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, Labahnn |
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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 | #include "config.h" |
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19 | |
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20 | #include "cf_assert.h" |
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21 | #include "debug.h" |
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22 | #include "timing.h" |
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23 | |
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24 | #include "canonicalform.h" |
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25 | #include "algext.h" |
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26 | #include "cf_map.h" |
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27 | #include "cf_util.h" |
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28 | #include "templates/ftmpl_functions.h" |
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29 | #include "cf_random.h" |
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30 | #include "cf_reval.h" |
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31 | #include "facHensel.h" |
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32 | #include "cf_iter.h" |
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33 | #include "cfNewtonPolygon.h" |
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34 | #include "cf_algorithm.h" |
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35 | |
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36 | // iinline helper functions: |
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37 | #include "cf_map_ext.h" |
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38 | |
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39 | #ifdef HAVE_NTL |
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40 | #include <NTLconvert.h> |
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41 | #endif |
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42 | |
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43 | #ifdef HAVE_FLINT |
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44 | #include "FLINTconvert.h" |
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45 | #endif |
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46 | |
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47 | #include "cf_gcd_smallp.h" |
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48 | |
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49 | TIMING_DEFINE_PRINT(gcd_recursion) |
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50 | TIMING_DEFINE_PRINT(newton_interpolation) |
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51 | TIMING_DEFINE_PRINT(termination_test) |
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52 | TIMING_DEFINE_PRINT(ez_p_compress) |
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53 | TIMING_DEFINE_PRINT(ez_p_hensel_lift) |
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54 | TIMING_DEFINE_PRINT(ez_p_eval) |
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55 | TIMING_DEFINE_PRINT(ez_p_content) |
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56 | |
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57 | bool |
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58 | terminationTest (const CanonicalForm& F, const CanonicalForm& G, |
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59 | const CanonicalForm& coF, const CanonicalForm& coG, |
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60 | const CanonicalForm& cand) |
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61 | { |
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62 | CanonicalForm LCCand= abs (LC (cand)); |
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63 | if (LCCand*abs (LC (coF)) == abs (LC (F))) |
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64 | { |
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65 | if (LCCand*abs (LC (coG)) == abs (LC (G))) |
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66 | { |
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67 | if (abs (cand)*abs (coF) == abs (F)) |
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68 | { |
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69 | if (abs (cand)*abs (coG) == abs (G)) |
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70 | return true; |
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71 | } |
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72 | return false; |
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73 | } |
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74 | return false; |
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75 | } |
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76 | return false; |
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77 | } |
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78 | |
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79 | #ifdef HAVE_NTL |
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80 | |
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81 | static const double log2exp= 1.442695041; |
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82 | |
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83 | /// compressing two polynomials F and G, M is used for compressing, |
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84 | /// N to reverse the compression |
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85 | int myCompress (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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86 | CFMap & N, bool topLevel) |
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87 | { |
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88 | int n= tmax (F.level(), G.level()); |
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89 | int * degsf= new int [n + 1]; |
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90 | int * degsg= new int [n + 1]; |
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91 | |
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92 | for (int i = 0; i <= n; i++) |
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93 | degsf[i]= degsg[i]= 0; |
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94 | |
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95 | degsf= degrees (F, degsf); |
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96 | degsg= degrees (G, degsg); |
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97 | |
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98 | int both_non_zero= 0; |
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99 | int f_zero= 0; |
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100 | int g_zero= 0; |
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101 | int both_zero= 0; |
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102 | |
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103 | if (topLevel) |
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104 | { |
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105 | for (int i= 1; i <= n; i++) |
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106 | { |
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107 | if (degsf[i] != 0 && degsg[i] != 0) |
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108 | { |
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109 | both_non_zero++; |
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110 | continue; |
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111 | } |
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112 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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113 | { |
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114 | f_zero++; |
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115 | continue; |
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116 | } |
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117 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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118 | { |
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119 | g_zero++; |
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120 | continue; |
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121 | } |
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122 | } |
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123 | |
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124 | if (both_non_zero == 0) |
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125 | { |
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126 | delete [] degsf; |
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127 | delete [] degsg; |
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128 | return 0; |
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129 | } |
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130 | |
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131 | // map Variables which do not occur in both polynomials to higher levels |
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132 | int k= 1; |
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133 | int l= 1; |
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134 | for (int i= 1; i <= n; i++) |
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135 | { |
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136 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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137 | { |
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138 | if (k + both_non_zero != i) |
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139 | { |
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140 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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141 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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142 | } |
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143 | k++; |
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144 | } |
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145 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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146 | { |
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147 | if (l + g_zero + both_non_zero != i) |
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148 | { |
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149 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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150 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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151 | } |
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152 | l++; |
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153 | } |
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154 | } |
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155 | |
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156 | // sort Variables x_{i} in increasing order of |
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157 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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158 | int m= tmax (F.level(), G.level()); |
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159 | int min_max_deg; |
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160 | k= both_non_zero; |
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161 | l= 0; |
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162 | int i= 1; |
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163 | while (k > 0) |
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164 | { |
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165 | if (degsf [i] != 0 && degsg [i] != 0) |
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166 | min_max_deg= tmax (degsf[i], degsg[i]); |
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167 | else |
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168 | min_max_deg= 0; |
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169 | while (min_max_deg == 0) |
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170 | { |
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171 | i++; |
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172 | if (degsf [i] != 0 && degsg [i] != 0) |
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173 | min_max_deg= tmax (degsf[i], degsg[i]); |
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174 | else |
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175 | min_max_deg= 0; |
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176 | } |
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177 | for (int j= i + 1; j <= m; j++) |
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178 | { |
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179 | if (degsf[j] != 0 && degsg [j] != 0 && |
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180 | tmax (degsf[j],degsg[j]) <= min_max_deg) |
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181 | { |
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182 | min_max_deg= tmax (degsf[j], degsg[j]); |
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183 | l= j; |
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184 | } |
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185 | } |
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186 | if (l != 0) |
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187 | { |
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188 | if (l != k) |
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189 | { |
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190 | M.newpair (Variable (l), Variable(k)); |
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191 | N.newpair (Variable (k), Variable(l)); |
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192 | degsf[l]= 0; |
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193 | degsg[l]= 0; |
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194 | l= 0; |
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195 | } |
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196 | else |
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197 | { |
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198 | degsf[l]= 0; |
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199 | degsg[l]= 0; |
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200 | l= 0; |
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201 | } |
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202 | } |
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203 | else if (l == 0) |
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204 | { |
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205 | if (i != k) |
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206 | { |
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207 | M.newpair (Variable (i), Variable (k)); |
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208 | N.newpair (Variable (k), Variable (i)); |
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209 | degsf[i]= 0; |
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210 | degsg[i]= 0; |
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211 | } |
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212 | else |
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213 | { |
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214 | degsf[i]= 0; |
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215 | degsg[i]= 0; |
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216 | } |
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217 | i++; |
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218 | } |
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219 | k--; |
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220 | } |
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221 | } |
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222 | else |
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223 | { |
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224 | //arrange Variables such that no gaps occur |
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225 | for (int i= 1; i <= n; i++) |
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226 | { |
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227 | if (degsf[i] == 0 && degsg[i] == 0) |
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228 | { |
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229 | both_zero++; |
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230 | continue; |
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231 | } |
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232 | else |
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233 | { |
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234 | if (both_zero != 0) |
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235 | { |
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236 | M.newpair (Variable (i), Variable (i - both_zero)); |
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237 | N.newpair (Variable (i - both_zero), Variable (i)); |
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238 | } |
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239 | } |
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240 | } |
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241 | } |
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242 | |
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243 | delete [] degsf; |
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244 | delete [] degsg; |
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245 | |
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246 | return 1; |
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247 | } |
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248 | |
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249 | static inline CanonicalForm |
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250 | uni_content (const CanonicalForm & F); |
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251 | |
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252 | CanonicalForm |
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253 | uni_content (const CanonicalForm& F, const Variable& x) |
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254 | { |
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255 | if (F.inCoeffDomain()) |
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256 | return F.genOne(); |
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257 | if (F.level() == x.level() && F.isUnivariate()) |
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258 | return F; |
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259 | if (F.level() != x.level() && F.isUnivariate()) |
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260 | return F.genOne(); |
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261 | |
