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 "cf_assert.h" |
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7 | |
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8 | #include "cf_defs.h" |
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9 | #include "cf_random.h" |
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10 | #include "cf_util.h" |
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11 | #include "fac_cantzass.h" |
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12 | #include "fac_sqrfree.h" |
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13 | #include "gmpext.h" |
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14 | |
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15 | #include <factory/cf_gmp.h> |
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16 | |
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17 | static CanonicalForm randomPoly( int n, const Variable & x, const CFRandom & gen ); |
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18 | |
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19 | static CFFList CantorZassenhausFactorFFGF( const CanonicalForm & f, int d, int q, const CFRandom & ); |
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20 | |
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21 | static CFFList CantorZassenhausFactorExt( const CanonicalForm & g, int s, mpz_t q, const CFRandom & gen ); |
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22 | |
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23 | static CFFList distinctDegreeFactorFFGF ( const CanonicalForm & f, int q ); |
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24 | |
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25 | static CFFList distinctDegreeFactorExt ( const CanonicalForm & f, int p, int n ); |
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26 | |
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27 | // calculates f^m % d |
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28 | |
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29 | static CanonicalForm powerMod( const CanonicalForm & f, int m, const CanonicalForm & d ); |
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30 | |
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31 | // calculates f^(p^s) % d |
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32 | |
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33 | static CanonicalForm powerMod( const CanonicalForm & f, int p, int s, const CanonicalForm & d ); |
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34 | |
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35 | // calculates f^((p^s-1)/2) % d |
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36 | |
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37 | static CanonicalForm powerMod2( const CanonicalForm & f, int p, int s, const CanonicalForm & d ); |
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38 | |
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39 | static CanonicalForm powerMod2( const CanonicalForm & f, mpz_t q, int s, const CanonicalForm & d ); |
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40 | |
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41 | CFFList FpFactorizeUnivariateCZ( const CanonicalForm& f, bool issqrfree, int numext, const Variable alpha, const Variable beta ) |
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42 | { |
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43 | CFFList F, G, H, HH; |
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44 | CanonicalForm fac; |
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45 | ListIterator<CFFactor> i, j, k; |
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46 | int d, q, n = 0; |
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47 | bool galoisfield = getGFDegree() > 1; |
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48 | mpz_t qq; |
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49 | |
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50 | if ( galoisfield ) |
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51 | q = ipower( getCharacteristic(), getGFDegree() ); |
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52 | else |
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53 | q = getCharacteristic(); |
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54 | if ( numext > 0 ) { |
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55 | if ( numext == 1 ) |
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56 | n = getMipo( alpha ).degree(); |
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57 | else |
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58 | n = getMipo( alpha ).degree() * getMipo( beta ).degree(); |
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59 | mpz_init( qq ); |
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60 | mpz_ui_pow_ui ( qq, q, n ); |
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61 | } |
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62 | if ( LC( f ).isOne() ) |
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63 | if ( issqrfree ) |
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64 | F.append( CFFactor( f, 1 ) ); |
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65 | else |
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66 | F = sqrFreeFp( f ); |
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67 | else { |
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68 | if ( issqrfree ) |
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69 | F.append( CFFactor( f / LC( f ), 1 ) ); |
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70 | else |
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71 | F = sqrFreeFp( f / LC( f ) ); |
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72 | H.append( LC( f ) ); |
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73 | } |
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74 | for ( i = F; i.hasItem(); ++i ) { |
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75 | d = i.getItem().exp(); |
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76 | if ( numext > 0 ) |
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77 | G = distinctDegreeFactorExt( i.getItem().factor(), q, n ); |
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78 | else |
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79 | G = distinctDegreeFactorFFGF( i.getItem().factor(), q ); |
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80 | for ( j = G; j.hasItem(); ++j ) { |
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81 | if ( numext > 0 ) { |
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82 | if ( numext == 1 ) { |
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83 | AlgExtRandomF tmpalpha( alpha ); |
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84 | HH = CantorZassenhausFactorExt( j.getItem().factor(), j.getItem().exp(), qq, tmpalpha ); |
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85 | } |
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86 | else { |
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87 | AlgExtRandomF tmpalphabeta( alpha, beta ); |
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88 | HH = CantorZassenhausFactorExt( j.getItem().factor(), j.getItem().exp(), qq, tmpalphabeta ); |
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89 | } |
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90 | } |
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91 | else if ( galoisfield ) |
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92 | HH = CantorZassenhausFactorFFGF( j.getItem().factor(), j.getItem().exp(), q, GFRandom() ); |
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93 | else |
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94 | HH = CantorZassenhausFactorFFGF( j.getItem().factor(), j.getItem().exp(), q, FFRandom() ); |
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95 | for ( k = HH; k.hasItem(); ++k ) { |
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96 | fac = k.getItem().factor(); |
