1 | // -*- c++ -*- |
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2 | //***************************************************************************** |
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3 | /** @file cf_gcd_smallp.cc |
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4 | * |
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5 | * @author Martin Lee |
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6 | * @date 22.10.2009 |
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7 | * |
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8 | * This file implements the GCD of two polynomials over \f$ F_{p} \f$ , |
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9 | * \f$ F_{p}(\alpha ) \f$ or GF based on Alg. 7.2. as described in "Algorithms |
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10 | * for Computer Algebra" by Geddes, Czapor, Labahn |
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11 | * |
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12 | * @par Copyright: |
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13 | * (c) by The SINGULAR Team, see LICENSE file |
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14 | * |
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15 | **/ |
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16 | //***************************************************************************** |
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17 | |
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18 | |
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19 | #include "config.h" |
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20 | |
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21 | |
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22 | #include "cf_assert.h" |
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23 | #include "debug.h" |
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24 | #include "timing.h" |
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25 | |
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26 | #include "canonicalform.h" |
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27 | #include "cfGcdAlgExt.h" |
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28 | #include "cf_map.h" |
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29 | #include "cf_util.h" |
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30 | #include "templates/ftmpl_functions.h" |
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31 | #include "cf_random.h" |
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32 | #include "cf_reval.h" |
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33 | #include "facHensel.h" |
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34 | #include "cf_iter.h" |
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35 | #include "cfNewtonPolygon.h" |
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36 | #include "cf_algorithm.h" |
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37 | #include "cf_primes.h" |
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38 | |
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39 | // iinline helper functions: |
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40 | #include "cf_map_ext.h" |
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41 | |
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42 | #ifdef HAVE_NTL |
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43 | #include <NTLconvert.h> |
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44 | #endif |
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45 | |
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46 | #ifdef HAVE_FLINT |
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47 | #include "FLINTconvert.h" |
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48 | #endif |
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49 | |
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50 | #include "cf_gcd_smallp.h" |
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51 | |
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52 | TIMING_DEFINE_PRINT(gcd_recursion) |
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53 | TIMING_DEFINE_PRINT(newton_interpolation) |
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54 | TIMING_DEFINE_PRINT(termination_test) |
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55 | TIMING_DEFINE_PRINT(ez_p_compress) |
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56 | TIMING_DEFINE_PRINT(ez_p_hensel_lift) |
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57 | TIMING_DEFINE_PRINT(ez_p_eval) |
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58 | TIMING_DEFINE_PRINT(ez_p_content) |
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59 | |
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60 | bool |
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61 | terminationTest (const CanonicalForm& F, const CanonicalForm& G, |
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62 | const CanonicalForm& coF, const CanonicalForm& coG, |
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63 | const CanonicalForm& cand) |
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64 | { |
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65 | CanonicalForm LCCand= abs (LC (cand)); |
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66 | if (LCCand*abs (LC (coF)) == abs (LC (F))) |
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67 | { |
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68 | if (LCCand*abs (LC (coG)) == abs (LC (G))) |
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69 | { |
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70 | if (abs (cand)*abs (coF) == abs (F)) |
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71 | { |
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72 | if (abs (cand)*abs (coG) == abs (G)) |
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73 | return true; |
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74 | } |
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75 | return false; |
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76 | } |
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77 | return false; |
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78 | } |
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79 | return false; |
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80 | } |
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81 | |
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82 | #ifdef HAVE_NTL |
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83 | |
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84 | static const double log2exp= 1.442695041; |
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85 | |
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86 | /// compressing two polynomials F and G, M is used for compressing, |
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87 | /// N to reverse the compression |
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88 | int myCompress (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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89 | CFMap & N, bool topLevel) |
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90 | { |
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91 | int n= tmax (F.level(), G.level()); |
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92 | int * degsf= new int [n + 1]; |
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93 | int * degsg= new int [n + 1]; |
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94 | |
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95 | for (int i = 0; i <= n; i++) |
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96 | degsf[i]= degsg[i]= 0; |
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97 | |
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98 | degsf= degrees (F, degsf); |
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99 | degsg= degrees (G, degsg); |
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100 | |
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101 | int both_non_zero= 0; |
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102 | int f_zero= 0; |
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103 | int g_zero= 0; |
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104 | int both_zero= 0; |
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105 | |
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106 | if (topLevel) |
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107 | { |
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108 | for (int i= 1; i <= n; i++) |
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109 | { |
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110 | if (degsf[i] != 0 && degsg[i] != 0) |
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111 | { |
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112 | both_non_zero++; |
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113 | continue; |
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114 | } |
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115 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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116 | { |
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117 | f_zero++; |
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118 | continue; |
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119 | } |
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120 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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121 | { |
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122 | g_zero++; |
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123 | continue; |
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124 | } |
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125 | } |
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126 | |
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127 | if (both_non_zero == 0) |
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128 | { |
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129 | delete [] degsf; |
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130 | delete [] degsg; |
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131 | return 0; |
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132 | } |
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133 | |
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134 | // map Variables which do not occur in both polynomials to higher levels |
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135 | int k= 1; |
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136 | int l= 1; |
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137 | for (int i= 1; i <= n; i++) |
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138 | { |
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139 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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140 | { |
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141 | if (k + both_non_zero != i) |
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142 | { |
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143 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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144 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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145 | } |
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146 | k++; |
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147 | } |
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148 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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149 | { |
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150 | if (l + g_zero + both_non_zero != i) |
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151 | { |
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152 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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153 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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154 | } |
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155 | l++; |
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156 | } |
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157 | } |
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158 | |
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159 | // sort Variables x_{i} in increasing order of |
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160 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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161 | int m= tmax (F.level(), G.level()); |
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162 | int min_max_deg; |
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163 | k= both_non_zero; |
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164 | l= 0; |
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165 | int i= 1; |
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166 | while (k > 0) |
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167 | { |
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168 | if (degsf [i] != 0 && degsg [i] != 0) |
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169 | min_max_deg= tmax (degsf[i], degsg[i]); |
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170 | else |
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171 | min_max_deg= 0; |
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172 | while (min_max_deg == 0) |
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173 | { |
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174 | i++; |
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175 | if (degsf [i] != 0 && degsg [i] != 0) |
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176 | min_max_deg= tmax (degsf[i], degsg[i]); |
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177 | else |
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178 | min_max_deg= 0; |
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179 | } |
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180 | for (int j= i + 1; j <= m; j++) |
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181 | { |
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182 | if (degsf[j] != 0 && degsg [j] != 0 && |
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183 | tmax (degsf[j],degsg[j]) <= min_max_deg) |
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184 | { |
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185 | min_max_deg= tmax (degsf[j], degsg[j]); |
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186 | l= j; |
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187 | } |
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188 | } |
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189 | if (l != 0) |
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190 | { |
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191 | if (l != k) |
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192 | { |
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193 | M.newpair (Variable (l), Variable(k)); |
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194 | N.newpair (Variable (k), Variable(l)); |
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195 | degsf[l]= 0; |
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196 | degsg[l]= 0; |
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197 | l= 0; |
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198 | } |
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199 | else |
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200 | { |
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201 | degsf[l]= 0; |
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202 | degsg[l]= 0; |
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203 | l= 0; |
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204 | } |
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205 | } |
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206 | else if (l == 0) |
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207 | { |
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208 | if (i != k) |
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209 | { |
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210 | M.newpair (Variable (i), Variable (k)); |
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211 | N.newpair (Variable (k), Variable (i)); |
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212 | degsf[i]= 0; |
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213 | degsg[i]= 0; |
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214 | } |
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215 | else |
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216 | { |
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217 | degsf[i]= 0; |
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218 | degsg[i]= 0; |
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219 | } |
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220 | i++; |
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221 | } |
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222 | k--; |
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223 | } |
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224 | } |
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225 | else |
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226 | { |
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227 | //arrange Variables such that no gaps occur |
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228 | for (int i= 1; i <= n; i++) |
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229 | { |
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230 | if (degsf[i] == 0 && degsg[i] == 0) |
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231 | { |
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232 | both_zero++; |
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233 | continue; |
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234 | } |
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235 | else |
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236 | { |
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237 | if (both_zero != 0) |
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238 | { |
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239 | M.newpair (Variable (i), Variable (i - both_zero)); |
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240 | N.newpair (Variable (i - both_zero), Variable (i)); |
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241 | } |
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242 | } |
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243 | } |
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244 | } |
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245 | |
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246 | delete [] degsf; |
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247 | delete [] degsg; |
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248 | |
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249 | return 1; |
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250 | } |
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251 | |
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252 | static inline CanonicalForm |
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253 | uni_content (const CanonicalForm & F); |
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254 | |
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255 | CanonicalForm |
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256 | uni_content (const CanonicalForm& F, const Variable& x) |
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257 | { |
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258 | if (F.inCoeffDomain()) |
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259 | return F.genOne(); |
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260 | if (F.level() == x.level() && F.isUnivariate()) |
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261 | return F; |
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262 | if (F.level() != x.level() && F.isUnivariate()) |
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263 | return F.genOne(); |
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264 | |
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265 | if (x.level() != 1) |
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266 | { |
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267 | CanonicalForm f= swapvar (F, x, Variable (1)); |
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268 | CanonicalForm result= uni_content (f); |
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269 | return swapvar (result, x, Variable (1)); |
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270 | } |
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271 | else |
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272 | return uni_content (F); |
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273 | } |
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274 | |
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275 | /// compute the content of F, where F is considered as an element of |
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276 | /// \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$ |
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277 | static inline CanonicalForm |
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278 | uni_content (const CanonicalForm & F) |
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279 | { |
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280 | if (F.inBaseDomain()) |
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281 | return F.genOne(); |
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282 | if (F.level() == 1 && F.isUnivariate()) |
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283 | return F; |
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284 | if (F.level() != 1 && F.isUnivariate()) |
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285 | return F.genOne(); |
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286 | if (degree (F,1) == 0) return F.genOne(); |
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287 | |
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288 | int l= F.level(); |
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289 | if (l == 2) |
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290 | return content(F); |
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291 | else |
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292 | { |
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293 | CanonicalForm pol, c = 0; |
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294 | CFIterator i = F; |
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295 | for (; i.hasTerms(); i++) |
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296 | { |
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297 | pol= i.coeff(); |
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298 | pol= uni_content (pol); |
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299 | c= gcd (c, pol); |
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300 | if (c.isOne()) |
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301 | return c; |
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302 | } |
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303 | return c; |
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304 | } |
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305 | } |