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262 | if (x.level() != 1) |
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263 | { |
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264 | CanonicalForm f= swapvar (F, x, Variable (1)); |
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265 | CanonicalForm result= uni_content (f); |
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266 | return swapvar (result, x, Variable (1)); |
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267 | } |
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268 | else |
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269 | return uni_content (F); |
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270 | } |
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271 | |
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272 | /// compute the content of F, where F is considered as an element of |
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273 | /// \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$ |
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274 | static inline CanonicalForm |
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275 | uni_content (const CanonicalForm & F) |
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276 | { |
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277 | if (F.inBaseDomain()) |
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278 | return F.genOne(); |
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279 | if (F.level() == 1 && F.isUnivariate()) |
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280 | return F; |
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281 | if (F.level() != 1 && F.isUnivariate()) |
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282 | return F.genOne(); |
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283 | if (degree (F,1) == 0) return F.genOne(); |
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284 | |
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285 | int l= F.level(); |
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286 | if (l == 2) |
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287 | return content(F); |
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288 | else |
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289 | { |
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290 | CanonicalForm pol, c = 0; |
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291 | CFIterator i = F; |
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292 | for (; i.hasTerms(); i++) |
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293 | { |
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294 | pol= i.coeff(); |
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295 | pol= uni_content (pol); |
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296 | c= gcd (c, pol); |
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297 | if (c.isOne()) |
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298 | return c; |
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299 | } |
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300 | return c; |
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301 | } |
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302 | } |
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303 | |
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304 | CanonicalForm |
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305 | extractContents (const CanonicalForm& F, const CanonicalForm& G, |
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306 | CanonicalForm& contentF, CanonicalForm& contentG, |
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307 | CanonicalForm& ppF, CanonicalForm& ppG, const int d) |
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308 | { |
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309 | CanonicalForm uniContentF, uniContentG, gcdcFcG; |
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310 | contentF= 1; |
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311 | contentG= 1; |
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312 | ppF= F; |
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313 | ppG= G; |
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314 | CanonicalForm result= 1; |
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315 | for (int i= 1; i <= d; i++) |
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316 | { |
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317 | uniContentF= uni_content (F, Variable (i)); |
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318 | uniContentG= uni_content (G, Variable (i)); |
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319 | gcdcFcG= gcd (uniContentF, uniContentG); |
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320 | contentF *= uniContentF; |
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321 | contentG *= uniContentG; |
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322 | ppF /= uniContentF; |
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323 | ppG /= uniContentG; |
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324 | result *= gcdcFcG; |
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325 | } |
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326 | return result; |
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327 | } |
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328 | |
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329 | /// compute the leading coefficient of F, where F is considered as an element |
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330 | /// of \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$, order on Mon (x_{2},\ldots ,x_{n}) |
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331 | /// is dp. |
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332 | static inline |
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333 | CanonicalForm uni_lcoeff (const CanonicalForm& F) |
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334 | { |
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335 | if (F.level() > 1) |
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336 | { |
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337 | Variable x= Variable (2); |
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338 | int deg= totaldegree (F, x, F.mvar()); |
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339 | for (CFIterator i= F; i.hasTerms(); i++) |
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340 | { |
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341 | if (i.exp() + totaldegree (i.coeff(), x, i.coeff().mvar()) == deg) |
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342 | return uni_lcoeff (i.coeff()); |
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343 | } |
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344 | } |
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345 | return F; |
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346 | } |
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347 | |
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348 | /// Newton interpolation - Incremental algorithm. |
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349 | /// Given a list of values alpha_i and a list of polynomials u_i, 1 <= i <= n, |
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350 | /// computes the interpolation polynomial assuming that |
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351 | /// the polynomials in u are the results of evaluating the variabe x |
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352 | /// of the unknown polynomial at the alpha values. |
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353 | /// This incremental version receives only the values of alpha_n and u_n and |
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354 | /// the previous interpolation polynomial for points 1 <= i <= n-1, and computes |
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355 | /// the polynomial interpolating in all the points. |
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356 | /// newtonPoly must be equal to (x - alpha_1) * ... * (x - alpha_{n-1}) |
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357 | static inline CanonicalForm |
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358 | newtonInterp(const CanonicalForm alpha, const CanonicalForm u, |
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359 | const CanonicalForm newtonPoly, const CanonicalForm oldInterPoly, |
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360 | const Variable & x) |
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361 | { |
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362 | CanonicalForm interPoly; |
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363 | |
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364 | interPoly= oldInterPoly + ((u - oldInterPoly(alpha, x))/newtonPoly(alpha, x)) |
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365 | *newtonPoly; |
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366 | return interPoly; |
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367 | } |
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368 | |
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369 | /// compute a random element a of \f$ F_{p}(\alpha ) \f$ , |
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370 | /// s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns |
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371 | /// fail if there are no field elements left which have not been used before |
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372 | static inline CanonicalForm |
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373 | randomElement (const CanonicalForm & F, const Variable & alpha, CFList & list, |
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374 | bool & fail) |
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375 | { |
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376 | fail= false; |
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377 | Variable x= F.mvar(); |
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378 | AlgExtRandomF genAlgExt (alpha); |
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379 | FFRandom genFF; |
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380 | CanonicalForm random, mipo; |
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381 | mipo= getMipo (alpha); |
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382 | int p= getCharacteristic (); |
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383 | int d= degree (mipo); |
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384 | int bound= ipower (p, d); |
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385 | do |
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386 | { |
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387 | if (list.length() == bound) |
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388 | { |
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389 | fail= true; |
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390 | break; |
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391 | } |
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392 | if (list.length() < p) |
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393 | { |
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394 | random= genFF.generate(); |
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395 | while (find (list, random)) |
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396 | random= genFF.generate(); |
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397 | } |
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398 | else |
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399 | { |
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400 | random= genAlgExt.generate(); |
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401 | while (find (list, random)) |
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402 | random= genAlgExt.generate(); |
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403 | } |
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404 | if (F (random, x) == 0) |
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405 | { |
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406 | list.append (random); |
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407 | continue; |
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408 | } |
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409 | } while (find (list, random)); |
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410 | return random; |
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411 | } |
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412 | |
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413 | static inline |
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414 | Variable chooseExtension (const Variable & alpha) |
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415 | { |
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416 | zz_p::init (getCharacteristic()); |
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417 | zz_pX NTLIrredpoly; |
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418 | int i, m; |
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419 | // extension of F_p needed |
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420 | if (alpha.level() == 1) |
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421 | { |
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422 | i= 1; |
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423 | m= 2; |
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424 | } //extension of F_p(alpha) |
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425 | if (alpha.level() != 1) |
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426 | { |
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427 | i= 4; |
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428 | m= degree (getMipo (alpha)); |
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429 | } |
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430 | BuildIrred (NTLIrredpoly, i*m); |
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431 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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432 | return rootOf (newMipo); |
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433 | } |
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434 | |
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435 | /// chooses a suitable extension of \f$ F_{p}(\alpha ) \f$ |
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436 | /// we do not extend \f$ F_{p}(\alpha ) \f$ itself but extend \f$ F_{p} \f$ , |
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437 | /// s.t. \f$ F_{p}(\alpha ) \subset F_{p}(\beta ) \f$ |
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438 | static inline |
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439 | void choose_extension (const int& d, const int& num_vars, Variable& beta) |
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440 | { |
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441 | int p= getCharacteristic(); |
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442 | zz_p::init (p); |
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443 | zz_pX NTLirredpoly; |
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444 | //TODO: replace d by max_{i} (deg_x{i}(f)) |
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445 | int i= (int) (log ((double) ipower (d + 1, num_vars))/log ((double) p)); |
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446 | int m= degree (getMipo (beta)); |
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447 | if (i <= 1) |
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448 | i= 2; |
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449 | BuildIrred (NTLirredpoly, i*m); |
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450 | CanonicalForm mipo= convertNTLzzpX2CF (NTLirredpoly, Variable(1)); |
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451 | beta= rootOf (mipo); |
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452 | } |
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453 | |
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454 | CanonicalForm |
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455 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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456 | CanonicalForm& coF, CanonicalForm& coG, |
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457 | Variable & alpha, CFList& l, bool& topLevel); |
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458 | |
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459 | CanonicalForm |
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460 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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461 | Variable & alpha, CFList& l, bool& topLevel) |
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462 | { |
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463 | CanonicalForm dummy1, dummy2; |
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464 | CanonicalForm result= GCD_Fp_extension (F, G, dummy1, dummy2, alpha, l, |
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465 | topLevel); |
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466 | return result; |
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467 | } |
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468 | |
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469 | /// GCD of F and G over \f$ F_{p}(\alpha ) \f$ , |
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470 | /// l and topLevel are only used internally, output is monic |
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471 | /// based on Alg. 7.2. as described in "Algorithms for |
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472 | /// Computer Algebra" by Geddes, Czapor, Labahn |
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473 | CanonicalForm |
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474 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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475 | CanonicalForm& coF, CanonicalForm& coG, |
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476 | Variable & alpha, CFList& l, bool& topLevel) |
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477 | { |
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478 | CanonicalForm A= F; |
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479 | CanonicalForm B= G; |
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480 | if (F.isZero() && degree(G) > 0) |
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481 | { |
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482 | coF= 0; |
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483 | coG= Lc (G); |