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97 | H.append( CFFactor( fac / LC( fac ), d ) ); |
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98 | } |
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99 | } |
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100 | } |
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101 | if ( numext > 0 ) |
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102 | mpz_clear( qq ); |
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103 | return H; |
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104 | } |
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105 | |
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106 | CFFList distinctDegreeFactorFFGF ( const CanonicalForm & f, int q ) |
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107 | { |
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108 | int i; |
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109 | Variable x = f.mvar(); |
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110 | CanonicalForm g = f, h, r = x; |
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111 | CFFList F; |
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112 | i = 1; |
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113 | while ( g.degree(x) > 0 && i <= g.degree(x) ) { |
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114 | r = powerMod( r, q, g ); |
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115 | h = gcd( g, r - x ); |
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116 | if ( h.degree(x) > 0 ) { |
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117 | F.append( CFFactor( h, i ) ); |
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118 | g /= h; |
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119 | } |
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120 | i++; |
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121 | } |
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122 | ASSERT( g.degree(x) == 0, "fatal fatal" ); |
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123 | return F; |
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124 | } |
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125 | |
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126 | CFFList distinctDegreeFactorExt ( const CanonicalForm & f, int p, int n ) |
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127 | { |
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128 | int i; |
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129 | Variable x = f.mvar(); |
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130 | CanonicalForm g = f, h, r = x; |
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131 | CFFList F; |
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132 | i = 1; |
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133 | while ( g.degree(x) > 0 && i <= g.degree(x) ) { |
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134 | r = powerMod( r, p, n, g ); |
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135 | h = gcd( g, r - x ); |
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136 | if ( h.degree(x) > 0 ) { |
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137 | F.append( CFFactor( h, i ) ); |
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138 | g /= h; |
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139 | } |
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140 | i++; |
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141 | } |
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142 | ASSERT( g.degree(x) == 0, "fatal fatal" ); |
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143 | return F; |
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144 | } |
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145 | |
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146 | CFFList CantorZassenhausFactorFFGF( const CanonicalForm & g, int s, int q, const CFRandom & gen ) |
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147 | { |
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148 | CanonicalForm f = g; |
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149 | CanonicalForm b, f1; |
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150 | int d, d1; |
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151 | Variable x = f.mvar(); |
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152 | |
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153 | if ( (d=f.degree(x)) == s ) |
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154 | return CFFactor( f, 1 ); |
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155 | else while ( 1 ) { |
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156 | b = randomPoly( d, x, gen ); |
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157 | f1 = gcd( b, f ); |
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158 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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159 | CFFList firstFactor = CantorZassenhausFactorFFGF( f1, s, q, gen ); |
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160 | CFFList secondFactor = CantorZassenhausFactorFFGF( f/f1, s, q, gen ); |
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161 | return Union( firstFactor, secondFactor ); |
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162 | } else { |
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163 | f1 = gcd( f, powerMod2( b, q, s, f ) - 1 ); |
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164 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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165 | CFFList firstFactor = CantorZassenhausFactorFFGF( f1, s, q, gen ); |
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166 | CFFList secondFactor = CantorZassenhausFactorFFGF( f/f1, s, q, gen ); |
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167 | return Union( firstFactor, secondFactor ); |
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168 | } |
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169 | } |
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170 | } |
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171 | } |
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172 | |
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173 | CFFList CantorZassenhausFactorExt( const CanonicalForm & g, int s, mpz_t q, const CFRandom & gen ) |
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174 | { |
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175 | CanonicalForm f = g; |
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176 | CanonicalForm b, f1; |
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177 | int d, d1; |
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178 | Variable x = f.mvar(); |
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179 | |
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180 | if ( (d=f.degree(x)) == s ) |
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181 | return CFFactor( f, 1 ); |
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182 | else while ( 1 ) { |
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183 | b = randomPoly( d, x, gen ); |
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184 | f1 = gcd( b, f ); |
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185 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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186 | CFFList firstFactor = CantorZassenhausFactorExt( f1, s, q, gen ); |
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187 | CFFList secondFactor = CantorZassenhausFactorExt( f/f1, s, q, gen ); |
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188 | return Union( firstFactor, secondFactor ); |
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189 | } else { |
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190 | f1 = gcd( f, powerMod2( b, q, s, f ) - 1 ); |
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191 | if ( (d1 = f1.degree(x)) > 0 && d1 < d ) { |
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192 | CFFList firstFactor = CantorZassenhausFactorExt( f1, s, q, gen ); |