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306 | |
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307 | CanonicalForm |
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308 | extractContents (const CanonicalForm& F, const CanonicalForm& G, |
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309 | CanonicalForm& contentF, CanonicalForm& contentG, |
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310 | CanonicalForm& ppF, CanonicalForm& ppG, const int d) |
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311 | { |
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312 | CanonicalForm uniContentF, uniContentG, gcdcFcG; |
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313 | contentF= 1; |
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314 | contentG= 1; |
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315 | ppF= F; |
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316 | ppG= G; |
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317 | CanonicalForm result= 1; |
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318 | for (int i= 1; i <= d; i++) |
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319 | { |
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320 | uniContentF= uni_content (F, Variable (i)); |
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321 | uniContentG= uni_content (G, Variable (i)); |
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322 | gcdcFcG= gcd (uniContentF, uniContentG); |
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323 | contentF *= uniContentF; |
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324 | contentG *= uniContentG; |
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325 | ppF /= uniContentF; |
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326 | ppG /= uniContentG; |
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327 | result *= gcdcFcG; |
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328 | } |
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329 | return result; |
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330 | } |
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331 | |
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332 | /// compute the leading coefficient of F, where F is considered as an element |
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333 | /// of \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$, order on Mon (x_{2},\ldots ,x_{n}) |
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334 | /// is dp. |
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335 | static inline |
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336 | CanonicalForm uni_lcoeff (const CanonicalForm& F) |
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337 | { |
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338 | if (F.level() > 1) |
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339 | { |
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340 | Variable x= Variable (2); |
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341 | int deg= totaldegree (F, x, F.mvar()); |
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342 | for (CFIterator i= F; i.hasTerms(); i++) |
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343 | { |
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344 | if (i.exp() + totaldegree (i.coeff(), x, i.coeff().mvar()) == deg) |
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345 | return uni_lcoeff (i.coeff()); |
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346 | } |
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347 | } |
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348 | return F; |
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349 | } |
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350 | |
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351 | /// Newton interpolation - Incremental algorithm. |
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352 | /// Given a list of values alpha_i and a list of polynomials u_i, 1 <= i <= n, |
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353 | /// computes the interpolation polynomial assuming that |
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354 | /// the polynomials in u are the results of evaluating the variabe x |
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355 | /// of the unknown polynomial at the alpha values. |
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356 | /// This incremental version receives only the values of alpha_n and u_n and |
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357 | /// the previous interpolation polynomial for points 1 <= i <= n-1, and computes |
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358 | /// the polynomial interpolating in all the points. |
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359 | /// newtonPoly must be equal to (x - alpha_1) * ... * (x - alpha_{n-1}) |
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360 | static inline CanonicalForm |
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361 | newtonInterp(const CanonicalForm & alpha, const CanonicalForm & u, |
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362 | const CanonicalForm & newtonPoly, const CanonicalForm & oldInterPoly, |
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363 | const Variable & x) |
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364 | { |
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365 | CanonicalForm interPoly; |
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366 | |
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367 | interPoly= oldInterPoly + ((u - oldInterPoly(alpha, x))/newtonPoly(alpha, x)) |
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368 | *newtonPoly; |
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369 | return interPoly; |
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370 | } |
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371 | |
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372 | /// compute a random element a of \f$ F_{p}(\alpha ) \f$ , |
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373 | /// s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns |
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374 | /// fail if there are no field elements left which have not been used before |
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375 | static inline CanonicalForm |
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376 | randomElement (const CanonicalForm & F, const Variable & alpha, CFList & list, |
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377 | bool & fail) |
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378 | { |
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379 | fail= false; |
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380 | Variable x= F.mvar(); |
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381 | AlgExtRandomF genAlgExt (alpha); |
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382 | FFRandom genFF; |
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383 | CanonicalForm random, mipo; |
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384 | mipo= getMipo (alpha); |
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385 | int p= getCharacteristic (); |
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386 | int d= degree (mipo); |
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387 | double bound= pow ((double) p, (double) d); |
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388 | do |
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389 | { |
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390 | if (list.length() == bound) |
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391 | { |
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392 | fail= true; |
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393 | break; |
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394 | } |
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395 | if (list.length() < p) |
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396 | { |
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397 | random= genFF.generate(); |
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398 | while (find (list, random)) |
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399 | random= genFF.generate(); |
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400 | } |
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401 | else |
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402 | { |
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403 | random= genAlgExt.generate(); |
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404 | while (find (list, random)) |
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405 | random= genAlgExt.generate(); |
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406 | } |
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407 | if (F (random, x) == 0) |
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408 | { |
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409 | list.append (random); |
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410 | continue; |
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411 | } |
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412 | } while (find (list, random)); |
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413 | return random; |
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414 | } |
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415 | |
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416 | static inline |
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417 | Variable chooseExtension (const Variable & alpha) |
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418 | { |
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419 | if (fac_NTL_char != getCharacteristic()) |
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420 | { |
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421 | fac_NTL_char= getCharacteristic(); |
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422 | zz_p::init (getCharacteristic()); |
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423 | } |
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424 | zz_pX NTLIrredpoly; |
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425 | int i, m; |
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426 | // extension of F_p needed |
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427 | if (alpha.level() == 1) |
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428 | { |
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429 | i= 1; |
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430 | m= 2; |
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431 | } //extension of F_p(alpha) |
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432 | if (alpha.level() != 1) |
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433 | { |
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434 | i= 4; |
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435 | m= degree (getMipo (alpha)); |
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436 | } |
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437 | BuildIrred (NTLIrredpoly, i*m); |
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438 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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439 | return rootOf (newMipo); |
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440 | } |
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441 | |
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442 | CanonicalForm |
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443 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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444 | CanonicalForm& coF, CanonicalForm& coG, |
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445 | Variable & alpha, CFList& l, bool& topLevel); |
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446 | |
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447 | CanonicalForm |
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448 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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449 | Variable & alpha, CFList& l, bool& topLevel) |
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450 | { |
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451 | CanonicalForm dummy1, dummy2; |
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452 | CanonicalForm result= GCD_Fp_extension (F, G, dummy1, dummy2, alpha, l, |
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453 | topLevel); |
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454 | return result; |
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455 | } |
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456 | |
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457 | /// GCD of F and G over \f$ F_{p}(\alpha ) \f$ , |
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458 | /// l and topLevel are only used internally, output is monic |
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459 | /// based on Alg. 7.2. as described in "Algorithms for |
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460 | /// Computer Algebra" by Geddes, Czapor, Labahn |
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461 | CanonicalForm |
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462 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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463 | CanonicalForm& coF, CanonicalForm& coG, |
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464 | Variable & alpha, CFList& l, bool& topLevel) |
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465 | { |
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466 | CanonicalForm A= F; |
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467 | CanonicalForm B= G; |
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468 | if (F.isZero() && degree(G) > 0) |
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469 | { |
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470 | coF= 0; |
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471 | coG= Lc (G); |
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472 | return G/Lc(G); |
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473 | } |
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474 | else if (G.isZero() && degree (F) > 0) |
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475 | { |
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476 | coF= Lc (F); |
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477 | coG= 0; |
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478 | return F/Lc(F); |
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479 | } |
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480 | else if (F.isZero() && G.isZero()) |
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481 | { |
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482 | coF= coG= 0; |
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483 | return F.genOne(); |
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484 | } |
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485 | if (F.inBaseDomain() || G.inBaseDomain()) |
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486 | { |
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487 | coF= F; |
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488 | coG= G; |
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489 | return F.genOne(); |
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490 | } |
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491 | if (F.isUnivariate() && fdivides(F, G, coG)) |
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492 | { |
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493 | coF= Lc (F); |
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494 | return F/Lc(F); |
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495 | } |
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496 | if (G.isUnivariate() && fdivides(G, F, coF)) |
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497 | { |
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498 | coG= Lc (G); |
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499 | return G/Lc(G); |
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500 | } |
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501 | if (F == G) |
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502 | { |
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503 | coF= coG= Lc (F); |
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504 | return F/Lc(F); |
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505 | } |
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506 | |
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507 | CFMap M,N; |
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508 | int best_level= myCompress (A, B, M, N, topLevel); |
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509 | |
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510 | if (best_level == 0) |
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511 | { |
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512 | coF= F; |
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513 | coG= G; |
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514 | return B.genOne(); |
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515 | } |
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516 | |
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517 | A= M(A); |
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518 | B= M(B); |
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519 | |
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520 | Variable x= Variable(1); |
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521 | |
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522 | //univariate case |
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523 | if (A.isUnivariate() && B.isUnivariate()) |
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524 | { |
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525 | CanonicalForm result= gcd (A, B); |
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526 | coF= N (A/result); |
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527 | coG= N (B/result); |
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528 | return N (result); |
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529 | } |
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530 | |
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531 | CanonicalForm cA, cB; // content of A and B |
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532 | CanonicalForm ppA, ppB; // primitive part of A and B |
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533 | CanonicalForm gcdcAcB; |
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534 | |
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535 | cA = uni_content (A); |
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536 | cB = uni_content (B); |
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537 | gcdcAcB= gcd (cA, cB); |
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538 | ppA= A/cA; |
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539 | ppB= B/cB; |
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540 | |
---|
541 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
542 | CanonicalForm gcdlcAlcB; |
---|
543 | |
---|
544 | lcA= uni_lcoeff (ppA); |
---|
545 | lcB= uni_lcoeff (ppB); |
---|
546 | |
---|
547 | gcdlcAlcB= gcd (lcA, lcB); |
---|
548 | |
---|
549 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
550 | |
---|
551 | if (d == 0) |
---|
552 | { |
---|
553 | coF= N (ppA*(cA/gcdcAcB)); |
---|
554 | coG= N (ppB*(cB/gcdcAcB)); |
---|
555 | return N(gcdcAcB); |
---|
556 | } |
---|
557 | |
---|
558 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
559 | if (d0 < d) |
---|
560 | d= d0; |
---|
561 | if (d == 0) |
---|
562 | { |
---|
563 | coF= N (ppA*(cA/gcdcAcB)); |
---|
564 | coG= N (ppB*(cB/gcdcAcB)); |
---|
565 | return N(gcdcAcB); |
---|
566 | } |
---|
567 | |
---|
568 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
569 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
570 | coG_m, ppCoF, ppCoG; |
---|
571 | |
---|
572 | newtonPoly= 1; |
---|
573 | m= gcdlcAlcB; |
---|
574 | G_m= 0; |
---|
575 | coF= 0; |
---|
576 | coG= 0; |
---|
577 | H= 0; |
---|
578 | bool fail= false; |
---|
579 | topLevel= false; |
---|
580 | bool inextension= false; |
---|
581 | Variable V_buf= alpha; |
---|
582 | CanonicalForm prim_elem, im_prim_elem; |
---|
583 | CFList source, dest; |
---|
584 | int bound1= degree (ppA, 1); |
---|
585 | int bound2= degree (ppB, 1); |
---|
586 | do |
---|
587 | { |
---|
588 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
589 | if (fail) |
---|
590 | { |
---|
591 | source= CFList(); |
---|
592 | dest= CFList(); |
---|
593 | |
---|
594 | Variable V_buf3= V_buf; |
---|
595 | V_buf= chooseExtension (V_buf); |
---|
596 | bool prim_fail= false; |
---|
597 | Variable V_buf2; |
---|
598 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
599 | |
---|
600 | if (V_buf3 != alpha) |
---|
601 | { |
---|
602 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
603 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
604 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
605 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
606 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
607 | source, dest); |
---|
608 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
609 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
610 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
611 | source, dest); |
---|
612 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
613 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
614 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
615 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
616 | source, dest); |
---|
617 | } |
---|
618 | |
---|
619 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
620 | if (prim_fail) |
---|
621 | ; //ERROR |
---|
622 | else |
---|
623 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
624 | |
---|
625 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
626 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
627 | inextension= true; |
---|
628 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
629 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
630 | im_prim_elem, source, dest); |
---|
631 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
632 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
633 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
634 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
635 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
636 | source, dest); |
---|
637 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
638 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
639 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
640 | source, dest); |
---|
641 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
642 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
643 | |
---|
644 | fail= false; |
---|
645 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
646 | DEBOUTLN (cerr, "fail= " << fail); |
---|
647 | CFList list; |
---|
648 | TIMING_START (gcd_recursion); |
---|
649 | G_random_element= |
---|
650 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
651 | coF_random_element, coG_random_element, V_buf, |
---|
652 | list, topLevel); |
---|
653 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
654 | "time for recursive call: "); |
---|
655 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
656 | } |