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484 | return G/Lc(G); |
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485 | } |
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486 | else if (G.isZero() && degree (F) > 0) |
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487 | { |
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488 | coF= Lc (F); |
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489 | coG= 0; |
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490 | return F/Lc(F); |
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491 | } |
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492 | else if (F.isZero() && G.isZero()) |
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493 | { |
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494 | coF= coG= 0; |
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495 | return F.genOne(); |
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496 | } |
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497 | if (F.inBaseDomain() || G.inBaseDomain()) |
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498 | { |
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499 | coF= F; |
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500 | coG= G; |
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501 | return F.genOne(); |
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502 | } |
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503 | if (F.isUnivariate() && fdivides(F, G, coG)) |
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504 | { |
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505 | coF= Lc (F); |
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506 | return F/Lc(F); |
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507 | } |
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508 | if (G.isUnivariate() && fdivides(G, F, coF)) |
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509 | { |
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510 | coG= Lc (G); |
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511 | return G/Lc(G); |
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512 | } |
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513 | if (F == G) |
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514 | { |
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515 | coF= coG= Lc (F); |
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516 | return F/Lc(F); |
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517 | } |
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518 | |
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519 | CFMap M,N; |
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520 | int best_level= myCompress (A, B, M, N, topLevel); |
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521 | |
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522 | if (best_level == 0) |
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523 | { |
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524 | coF= F; |
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525 | coG= G; |
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526 | return B.genOne(); |
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527 | } |
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528 | |
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529 | A= M(A); |
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530 | B= M(B); |
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531 | |
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532 | Variable x= Variable(1); |
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533 | |
---|
534 | //univariate case |
---|
535 | if (A.isUnivariate() && B.isUnivariate()) |
---|
536 | { |
---|
537 | CanonicalForm result= gcd (A, B); |
---|
538 | coF= N (A/result); |
---|
539 | coG= N (B/result); |
---|
540 | return N (result); |
---|
541 | } |
---|
542 | |
---|
543 | CanonicalForm cA, cB; // content of A and B |
---|
544 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
545 | CanonicalForm gcdcAcB; |
---|
546 | |
---|
547 | cA = uni_content (A); |
---|
548 | cB = uni_content (B); |
---|
549 | gcdcAcB= gcd (cA, cB); |
---|
550 | ppA= A/cA; |
---|
551 | ppB= B/cB; |
---|
552 | |
---|
553 | int sizeNewtonPolyg; |
---|
554 | int ** newtonPolyg= NULL; |
---|
555 | mat_ZZ MM; |
---|
556 | vec_ZZ V; |
---|
557 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
558 | if (compressConvexDense) |
---|
559 | { |
---|
560 | CanonicalForm bufcA= cA; |
---|
561 | CanonicalForm bufcB= cB; |
---|
562 | cA= content (ppA, 1); |
---|
563 | cB= content (ppB, 1); |
---|
564 | ppA /= cA; |
---|
565 | ppB /= cB; |
---|
566 | gcdcAcB *= gcd (cA, cB); |
---|
567 | cA *= bufcA; |
---|
568 | cB *= bufcB; |
---|
569 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
570 | { |
---|
571 | if (ppA.level() == ppB.level()) |
---|
572 | { |
---|
573 | CanonicalForm result= gcd (ppA, ppB); |
---|
574 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
575 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
576 | return N (result*gcdcAcB); |
---|
577 | } |
---|
578 | else |
---|
579 | { |
---|
580 | coF= N (ppA*(cA/gcdcAcB)); |
---|
581 | coG= N (ppB*(cB/gcdcAcB)); |
---|
582 | return N (gcdcAcB); |
---|
583 | } |
---|
584 | } |
---|
585 | |
---|
586 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
587 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
588 | |
---|
589 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
590 | delete [] newtonPolyg[i]; |
---|
591 | delete [] newtonPolyg; |
---|
592 | |
---|
593 | ppA= compress (ppA, MM, V, false); |
---|
594 | ppB= compress (ppB, MM, V, false); |
---|
595 | MM= inv (MM); |
---|
596 | |
---|
597 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
598 | { |
---|
599 | if (ppA.level() == ppB.level()) |
---|
600 | { |
---|
601 | CanonicalForm result= gcd (ppA, ppB); |
---|
602 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
603 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
604 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
605 | } |
---|
606 | else |
---|
607 | { |
---|
608 | coF= N (decompress (ppA, MM, V)); |
---|
609 | coG= N (decompress (ppB, MM, V)); |
---|
610 | return N (gcdcAcB); |
---|
611 | } |
---|
612 | } |
---|
613 | } |
---|
614 | |
---|
615 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
616 | CanonicalForm gcdlcAlcB; |
---|
617 | |
---|
618 | lcA= uni_lcoeff (ppA); |
---|
619 | lcB= uni_lcoeff (ppB); |
---|
620 | |
---|
621 | /*if (fdivides (lcA, lcB)) |
---|
622 | { |
---|
623 | if (fdivides (A, B)) |
---|
624 | return F/Lc(F); |
---|
625 | } |
---|
626 | if (fdivides (lcB, lcA)) |
---|
627 | { |
---|
628 | if (fdivides (B, A)) |
---|
629 | return G/Lc(G); |
---|
630 | }*/ |
---|
631 | |
---|
632 | gcdlcAlcB= gcd (lcA, lcB); |
---|
633 | |
---|
634 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
635 | |
---|
636 | if (d == 0) |
---|
637 | { |
---|
638 | coF= N (ppA*(cA/gcdcAcB)); |
---|
639 | coG= N (ppB*(cB/gcdcAcB)); |
---|
640 | return N(gcdcAcB); |
---|
641 | } |
---|
642 | |
---|
643 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
644 | if (d0 < d) |
---|
645 | d= d0; |
---|
646 | if (d == 0) |
---|
647 | { |
---|
648 | coF= N (ppA*(cA/gcdcAcB)); |
---|
649 | coG= N (ppB*(cB/gcdcAcB)); |
---|
650 | return N(gcdcAcB); |
---|
651 | } |
---|
652 | |
---|
653 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
654 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
655 | coG_m, ppCoF, ppCoG; |
---|
656 | |
---|
657 | newtonPoly= 1; |
---|
658 | m= gcdlcAlcB; |
---|
659 | G_m= 0; |
---|
660 | coF= 0; |
---|
661 | coG= 0; |
---|
662 | H= 0; |
---|
663 | bool fail= false; |
---|
664 | topLevel= false; |
---|
665 | bool inextension= false; |
---|
666 | Variable V_buf= alpha; |
---|
667 | CanonicalForm prim_elem, im_prim_elem; |
---|
668 | CFList source, dest; |
---|
669 | int bound1= degree (ppA, 1); |
---|
670 | int bound2= degree (ppB, 1); |
---|
671 | do |
---|
672 | { |
---|
673 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
674 | if (fail) |
---|
675 | { |
---|
676 | source= CFList(); |
---|
677 | dest= CFList(); |
---|
678 | |
---|
679 | Variable V_buf3= V_buf; |
---|
680 | V_buf= chooseExtension (V_buf); |
---|
681 | bool prim_fail= false; |
---|
682 | Variable V_buf2; |
---|
683 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
684 | |
---|
685 | if (V_buf3 != alpha) |
---|
686 | { |
---|
687 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
688 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
689 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
690 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
691 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
692 | source, dest); |
---|
693 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
694 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
695 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
696 | source, dest); |
---|
697 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
698 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
699 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
700 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
701 | source, dest); |
---|
702 | } |
---|
703 | |
---|
704 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
705 | if (prim_fail) |
---|
706 | ; //ERROR |
---|
707 | else |
---|
708 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
709 | |
---|
710 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
711 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
712 | inextension= true; |
---|
713 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
714 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
715 | im_prim_elem, source, dest); |
---|
716 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
717 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
718 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
719 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
720 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
721 | source, dest); |
---|
722 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
723 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
724 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
725 | source, dest); |
---|
726 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
727 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
728 | |
---|
729 | fail= false; |
---|
730 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
731 | DEBOUTLN (cerr, "fail= " << fail); |
---|
732 | CFList list; |
---|
733 | TIMING_START (gcd_recursion); |
---|
734 | G_random_element= |
---|
735 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
736 | coF_random_element, coG_random_element, V_buf, |
---|
737 | list, topLevel); |
---|
738 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
739 | "time for recursive call: "); |
---|
740 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
741 | } |
---|
742 | else |
---|
743 | { |
---|
744 | CFList list; |
---|
745 | TIMING_START (gcd_recursion); |
---|
746 | G_random_element= |
---|
747 | GCD_Fp_extension (ppA(random_element, x), ppB(random_element, x), |
---|
748 | coF_random_element, coG_random_element, V_buf, |
---|
749 | list, topLevel); |
---|
750 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
751 | "time for recursive call: "); |
---|
752 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
753 | } |
---|
754 | |
---|
755 | if (!G_random_element.inCoeffDomain()) |
---|
756 | d0= totaldegree (G_random_element, Variable(2), |
---|
757 | Variable (G_random_element.level())); |
---|
758 | else |
---|
759 | d0= 0; |
---|
760 | |
---|
761 | if (d0 == 0) |
---|
762 | { |
---|
763 | coF= N (ppA*(cA/gcdcAcB)); |
---|
764 | coG= N (ppB*(cB/gcdcAcB)); |
---|
765 | return N(gcdcAcB); |
---|
766 | } |
---|
767 | if (d0 > d) |
---|
768 | { |
---|
769 | if (!find (l, random_element)) |
---|
770 | l.append (random_element); |
---|
771 | continue; |
---|
772 | } |
---|
773 | |
---|
774 | G_random_element= |
---|
775 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
776 | * G_random_element; |
---|
777 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
778 | *coF_random_element; |
---|
779 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
780 | *coG_random_element; |
---|
781 | |
---|
782 | if (!G_random_element.inCoeffDomain()) |
---|
783 | d0= totaldegree (G_random_element, Variable(2), |
---|
784 | Variable (G_random_element.level())); |
---|
785 | else |
---|
786 | d0= 0; |
---|
787 | |
---|
788 | if (d0 < d) |
---|
789 | { |
---|
790 | m= gcdlcAlcB; |
---|
791 | newtonPoly= 1; |
---|
792 | G_m= 0; |
---|
793 | d= d0; |
---|
794 | coF_m= 0; |
---|
795 | coG_m= 0; |
---|
796 | } |
---|
797 | |
---|
798 | TIMING_START (newton_interpolation); |
---|
799 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
800 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
801 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
802 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
803 | "time for newton interpolation: "); |
---|
804 | |
---|
805 | //termination test |
---|
806 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
807 | { |
---|
808 | TIMING_START (termination_test); |
---|
809 | if (gcdlcAlcB.isOne()) |
---|
810 | cH= 1; |
---|
811 | else |
---|
812 | cH= uni_content (H); |
---|
813 | ppH= H/cH; |
---|
814 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
815 | CanonicalForm ccoF= lcA/lcppH; |
---|
816 | ccoF /= Lc (ccoF); |
---|
817 | CanonicalForm ccoG= lcB/lcppH; |
---|
818 | ccoG /= Lc (ccoG); |
---|
819 | ppCoF= coF/ccoF; |
---|
820 | ppCoG= coG/ccoG; |
---|
821 | if (inextension) |
---|
822 | { |
---|
823 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
824 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
825 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
826 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
827 | { |
---|
828 | CFList u, v; |
---|
829 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
830 | ppH /= Lc(ppH); |
---|
831 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
832 | ppCoF= mapDown (ppCoF, prim_elem, im_prim_elem, alpha, u, v); |
---|
833 | ppCoF= mapDown (ppCoG, prim_elem, im_prim_elem, alpha, u, v); |
---|
834 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
835 | if (compressConvexDense) |
---|
836 | { |
---|
837 | ppH= decompress (ppH, MM, V); |
---|
838 | ppCoF= decompress (ppCoF, MM, V); |
---|
839 | ppCoG= decompress (ppCoG, MM, V); |
---|
840 | } |
---|
841 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
842 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
843 | TIMING_END_AND_PRINT (termination_test, |
---|
844 | "time for successful termination test Fq: "); |
---|
845 | return N(gcdcAcB*ppH); |
---|
846 | } |
---|
847 | } |
---|
848 | else if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
849 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
850 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
851 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
852 | { |
---|
853 | if (compressConvexDense) |
---|
854 | { |
---|
855 | ppH= decompress (ppH, MM, V); |
---|
856 | ppCoF= decompress (ppCoF, MM, V); |
---|
857 | ppCoG= decompress (ppCoG, MM, V); |
---|
858 | } |
---|
859 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
860 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
861 | TIMING_END_AND_PRINT (termination_test, |
---|
862 | "time for successful termination test Fq: "); |
---|
863 | return N(gcdcAcB*ppH); |
---|
864 | } |
---|
865 | TIMING_END_AND_PRINT (termination_test, |
---|
866 | "time for unsuccessful termination test Fq: "); |
---|
867 | } |
---|
868 | |
---|
869 | G_m= H; |
---|
870 | coF_m= coF; |
---|
871 | coG_m= coG; |
---|
872 | newtonPoly= newtonPoly*(x - random_element); |
---|
873 | m= m*(x - random_element); |
---|
874 | if (!find (l, random_element)) |
---|
875 | l.append (random_element); |
---|
876 | } while (1); |
---|
877 | } |
---|
878 | |
---|
879 | /// compute a random element a of GF, s.t. F(a) \f$ \neq 0 \f$ , F is a |
---|
880 | /// univariate polynomial, returns fail if there are no field elements left |
---|
881 | /// which have not been used before |
---|
882 | static inline |
---|
883 | CanonicalForm |
---|
884 | GFRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
885 | { |
---|
886 | fail= false; |
---|
887 | Variable x= F.mvar(); |
---|
888 | GFRandom genGF; |
---|
889 | CanonicalForm random; |
---|
890 | int p= getCharacteristic(); |
---|
891 | int d= getGFDegree(); |
---|
892 | int bound= ipower (p, d); |
---|
893 | do |
---|
894 | { |
---|
895 | if (list.length() == bound) |
---|
896 | { |
---|
897 | fail= true; |
---|
898 | break; |
---|
899 | } |
---|
900 | if (list.length() < 1) |
---|
901 | random= 0; |
---|
902 | else |
---|
903 | { |
---|
904 | random= genGF.generate(); |
---|
905 | while (find (list, random)) |
---|
906 | random= genGF.generate(); |
---|
907 | } |
---|
908 | if (F (random, x) == 0) |
---|
909 | { |
---|
910 | list.append (random); |
---|
911 | continue; |
---|
912 | } |
---|
913 | } while (find (list, random)); |
---|
914 | return random; |
---|
915 | } |
---|
916 | |
---|
917 | CanonicalForm |
---|
918 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
919 | CanonicalForm& coF, CanonicalForm& coG, |
---|
920 | CFList& l, bool& topLevel); |
---|
921 | |
---|
922 | CanonicalForm |
---|
923 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, CFList& l, |
---|
924 | bool& topLevel) |
---|
925 | { |
---|
926 | CanonicalForm dummy1, dummy2; |
---|
927 | CanonicalForm result= GCD_GF (F, G, dummy1, dummy2, l, topLevel); |
---|
928 | return result; |
---|
929 | } |
---|
930 | |
---|
931 | /// GCD of F and G over GF, based on Alg. 7.2. as described in "Algorithms for |
---|
932 | /// Computer Algebra" by Geddes, Czapor, Labahn |
---|
933 | /// Usually this algorithm will be faster than GCD_Fp_extension since GF has |
---|
934 | /// faster field arithmetics, however it might fail if the input is large since |
---|
935 | /// the size of the base field is bounded by 2^16, output is monic |
---|
936 | CanonicalForm |
---|
937 | GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
938 | CanonicalForm& coF, CanonicalForm& coG, |
---|
939 | CFList& l, bool& topLevel) |
---|
940 | { |
---|
941 | CanonicalForm A= F; |
---|
942 | CanonicalForm B= G; |
---|
943 | if (F.isZero() && degree(G) > 0) |
---|
944 | { |
---|
945 | coF= 0; |
---|
946 | coG= Lc (G); |
---|
947 | return G/Lc(G); |
---|
948 | } |
---|
949 | else if (G.isZero() && degree (F) > 0) |
---|
950 | { |
---|
951 | coF= Lc (F); |
---|
952 | coG= 0; |
---|
953 | return F/Lc(F); |
---|
954 | } |
---|
955 | else if (F.isZero() && G.isZero()) |
---|
956 | { |
---|
957 | coF= coG= 0; |
---|
958 | return F.genOne(); |
---|
959 | } |
---|
960 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
961 | { |
---|
962 | coF= F; |
---|
963 | coG= G; |
---|
964 | return F.genOne(); |
---|
965 | } |
---|
966 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
967 | { |
---|
968 | coF= Lc (F); |
---|
969 | return F/Lc(F); |
