1 | #include "config.h" |
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2 | |
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3 | #include "canonicalform.h" |
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4 | #include "cf_factory.h" |
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5 | #include "cf_reval.h" |
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6 | #include "cf_util.h" |
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7 | #include "cf_iter.h" |
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8 | #include "gfops.h" |
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9 | #include "cf_map_ext.h" |
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10 | #include "templates/ftmpl_functions.h" |
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11 | |
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12 | #ifdef HAVE_NTL |
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13 | #include "NTLconvert.h" |
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14 | #endif |
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15 | |
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16 | /// Coprimality Check. f and g are assumed to have the same level. If swap is |
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17 | /// true, the main variables of f and g are swapped with Variable(1). If the |
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18 | /// result is false, d is set to the degree of the gcd of f and g evaluated at a |
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19 | /// random point in K^n-1. This gcd is a gcd of univariate polynomials. |
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20 | bool |
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21 | gcd_test_one ( const CanonicalForm & f, const CanonicalForm & g, bool swap, int & d ) |
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22 | { |
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23 | d= 0; |
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24 | int count = 0; |
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25 | // assume polys have same level; |
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26 | |
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27 | Variable v= Variable (1); |
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28 | bool algExtension= (hasFirstAlgVar (f, v) || hasFirstAlgVar (g, v)); |
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29 | CanonicalForm lcf, lcg; |
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30 | if ( swap ) |
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31 | { |
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32 | lcf = swapvar( LC( f ), Variable(1), f.mvar() ); |
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33 | lcg = swapvar( LC( g ), Variable(1), f.mvar() ); |
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34 | } |
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35 | else |
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36 | { |
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37 | lcf = LC( f, Variable(1) ); |
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38 | lcg = LC( g, Variable(1) ); |
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39 | } |
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40 | |
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41 | CanonicalForm F, G; |
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42 | if ( swap ) |
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43 | { |
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44 | F=swapvar( f, Variable(1), f.mvar() ); |
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45 | G=swapvar( g, Variable(1), g.mvar() ); |
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46 | } |
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47 | else |
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48 | { |
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49 | F = f; |
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50 | G = g; |
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51 | } |
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52 | |
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53 | #define TEST_ONE_MAX 50 |
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54 | int p= getCharacteristic(); |
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55 | bool passToGF= false; |
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56 | int k= 1; |
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57 | bool extOfExt= false; |
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58 | Variable v3; |
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59 | if (p > 0 && p < TEST_ONE_MAX && CFFactory::gettype() != GaloisFieldDomain && !algExtension) |
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60 | { |
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61 | if (p == 2) |
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62 | setCharacteristic (2, 6, 'Z'); |
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63 | else if (p == 3) |
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64 | setCharacteristic (3, 4, 'Z'); |
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65 | else if (p == 5 || p == 7) |
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66 | setCharacteristic (p, 3, 'Z'); |
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67 | else |
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68 | setCharacteristic (p, 2, 'Z'); |
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69 | passToGF= true; |
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70 | } |
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71 | else if (p > 0 && CFFactory::gettype() == GaloisFieldDomain && ipower (p , getGFDegree()) < TEST_ONE_MAX) |
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72 | { |
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73 | k= getGFDegree(); |
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74 | if (ipower (p, 2*k) > TEST_ONE_MAX) |
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75 | setCharacteristic (p, 2*k, gf_name); |
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76 | else |
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77 | setCharacteristic (p, 3*k, gf_name); |
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78 | F= GFMapUp (F, k); |
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79 | G= GFMapUp (G, k); |
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80 | lcf= GFMapUp (lcf, k); |
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81 | lcg= GFMapUp (lcg, k); |
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82 | } |
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83 | else if (p > 0 && p < TEST_ONE_MAX && algExtension) |
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84 | { |
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85 | #ifdef HAVE_NTL |
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86 | int d= degree (getMipo (v)); |
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87 | CFList source, dest; |
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88 | Variable v2; |
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89 | CanonicalForm primElem, imPrimElem; |
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90 | if (p == 2 && d < 6) |
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91 | { |
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92 | if (fac_NTL_char != 2) |
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93 | { |
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94 | fac_NTL_char= 2; |
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95 | zz_p::init (p); |
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96 | } |
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97 | bool primFail= false; |
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98 | Variable vBuf; |
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99 | primElem= primitiveElement (v, vBuf, primFail); |
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100 | ASSERT (!primFail, "failure in integer factorizer"); |
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101 | if (d < 3) |
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102 | { |
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103 | zz_pX NTLIrredpoly; |
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104 | BuildIrred (NTLIrredpoly, d*3); |
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105 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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106 | v2= rootOf (newMipo); |
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107 | } |
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108 | else |
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109 | { |
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110 | zz_pX NTLIrredpoly; |
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111 | BuildIrred (NTLIrredpoly, d*2); |
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112 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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113 | v2= rootOf (newMipo); |
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114 | } |
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115 | imPrimElem= mapPrimElem (primElem, v, v2); |
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116 | extOfExt= true; |
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117 | } |
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118 | else if ((p == 3 && d < 4) || ((p == 5 || p == 7) && d < 3)) |
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119 | { |
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120 | if (fac_NTL_char != p) |
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121 | { |
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122 | fac_NTL_char= p; |
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123 | zz_p::init (p); |
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124 | } |
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125 | bool primFail= false; |
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126 | Variable vBuf; |
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127 | primElem= primitiveElement (v, vBuf, primFail); |
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128 | ASSERT (!primFail, "failure in integer factorizer"); |
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129 | zz_pX NTLIrredpoly; |
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130 | BuildIrred (NTLIrredpoly, d*2); |
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131 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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132 | v2= rootOf (newMipo); |
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133 | imPrimElem= mapPrimElem (primElem, v, v2); |
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134 | extOfExt= true; |
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135 | } |
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136 | if (extOfExt) |
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137 | { |
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138 | v3= v; |