---|
657 | else |
---|
658 | { |
---|
659 | CFList list; |
---|
660 | TIMING_START (gcd_recursion); |
---|
661 | G_random_element= |
---|
662 | GCD_Fp_extension (ppA(random_element, x), ppB(random_element, x), |
---|
663 | coF_random_element, coG_random_element, V_buf, |
---|
664 | list, topLevel); |
---|
665 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
666 | "time for recursive call: "); |
---|
667 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
668 | } |
---|
669 | |
---|
670 | if (!G_random_element.inCoeffDomain()) |
---|
671 | d0= totaldegree (G_random_element, Variable(2), |
---|
672 | Variable (G_random_element.level())); |
---|
673 | else |
---|
674 | d0= 0; |
---|
675 | |
---|
676 | if (d0 == 0) |
---|
677 | { |
---|
678 | coF= N (ppA*(cA/gcdcAcB)); |
---|
679 | coG= N (ppB*(cB/gcdcAcB)); |
---|
680 | return N(gcdcAcB); |
---|
681 | } |
---|
682 | if (d0 > d) |
---|
683 | { |
---|
684 | if (!find (l, random_element)) |
---|
685 | l.append (random_element); |
---|
686 | continue; |
---|
687 | } |
---|
688 | |
---|
689 | G_random_element= |
---|
690 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
691 | * G_random_element; |
---|
692 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
693 | *coF_random_element; |
---|
694 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
695 | *coG_random_element; |
---|
696 | |
---|
697 | if (!G_random_element.inCoeffDomain()) |
---|
698 | d0= totaldegree (G_random_element, Variable(2), |
---|
699 | Variable (G_random_element.level())); |
---|
700 | else |
---|
701 | d0= 0; |
---|
702 | |
---|
703 | if (d0 < d) |
---|
704 | { |
---|
705 | m= gcdlcAlcB; |
---|
706 | newtonPoly= 1; |
---|
707 | G_m= 0; |
---|
708 | d= d0; |
---|
709 | coF_m= 0; |
---|
710 | coG_m= 0; |
---|
711 | } |
---|
712 | |
---|
713 | TIMING_START (newton_interpolation); |
---|
714 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
715 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
716 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
717 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
718 | "time for newton interpolation: "); |
---|
719 | |
---|
720 | //termination test |
---|
721 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
722 | { |
---|
723 | TIMING_START (termination_test); |
---|
724 | if (gcdlcAlcB.isOne()) |
---|
725 | cH= 1; |
---|
726 | else |
---|
727 | cH= uni_content (H); |
---|
728 | ppH= H/cH; |
---|
729 | ppH /= Lc (ppH); |
---|
730 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
731 | CanonicalForm ccoF= lcppH/Lc (lcppH); |
---|
732 | CanonicalForm ccoG= lcppH/Lc (lcppH); |
---|
733 | ppCoF= coF/ccoF; |
---|
734 | ppCoG= coG/ccoG; |
---|
735 | if (inextension) |
---|
736 | { |
---|
737 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
738 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
739 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
740 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
741 | { |
---|
742 | CFList u, v; |
---|
743 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
744 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
745 | ppCoF= mapDown (ppCoF, prim_elem, im_prim_elem, alpha, u, v); |
---|
746 | ppCoG= mapDown (ppCoG, prim_elem, im_prim_elem, alpha, u, v); |
---|
747 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
748 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
749 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
750 | TIMING_END_AND_PRINT (termination_test, |
---|
751 | "time for successful termination test Fq: "); |
---|
752 | return N(gcdcAcB*ppH); |
---|
753 | } |
---|
754 | } |
---|
755 | else if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
756 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
757 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
758 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
759 | { |
---|
760 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
761 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
762 | TIMING_END_AND_PRINT (termination_test, |
---|
763 | "time for successful termination test Fq: "); |
---|
764 | return N(gcdcAcB*ppH); |
---|
765 | } |
---|
766 | TIMING_END_AND_PRINT (termination_test, |
---|
767 | "time for unsuccessful termination test Fq: "); |
---|
768 | } |
---|
769 | |
---|
770 | G_m= H; |
---|
771 | coF_m= coF; |
---|
772 | coG_m= coG; |
---|
773 | newtonPoly= newtonPoly*(x - random_element); |
---|
774 | m= m*(x - random_element); |
---|
775 | if (!find (l, random_element)) |
---|
776 | l.append (random_element); |
---|
777 | } while (1); |
---|
778 | } |
---|
779 | |
---|
780 | /// compute a random element a of GF, s.t. F(a) \f$ \neq 0 \f$ , F is a |
---|
781 | /// univariate polynomial, returns fail if there are no field elements left |
---|
782 | /// which have not been used before |
---|
783 | static inline |
---|
784 | CanonicalForm |
---|
785 | GFRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
786 | { |
---|
787 | fail= false; |
---|
788 | Variable x= F.mvar(); |
---|
789 | GFRandom genGF; |
---|
790 | CanonicalForm random; |
---|
791 | int p= getCharacteristic(); |
---|
792 | int d= getGFDegree(); |
---|
793 | int bound= ipower (p, d); |
---|
794 | do |
---|
795 | { |
---|
796 | if (list.length() == bound) |
---|
797 | { |
---|
798 | fail= true; |
---|
799 | break; |
---|
800 | } |
---|
801 | if (list.length() < 1) |
---|
802 | random= 0; |
---|
803 | else |
---|
804 | { |
---|
805 | random= genGF.generate(); |
---|
806 | while (find (list, random)) |
---|
807 | random= genGF.generate(); |
---|
808 | } |
---|
809 | if (F (random, x) == 0) |
---|
810 | { |
---|
811 | list.append (random); |
---|
812 | continue; |
---|
813 | } |
---|
814 | } while (find (list, random)); |
---|
815 | return random; |
---|
816 | } |
---|
817 | |
---|
818 | CanonicalForm |
---|
819 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
820 | CanonicalForm& coF, CanonicalForm& coG, |
---|
821 | CFList& l, bool& topLevel); |
---|
822 | |
---|
823 | CanonicalForm |
---|
824 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, CFList& l, |
---|
825 | bool& topLevel) |
---|
826 | { |
---|
827 | CanonicalForm dummy1, dummy2; |
---|
828 | CanonicalForm result= GCD_GF (F, G, dummy1, dummy2, l, topLevel); |
---|
829 | return result; |
---|
830 | } |
---|
831 | |
---|
832 | /// GCD of F and G over GF, based on Alg. 7.2. as described in "Algorithms for |
---|
833 | /// Computer Algebra" by Geddes, Czapor, Labahn |
---|
834 | /// Usually this algorithm will be faster than GCD_Fp_extension since GF has |
---|
835 | /// faster field arithmetics, however it might fail if the input is large since |
---|
836 | /// the size of the base field is bounded by 2^16, output is monic |
---|
837 | CanonicalForm |
---|
838 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
839 | CanonicalForm& coF, CanonicalForm& coG, |
---|
840 | CFList& l, bool& topLevel) |
---|
841 | { |
---|
842 | CanonicalForm A= F; |
---|
843 | CanonicalForm B= G; |
---|
844 | if (F.isZero() && degree(G) > 0) |
---|
845 | { |
---|
846 | coF= 0; |
---|
847 | coG= Lc (G); |
---|
848 | return G/Lc(G); |
---|
849 | } |
---|
850 | else if (G.isZero() && degree (F) > 0) |
---|
851 | { |
---|
852 | coF= Lc (F); |
---|
853 | coG= 0; |
---|
854 | return F/Lc(F); |
---|
855 | } |
---|
856 | else if (F.isZero() && G.isZero()) |
---|
857 | { |
---|
858 | coF= coG= 0; |
---|
859 | return F.genOne(); |
---|
860 | } |
---|
861 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
862 | { |
---|
863 | coF= F; |
---|
864 | coG= G; |
---|
865 | return F.genOne(); |
---|
866 | } |
---|
867 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
868 | { |
---|
869 | coF= Lc (F); |
---|
870 | return F/Lc(F); |
---|
871 | } |
---|
872 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
873 | { |
---|
874 | coG= Lc (G); |
---|
875 | return G/Lc(G); |
---|
876 | } |
---|
877 | if (F == G) |
---|
878 | { |
---|
879 | coF= coG= Lc (F); |
---|
880 | return F/Lc(F); |
---|
881 | } |
---|
882 | |
---|
883 | CFMap M,N; |
---|
884 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
885 | |
---|
886 | if (best_level == 0) |
---|
887 | { |
---|
888 | coF= F; |
---|
889 | coG= G; |
---|
890 | return B.genOne(); |
---|
891 | } |
---|
892 | |
---|
893 | A= M(A); |
---|
894 | B= M(B); |
---|
895 | |
---|
896 | Variable x= Variable(1); |
---|
897 | |
---|
898 | //univariate case |
---|
899 | if (A.isUnivariate() && B.isUnivariate()) |
---|
900 | { |
---|
901 | CanonicalForm result= gcd (A, B); |
---|
902 | coF= N (A/result); |
---|
903 | coG= N (B/result); |
---|
904 | return N (result); |
---|
905 | } |
---|
906 | |
---|
907 | CanonicalForm cA, cB; // content of A and B |
---|
908 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
909 | CanonicalForm gcdcAcB; |
---|
910 | |
---|
911 | cA = uni_content (A); |
---|
912 | cB = uni_content (B); |
---|
913 | gcdcAcB= gcd (cA, cB); |
---|
914 | ppA= A/cA; |
---|
915 | ppB= B/cB; |
---|
916 | |
---|
917 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
918 | CanonicalForm gcdlcAlcB; |
---|
919 | |
---|
920 | lcA= uni_lcoeff (ppA); |
---|
921 | lcB= uni_lcoeff (ppB); |
---|
922 | |
---|
923 | gcdlcAlcB= gcd (lcA, lcB); |
---|
924 | |
---|
925 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
926 | if (d == 0) |
---|
927 | { |
---|
928 | coF= N (ppA*(cA/gcdcAcB)); |
---|
929 | coG= N (ppB*(cB/gcdcAcB)); |
---|
930 | return N(gcdcAcB); |
---|
931 | } |
---|
932 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
933 | if (d0 < d) |
---|
934 | d= d0; |
---|
935 | if (d == 0) |
---|
936 | { |
---|
937 | coF= N (ppA*(cA/gcdcAcB)); |
---|
938 | coG= N (ppB*(cB/gcdcAcB)); |
---|
939 | return N(gcdcAcB); |
---|
940 | } |
---|
941 | |
---|
942 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
943 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
944 | coG_m, ppCoF, ppCoG; |
---|
945 | |
---|
946 | newtonPoly= 1; |
---|
947 | m= gcdlcAlcB; |
---|
948 | G_m= 0; |
---|
949 | coF= 0; |
---|
950 | coG= 0; |
---|
951 | H= 0; |
---|
952 | bool fail= false; |
---|
953 | topLevel= false; |
---|
954 | bool inextension= false; |
---|
955 | int p=-1; |
---|
956 | int k= getGFDegree(); |
---|
957 | int kk; |
---|
958 | int expon; |
---|
959 | char gf_name_buf= gf_name; |
---|
960 | int bound1= degree (ppA, 1); |
---|
961 | int bound2= degree (ppB, 1); |
---|
962 | do |
---|
963 | { |
---|
964 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
965 | if (fail) |
---|
966 | { |
---|
967 | p= getCharacteristic(); |
---|
968 | expon= 2; |
---|
969 | kk= getGFDegree(); |
---|
970 | if (ipower (p, kk*expon) < (1 << 16)) |
---|
971 | setCharacteristic (p, kk*(int)expon, 'b'); |
---|
972 | else |
---|
973 | { |
---|
974 | expon= (int) floor((log ((double)((1<<16) - 1)))/(log((double)p)*kk)); |
---|
975 | ASSERT (expon >= 2, "not enough points in GCD_GF"); |
---|
976 | setCharacteristic (p, (int)(kk*expon), 'b'); |
---|
977 | } |
---|
978 | inextension= true; |
---|
979 | fail= false; |
---|
980 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
981 | i.getItem()= GFMapUp (i.getItem(), kk); |
---|
982 | m= GFMapUp (m, kk); |
---|
983 | G_m= GFMapUp (G_m, kk); |
---|
984 | newtonPoly= GFMapUp (newtonPoly, kk); |
---|
985 | coF_m= GFMapUp (coF_m, kk); |
---|
986 | coG_m= GFMapUp (coG_m, kk); |
---|
987 | ppA= GFMapUp (ppA, kk); |
---|
988 | ppB= GFMapUp (ppB, kk); |
---|
989 | gcdlcAlcB= GFMapUp (gcdlcAlcB, kk); |
---|
990 | lcA= GFMapUp (lcA, kk); |
---|
991 | lcB= GFMapUp (lcB, kk); |
---|
992 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
993 | DEBOUTLN (cerr, "fail= " << fail); |
---|
994 | CFList list; |
---|
995 | TIMING_START (gcd_recursion); |
---|
996 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
997 | coF_random_element, coG_random_element, |
---|
998 | list, topLevel); |
---|
999 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1000 | "time for recursive call: "); |
---|
1001 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1002 | } |
---|
1003 | else |
---|
1004 | { |
---|
1005 | CFList list; |
---|
1006 | TIMING_START (gcd_recursion); |
---|
1007 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
1008 | coF_random_element, coG_random_element, |
---|
1009 | list, topLevel); |
---|
1010 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1011 | "time for recursive call: "); |
---|
1012 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1013 | } |
---|
1014 | |
---|
1015 | if (!G_random_element.inCoeffDomain()) |
---|
1016 | d0= totaldegree (G_random_element, Variable(2), |
---|
1017 | Variable (G_random_element.level())); |
---|
1018 | else |
---|
1019 | d0= 0; |
---|
1020 | |
---|
1021 | if (d0 == 0) |
---|
1022 | { |
---|
1023 | if (inextension) |
---|
1024 | { |
---|
1025 | ppA= GFMapDown (ppA, k); |
---|
1026 | ppB= GFMapDown (ppB, k); |
---|
1027 | setCharacteristic (p, k, gf_name_buf); |
---|
1028 | } |
---|
1029 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1030 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1031 | return N(gcdcAcB); |
---|
1032 | } |
---|
1033 | if (d0 > d) |
---|
1034 | { |
---|
1035 | if (!find (l, random_element)) |
---|
1036 | l.append (random_element); |
---|
1037 | continue; |
---|
1038 | } |
---|
1039 | |
---|
1040 | G_random_element= |
---|
1041 | (gcdlcAlcB(random_element, x)/uni_lcoeff(G_random_element)) * |
---|
1042 | G_random_element; |
---|
1043 | |
---|
1044 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
1045 | *coF_random_element; |
---|
1046 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
1047 | *coG_random_element; |
---|
1048 | |
---|
1049 | if (!G_random_element.inCoeffDomain()) |
---|
1050 | d0= totaldegree (G_random_element, Variable(2), |
---|
1051 | Variable (G_random_element.level())); |
---|
1052 | else |
---|
1053 | d0= 0; |
---|
1054 | |
---|
1055 | if (d0 < d) |
---|
1056 | { |
---|
1057 | m= gcdlcAlcB; |
---|
1058 | newtonPoly= 1; |
---|
1059 | G_m= 0; |
---|
1060 | d= d0; |
---|
1061 | coF_m= 0; |
---|
1062 | coG_m= 0; |
---|
1063 | } |
---|
1064 | |
---|
1065 | TIMING_START (newton_interpolation); |
---|
1066 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
1067 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
1068 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
1069 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
1070 | "time for newton interpolation: "); |
---|
1071 | |
---|
1072 | //termination test |
---|
1073 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
1074 | { |
---|
1075 | TIMING_START (termination_test); |
---|
1076 | if (gcdlcAlcB.isOne()) |
---|
1077 | cH= 1; |
---|
1078 | else |
---|
1079 | cH= uni_content (H); |
---|
1080 | ppH= H/cH; |
---|
1081 | ppH /= Lc (ppH); |
---|
1082 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
1083 | CanonicalForm ccoF= lcppH/Lc (lcppH); |
---|
1084 | CanonicalForm ccoG= lcppH/Lc (lcppH); |
---|
1085 | ppCoF= coF/ccoF; |
---|
1086 | ppCoG= coG/ccoG; |
---|
1087 | if (inextension) |
---|
1088 | { |
---|
1089 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
1090 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
1091 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
1092 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
1093 | { |
---|
1094 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
1095 | ppH= GFMapDown (ppH, k); |
---|
1096 | ppCoF= GFMapDown (ppCoF, k); |
---|
1097 | ppCoG= GFMapDown (ppCoG, k); |
---|
1098 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
1099 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
1100 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
1101 | setCharacteristic (p, k, gf_name_buf); |
---|
1102 | TIMING_END_AND_PRINT (termination_test, |
---|
1103 | "time for successful termination GF: "); |
---|
1104 | return N(gcdcAcB*ppH); |
---|
1105 | } |
---|
1106 | } |
---|
1107 | else |
---|
1108 | { |
---|
1109 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
1110 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
1111 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
1112 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
1113 | { |
---|
1114 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
1115 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
1116 | TIMING_END_AND_PRINT (termination_test, |
---|
1117 | "time for successful termination GF: "); |
---|
1118 | return N(gcdcAcB*ppH); |
---|
1119 | } |
---|
1120 | } |
---|
1121 | TIMING_END_AND_PRINT (termination_test, |
---|
1122 | "time for unsuccessful termination GF: "); |
---|
1123 | } |
---|
1124 | |
---|
1125 | G_m= H; |
---|
1126 | coF_m= coF; |
---|
1127 | coG_m= coG; |
---|
1128 | newtonPoly= newtonPoly*(x - random_element); |
---|
1129 | m= m*(x - random_element); |
---|
1130 | if (!find (l, random_element)) |
---|
1131 | l.append (random_element); |
---|
1132 | } while (1); |
---|
1133 | } |
---|
1134 | |
---|
1135 | /// computes a random monic irreducible univariate polynomial in x of random |
---|
1136 | /// degree < i |
---|
1137 | CanonicalForm |
---|
1138 | randomIrredpoly (int i, const Variable & x) |
---|
1139 | { |
---|
1140 | int p= getCharacteristic(); |
---|
1141 | if (fac_NTL_char != p) |
---|
1142 | { |
---|
1143 | fac_NTL_char= p; |
---|
1144 | zz_p::init (p); |
---|
1145 | } |
---|
1146 | zz_pX NTLirredpoly; |
---|
1147 | CanonicalForm CFirredpoly; |
---|
1148 | BuildIrred (NTLirredpoly, i + 1); |
---|
1149 | CFirredpoly= convertNTLzzpX2CF (NTLirredpoly, x); |
---|
1150 | return CFirredpoly; |
---|
1151 | } |
---|
1152 | |
---|
1153 | static inline |
---|
1154 | CanonicalForm |
---|
1155 | FpRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
1156 | { |
---|
1157 | fail= false; |
---|
1158 | Variable x= F.mvar(); |
---|
1159 | FFRandom genFF; |
---|
1160 | CanonicalForm random; |
---|
1161 | int p= getCharacteristic(); |
---|
1162 | int bound= p; |
---|
1163 | do |
---|
1164 | { |
---|
1165 | if (list.length() == bound) |
---|
1166 | { |
---|
1167 | fail= true; |
---|
1168 | break; |
---|
1169 | } |
---|
1170 | if (list.length() < 1) |
---|
1171 | random= 0; |
---|
1172 | else |
---|
1173 | { |
---|
1174 | random= genFF.generate(); |
---|
1175 | while (find (list, random)) |
---|
1176 | random= genFF.generate(); |
---|
1177 | } |
---|
1178 | if (F (random, x) == 0) |
---|
1179 | { |
---|
1180 | list.append (random); |
---|
1181 | continue; |
---|
1182 | } |
---|
1183 | } while (find (list, random)); |
---|
1184 | return random; |
---|
1185 | } |
---|
1186 | |
---|
1187 | CanonicalForm |
---|
1188 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1189 | CanonicalForm& coF, CanonicalForm& coG, |
---|
1190 | bool& topLevel, CFList& l); |
---|
1191 | |
---|
1192 | CanonicalForm |
---|
1193 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1194 | bool& topLevel, CFList& l) |
---|
1195 | { |
---|
1196 | CanonicalForm dummy1, dummy2; |
---|
1197 | CanonicalForm result= GCD_small_p (F, G, dummy1, dummy2, topLevel, l); |
---|
1198 | return result; |
---|
1199 | } |
---|
1200 | |
---|
1201 | CanonicalForm |
---|
1202 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1203 | CanonicalForm& coF, CanonicalForm& coG, |
---|
1204 | bool& topLevel, CFList& l) |
---|
1205 | { |
---|
1206 | CanonicalForm A= F; |
---|
1207 | CanonicalForm B= G; |
---|
1208 | if (F.isZero() && degree(G) > 0) |
---|
1209 | { |
---|
1210 | coF= 0; |
---|
1211 | coG= Lc (G); |
---|
1212 | return G/Lc(G); |
---|
1213 | } |
---|
1214 | else if (G.isZero() && degree (F) > 0) |
---|
1215 | { |
---|
1216 | coF= Lc (F); |
---|
1217 | coG= 0; |
---|
1218 | return F/Lc(F); |
---|
1219 | } |
---|
1220 | else if (F.isZero() && G.isZero()) |
---|
1221 | { |
---|
1222 | coF= coG= 0; |
---|
1223 | return F.genOne(); |
---|
1224 | } |
---|
1225 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
1226 | { |
---|
1227 | coF= F; |
---|
1228 | coG= G; |
---|
1229 | return F.genOne(); |
---|
1230 | } |
---|
1231 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
1232 | { |
---|
1233 | coF= Lc (F); |
---|
1234 | return F/Lc(F); |
---|
1235 | } |
---|
1236 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
1237 | { |
---|
1238 | coG= Lc (G); |
---|
1239 | return G/Lc(G); |
---|
1240 | } |
---|
1241 | if (F == G) |
---|
1242 | { |
---|
1243 | coF= coG= Lc (F); |
---|
1244 | return F/Lc(F); |
---|
1245 | } |
---|
1246 | CFMap M,N; |
---|
1247 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
1248 | |
---|
1249 | if (best_level == 0) |
---|
1250 | { |
---|
1251 | coF= F; |
---|
1252 | coG= G; |
---|
1253 | return B.genOne(); |
---|
1254 | } |
---|
1255 | |
---|
1256 | A= M(A); |
---|
1257 | B= M(B); |
---|
1258 | |
---|
1259 | Variable x= Variable (1); |
---|
1260 | |
---|
1261 | //univariate case |
---|
1262 | if (A.isUnivariate() && B.isUnivariate()) |
---|
1263 | { |
---|
1264 | CanonicalForm result= gcd (A, B); |
---|
1265 | coF= N (A/result); |
---|
1266 | coG= N (B/result); |
---|
1267 | return N (result); |
---|
1268 | } |
---|
1269 | |
---|
1270 | CanonicalForm cA, cB; // content of A and B |
---|
1271 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
1272 | CanonicalForm gcdcAcB; |
---|
1273 | |
---|
1274 | cA = uni_content (A); |
---|
1275 | cB = uni_content (B); |
---|
1276 | gcdcAcB= gcd (cA, cB); |
---|
1277 | ppA= A/cA; |
---|
1278 | ppB= B/cB; |
---|
1279 | |
---|
1280 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
1281 | CanonicalForm gcdlcAlcB; |
---|
1282 | lcA= uni_lcoeff (ppA); |
---|
1283 | lcB= uni_lcoeff (ppB); |
---|
1284 | |
---|
1285 | gcdlcAlcB= gcd (lcA, lcB); |
---|
1286 | |
---|
1287 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
1288 | int d0; |
---|
1289 | |
---|
1290 | if (d == 0) |
---|
1291 | { |
---|
1292 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1293 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1294 | return N(gcdcAcB); |
---|
1295 | } |
---|
1296 | |
---|
1297 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
1298 | |
---|
1299 | if (d0 < d) |
---|
1300 | d= d0; |
---|
1301 | |
---|
1302 | if (d == 0) |
---|
1303 | { |
---|
1304 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1305 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1306 | return N(gcdcAcB); |
---|
1307 | } |
---|
1308 | |
---|
1309 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
1310 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, |
---|
1311 | coF_m, coG_m, ppCoF, ppCoG; |
---|
1312 | |
---|
1313 | newtonPoly= 1; |
---|
1314 | m= gcdlcAlcB; |
---|
1315 | H= 0; |
---|
1316 | coF= 0; |
---|
1317 | coG= 0; |
---|
1318 | G_m= 0; |
---|
1319 | Variable alpha, V_buf; |
---|
1320 | bool fail= false; |
---|
1321 | bool inextension= false; |
---|
1322 | topLevel= false; |
---|
1323 | CFList source, dest; |
---|
1324 | int bound1= degree (ppA, 1); |
---|
1325 | int bound2= degree (ppB, 1); |
---|
1326 | do |
---|
1327 | { |
---|
1328 | if (inextension) |
---|
1329 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
1330 | else |
---|
1331 | random_element= FpRandomElement (m*lcA*lcB, l, fail); |
---|
1332 | |
---|
1333 | if (!fail && !inextension) |
---|
1334 | { |
---|
1335 | CFList list; |
---|
1336 | TIMING_START (gcd_recursion); |
---|
1337 | G_random_element= |
---|
1338 | GCD_small_p (ppA (random_element,x), ppB (random_element,x), |
---|
1339 | coF_random_element, coG_random_element, topLevel, |
---|
1340 | list); |
---|
1341 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1342 | "time for recursive call: "); |
---|
1343 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1344 | } |
---|
1345 | else if (!fail && inextension) |
---|
1346 | { |
---|
1347 | CFList list; |
---|
1348 | TIMING_START (gcd_recursion); |
---|
1349 | G_random_element= |
---|
1350 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
1351 | coF_random_element, coG_random_element, V_buf, |
---|
1352 | list, topLevel); |
---|
1353 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1354 | "time for recursive call: "); |
---|