---|
970 | } |
---|
971 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
972 | { |
---|
973 | coG= Lc (G); |
---|
974 | return G/Lc(G); |
---|
975 | } |
---|
976 | if (F == G) |
---|
977 | { |
---|
978 | coF= coG= Lc (F); |
---|
979 | return F/Lc(F); |
---|
980 | } |
---|
981 | |
---|
982 | CFMap M,N; |
---|
983 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
984 | |
---|
985 | if (best_level == 0) |
---|
986 | { |
---|
987 | coF= F; |
---|
988 | coG= G; |
---|
989 | return B.genOne(); |
---|
990 | } |
---|
991 | |
---|
992 | A= M(A); |
---|
993 | B= M(B); |
---|
994 | |
---|
995 | Variable x= Variable(1); |
---|
996 | |
---|
997 | //univariate case |
---|
998 | if (A.isUnivariate() && B.isUnivariate()) |
---|
999 | { |
---|
1000 | CanonicalForm result= gcd (A, B); |
---|
1001 | coF= N (A/result); |
---|
1002 | coG= N (B/result); |
---|
1003 | return N (result); |
---|
1004 | } |
---|
1005 | |
---|
1006 | CanonicalForm cA, cB; // content of A and B |
---|
1007 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
1008 | CanonicalForm gcdcAcB; |
---|
1009 | |
---|
1010 | cA = uni_content (A); |
---|
1011 | cB = uni_content (B); |
---|
1012 | gcdcAcB= gcd (cA, cB); |
---|
1013 | ppA= A/cA; |
---|
1014 | ppB= B/cB; |
---|
1015 | |
---|
1016 | int sizeNewtonPolyg; |
---|
1017 | int ** newtonPolyg= NULL; |
---|
1018 | mat_ZZ MM; |
---|
1019 | vec_ZZ V; |
---|
1020 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
1021 | if (compressConvexDense) |
---|
1022 | { |
---|
1023 | CanonicalForm bufcA= cA; |
---|
1024 | CanonicalForm bufcB= cB; |
---|
1025 | cA= content (ppA, 1); |
---|
1026 | cB= content (ppB, 1); |
---|
1027 | ppA /= cA; |
---|
1028 | ppB /= cB; |
---|
1029 | gcdcAcB *= gcd (cA, cB); |
---|
1030 | cA *= bufcA; |
---|
1031 | cB *= bufcB; |
---|
1032 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
1033 | { |
---|
1034 | if (ppA.level() == ppB.level()) |
---|
1035 | { |
---|
1036 | CanonicalForm result= gcd (ppA, ppB); |
---|
1037 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
1038 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
1039 | return N (result*gcdcAcB); |
---|
1040 | } |
---|
1041 | else |
---|
1042 | { |
---|
1043 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1044 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1045 | return N (gcdcAcB); |
---|
1046 | } |
---|
1047 | } |
---|
1048 | |
---|
1049 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
1050 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
1051 | |
---|
1052 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
1053 | delete [] newtonPolyg[i]; |
---|
1054 | delete [] newtonPolyg; |
---|
1055 | |
---|
1056 | ppA= compress (ppA, MM, V, false); |
---|
1057 | ppB= compress (ppB, MM, V, false); |
---|
1058 | MM= inv (MM); |
---|
1059 | |
---|
1060 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
1061 | { |
---|
1062 | if (ppA.level() == ppB.level()) |
---|
1063 | { |
---|
1064 | CanonicalForm result= gcd (ppA, ppB); |
---|
1065 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
1066 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
1067 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
1068 | } |
---|
1069 | else |
---|
1070 | { |
---|
1071 | coF= N (decompress (ppA, MM, V)); |
---|
1072 | coG= N (decompress (ppB, MM, V)); |
---|
1073 | return N (gcdcAcB); |
---|
1074 | } |
---|
1075 | } |
---|
1076 | } |
---|
1077 | |
---|
1078 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
1079 | CanonicalForm gcdlcAlcB; |
---|
1080 | |
---|
1081 | lcA= uni_lcoeff (ppA); |
---|
1082 | lcB= uni_lcoeff (ppB); |
---|
1083 | |
---|
1084 | /*if (fdivides (lcA, lcB)) |
---|
1085 | { |
---|
1086 | if (fdivides (ppA, ppB, coG)) |
---|
1087 | { |
---|
1088 | coF= 1; |
---|
1089 | if (compressConvexDense) |
---|
1090 | coG= decompress (coG, MM, V); |
---|
1091 | coG= N (coG*(cB/gcdcAcB)); |
---|
1092 | return F; |
---|
1093 | } |
---|
1094 | } |
---|
1095 | if (fdivides (lcB, lcA)) |
---|
1096 | { |
---|
1097 | if (fdivides (ppB, ppA, coF)) |
---|
1098 | { |
---|
1099 | coG= 1; |
---|
1100 | if (compressConvexDense) |
---|
1101 | coF= decompress (coF, MM, V); |
---|
1102 | coF= N (coF*(cA/gcdcAcB)); |
---|
1103 | return G; |
---|
1104 | } |
---|
1105 | }*/ |
---|
1106 | |
---|
1107 | gcdlcAlcB= gcd (lcA, lcB); |
---|
1108 | |
---|
1109 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
1110 | if (d == 0) |
---|
1111 | { |
---|
1112 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1113 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1114 | return N(gcdcAcB); |
---|
1115 | } |
---|
1116 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
1117 | if (d0 < d) |
---|
1118 | d= d0; |
---|
1119 | if (d == 0) |
---|
1120 | { |
---|
1121 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1122 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1123 | return N(gcdcAcB); |
---|
1124 | } |
---|
1125 | |
---|
1126 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
1127 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, coF_m, |
---|
1128 | coG_m, ppCoF, ppCoG; |
---|
1129 | |
---|
1130 | newtonPoly= 1; |
---|
1131 | m= gcdlcAlcB; |
---|
1132 | G_m= 0; |
---|
1133 | coF= 0; |
---|
1134 | coG= 0; |
---|
1135 | H= 0; |
---|
1136 | bool fail= false; |
---|
1137 | //topLevel= false; |
---|
1138 | bool inextension= false; |
---|
1139 | int p=-1; |
---|
1140 | int k= getGFDegree(); |
---|
1141 | int kk; |
---|
1142 | int expon; |
---|
1143 | char gf_name_buf= gf_name; |
---|
1144 | int bound1= degree (ppA, 1); |
---|
1145 | int bound2= degree (ppB, 1); |
---|
1146 | do |
---|
1147 | { |
---|
1148 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
1149 | if (fail) |
---|
1150 | { |
---|
1151 | p= getCharacteristic(); |
---|
1152 | expon= 2; |
---|
1153 | kk= getGFDegree(); |
---|
1154 | if (ipower (p, kk*expon) < (1 << 16)) |
---|
1155 | setCharacteristic (p, kk*(int)expon, 'b'); |
---|
1156 | else |
---|
1157 | { |
---|
1158 | expon= (int) floor((log ((double)((1<<16) - 1)))/(log((double)p)*kk)); |
---|
1159 | ASSERT (expon >= 2, "not enough points in GCD_GF"); |
---|
1160 | setCharacteristic (p, (int)(kk*expon), 'b'); |
---|
1161 | } |
---|
1162 | inextension= true; |
---|
1163 | fail= false; |
---|
1164 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1165 | i.getItem()= GFMapUp (i.getItem(), kk); |
---|
1166 | m= GFMapUp (m, kk); |
---|
1167 | G_m= GFMapUp (G_m, kk); |
---|
1168 | newtonPoly= GFMapUp (newtonPoly, kk); |
---|
1169 | coF_m= GFMapUp (coF_m, kk); |
---|
1170 | coG_m= GFMapUp (coG_m, kk); |
---|
1171 | ppA= GFMapUp (ppA, kk); |
---|
1172 | ppB= GFMapUp (ppB, kk); |
---|
1173 | gcdlcAlcB= GFMapUp (gcdlcAlcB, kk); |
---|
1174 | lcA= GFMapUp (lcA, kk); |
---|
1175 | lcB= GFMapUp (lcB, kk); |
---|
1176 | random_element= GFRandomElement (m*lcA*lcB, l, fail); |
---|
1177 | DEBOUTLN (cerr, "fail= " << fail); |
---|
1178 | CFList list; |
---|
1179 | TIMING_START (gcd_recursion); |
---|
1180 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
1181 | coF_random_element, coG_random_element, |
---|
1182 | list, topLevel); |
---|
1183 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1184 | "time for recursive call: "); |
---|
1185 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1186 | } |
---|
1187 | else |
---|
1188 | { |
---|
1189 | CFList list; |
---|
1190 | TIMING_START (gcd_recursion); |
---|
1191 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
1192 | coF_random_element, coG_random_element, |
---|
1193 | list, topLevel); |
---|
1194 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1195 | "time for recursive call: "); |
---|
1196 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1197 | } |
---|
1198 | |
---|
1199 | if (!G_random_element.inCoeffDomain()) |
---|
1200 | d0= totaldegree (G_random_element, Variable(2), |
---|
1201 | Variable (G_random_element.level())); |
---|
1202 | else |
---|
1203 | d0= 0; |
---|
1204 | |
---|
1205 | if (d0 == 0) |
---|
1206 | { |
---|
1207 | if (inextension) |
---|
1208 | setCharacteristic (p, k, gf_name_buf); |
---|
1209 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1210 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1211 | return N(gcdcAcB); |
---|
1212 | } |
---|
1213 | if (d0 > d) |
---|
1214 | { |
---|
1215 | if (!find (l, random_element)) |
---|
1216 | l.append (random_element); |
---|
1217 | continue; |
---|
1218 | } |
---|
1219 | |
---|
1220 | G_random_element= |
---|
1221 | (gcdlcAlcB(random_element, x)/uni_lcoeff(G_random_element)) * |
---|
1222 | G_random_element; |
---|
1223 | |
---|
1224 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
1225 | *coF_random_element; |
---|
1226 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
1227 | *coG_random_element; |
---|
1228 | |
---|
1229 | if (!G_random_element.inCoeffDomain()) |
---|
1230 | d0= totaldegree (G_random_element, Variable(2), |
---|
1231 | Variable (G_random_element.level())); |
---|
1232 | else |
---|
1233 | d0= 0; |
---|
1234 | |
---|
1235 | if (d0 < d) |
---|
1236 | { |
---|
1237 | m= gcdlcAlcB; |
---|
1238 | newtonPoly= 1; |
---|
1239 | G_m= 0; |
---|
1240 | d= d0; |
---|
1241 | coF_m= 0; |
---|
1242 | coG_m= 0; |
---|
1243 | } |
---|
1244 | |
---|
1245 | TIMING_START (newton_interpolation); |
---|
1246 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
1247 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
1248 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
1249 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
1250 | "time for newton interpolation: "); |
---|
1251 | |
---|
1252 | //termination test |
---|
1253 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
1254 | { |
---|
1255 | TIMING_START (termination_test); |
---|
1256 | if (gcdlcAlcB.isOne()) |
---|
1257 | cH= 1; |
---|
1258 | else |
---|
1259 | cH= uni_content (H); |
---|
1260 | ppH= H/cH; |
---|
1261 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
1262 | CanonicalForm ccoF= lcA/lcppH; |
---|
1263 | ccoF /= Lc (ccoF); |
---|
1264 | CanonicalForm ccoG= lcB/lcppH; |
---|
1265 | ccoG /= Lc (ccoG); |
---|
1266 | ppCoF= coF/ccoF; |
---|
1267 | ppCoG= coG/ccoG; |
---|
1268 | if (inextension) |
---|
1269 | { |
---|
1270 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
1271 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
1272 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
1273 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
1274 | { |
---|
1275 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
1276 | ppH= GFMapDown (ppH, k); |
---|
1277 | ppCoF= GFMapDown (ppCoF, k); |
---|
1278 | ppCoG= GFMapDown (ppCoG, k); |
---|
1279 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
1280 | if (compressConvexDense) |
---|
1281 | { |
---|
1282 | ppH= decompress (ppH, MM, V); |
---|
1283 | ppCoF= decompress (ppCoF, MM, V); |
---|
1284 | ppCoG= decompress (ppCoG, MM, V); |
---|
1285 | } |
---|
1286 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
1287 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
1288 | setCharacteristic (p, k, gf_name_buf); |
---|
1289 | TIMING_END_AND_PRINT (termination_test, |
---|
1290 | "time for successful termination GF: "); |
---|
1291 | return N(gcdcAcB*ppH); |
---|
1292 | } |
---|
1293 | } |
---|
1294 | else |
---|
1295 | { |
---|
1296 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
1297 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
1298 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
1299 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
1300 | { |
---|
1301 | if (compressConvexDense) |
---|
1302 | { |
---|
1303 | ppH= decompress (ppH, MM, V); |
---|
1304 | ppCoF= decompress (ppCoF, MM, V); |
---|
1305 | ppCoG= decompress (ppCoG, MM, V); |
---|
1306 | } |
---|
1307 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
1308 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
1309 | TIMING_END_AND_PRINT (termination_test, |
---|
1310 | "time for successful termination GF: "); |
---|
1311 | return N(gcdcAcB*ppH); |
---|
1312 | } |
---|
1313 | } |
---|
1314 | TIMING_END_AND_PRINT (termination_test, |
---|
1315 | "time for unsuccessful termination GF: "); |
---|
1316 | } |
---|
1317 | |
---|
1318 | G_m= H; |
---|
1319 | coF_m= coF; |
---|
1320 | coG_m= coG; |
---|
1321 | newtonPoly= newtonPoly*(x - random_element); |
---|
1322 | m= m*(x - random_element); |
---|
1323 | if (!find (l, random_element)) |
---|
1324 | l.append (random_element); |
---|
1325 | } while (1); |
---|
1326 | } |
---|
1327 | |
---|
1328 | /// F is assumed to be an univariate polynomial in x, |
---|
1329 | /// computes a random monic irreducible univariate polynomial of random |
---|
1330 | /// degree < i in x which does not divide F |
---|
1331 | CanonicalForm |
---|
1332 | randomIrredpoly (int i, const Variable & x) |
---|
1333 | { |
---|
1334 | int p= getCharacteristic(); |
---|
1335 | zz_p::init (p); |
---|
1336 | zz_pX NTLirredpoly; |
---|
1337 | CanonicalForm CFirredpoly; |
---|
1338 | BuildIrred (NTLirredpoly, i + 1); |
---|
1339 | CFirredpoly= convertNTLzzpX2CF (NTLirredpoly, x); |
---|
1340 | return CFirredpoly; |
---|
1341 | } |
---|
1342 | |
---|
1343 | static inline |
---|
1344 | CanonicalForm |
---|
1345 | FpRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
1346 | { |
---|
1347 | fail= false; |
---|
1348 | Variable x= F.mvar(); |
---|
1349 | FFRandom genFF; |
---|
1350 | CanonicalForm random; |
---|
1351 | int p= getCharacteristic(); |
---|
1352 | int bound= p; |
---|
1353 | do |
---|
1354 | { |
---|
1355 | if (list.length() == bound) |
---|
1356 | { |
---|
1357 | fail= true; |
---|
1358 | break; |
---|
1359 | } |
---|
1360 | if (list.length() < 1) |
---|
1361 | random= 0; |
---|
1362 | else |
---|
1363 | { |
---|
1364 | random= genFF.generate(); |
---|
1365 | while (find (list, random)) |
---|
1366 | random= genFF.generate(); |
---|
1367 | } |
---|
1368 | if (F (random, x) == 0) |
---|
1369 | { |
---|
1370 | list.append (random); |
---|
1371 | continue; |
---|
1372 | } |
---|
1373 | } while (find (list, random)); |
---|
1374 | return random; |
---|
1375 | } |
---|
1376 | |
---|
1377 | CanonicalForm |
---|
1378 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1379 | CanonicalForm& coF, CanonicalForm& coG, |
---|
1380 | bool& topLevel, CFList& l); |
---|
1381 | |
---|
1382 | CanonicalForm |
---|
1383 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1384 | bool& topLevel, CFList& l) |
---|
1385 | { |
---|
1386 | CanonicalForm dummy1, dummy2; |
---|
1387 | CanonicalForm result= GCD_small_p (F, G, dummy1, dummy2, topLevel, l); |
---|
1388 | return result; |
---|
1389 | } |
---|
1390 | |
---|
1391 | CanonicalForm |
---|
1392 | GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1393 | CanonicalForm& coF, CanonicalForm& coG, |
---|
1394 | bool& topLevel, CFList& l) |
---|
1395 | { |
---|
1396 | CanonicalForm A= F; |
---|
1397 | CanonicalForm B= G; |
---|
1398 | if (F.isZero() && degree(G) > 0) |
---|
1399 | { |
---|
1400 | coF= 0; |
---|
1401 | coG= Lc (G); |
---|
1402 | return G/Lc(G); |
---|
1403 | } |
---|
1404 | else if (G.isZero() && degree (F) > 0) |
---|
1405 | { |
---|
1406 | coF= Lc (F); |
---|
1407 | coG= 0; |
---|
1408 | return F/Lc(F); |
---|
1409 | } |
---|
1410 | else if (F.isZero() && G.isZero()) |
---|
1411 | { |
---|
1412 | coF= coG= 0; |
---|
1413 | return F.genOne(); |
---|
1414 | } |
---|
1415 | if (F.inBaseDomain() || G.inBaseDomain()) |
---|
1416 | { |
---|
1417 | coF= F; |
---|
1418 | coG= G; |
---|
1419 | return F.genOne(); |
---|
1420 | } |
---|
1421 | if (F.isUnivariate() && fdivides(F, G, coG)) |
---|
1422 | { |
---|
1423 | coF= Lc (F); |
---|
1424 | return F/Lc(F); |
---|
1425 | } |
---|
1426 | if (G.isUnivariate() && fdivides(G, F, coF)) |
---|
1427 | { |
---|
1428 | coG= Lc (G); |
---|
1429 | return G/Lc(G); |
---|
1430 | } |
---|
1431 | if (F == G) |
---|
1432 | { |
---|
1433 | coF= coG= Lc (F); |
---|
1434 | return F/Lc(F); |
---|
1435 | } |
---|
1436 | CFMap M,N; |
---|
1437 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
1438 | |
---|
1439 | if (best_level == 0) |
---|
1440 | { |
---|
1441 | coF= F; |
---|
1442 | coG= G; |
---|
1443 | return B.genOne(); |
---|
1444 | } |
---|
1445 | |
---|
1446 | A= M(A); |
---|
1447 | B= M(B); |
---|
1448 | |
---|
1449 | Variable x= Variable (1); |
---|
1450 | |
---|
1451 | //univariate case |
---|
1452 | if (A.isUnivariate() && B.isUnivariate()) |
---|
1453 | { |
---|
1454 | CanonicalForm result= gcd (A, B); |
---|
1455 | coF= N (A/result); |
---|
1456 | coG= N (B/result); |
---|
1457 | return N (result); |
---|
1458 | } |
---|
1459 | |
---|
1460 | CanonicalForm cA, cB; // content of A and B |
---|
1461 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
1462 | CanonicalForm gcdcAcB; |
---|
1463 | |
---|
1464 | cA = uni_content (A); |
---|
1465 | cB = uni_content (B); |
---|
1466 | gcdcAcB= gcd (cA, cB); |
---|
1467 | ppA= A/cA; |
---|
1468 | ppB= B/cB; |
---|
1469 | |
---|
1470 | int sizeNewtonPolyg; |
---|
1471 | int ** newtonPolyg= NULL; |
---|
1472 | mat_ZZ MM; |
---|
1473 | vec_ZZ V; |
---|
1474 | bool compressConvexDense= false; //(ppA.level() == 2 && ppB.level() == 2); |
---|
1475 | if (compressConvexDense) |
---|
1476 | { |
---|
1477 | CanonicalForm bufcA= cA; |
---|
1478 | CanonicalForm bufcB= cB; |
---|
1479 | cA= content (ppA, 1); |
---|
1480 | cB= content (ppB, 1); |
---|
1481 | ppA /= cA; |
---|
1482 | ppB /= cB; |
---|
1483 | gcdcAcB *= gcd (cA, cB); |
---|
1484 | cA *= bufcA; |
---|
1485 | cB *= bufcB; |
---|
1486 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
1487 | { |
---|
1488 | if (ppA.level() == ppB.level()) |
---|
1489 | { |
---|
1490 | CanonicalForm result= gcd (ppA, ppB); |
---|
1491 | coF= N ((ppA/result)*(cA/gcdcAcB)); |
---|
1492 | coG= N ((ppB/result)*(cB/gcdcAcB)); |
---|
1493 | return N (result*gcdcAcB); |
---|
1494 | } |
---|
1495 | else |
---|
1496 | { |
---|
1497 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1498 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1499 | return N (gcdcAcB); |
---|
1500 | } |
---|
1501 | } |
---|
1502 | |
---|
1503 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
1504 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
1505 | |
---|
1506 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
1507 | delete [] newtonPolyg[i]; |
---|
1508 | delete [] newtonPolyg; |
---|
1509 | |
---|
1510 | ppA= compress (ppA, MM, V, false); |
---|
1511 | ppB= compress (ppB, MM, V, false); |
---|
1512 | MM= inv (MM); |
---|
1513 | |
---|
1514 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
1515 | { |
---|
1516 | if (ppA.level() == ppB.level()) |
---|
1517 | { |
---|
1518 | CanonicalForm result= gcd (ppA, ppB); |
---|
1519 | coF= N (decompress ((ppA/result), MM, V)*(cA/gcdcAcB)); |
---|
1520 | coG= N (decompress ((ppB/result), MM, V)*(cB/gcdcAcB)); |
---|
1521 | return N (decompress (result, MM, V)*gcdcAcB); |
---|
1522 | } |
---|
1523 | else |
---|
1524 | { |
---|
1525 | coF= N (decompress (ppA, MM, V)); |
---|
1526 | coG= N (decompress (ppB, MM, V)); |
---|
1527 | return N (gcdcAcB); |
---|
1528 | } |
---|
1529 | } |
---|
1530 | } |
---|
1531 | |
---|