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139 | F= mapUp (F, v, v2, primElem, imPrimElem, source, dest); |
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140 | G= mapUp (G, v, v2, primElem, imPrimElem, source, dest); |
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141 | lcf= mapUp (lcf, v, v2, primElem, imPrimElem, source, dest); |
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142 | lcg= mapUp (lcg, v, v2, primElem, imPrimElem, source, dest); |
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143 | v= v2; |
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144 | } |
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145 | #endif |
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146 | } |
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147 | |
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148 | CFRandom * sample; |
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149 | if ((!algExtension && p > 0) || p == 0) |
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150 | sample = CFRandomFactory::generate(); |
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151 | else |
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152 | sample = AlgExtRandomF (v).clone(); |
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153 | |
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154 | REvaluation e( 2, tmax( f.level(), g.level() ), *sample ); |
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155 | delete sample; |
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156 | |
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157 | if (passToGF) |
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158 | { |
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159 | lcf= lcf.mapinto(); |
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160 | lcg= lcg.mapinto(); |
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161 | } |
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162 | |
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163 | CanonicalForm eval1, eval2; |
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164 | if (passToGF) |
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165 | { |
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166 | eval1= e (lcf); |
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167 | eval2= e (lcg); |
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168 | } |
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169 | else |
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170 | { |
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171 | eval1= e (lcf); |
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172 | eval2= e (lcg); |
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173 | } |
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174 | |
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175 | while ( ( eval1.isZero() || eval2.isZero() ) && count < TEST_ONE_MAX ) |
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176 | { |
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177 | e.nextpoint(); |
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178 | count++; |
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179 | eval1= e (lcf); |
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180 | eval2= e (lcg); |
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181 | } |
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182 | if ( count >= TEST_ONE_MAX ) |
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183 | { |
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184 | if (passToGF) |
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185 | setCharacteristic (p); |
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186 | if (k > 1) |
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187 | setCharacteristic (p, k, gf_name); |
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188 | if (extOfExt) |
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189 | prune1 (v3); |
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190 | return false; |
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191 | } |
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192 | |
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193 | |
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194 | if (passToGF) |
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195 | { |
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196 | F= F.mapinto(); |
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197 | G= G.mapinto(); |
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198 | eval1= e (F); |
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199 | eval2= e (G); |
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200 | } |
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201 | else |
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202 | { |
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203 | eval1= e (F); |
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204 | eval2= e (G); |
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205 | } |
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206 | |
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207 | CanonicalForm c= gcd (eval1, eval2); |
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208 | d= c.degree(); |
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209 | bool result= d < 1; |
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210 | if (d < 0) |
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211 | d= 0; |
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212 | |
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213 | if (passToGF) |
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214 | setCharacteristic (p); |
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215 | if (k > 1) |
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216 | setCharacteristic (p, k, gf_name); |
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217 | if (extOfExt) |
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218 | prune1 (v3); |
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219 | return result; |
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220 | } |
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221 | |
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222 | /** |
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223 | * same as balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
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224 | * but qh= q/2 is provided, too. |
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225 | **/ |
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226 | CanonicalForm |
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227 | balance_p ( const CanonicalForm & f, const CanonicalForm & q, const CanonicalForm & qh ) |
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228 | { |
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229 | Variable x = f.mvar(); |
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230 | CanonicalForm result = 0; |
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231 | CanonicalForm c; |
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232 | CFIterator i; |
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233 | for ( i = f; i.hasTerms(); i++ ) |
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234 | { |
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235 | c = i.coeff(); |
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236 | if ( c.inCoeffDomain()) |
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237 | { |
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238 | if ( c > qh ) |
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239 | result += power( x, i.exp() ) * (c - q); |
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240 | else |
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241 | result += power( x, i.exp() ) * c; |
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242 | } |
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243 | else |
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244 | result += power( x, i.exp() ) * balance_p(c,q,qh); |
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245 | } |
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246 | return result; |
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247 | } |
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248 | |
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249 | /** static CanonicalForm balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
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250 | * |
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251 | * balance_p() - map f from positive to symmetric representation |
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252 | * mod q. |
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253 | * |
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254 | * This makes sense for polynomials over Z only. |
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255 | * q should be an integer. |
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256 | * |
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257 | **/ |
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258 | CanonicalForm |
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259 | balance_p ( const CanonicalForm & f, const CanonicalForm & q ) |
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260 | { |
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261 | CanonicalForm qh = q / 2; |
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262 | return balance_p (f, q, qh); |
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263 | } |
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264 | |
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265 | |
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266 | /*static CanonicalForm |
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267 | balance ( const CanonicalForm & f, const CanonicalForm & q ) |
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268 | { |
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269 | Variable x = f.mvar(); |
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270 | CanonicalForm result = 0, qh = q / 2; |
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271 | CanonicalForm c; |
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272 | CFIterator i; |
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273 | for ( i = f; i.hasTerms(); i++ ) { |
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274 | c = mod( i.coeff(), q ); |
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275 | if ( c > qh ) |
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276 | result += power( x, i.exp() ) * (c - q); |
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277 | else |
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278 | result += power( x, i.exp() ) * c; |
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279 | } |
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280 | return result; |
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281 | }*/ |
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