1355 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1356 | } |
---|
1357 | else if (fail && !inextension) |
---|
1358 | { |
---|
1359 | source= CFList(); |
---|
1360 | dest= CFList(); |
---|
1361 | CFList list; |
---|
1362 | CanonicalForm mipo; |
---|
1363 | int deg= 2; |
---|
1364 | do { |
---|
1365 | mipo= randomIrredpoly (deg, x); |
---|
1366 | alpha= rootOf (mipo); |
---|
1367 | inextension= true; |
---|
1368 | fail= false; |
---|
1369 | random_element= randomElement (m*lcA*lcB, alpha, l, fail); |
---|
1370 | deg++; |
---|
1371 | } while (fail); |
---|
1372 | list= CFList(); |
---|
1373 | V_buf= alpha; |
---|
1374 | TIMING_START (gcd_recursion); |
---|
1375 | G_random_element= |
---|
1376 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
1377 | coF_random_element, coG_random_element, alpha, |
---|
1378 | list, topLevel); |
---|
1379 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1380 | "time for recursive call: "); |
---|
1381 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1382 | } |
---|
1383 | else if (fail && inextension) |
---|
1384 | { |
---|
1385 | source= CFList(); |
---|
1386 | dest= CFList(); |
---|
1387 | |
---|
1388 | Variable V_buf3= V_buf; |
---|
1389 | V_buf= chooseExtension (V_buf); |
---|
1390 | bool prim_fail= false; |
---|
1391 | Variable V_buf2; |
---|
1392 | CanonicalForm prim_elem, im_prim_elem; |
---|
1393 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
1394 | |
---|
1395 | if (V_buf3 != alpha) |
---|
1396 | { |
---|
1397 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1398 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1399 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1400 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1401 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
1402 | source, dest); |
---|
1403 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1404 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1405 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
1406 | dest); |
---|
1407 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1408 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1409 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1410 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
1411 | source, dest); |
---|
1412 | } |
---|
1413 | |
---|
1414 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
1415 | if (prim_fail) |
---|
1416 | ; //ERROR |
---|
1417 | else |
---|
1418 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
1419 | |
---|
1420 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
1421 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
1422 | |
---|
1423 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1424 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
1425 | im_prim_elem, source, dest); |
---|
1426 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1427 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1428 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1429 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1430 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1431 | source, dest); |
---|
1432 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1433 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1434 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1435 | source, dest); |
---|
1436 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1437 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1438 | fail= false; |
---|
1439 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
1440 | DEBOUTLN (cerr, "fail= " << fail); |
---|
1441 | CFList list; |
---|
1442 | TIMING_START (gcd_recursion); |
---|
1443 | G_random_element= |
---|
1444 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
1445 | coF_random_element, coG_random_element, V_buf, |
---|
1446 | list, topLevel); |
---|
1447 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1448 | "time for recursive call: "); |
---|
1449 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1450 | } |
---|
1451 | |
---|
1452 | if (!G_random_element.inCoeffDomain()) |
---|
1453 | d0= totaldegree (G_random_element, Variable(2), |
---|
1454 | Variable (G_random_element.level())); |
---|
1455 | else |
---|
1456 | d0= 0; |
---|
1457 | |
---|
1458 | if (d0 == 0) |
---|
1459 | { |
---|
1460 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1461 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1462 | return N(gcdcAcB); |
---|
1463 | } |
---|
1464 | |
---|
1465 | if (d0 > d) |
---|
1466 | { |
---|
1467 | if (!find (l, random_element)) |
---|
1468 | l.append (random_element); |
---|
1469 | continue; |
---|
1470 | } |
---|
1471 | |
---|
1472 | G_random_element= (gcdlcAlcB(random_element,x)/uni_lcoeff(G_random_element)) |
---|
1473 | *G_random_element; |
---|
1474 | |
---|
1475 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
1476 | *coF_random_element; |
---|
1477 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
1478 | *coG_random_element; |
---|
1479 | |
---|
1480 | if (!G_random_element.inCoeffDomain()) |
---|
1481 | d0= totaldegree (G_random_element, Variable(2), |
---|
1482 | Variable (G_random_element.level())); |
---|
1483 | else |
---|
1484 | d0= 0; |
---|
1485 | |
---|
1486 | if (d0 < d) |
---|
1487 | { |
---|
1488 | m= gcdlcAlcB; |
---|
1489 | newtonPoly= 1; |
---|
1490 | G_m= 0; |
---|
1491 | d= d0; |
---|
1492 | coF_m= 0; |
---|
1493 | coG_m= 0; |
---|
1494 | } |
---|
1495 | |
---|
1496 | TIMING_START (newton_interpolation); |
---|
1497 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
1498 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
1499 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
1500 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
1501 | "time for newton_interpolation: "); |
---|
1502 | |
---|
1503 | //termination test |
---|
1504 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
1505 | { |
---|
1506 | TIMING_START (termination_test); |
---|
1507 | if (gcdlcAlcB.isOne()) |
---|
1508 | cH= 1; |
---|
1509 | else |
---|
1510 | cH= uni_content (H); |
---|
1511 | ppH= H/cH; |
---|
1512 | ppH /= Lc (ppH); |
---|
1513 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
1514 | CanonicalForm ccoF= lcppH/Lc (lcppH); |
---|
1515 | CanonicalForm ccoG= lcppH/Lc (lcppH); |
---|
1516 | ppCoF= coF/ccoF; |
---|
1517 | ppCoG= coG/ccoG; |
---|
1518 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
1519 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
1520 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
1521 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
1522 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
1523 | { |
---|
1524 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
1525 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
1526 | TIMING_END_AND_PRINT (termination_test, |
---|
1527 | "time for successful termination Fp: "); |
---|
1528 | return N(gcdcAcB*ppH); |
---|
1529 | } |
---|
1530 | TIMING_END_AND_PRINT (termination_test, |
---|
1531 | "time for unsuccessful termination Fp: "); |
---|
1532 | } |
---|
1533 | |
---|
1534 | G_m= H; |
---|
1535 | coF_m= coF; |
---|
1536 | coG_m= coG; |
---|
1537 | newtonPoly= newtonPoly*(x - random_element); |
---|
1538 | m= m*(x - random_element); |
---|
1539 | if (!find (l, random_element)) |
---|
1540 | l.append (random_element); |
---|
1541 | } while (1); |
---|
1542 | } |
---|
1543 | |
---|
1544 | CFArray |
---|
1545 | solveVandermonde (const CFArray& M, const CFArray& A) |
---|
1546 | { |
---|
1547 | int r= M.size(); |
---|
1548 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
1549 | |
---|
1550 | if (r == 1) |
---|
1551 | { |
---|
1552 | CFArray result= CFArray (1); |
---|
1553 | result [0]= A [0] / M [0]; |
---|
1554 | return result; |
---|
1555 | } |
---|
1556 | // check solvability |
---|
1557 | bool notDistinct= false; |
---|
1558 | for (int i= 0; i < r - 1; i++) |
---|
1559 | { |
---|
1560 | for (int j= i + 1; j < r; j++) |
---|
1561 | { |
---|
1562 | if (M [i] == M [j]) |
---|
1563 | { |
---|
1564 | notDistinct= true; |
---|
1565 | break; |
---|
1566 | } |
---|
1567 | } |
---|
1568 | } |
---|
1569 | if (notDistinct) |
---|
1570 | return CFArray(); |
---|
1571 | |
---|
1572 | CanonicalForm master= 1; |
---|
1573 | Variable x= Variable (1); |
---|
1574 | for (int i= 0; i < r; i++) |
---|
1575 | master *= x - M [i]; |
---|
1576 | CFList Pj; |
---|
1577 | CanonicalForm tmp; |
---|
1578 | for (int i= 0; i < r; i++) |
---|
1579 | { |
---|
1580 | tmp= master/(x - M [i]); |
---|
1581 | tmp /= tmp (M [i], 1); |
---|
1582 | Pj.append (tmp); |
---|
1583 | } |
---|
1584 | CFArray result= CFArray (r); |
---|
1585 | |
---|
1586 | CFListIterator j= Pj; |
---|
1587 | for (int i= 1; i <= r; i++, j++) |
---|
1588 | { |
---|
1589 | tmp= 0; |
---|
1590 | for (int l= 0; l < A.size(); l++) |
---|
1591 | tmp += A[l]*j.getItem()[l]; |
---|
1592 | result[i - 1]= tmp; |
---|
1593 | } |
---|
1594 | return result; |
---|
1595 | } |
---|
1596 | |
---|
1597 | CFArray |
---|
1598 | solveGeneralVandermonde (const CFArray& M, const CFArray& A) |
---|
1599 | { |
---|
1600 | int r= M.size(); |
---|
1601 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
1602 | if (r == 1) |
---|
1603 | { |
---|
1604 | CFArray result= CFArray (1); |
---|
1605 | result [0]= A[0] / M [0]; |
---|
1606 | return result; |
---|
1607 | } |
---|
1608 | // check solvability |
---|
1609 | bool notDistinct= false; |
---|
1610 | for (int i= 0; i < r - 1; i++) |
---|
1611 | { |
---|
1612 | for (int j= i + 1; j < r; j++) |
---|
1613 | { |
---|
1614 | if (M [i] == M [j]) |
---|
1615 | { |
---|
1616 | notDistinct= true; |
---|
1617 | break; |
---|
1618 | } |
---|
1619 | } |
---|
1620 | } |
---|
1621 | if (notDistinct) |
---|
1622 | return CFArray(); |
---|
1623 | |
---|
1624 | CanonicalForm master= 1; |
---|
1625 | Variable x= Variable (1); |
---|
1626 | for (int i= 0; i < r; i++) |
---|
1627 | master *= x - M [i]; |
---|
1628 | master *= x; |
---|
1629 | CFList Pj; |
---|
1630 | CanonicalForm tmp; |
---|
1631 | for (int i= 0; i < r; i++) |
---|
1632 | { |
---|
1633 | tmp= master/(x - M [i]); |
---|
1634 | tmp /= tmp (M [i], 1); |
---|
1635 | Pj.append (tmp); |
---|
1636 | } |
---|
1637 | |
---|
1638 | CFArray result= CFArray (r); |
---|
1639 | |
---|
1640 | CFListIterator j= Pj; |
---|
1641 | for (int i= 1; i <= r; i++, j++) |
---|
1642 | { |
---|
1643 | tmp= 0; |
---|
1644 | |
---|
1645 | for (int l= 1; l <= A.size(); l++) |
---|
1646 | tmp += A[l - 1]*j.getItem()[l]; |
---|
1647 | result[i - 1]= tmp; |
---|
1648 | } |
---|
1649 | return result; |
---|
1650 | } |
---|
1651 | |
---|
1652 | /// M in row echolon form, rk rank of M |
---|
1653 | CFArray |
---|
1654 | readOffSolution (const CFMatrix& M, const long rk) |
---|
1655 | { |
---|
1656 | CFArray result= CFArray (rk); |
---|
1657 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1658 | for (int i= rk; i >= 1; i--) |
---|
1659 | { |
---|
1660 | tmp3= 0; |
---|
1661 | tmp1= M (i, M.columns()); |
---|
1662 | for (int j= M.columns() - 1; j >= 1; j--) |
---|
1663 | { |
---|
1664 | tmp2= M (i, j); |
---|
1665 | if (j == i) |
---|
1666 | break; |
---|
1667 | else |
---|
1668 | tmp3 += tmp2*result[j - 1]; |
---|
1669 | } |
---|
1670 | result[i - 1]= (tmp1 - tmp3)/tmp2; |
---|
1671 | } |
---|
1672 | return result; |
---|
1673 | } |
---|
1674 | |
---|
1675 | CFArray |
---|
1676 | readOffSolution (const CFMatrix& M, const CFArray& L, const CFArray& partialSol) |
---|
1677 | { |
---|
1678 | CFArray result= CFArray (M.rows()); |
---|
1679 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1680 | int k; |
---|
1681 | for (int i= M.rows(); i >= 1; i--) |
---|
1682 | { |
---|
1683 | tmp3= 0; |
---|
1684 | tmp1= L[i - 1]; |
---|
1685 | k= 0; |
---|
1686 | for (int j= M.columns(); j >= 1; j--, k++) |
---|
1687 | { |
---|
1688 | tmp2= M (i, j); |
---|
1689 | if (j == i) |
---|
1690 | break; |
---|
1691 | else |
---|
1692 | { |
---|
1693 | if (k > partialSol.size() - 1) |
---|
1694 | tmp3 += tmp2*result[j - 1]; |
---|
1695 | else |
---|
1696 | tmp3 += tmp2*partialSol[partialSol.size() - k - 1]; |
---|
1697 | } |
---|
1698 | } |
---|
1699 | result [i - 1]= (tmp1 - tmp3)/tmp2; |
---|
1700 | } |
---|
1701 | return result; |
---|
1702 | } |
---|
1703 | |
---|
1704 | long |
---|
1705 | gaussianElimFp (CFMatrix& M, CFArray& L) |
---|
1706 | { |
---|
1707 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1708 | CFMatrix *N; |
---|
1709 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1710 | |
---|
1711 | for (int i= 1; i <= M.rows(); i++) |
---|
1712 | for (int j= 1; j <= M.columns(); j++) |
---|
1713 | (*N) (i, j)= M (i, j); |
---|
1714 | |
---|
1715 | int j= 1; |
---|
1716 | for (int i= 0; i < L.size(); i++, j++) |
---|
1717 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1718 | #ifdef HAVE_FLINT |
---|
1719 | nmod_mat_t FLINTN; |
---|
1720 | convertFacCFMatrix2nmod_mat_t (FLINTN, *N); |
---|
1721 | long rk= nmod_mat_rref (FLINTN); |
---|
1722 | |
---|
1723 | delete N; |
---|
1724 | N= convertNmod_mat_t2FacCFMatrix (FLINTN); |
---|
1725 | nmod_mat_clear (FLINTN); |
---|
1726 | #else |
---|
1727 | int p= getCharacteristic (); |
---|
1728 | if (fac_NTL_char != p) |
---|
1729 | { |
---|
1730 | fac_NTL_char= p; |
---|
1731 | zz_p::init (p); |
---|
1732 | } |
---|
1733 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
1734 | delete N; |
---|
1735 | long rk= gauss (*NTLN); |
---|
1736 | |
---|
1737 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
1738 | delete NTLN; |
---|
1739 | #endif |
---|
1740 | |
---|
1741 | L= CFArray (M.rows()); |
---|
1742 | for (int i= 0; i < M.rows(); i++) |
---|
1743 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
1744 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
1745 | delete N; |
---|
1746 | return rk; |
---|
1747 | } |
---|
1748 | |
---|
1749 | long |
---|
1750 | gaussianElimFq (CFMatrix& M, CFArray& L, const Variable& alpha) |
---|
1751 | { |
---|
1752 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1753 | CFMatrix *N; |
---|
1754 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1755 | |
---|
1756 | for (int i= 1; i <= M.rows(); i++) |
---|
1757 | for (int j= 1; j <= M.columns(); j++) |
---|
1758 | (*N) (i, j)= M (i, j); |
---|
1759 | |
---|
1760 | int j= 1; |
---|
1761 | for (int i= 0; i < L.size(); i++, j++) |
---|
1762 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1763 | int p= getCharacteristic (); |
---|
1764 | if (fac_NTL_char != p) |
---|
1765 | { |
---|
1766 | fac_NTL_char= p; |
---|
1767 | zz_p::init (p); |
---|
1768 | } |
---|
1769 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1770 | zz_pE::init (NTLMipo); |
---|
1771 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
1772 | long rk= gauss (*NTLN); |
---|
1773 | |
---|
1774 | delete N; |
---|
1775 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
1776 | |
---|
1777 | delete NTLN; |
---|
1778 | |
---|
1779 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
1780 | L= CFArray (M.rows()); |
---|
1781 | for (int i= 0; i < M.rows(); i++) |
---|
1782 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
1783 | |
---|
1784 | delete N; |
---|
1785 | return rk; |
---|
1786 | } |
---|
1787 | |
---|
1788 | CFArray |
---|
1789 | solveSystemFp (const CFMatrix& M, const CFArray& L) |
---|
1790 | { |
---|
1791 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1792 | CFMatrix *N; |
---|
1793 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1794 | |
---|
1795 | for (int i= 1; i <= M.rows(); i++) |
---|
1796 | for (int j= 1; j <= M.columns(); j++) |
---|
1797 | (*N) (i, j)= M (i, j); |
---|
1798 | |
---|
1799 | int j= 1; |
---|
1800 | for (int i= 0; i < L.size(); i++, j++) |
---|
1801 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1802 | |
---|
1803 | #ifdef HAVE_FLINT |
---|
1804 | nmod_mat_t FLINTN; |
---|
1805 | convertFacCFMatrix2nmod_mat_t (FLINTN, *N); |
---|
1806 | long rk= nmod_mat_rref (FLINTN); |
---|
1807 | #else |
---|
1808 | int p= getCharacteristic (); |
---|
1809 | if (fac_NTL_char != p) |
---|
1810 | { |
---|
1811 | fac_NTL_char= p; |
---|
1812 | zz_p::init (p); |
---|
1813 | } |
---|
1814 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
1815 | long rk= gauss (*NTLN); |
---|
1816 | #endif |
---|
1817 | delete N; |
---|
1818 | if (rk != M.columns()) |
---|
1819 | { |
---|
1820 | #ifdef HAVE_FLINT |
---|
1821 | nmod_mat_clear (FLINTN); |
---|
1822 | #else |
---|
1823 | delete NTLN; |
---|
1824 | #endif |
---|
1825 | return CFArray(); |
---|
1826 | } |
---|
1827 | #ifdef HAVE_FLINT |
---|
1828 | N= convertNmod_mat_t2FacCFMatrix (FLINTN); |
---|
1829 | nmod_mat_clear (FLINTN); |
---|
1830 | #else |
---|
1831 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
1832 | delete NTLN; |
---|
1833 | #endif |
---|
1834 | CFArray A= readOffSolution (*N, rk); |
---|
1835 | |
---|
1836 | delete N; |
---|
1837 | return A; |
---|
1838 | } |
---|
1839 | |
---|
1840 | CFArray |
---|
1841 | solveSystemFq (const CFMatrix& M, const CFArray& L, const Variable& alpha) |
---|
1842 | { |
---|
1843 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1844 | CFMatrix *N; |
---|
1845 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1846 | |
---|
1847 | for (int i= 1; i <= M.rows(); i++) |
---|
1848 | for (int j= 1; j <= M.columns(); j++) |
---|
1849 | (*N) (i, j)= M (i, j); |
---|
1850 | int j= 1; |
---|
1851 | for (int i= 0; i < L.size(); i++, j++) |
---|
1852 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1853 | int p= getCharacteristic (); |
---|
1854 | if (fac_NTL_char != p) |
---|
1855 | { |
---|
1856 | fac_NTL_char= p; |
---|
1857 | zz_p::init (p); |
---|
1858 | } |
---|
1859 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1860 | zz_pE::init (NTLMipo); |
---|
1861 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
1862 | long rk= gauss (*NTLN); |
---|
1863 | |
---|
1864 | delete N; |
---|
1865 | if (rk != M.columns()) |
---|
1866 | { |
---|
1867 | delete NTLN; |
---|
1868 | return CFArray(); |
---|
1869 | } |
---|
1870 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
1871 | |
---|
1872 | delete NTLN; |
---|
1873 | |
---|
1874 | CFArray A= readOffSolution (*N, rk); |
---|
1875 | |
---|
1876 | delete N; |
---|
1877 | return A; |
---|
1878 | } |
---|
1879 | #endif |
---|
1880 | |
---|
1881 | CFArray |
---|
1882 | getMonoms (const CanonicalForm& F) |
---|
1883 | { |
---|
1884 | if (F.inCoeffDomain()) |
---|
1885 | { |
---|
1886 | CFArray result= CFArray (1); |
---|
1887 | result [0]= 1; |
---|
1888 | return result; |
---|
1889 | } |
---|
1890 | if (F.isUnivariate()) |
---|
1891 | { |
---|
1892 | CFArray result= CFArray (size(F)); |
---|
1893 | int j= 0; |
---|
1894 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
1895 | result[j]= power (F.mvar(), i.exp()); |
---|
1896 | return result; |
---|
1897 | } |
---|
1898 | int numMon= size (F); |
---|
1899 | CFArray result= CFArray (numMon); |
---|
1900 | int j= 0; |
---|
1901 | CFArray recResult; |
---|
1902 | Variable x= F.mvar(); |
---|
1903 | CanonicalForm powX; |
---|
1904 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
1905 | { |
---|
1906 | powX= power (x, i.exp()); |
---|
1907 | recResult= getMonoms (i.coeff()); |
---|
1908 | for (int k= 0; k < recResult.size(); k++) |
---|
1909 | result[j+k]= powX*recResult[k]; |
---|
1910 | j += recResult.size(); |
---|
1911 | } |
---|
1912 | return result; |
---|
1913 | } |
---|
1914 | |
---|
1915 | #ifdef HAVE_NTL |
---|
1916 | CFArray |
---|
1917 | evaluateMonom (const CanonicalForm& F, const CFList& evalPoints) |
---|
1918 | { |
---|
1919 | if (F.inCoeffDomain()) |
---|
1920 | { |
---|
1921 | CFArray result= CFArray (1); |
---|
1922 | result [0]= F; |
---|
1923 | return result; |
---|
1924 | } |
---|
1925 | if (F.isUnivariate()) |
---|
1926 | { |
---|
1927 | ASSERT (evalPoints.length() == 1, |
---|
1928 | "expected an eval point with only one component"); |
---|
1929 | CFArray result= CFArray (size(F)); |
---|
1930 | int j= 0; |
---|
1931 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
1932 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
1933 | result[j]= power (evalPoint, i.exp()); |
---|
1934 | return result; |
---|
1935 | } |
---|
1936 | int numMon= size (F); |
---|
1937 | CFArray result= CFArray (numMon); |
---|
1938 | int j= 0; |
---|
1939 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
1940 | CFList buf= evalPoints; |
---|
1941 | buf.removeLast(); |
---|
1942 | CFArray recResult; |
---|
1943 | CanonicalForm powEvalPoint; |
---|
1944 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
1945 | { |
---|
1946 | powEvalPoint= power (evalPoint, i.exp()); |
---|
1947 | recResult= evaluateMonom (i.coeff(), buf); |
---|
1948 | for (int k= 0; k < recResult.size(); k++) |
---|
1949 | result[j+k]= powEvalPoint*recResult[k]; |
---|
1950 | j += recResult.size(); |
---|
1951 | } |
---|
1952 | return result; |
---|
1953 | } |
---|
1954 | |
---|
1955 | CFArray |
---|
1956 | evaluate (const CFArray& A, const CFList& evalPoints) |
---|
1957 | { |
---|
1958 | CFArray result= A.size(); |
---|
1959 | CanonicalForm tmp; |
---|
1960 | int k; |
---|
1961 | for (int i= 0; i < A.size(); i++) |
---|
1962 | { |
---|
1963 | tmp= A[i]; |
---|
1964 | k= 1; |
---|
1965 | for (CFListIterator j= evalPoints; j.hasItem(); j++, k++) |
---|
1966 | tmp= tmp (j.getItem(), k); |
---|
1967 | result[i]= tmp; |
---|
1968 | } |
---|
1969 | return result; |
---|
1970 | } |
---|
1971 | |
---|
1972 | CFList |
---|
1973 | evaluationPoints (const CanonicalForm& F, const CanonicalForm& G, |
---|
1974 | CanonicalForm& Feval, CanonicalForm& Geval, |
---|
1975 | const CanonicalForm& LCF, const bool& GF, |
---|
1976 | const Variable& alpha, bool& fail, CFList& list |
---|
1977 | ) |
---|
1978 | { |
---|
1979 | int k= tmax (F.level(), G.level()) - 1; |
---|
1980 | Variable x= Variable (1); |
---|
1981 | CFList result; |
---|
1982 | FFRandom genFF; |
---|
1983 | GFRandom genGF; |
---|
1984 | int p= getCharacteristic (); |
---|
1985 | double bound; |
---|
1986 | if (alpha != Variable (1)) |
---|
1987 | { |
---|
1988 | bound= pow ((double) p, (double) degree (getMipo(alpha))); |
---|
1989 | bound= pow (bound, (double) k); |
---|
1990 | } |
---|
1991 | else if (GF) |
---|
1992 | { |
---|
1993 | bound= pow ((double) p, (double) getGFDegree()); |
---|
1994 | bound= pow ((double) bound, (double) k); |
---|
1995 | } |
---|
1996 | else |
---|
1997 | bound= pow ((double) p, (double) k); |
---|
1998 | |
---|
1999 | CanonicalForm random; |
---|
2000 | int j; |
---|
2001 | bool zeroOneOccured= false; |
---|
2002 | bool allEqual= false; |
---|
2003 | CanonicalForm buf; |
---|
2004 | do |
---|
2005 | { |
---|
2006 | random= 0; |
---|
2007 | // possible overflow if list.length() does not fit into a int |
---|
2008 | if (list.length() >= bound) |
---|
2009 | { |
---|
2010 | fail= true; |
---|
2011 | break; |
---|
2012 | } |
---|
2013 | for (int i= 0; i < k; i++) |
---|
2014 | { |
---|
2015 | if (GF) |
---|
2016 | { |
---|
2017 | result.append (genGF.generate()); |
---|
2018 | random += result.getLast()*power (x, i); |
---|
2019 | } |
---|
2020 | else if (alpha.level() != 1) |
---|
2021 | { |
---|
2022 | AlgExtRandomF genAlgExt (alpha); |
---|
2023 | result.append (genAlgExt.generate()); |
---|
2024 | random += result.getLast()*power (x, i); |
---|
2025 | } |
---|
2026 | else |
---|
2027 | { |
---|
2028 | result.append (genFF.generate()); |
---|
2029 | random += result.getLast()*power (x, i); |
---|
2030 | } |
---|
2031 | if (result.getLast().isOne() || result.getLast().isZero()) |
---|
2032 | zeroOneOccured= true; |
---|
2033 | } |
---|
2034 | if (find (list, random)) |
---|
2035 | { |
---|
2036 | zeroOneOccured= false; |
---|
2037 | allEqual= false; |
---|
2038 | result= CFList(); |
---|
2039 | continue; |
---|
2040 | } |
---|
2041 | if (zeroOneOccured) |
---|
2042 | { |
---|
2043 | list.append (random); |
---|
2044 | zeroOneOccured= false; |
---|
2045 | allEqual= false; |
---|
2046 | result= CFList(); |
---|
2047 | continue; |
---|
2048 | } |
---|