1532 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
1533 | CanonicalForm gcdlcAlcB; |
---|
1534 | lcA= uni_lcoeff (ppA); |
---|
1535 | lcB= uni_lcoeff (ppB); |
---|
1536 | |
---|
1537 | /*if (fdivides (lcA, lcB)) |
---|
1538 | { |
---|
1539 | if (fdivides (A, B)) |
---|
1540 | return F/Lc(F); |
---|
1541 | } |
---|
1542 | if (fdivides (lcB, lcA)) |
---|
1543 | { |
---|
1544 | if (fdivides (B, A)) |
---|
1545 | return G/Lc(G); |
---|
1546 | }*/ |
---|
1547 | |
---|
1548 | gcdlcAlcB= gcd (lcA, lcB); |
---|
1549 | |
---|
1550 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
1551 | int d0; |
---|
1552 | |
---|
1553 | if (d == 0) |
---|
1554 | { |
---|
1555 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1556 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1557 | return N(gcdcAcB); |
---|
1558 | } |
---|
1559 | |
---|
1560 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
1561 | |
---|
1562 | if (d0 < d) |
---|
1563 | d= d0; |
---|
1564 | |
---|
1565 | if (d == 0) |
---|
1566 | { |
---|
1567 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1568 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1569 | return N(gcdcAcB); |
---|
1570 | } |
---|
1571 | |
---|
1572 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
1573 | CanonicalForm newtonPoly, coF_random_element, coG_random_element, |
---|
1574 | coF_m, coG_m, ppCoF, ppCoG; |
---|
1575 | |
---|
1576 | newtonPoly= 1; |
---|
1577 | m= gcdlcAlcB; |
---|
1578 | H= 0; |
---|
1579 | coF= 0; |
---|
1580 | coG= 0; |
---|
1581 | G_m= 0; |
---|
1582 | Variable alpha, V_buf; |
---|
1583 | bool fail= false; |
---|
1584 | bool inextension= false; |
---|
1585 | topLevel= false; |
---|
1586 | CFList source, dest; |
---|
1587 | int bound1= degree (ppA, 1); |
---|
1588 | int bound2= degree (ppB, 1); |
---|
1589 | do |
---|
1590 | { |
---|
1591 | if (inextension) |
---|
1592 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail); |
---|
1593 | else |
---|
1594 | random_element= FpRandomElement (m*lcA*lcB, l, fail); |
---|
1595 | |
---|
1596 | if (!fail && !inextension) |
---|
1597 | { |
---|
1598 | CFList list; |
---|
1599 | TIMING_START (gcd_recursion); |
---|
1600 | G_random_element= |
---|
1601 | GCD_small_p (ppA (random_element,x), ppB (random_element,x), |
---|
1602 | coF_random_element, coG_random_element, topLevel, |
---|
1603 | list); |
---|
1604 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1605 | "time for recursive call: "); |
---|
1606 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1607 | } |
---|
1608 | else if (!fail && inextension) |
---|
1609 | { |
---|
1610 | CFList list; |
---|
1611 | TIMING_START (gcd_recursion); |
---|
1612 | G_random_element= |
---|
1613 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
1614 | coF_random_element, coG_random_element, alpha, |
---|
1615 | list, topLevel); |
---|
1616 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1617 | "time for recursive call: "); |
---|
1618 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1619 | } |
---|
1620 | else if (fail && !inextension) |
---|
1621 | { |
---|
1622 | source= CFList(); |
---|
1623 | dest= CFList(); |
---|
1624 | CFList list; |
---|
1625 | CanonicalForm mipo; |
---|
1626 | int deg= 2; |
---|
1627 | do { |
---|
1628 | mipo= randomIrredpoly (deg, x); |
---|
1629 | alpha= rootOf (mipo); |
---|
1630 | inextension= true; |
---|
1631 | fail= false; |
---|
1632 | random_element= randomElement (m*lcA*lcB, alpha, l, fail); |
---|
1633 | deg++; |
---|
1634 | } while (fail); |
---|
1635 | list= CFList(); |
---|
1636 | V_buf= alpha; |
---|
1637 | TIMING_START (gcd_recursion); |
---|
1638 | G_random_element= |
---|
1639 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
1640 | coF_random_element, coG_random_element, alpha, |
---|
1641 | list, topLevel); |
---|
1642 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1643 | "time for recursive call: "); |
---|
1644 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1645 | } |
---|
1646 | else if (fail && inextension) |
---|
1647 | { |
---|
1648 | source= CFList(); |
---|
1649 | dest= CFList(); |
---|
1650 | |
---|
1651 | Variable V_buf3= V_buf; |
---|
1652 | V_buf= chooseExtension (V_buf); |
---|
1653 | bool prim_fail= false; |
---|
1654 | Variable V_buf2; |
---|
1655 | CanonicalForm prim_elem, im_prim_elem; |
---|
1656 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
1657 | |
---|
1658 | if (V_buf3 != alpha) |
---|
1659 | { |
---|
1660 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1661 | G_m= mapDown (G_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1662 | coF_m= mapDown (coF_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1663 | coG_m= mapDown (coG_m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1664 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
1665 | source, dest); |
---|
1666 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1667 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1668 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
1669 | dest); |
---|
1670 | lcA= mapDown (lcA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1671 | lcB= mapDown (lcB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1672 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1673 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
1674 | source, dest); |
---|
1675 | } |
---|
1676 | |
---|
1677 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
1678 | if (prim_fail) |
---|
1679 | ; //ERROR |
---|
1680 | else |
---|
1681 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
1682 | |
---|
1683 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
1684 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
1685 | |
---|
1686 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1687 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
1688 | im_prim_elem, source, dest); |
---|
1689 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1690 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1691 | coF_m= mapUp (coF_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1692 | coG_m= mapUp (coG_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1693 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1694 | source, dest); |
---|
1695 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1696 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1697 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1698 | source, dest); |
---|
1699 | lcA= mapUp (lcA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1700 | lcB= mapUp (lcB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1701 | fail= false; |
---|
1702 | random_element= randomElement (m*lcA*lcB, V_buf, l, fail ); |
---|
1703 | DEBOUTLN (cerr, "fail= " << fail); |
---|
1704 | CFList list; |
---|
1705 | TIMING_START (gcd_recursion); |
---|
1706 | G_random_element= |
---|
1707 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), |
---|
1708 | coF_random_element, coG_random_element, V_buf, |
---|
1709 | list, topLevel); |
---|
1710 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1711 | "time for recursive call: "); |
---|
1712 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1713 | } |
---|
1714 | |
---|
1715 | if (!G_random_element.inCoeffDomain()) |
---|
1716 | d0= totaldegree (G_random_element, Variable(2), |
---|
1717 | Variable (G_random_element.level())); |
---|
1718 | else |
---|
1719 | d0= 0; |
---|
1720 | |
---|
1721 | if (d0 == 0) |
---|
1722 | { |
---|
1723 | coF= N (ppA*(cA/gcdcAcB)); |
---|
1724 | coG= N (ppB*(cB/gcdcAcB)); |
---|
1725 | return N(gcdcAcB); |
---|
1726 | } |
---|
1727 | |
---|
1728 | if (d0 > d) |
---|
1729 | { |
---|
1730 | if (!find (l, random_element)) |
---|
1731 | l.append (random_element); |
---|
1732 | continue; |
---|
1733 | } |
---|
1734 | |
---|
1735 | G_random_element= (gcdlcAlcB(random_element,x)/uni_lcoeff(G_random_element)) |
---|
1736 | *G_random_element; |
---|
1737 | |
---|
1738 | coF_random_element= (lcA(random_element,x)/uni_lcoeff(coF_random_element)) |
---|
1739 | *coF_random_element; |
---|
1740 | coG_random_element= (lcB(random_element,x)/uni_lcoeff(coG_random_element)) |
---|
1741 | *coG_random_element; |
---|
1742 | |
---|
1743 | if (!G_random_element.inCoeffDomain()) |
---|
1744 | d0= totaldegree (G_random_element, Variable(2), |
---|
1745 | Variable (G_random_element.level())); |
---|
1746 | else |
---|
1747 | d0= 0; |
---|
1748 | |
---|
1749 | if (d0 < d) |
---|
1750 | { |
---|
1751 | m= gcdlcAlcB; |
---|
1752 | newtonPoly= 1; |
---|
1753 | G_m= 0; |
---|
1754 | d= d0; |
---|
1755 | coF_m= 0; |
---|
1756 | coG_m= 0; |
---|
1757 | } |
---|
1758 | |
---|
1759 | TIMING_START (newton_interpolation); |
---|
1760 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
1761 | coF= newtonInterp (random_element, coF_random_element, newtonPoly, coF_m,x); |
---|
1762 | coG= newtonInterp (random_element, coG_random_element, newtonPoly, coG_m,x); |
---|
1763 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
1764 | "time for newton_interpolation: "); |
---|
1765 | |
---|
1766 | //termination test |
---|
1767 | if ((uni_lcoeff (H) == gcdlcAlcB) || (G_m == H)) |
---|
1768 | { |
---|
1769 | TIMING_START (termination_test); |
---|
1770 | if (gcdlcAlcB.isOne()) |
---|
1771 | cH= 1; |
---|
1772 | else |
---|
1773 | cH= uni_content (H); |
---|
1774 | ppH= H/cH; |
---|
1775 | ppH /= Lc (ppH); |
---|
1776 | CanonicalForm lcppH= gcdlcAlcB/cH; |
---|
1777 | CanonicalForm ccoF= lcppH/Lc (lcppH); |
---|
1778 | CanonicalForm ccoG= lcppH/Lc (lcppH); |
---|
1779 | ppCoF= coF/ccoF; |
---|
1780 | ppCoG= coG/ccoG; |
---|
1781 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
1782 | if (((degree (ppCoF,1)+degree (ppH,1) == bound1) && |
---|
1783 | (degree (ppCoG,1)+degree (ppH,1) == bound2) && |
---|
1784 | terminationTest (ppA, ppB, ppCoF, ppCoG, ppH)) || |
---|
1785 | (fdivides (ppH, ppA, ppCoF) && fdivides (ppH, ppB, ppCoG))) |
---|
1786 | { |
---|
1787 | if (compressConvexDense) |
---|
1788 | { |
---|
1789 | ppH= decompress (ppH, MM, V); |
---|
1790 | ppCoF= decompress (ppCoF, MM, V); |
---|
1791 | ppCoG= decompress (ppCoG, MM, V); |
---|
1792 | } |
---|
1793 | coF= N ((cA/gcdcAcB)*ppCoF); |
---|
1794 | coG= N ((cB/gcdcAcB)*ppCoG); |
---|
1795 | TIMING_END_AND_PRINT (termination_test, |
---|
1796 | "time for successful termination Fp: "); |
---|
1797 | return N(gcdcAcB*ppH); |
---|
1798 | } |
---|
1799 | TIMING_END_AND_PRINT (termination_test, |
---|
1800 | "time for unsuccessful termination Fp: "); |
---|
1801 | } |
---|
1802 | |
---|
1803 | G_m= H; |
---|
1804 | coF_m= coF; |
---|
1805 | coG_m= coG; |
---|
1806 | newtonPoly= newtonPoly*(x - random_element); |
---|
1807 | m= m*(x - random_element); |
---|
1808 | if (!find (l, random_element)) |
---|
1809 | l.append (random_element); |
---|
1810 | } while (1); |
---|
1811 | } |
---|
1812 | |
---|
1813 | CFArray |
---|
1814 | solveVandermonde (const CFArray& M, const CFArray& A) |
---|
1815 | { |
---|
1816 | int r= M.size(); |
---|
1817 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
1818 | |
---|
1819 | if (r == 1) |
---|
1820 | { |
---|
1821 | CFArray result= CFArray (1); |
---|
1822 | result [0]= A [0] / M [0]; |
---|
1823 | return result; |
---|
1824 | } |
---|
1825 | // check solvability |
---|
1826 | bool notDistinct= false; |
---|
1827 | for (int i= 0; i < r - 1; i++) |
---|
1828 | { |
---|
1829 | for (int j= i + 1; j < r; j++) |
---|
1830 | { |
---|
1831 | if (M [i] == M [j]) |
---|
1832 | { |
---|
1833 | notDistinct= true; |
---|
1834 | break; |
---|
1835 | } |
---|
1836 | } |
---|
1837 | } |
---|
1838 | if (notDistinct) |
---|
1839 | return CFArray(); |
---|
1840 | |
---|
1841 | CanonicalForm master= 1; |
---|
1842 | Variable x= Variable (1); |
---|
1843 | for (int i= 0; i < r; i++) |
---|
1844 | master *= x - M [i]; |
---|
1845 | CFList Pj; |
---|
1846 | CanonicalForm tmp; |
---|
1847 | for (int i= 0; i < r; i++) |
---|
1848 | { |
---|
1849 | tmp= master/(x - M [i]); |
---|
1850 | tmp /= tmp (M [i], 1); |
---|
1851 | Pj.append (tmp); |
---|
1852 | } |
---|
1853 | CFArray result= CFArray (r); |
---|
1854 | |
---|
1855 | CFListIterator j= Pj; |
---|
1856 | for (int i= 1; i <= r; i++, j++) |
---|
1857 | { |
---|
1858 | tmp= 0; |
---|
1859 | for (int l= 0; l < A.size(); l++) |
---|
1860 | tmp += A[l]*j.getItem()[l]; |
---|
1861 | result[i - 1]= tmp; |
---|
1862 | } |
---|
1863 | return result; |
---|
1864 | } |
---|
1865 | |
---|
1866 | CFArray |
---|
1867 | solveGeneralVandermonde (const CFArray& M, const CFArray& A) |
---|
1868 | { |
---|
1869 | int r= M.size(); |
---|
1870 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
1871 | if (r == 1) |
---|
1872 | { |
---|
1873 | CFArray result= CFArray (1); |
---|
1874 | result [0]= A[0] / M [0]; |
---|
1875 | return result; |
---|
1876 | } |
---|
1877 | // check solvability |
---|
1878 | bool notDistinct= false; |
---|
1879 | for (int i= 0; i < r - 1; i++) |
---|
1880 | { |
---|
1881 | for (int j= i + 1; j < r; j++) |
---|
1882 | { |
---|
1883 | if (M [i] == M [j]) |
---|
1884 | { |
---|
1885 | notDistinct= true; |
---|
1886 | break; |
---|
1887 | } |
---|
1888 | } |
---|
1889 | } |
---|
1890 | if (notDistinct) |
---|
1891 | return CFArray(); |
---|
1892 | |
---|
1893 | CanonicalForm master= 1; |
---|
1894 | Variable x= Variable (1); |
---|
1895 | for (int i= 0; i < r; i++) |
---|
1896 | master *= x - M [i]; |
---|
1897 | master *= x; |
---|
1898 | CFList Pj; |
---|
1899 | CanonicalForm tmp; |
---|
1900 | for (int i= 0; i < r; i++) |
---|
1901 | { |
---|
1902 | tmp= master/(x - M [i]); |
---|
1903 | tmp /= tmp (M [i], 1); |
---|
1904 | Pj.append (tmp); |
---|
1905 | } |
---|
1906 | |
---|
1907 | CFArray result= CFArray (r); |
---|
1908 | |
---|
1909 | CFListIterator j= Pj; |
---|
1910 | for (int i= 1; i <= r; i++, j++) |
---|
1911 | { |
---|
1912 | tmp= 0; |
---|
1913 | |
---|
1914 | for (int l= 1; l <= A.size(); l++) |
---|
1915 | tmp += A[l - 1]*j.getItem()[l]; |
---|
1916 | result[i - 1]= tmp; |
---|
1917 | } |
---|
1918 | return result; |
---|
1919 | } |
---|
1920 | |
---|
1921 | /// M in row echolon form, rk rank of M |
---|
1922 | CFArray |
---|
1923 | readOffSolution (const CFMatrix& M, const long rk) |
---|
1924 | { |
---|
1925 | CFArray result= CFArray (rk); |
---|
1926 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1927 | for (int i= rk; i >= 1; i--) |
---|
1928 | { |
---|
1929 | tmp3= 0; |
---|
1930 | tmp1= M (i, M.columns()); |
---|
1931 | for (int j= M.columns() - 1; j >= 1; j--) |
---|
1932 | { |
---|
1933 | tmp2= M (i, j); |
---|
1934 | if (j == i) |
---|
1935 | break; |
---|
1936 | else |
---|
1937 | tmp3 += tmp2*result[j - 1]; |
---|
1938 | } |
---|
1939 | result[i - 1]= (tmp1 - tmp3)/tmp2; |
---|
1940 | } |
---|
1941 | return result; |
---|
1942 | } |
---|
1943 | |
---|
1944 | CFArray |
---|
1945 | readOffSolution (const CFMatrix& M, const CFArray& L, const CFArray& partialSol) |
---|
1946 | { |
---|
1947 | CFArray result= CFArray (M.rows()); |
---|
1948 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1949 | int k; |
---|
1950 | for (int i= M.rows(); i >= 1; i--) |
---|
1951 | { |
---|
1952 | tmp3= 0; |
---|
1953 | tmp1= L[i - 1]; |
---|
1954 | k= 0; |
---|
1955 | for (int j= M.columns(); j >= 1; j--, k++) |
---|
1956 | { |
---|
1957 | tmp2= M (i, j); |
---|
1958 | if (j == i) |
---|
1959 | break; |
---|
1960 | else |
---|
1961 | { |
---|
1962 | if (k > partialSol.size() - 1) |
---|
1963 | tmp3 += tmp2*result[j - 1]; |
---|
1964 | else |
---|
1965 | tmp3 += tmp2*partialSol[partialSol.size() - k - 1]; |
---|
1966 | } |
---|
1967 | } |
---|
1968 | result [i - 1]= (tmp1 - tmp3)/tmp2; |
---|
1969 | } |
---|
1970 | return result; |
---|
1971 | } |
---|
1972 | |
---|
1973 | long |
---|
1974 | gaussianElimFp (CFMatrix& M, CFArray& L) |
---|
1975 | { |
---|
1976 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1977 | CFMatrix *N; |
---|
1978 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1979 | |
---|
1980 | for (int i= 1; i <= M.rows(); i++) |
---|
1981 | for (int j= 1; j <= M.columns(); j++) |
---|
1982 | (*N) (i, j)= M (i, j); |
---|
1983 | |
---|
1984 | int j= 1; |
---|
1985 | for (int i= 0; i < L.size(); i++, j++) |
---|
1986 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1987 | #ifdef HAVE_FLINT |
---|
1988 | nmod_mat_t FLINTN; |
---|
1989 | convertFacCFMatrix2nmod_mat_t (FLINTN, *N); |
---|
1990 | long* dummy= new long [M.rows()]; |
---|
1991 | for (int i= 0; i < M.rows(); i++) |
---|
1992 | dummy[i]= 0; |
---|
1993 | long rk= nmod_mat_rref (dummy, FLINTN); |
---|
1994 | |
---|
1995 | N= convertNmod_mat_t2FacCFMatrix (FLINTN); |
---|
1996 | nmod_mat_clear (FLINTN); |
---|
1997 | delete dummy; |
---|
1998 | #else |
---|
1999 | int p= getCharacteristic (); |
---|
2000 | zz_p::init (p); |
---|
2001 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
2002 | long rk= gauss (*NTLN); |
---|
2003 | |
---|
2004 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
2005 | #endif |
---|
2006 | |
---|
2007 | L= CFArray (M.rows()); |
---|
2008 | for (int i= 0; i < M.rows(); i++) |
---|
2009 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
2010 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
2011 | delete N; |
---|
2012 | return rk; |
---|
2013 | } |
---|
2014 | |
---|
2015 | long |
---|
2016 | gaussianElimFq (CFMatrix& M, CFArray& L, const Variable& alpha) |
---|
2017 | { |
---|
2018 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
2019 | CFMatrix *N; |
---|
2020 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
2021 | |
---|
2022 | for (int i= 1; i <= M.rows(); i++) |
---|
2023 | for (int j= 1; j <= M.columns(); j++) |
---|
2024 | (*N) (i, j)= M (i, j); |
---|
2025 | |
---|
2026 | int j= 1; |
---|
2027 | for (int i= 0; i < L.size(); i++, j++) |
---|
2028 | (*N) (j, M.columns() + 1)= L[i]; |
---|
2029 | int p= getCharacteristic (); |
---|
2030 | zz_p::init (p); |
---|
2031 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
2032 | zz_pE::init (NTLMipo); |
---|
2033 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
2034 | long rk= gauss (*NTLN); |
---|
2035 | |
---|
2036 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
2037 | |
---|
2038 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
2039 | L= CFArray (M.rows()); |
---|
2040 | for (int i= 0; i < M.rows(); i++) |
---|
2041 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
2042 | |
---|
2043 | delete N; |
---|
2044 | return rk; |
---|
2045 | } |
---|
2046 | |
---|
2047 | CFArray |
---|
2048 | solveSystemFp (const CFMatrix& M, const CFArray& L) |
---|
2049 | { |
---|
2050 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
2051 | CFMatrix *N; |
---|
2052 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
2053 | |
---|
2054 | for (int i= 1; i <= M.rows(); i++) |
---|
2055 | for (int j= 1; j <= M.columns(); j++) |
---|
2056 | (*N) (i, j)= M (i, j); |
---|
2057 | |
---|
2058 | int j= 1; |
---|
2059 | for (int i= 0; i < L.size(); i++, j++) |
---|
2060 | (*N) (j, M.columns() + 1)= L[i]; |
---|
2061 | |
---|
2062 | #ifdef HAVE_FLINT |
---|
2063 | nmod_mat_t FLINTN; |
---|
2064 | convertFacCFMatrix2nmod_mat_t (FLINTN, *N); |
---|
2065 | long* dummy= new long [M.rows()]; |