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193 | CFFList secondFactor = CantorZassenhausFactorExt( f/f1, s, q, gen ); |
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194 | return Union( firstFactor, secondFactor ); |
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195 | } |
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196 | } |
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197 | } |
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198 | } |
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199 | |
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200 | CanonicalForm randomPoly( int d, const Variable & x, const CFRandom & g ) |
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201 | { |
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202 | CanonicalForm result = 0; |
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203 | for ( int i = 0; i < d; i++ ) |
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204 | result += power( x, i ) * g.generate(); |
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205 | result += power( x, d ); |
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206 | return result; |
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207 | } |
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208 | |
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209 | CanonicalForm powerMod( const CanonicalForm & f, int m, const CanonicalForm & d ) |
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210 | { |
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211 | CanonicalForm prod = 1; |
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212 | CanonicalForm b = f % d; |
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213 | |
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214 | while ( m != 0 ) { |
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215 | if ( m % 2 != 0 ) |
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216 | prod = (prod * b) % d; |
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217 | m /= 2; |
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218 | if ( m != 0 ) |
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219 | b = (b * b) % d; |
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220 | } |
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221 | return prod; |
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222 | } |
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223 | |
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224 | CanonicalForm powerMod( const CanonicalForm & f, int p, int s, const CanonicalForm & d ) |
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225 | { |
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226 | CanonicalForm prod = 1; |
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227 | CanonicalForm b = f % d; |
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228 | int odd; |
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229 | |
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230 | mpz_t m; |
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231 | |
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232 | mpz_init( m ); |
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233 | mpz_ui_pow_ui ( m, p, s ); |
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234 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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235 | { |
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236 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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237 | if ( odd != 0 ) |
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238 | prod = (prod * b) % d; |
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239 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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240 | b = (b*b) % d; |
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241 | } |
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242 | mpz_clear( m ); |
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243 | return prod; |
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244 | } |
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245 | |
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246 | CanonicalForm powerMod2( const CanonicalForm & f, int p, int s, const CanonicalForm & d ) |
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247 | { |
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248 | CanonicalForm prod = 1; |
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249 | CanonicalForm b = f % d; |
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250 | int odd; |
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251 | |
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252 | mpz_t m; |
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253 | |
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254 | mpz_init( m ); |
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255 | mpz_ui_pow_ui ( m, p, s ); |
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256 | mpz_sub_ui( m, m, 1 ); |
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257 | mpz_fdiv_q_ui( m, m, 2 ); |
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258 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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259 | { |
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260 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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261 | if ( odd != 0 ) |
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262 | prod = (prod * b) % d; |
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263 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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264 | b = (b*b) % d; |
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265 | } |
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266 | mpz_clear( m ); |
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267 | return prod; |
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268 | } |
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269 | |
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270 | CanonicalForm powerMod2( const CanonicalForm & f, mpz_t q, int s, const CanonicalForm & d ) |
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271 | { |
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272 | CanonicalForm prod = 1; |
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273 | CanonicalForm b = f % d; |
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274 | int odd; |
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275 | |
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276 | mpz_t m; |
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277 | |
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278 | mpz_init( m ); |
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279 | mpz_pow_ui( m, q, s ); |
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280 | mpz_sub_ui( m, m, 1 ); |
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281 | mpz_fdiv_q_ui( m, m, 2 ); |
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282 | while ( mpz_cmp_si( m, 0 ) != 0 ) |
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283 | { |
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284 | odd = mpz_fdiv_q_ui( m, m, 2 ); |
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285 | if ( odd != 0 ) |
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286 | prod = (prod * b) % d; |
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287 | if ( mpz_cmp_si( m, 0 ) != 0 ) |
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288 | b = (b*b) % d; |
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289 | } |
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290 | mpz_clear( m ); |
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291 | return prod; |
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292 | } |
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