2049 | // no zero at this point |
---|
2050 | if (k > 1) |
---|
2051 | { |
---|
2052 | allEqual= true; |
---|
2053 | CFIterator iter= random; |
---|
2054 | buf= iter.coeff(); |
---|
2055 | iter++; |
---|
2056 | for (; iter.hasTerms(); iter++) |
---|
2057 | if (buf != iter.coeff()) |
---|
2058 | allEqual= false; |
---|
2059 | } |
---|
2060 | if (allEqual) |
---|
2061 | { |
---|
2062 | list.append (random); |
---|
2063 | allEqual= false; |
---|
2064 | zeroOneOccured= false; |
---|
2065 | result= CFList(); |
---|
2066 | continue; |
---|
2067 | } |
---|
2068 | |
---|
2069 | Feval= F; |
---|
2070 | Geval= G; |
---|
2071 | CanonicalForm LCeval= LCF; |
---|
2072 | j= 1; |
---|
2073 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
2074 | { |
---|
2075 | Feval= Feval (i.getItem(), j); |
---|
2076 | Geval= Geval (i.getItem(), j); |
---|
2077 | LCeval= LCeval (i.getItem(), j); |
---|
2078 | } |
---|
2079 | |
---|
2080 | if (LCeval.isZero()) |
---|
2081 | { |
---|
2082 | if (!find (list, random)) |
---|
2083 | list.append (random); |
---|
2084 | zeroOneOccured= false; |
---|
2085 | allEqual= false; |
---|
2086 | result= CFList(); |
---|
2087 | continue; |
---|
2088 | } |
---|
2089 | |
---|
2090 | if (list.length() >= bound) |
---|
2091 | { |
---|
2092 | fail= true; |
---|
2093 | break; |
---|
2094 | } |
---|
2095 | } while (find (list, random)); |
---|
2096 | |
---|
2097 | return result; |
---|
2098 | } |
---|
2099 | |
---|
2100 | /// multiply two lists componentwise |
---|
2101 | void mult (CFList& L1, const CFList& L2) |
---|
2102 | { |
---|
2103 | ASSERT (L1.length() == L2.length(), "lists of the same size expected"); |
---|
2104 | |
---|
2105 | CFListIterator j= L2; |
---|
2106 | for (CFListIterator i= L1; i.hasItem(); i++, j++) |
---|
2107 | i.getItem() *= j.getItem(); |
---|
2108 | } |
---|
2109 | |
---|
2110 | void eval (const CanonicalForm& A, const CanonicalForm& B, CanonicalForm& Aeval, |
---|
2111 | CanonicalForm& Beval, const CFList& L) |
---|
2112 | { |
---|
2113 | Aeval= A; |
---|
2114 | Beval= B; |
---|
2115 | int j= 1; |
---|
2116 | for (CFListIterator i= L; i.hasItem(); i++, j++) |
---|
2117 | { |
---|
2118 | Aeval= Aeval (i.getItem(), j); |
---|
2119 | Beval= Beval (i.getItem(), j); |
---|
2120 | } |
---|
2121 | } |
---|
2122 | |
---|
2123 | CanonicalForm |
---|
2124 | monicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
2125 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
2126 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
2127 | ) |
---|
2128 | { |
---|
2129 | CanonicalForm A= F; |
---|
2130 | CanonicalForm B= G; |
---|
2131 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
2132 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
2133 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
2134 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
2135 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
2136 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
2137 | if (F == G) return F/Lc(F); |
---|
2138 | |
---|
2139 | ASSERT (degree (A, 1) == 0, "expected degree (F, 1) == 0"); |
---|
2140 | ASSERT (degree (B, 1) == 0, "expected degree (G, 1) == 0"); |
---|
2141 | |
---|
2142 | CFMap M,N; |
---|
2143 | int best_level= myCompress (A, B, M, N, false); |
---|
2144 | |
---|
2145 | if (best_level == 0) |
---|
2146 | return B.genOne(); |
---|
2147 | |
---|
2148 | A= M(A); |
---|
2149 | B= M(B); |
---|
2150 | |
---|
2151 | Variable x= Variable (1); |
---|
2152 | |
---|
2153 | //univariate case |
---|
2154 | if (A.isUnivariate() && B.isUnivariate()) |
---|
2155 | return N (gcd (A, B)); |
---|
2156 | |
---|
2157 | CanonicalForm skel= M(skeleton); |
---|
2158 | CanonicalForm cA, cB; // content of A and B |
---|
2159 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
2160 | CanonicalForm gcdcAcB; |
---|
2161 | cA = uni_content (A); |
---|
2162 | cB = uni_content (B); |
---|
2163 | gcdcAcB= gcd (cA, cB); |
---|
2164 | ppA= A/cA; |
---|
2165 | ppB= B/cB; |
---|
2166 | |
---|
2167 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
2168 | CanonicalForm gcdlcAlcB; |
---|
2169 | lcA= uni_lcoeff (ppA); |
---|
2170 | lcB= uni_lcoeff (ppB); |
---|
2171 | |
---|
2172 | if (fdivides (lcA, lcB)) |
---|
2173 | { |
---|
2174 | if (fdivides (A, B)) |
---|
2175 | return F/Lc(F); |
---|
2176 | } |
---|
2177 | if (fdivides (lcB, lcA)) |
---|
2178 | { |
---|
2179 | if (fdivides (B, A)) |
---|
2180 | return G/Lc(G); |
---|
2181 | } |
---|
2182 | |
---|
2183 | gcdlcAlcB= gcd (lcA, lcB); |
---|
2184 | int skelSize= size (skel, skel.mvar()); |
---|
2185 | |
---|
2186 | int j= 0; |
---|
2187 | int biggestSize= 0; |
---|
2188 | |
---|
2189 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2190 | biggestSize= tmax (biggestSize, size (i.coeff())); |
---|
2191 | |
---|
2192 | CanonicalForm g, Aeval, Beval; |
---|
2193 | |
---|
2194 | CFList evalPoints; |
---|
2195 | bool evalFail= false; |
---|
2196 | CFList list; |
---|
2197 | bool GF= false; |
---|
2198 | CanonicalForm LCA= LC (A); |
---|
2199 | CanonicalForm tmp; |
---|
2200 | CFArray gcds= CFArray (biggestSize); |
---|
2201 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
2202 | Variable V_buf= alpha; |
---|
2203 | CFList source, dest; |
---|
2204 | CanonicalForm prim_elem, im_prim_elem; |
---|
2205 | for (int i= 0; i < biggestSize; i++) |
---|
2206 | { |
---|
2207 | if (i == 0) |
---|
2208 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, evalFail, |
---|
2209 | list); |
---|
2210 | else |
---|
2211 | { |
---|
2212 | mult (evalPoints, pEvalPoints [0]); |
---|
2213 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2214 | } |
---|
2215 | |
---|
2216 | if (evalFail) |
---|
2217 | { |
---|
2218 | if (V_buf.level() != 1) |
---|
2219 | { |
---|
2220 | do |
---|
2221 | { |
---|
2222 | Variable V_buf2= chooseExtension (V_buf); |
---|
2223 | source= CFList(); |
---|
2224 | dest= CFList(); |
---|
2225 | |
---|
2226 | bool prim_fail= false; |
---|
2227 | Variable V_buf3; |
---|
2228 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
2229 | |
---|
2230 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
2231 | if (prim_fail) |
---|
2232 | ; //ERROR |
---|
2233 | else |
---|
2234 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
2235 | |
---|
2236 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
2237 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
2238 | |
---|
2239 | for (CFListIterator j= list; j.hasItem(); j++) |
---|
2240 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
2241 | im_prim_elem, source, dest); |
---|
2242 | for (int k= 0; k < i; k++) |
---|
2243 | { |
---|
2244 | for (CFListIterator j= pEvalPoints[k]; j.hasItem(); j++) |
---|
2245 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
2246 | im_prim_elem, source, dest); |
---|
2247 | gcds[k]= mapUp (gcds[k], V_buf, V_buf2, prim_elem, im_prim_elem, |
---|
2248 | source, dest); |
---|
2249 | } |
---|
2250 | |
---|
2251 | if (alpha.level() != 1) |
---|
2252 | { |
---|
2253 | A= mapUp (A, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
2254 | B= mapUp (B, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
2255 | } |
---|
2256 | evalFail= false; |
---|
2257 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2258 | evalFail, list); |
---|
2259 | } while (evalFail); |
---|
2260 | } |
---|
2261 | else |
---|
2262 | { |
---|
2263 | CanonicalForm mipo; |
---|
2264 | int deg= 2; |
---|
2265 | do { |
---|
2266 | mipo= randomIrredpoly (deg, x); |
---|
2267 | V_buf= rootOf (mipo); |
---|
2268 | evalFail= false; |
---|
2269 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2270 | evalFail, list); |
---|
2271 | deg++; |
---|
2272 | } while (evalFail); |
---|
2273 | } |
---|
2274 | } |
---|
2275 | |
---|
2276 | g= gcd (Aeval, Beval); |
---|
2277 | g /= Lc (g); |
---|
2278 | |
---|
2279 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2280 | { |
---|
2281 | delete[] pEvalPoints; |
---|
2282 | fail= true; |
---|
2283 | return 0; |
---|
2284 | } |
---|
2285 | CFIterator l= skel; |
---|
2286 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2287 | { |
---|
2288 | if (k.exp() != l.exp()) |
---|
2289 | { |
---|
2290 | delete[] pEvalPoints; |
---|
2291 | fail= true; |
---|
2292 | return 0; |
---|
2293 | } |
---|
2294 | } |
---|
2295 | pEvalPoints[i]= evalPoints; |
---|
2296 | gcds[i]= g; |
---|
2297 | |
---|
2298 | tmp= 0; |
---|
2299 | int j= 0; |
---|
2300 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
2301 | tmp += k.getItem()*power (x, j); |
---|
2302 | list.append (tmp); |
---|
2303 | } |
---|
2304 | |
---|
2305 | if (Monoms.size() == 0) |
---|
2306 | Monoms= getMonoms (skel); |
---|
2307 | |
---|
2308 | coeffMonoms= new CFArray [skelSize]; |
---|
2309 | j= 0; |
---|
2310 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2311 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
2312 | |
---|
2313 | CFArray* pL= new CFArray [skelSize]; |
---|
2314 | CFArray* pM= new CFArray [skelSize]; |
---|
2315 | for (int i= 0; i < biggestSize; i++) |
---|
2316 | { |
---|
2317 | CFIterator l= gcds [i]; |
---|
2318 | evalPoints= pEvalPoints [i]; |
---|
2319 | for (int k= 0; k < skelSize; k++, l++) |
---|
2320 | { |
---|
2321 | if (i == 0) |
---|
2322 | pL[k]= CFArray (biggestSize); |
---|
2323 | pL[k] [i]= l.coeff(); |
---|
2324 | |
---|
2325 | if (i == 0) |
---|
2326 | pM[k]= evaluate (coeffMonoms [k], evalPoints); |
---|
2327 | } |
---|
2328 | } |
---|
2329 | |
---|
2330 | CFArray solution; |
---|
2331 | CanonicalForm result= 0; |
---|
2332 | int ind= 0; |
---|
2333 | CFArray bufArray; |
---|
2334 | CFMatrix Mat; |
---|
2335 | for (int k= 0; k < skelSize; k++) |
---|
2336 | { |
---|
2337 | if (biggestSize != coeffMonoms[k].size()) |
---|
2338 | { |
---|
2339 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
2340 | for (int i= 0; i < coeffMonoms[k].size(); i++) |
---|
2341 | bufArray [i]= pL[k] [i]; |
---|
2342 | solution= solveGeneralVandermonde (pM [k], bufArray); |
---|
2343 | } |
---|
2344 | else |
---|
2345 | solution= solveGeneralVandermonde (pM [k], pL[k]); |
---|
2346 | |
---|
2347 | if (solution.size() == 0) |
---|
2348 | { |
---|
2349 | delete[] pEvalPoints; |
---|
2350 | delete[] pM; |
---|
2351 | delete[] pL; |
---|
2352 | delete[] coeffMonoms; |
---|
2353 | fail= true; |
---|
2354 | return 0; |
---|
2355 | } |
---|
2356 | for (int l= 0; l < solution.size(); l++) |
---|
2357 | result += solution[l]*Monoms [ind + l]; |
---|
2358 | ind += solution.size(); |
---|
2359 | } |
---|
2360 | |
---|
2361 | delete[] pEvalPoints; |
---|
2362 | delete[] pM; |
---|
2363 | delete[] pL; |
---|
2364 | delete[] coeffMonoms; |
---|
2365 | |
---|
2366 | if (alpha.level() != 1 && V_buf != alpha) |
---|
2367 | { |
---|
2368 | CFList u, v; |
---|
2369 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
2370 | } |
---|
2371 | |
---|
2372 | result= N(result); |
---|
2373 | if (fdivides (result, F) && fdivides (result, G)) |
---|
2374 | return result; |
---|
2375 | else |
---|
2376 | { |
---|
2377 | fail= true; |
---|
2378 | return 0; |
---|
2379 | } |
---|
2380 | } |
---|
2381 | |
---|
2382 | CanonicalForm |
---|
2383 | nonMonicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
2384 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
2385 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
2386 | ) |
---|
2387 | { |
---|
2388 | CanonicalForm A= F; |
---|
2389 | CanonicalForm B= G; |
---|
2390 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
2391 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
2392 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
2393 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
2394 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
2395 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
2396 | if (F == G) return F/Lc(F); |
---|
2397 | |
---|
2398 | ASSERT (degree (A, 1) == 0, "expected degree (F, 1) == 0"); |
---|
2399 | ASSERT (degree (B, 1) == 0, "expected degree (G, 1) == 0"); |
---|
2400 | |
---|
2401 | CFMap M,N; |
---|
2402 | int best_level= myCompress (A, B, M, N, false); |
---|
2403 | |
---|
2404 | if (best_level == 0) |
---|
2405 | return B.genOne(); |
---|
2406 | |
---|
2407 | A= M(A); |
---|
2408 | B= M(B); |
---|
2409 | |
---|
2410 | Variable x= Variable (1); |
---|
2411 | |
---|
2412 | //univariate case |
---|
2413 | if (A.isUnivariate() && B.isUnivariate()) |
---|
2414 | return N (gcd (A, B)); |
---|
2415 | |
---|
2416 | CanonicalForm skel= M(skeleton); |
---|
2417 | |
---|
2418 | CanonicalForm cA, cB; // content of A and B |
---|
2419 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
2420 | CanonicalForm gcdcAcB; |
---|
2421 | cA = uni_content (A); |
---|
2422 | cB = uni_content (B); |
---|
2423 | gcdcAcB= gcd (cA, cB); |
---|
2424 | ppA= A/cA; |
---|
2425 | ppB= B/cB; |
---|
2426 | |
---|
2427 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
2428 | CanonicalForm gcdlcAlcB; |
---|
2429 | lcA= uni_lcoeff (ppA); |
---|
2430 | lcB= uni_lcoeff (ppB); |
---|
2431 | |
---|
2432 | if (fdivides (lcA, lcB)) |
---|
2433 | { |
---|
2434 | if (fdivides (A, B)) |
---|
2435 | return F/Lc(F); |
---|
2436 | } |
---|
2437 | if (fdivides (lcB, lcA)) |
---|
2438 | { |
---|
2439 | if (fdivides (B, A)) |
---|
2440 | return G/Lc(G); |
---|
2441 | } |
---|
2442 | |
---|
2443 | gcdlcAlcB= gcd (lcA, lcB); |
---|
2444 | int skelSize= size (skel, skel.mvar()); |
---|
2445 | |
---|
2446 | int j= 0; |
---|
2447 | int biggestSize= 0; |
---|
2448 | int bufSize; |
---|
2449 | int numberUni= 0; |
---|
2450 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2451 | { |
---|
2452 | bufSize= size (i.coeff()); |
---|
2453 | biggestSize= tmax (biggestSize, bufSize); |
---|
2454 | numberUni += bufSize; |
---|
2455 | } |
---|
2456 | numberUni--; |
---|
2457 | numberUni= (int) ceil ( (double) numberUni / (skelSize - 1)); |
---|
2458 | biggestSize= tmax (biggestSize , numberUni); |
---|
2459 | |
---|
2460 | numberUni= biggestSize + size (LC(skel)) - 1; |
---|
2461 | int biggestSize2= tmax (numberUni, biggestSize); |
---|
2462 | |
---|
2463 | CanonicalForm g, Aeval, Beval; |
---|
2464 | |
---|
2465 | CFList evalPoints; |
---|
2466 | CFArray coeffEval; |
---|
2467 | bool evalFail= false; |
---|
2468 | CFList list; |
---|
2469 | bool GF= false; |
---|
2470 | CanonicalForm LCA= LC (A); |
---|
2471 | CanonicalForm tmp; |
---|
2472 | CFArray gcds= CFArray (biggestSize); |
---|
2473 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
2474 | Variable V_buf= alpha; |
---|
2475 | CFList source, dest; |
---|
2476 | CanonicalForm prim_elem, im_prim_elem; |
---|
2477 | for (int i= 0; i < biggestSize; i++) |
---|
2478 | { |
---|
2479 | if (i == 0) |
---|
2480 | { |
---|
2481 | if (getCharacteristic() > 3) |
---|
2482 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2483 | evalFail, list); |
---|
2484 | else |
---|
2485 | evalFail= true; |
---|
2486 | |
---|
2487 | if (evalFail) |
---|
2488 | { |
---|
2489 | if (V_buf.level() != 1) |
---|
2490 | { |
---|
2491 | do |
---|
2492 | { |
---|
2493 | Variable V_buf2= chooseExtension (V_buf); |
---|
2494 | source= CFList(); |
---|
2495 | dest= CFList(); |
---|
2496 | |
---|
2497 | bool prim_fail= false; |
---|
2498 | Variable V_buf3; |
---|
2499 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
2500 | |
---|
2501 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
2502 | if (prim_fail) |
---|
2503 | ; //ERROR |
---|
2504 | else |
---|
2505 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
2506 | |
---|
2507 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
2508 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
2509 | |
---|
2510 | for (CFListIterator i= list; i.hasItem(); i++) |
---|
2511 | i.getItem()= mapUp (i.getItem(), V_buf, V_buf2, prim_elem, |
---|
2512 | im_prim_elem, source, dest); |
---|
2513 | evalFail= false; |
---|
2514 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2515 | evalFail, list); |
---|
2516 | } while (evalFail); |
---|
2517 | } |
---|
2518 | else |
---|
2519 | { |
---|
2520 | CanonicalForm mipo; |
---|
2521 | int deg= 2; |
---|
2522 | do { |
---|
2523 | mipo= randomIrredpoly (deg, x); |
---|
2524 | V_buf= rootOf (mipo); |
---|
2525 | evalFail= false; |
---|
2526 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2527 | evalFail, list); |
---|
2528 | deg++; |
---|
2529 | } while (evalFail); |
---|
2530 | } |
---|
2531 | } |
---|
2532 | } |
---|
2533 | else |
---|
2534 | { |
---|
2535 | mult (evalPoints, pEvalPoints[0]); |
---|
2536 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2537 | } |
---|
2538 | |
---|
2539 | g= gcd (Aeval, Beval); |
---|
2540 | g /= Lc (g); |
---|
2541 | |
---|
2542 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2543 | { |
---|
2544 | delete[] pEvalPoints; |
---|
2545 | fail= true; |
---|
2546 | return 0; |
---|
2547 | } |
---|
2548 | CFIterator l= skel; |
---|
2549 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2550 | { |
---|
2551 | if (k.exp() != l.exp()) |
---|
2552 | { |
---|
2553 | delete[] pEvalPoints; |
---|
2554 | fail= true; |
---|
2555 | return 0; |
---|
2556 | } |
---|
2557 | } |
---|
2558 | pEvalPoints[i]= evalPoints; |
---|
2559 | gcds[i]= g; |
---|
2560 | |
---|
2561 | tmp= 0; |
---|
2562 | int j= 0; |
---|
2563 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
2564 | tmp += k.getItem()*power (x, j); |
---|
2565 | list.append (tmp); |
---|
2566 | } |
---|
2567 | |
---|
2568 | if (Monoms.size() == 0) |
---|
2569 | Monoms= getMonoms (skel); |
---|
2570 | |
---|
2571 | coeffMonoms= new CFArray [skelSize]; |
---|
2572 | |
---|
2573 | j= 0; |
---|
2574 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2575 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
2576 | |
---|
2577 | int minimalColumnsIndex; |
---|
2578 | if (skelSize > 1) |
---|
2579 | minimalColumnsIndex= 1; |
---|
2580 | else |
---|
2581 | minimalColumnsIndex= 0; |
---|
2582 | int minimalColumns=-1; |
---|
2583 | |
---|
2584 | CFArray* pM= new CFArray [skelSize]; |
---|
2585 | CFMatrix Mat; |
---|
2586 | // find the Matrix with minimal number of columns |
---|
2587 | for (int i= 0; i < skelSize; i++) |
---|
2588 | { |
---|
2589 | pM[i]= CFArray (coeffMonoms[i].size()); |
---|
2590 | if (i == 1) |
---|
2591 | minimalColumns= coeffMonoms[i].size(); |
---|
2592 | if (i > 1) |
---|
2593 | { |
---|
2594 | if (minimalColumns > coeffMonoms[i].size()) |
---|
2595 | { |
---|
2596 | minimalColumns= coeffMonoms[i].size(); |
---|
2597 | minimalColumnsIndex= i; |
---|
2598 | } |
---|
2599 | } |
---|
2600 | } |
---|
2601 | CFMatrix* pMat= new CFMatrix [2]; |
---|
2602 | pMat[0]= CFMatrix (biggestSize, coeffMonoms[0].size()); |
---|
2603 | pMat[1]= CFMatrix (biggestSize, coeffMonoms[minimalColumnsIndex].size()); |
---|
2604 | CFArray* pL= new CFArray [skelSize]; |
---|
2605 | for (int i= 0; i < biggestSize; i++) |
---|
2606 | { |
---|
2607 | CFIterator l= gcds [i]; |
---|
2608 | evalPoints= pEvalPoints [i]; |
---|
2609 | for (int k= 0; k < skelSize; k++, l++) |
---|
2610 | { |
---|
2611 | if (i == 0) |
---|
2612 | pL[k]= CFArray (biggestSize); |
---|
2613 | pL[k] [i]= l.coeff(); |
---|
2614 | |
---|
2615 | if (i == 0 && k != 0 && k != minimalColumnsIndex) |
---|
2616 | pM[k]= evaluate (coeffMonoms[k], evalPoints); |
---|
2617 | else if (i == 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
2618 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2619 | if (i > 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
2620 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2621 | |
---|
2622 | if (k == 0) |
---|
2623 | { |
---|
2624 | if (pMat[k].rows() >= i + 1) |
---|
2625 | { |
---|
2626 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2627 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2628 | } |
---|
2629 | } |
---|
2630 | if (k == minimalColumnsIndex) |
---|
2631 | { |
---|
2632 | if (pMat[1].rows() >= i + 1) |
---|
2633 | { |
---|
2634 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2635 | pMat[1] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2636 | } |
---|
2637 | } |
---|
2638 | } |
---|
2639 | } |
---|
2640 | |
---|
2641 | CFArray solution; |
---|
2642 | CanonicalForm result= 0; |
---|
2643 | int ind= 1; |
---|
2644 | int matRows, matColumns; |
---|
2645 | matRows= pMat[1].rows(); |
---|
2646 | matColumns= pMat[0].columns() - 1; |
---|
2647 | matColumns += pMat[1].columns(); |
---|
2648 | |
---|
2649 | Mat= CFMatrix (matRows, matColumns); |
---|
2650 | for (int i= 1; i <= matRows; i++) |
---|
2651 | for (int j= 1; j <= pMat[1].columns(); j++) |
---|
2652 | Mat (i, j)= pMat[1] (i, j); |
---|
2653 | |
---|
2654 | for (int j= pMat[1].columns() + 1; j <= matColumns; |
---|
2655 | j++, ind++) |
---|
2656 | { |
---|
2657 | for (int i= 1; i <= matRows; i++) |
---|
2658 | Mat (i, j)= (-pMat [0] (i, ind + 1))*pL[minimalColumnsIndex] [i - 1]; |
---|
2659 | } |
---|
2660 | |
---|
2661 | CFArray firstColumn= CFArray (pMat[0].rows()); |
---|
2662 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
2663 | firstColumn [i]= pMat[0] (i + 1, 1); |
---|
2664 | |
---|
2665 | CFArray bufArray= pL[minimalColumnsIndex]; |
---|
2666 | |
---|
2667 | for (int i= 0; i < biggestSize; i++) |
---|
2668 | pL[minimalColumnsIndex] [i] *= firstColumn[i]; |
---|
2669 | |
---|
2670 | CFMatrix bufMat= pMat[1]; |
---|
2671 | pMat[1]= Mat; |
---|
2672 | |
---|
2673 | if (V_buf.level() != 1) |
---|
2674 | solution= solveSystemFq (pMat[1], |
---|
2675 | pL[minimalColumnsIndex], V_buf); |
---|
2676 | else |
---|
2677 | solution= solveSystemFp (pMat[1], |
---|
2678 | pL[minimalColumnsIndex]); |
---|
2679 | |
---|
2680 | if (solution.size() == 0) |
---|
2681 | { //Javadi's method failed, try deKleine, Monagan, Wittkopf instead |
---|
2682 | CFMatrix bufMat0= pMat[0]; |
---|
2683 | delete [] pMat; |
---|
2684 | pMat= new CFMatrix [skelSize]; |
---|
2685 | pL[minimalColumnsIndex]= bufArray; |
---|
2686 | CFList* bufpEvalPoints= NULL; |
---|
2687 | CFArray bufGcds; |
---|
2688 | if (biggestSize != biggestSize2) |
---|
2689 | { |
---|
2690 | bufpEvalPoints= pEvalPoints; |
---|
2691 | pEvalPoints= new CFList [biggestSize2]; |
---|
2692 | bufGcds= gcds; |
---|
2693 | gcds= CFArray (biggestSize2); |
---|
2694 | for (int i= 0; i < biggestSize; i++) |
---|
2695 | { |
---|
2696 | pEvalPoints[i]= bufpEvalPoints [i]; |
---|
2697 | gcds[i]= bufGcds[i]; |
---|
2698 | } |
---|
2699 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
2700 | { |
---|
2701 | mult (evalPoints, pEvalPoints[0]); |
---|
2702 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2703 | g= gcd (Aeval, Beval); |
---|
2704 | g /= Lc (g); |
---|
2705 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2706 | { |
---|
2707 | delete[] pEvalPoints; |
---|
2708 | delete[] pMat; |
---|
2709 | delete[] pL; |
---|
2710 | delete[] coeffMonoms; |
---|
2711 | delete[] pM; |
---|
2712 | if (bufpEvalPoints != NULL) |
---|
2713 | delete [] bufpEvalPoints; |
---|
2714 | fail= true; |
---|
2715 | return 0; |
---|
2716 | } |
---|
2717 | CFIterator l= skel; |
---|
2718 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2719 | { |
---|
2720 | if (k.exp() != l.exp()) |
---|
2721 | { |
---|
2722 | delete[] pEvalPoints; |
---|
2723 | delete[] pMat; |
---|
2724 | delete[] pL; |
---|
2725 | delete[] coeffMonoms; |
---|
2726 | delete[] pM; |
---|
2727 | if (bufpEvalPoints != NULL) |
---|
2728 | delete [] bufpEvalPoints; |
---|
2729 | fail= true; |
---|
2730 | return 0; |
---|
2731 | } |
---|
2732 | } |
---|
2733 | pEvalPoints[i + biggestSize]= evalPoints; |
---|
2734 | gcds[i + biggestSize]= g; |
---|
2735 | } |
---|
2736 | } |
---|
2737 | for (int i= 0; i < biggestSize; i++) |
---|
2738 | { |
---|
2739 | CFIterator l= gcds [i]; |
---|
2740 | evalPoints= pEvalPoints [i]; |
---|
2741 | for (int k= 1; k < skelSize; k++, l++) |
---|
2742 | { |
---|
2743 | if (i == 0) |
---|
2744 | pMat[k]= CFMatrix (biggestSize2,coeffMonoms[k].size()+biggestSize2-1); |
---|
2745 | if (k == minimalColumnsIndex) |
---|
2746 | continue; |
---|
2747 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2748 | if (pMat[k].rows() >= i + 1) |