---|
2066 | for (int i= 0; i < M.rows(); i++) |
---|
2067 | dummy[i]= 0; |
---|
2068 | long rk= nmod_mat_rref (dummy, FLINTN); |
---|
2069 | #else |
---|
2070 | int p= getCharacteristic (); |
---|
2071 | zz_p::init (p); |
---|
2072 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
2073 | long rk= gauss (*NTLN); |
---|
2074 | #endif |
---|
2075 | if (rk != M.columns()) |
---|
2076 | { |
---|
2077 | #ifdef HAVE_FLINT |
---|
2078 | nmod_mat_clear (FLINTN); |
---|
2079 | delete dummy; |
---|
2080 | #endif |
---|
2081 | delete N; |
---|
2082 | return CFArray(); |
---|
2083 | } |
---|
2084 | #ifdef HAVE_FLINT |
---|
2085 | N= convertNmod_mat_t2FacCFMatrix (FLINTN); |
---|
2086 | nmod_mat_clear (FLINTN); |
---|
2087 | delete dummy; |
---|
2088 | #else |
---|
2089 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
2090 | #endif |
---|
2091 | CFArray A= readOffSolution (*N, rk); |
---|
2092 | |
---|
2093 | delete N; |
---|
2094 | return A; |
---|
2095 | } |
---|
2096 | |
---|
2097 | CFArray |
---|
2098 | solveSystemFq (const CFMatrix& M, const CFArray& L, const Variable& alpha) |
---|
2099 | { |
---|
2100 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
2101 | CFMatrix *N; |
---|
2102 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
2103 | |
---|
2104 | for (int i= 1; i <= M.rows(); i++) |
---|
2105 | for (int j= 1; j <= M.columns(); j++) |
---|
2106 | (*N) (i, j)= M (i, j); |
---|
2107 | int j= 1; |
---|
2108 | for (int i= 0; i < L.size(); i++, j++) |
---|
2109 | (*N) (j, M.columns() + 1)= L[i]; |
---|
2110 | int p= getCharacteristic (); |
---|
2111 | zz_p::init (p); |
---|
2112 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
2113 | zz_pE::init (NTLMipo); |
---|
2114 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
2115 | long rk= gauss (*NTLN); |
---|
2116 | if (rk != M.columns()) |
---|
2117 | { |
---|
2118 | delete N; |
---|
2119 | return CFArray(); |
---|
2120 | } |
---|
2121 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
2122 | |
---|
2123 | CFArray A= readOffSolution (*N, rk); |
---|
2124 | |
---|
2125 | delete N; |
---|
2126 | return A; |
---|
2127 | } |
---|
2128 | #endif |
---|
2129 | |
---|
2130 | CFArray |
---|
2131 | getMonoms (const CanonicalForm& F) |
---|
2132 | { |
---|
2133 | if (F.inCoeffDomain()) |
---|
2134 | { |
---|
2135 | CFArray result= CFArray (1); |
---|
2136 | result [0]= 1; |
---|
2137 | return result; |
---|
2138 | } |
---|
2139 | if (F.isUnivariate()) |
---|
2140 | { |
---|
2141 | CFArray result= CFArray (size(F)); |
---|
2142 | int j= 0; |
---|
2143 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
2144 | result[j]= power (F.mvar(), i.exp()); |
---|
2145 | return result; |
---|
2146 | } |
---|
2147 | int numMon= size (F); |
---|
2148 | CFArray result= CFArray (numMon); |
---|
2149 | int j= 0; |
---|
2150 | CFArray recResult; |
---|
2151 | Variable x= F.mvar(); |
---|
2152 | CanonicalForm powX; |
---|
2153 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
2154 | { |
---|
2155 | powX= power (x, i.exp()); |
---|
2156 | recResult= getMonoms (i.coeff()); |
---|
2157 | for (int k= 0; k < recResult.size(); k++) |
---|
2158 | result[j+k]= powX*recResult[k]; |
---|
2159 | j += recResult.size(); |
---|
2160 | } |
---|
2161 | return result; |
---|
2162 | } |
---|
2163 | |
---|
2164 | #ifdef HAVE_NTL |
---|
2165 | CFArray |
---|
2166 | evaluateMonom (const CanonicalForm& F, const CFList& evalPoints) |
---|
2167 | { |
---|
2168 | if (F.inCoeffDomain()) |
---|
2169 | { |
---|
2170 | CFArray result= CFArray (1); |
---|
2171 | result [0]= F; |
---|
2172 | return result; |
---|
2173 | } |
---|
2174 | if (F.isUnivariate()) |
---|
2175 | { |
---|
2176 | ASSERT (evalPoints.length() == 1, |
---|
2177 | "expected an eval point with only one component"); |
---|
2178 | CFArray result= CFArray (size(F)); |
---|
2179 | int j= 0; |
---|
2180 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
2181 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
2182 | result[j]= power (evalPoint, i.exp()); |
---|
2183 | return result; |
---|
2184 | } |
---|
2185 | int numMon= size (F); |
---|
2186 | CFArray result= CFArray (numMon); |
---|
2187 | int j= 0; |
---|
2188 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
2189 | CFList buf= evalPoints; |
---|
2190 | buf.removeLast(); |
---|
2191 | CFArray recResult; |
---|
2192 | CanonicalForm powEvalPoint; |
---|
2193 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
2194 | { |
---|
2195 | powEvalPoint= power (evalPoint, i.exp()); |
---|
2196 | recResult= evaluateMonom (i.coeff(), buf); |
---|
2197 | for (int k= 0; k < recResult.size(); k++) |
---|
2198 | result[j+k]= powEvalPoint*recResult[k]; |
---|
2199 | j += recResult.size(); |
---|
2200 | } |
---|
2201 | return result; |
---|
2202 | } |
---|
2203 | |
---|
2204 | CFArray |
---|
2205 | evaluate (const CFArray& A, const CFList& evalPoints) |
---|
2206 | { |
---|
2207 | CFArray result= A.size(); |
---|
2208 | CanonicalForm tmp; |
---|
2209 | int k; |
---|
2210 | for (int i= 0; i < A.size(); i++) |
---|
2211 | { |
---|
2212 | tmp= A[i]; |
---|
2213 | k= 1; |
---|
2214 | for (CFListIterator j= evalPoints; j.hasItem(); j++, k++) |
---|
2215 | tmp= tmp (j.getItem(), k); |
---|
2216 | result[i]= tmp; |
---|
2217 | } |
---|
2218 | return result; |
---|
2219 | } |
---|
2220 | |
---|
2221 | CFList |
---|
2222 | evaluationPoints (const CanonicalForm& F, const CanonicalForm& G, |
---|
2223 | CanonicalForm& Feval, CanonicalForm& Geval, |
---|
2224 | const CanonicalForm& LCF, const bool& GF, |
---|
2225 | const Variable& alpha, bool& fail, CFList& list |
---|
2226 | ) |
---|
2227 | { |
---|
2228 | int k= tmax (F.level(), G.level()) - 1; |
---|
2229 | Variable x= Variable (1); |
---|
2230 | CFList result; |
---|
2231 | FFRandom genFF; |
---|
2232 | GFRandom genGF; |
---|
2233 | int p= getCharacteristic (); |
---|
2234 | int bound; |
---|
2235 | if (alpha != Variable (1)) |
---|
2236 | { |
---|
2237 | bound= ipower (p, degree (getMipo(alpha))); |
---|
2238 | bound= ipower (bound, k); |
---|
2239 | } |
---|
2240 | else if (GF) |
---|
2241 | { |
---|
2242 | bound= ipower (p, getGFDegree()); |
---|
2243 | bound= ipower (bound, k); |
---|
2244 | } |
---|
2245 | else |
---|
2246 | bound= ipower (p, k); |
---|
2247 | |
---|
2248 | CanonicalForm random; |
---|
2249 | int j; |
---|
2250 | bool zeroOneOccured= false; |
---|
2251 | bool allEqual= false; |
---|
2252 | CanonicalForm buf; |
---|
2253 | do |
---|
2254 | { |
---|
2255 | random= 0; |
---|
2256 | // possible overflow if list.length() does not fit into a int |
---|
2257 | if (list.length() >= bound) |
---|
2258 | { |
---|
2259 | fail= true; |
---|
2260 | break; |
---|
2261 | } |
---|
2262 | for (int i= 0; i < k; i++) |
---|
2263 | { |
---|
2264 | if (GF) |
---|
2265 | { |
---|
2266 | result.append (genGF.generate()); |
---|
2267 | random += result.getLast()*power (x, i); |
---|
2268 | } |
---|
2269 | else if (alpha.level() != 1) |
---|
2270 | { |
---|
2271 | AlgExtRandomF genAlgExt (alpha); |
---|
2272 | result.append (genAlgExt.generate()); |
---|
2273 | random += result.getLast()*power (x, i); |
---|
2274 | } |
---|
2275 | else |
---|
2276 | { |
---|
2277 | result.append (genFF.generate()); |
---|
2278 | random += result.getLast()*power (x, i); |
---|
2279 | } |
---|
2280 | if (result.getLast().isOne() || result.getLast().isZero()) |
---|
2281 | zeroOneOccured= true; |
---|
2282 | } |
---|
2283 | if (find (list, random)) |
---|
2284 | { |
---|
2285 | zeroOneOccured= false; |
---|
2286 | allEqual= false; |
---|
2287 | result= CFList(); |
---|
2288 | continue; |
---|
2289 | } |
---|
2290 | if (zeroOneOccured) |
---|
2291 | { |
---|
2292 | list.append (random); |
---|
2293 | zeroOneOccured= false; |
---|
2294 | allEqual= false; |
---|
2295 | result= CFList(); |
---|
2296 | continue; |
---|
2297 | } |
---|
2298 | // no zero at this point |
---|
2299 | if (k > 1) |
---|
2300 | { |
---|
2301 | allEqual= true; |
---|
2302 | CFIterator iter= random; |
---|
2303 | buf= iter.coeff(); |
---|
2304 | iter++; |
---|
2305 | for (; iter.hasTerms(); iter++) |
---|
2306 | if (buf != iter.coeff()) |
---|
2307 | allEqual= false; |
---|
2308 | } |
---|
2309 | if (allEqual) |
---|
2310 | { |
---|
2311 | list.append (random); |
---|
2312 | allEqual= false; |
---|
2313 | zeroOneOccured= false; |
---|
2314 | result= CFList(); |
---|
2315 | continue; |
---|
2316 | } |
---|
2317 | |
---|
2318 | Feval= F; |
---|
2319 | Geval= G; |
---|
2320 | CanonicalForm LCeval= LCF; |
---|
2321 | j= 1; |
---|
2322 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
2323 | { |
---|
2324 | Feval= Feval (i.getItem(), j); |
---|
2325 | Geval= Geval (i.getItem(), j); |
---|
2326 | LCeval= LCeval (i.getItem(), j); |
---|
2327 | } |
---|
2328 | |
---|
2329 | if (LCeval.isZero()) |
---|
2330 | { |
---|
2331 | if (!find (list, random)) |
---|
2332 | list.append (random); |
---|
2333 | zeroOneOccured= false; |
---|
2334 | allEqual= false; |
---|
2335 | result= CFList(); |
---|
2336 | continue; |
---|
2337 | } |
---|
2338 | |
---|
2339 | if (list.length() >= bound) |
---|
2340 | { |
---|
2341 | fail= true; |
---|
2342 | break; |
---|
2343 | } |
---|
2344 | } while (find (list, random)); |
---|
2345 | |
---|
2346 | return result; |
---|
2347 | } |
---|
2348 | |
---|
2349 | /// multiply two lists componentwise |
---|
2350 | void mult (CFList& L1, const CFList& L2) |
---|
2351 | { |
---|
2352 | ASSERT (L1.length() == L2.length(), "lists of the same size expected"); |
---|
2353 | |
---|
2354 | CFListIterator j= L2; |
---|
2355 | for (CFListIterator i= L1; i.hasItem(); i++, j++) |
---|
2356 | i.getItem() *= j.getItem(); |
---|
2357 | } |
---|
2358 | |
---|
2359 | void eval (const CanonicalForm& A, const CanonicalForm& B, CanonicalForm& Aeval, |
---|
2360 | CanonicalForm& Beval, const CFList& L) |
---|
2361 | { |
---|
2362 | Aeval= A; |
---|
2363 | Beval= B; |
---|
2364 | int j= 1; |
---|
2365 | for (CFListIterator i= L; i.hasItem(); i++, j++) |
---|
2366 | { |
---|
2367 | Aeval= Aeval (i.getItem(), j); |
---|
2368 | Beval= Beval (i.getItem(), j); |
---|
2369 | } |
---|
2370 | } |
---|
2371 | |
---|
2372 | CanonicalForm |
---|
2373 | monicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
2374 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
2375 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
2376 | ) |
---|
2377 | { |
---|
2378 | CanonicalForm A= F; |
---|
2379 | CanonicalForm B= G; |
---|
2380 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
2381 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
2382 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
2383 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
2384 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
2385 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
2386 | if (F == G) return F/Lc(F); |
---|
2387 | |
---|
2388 | CFMap M,N; |
---|
2389 | int best_level= myCompress (A, B, M, N, false); |
---|
2390 | |
---|
2391 | if (best_level == 0) |
---|
2392 | return B.genOne(); |
---|
2393 | |
---|
2394 | A= M(A); |
---|
2395 | B= M(B); |
---|
2396 | |
---|
2397 | Variable x= Variable (1); |
---|
2398 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
2399 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
2400 | |
---|
2401 | //univariate case |
---|
2402 | if (A.isUnivariate() && B.isUnivariate()) |
---|
2403 | return N (gcd (A, B)); |
---|
2404 | |
---|
2405 | CanonicalForm skel= M(skeleton); |
---|
2406 | CanonicalForm cA, cB; // content of A and B |
---|
2407 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
2408 | CanonicalForm gcdcAcB; |
---|
2409 | cA = uni_content (A); |
---|
2410 | cB = uni_content (B); |
---|
2411 | gcdcAcB= gcd (cA, cB); |
---|
2412 | ppA= A/cA; |
---|
2413 | ppB= B/cB; |
---|
2414 | |
---|
2415 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
2416 | CanonicalForm gcdlcAlcB; |
---|
2417 | lcA= uni_lcoeff (ppA); |
---|
2418 | lcB= uni_lcoeff (ppB); |
---|
2419 | |
---|
2420 | if (fdivides (lcA, lcB)) |
---|
2421 | { |
---|
2422 | if (fdivides (A, B)) |
---|
2423 | return F/Lc(F); |
---|
2424 | } |
---|
2425 | if (fdivides (lcB, lcA)) |
---|
2426 | { |
---|
2427 | if (fdivides (B, A)) |
---|
2428 | return G/Lc(G); |
---|
2429 | } |
---|
2430 | |
---|
2431 | gcdlcAlcB= gcd (lcA, lcB); |
---|
2432 | int skelSize= size (skel, skel.mvar()); |
---|
2433 | |
---|
2434 | int j= 0; |
---|
2435 | int biggestSize= 0; |
---|
2436 | |
---|
2437 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2438 | biggestSize= tmax (biggestSize, size (i.coeff())); |
---|
2439 | |
---|
2440 | CanonicalForm g, Aeval, Beval; |
---|
2441 | |
---|
2442 | CFList evalPoints; |
---|
2443 | bool evalFail= false; |
---|
2444 | CFList list; |
---|
2445 | bool GF= false; |
---|
2446 | CanonicalForm LCA= LC (A); |
---|
2447 | CanonicalForm tmp; |
---|
2448 | CFArray gcds= CFArray (biggestSize); |
---|
2449 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
2450 | Variable V_buf= alpha; |
---|
2451 | CFList source, dest; |
---|
2452 | CanonicalForm prim_elem, im_prim_elem; |
---|
2453 | for (int i= 0; i < biggestSize; i++) |
---|
2454 | { |
---|
2455 | if (i == 0) |
---|
2456 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, evalFail, |
---|
2457 | list); |
---|
2458 | else |
---|
2459 | { |
---|
2460 | mult (evalPoints, pEvalPoints [0]); |
---|
2461 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2462 | } |
---|
2463 | |
---|
2464 | if (evalFail) |
---|
2465 | { |
---|
2466 | if (V_buf.level() != 1) |
---|
2467 | { |
---|
2468 | do |
---|
2469 | { |
---|
2470 | Variable V_buf2= chooseExtension (V_buf); |
---|
2471 | source= CFList(); |
---|
2472 | dest= CFList(); |
---|
2473 | |
---|
2474 | bool prim_fail= false; |
---|
2475 | Variable V_buf3; |
---|
2476 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
2477 | |
---|
2478 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
2479 | if (prim_fail) |
---|
2480 | ; //ERROR |
---|
2481 | else |
---|
2482 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
2483 | |
---|
2484 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
2485 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
2486 | |
---|
2487 | for (CFListIterator j= list; j.hasItem(); j++) |
---|
2488 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
2489 | im_prim_elem, source, dest); |
---|
2490 | for (int k= 0; k < i; k++) |
---|
2491 | { |
---|
2492 | for (CFListIterator j= pEvalPoints[k]; j.hasItem(); j++) |
---|
2493 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
2494 | im_prim_elem, source, dest); |
---|
2495 | gcds[k]= mapUp (gcds[k], V_buf, V_buf2, prim_elem, im_prim_elem, |
---|
2496 | source, dest); |
---|
2497 | } |
---|
2498 | |
---|
2499 | if (alpha.level() != 1) |
---|
2500 | { |
---|
2501 | A= mapUp (A, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
2502 | B= mapUp (B, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
2503 | } |
---|
2504 | evalFail= false; |
---|
2505 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2506 | evalFail, list); |
---|
2507 | } while (evalFail); |
---|
2508 | } |
---|
2509 | else |
---|
2510 | { |
---|
2511 | CanonicalForm mipo; |
---|
2512 | int deg= 2; |
---|
2513 | do { |
---|
2514 | mipo= randomIrredpoly (deg, x); |
---|
2515 | V_buf= rootOf (mipo); |
---|
2516 | evalFail= false; |
---|
2517 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2518 | evalFail, list); |
---|
2519 | deg++; |
---|
2520 | } while (evalFail); |
---|
2521 | } |
---|
2522 | } |
---|
2523 | |
---|
2524 | g= gcd (Aeval, Beval); |
---|
2525 | g /= Lc (g); |
---|
2526 | |
---|
2527 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2528 | { |
---|
2529 | delete[] pEvalPoints; |
---|
2530 | fail= true; |
---|
2531 | return 0; |
---|
2532 | } |
---|
2533 | CFIterator l= skel; |
---|
2534 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2535 | { |
---|
2536 | if (k.exp() != l.exp()) |
---|
2537 | { |
---|
2538 | delete[] pEvalPoints; |
---|
2539 | fail= true; |
---|
2540 | return 0; |
---|
2541 | } |
---|
2542 | } |
---|
2543 | pEvalPoints[i]= evalPoints; |
---|
2544 | gcds[i]= g; |
---|
2545 | |
---|
2546 | tmp= 0; |
---|
2547 | int j= 0; |
---|
2548 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
2549 | tmp += k.getItem()*power (x, j); |
---|
2550 | list.append (tmp); |
---|
2551 | } |
---|
2552 | |
---|
2553 | if (Monoms.size() == 0) |
---|
2554 | Monoms= getMonoms (skel); |
---|
2555 | if (coeffMonoms == NULL) |
---|
2556 | coeffMonoms= new CFArray [skelSize]; |
---|
2557 | j= 0; |
---|
2558 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2559 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
2560 | |
---|
2561 | CFArray* pL= new CFArray [skelSize]; |
---|
2562 | CFArray* pM= new CFArray [skelSize]; |
---|
2563 | for (int i= 0; i < biggestSize; i++) |
---|
2564 | { |
---|
2565 | CFIterator l= gcds [i]; |
---|
2566 | evalPoints= pEvalPoints [i]; |
---|
2567 | for (int k= 0; k < skelSize; k++, l++) |
---|
2568 | { |
---|
2569 | if (i == 0) |
---|
2570 | pL[k]= CFArray (biggestSize); |
---|
2571 | pL[k] [i]= l.coeff(); |
---|
2572 | |
---|
2573 | if (i == 0) |
---|
2574 | pM[k]= evaluate (coeffMonoms [k], evalPoints); |
---|
2575 | } |
---|
2576 | } |
---|
2577 | |
---|
2578 | CFArray solution; |
---|
2579 | CanonicalForm result= 0; |
---|
2580 | int ind= 0; |
---|
2581 | CFArray bufArray; |
---|
2582 | CFMatrix Mat; |
---|
2583 | for (int k= 0; k < skelSize; k++) |
---|
2584 | { |
---|
2585 | if (biggestSize != coeffMonoms[k].size()) |
---|
2586 | { |
---|
2587 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
2588 | for (int i= 0; i < coeffMonoms[k].size(); i++) |
---|
2589 | bufArray [i]= pL[k] [i]; |
---|
2590 | solution= solveGeneralVandermonde (pM [k], bufArray); |
---|
2591 | } |
---|
2592 | else |
---|
2593 | solution= solveGeneralVandermonde (pM [k], pL[k]); |
---|
2594 | |
---|
2595 | if (solution.size() == 0) |
---|
2596 | { |
---|
2597 | delete[] pEvalPoints; |
---|
2598 | delete[] pM; |
---|
2599 | delete[] pL; |
---|
2600 | delete[] coeffMonoms; |
---|
2601 | fail= true; |
---|
2602 | return 0; |
---|
2603 | } |
---|
2604 | for (int l= 0; l < solution.size(); l++) |
---|
2605 | result += solution[l]*Monoms [ind + l]; |
---|
2606 | ind += solution.size(); |
---|
2607 | } |
---|
2608 | |
---|
2609 | delete[] pEvalPoints; |
---|
2610 | delete[] pM; |
---|
2611 | delete[] pL; |
---|
2612 | |
---|
2613 | if (alpha.level() != 1 && V_buf != alpha) |
---|
2614 | { |
---|
2615 | CFList u, v; |
---|
2616 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
2617 | } |
---|
2618 | |
---|
2619 | result= N(result); |
---|
2620 | if (fdivides (result, F) && fdivides (result, G)) |
---|
2621 | return result; |
---|
2622 | else |
---|
2623 | { |
---|
2624 | delete[] coeffMonoms; |
---|
2625 | fail= true; |
---|
2626 | return 0; |
---|
2627 | } |
---|
2628 | } |
---|
2629 | |
---|
2630 | CanonicalForm |
---|
2631 | nonMonicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
2632 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
2633 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
2634 | ) |
---|
2635 | { |
---|
2636 | CanonicalForm A= F; |
