289 | ASSERT( gcdfound, "fatal error in algorithm" ); |
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290 | Dt = pp( DD[1] ); |
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291 | } |
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292 | DEBOUTLN( cerr, "ezgcdspec: (S7)" ); |
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293 | Ds = Ds * Dt; |
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294 | Fb = Fb / Db; |
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295 | Gb = Gb / Db; |
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296 | } |
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297 | // this point is never reached, but to avoid compiler warnings let's return a value |
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298 | return 0; |
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299 | #endif |
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300 | } |
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301 | |
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302 | static void |
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303 | findeval( const CanonicalForm & F, const CanonicalForm & G, CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, REvaluation & b, int delta, int degF, int degG ) |
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304 | { |
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305 | bool ok; |
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306 | if ( delta != 0 ) |
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307 | b.nextpoint(); |
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308 | DEBOUTLN( cerr, "ezgcd: (findeval) F = " << F <<", G="<< G); |
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309 | DEBOUTLN( cerr, "ezgcd: (findeval) degF = " << degF << ", degG="<<degG ); |
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310 | do { |
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311 | DEBOUTLN( cerr, "ezgcd: (findeval) b = " << b ); |
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312 | Fb = b( F ); |
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313 | ok = degree( Fb ) == degF; |
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314 | if ( ok ) { |
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315 | Gb = b( G ); |
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316 | ok = degree( Gb ) == degG; |
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317 | } |
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318 | |
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319 | if ( ok ) |
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320 | { |
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321 | Db = gcd( Fb, Gb ); |
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322 | if ( delta > 0 ) |
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323 | ok = degree( Db ) < delta; |
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324 | } |
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325 | if ( ! ok ) |
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326 | { |
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327 | b.nextpoint(); |
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328 | } |
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329 | } while ( ! ok ); |
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330 | } |
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331 | |
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332 | static modpk |
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333 | enlargeBound ( const CanonicalForm & F, const CanonicalForm & Lb, const CanonicalForm & Db, const modpk & pk ) |
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334 | { |
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335 | DEBOUTLN( cerr, "ezgcd: (enlarge bound) F = " << F ); |
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336 | DEBOUTLN( cerr, "ezgcd: (enlarge bound) Lb = " << Lb ); |
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337 | DEBOUTLN( cerr, "ezgcd: (enlarge bound) Db = " << Db ); |
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338 | DEBOUTLN( cerr, "ezgcd: (enlarge bound) Lb % p = " << mod( Lb, pk.getp() ) ); |
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339 | DEBOUTLN( cerr, "ezgcd: (enlarge bound) Db % p = " << mod( Db, pk.getp() ) ); |
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340 | |
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341 | CanonicalForm limit = power( CanonicalForm(2), degree( Db ) ) * |
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342 | tmax( maxNorm( Lb ), tmax( maxNorm( Db ), maxNorm( F ) ) ); |
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343 | int p = pk.getp(); |
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344 | int k = pk.getk(); |
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345 | CanonicalForm bound = pk.getpk(); |
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346 | while ( bound < limit ) { |
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347 | k++; |
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348 | bound *= p; |
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349 | } |
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350 | k *= 2; |
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351 | DEBOUTLN( cerr, "ezgcd: (enlarge bound) newbound = " << power( CanonicalForm( p ), k ) ); |
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352 | return modpk( p, k ); |
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353 | } |
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354 | |
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355 | static modpk |
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356 | findBound ( const CanonicalForm & F, const CanonicalForm & G, const CanonicalForm & lcF, const CanonicalForm & lcG, int degF, int degG ) |
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357 | { |
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358 | CanonicalForm limit = power( CanonicalForm(2), tmin( degF, degG ) ) * |
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359 | gcd( icontent( lcF ), icontent( lcG ) ) * tmin( maxNorm( F ), maxNorm( G ) ); |
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360 | int p, i = 0; |
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361 | do { |
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362 | p = cf_getBigPrime( i ); |
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363 | i++; |
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364 | } while ( mod( lcF, p ).isZero() && mod( lcG, p ).isZero() ); |
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365 | CanonicalForm bound = p; |
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366 | i = 1; |
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367 | while ( bound < limit ) { |
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368 | i++; |
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369 | bound *= p; |
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370 | } |
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371 | return modpk( p, i ); |
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372 | } |
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