---|
2749 | { |
---|
2750 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2751 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2752 | } |
---|
2753 | } |
---|
2754 | } |
---|
2755 | Mat= bufMat0; |
---|
2756 | pMat[0]= CFMatrix (biggestSize2, coeffMonoms[0].size() + biggestSize2 - 1); |
---|
2757 | for (int j= 1; j <= Mat.rows(); j++) |
---|
2758 | for (int k= 1; k <= Mat.columns(); k++) |
---|
2759 | pMat [0] (j,k)= Mat (j,k); |
---|
2760 | Mat= bufMat; |
---|
2761 | for (int j= 1; j <= Mat.rows(); j++) |
---|
2762 | for (int k= 1; k <= Mat.columns(); k++) |
---|
2763 | pMat [minimalColumnsIndex] (j,k)= Mat (j,k); |
---|
2764 | // write old matrix entries into new matrices |
---|
2765 | for (int i= 0; i < skelSize; i++) |
---|
2766 | { |
---|
2767 | bufArray= pL[i]; |
---|
2768 | pL[i]= CFArray (biggestSize2); |
---|
2769 | for (int j= 0; j < bufArray.size(); j++) |
---|
2770 | pL[i] [j]= bufArray [j]; |
---|
2771 | } |
---|
2772 | //write old vector entries into new and add new entries to old matrices |
---|
2773 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
2774 | { |
---|
2775 | CFIterator l= gcds [i + biggestSize]; |
---|
2776 | evalPoints= pEvalPoints [i + biggestSize]; |
---|
2777 | for (int k= 0; k < skelSize; k++, l++) |
---|
2778 | { |
---|
2779 | pL[k] [i + biggestSize]= l.coeff(); |
---|
2780 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2781 | if (pMat[k].rows() >= i + biggestSize + 1) |
---|
2782 | { |
---|
2783 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2784 | pMat[k] (i + biggestSize + 1, ind)= coeffEval[ind - 1]; |
---|
2785 | } |
---|
2786 | } |
---|
2787 | } |
---|
2788 | // begin new |
---|
2789 | for (int i= 0; i < skelSize; i++) |
---|
2790 | { |
---|
2791 | if (pL[i].size() > 1) |
---|
2792 | { |
---|
2793 | for (int j= 2; j <= pMat[i].rows(); j++) |
---|
2794 | pMat[i] (j, coeffMonoms[i].size() + j - 1)= |
---|
2795 | -pL[i] [j - 1]; |
---|
2796 | } |
---|
2797 | } |
---|
2798 | |
---|
2799 | matColumns= biggestSize2 - 1; |
---|
2800 | matRows= 0; |
---|
2801 | for (int i= 0; i < skelSize; i++) |
---|
2802 | { |
---|
2803 | if (V_buf.level() == 1) |
---|
2804 | (void) gaussianElimFp (pMat[i], pL[i]); |
---|
2805 | else |
---|
2806 | (void) gaussianElimFq (pMat[i], pL[i], V_buf); |
---|
2807 | |
---|
2808 | if (pMat[i] (coeffMonoms[i].size(), coeffMonoms[i].size()) == 0) |
---|
2809 | { |
---|
2810 | delete[] pEvalPoints; |
---|
2811 | delete[] pMat; |
---|
2812 | delete[] pL; |
---|
2813 | delete[] coeffMonoms; |
---|
2814 | delete[] pM; |
---|
2815 | if (bufpEvalPoints != NULL) |
---|
2816 | delete [] bufpEvalPoints; |
---|
2817 | fail= true; |
---|
2818 | return 0; |
---|
2819 | } |
---|
2820 | matRows += pMat[i].rows() - coeffMonoms[i].size(); |
---|
2821 | } |
---|
2822 | |
---|
2823 | CFMatrix bufMat; |
---|
2824 | Mat= CFMatrix (matRows, matColumns); |
---|
2825 | ind= 0; |
---|
2826 | bufArray= CFArray (matRows); |
---|
2827 | CFArray bufArray2; |
---|
2828 | for (int i= 0; i < skelSize; i++) |
---|
2829 | { |
---|
2830 | bufMat= pMat[i] (coeffMonoms[i].size() + 1, pMat[i].rows(), |
---|
2831 | coeffMonoms[i].size() + 1, pMat[i].columns()); |
---|
2832 | |
---|
2833 | for (int j= 1; j <= bufMat.rows(); j++) |
---|
2834 | for (int k= 1; k <= bufMat.columns(); k++) |
---|
2835 | Mat (j + ind, k)= bufMat(j, k); |
---|
2836 | bufArray2= coeffMonoms[i].size(); |
---|
2837 | for (int j= 1; j <= pMat[i].rows(); j++) |
---|
2838 | { |
---|
2839 | if (j > coeffMonoms[i].size()) |
---|
2840 | bufArray [j-coeffMonoms[i].size() + ind - 1]= pL[i] [j - 1]; |
---|
2841 | else |
---|
2842 | bufArray2 [j - 1]= pL[i] [j - 1]; |
---|
2843 | } |
---|
2844 | pL[i]= bufArray2; |
---|
2845 | ind += bufMat.rows(); |
---|
2846 | pMat[i]= pMat[i] (1, coeffMonoms[i].size(), 1, pMat[i].columns()); |
---|
2847 | } |
---|
2848 | |
---|
2849 | if (V_buf.level() != 1) |
---|
2850 | solution= solveSystemFq (Mat, bufArray, V_buf); |
---|
2851 | else |
---|
2852 | solution= solveSystemFp (Mat, bufArray); |
---|
2853 | |
---|
2854 | if (solution.size() == 0) |
---|
2855 | { |
---|
2856 | delete[] pEvalPoints; |
---|
2857 | delete[] pMat; |
---|
2858 | delete[] pL; |
---|
2859 | delete[] coeffMonoms; |
---|
2860 | delete[] pM; |
---|
2861 | if (bufpEvalPoints != NULL) |
---|
2862 | delete [] bufpEvalPoints; |
---|
2863 | fail= true; |
---|
2864 | return 0; |
---|
2865 | } |
---|
2866 | |
---|
2867 | ind= 0; |
---|
2868 | result= 0; |
---|
2869 | CFArray bufSolution; |
---|
2870 | for (int i= 0; i < skelSize; i++) |
---|
2871 | { |
---|
2872 | bufSolution= readOffSolution (pMat[i], pL[i], solution); |
---|
2873 | for (int i= 0; i < bufSolution.size(); i++, ind++) |
---|
2874 | result += Monoms [ind]*bufSolution[i]; |
---|
2875 | } |
---|
2876 | if (alpha.level() != 1 && V_buf != alpha) |
---|
2877 | { |
---|
2878 | CFList u, v; |
---|
2879 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
2880 | } |
---|
2881 | result= N(result); |
---|
2882 | delete[] pEvalPoints; |
---|
2883 | delete[] pMat; |
---|
2884 | delete[] pL; |
---|
2885 | delete[] coeffMonoms; |
---|
2886 | delete[] pM; |
---|
2887 | |
---|
2888 | if (bufpEvalPoints != NULL) |
---|
2889 | delete [] bufpEvalPoints; |
---|
2890 | if (fdivides (result, F) && fdivides (result, G)) |
---|
2891 | return result; |
---|
2892 | else |
---|
2893 | { |
---|
2894 | fail= true; |
---|
2895 | return 0; |
---|
2896 | } |
---|
2897 | } // end of deKleine, Monagan & Wittkopf |
---|
2898 | |
---|
2899 | result += Monoms[0]; |
---|
2900 | int ind2= 0, ind3= 2; |
---|
2901 | ind= 0; |
---|
2902 | for (int l= 0; l < minimalColumnsIndex; l++) |
---|
2903 | ind += coeffMonoms[l].size(); |
---|
2904 | for (int l= solution.size() - pMat[0].columns() + 1; l < solution.size(); |
---|
2905 | l++, ind2++, ind3++) |
---|
2906 | { |
---|
2907 | result += solution[l]*Monoms [1 + ind2]; |
---|
2908 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
2909 | firstColumn[i] += solution[l]*pMat[0] (i + 1, ind3); |
---|
2910 | } |
---|
2911 | for (int l= 0; l < solution.size() + 1 - pMat[0].columns(); l++) |
---|
2912 | result += solution[l]*Monoms [ind + l]; |
---|
2913 | ind= coeffMonoms[0].size(); |
---|
2914 | for (int k= 1; k < skelSize; k++) |
---|
2915 | { |
---|
2916 | if (k == minimalColumnsIndex) |
---|
2917 | { |
---|
2918 | ind += coeffMonoms[k].size(); |
---|
2919 | continue; |
---|
2920 | } |
---|
2921 | if (k != minimalColumnsIndex) |
---|
2922 | { |
---|
2923 | for (int i= 0; i < biggestSize; i++) |
---|
2924 | pL[k] [i] *= firstColumn [i]; |
---|
2925 | } |
---|
2926 | |
---|
2927 | if (biggestSize != coeffMonoms[k].size() && k != minimalColumnsIndex) |
---|
2928 | { |
---|
2929 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
2930 | for (int i= 0; i < bufArray.size(); i++) |
---|
2931 | bufArray [i]= pL[k] [i]; |
---|
2932 | solution= solveGeneralVandermonde (pM[k], bufArray); |
---|
2933 | } |
---|
2934 | else |
---|
2935 | solution= solveGeneralVandermonde (pM[k], pL[k]); |
---|
2936 | |
---|
2937 | if (solution.size() == 0) |
---|
2938 | { |
---|
2939 | delete[] pEvalPoints; |
---|
2940 | delete[] pMat; |
---|
2941 | delete[] pL; |
---|
2942 | delete[] coeffMonoms; |
---|
2943 | delete[] pM; |
---|
2944 | fail= true; |
---|
2945 | return 0; |
---|
2946 | } |
---|
2947 | if (k != minimalColumnsIndex) |
---|
2948 | { |
---|
2949 | for (int l= 0; l < solution.size(); l++) |
---|
2950 | result += solution[l]*Monoms [ind + l]; |
---|
2951 | ind += solution.size(); |
---|
2952 | } |
---|
2953 | } |
---|
2954 | |
---|
2955 | delete[] pEvalPoints; |
---|
2956 | delete[] pMat; |
---|
2957 | delete[] pL; |
---|
2958 | delete[] pM; |
---|
2959 | delete[] coeffMonoms; |
---|
2960 | |
---|
2961 | if (alpha.level() != 1 && V_buf != alpha) |
---|
2962 | { |
---|
2963 | CFList u, v; |
---|
2964 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
2965 | } |
---|
2966 | result= N(result); |
---|
2967 | |
---|
2968 | if (fdivides (result, F) && fdivides (result, G)) |
---|
2969 | return result; |
---|
2970 | else |
---|
2971 | { |
---|
2972 | fail= true; |
---|
2973 | return 0; |
---|
2974 | } |
---|
2975 | } |
---|
2976 | |
---|
2977 | CanonicalForm sparseGCDFq (const CanonicalForm& F, const CanonicalForm& G, |
---|
2978 | const Variable & alpha, CFList& l, bool& topLevel) |
---|
2979 | { |
---|
2980 | CanonicalForm A= F; |
---|
2981 | CanonicalForm B= G; |
---|
2982 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
2983 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
2984 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
2985 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
2986 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
2987 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
2988 | if (F == G) return F/Lc(F); |
---|
2989 | |
---|
2990 | CFMap M,N; |
---|
2991 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
2992 | |
---|
2993 | if (best_level == 0) return B.genOne(); |
---|
2994 | |
---|
2995 | A= M(A); |
---|
2996 | B= M(B); |
---|
2997 | |
---|
2998 | Variable x= Variable (1); |
---|
2999 | |
---|
3000 | //univariate case |
---|
3001 | if (A.isUnivariate() && B.isUnivariate()) |
---|
3002 | return N (gcd (A, B)); |
---|
3003 | |
---|
3004 | CanonicalForm cA, cB; // content of A and B |
---|
3005 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
3006 | CanonicalForm gcdcAcB; |
---|
3007 | |
---|
3008 | cA = uni_content (A); |
---|
3009 | cB = uni_content (B); |
---|
3010 | gcdcAcB= gcd (cA, cB); |
---|
3011 | ppA= A/cA; |
---|
3012 | ppB= B/cB; |
---|
3013 | |
---|
3014 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
3015 | CanonicalForm gcdlcAlcB; |
---|
3016 | lcA= uni_lcoeff (ppA); |
---|
3017 | lcB= uni_lcoeff (ppB); |
---|
3018 | |
---|
3019 | if (fdivides (lcA, lcB)) |
---|
3020 | { |
---|
3021 | if (fdivides (A, B)) |
---|
3022 | return F/Lc(F); |
---|
3023 | } |
---|
3024 | if (fdivides (lcB, lcA)) |
---|
3025 | { |
---|
3026 | if (fdivides (B, A)) |
---|
3027 | return G/Lc(G); |
---|
3028 | } |
---|
3029 | |
---|
3030 | gcdlcAlcB= gcd (lcA, lcB); |
---|
3031 | |
---|
3032 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
3033 | int d0; |
---|
3034 | |
---|
3035 | if (d == 0) |
---|
3036 | return N(gcdcAcB); |
---|
3037 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
3038 | |
---|
3039 | if (d0 < d) |
---|
3040 | d= d0; |
---|
3041 | |
---|
3042 | if (d == 0) |
---|
3043 | return N(gcdcAcB); |
---|
3044 | |
---|
3045 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
3046 | CanonicalForm newtonPoly= 1; |
---|
3047 | m= gcdlcAlcB; |
---|
3048 | G_m= 0; |
---|
3049 | H= 0; |
---|
3050 | bool fail= false; |
---|
3051 | topLevel= false; |
---|
3052 | bool inextension= false; |
---|
3053 | Variable V_buf= alpha; |
---|
3054 | CanonicalForm prim_elem, im_prim_elem; |
---|
3055 | CFList source, dest; |
---|
3056 | do // first do |
---|
3057 | { |
---|
3058 | random_element= randomElement (m, V_buf, l, fail); |
---|
3059 | if (random_element == 0 && !fail) |
---|
3060 | { |
---|
3061 | if (!find (l, random_element)) |
---|
3062 | l.append (random_element); |
---|
3063 | continue; |
---|
3064 | } |
---|
3065 | if (fail) |
---|
3066 | { |
---|
3067 | source= CFList(); |
---|
3068 | dest= CFList(); |
---|
3069 | |
---|
3070 | Variable V_buf3= V_buf; |
---|
3071 | V_buf= chooseExtension (V_buf); |
---|
3072 | bool prim_fail= false; |
---|
3073 | Variable V_buf2; |
---|
3074 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3075 | |
---|
3076 | if (V_buf3 != alpha) |
---|
3077 | { |
---|
3078 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3079 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3080 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3081 | source, dest); |
---|
3082 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3083 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3084 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
3085 | dest); |
---|
3086 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3087 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3088 | source, dest); |
---|
3089 | } |
---|
3090 | |
---|
3091 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3092 | if (prim_fail) |
---|
3093 | ; //ERROR |
---|
3094 | else |
---|
3095 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3096 | |
---|
3097 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3098 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
3099 | inextension= true; |
---|
3100 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3101 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3102 | im_prim_elem, source, dest); |
---|
3103 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3104 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3105 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3106 | source, dest); |
---|
3107 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3108 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3109 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3110 | source, dest); |
---|
3111 | |
---|
3112 | fail= false; |
---|
3113 | random_element= randomElement (m, V_buf, l, fail ); |
---|
3114 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3115 | CFList list; |
---|
3116 | TIMING_START (gcd_recursion); |
---|
3117 | G_random_element= |
---|
3118 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
3119 | list, topLevel); |
---|
3120 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3121 | "time for recursive call: "); |
---|
3122 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3123 | } |
---|
3124 | else |
---|
3125 | { |
---|
3126 | CFList list; |
---|
3127 | TIMING_START (gcd_recursion); |
---|
3128 | G_random_element= |
---|
3129 | sparseGCDFq (ppA(random_element, x), ppB(random_element, x), V_buf, |
---|
3130 | list, topLevel); |
---|
3131 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3132 | "time for recursive call: "); |
---|
3133 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3134 | } |
---|
3135 | |
---|
3136 | if (!G_random_element.inCoeffDomain()) |
---|
3137 | d0= totaldegree (G_random_element, Variable(2), |
---|
3138 | Variable (G_random_element.level())); |
---|
3139 | else |
---|
3140 | d0= 0; |
---|
3141 | |
---|
3142 | if (d0 == 0) |
---|
3143 | return N(gcdcAcB); |
---|
3144 | if (d0 > d) |
---|
3145 | { |
---|
3146 | if (!find (l, random_element)) |
---|
3147 | l.append (random_element); |
---|
3148 | continue; |
---|
3149 | } |
---|
3150 | |
---|
3151 | G_random_element= |
---|
3152 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3153 | * G_random_element; |
---|
3154 | |
---|
3155 | skeleton= G_random_element; |
---|
3156 | if (!G_random_element.inCoeffDomain()) |
---|
3157 | d0= totaldegree (G_random_element, Variable(2), |
---|
3158 | Variable (G_random_element.level())); |
---|
3159 | else |
---|
3160 | d0= 0; |
---|
3161 | |
---|
3162 | if (d0 < d) |
---|
3163 | { |
---|
3164 | m= gcdlcAlcB; |
---|
3165 | newtonPoly= 1; |
---|
3166 | G_m= 0; |
---|
3167 | d= d0; |
---|
3168 | } |
---|
3169 | |
---|
3170 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3171 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3172 | { |
---|
3173 | cH= uni_content (H); |
---|
3174 | ppH= H/cH; |
---|
3175 | if (inextension) |
---|
3176 | { |
---|
3177 | CFList u, v; |
---|
3178 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
3179 | //mapping down |
---|
3180 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3181 | { |
---|
3182 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
3183 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
3184 | ppH /= Lc(ppH); |
---|
3185 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
3186 | return N(gcdcAcB*ppH); |
---|
3187 | } |
---|
3188 | } |
---|
3189 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3190 | return N(gcdcAcB*ppH); |
---|
3191 | } |
---|
3192 | G_m= H; |
---|
3193 | newtonPoly= newtonPoly*(x - random_element); |
---|
3194 | m= m*(x - random_element); |
---|
3195 | if (!find (l, random_element)) |
---|
3196 | l.append (random_element); |
---|
3197 | |
---|
3198 | if (getCharacteristic () > 3 && size (skeleton) < 100) |
---|
3199 | { |
---|
3200 | CFArray Monoms; |
---|
3201 | CFArray *coeffMonoms; |
---|
3202 | do //second do |
---|
3203 | { |
---|
3204 | random_element= randomElement (m, V_buf, l, fail); |
---|
3205 | if (random_element == 0 && !fail) |
---|
3206 | { |
---|
3207 | if (!find (l, random_element)) |
---|
3208 | l.append (random_element); |
---|
3209 | continue; |
---|
3210 | } |
---|
3211 | if (fail) |
---|
3212 | { |
---|
3213 | source= CFList(); |
---|
3214 | dest= CFList(); |
---|
3215 | |
---|
3216 | Variable V_buf3= V_buf; |
---|
3217 | V_buf= chooseExtension (V_buf); |
---|
3218 | bool prim_fail= false; |
---|
3219 | Variable V_buf2; |
---|
3220 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3221 | |
---|
3222 | if (V_buf3 != alpha) |
---|
3223 | { |
---|
3224 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3225 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3226 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3227 | source, dest); |
---|
3228 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3229 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3230 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
3231 | source, dest); |
---|
3232 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3233 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3234 | source, dest); |
---|
3235 | } |
---|
3236 | |
---|
3237 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3238 | if (prim_fail) |
---|
3239 | ; //ERROR |
---|
3240 | else |
---|
3241 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3242 | |
---|
3243 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3244 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
3245 | inextension= true; |
---|
3246 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3247 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3248 | im_prim_elem, source, dest); |
---|
3249 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3250 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3251 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3252 | source, dest); |
---|
3253 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3254 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3255 | |
---|
3256 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3257 | source, dest); |
---|
3258 | |
---|
3259 | fail= false; |
---|
3260 | random_element= randomElement (m, V_buf, l, fail); |
---|
3261 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3262 | CFList list; |
---|
3263 | TIMING_START (gcd_recursion); |
---|
3264 | |
---|
3265 | //sparseInterpolation |
---|
3266 | bool sparseFail= false; |
---|
3267 | if (LC (skeleton).inCoeffDomain()) |
---|
3268 | G_random_element= |
---|
3269 | monicSparseInterpol (ppA (random_element, x), ppB(random_element,x), |
---|
3270 | skeleton,V_buf, sparseFail, coeffMonoms,Monoms); |
---|
3271 | else |
---|
3272 | G_random_element= |
---|
3273 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
3274 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3275 | Monoms); |
---|
3276 | if (sparseFail) |
---|
3277 | break; |
---|
3278 | |
---|
3279 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3280 | "time for recursive call: "); |
---|
3281 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3282 | } |
---|
3283 | else |
---|
3284 | { |
---|
3285 | CFList list; |
---|
3286 | TIMING_START (gcd_recursion); |
---|
3287 | bool sparseFail= false; |
---|
3288 | if (LC (skeleton).inCoeffDomain()) |
---|
3289 | G_random_element= |
---|
3290 | monicSparseInterpol (ppA (random_element, x),ppB(random_element, x), |
---|
3291 | skeleton,V_buf, sparseFail,coeffMonoms, Monoms); |
---|
3292 | else |
---|
3293 | G_random_element= |
---|
3294 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
3295 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3296 | Monoms); |
---|
3297 | if (sparseFail) |
---|
3298 | break; |
---|
3299 | |
---|
3300 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3301 | "time for recursive call: "); |
---|
3302 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3303 | } |
---|
3304 | |
---|
3305 | if (!G_random_element.inCoeffDomain()) |
---|
3306 | d0= totaldegree (G_random_element, Variable(2), |
---|
3307 | Variable (G_random_element.level())); |
---|
3308 | else |
---|
3309 | d0= 0; |
---|
3310 | |
---|
3311 | if (d0 == 0) |
---|
3312 | return N(gcdcAcB); |
---|
3313 | if (d0 > d) |
---|
3314 | { |
---|
3315 | if (!find (l, random_element)) |
---|
3316 | l.append (random_element); |
---|
3317 | continue; |
---|
3318 | } |
---|
3319 | |
---|
3320 | G_random_element= |
---|
3321 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3322 | * G_random_element; |
---|
3323 | |
---|
3324 | if (!G_random_element.inCoeffDomain()) |
---|
3325 | d0= totaldegree (G_random_element, Variable(2), |
---|
3326 | Variable (G_random_element.level())); |
---|
3327 | else |
---|
3328 | d0= 0; |
---|
3329 | |
---|
3330 | if (d0 < d) |
---|
3331 | { |
---|
3332 | m= gcdlcAlcB; |
---|
3333 | newtonPoly= 1; |
---|
3334 | G_m= 0; |
---|
3335 | d= d0; |
---|
3336 | } |
---|
3337 | |
---|
3338 | TIMING_START (newton_interpolation); |
---|
3339 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3340 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
3341 | "time for newton interpolation: "); |
---|
3342 | |
---|
3343 | //termination test |
---|
3344 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3345 | { |
---|
3346 | cH= uni_content (H); |
---|
3347 | ppH= H/cH; |
---|
3348 | if (inextension) |
---|
3349 | { |
---|
3350 | CFList u, v; |
---|
3351 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
3352 | //mapping down |
---|
3353 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3354 | { |
---|
3355 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
3356 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
3357 | ppH /= Lc(ppH); |
---|
3358 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
3359 | return N(gcdcAcB*ppH); |
---|
3360 | } |
---|
3361 | } |
---|
3362 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3363 | { |
---|
3364 | return N(gcdcAcB*ppH); |
---|
3365 | } |
---|
3366 | } |
---|
3367 | |
---|
3368 | G_m= H; |
---|
3369 | newtonPoly= newtonPoly*(x - random_element); |
---|
3370 | m= m*(x - random_element); |
---|
3371 | if (!find (l, random_element)) |
---|
3372 | l.append (random_element); |
---|
3373 | |
---|
3374 | } while (1); |
---|
3375 | } |
---|
3376 | } while (1); |
---|
3377 | } |
---|
3378 | |
---|
3379 | CanonicalForm sparseGCDFp (const CanonicalForm& F, const CanonicalForm& G, |
---|
3380 | bool& topLevel, CFList& l) |
---|
3381 | { |
---|
3382 | CanonicalForm A= F; |
---|
3383 | CanonicalForm B= G; |
---|
3384 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
3385 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
3386 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
3387 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
3388 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
3389 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
3390 | if (F == G) return F/Lc(F); |
---|
3391 | |
---|
3392 | CFMap M,N; |
---|
3393 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
3394 | |
---|
3395 | if (best_level == 0) return B.genOne(); |
---|
3396 | |
---|
3397 | A= M(A); |
---|
3398 | B= M(B); |
---|
3399 | |
---|
3400 | Variable x= Variable (1); |
---|
3401 | |
---|
3402 | //univariate case |
---|
3403 | if (A.isUnivariate() && B.isUnivariate()) |
---|
3404 | return N (gcd (A, B)); |
---|
3405 | |
---|
3406 | CanonicalForm cA, cB; // content of A and B |
---|
3407 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
3408 | CanonicalForm gcdcAcB; |
---|
3409 | |
---|
3410 | cA = uni_content (A); |
---|
3411 | cB = uni_content (B); |
---|