---|
2637 | CanonicalForm B= G; |
---|
2638 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
2639 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
2640 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
2641 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
2642 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
2643 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
2644 | if (F == G) return F/Lc(F); |
---|
2645 | |
---|
2646 | CFMap M,N; |
---|
2647 | int best_level= myCompress (A, B, M, N, false); |
---|
2648 | |
---|
2649 | if (best_level == 0) |
---|
2650 | return B.genOne(); |
---|
2651 | |
---|
2652 | A= M(A); |
---|
2653 | B= M(B); |
---|
2654 | |
---|
2655 | Variable x= Variable (1); |
---|
2656 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
2657 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
2658 | |
---|
2659 | //univariate case |
---|
2660 | if (A.isUnivariate() && B.isUnivariate()) |
---|
2661 | return N (gcd (A, B)); |
---|
2662 | |
---|
2663 | CanonicalForm skel= M(skeleton); |
---|
2664 | |
---|
2665 | CanonicalForm cA, cB; // content of A and B |
---|
2666 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
2667 | CanonicalForm gcdcAcB; |
---|
2668 | cA = uni_content (A); |
---|
2669 | cB = uni_content (B); |
---|
2670 | gcdcAcB= gcd (cA, cB); |
---|
2671 | ppA= A/cA; |
---|
2672 | ppB= B/cB; |
---|
2673 | |
---|
2674 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
2675 | CanonicalForm gcdlcAlcB; |
---|
2676 | lcA= uni_lcoeff (ppA); |
---|
2677 | lcB= uni_lcoeff (ppB); |
---|
2678 | |
---|
2679 | if (fdivides (lcA, lcB)) |
---|
2680 | { |
---|
2681 | if (fdivides (A, B)) |
---|
2682 | return F/Lc(F); |
---|
2683 | } |
---|
2684 | if (fdivides (lcB, lcA)) |
---|
2685 | { |
---|
2686 | if (fdivides (B, A)) |
---|
2687 | return G/Lc(G); |
---|
2688 | } |
---|
2689 | |
---|
2690 | gcdlcAlcB= gcd (lcA, lcB); |
---|
2691 | int skelSize= size (skel, skel.mvar()); |
---|
2692 | |
---|
2693 | int j= 0; |
---|
2694 | int biggestSize= 0; |
---|
2695 | int bufSize; |
---|
2696 | int numberUni= 0; |
---|
2697 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2698 | { |
---|
2699 | bufSize= size (i.coeff()); |
---|
2700 | biggestSize= tmax (biggestSize, bufSize); |
---|
2701 | numberUni += bufSize; |
---|
2702 | } |
---|
2703 | numberUni--; |
---|
2704 | numberUni= (int) ceil ( (double) numberUni / (skelSize - 1)); |
---|
2705 | biggestSize= tmax (biggestSize , numberUni); |
---|
2706 | |
---|
2707 | numberUni= biggestSize + size (LC(skel)) - 1; |
---|
2708 | int biggestSize2= tmax (numberUni, biggestSize); |
---|
2709 | |
---|
2710 | CanonicalForm g, Aeval, Beval; |
---|
2711 | |
---|
2712 | CFList evalPoints; |
---|
2713 | CFArray coeffEval; |
---|
2714 | bool evalFail= false; |
---|
2715 | CFList list; |
---|
2716 | bool GF= false; |
---|
2717 | CanonicalForm LCA= LC (A); |
---|
2718 | CanonicalForm tmp; |
---|
2719 | CFArray gcds= CFArray (biggestSize); |
---|
2720 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
2721 | Variable V_buf= alpha; |
---|
2722 | CFList source, dest; |
---|
2723 | CanonicalForm prim_elem, im_prim_elem; |
---|
2724 | for (int i= 0; i < biggestSize; i++) |
---|
2725 | { |
---|
2726 | if (i == 0) |
---|
2727 | { |
---|
2728 | if (getCharacteristic() > 3) |
---|
2729 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2730 | evalFail, list); |
---|
2731 | else |
---|
2732 | evalFail= true; |
---|
2733 | |
---|
2734 | if (evalFail) |
---|
2735 | { |
---|
2736 | if (V_buf.level() != 1) |
---|
2737 | { |
---|
2738 | do |
---|
2739 | { |
---|
2740 | Variable V_buf2= chooseExtension (V_buf); |
---|
2741 | source= CFList(); |
---|
2742 | dest= CFList(); |
---|
2743 | |
---|
2744 | bool prim_fail= false; |
---|
2745 | Variable V_buf3; |
---|
2746 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
2747 | |
---|
2748 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
2749 | if (prim_fail) |
---|
2750 | ; //ERROR |
---|
2751 | else |
---|
2752 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
2753 | |
---|
2754 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
2755 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
2756 | |
---|
2757 | for (CFListIterator i= list; i.hasItem(); i++) |
---|
2758 | i.getItem()= mapUp (i.getItem(), V_buf, V_buf2, prim_elem, |
---|
2759 | im_prim_elem, source, dest); |
---|
2760 | evalFail= false; |
---|
2761 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2762 | evalFail, list); |
---|
2763 | } while (evalFail); |
---|
2764 | } |
---|
2765 | else |
---|
2766 | { |
---|
2767 | CanonicalForm mipo; |
---|
2768 | int deg= 2; |
---|
2769 | do { |
---|
2770 | mipo= randomIrredpoly (deg, x); |
---|
2771 | V_buf= rootOf (mipo); |
---|
2772 | evalFail= false; |
---|
2773 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2774 | evalFail, list); |
---|
2775 | deg++; |
---|
2776 | } while (evalFail); |
---|
2777 | } |
---|
2778 | } |
---|
2779 | } |
---|
2780 | else |
---|
2781 | { |
---|
2782 | mult (evalPoints, pEvalPoints[0]); |
---|
2783 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2784 | } |
---|
2785 | |
---|
2786 | g= gcd (Aeval, Beval); |
---|
2787 | g /= Lc (g); |
---|
2788 | |
---|
2789 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2790 | { |
---|
2791 | delete[] pEvalPoints; |
---|
2792 | fail= true; |
---|
2793 | return 0; |
---|
2794 | } |
---|
2795 | CFIterator l= skel; |
---|
2796 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2797 | { |
---|
2798 | if (k.exp() != l.exp()) |
---|
2799 | { |
---|
2800 | delete[] pEvalPoints; |
---|
2801 | fail= true; |
---|
2802 | return 0; |
---|
2803 | } |
---|
2804 | } |
---|
2805 | pEvalPoints[i]= evalPoints; |
---|
2806 | gcds[i]= g; |
---|
2807 | |
---|
2808 | tmp= 0; |
---|
2809 | int j= 0; |
---|
2810 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
2811 | tmp += k.getItem()*power (x, j); |
---|
2812 | list.append (tmp); |
---|
2813 | } |
---|
2814 | |
---|
2815 | if (Monoms.size() == 0) |
---|
2816 | Monoms= getMonoms (skel); |
---|
2817 | |
---|
2818 | if (coeffMonoms == NULL) |
---|
2819 | coeffMonoms= new CFArray [skelSize]; |
---|
2820 | |
---|
2821 | j= 0; |
---|
2822 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2823 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
2824 | |
---|
2825 | int minimalColumnsIndex; |
---|
2826 | if (skelSize > 1) |
---|
2827 | minimalColumnsIndex= 1; |
---|
2828 | else |
---|
2829 | minimalColumnsIndex= 0; |
---|
2830 | int minimalColumns=-1; |
---|
2831 | |
---|
2832 | CFArray* pM= new CFArray [skelSize]; |
---|
2833 | CFMatrix Mat; |
---|
2834 | // find the Matrix with minimal number of columns |
---|
2835 | for (int i= 0; i < skelSize; i++) |
---|
2836 | { |
---|
2837 | pM[i]= CFArray (coeffMonoms[i].size()); |
---|
2838 | if (i == 1) |
---|
2839 | minimalColumns= coeffMonoms[i].size(); |
---|
2840 | if (i > 1) |
---|
2841 | { |
---|
2842 | if (minimalColumns > coeffMonoms[i].size()) |
---|
2843 | { |
---|
2844 | minimalColumns= coeffMonoms[i].size(); |
---|
2845 | minimalColumnsIndex= i; |
---|
2846 | } |
---|
2847 | } |
---|
2848 | } |
---|
2849 | CFMatrix* pMat= new CFMatrix [2]; |
---|
2850 | pMat[0]= CFMatrix (biggestSize, coeffMonoms[0].size()); |
---|
2851 | pMat[1]= CFMatrix (biggestSize, coeffMonoms[minimalColumnsIndex].size()); |
---|
2852 | CFArray* pL= new CFArray [skelSize]; |
---|
2853 | for (int i= 0; i < biggestSize; i++) |
---|
2854 | { |
---|
2855 | CFIterator l= gcds [i]; |
---|
2856 | evalPoints= pEvalPoints [i]; |
---|
2857 | for (int k= 0; k < skelSize; k++, l++) |
---|
2858 | { |
---|
2859 | if (i == 0) |
---|
2860 | pL[k]= CFArray (biggestSize); |
---|
2861 | pL[k] [i]= l.coeff(); |
---|
2862 | |
---|
2863 | if (i == 0 && k != 0 && k != minimalColumnsIndex) |
---|
2864 | pM[k]= evaluate (coeffMonoms[k], evalPoints); |
---|
2865 | else if (i == 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
2866 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2867 | if (i > 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
2868 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2869 | |
---|
2870 | if (k == 0) |
---|
2871 | { |
---|
2872 | if (pMat[k].rows() >= i + 1) |
---|
2873 | { |
---|
2874 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2875 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2876 | } |
---|
2877 | } |
---|
2878 | if (k == minimalColumnsIndex) |
---|
2879 | { |
---|
2880 | if (pMat[1].rows() >= i + 1) |
---|
2881 | { |
---|
2882 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2883 | pMat[1] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2884 | } |
---|
2885 | } |
---|
2886 | } |
---|
2887 | } |
---|
2888 | |
---|
2889 | CFArray solution; |
---|
2890 | CanonicalForm result= 0; |
---|
2891 | int ind= 1; |
---|
2892 | int matRows, matColumns; |
---|
2893 | matRows= pMat[1].rows(); |
---|
2894 | matColumns= pMat[0].columns() - 1; |
---|
2895 | matColumns += pMat[1].columns(); |
---|
2896 | |
---|
2897 | Mat= CFMatrix (matRows, matColumns); |
---|
2898 | for (int i= 1; i <= matRows; i++) |
---|
2899 | for (int j= 1; j <= pMat[1].columns(); j++) |
---|
2900 | Mat (i, j)= pMat[1] (i, j); |
---|
2901 | |
---|
2902 | for (int j= pMat[1].columns() + 1; j <= matColumns; |
---|
2903 | j++, ind++) |
---|
2904 | { |
---|
2905 | for (int i= 1; i <= matRows; i++) |
---|
2906 | Mat (i, j)= (-pMat [0] (i, ind + 1))*pL[minimalColumnsIndex] [i - 1]; |
---|
2907 | } |
---|
2908 | |
---|
2909 | CFArray firstColumn= CFArray (pMat[0].rows()); |
---|
2910 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
2911 | firstColumn [i]= pMat[0] (i + 1, 1); |
---|
2912 | |
---|
2913 | CFArray bufArray= pL[minimalColumnsIndex]; |
---|
2914 | |
---|
2915 | for (int i= 0; i < biggestSize; i++) |
---|
2916 | pL[minimalColumnsIndex] [i] *= firstColumn[i]; |
---|
2917 | |
---|
2918 | CFMatrix bufMat= pMat[1]; |
---|
2919 | pMat[1]= Mat; |
---|
2920 | |
---|
2921 | if (V_buf.level() != 1) |
---|
2922 | solution= solveSystemFq (pMat[1], |
---|
2923 | pL[minimalColumnsIndex], V_buf); |
---|
2924 | else |
---|
2925 | solution= solveSystemFp (pMat[1], |
---|
2926 | pL[minimalColumnsIndex]); |
---|
2927 | |
---|
2928 | if (solution.size() == 0) |
---|
2929 | { //Javadi's method failed, try deKleine, Monagan, Wittkopf instead |
---|
2930 | CFMatrix bufMat0= pMat[0]; |
---|
2931 | delete [] pMat; |
---|
2932 | pMat= new CFMatrix [skelSize]; |
---|
2933 | pL[minimalColumnsIndex]= bufArray; |
---|
2934 | CFList* bufpEvalPoints= NULL; |
---|
2935 | CFArray bufGcds; |
---|
2936 | if (biggestSize != biggestSize2) |
---|
2937 | { |
---|
2938 | bufpEvalPoints= pEvalPoints; |
---|
2939 | pEvalPoints= new CFList [biggestSize2]; |
---|
2940 | bufGcds= gcds; |
---|
2941 | gcds= CFArray (biggestSize2); |
---|
2942 | for (int i= 0; i < biggestSize; i++) |
---|
2943 | { |
---|
2944 | pEvalPoints[i]= bufpEvalPoints [i]; |
---|
2945 | gcds[i]= bufGcds[i]; |
---|
2946 | } |
---|
2947 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
2948 | { |
---|
2949 | mult (evalPoints, pEvalPoints[0]); |
---|
2950 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2951 | g= gcd (Aeval, Beval); |
---|
2952 | g /= Lc (g); |
---|
2953 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2954 | { |
---|
2955 | delete[] pEvalPoints; |
---|
2956 | delete[] pMat; |
---|
2957 | delete[] pL; |
---|
2958 | delete[] coeffMonoms; |
---|
2959 | delete[] pM; |
---|
2960 | if (bufpEvalPoints != NULL) |
---|
2961 | delete [] bufpEvalPoints; |
---|
2962 | fail= true; |
---|
2963 | return 0; |
---|
2964 | } |
---|
2965 | CFIterator l= skel; |
---|
2966 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2967 | { |
---|
2968 | if (k.exp() != l.exp()) |
---|
2969 | { |
---|
2970 | delete[] pEvalPoints; |
---|
2971 | delete[] pMat; |
---|
2972 | delete[] pL; |
---|
2973 | delete[] coeffMonoms; |
---|
2974 | delete[] pM; |
---|
2975 | if (bufpEvalPoints != NULL) |
---|
2976 | delete [] bufpEvalPoints; |
---|
2977 | fail= true; |
---|
2978 | return 0; |
---|
2979 | } |
---|
2980 | } |
---|
2981 | pEvalPoints[i + biggestSize]= evalPoints; |
---|
2982 | gcds[i + biggestSize]= g; |
---|
2983 | } |
---|
2984 | } |
---|
2985 | for (int i= 0; i < biggestSize; i++) |
---|
2986 | { |
---|
2987 | CFIterator l= gcds [i]; |
---|
2988 | evalPoints= pEvalPoints [i]; |
---|
2989 | for (int k= 1; k < skelSize; k++, l++) |
---|
2990 | { |
---|
2991 | if (i == 0) |
---|
2992 | pMat[k]= CFMatrix (biggestSize2,coeffMonoms[k].size()+biggestSize2-1); |
---|
2993 | if (k == minimalColumnsIndex) |
---|
2994 | continue; |
---|
2995 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2996 | if (pMat[k].rows() >= i + 1) |
---|
2997 | { |
---|
2998 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2999 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
3000 | } |
---|
3001 | } |
---|
3002 | } |
---|
3003 | Mat= bufMat0; |
---|
3004 | pMat[0]= CFMatrix (biggestSize2, coeffMonoms[0].size() + biggestSize2 - 1); |
---|
3005 | for (int j= 1; j <= Mat.rows(); j++) |
---|
3006 | for (int k= 1; k <= Mat.columns(); k++) |
---|
3007 | pMat [0] (j,k)= Mat (j,k); |
---|
3008 | Mat= bufMat; |
---|
3009 | for (int j= 1; j <= Mat.rows(); j++) |
---|
3010 | for (int k= 1; k <= Mat.columns(); k++) |
---|
3011 | pMat [minimalColumnsIndex] (j,k)= Mat (j,k); |
---|
3012 | // write old matrix entries into new matrices |
---|
3013 | for (int i= 0; i < skelSize; i++) |
---|
3014 | { |
---|
3015 | bufArray= pL[i]; |
---|
3016 | pL[i]= CFArray (biggestSize2); |
---|
3017 | for (int j= 0; j < bufArray.size(); j++) |
---|
3018 | pL[i] [j]= bufArray [j]; |
---|
3019 | } |
---|
3020 | //write old vector entries into new and add new entries to old matrices |
---|
3021 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
3022 | { |
---|
3023 | CFIterator l= gcds [i + biggestSize]; |
---|
3024 | evalPoints= pEvalPoints [i + biggestSize]; |
---|
3025 | for (int k= 0; k < skelSize; k++, l++) |
---|
3026 | { |
---|
3027 | pL[k] [i + biggestSize]= l.coeff(); |
---|
3028 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
3029 | if (pMat[k].rows() >= i + biggestSize + 1) |
---|
3030 | { |
---|
3031 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
3032 | pMat[k] (i + biggestSize + 1, ind)= coeffEval[ind - 1]; |
---|
3033 | } |
---|
3034 | } |
---|
3035 | } |
---|
3036 | // begin new |
---|
3037 | for (int i= 0; i < skelSize; i++) |
---|
3038 | { |
---|
3039 | if (pL[i].size() > 1) |
---|
3040 | { |
---|
3041 | for (int j= 2; j <= pMat[i].rows(); j++) |
---|
3042 | pMat[i] (j, coeffMonoms[i].size() + j - 1)= |
---|
3043 | -pL[i] [j - 1]; |
---|
3044 | } |
---|
3045 | } |
---|
3046 | |
---|
3047 | matColumns= biggestSize2 - 1; |
---|
3048 | matRows= 0; |
---|
3049 | for (int i= 0; i < skelSize; i++) |
---|
3050 | { |
---|
3051 | if (V_buf.level() == 1) |
---|
3052 | (void) gaussianElimFp (pMat[i], pL[i]); |
---|
3053 | else |
---|
3054 | (void) gaussianElimFq (pMat[i], pL[i], V_buf); |
---|
3055 | |
---|
3056 | if (pMat[i] (coeffMonoms[i].size(), coeffMonoms[i].size()) == 0) |
---|
3057 | { |
---|
3058 | delete[] pEvalPoints; |
---|
3059 | delete[] pMat; |
---|
3060 | delete[] pL; |
---|
3061 | delete[] coeffMonoms; |
---|
3062 | delete[] pM; |
---|
3063 | if (bufpEvalPoints != NULL) |
---|
3064 | delete [] bufpEvalPoints; |
---|
3065 | fail= true; |
---|
3066 | return 0; |
---|
3067 | } |
---|
3068 | matRows += pMat[i].rows() - coeffMonoms[i].size(); |
---|
3069 | } |
---|
3070 | |
---|
3071 | CFMatrix bufMat; |
---|
3072 | Mat= CFMatrix (matRows, matColumns); |
---|
3073 | ind= 0; |
---|
3074 | bufArray= CFArray (matRows); |
---|
3075 | CFArray bufArray2; |
---|
3076 | for (int i= 0; i < skelSize; i++) |
---|
3077 | { |
---|
3078 | bufMat= pMat[i] (coeffMonoms[i].size() + 1, pMat[i].rows(), |
---|
3079 | coeffMonoms[i].size() + 1, pMat[i].columns()); |
---|
3080 | |
---|
3081 | for (int j= 1; j <= bufMat.rows(); j++) |
---|
3082 | for (int k= 1; k <= bufMat.columns(); k++) |
---|
3083 | Mat (j + ind, k)= bufMat(j, k); |
---|
3084 | bufArray2= coeffMonoms[i].size(); |
---|
3085 | for (int j= 1; j <= pMat[i].rows(); j++) |
---|
3086 | { |
---|
3087 | if (j > coeffMonoms[i].size()) |
---|
3088 | bufArray [j-coeffMonoms[i].size() + ind - 1]= pL[i] [j - 1]; |
---|
3089 | else |
---|
3090 | bufArray2 [j - 1]= pL[i] [j - 1]; |
---|
3091 | } |
---|
3092 | pL[i]= bufArray2; |
---|
3093 | ind += bufMat.rows(); |
---|
3094 | pMat[i]= pMat[i] (1, coeffMonoms[i].size(), 1, pMat[i].columns()); |
---|
3095 | } |
---|
3096 | |
---|
3097 | if (V_buf.level() != 1) |
---|
3098 | solution= solveSystemFq (Mat, bufArray, V_buf); |
---|
3099 | else |
---|
3100 | solution= solveSystemFp (Mat, bufArray); |
---|
3101 | |
---|
3102 | if (solution.size() == 0) |
---|
3103 | { |
---|
3104 | delete[] pEvalPoints; |
---|
3105 | delete[] pMat; |
---|
3106 | delete[] pL; |
---|
3107 | delete[] coeffMonoms; |
---|
3108 | delete[] pM; |
---|
3109 | if (bufpEvalPoints != NULL) |
---|
3110 | delete [] bufpEvalPoints; |
---|
3111 | fail= true; |
---|
3112 | return 0; |
---|
3113 | } |
---|
3114 | |
---|
3115 | ind= 0; |
---|
3116 | result= 0; |
---|
3117 | CFArray bufSolution; |
---|
3118 | for (int i= 0; i < skelSize; i++) |
---|
3119 | { |
---|
3120 | bufSolution= readOffSolution (pMat[i], pL[i], solution); |
---|
3121 | for (int i= 0; i < bufSolution.size(); i++, ind++) |
---|
3122 | result += Monoms [ind]*bufSolution[i]; |
---|
3123 | } |
---|
3124 | if (alpha.level() != 1 && V_buf != alpha) |
---|
3125 | { |
---|
3126 | CFList u, v; |
---|
3127 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
3128 | } |
---|
3129 | result= N(result); |
---|
3130 | if (fdivides (result, F) && fdivides (result, G)) |
---|
3131 | { |
---|
3132 | delete[] pEvalPoints; |
---|
3133 | delete[] pMat; |
---|
3134 | delete[] pL; |
---|
3135 | delete[] pM; |
---|
3136 | if (bufpEvalPoints != NULL) |
---|
3137 | delete [] bufpEvalPoints; |
---|
3138 | return result; |
---|
3139 | } |
---|
3140 | else |
---|
3141 | { |
---|
3142 | delete[] pEvalPoints; |
---|
3143 | delete[] pMat; |
---|
3144 | delete[] pL; |
---|
3145 | delete[] coeffMonoms; |
---|
3146 | delete[] pM; |
---|
3147 | if (bufpEvalPoints != NULL) |
---|
3148 | delete [] bufpEvalPoints; |
---|
3149 | fail= true; |
---|
3150 | return 0; |
---|
3151 | } |
---|
3152 | } // end of deKleine, Monagan & Wittkopf |
---|
3153 | |
---|
3154 | result += Monoms[0]; |
---|
3155 | int ind2= 0, ind3= 2; |
---|
3156 | ind= 0; |
---|
3157 | for (int l= 0; l < minimalColumnsIndex; l++) |
---|
3158 | ind += coeffMonoms[l].size(); |
---|
3159 | for (int l= solution.size() - pMat[0].columns() + 1; l < solution.size(); |
---|
3160 | l++, ind2++, ind3++) |
---|
3161 | { |
---|
3162 | result += solution[l]*Monoms [1 + ind2]; |
---|
3163 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
3164 | firstColumn[i] += solution[l]*pMat[0] (i + 1, ind3); |
---|
3165 | } |
---|
3166 | for (int l= 0; l < solution.size() + 1 - pMat[0].columns(); l++) |
---|
3167 | result += solution[l]*Monoms [ind + l]; |
---|
3168 | ind= coeffMonoms[0].size(); |
---|
3169 | for (int k= 1; k < skelSize; k++) |