3412 | gcdcAcB= gcd (cA, cB); |
---|
3413 | ppA= A/cA; |
---|
3414 | ppB= B/cB; |
---|
3415 | |
---|
3416 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
3417 | CanonicalForm gcdlcAlcB; |
---|
3418 | lcA= uni_lcoeff (ppA); |
---|
3419 | lcB= uni_lcoeff (ppB); |
---|
3420 | |
---|
3421 | if (fdivides (lcA, lcB)) |
---|
3422 | { |
---|
3423 | if (fdivides (A, B)) |
---|
3424 | return F/Lc(F); |
---|
3425 | } |
---|
3426 | if (fdivides (lcB, lcA)) |
---|
3427 | { |
---|
3428 | if (fdivides (B, A)) |
---|
3429 | return G/Lc(G); |
---|
3430 | } |
---|
3431 | |
---|
3432 | gcdlcAlcB= gcd (lcA, lcB); |
---|
3433 | |
---|
3434 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
3435 | int d0; |
---|
3436 | |
---|
3437 | if (d == 0) |
---|
3438 | return N(gcdcAcB); |
---|
3439 | |
---|
3440 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
3441 | |
---|
3442 | if (d0 < d) |
---|
3443 | d= d0; |
---|
3444 | |
---|
3445 | if (d == 0) |
---|
3446 | return N(gcdcAcB); |
---|
3447 | |
---|
3448 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
3449 | CanonicalForm newtonPoly= 1; |
---|
3450 | m= gcdlcAlcB; |
---|
3451 | G_m= 0; |
---|
3452 | H= 0; |
---|
3453 | bool fail= false; |
---|
3454 | topLevel= false; |
---|
3455 | bool inextension= false; |
---|
3456 | Variable V_buf, alpha; |
---|
3457 | CanonicalForm prim_elem, im_prim_elem; |
---|
3458 | CFList source, dest; |
---|
3459 | do //first do |
---|
3460 | { |
---|
3461 | if (inextension) |
---|
3462 | random_element= randomElement (m, V_buf, l, fail); |
---|
3463 | else |
---|
3464 | random_element= FpRandomElement (m, l, fail); |
---|
3465 | if (random_element == 0 && !fail) |
---|
3466 | { |
---|
3467 | if (!find (l, random_element)) |
---|
3468 | l.append (random_element); |
---|
3469 | continue; |
---|
3470 | } |
---|
3471 | |
---|
3472 | if (!fail && !inextension) |
---|
3473 | { |
---|
3474 | CFList list; |
---|
3475 | TIMING_START (gcd_recursion); |
---|
3476 | G_random_element= |
---|
3477 | sparseGCDFp (ppA (random_element,x), ppB (random_element,x), topLevel, |
---|
3478 | list); |
---|
3479 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3480 | "time for recursive call: "); |
---|
3481 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3482 | } |
---|
3483 | else if (!fail && inextension) |
---|
3484 | { |
---|
3485 | CFList list; |
---|
3486 | TIMING_START (gcd_recursion); |
---|
3487 | G_random_element= |
---|
3488 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
3489 | list, topLevel); |
---|
3490 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3491 | "time for recursive call: "); |
---|
3492 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3493 | } |
---|
3494 | else if (fail && !inextension) |
---|
3495 | { |
---|
3496 | source= CFList(); |
---|
3497 | dest= CFList(); |
---|
3498 | CFList list; |
---|
3499 | CanonicalForm mipo; |
---|
3500 | int deg= 2; |
---|
3501 | do |
---|
3502 | { |
---|
3503 | mipo= randomIrredpoly (deg, x); |
---|
3504 | alpha= rootOf (mipo); |
---|
3505 | inextension= true; |
---|
3506 | fail= false; |
---|
3507 | random_element= randomElement (m, alpha, l, fail); |
---|
3508 | deg++; |
---|
3509 | } while (fail); |
---|
3510 | V_buf= alpha; |
---|
3511 | list= CFList(); |
---|
3512 | TIMING_START (gcd_recursion); |
---|
3513 | G_random_element= |
---|
3514 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
3515 | list, topLevel); |
---|
3516 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3517 | "time for recursive call: "); |
---|
3518 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3519 | } |
---|
3520 | else if (fail && inextension) |
---|
3521 | { |
---|
3522 | source= CFList(); |
---|
3523 | dest= CFList(); |
---|
3524 | |
---|
3525 | Variable V_buf3= V_buf; |
---|
3526 | V_buf= chooseExtension (V_buf); |
---|
3527 | bool prim_fail= false; |
---|
3528 | Variable V_buf2; |
---|
3529 | CanonicalForm prim_elem, im_prim_elem; |
---|
3530 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3531 | |
---|
3532 | if (V_buf3 != alpha) |
---|
3533 | { |
---|
3534 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3535 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3536 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, source, |
---|
3537 | dest); |
---|
3538 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3539 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3540 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
3541 | dest); |
---|
3542 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3543 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3544 | source, dest); |
---|
3545 | } |
---|
3546 | |
---|
3547 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3548 | if (prim_fail) |
---|
3549 | ; //ERROR |
---|
3550 | else |
---|
3551 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3552 | |
---|
3553 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3554 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
3555 | |
---|
3556 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3557 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3558 | im_prim_elem, source, dest); |
---|
3559 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3560 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3561 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3562 | source, dest); |
---|
3563 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3564 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3565 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3566 | source, dest); |
---|
3567 | fail= false; |
---|
3568 | random_element= randomElement (m, V_buf, l, fail ); |
---|
3569 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3570 | CFList list; |
---|
3571 | TIMING_START (gcd_recursion); |
---|
3572 | G_random_element= |
---|
3573 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
3574 | list, topLevel); |
---|
3575 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3576 | "time for recursive call: "); |
---|
3577 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3578 | } |
---|
3579 | |
---|
3580 | if (!G_random_element.inCoeffDomain()) |
---|
3581 | d0= totaldegree (G_random_element, Variable(2), |
---|
3582 | Variable (G_random_element.level())); |
---|
3583 | else |
---|
3584 | d0= 0; |
---|
3585 | |
---|
3586 | if (d0 == 0) |
---|
3587 | return N(gcdcAcB); |
---|
3588 | if (d0 > d) |
---|
3589 | { |
---|
3590 | if (!find (l, random_element)) |
---|
3591 | l.append (random_element); |
---|
3592 | continue; |
---|
3593 | } |
---|
3594 | |
---|
3595 | G_random_element= |
---|
3596 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3597 | * G_random_element; |
---|
3598 | |
---|
3599 | skeleton= G_random_element; |
---|
3600 | |
---|
3601 | if (!G_random_element.inCoeffDomain()) |
---|
3602 | d0= totaldegree (G_random_element, Variable(2), |
---|
3603 | Variable (G_random_element.level())); |
---|
3604 | else |
---|
3605 | d0= 0; |
---|
3606 | |
---|
3607 | if (d0 < d) |
---|
3608 | { |
---|
3609 | m= gcdlcAlcB; |
---|
3610 | newtonPoly= 1; |
---|
3611 | G_m= 0; |
---|
3612 | d= d0; |
---|
3613 | } |
---|
3614 | |
---|
3615 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3616 | |
---|
3617 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3618 | { |
---|
3619 | cH= uni_content (H); |
---|
3620 | ppH= H/cH; |
---|
3621 | ppH /= Lc (ppH); |
---|
3622 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
3623 | |
---|
3624 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3625 | return N(gcdcAcB*ppH); |
---|
3626 | } |
---|
3627 | G_m= H; |
---|
3628 | newtonPoly= newtonPoly*(x - random_element); |
---|
3629 | m= m*(x - random_element); |
---|
3630 | if (!find (l, random_element)) |
---|
3631 | l.append (random_element); |
---|
3632 | |
---|
3633 | if ((getCharacteristic() > 3 && size (skeleton) < 200)) |
---|
3634 | { |
---|
3635 | CFArray Monoms; |
---|
3636 | CFArray* coeffMonoms; |
---|
3637 | |
---|
3638 | do //second do |
---|
3639 | { |
---|
3640 | if (inextension) |
---|
3641 | random_element= randomElement (m, alpha, l, fail); |
---|
3642 | else |
---|
3643 | random_element= FpRandomElement (m, l, fail); |
---|
3644 | if (random_element == 0 && !fail) |
---|
3645 | { |
---|
3646 | if (!find (l, random_element)) |
---|
3647 | l.append (random_element); |
---|
3648 | continue; |
---|
3649 | } |
---|
3650 | |
---|
3651 | bool sparseFail= false; |
---|
3652 | if (!fail && !inextension) |
---|
3653 | { |
---|
3654 | CFList list; |
---|
3655 | TIMING_START (gcd_recursion); |
---|
3656 | if (LC (skeleton).inCoeffDomain()) |
---|
3657 | G_random_element= |
---|
3658 | monicSparseInterpol(ppA(random_element, x), ppB (random_element, x), |
---|
3659 | skeleton, Variable(1), sparseFail, coeffMonoms, |
---|
3660 | Monoms); |
---|
3661 | else |
---|
3662 | G_random_element= |
---|
3663 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3664 | skeleton, Variable (1), sparseFail, |
---|
3665 | coeffMonoms, Monoms); |
---|
3666 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3667 | "time for recursive call: "); |
---|
3668 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3669 | } |
---|
3670 | else if (!fail && inextension) |
---|
3671 | { |
---|
3672 | CFList list; |
---|
3673 | TIMING_START (gcd_recursion); |
---|
3674 | if (LC (skeleton).inCoeffDomain()) |
---|
3675 | G_random_element= |
---|
3676 | monicSparseInterpol(ppA (random_element,x), ppB (random_element, x), |
---|
3677 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3678 | Monoms); |
---|
3679 | else |
---|
3680 | G_random_element= |
---|
3681 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3682 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3683 | Monoms); |
---|
3684 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3685 | "time for recursive call: "); |
---|
3686 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3687 | } |
---|
3688 | else if (fail && !inextension) |
---|
3689 | { |
---|
3690 | source= CFList(); |
---|
3691 | dest= CFList(); |
---|
3692 | CFList list; |
---|
3693 | CanonicalForm mipo; |
---|
3694 | int deg= 2; |
---|
3695 | do |
---|
3696 | { |
---|
3697 | mipo= randomIrredpoly (deg, x); |
---|
3698 | alpha= rootOf (mipo); |
---|
3699 | inextension= true; |
---|
3700 | fail= false; |
---|
3701 | random_element= randomElement (m, alpha, l, fail); |
---|
3702 | deg++; |
---|
3703 | } while (fail); |
---|
3704 | V_buf= alpha; |
---|
3705 | list= CFList(); |
---|
3706 | TIMING_START (gcd_recursion); |
---|
3707 | if (LC (skeleton).inCoeffDomain()) |
---|
3708 | G_random_element= |
---|
3709 | monicSparseInterpol (ppA (random_element,x), ppB (random_element,x), |
---|
3710 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3711 | Monoms); |
---|
3712 | else |
---|
3713 | G_random_element= |
---|
3714 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3715 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3716 | Monoms); |
---|
3717 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3718 | "time for recursive call: "); |
---|
3719 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3720 | } |
---|
3721 | else if (fail && inextension) |
---|
3722 | { |
---|
3723 | source= CFList(); |
---|
3724 | dest= CFList(); |
---|
3725 | |
---|
3726 | Variable V_buf3= V_buf; |
---|
3727 | V_buf= chooseExtension (V_buf); |
---|
3728 | bool prim_fail= false; |
---|
3729 | Variable V_buf2; |
---|
3730 | CanonicalForm prim_elem, im_prim_elem; |
---|
3731 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3732 | |
---|
3733 | if (V_buf3 != alpha) |
---|
3734 | { |
---|
3735 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3736 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3737 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3738 | source, dest); |
---|
3739 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3740 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3741 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
3742 | source, dest); |
---|
3743 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3744 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3745 | source, dest); |
---|
3746 | } |
---|
3747 | |
---|
3748 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3749 | if (prim_fail) |
---|
3750 | ; //ERROR |
---|
3751 | else |
---|
3752 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3753 | |
---|
3754 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3755 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
3756 | |
---|
3757 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3758 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3759 | im_prim_elem, source, dest); |
---|
3760 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3761 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3762 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3763 | source, dest); |
---|
3764 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3765 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3766 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3767 | source, dest); |
---|
3768 | fail= false; |
---|
3769 | random_element= randomElement (m, V_buf, l, fail ); |
---|
3770 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3771 | CFList list; |
---|
3772 | TIMING_START (gcd_recursion); |
---|
3773 | if (LC (skeleton).inCoeffDomain()) |
---|
3774 | G_random_element= |
---|
3775 | monicSparseInterpol (ppA (random_element, x), ppB (random_element, x), |
---|
3776 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3777 | Monoms); |
---|
3778 | else |
---|
3779 | G_random_element= |
---|
3780 | nonMonicSparseInterpol (ppA(random_element,x), ppB(random_element,x), |
---|
3781 | skeleton, V_buf, sparseFail, |
---|
3782 | coeffMonoms, Monoms); |
---|
3783 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3784 | "time for recursive call: "); |
---|
3785 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3786 | } |
---|
3787 | |
---|
3788 | if (sparseFail) |
---|
3789 | break; |
---|
3790 | |
---|
3791 | if (!G_random_element.inCoeffDomain()) |
---|
3792 | d0= totaldegree (G_random_element, Variable(2), |
---|
3793 | Variable (G_random_element.level())); |
---|
3794 | else |
---|
3795 | d0= 0; |
---|
3796 | |
---|
3797 | if (d0 == 0) |
---|
3798 | return N(gcdcAcB); |
---|
3799 | if (d0 > d) |
---|
3800 | { |
---|
3801 | if (!find (l, random_element)) |
---|
3802 | l.append (random_element); |
---|
3803 | continue; |
---|
3804 | } |
---|
3805 | |
---|
3806 | G_random_element= |
---|
3807 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3808 | * G_random_element; |
---|
3809 | |
---|
3810 | if (!G_random_element.inCoeffDomain()) |
---|
3811 | d0= totaldegree (G_random_element, Variable(2), |
---|
3812 | Variable (G_random_element.level())); |
---|
3813 | else |
---|
3814 | d0= 0; |
---|
3815 | |
---|
3816 | if (d0 < d) |
---|
3817 | { |
---|
3818 | m= gcdlcAlcB; |
---|
3819 | newtonPoly= 1; |
---|
3820 | G_m= 0; |
---|
3821 | d= d0; |
---|
3822 | } |
---|
3823 | |
---|
3824 | TIMING_START (newton_interpolation); |
---|
3825 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3826 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
3827 | "time for newton interpolation: "); |
---|
3828 | |
---|
3829 | //termination test |
---|
3830 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3831 | { |
---|
3832 | cH= uni_content (H); |
---|
3833 | ppH= H/cH; |
---|
3834 | ppH /= Lc (ppH); |
---|
3835 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
3836 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3837 | return N(gcdcAcB*ppH); |
---|
3838 | } |
---|
3839 | |
---|
3840 | G_m= H; |
---|
3841 | newtonPoly= newtonPoly*(x - random_element); |
---|
3842 | m= m*(x - random_element); |
---|
3843 | if (!find (l, random_element)) |
---|
3844 | l.append (random_element); |
---|
3845 | |
---|
3846 | } while (1); //end of second do |
---|
3847 | } |
---|
3848 | else |
---|
3849 | return N(gcdcAcB*GCD_small_p (ppA, ppB)); |
---|
3850 | } while (1); //end of first do |
---|
3851 | } |
---|
3852 | |
---|
3853 | static inline |
---|
3854 | int compress4EZGCD (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
---|
3855 | CFMap & N, int& both_non_zero) |
---|
3856 | { |
---|
3857 | int n= tmax (F.level(), G.level()); |
---|
3858 | int * degsf= new int [n + 1]; |
---|
3859 | int * degsg= new int [n + 1]; |
---|
3860 | |
---|
3861 | for (int i = 0; i <= n; i++) |
---|
3862 | degsf[i]= degsg[i]= 0; |
---|
3863 | |
---|
3864 | degsf= degrees (F, degsf); |
---|
3865 | degsg= degrees (G, degsg); |
---|
3866 | |
---|
3867 | both_non_zero= 0; |
---|
3868 | int f_zero= 0; |
---|
3869 | int g_zero= 0; |
---|
3870 | |
---|
3871 | for (int i= 1; i <= n; i++) |
---|
3872 | { |
---|
3873 | if (degsf[i] != 0 && degsg[i] != 0) |
---|
3874 | { |
---|
3875 | both_non_zero++; |
---|
3876 | continue; |
---|
3877 | } |
---|
3878 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
3879 | { |
---|
3880 | f_zero++; |
---|
3881 | continue; |
---|
3882 | } |
---|
3883 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
---|
3884 | { |
---|
3885 | g_zero++; |
---|
3886 | continue; |
---|
3887 | } |
---|
3888 | } |
---|
3889 | |
---|
3890 | if (both_non_zero == 0) |
---|
3891 | { |
---|
3892 | delete [] degsf; |
---|
3893 | delete [] degsg; |
---|
3894 | return 0; |
---|
3895 | } |
---|
3896 | |
---|
3897 | // map Variables which do not occur in both polynomials to higher levels |
---|
3898 | int k= 1; |
---|
3899 | int l= 1; |
---|
3900 | for (int i= 1; i <= n; i++) |
---|
3901 | { |
---|
3902 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
---|
3903 | { |
---|
3904 | if (k + both_non_zero != i) |
---|
3905 | { |
---|
3906 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
---|
3907 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
---|
3908 | } |
---|
3909 | k++; |
---|
3910 | } |
---|
3911 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
3912 | { |
---|
3913 | if (l + g_zero + both_non_zero != i) |
---|
3914 | { |
---|
3915 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
---|
3916 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
---|
3917 | } |
---|
3918 | l++; |
---|
3919 | } |
---|
3920 | } |
---|
3921 | |
---|
3922 | // sort Variables x_{i} in decreasing order of |
---|
3923 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
---|
3924 | int m= tmin (F.level(), G.level()); |
---|
3925 | int max_min_deg; |
---|
3926 | k= both_non_zero; |
---|
3927 | l= 0; |
---|
3928 | int i= 1; |
---|
3929 | while (k > 0) |
---|
3930 | { |
---|
3931 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
3932 | while (max_min_deg == 0) |
---|
3933 | { |
---|
3934 | i++; |
---|
3935 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
3936 | } |
---|
3937 | for (int j= i + 1; j <= m; j++) |
---|
3938 | { |
---|
3939 | if ((tmin (degsf[j],degsg[j]) < max_min_deg) && |
---|
3940 | (tmin (degsf[j], degsg[j]) != 0)) |
---|
3941 | { |
---|
3942 | max_min_deg= tmin (degsf[j], degsg[j]); |
---|
3943 | l= j; |
---|
3944 | } |
---|
3945 | } |
---|
3946 | |
---|
3947 | if (l != 0) |
---|
3948 | { |
---|
3949 | if (l != k) |
---|
3950 | { |
---|
3951 | M.newpair (Variable (l), Variable(k)); |
---|
3952 | N.newpair (Variable (k), Variable(l)); |
---|
3953 | degsf[l]= 0; |
---|
3954 | degsg[l]= 0; |
---|
3955 | l= 0; |
---|
3956 | } |
---|
3957 | else |
---|
3958 | { |
---|
3959 | degsf[l]= 0; |
---|
3960 | degsg[l]= 0; |
---|
3961 | l= 0; |
---|
3962 | } |
---|
3963 | } |
---|
3964 | else if (l == 0) |
---|
3965 | { |
---|
3966 | if (i != k) |
---|
3967 | { |
---|
3968 | M.newpair (Variable (i), Variable (k)); |
---|
3969 | N.newpair (Variable (k), Variable (i)); |
---|
3970 | degsf[i]= 0; |
---|
3971 | degsg[i]= 0; |
---|
3972 | } |
---|
3973 | else |
---|
3974 | { |
---|
3975 | degsf[i]= 0; |
---|
3976 | degsg[i]= 0; |
---|
3977 | } |
---|
3978 | i++; |
---|
3979 | } |
---|
3980 | k--; |
---|
3981 | } |
---|
3982 | |
---|
3983 | delete [] degsf; |
---|
3984 | delete [] degsg; |
---|
3985 | |
---|
3986 | return both_non_zero; |
---|
3987 | } |
---|
3988 | |
---|
3989 | static inline |
---|
3990 | CanonicalForm myShift2Zero (const CanonicalForm& F, CFList& Feval, |
---|
3991 | const CFList& evaluation) |
---|
3992 | { |
---|
3993 | CanonicalForm A= F; |
---|
3994 | int k= 2; |
---|
3995 | for (CFListIterator i= evaluation; i.hasItem(); i++, k++) |
---|
3996 | A= A (Variable (k) + i.getItem(), k); |
---|
3997 | |
---|
3998 | CanonicalForm buf= A; |
---|
3999 | Feval= CFList(); |
---|
4000 | Feval.append (buf); |
---|
4001 | for (k= evaluation.length() + 1; k > 2; k--) |
---|
4002 | { |
---|
4003 | buf= mod (buf, Variable (k)); |
---|
4004 | Feval.insert (buf); |
---|
4005 | } |
---|
4006 | return A; |
---|
4007 | } |
---|
4008 | |
---|
4009 | static inline |
---|
4010 | CanonicalForm myReverseShift (const CanonicalForm& F, const CFList& evaluation) |
---|
4011 | { |
---|
4012 | int l= evaluation.length() + 1; |
---|
4013 | CanonicalForm result= F; |
---|
4014 | CFListIterator j= evaluation; |
---|
4015 | for (int i= 2; i < l + 1; i++, j++) |
---|
4016 | { |
---|
4017 | if (F.level() < i) |
---|
4018 | continue; |
---|
4019 | result= result (Variable (i) - j.getItem(), i); |
---|
4020 | } |
---|
4021 | return result; |
---|
4022 | } |
---|
4023 | |
---|
4024 | static inline |
---|
4025 | Evaluation optimize4Lift (const CanonicalForm& F, CFMap & M, |
---|
4026 | CFMap & N, const Evaluation& A) |
---|
4027 | { |
---|
4028 | int n= F.level(); |
---|
4029 | int * degsf= new int [n + 1]; |
---|
4030 | |
---|
4031 | for (int i = 0; i <= n; i++) |
---|
4032 | degsf[i]= 0; |
---|
4033 | |
---|
4034 | degsf= degrees (F, degsf); |
---|
4035 | |
---|
4036 | Evaluation result= Evaluation (A.min(), A.max()); |
---|
4037 | ASSERT (A.min() == 2, "expected A.min() == 2"); |
---|
4038 | int max_deg; |
---|
4039 | int k= n; |
---|
4040 | int l= 1; |
---|
4041 | int i= 2; |
---|
4042 | int pos= 2; |
---|
4043 | while (k > 1) |
---|
4044 | { |
---|
4045 | max_deg= degsf [i]; |
---|
4046 | while (max_deg == 0) |
---|
4047 | { |
---|
4048 | i++; |
---|
4049 | max_deg= degsf [i]; |
---|
4050 | } |
---|
4051 | l= i; |
---|
4052 | for (int j= i + 1; j <= n; j++) |
---|
4053 | { |
---|
4054 | if (degsf[j] > max_deg) |
---|
4055 | { |
---|
4056 | max_deg= degsf[j]; |
---|
4057 | l= j; |
---|
4058 | } |
---|
4059 | } |
---|
4060 | |
---|
4061 | if (l <= n) |
---|
4062 | { |
---|
4063 | if (l != pos) |
---|
4064 | { |
---|
4065 | result.setValue (pos, A [l]); |
---|
4066 | M.newpair (Variable (l), Variable (pos)); |
---|
4067 | N.newpair (Variable (pos), Variable (l)); |
---|
4068 | degsf[l]= 0; |
---|
4069 | l= 2; |
---|
4070 | if (k == 2 && n == 3) |
---|
4071 | { |
---|
4072 | result.setValue (l, A [pos]); |
---|
4073 | M.newpair (Variable (pos), Variable (l)); |
---|
4074 | N.newpair (Variable (l), Variable (pos)); |
---|
4075 | degsf[pos]= 0; |
---|
4076 | } |
---|
4077 | } |
---|
4078 | else |
---|
4079 | { |
---|
4080 | result.setValue (l, A [l]); |
---|
4081 | degsf [l]= 0; |
---|
4082 | } |
---|
4083 | } |
---|
4084 | pos++; |
---|
4085 | k--; |
---|
4086 | l= 2; |
---|
4087 | } |
---|
4088 | |
---|
4089 | delete [] degsf; |
---|
4090 | |
---|
4091 | return result; |
---|
4092 | } |
---|
4093 | |
---|
4094 | static inline |
---|
4095 | int Hensel_P (const CanonicalForm & UU, CFArray & G, const Evaluation & AA, |
---|
4096 | const CFArray& LeadCoeffs ) |
---|
4097 | { |
---|
4098 | CFList factors; |
---|
4099 | factors.append (G[1]); |
---|
4100 | factors.append (G[2]); |
---|
4101 | |
---|
4102 | CFMap NN, MM; |
---|
4103 | Evaluation A= optimize4Lift (UU, MM, NN, AA); |
---|
4104 | |
---|
4105 | CanonicalForm U= MM (UU); |
---|
4106 | CFArray LCs= CFArray (1,2); |
---|
4107 | LCs [1]= MM (LeadCoeffs [1]); |
---|
4108 | LCs [2]= MM (LeadCoeffs [2]); |
---|
4109 | |
---|
4110 | CFList evaluation; |
---|
4111 | long termEstimate= size (U); |
---|
4112 | for (int i= A.min(); i <= A.max(); i++) |
---|
4113 | { |
---|
4114 | if (!A[i].isZero() && (getCharacteristic() > degree (U,i))) //TODO find a good estimate for getCharacteristic() <= degree (U,i) |
---|
4115 | { |
---|
4116 | termEstimate *= degree (U,i)*2; |
---|
4117 | termEstimate /= 3; |
---|
4118 | } |
---|
4119 | evaluation.append (A [i]); |
---|
4120 | } |
---|
4121 | if (termEstimate/getNumVars(U) > 500) |
---|
4122 | return -1; |
---|
4123 | CFList UEval; |
---|
4124 | CanonicalForm shiftedU= myShift2Zero (U, UEval, evaluation); |
---|
4125 | |
---|
4126 | if (size (shiftedU)/getNumVars (U) > 500) |
---|
4127 | return -1; |
---|
4128 | |
---|
4129 | CFArray shiftedLCs= CFArray (2); |
---|
4130 | CFList shiftedLCsEval1, shiftedLCsEval2; |
---|
4131 | shiftedLCs[0]= myShift2Zero (LCs[1], shiftedLCsEval1, evaluation); |
---|
4132 | shiftedLCs[1]= myShift2Zero (LCs[2], shiftedLCsEval2, evaluation); |
---|
4133 | factors.insert (1); |
---|
4134 | int liftBound= degree (UEval.getLast(), 2) + 1; |
---|
4135 | CFArray Pi; |
---|
4136 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
4137 | CFList diophant; |
---|
4138 | CFArray lcs= CFArray (2); |
---|
4139 | lcs [0]= shiftedLCsEval1.getFirst(); |
---|
4140 | lcs [1]= shiftedLCsEval2.getFirst(); |
---|
4141 | nonMonicHenselLift12 (UEval.getFirst(), factors, liftBound, Pi, diophant, M, |
---|
4142 | lcs, false); |
---|
4143 | |
---|
4144 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
4145 | { |
---|
4146 | if (!fdivides (i.getItem(), UEval.getFirst())) |
---|
4147 | return 0; |
---|
4148 | } |
---|
4149 | |
---|
4150 | int * liftBounds; |
---|
4151 | bool noOneToOne= false; |
---|
4152 | if (U.level() > 2) |
---|
4153 | { |
---|
4154 | liftBounds= new int [U.level() - 1]; /* index: 0.. U.level()-2 */ |
---|
4155 | liftBounds[0]= liftBound; |
---|
4156 | for (int i= 1; i < U.level() - 1; i++) |
---|
4157 | liftBounds[i]= degree (shiftedU, Variable (i + 2)) + 1; |
---|
4158 | factors= nonMonicHenselLift2 (UEval, factors, liftBounds, U.level() - 1, |
---|
4159 | false, shiftedLCsEval1, shiftedLCsEval2, Pi, |
---|
4160 | diophant, noOneToOne); |
---|
4161 | delete [] liftBounds; |
---|
4162 | if (noOneToOne) |
---|
4163 | return 0; |
---|
4164 | } |
---|
4165 | G[1]= factors.getFirst(); |
---|
4166 | G[2]= factors.getLast(); |
---|
4167 | G[1]= myReverseShift (G[1], evaluation); |
---|
4168 | G[2]= myReverseShift (G[2], evaluation); |
---|
4169 | G[1]= NN (G[1]); |
---|
4170 | G[2]= NN (G[2]); |
---|
4171 | return 1; |
---|
4172 | } |
---|
4173 | |
---|
4174 | static inline |
---|
4175 | bool findeval_P (const CanonicalForm & F, const CanonicalForm & G, |
---|
4176 | CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, |
---|
4177 | REvaluation & b, int delta, int degF, int degG, int maxeval, |
---|
4178 | int & count, int& k, int bound, int& l) |
---|
4179 | { |
---|
4180 | if( count == 0 && delta != 0) |
---|
4181 | { |
---|
4182 | if( count++ > maxeval ) |
---|
4183 | return false; |
---|
4184 | } |
---|
4185 | if (count > 0) |
---|
4186 | { |
---|
4187 | b.nextpoint(k); |
---|
4188 | if (k == 0) |
---|
4189 | k++; |
---|
4190 | l++; |
---|
4191 | if (l > bound) |
---|
4192 | { |
---|
4193 | l= 1; |
---|
4194 | k++; |
---|
4195 | if (k > tmax (F.level(), G.level()) - 1) |
---|
4196 | return false; |
---|
4197 | b.nextpoint (k); |
---|
4198 | } |
---|
4199 | if (count++ > maxeval) |
---|
4200 | return false; |
---|
4201 | } |
---|
4202 | while( true ) |
---|
4203 | { |
---|
4204 | Fb = b( F ); |
---|
4205 | if( degree( Fb, 1 ) == degF ) |
---|
4206 | { |
---|
4207 | Gb = b( G ); |
---|
4208 | if( degree( Gb, 1 ) == degG ) |
---|
4209 | { |
---|
4210 | Db = gcd( Fb, Gb ); |
---|
4211 | if( delta > 0 ) |
---|
4212 | { |
---|
4213 | if( degree( Db, 1 ) <= delta ) |
---|
4214 | return true; |
---|
4215 | } |
---|
4216 | else |
---|
4217 | return true; |
---|
4218 | } |
---|
4219 | } |
---|
4220 | if (k == 0) |
---|
4221 | k++; |
---|
4222 | b.nextpoint(k); |
---|
4223 | l++; |
---|
4224 | if (l > bound) |
---|
4225 | { |
---|
4226 | l= 1; |
---|
4227 | k++; |
---|
4228 | if (k > tmax (F.level(), G.level()) - 1) |
---|
4229 | return false; |
---|
4230 | b.nextpoint (k); |
---|
4231 | } |
---|
4232 | if( count++ > maxeval ) |
---|
4233 | return false; |
---|
4234 | } |
---|
4235 | } |
---|
4236 | |
---|
4237 | // parameters for heuristic |
---|
4238 | static int maxNumEval= 200; |
---|
4239 | static int sizePerVars1= 500; //try dense gcd if size/#variables is bigger |
---|
4240 | |
---|
4241 | /// Extended Zassenhaus GCD for finite fields |
---|
4242 | CanonicalForm EZGCD_P( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
4243 | { |
---|
4244 | if (FF.isZero() && degree(GG) > 0) return GG/Lc(GG); |
---|
4245 | else if (GG.isZero() && degree (FF) > 0) return FF/Lc(FF); |
---|
4246 | else if (FF.isZero() && GG.isZero()) return FF.genOne(); |
---|
4247 | if (FF.inBaseDomain() || GG.inBaseDomain()) return FF.genOne(); |
---|
4248 | if (FF.isUnivariate() && fdivides(FF, GG)) return FF/Lc(FF); |
---|
4249 | if (GG.isUnivariate() && fdivides(GG, FF)) return GG/Lc(GG); |
---|
4250 | if (FF == GG) return FF/Lc(FF); |
---|
4251 | |
---|
4252 | int maxNumVars= tmax (getNumVars (FF), getNumVars (GG)); |
---|
4253 | Variable a, oldA; |
---|
4254 | int sizeF= size (FF); |
---|
4255 | int sizeG= size (GG); |
---|
4256 | |
---|
4257 | if (sizeF/maxNumVars > sizePerVars1 && sizeG/maxNumVars > sizePerVars1) |
---|
4258 | { |
---|
4259 | if (hasFirstAlgVar (FF, a) || hasFirstAlgVar (GG, a)) |
---|
4260 | return GCD_Fp_extension (FF, GG, a); |
---|
4261 | else if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4262 | return GCD_GF (FF, GG); |
---|
4263 | else |
---|
4264 | return GCD_small_p (FF, GG); |
---|
4265 | } |
---|
4266 | |
---|
4267 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, |
---|
4268 | lcD; |
---|
4269 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
---|
4270 | int degF, degG, delta, count; |
---|
4271 | int maxeval; |
---|
4272 | maxeval= tmin((getCharacteristic()/ |
---|
4273 | (int)(ilog2(getCharacteristic())*log2exp))*2, maxNumEval); |
---|
4274 | count= 0; // number of eval. used |
---|
4275 | REvaluation b, bt; |
---|
4276 | int gcdfound = 0; |
---|
4277 | Variable x = Variable(1); |
---|
4278 | |
---|
4279 | F= FF; |
---|
4280 | G= GG; |
---|
4281 | |
---|
4282 | CFMap M,N; |
---|
4283 | int smallestDegLev; |
---|
4284 | TIMING_START (ez_p_compress) |
---|
4285 | int best_level= compress4EZGCD (F, G, M, N, smallestDegLev); |
---|
4286 | |
---|
4287 | if (best_level == 0) return G.genOne(); |
---|
4288 | |
---|
4289 | F= M (F); |
---|
4290 | G= M (G); |
---|
4291 | TIMING_END_AND_PRINT (ez_p_compress, "time for compression in EZ_P: ") |
---|
4292 | |
---|
4293 | TIMING_START (ez_p_content) |
---|
4294 | f = content( F, x ); g = content( G, x ); |
---|
4295 | d = gcd( f, g ); |
---|
4296 | F /= f; G /= g; |
---|
4297 | TIMING_END_AND_PRINT (ez_p_content, "time to extract content in EZ_P: ") |
---|
4298 | |
---|
4299 | if( F.isUnivariate() && G.isUnivariate() ) |
---|
4300 | { |
---|
4301 | if( F.mvar() == G.mvar() ) |
---|
4302 | d *= gcd( F, G ); |
---|
4303 | else |
---|
4304 | return N (d); |
---|
4305 | return N (d); |
---|
4306 | } |
---|
4307 | if ( F.isUnivariate()) |
---|
4308 | { |
---|
4309 | g= content (G,G.mvar()); |
---|
4310 | return N(d*gcd(F,g)); |
---|
4311 | } |
---|
4312 | if ( G.isUnivariate()) |
---|
4313 | { |
---|
4314 | f= content (F,F.mvar()); |
---|
4315 | return N(d*gcd(G,f)); |
---|
4316 | } |
---|
4317 | |
---|
4318 | maxNumVars= tmax (getNumVars (F), getNumVars (G)); |
---|
4319 | sizeF= size (F); |
---|
4320 | sizeG= size (G); |
---|
4321 | |
---|
4322 | if (sizeF/maxNumVars > sizePerVars1 && sizeG/maxNumVars > sizePerVars1) |
---|
4323 | { |
---|
4324 | if (hasFirstAlgVar (F, a) || hasFirstAlgVar (G, a)) |
---|
4325 | return N (d*GCD_Fp_extension (F, G, a)); |
---|
4326 | else if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4327 | return N (d*GCD_GF (F, G)); |
---|
4328 | else |
---|
4329 | return N (d*GCD_small_p (F, G)); |
---|
4330 | } |
---|
4331 | |
---|
4332 | int dummy= 0; |
---|
4333 | if( gcd_test_one( F, G, false, dummy ) ) |
---|
4334 | { |
---|
4335 | return N (d); |
---|
4336 | } |
---|
4337 | |
---|
4338 | bool passToGF= false; |
---|
4339 | bool extOfExt= false; |
---|
4340 | int p= getCharacteristic(); |
---|
4341 | bool algExtension= (hasFirstAlgVar(F,a) || hasFirstAlgVar(G,a)); |
---|
4342 | int k= 1; |
---|
4343 | CanonicalForm primElem, imPrimElem; |
---|
4344 | CFList source, dest; |
---|
4345 | if (p < 50 && CFFactory::gettype() != GaloisFieldDomain && !algExtension) |
---|
4346 | { |
---|
4347 | if (p == 2) |
---|
4348 | setCharacteristic (2, 12, 'Z'); |
---|
4349 | else if (p == 3) |
---|
4350 | setCharacteristic (3, 4, 'Z'); |
---|
4351 | else if (p == 5 || p == 7) |
---|
4352 | setCharacteristic (p, 3, 'Z'); |
---|
4353 | else |
---|
4354 | setCharacteristic (p, 2, 'Z'); |
---|
4355 | passToGF= true; |
---|
4356 | F= F.mapinto(); |
---|
4357 | G= G.mapinto(); |
---|
4358 | maxeval= 2*ipower (p, getGFDegree()); |
---|
4359 | } |
---|
4360 | else if (CFFactory::gettype() == GaloisFieldDomain && |
---|
4361 | ipower (p , getGFDegree()) < 50) |
---|
4362 | { |
---|
4363 | k= getGFDegree(); |
---|
4364 | if (ipower (p, 2*k) > 50) |
---|
4365 | setCharacteristic (p, 2*k, gf_name); |
---|
4366 | else |
---|
4367 | setCharacteristic (p, 3*k, gf_name); |
---|
4368 | F= GFMapUp (F, k); |
---|
4369 | G= GFMapUp (G, k); |
---|
4370 | maxeval= tmin (2*ipower (p, getGFDegree()), maxNumEval); |
---|
4371 | } |
---|
4372 | else if (p < 50 && algExtension && CFFactory::gettype() != GaloisFieldDomain) |
---|
4373 | { |
---|
4374 | int d= degree (getMipo (a)); |
---|
4375 | oldA= a; |
---|
4376 | Variable v2; |
---|
4377 | if (p == 2 && d < 6) |
---|
4378 | { |
---|
4379 | if (fac_NTL_char != p) |
---|
4380 | { |
---|
4381 | fac_NTL_char= p; |
---|
4382 | zz_p::init (p); |
---|
4383 | } |
---|
4384 | bool primFail= false; |
---|
4385 | Variable vBuf; |
---|
4386 | primElem= primitiveElement (a, vBuf, primFail); |
---|
4387 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
4388 | if (d < 3) |
---|
4389 | { |
---|
4390 | zz_pX NTLIrredpoly; |
---|
4391 | BuildIrred (NTLIrredpoly, d*3); |
---|
4392 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4393 | v2= rootOf (newMipo); |
---|
4394 | } |
---|
4395 | else |
---|
4396 | { |
---|
4397 | zz_pX NTLIrredpoly; |
---|
4398 | BuildIrred (NTLIrredpoly, d*2); |
---|
4399 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4400 | v2= rootOf (newMipo); |
---|
4401 | } |
---|
4402 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
4403 | extOfExt= true; |
---|
4404 | } |
---|
4405 | else if ((p == 3 && d < 4) || ((p == 5 || p == 7) && d < 3)) |
---|
4406 | { |
---|
4407 | if (fac_NTL_char != p) |
---|
4408 | { |
---|
4409 | fac_NTL_char= p; |
---|
4410 | zz_p::init (p); |
---|
4411 | } |
---|
4412 | bool primFail= false; |
---|
4413 | Variable vBuf; |
---|
4414 | primElem= primitiveElement (a, vBuf, primFail); |
---|
4415 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
4416 | zz_pX NTLIrredpoly; |
---|
4417 | BuildIrred (NTLIrredpoly, d*2); |
---|
4418 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4419 | v2= rootOf (newMipo); |
---|
4420 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
4421 | extOfExt= true; |
---|
4422 | } |
---|
4423 | if (extOfExt) |
---|
4424 | { |
---|
4425 | maxeval= tmin (2*ipower (p, degree (getMipo (v2))), maxNumEval); |
---|
4426 | F= mapUp (F, a, v2, primElem, imPrimElem, source, dest); |
---|
4427 | G= mapUp (G, a, v2, primElem, imPrimElem, source, dest); |
---|
4428 | a= v2; |
---|
4429 | } |
---|
4430 | } |
---|
4431 | |
---|
4432 | lcF = LC( F, x ); lcG = LC( G, x ); |
---|
4433 | lcD = gcd( lcF, lcG ); |
---|
4434 | |
---|
4435 | delta = 0; |
---|
4436 | degF = degree( F, x ); degG = degree( G, x ); |
---|
4437 | |
---|
4438 | if(hasFirstAlgVar(G,a)) |
---|
4439 | b = REvaluation( 2, tmax(F.level(), G.level()), AlgExtRandomF( a ) ); |
---|
4440 | else |
---|
4441 | { // both not in extension given by algebraic variable |
---|
4442 | if (CFFactory::gettype() != GaloisFieldDomain) |
---|
4443 | b = REvaluation( 2, tmax(F.level(), G.level()), FFRandom() ); |
---|
4444 | else |
---|
4445 | b = REvaluation( 2, tmax(F.level(), G.level()), GFRandom() ); |
---|
4446 | } |
---|
4447 | |
---|
4448 | CanonicalForm cand, contcand; |
---|
4449 | CanonicalForm result; |
---|
4450 | int o, t; |
---|
4451 | o= 0; |
---|
4452 | t= 1; |
---|
4453 | int goodPointCount= 0; |
---|
4454 | while( !gcdfound ) |
---|
4455 | { |
---|
4456 | TIMING_START (ez_p_eval); |
---|
4457 | if( !findeval_P( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count, o, |
---|
4458 | maxeval/maxNumVars, t )) |
---|
4459 | { // too many eval. used --> try another method |
---|
4460 | Off (SW_USE_EZGCD_P); |
---|
4461 | result= gcd (F,G); |
---|
4462 | On (SW_USE_EZGCD_P); |
---|
4463 | if (passToGF) |
---|
4464 | { |
---|
4465 | CanonicalForm mipo= gf_mipo; |
---|
4466 | setCharacteristic (p); |
---|
4467 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4468 | result= GF2FalphaRep (result, alpha); |
---|
4469 | } |
---|
4470 | if (k > 1) |
---|
4471 | { |
---|
4472 | result= GFMapDown (result, k); |
---|
4473 | setCharacteristic (p, k, gf_name); |
---|
4474 | } |
---|
4475 | if (extOfExt) |
---|
4476 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4477 | return N (d*result); |
---|
4478 | } |
---|
4479 | TIMING_END_AND_PRINT (ez_p_eval, "time for eval point search in EZ_P1: "); |
---|
4480 | delta = degree( Db ); |
---|
4481 | if (delta == degF) |
---|
4482 | { |
---|
4483 | if (degF <= degG && fdivides (F, G)) |
---|
4484 | { |
---|
4485 | if (passToGF) |
---|
4486 | { |
---|
4487 | CanonicalForm mipo= gf_mipo; |
---|
4488 | setCharacteristic (p); |
---|
4489 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4490 | F= GF2FalphaRep (F, alpha); |
---|
4491 | } |
---|
4492 | if (k > 1) |
---|
4493 | { |
---|
4494 | F= GFMapDown (F, k); |
---|
4495 | setCharacteristic (p, k, gf_name); |
---|
4496 | } |
---|
4497 | if (extOfExt) |
---|
4498 | F= mapDown (F, primElem, imPrimElem, oldA, dest, source); |
---|
4499 | return N (d*F); |
---|
4500 | } |
---|
4501 | else |
---|
4502 | delta--; |
---|
4503 | } |
---|
4504 | else if (delta == degG) |
---|
4505 | { |
---|
4506 | if (degG <= degF && fdivides (G, F)) |
---|
4507 | { |
---|
4508 | if (passToGF) |
---|
4509 | { |
---|
4510 | CanonicalForm mipo= gf_mipo; |
---|
4511 | setCharacteristic (p); |
---|
4512 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4513 | G= GF2FalphaRep (G, alpha); |
---|
4514 | } |
---|
4515 | if (k > 1) |
---|
4516 | { |
---|
4517 | G= GFMapDown (G, k); |
---|
4518 | setCharacteristic (p, k, gf_name); |
---|
4519 | } |
---|
4520 | if (extOfExt) |
---|
4521 | G= mapDown (G, primElem, imPrimElem, oldA, dest, source); |
---|
4522 | return N (d*G); |
---|
4523 | } |
---|
4524 | else |
---|
4525 | delta--; |
---|
4526 | } |
---|
4527 | if( delta == 0 ) |
---|
4528 | { |
---|
4529 | if (passToGF) |
---|
4530 | setCharacteristic (p); |
---|
4531 | if (k > 1) |
---|
4532 | setCharacteristic (p, k, gf_name); |
---|
4533 | return N (d); |
---|
4534 | } |
---|
4535 | while( true ) |
---|
4536 | { |
---|
4537 | bt = b; |
---|
4538 | TIMING_START (ez_p_eval); |
---|
4539 | if( !findeval_P(F,G,Fbt,Gbt,Dbt, bt, delta, degF, degG, maxeval, count, o, |
---|
4540 | maxeval/maxNumVars, t )) |
---|
4541 | { // too many eval. used --> try another method |
---|
4542 | Off (SW_USE_EZGCD_P); |
---|
4543 | result= gcd (F,G); |
---|
4544 | On (SW_USE_EZGCD_P); |
---|
4545 | if (passToGF) |
---|
4546 | { |
---|
4547 | CanonicalForm mipo= gf_mipo; |
---|
4548 | setCharacteristic (p); |
---|
4549 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4550 | result= GF2FalphaRep (result, alpha); |
---|
4551 | } |
---|
4552 | if (k > 1) |
---|
4553 | { |
---|
4554 | result= GFMapDown (result, k); |
---|
4555 | setCharacteristic (p, k, gf_name); |
---|
4556 | } |
---|
4557 | if (extOfExt) |
---|
4558 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4559 | return N (d*result); |
---|
4560 | } |
---|
4561 | TIMING_END_AND_PRINT (ez_p_eval, "time for eval point search in EZ_P2: "); |
---|
4562 | int dd = degree( Dbt ); |
---|
4563 | if( dd == 0 ) |
---|
4564 | { |
---|
4565 | if (passToGF) |
---|
4566 | setCharacteristic (p); |
---|
4567 | if (k > 1) |
---|
4568 | setCharacteristic (p, k, gf_name); |
---|
4569 | return N (d); |
---|
4570 | } |
---|
4571 | if( dd == delta ) |
---|
4572 | { |
---|
4573 | goodPointCount++; |
---|
4574 | if (goodPointCount == 5) |
---|
4575 | break; |
---|
4576 | } |
---|
4577 | if( dd < delta ) |
---|
4578 | { |
---|
4579 | goodPointCount= 0; |
---|
4580 | delta = dd; |
---|
4581 | b = bt; |
---|
4582 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
---|
4583 | } |
---|
4584 | if (delta == degF) |
---|
4585 | { |
---|
4586 | if (degF <= degG && fdivides (F, G)) |
---|
4587 | { |
---|
4588 | if (passToGF) |
---|
4589 | { |
---|
4590 | CanonicalForm mipo= gf_mipo; |
---|
4591 | setCharacteristic (p); |
---|
4592 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4593 | F= GF2FalphaRep (F, alpha); |
---|
4594 | } |
---|
4595 | if (k > 1) |
---|
4596 | { |
---|
4597 | F= GFMapDown (F, k); |
---|
4598 | setCharacteristic (p, k, gf_name); |
---|
4599 | } |
---|
4600 | if (extOfExt) |
---|
4601 | F= mapDown (F, primElem, imPrimElem, oldA, dest, source); |
---|
4602 | return N (d*F); |
---|
4603 | } |
---|
4604 | else |
---|
4605 | delta--; |
---|
4606 | } |
---|
4607 | else if (delta == degG) |
---|
4608 | { |
---|
4609 | if (degG <= degF && fdivides (G, F)) |
---|
4610 | { |
---|
4611 | if (passToGF) |
---|
4612 | { |
---|
4613 | CanonicalForm mipo= gf_mipo; |
---|
4614 | setCharacteristic (p); |
---|
4615 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4616 | G= GF2FalphaRep (G, alpha); |
---|
4617 | } |
---|
4618 | if (k > 1) |
---|
4619 | { |
---|
4620 | G= GFMapDown (G, k); |
---|
4621 | setCharacteristic (p, k, gf_name); |
---|
4622 | } |
---|
4623 | if (extOfExt) |
---|
4624 | G= mapDown (G, primElem, imPrimElem, oldA, dest, source); |
---|
4625 | return N (d*G); |
---|
4626 | } |
---|
4627 | else |
---|
4628 | delta--; |
---|
4629 | } |
---|
4630 | if( delta == 0 ) |
---|
4631 | { |
---|
4632 | if (passToGF) |
---|
4633 | setCharacteristic (p); |
---|
4634 | if (k > 1) |
---|
4635 | setCharacteristic (p, k, gf_name); |
---|
4636 | return N (d); |
---|
4637 | } |
---|
4638 | } |
---|
4639 | if( delta != degF && delta != degG ) |
---|
4640 | { |
---|
4641 | bool B_is_F; |
---|
4642 | CanonicalForm xxx1, xxx2; |
---|
4643 | CanonicalForm buf; |
---|
4644 | DD[1] = Fb / Db; |
---|
4645 | buf= Gb/Db; |
---|
4646 | xxx1 = gcd( DD[1], Db ); |
---|
4647 | xxx2 = gcd( buf, Db ); |
---|
4648 | if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
4649 | (size (F) <= size (G))) |
---|
4650 | || (xxx1.inCoeffDomain() && !xxx2.inCoeffDomain())) |
---|
4651 | { |
---|
4652 | B = F; |
---|
4653 | DD[2] = Db; |
---|
4654 | lcDD[1] = lcF; |
---|
4655 | lcDD[2] = lcD; |
---|
4656 | B_is_F = true; |
---|
4657 | } |
---|
4658 | else if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
4659 | (size (G) < size (F))) |
---|
4660 | || (!xxx1.inCoeffDomain() && xxx2.inCoeffDomain())) |
---|
4661 | { |
---|
4662 | DD[1] = buf; |
---|
4663 | B = G; |
---|
4664 | DD[2] = Db; |
---|
4665 | lcDD[1] = lcG; |
---|
4666 | lcDD[2] = lcD; |
---|
4667 | B_is_F = false; |
---|
4668 | } |
---|
4669 | else // special case handling |
---|
4670 | { |
---|
4671 | Off (SW_USE_EZGCD_P); |
---|
4672 | result= gcd (F,G); |
---|
4673 | On (SW_USE_EZGCD_P); |
---|
4674 | if (passToGF) |
---|
4675 | { |
---|
4676 | CanonicalForm mipo= gf_mipo; |
---|
4677 | setCharacteristic (p); |
---|
4678 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4679 | result= GF2FalphaRep (result, alpha); |
---|
4680 | } |
---|
4681 | if (k > 1) |
---|
4682 | { |
---|
4683 | result= GFMapDown (result, k); |
---|
4684 | setCharacteristic (p, k, gf_name); |
---|
4685 | } |
---|
4686 | if (extOfExt) |
---|
4687 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4688 | return N (d*result); |
---|
4689 | } |
---|
4690 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
---|
4691 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
---|
4692 | |
---|
4693 | if (size (B*lcDD[2])/maxNumVars > sizePerVars1) |
---|
4694 | { |
---|
4695 | if (algExtension) |
---|
4696 | { |
---|
4697 | result= GCD_Fp_extension (F, G, a); |
---|
4698 | if (extOfExt) |
---|
4699 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4700 | return N (d*result); |
---|
4701 | } |
---|
4702 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4703 | { |
---|
4704 | result= GCD_GF (F, G); |
---|
4705 | if (passToGF) |
---|
4706 | { |
---|
4707 | CanonicalForm mipo= gf_mipo; |
---|
4708 | setCharacteristic (p); |
---|
4709 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4710 | result= GF2FalphaRep (result, alpha); |
---|
4711 | } |
---|
4712 | if (k > 1) |
---|
4713 | { |
---|
4714 | result= GFMapDown (result, k); |
---|
4715 | setCharacteristic (p, k, gf_name); |
---|
4716 | } |
---|
4717 | return N (d*result); |
---|
4718 | } |
---|
4719 | else |
---|
4720 | return N (d*GCD_small_p (F,G)); |
---|
4721 | } |
---|
4722 | |
---|
4723 | TIMING_START (ez_p_hensel_lift); |
---|
4724 | gcdfound= Hensel_P (B*lcD, DD, b, lcDD); |
---|
4725 | TIMING_END_AND_PRINT (ez_p_hensel_lift, "time for Hensel lift in EZ_P: "); |
---|
4726 | |
---|
4727 | if (gcdfound == -1) //things became dense |
---|
4728 | { |
---|
4729 | if (algExtension) |
---|
4730 | { |
---|
4731 | result= GCD_Fp_extension (F, G, a); |
---|
4732 | if (extOfExt) |
---|
4733 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4734 | return N (d*result); |
---|
4735 | } |
---|
4736 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4737 | { |
---|
4738 | result= GCD_GF (F, G); |
---|
4739 | if (passToGF) |
---|
4740 | { |
---|
4741 | CanonicalForm mipo= gf_mipo; |
---|
4742 | setCharacteristic (p); |
---|
4743 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4744 | result= GF2FalphaRep (result, alpha); |
---|
4745 | } |
---|
4746 | if (k > 1) |
---|
4747 | { |
---|
4748 | result= GFMapDown (result, k); |
---|
4749 | setCharacteristic (p, k, gf_name); |
---|
4750 | } |
---|
4751 | return N (d*result); |
---|
4752 | } |
---|
4753 | else |
---|
4754 | { |
---|
4755 | if (p >= cf_getBigPrime(0)) |
---|
4756 | return N (d*sparseGCDFp (F,G)); |
---|
4757 | else |
---|
4758 | return N (d*GCD_small_p (F,G)); |
---|
4759 | } |
---|
4760 | } |
---|
4761 | |
---|
4762 | if (gcdfound == 1) |
---|
4763 | { |
---|
4764 | TIMING_START (termination_test); |
---|
4765 | contcand= content (DD[2], Variable (1)); |
---|
4766 | cand = DD[2] / contcand; |
---|
4767 | if (B_is_F) |
---|
4768 | gcdfound = fdivides( cand, G ) && cand*(DD[1]/(lcD/contcand)) == F; |
---|
4769 | else |
---|
4770 | gcdfound = fdivides( cand, F ) && cand*(DD[1]/(lcD/contcand)) == G; |
---|
4771 | TIMING_END_AND_PRINT (termination_test, |
---|
4772 | "time for termination test EZ_P: "); |
---|
4773 | |
---|
4774 | if (passToGF && gcdfound) |
---|
4775 | { |
---|
4776 | CanonicalForm mipo= gf_mipo; |
---|
4777 | setCharacteristic (p); |
---|
4778 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4779 | cand= GF2FalphaRep (cand, alpha); |
---|
4780 | } |
---|
4781 | if (k > 1 && gcdfound) |
---|
4782 | { |
---|
4783 | cand= GFMapDown (cand, k); |
---|
4784 | setCharacteristic (p, k, gf_name); |
---|
4785 | } |
---|
4786 | if (extOfExt && gcdfound) |
---|
4787 | cand= mapDown (cand, primElem, imPrimElem, oldA, dest, source); |
---|
4788 | } |
---|
4789 | } |
---|
4790 | delta--; |
---|
4791 | goodPointCount= 0; |
---|
4792 | } |
---|
4793 | return N (d*cand); |
---|
4794 | } |
---|
4795 | |
---|
4796 | |
---|
4797 | #endif |
---|