---|
3170 | { |
---|
3171 | if (k == minimalColumnsIndex) |
---|
3172 | { |
---|
3173 | ind += coeffMonoms[k].size(); |
---|
3174 | continue; |
---|
3175 | } |
---|
3176 | if (k != minimalColumnsIndex) |
---|
3177 | { |
---|
3178 | for (int i= 0; i < biggestSize; i++) |
---|
3179 | pL[k] [i] *= firstColumn [i]; |
---|
3180 | } |
---|
3181 | |
---|
3182 | if (biggestSize != coeffMonoms[k].size() && k != minimalColumnsIndex) |
---|
3183 | { |
---|
3184 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
3185 | for (int i= 0; i < bufArray.size(); i++) |
---|
3186 | bufArray [i]= pL[k] [i]; |
---|
3187 | solution= solveGeneralVandermonde (pM[k], bufArray); |
---|
3188 | } |
---|
3189 | else |
---|
3190 | solution= solveGeneralVandermonde (pM[k], pL[k]); |
---|
3191 | |
---|
3192 | if (solution.size() == 0) |
---|
3193 | { |
---|
3194 | delete[] pEvalPoints; |
---|
3195 | delete[] pMat; |
---|
3196 | delete[] pL; |
---|
3197 | delete[] coeffMonoms; |
---|
3198 | delete[] pM; |
---|
3199 | fail= true; |
---|
3200 | return 0; |
---|
3201 | } |
---|
3202 | if (k != minimalColumnsIndex) |
---|
3203 | { |
---|
3204 | for (int l= 0; l < solution.size(); l++) |
---|
3205 | result += solution[l]*Monoms [ind + l]; |
---|
3206 | ind += solution.size(); |
---|
3207 | } |
---|
3208 | } |
---|
3209 | |
---|
3210 | delete[] pEvalPoints; |
---|
3211 | delete[] pMat; |
---|
3212 | delete[] pL; |
---|
3213 | delete[] pM; |
---|
3214 | |
---|
3215 | if (alpha.level() != 1 && V_buf != alpha) |
---|
3216 | { |
---|
3217 | CFList u, v; |
---|
3218 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
3219 | } |
---|
3220 | result= N(result); |
---|
3221 | |
---|
3222 | if (fdivides (result, F) && fdivides (result, G)) |
---|
3223 | return result; |
---|
3224 | else |
---|
3225 | { |
---|
3226 | delete[] coeffMonoms; |
---|
3227 | fail= true; |
---|
3228 | return 0; |
---|
3229 | } |
---|
3230 | } |
---|
3231 | |
---|
3232 | CanonicalForm sparseGCDFq (const CanonicalForm& F, const CanonicalForm& G, |
---|
3233 | const Variable & alpha, CFList& l, bool& topLevel) |
---|
3234 | { |
---|
3235 | CanonicalForm A= F; |
---|
3236 | CanonicalForm B= G; |
---|
3237 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
3238 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
3239 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
3240 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
3241 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
3242 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
3243 | if (F == G) return F/Lc(F); |
---|
3244 | |
---|
3245 | CFMap M,N; |
---|
3246 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
3247 | |
---|
3248 | if (best_level == 0) return B.genOne(); |
---|
3249 | |
---|
3250 | A= M(A); |
---|
3251 | B= M(B); |
---|
3252 | |
---|
3253 | Variable x= Variable (1); |
---|
3254 | |
---|
3255 | //univariate case |
---|
3256 | if (A.isUnivariate() && B.isUnivariate()) |
---|
3257 | return N (gcd (A, B)); |
---|
3258 | |
---|
3259 | CanonicalForm cA, cB; // content of A and B |
---|
3260 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
3261 | CanonicalForm gcdcAcB; |
---|
3262 | |
---|
3263 | cA = uni_content (A); |
---|
3264 | cB = uni_content (B); |
---|
3265 | gcdcAcB= gcd (cA, cB); |
---|
3266 | ppA= A/cA; |
---|
3267 | ppB= B/cB; |
---|
3268 | |
---|
3269 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
3270 | CanonicalForm gcdlcAlcB; |
---|
3271 | lcA= uni_lcoeff (ppA); |
---|
3272 | lcB= uni_lcoeff (ppB); |
---|
3273 | |
---|
3274 | if (fdivides (lcA, lcB)) |
---|
3275 | { |
---|
3276 | if (fdivides (A, B)) |
---|
3277 | return F/Lc(F); |
---|
3278 | } |
---|
3279 | if (fdivides (lcB, lcA)) |
---|
3280 | { |
---|
3281 | if (fdivides (B, A)) |
---|
3282 | return G/Lc(G); |
---|
3283 | } |
---|
3284 | |
---|
3285 | gcdlcAlcB= gcd (lcA, lcB); |
---|
3286 | |
---|
3287 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
3288 | int d0; |
---|
3289 | |
---|
3290 | if (d == 0) |
---|
3291 | return N(gcdcAcB); |
---|
3292 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
3293 | |
---|
3294 | if (d0 < d) |
---|
3295 | d= d0; |
---|
3296 | |
---|
3297 | if (d == 0) |
---|
3298 | return N(gcdcAcB); |
---|
3299 | |
---|
3300 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
3301 | CanonicalForm newtonPoly= 1; |
---|
3302 | m= gcdlcAlcB; |
---|
3303 | G_m= 0; |
---|
3304 | H= 0; |
---|
3305 | bool fail= false; |
---|
3306 | topLevel= false; |
---|
3307 | bool inextension= false; |
---|
3308 | Variable V_buf= alpha; |
---|
3309 | CanonicalForm prim_elem, im_prim_elem; |
---|
3310 | CFList source, dest; |
---|
3311 | do // first do |
---|
3312 | { |
---|
3313 | random_element= randomElement (m, V_buf, l, fail); |
---|
3314 | if (random_element == 0 && !fail) |
---|
3315 | { |
---|
3316 | if (!find (l, random_element)) |
---|
3317 | l.append (random_element); |
---|
3318 | continue; |
---|
3319 | } |
---|
3320 | if (fail) |
---|
3321 | { |
---|
3322 | source= CFList(); |
---|
3323 | dest= CFList(); |
---|
3324 | |
---|
3325 | Variable V_buf3= V_buf; |
---|
3326 | V_buf= chooseExtension (V_buf); |
---|
3327 | bool prim_fail= false; |
---|
3328 | Variable V_buf2; |
---|
3329 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3330 | |
---|
3331 | if (V_buf3 != alpha) |
---|
3332 | { |
---|
3333 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3334 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3335 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3336 | source, dest); |
---|
3337 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3338 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3339 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
3340 | dest); |
---|
3341 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3342 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3343 | source, dest); |
---|
3344 | } |
---|
3345 | |
---|
3346 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3347 | if (prim_fail) |
---|
3348 | ; //ERROR |
---|
3349 | else |
---|
3350 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3351 | |
---|
3352 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3353 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
3354 | inextension= true; |
---|
3355 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3356 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3357 | im_prim_elem, source, dest); |
---|
3358 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3359 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3360 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3361 | source, dest); |
---|
3362 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3363 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3364 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3365 | source, dest); |
---|
3366 | |
---|
3367 | fail= false; |
---|
3368 | random_element= randomElement (m, V_buf, l, fail ); |
---|
3369 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3370 | CFList list; |
---|
3371 | TIMING_START (gcd_recursion); |
---|
3372 | G_random_element= |
---|
3373 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
3374 | list, topLevel); |
---|
3375 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3376 | "time for recursive call: "); |
---|
3377 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3378 | } |
---|
3379 | else |
---|
3380 | { |
---|
3381 | CFList list; |
---|
3382 | TIMING_START (gcd_recursion); |
---|
3383 | G_random_element= |
---|
3384 | sparseGCDFq (ppA(random_element, x), ppB(random_element, x), V_buf, |
---|
3385 | list, topLevel); |
---|
3386 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3387 | "time for recursive call: "); |
---|
3388 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3389 | } |
---|
3390 | |
---|
3391 | if (!G_random_element.inCoeffDomain()) |
---|
3392 | d0= totaldegree (G_random_element, Variable(2), |
---|
3393 | Variable (G_random_element.level())); |
---|
3394 | else |
---|
3395 | d0= 0; |
---|
3396 | |
---|
3397 | if (d0 == 0) |
---|
3398 | return N(gcdcAcB); |
---|
3399 | if (d0 > d) |
---|
3400 | { |
---|
3401 | if (!find (l, random_element)) |
---|
3402 | l.append (random_element); |
---|
3403 | continue; |
---|
3404 | } |
---|
3405 | |
---|
3406 | G_random_element= |
---|
3407 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3408 | * G_random_element; |
---|
3409 | |
---|
3410 | skeleton= G_random_element; |
---|
3411 | if (!G_random_element.inCoeffDomain()) |
---|
3412 | d0= totaldegree (G_random_element, Variable(2), |
---|
3413 | Variable (G_random_element.level())); |
---|
3414 | else |
---|
3415 | d0= 0; |
---|
3416 | |
---|
3417 | if (d0 < d) |
---|
3418 | { |
---|
3419 | m= gcdlcAlcB; |
---|
3420 | newtonPoly= 1; |
---|
3421 | G_m= 0; |
---|
3422 | d= d0; |
---|
3423 | } |
---|
3424 | |
---|
3425 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3426 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3427 | { |
---|
3428 | cH= uni_content (H); |
---|
3429 | ppH= H/cH; |
---|
3430 | if (inextension) |
---|
3431 | { |
---|
3432 | CFList u, v; |
---|
3433 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
3434 | //mapping down |
---|
3435 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3436 | { |
---|
3437 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
3438 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
3439 | ppH /= Lc(ppH); |
---|
3440 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
3441 | return N(gcdcAcB*ppH); |
---|
3442 | } |
---|
3443 | } |
---|
3444 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3445 | return N(gcdcAcB*ppH); |
---|
3446 | } |
---|
3447 | G_m= H; |
---|
3448 | newtonPoly= newtonPoly*(x - random_element); |
---|
3449 | m= m*(x - random_element); |
---|
3450 | if (!find (l, random_element)) |
---|
3451 | l.append (random_element); |
---|
3452 | |
---|
3453 | if (getCharacteristic () > 3 && size (skeleton) < 100) |
---|
3454 | { |
---|
3455 | CFArray Monoms; |
---|
3456 | CFArray *coeffMonoms= NULL; |
---|
3457 | do //second do |
---|
3458 | { |
---|
3459 | random_element= randomElement (m, V_buf, l, fail); |
---|
3460 | if (random_element == 0 && !fail) |
---|
3461 | { |
---|
3462 | if (!find (l, random_element)) |
---|
3463 | l.append (random_element); |
---|
3464 | continue; |
---|
3465 | } |
---|
3466 | if (fail) |
---|
3467 | { |
---|
3468 | source= CFList(); |
---|
3469 | dest= CFList(); |
---|
3470 | |
---|
3471 | Variable V_buf3= V_buf; |
---|
3472 | V_buf= chooseExtension (V_buf); |
---|
3473 | bool prim_fail= false; |
---|
3474 | Variable V_buf2; |
---|
3475 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3476 | |
---|
3477 | if (V_buf3 != alpha) |
---|
3478 | { |
---|
3479 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3480 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3481 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3482 | source, dest); |
---|
3483 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3484 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3485 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
3486 | source, dest); |
---|
3487 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3488 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3489 | source, dest); |
---|
3490 | } |
---|
3491 | |
---|
3492 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3493 | if (prim_fail) |
---|
3494 | ; //ERROR |
---|
3495 | else |
---|
3496 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3497 | |
---|
3498 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3499 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
3500 | inextension= true; |
---|
3501 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3502 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3503 | im_prim_elem, source, dest); |
---|
3504 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3505 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3506 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3507 | source, dest); |
---|
3508 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3509 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3510 | |
---|
3511 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3512 | source, dest); |
---|
3513 | |
---|
3514 | fail= false; |
---|
3515 | random_element= randomElement (m, V_buf, l, fail); |
---|
3516 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3517 | CFList list; |
---|
3518 | TIMING_START (gcd_recursion); |
---|
3519 | |
---|
3520 | //sparseInterpolation |
---|
3521 | bool sparseFail= false; |
---|
3522 | if (LC (skeleton).inCoeffDomain()) |
---|
3523 | G_random_element= |
---|
3524 | monicSparseInterpol (ppA (random_element, x), ppB(random_element,x), |
---|
3525 | skeleton,V_buf, sparseFail, coeffMonoms,Monoms); |
---|
3526 | else |
---|
3527 | G_random_element= |
---|
3528 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
3529 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3530 | Monoms); |
---|
3531 | if (sparseFail) |
---|
3532 | break; |
---|
3533 | |
---|
3534 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3535 | "time for recursive call: "); |
---|
3536 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3537 | } |
---|
3538 | else |
---|
3539 | { |
---|
3540 | CFList list; |
---|
3541 | TIMING_START (gcd_recursion); |
---|
3542 | bool sparseFail= false; |
---|
3543 | if (LC (skeleton).inCoeffDomain()) |
---|
3544 | G_random_element= |
---|
3545 | monicSparseInterpol (ppA (random_element, x),ppB(random_element, x), |
---|
3546 | skeleton,V_buf, sparseFail,coeffMonoms, Monoms); |
---|
3547 | else |
---|
3548 | G_random_element= |
---|
3549 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
3550 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3551 | Monoms); |
---|
3552 | if (sparseFail) |
---|
3553 | break; |
---|
3554 | |
---|
3555 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3556 | "time for recursive call: "); |
---|
3557 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3558 | } |
---|
3559 | |
---|
3560 | if (!G_random_element.inCoeffDomain()) |
---|
3561 | d0= totaldegree (G_random_element, Variable(2), |
---|
3562 | Variable (G_random_element.level())); |
---|
3563 | else |
---|
3564 | d0= 0; |
---|
3565 | |
---|
3566 | if (d0 == 0) |
---|
3567 | return N(gcdcAcB); |
---|
3568 | if (d0 > d) |
---|
3569 | { |
---|
3570 | if (!find (l, random_element)) |
---|
3571 | l.append (random_element); |
---|
3572 | continue; |
---|
3573 | } |
---|
3574 | |
---|
3575 | G_random_element= |
---|
3576 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3577 | * G_random_element; |
---|
3578 | |
---|
3579 | if (!G_random_element.inCoeffDomain()) |
---|
3580 | d0= totaldegree (G_random_element, Variable(2), |
---|
3581 | Variable (G_random_element.level())); |
---|
3582 | else |
---|
3583 | d0= 0; |
---|
3584 | |
---|
3585 | if (d0 < d) |
---|
3586 | { |
---|
3587 | m= gcdlcAlcB; |
---|
3588 | newtonPoly= 1; |
---|
3589 | G_m= 0; |
---|
3590 | d= d0; |
---|
3591 | } |
---|
3592 | |
---|
3593 | TIMING_START (newton_interpolation); |
---|
3594 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3595 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
3596 | "time for newton interpolation: "); |
---|
3597 | |
---|
3598 | //termination test |
---|
3599 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3600 | { |
---|
3601 | cH= uni_content (H); |
---|
3602 | ppH= H/cH; |
---|
3603 | if (inextension) |
---|
3604 | { |
---|
3605 | CFList u, v; |
---|
3606 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
3607 | //mapping down |
---|
3608 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3609 | { |
---|
3610 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
3611 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
3612 | ppH /= Lc(ppH); |
---|
3613 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
3614 | return N(gcdcAcB*ppH); |
---|
3615 | } |
---|
3616 | } |
---|
3617 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3618 | { |
---|
3619 | return N(gcdcAcB*ppH); |
---|
3620 | } |
---|
3621 | } |
---|
3622 | |
---|
3623 | G_m= H; |
---|
3624 | newtonPoly= newtonPoly*(x - random_element); |
---|
3625 | m= m*(x - random_element); |
---|
3626 | if (!find (l, random_element)) |
---|
3627 | l.append (random_element); |
---|
3628 | |
---|
3629 | } while (1); |
---|
3630 | } |
---|
3631 | } while (1); |
---|
3632 | } |
---|
3633 | |
---|
3634 | CanonicalForm sparseGCDFp (const CanonicalForm& F, const CanonicalForm& G, |
---|
3635 | bool& topLevel, CFList& l) |
---|
3636 | { |
---|
3637 | CanonicalForm A= F; |
---|
3638 | CanonicalForm B= G; |
---|
3639 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
3640 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
3641 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
3642 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
3643 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
3644 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
3645 | if (F == G) return F/Lc(F); |
---|
3646 | |
---|
3647 | CFMap M,N; |
---|
3648 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
3649 | |
---|
3650 | if (best_level == 0) return B.genOne(); |
---|
3651 | |
---|
3652 | A= M(A); |
---|
3653 | B= M(B); |
---|
3654 | |
---|
3655 | Variable x= Variable (1); |
---|
3656 | |
---|
3657 | //univariate case |
---|
3658 | if (A.isUnivariate() && B.isUnivariate()) |
---|
3659 | return N (gcd (A, B)); |
---|
3660 | |
---|
3661 | CanonicalForm cA, cB; // content of A and B |
---|
3662 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
3663 | CanonicalForm gcdcAcB; |
---|
3664 | |
---|
3665 | cA = uni_content (A); |
---|
3666 | cB = uni_content (B); |
---|
3667 | gcdcAcB= gcd (cA, cB); |
---|
3668 | ppA= A/cA; |
---|
3669 | ppB= B/cB; |
---|
3670 | |
---|
3671 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
3672 | CanonicalForm gcdlcAlcB; |
---|
3673 | lcA= uni_lcoeff (ppA); |
---|
3674 | lcB= uni_lcoeff (ppB); |
---|
3675 | |
---|
3676 | if (fdivides (lcA, lcB)) |
---|
3677 | { |
---|
3678 | if (fdivides (A, B)) |
---|
3679 | return F/Lc(F); |
---|
3680 | } |
---|
3681 | if (fdivides (lcB, lcA)) |
---|
3682 | { |
---|
3683 | if (fdivides (B, A)) |
---|
3684 | return G/Lc(G); |
---|
3685 | } |
---|
3686 | |
---|
3687 | gcdlcAlcB= gcd (lcA, lcB); |
---|
3688 | |
---|
3689 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
3690 | int d0; |
---|
3691 | |
---|
3692 | if (d == 0) |
---|
3693 | return N(gcdcAcB); |
---|
3694 | |
---|
3695 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
3696 | |
---|
3697 | if (d0 < d) |
---|
3698 | d= d0; |
---|
3699 | |
---|
3700 | if (d == 0) |
---|
3701 | return N(gcdcAcB); |
---|
3702 | |
---|
3703 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
3704 | CanonicalForm newtonPoly= 1; |
---|
3705 | m= gcdlcAlcB; |
---|
3706 | G_m= 0; |
---|
3707 | H= 0; |
---|
3708 | bool fail= false; |
---|
3709 | topLevel= false; |
---|
3710 | bool inextension= false; |
---|
3711 | Variable V_buf, alpha; |
---|
3712 | CanonicalForm prim_elem, im_prim_elem; |
---|
3713 | CFList source, dest; |
---|
3714 | do //first do |
---|
3715 | { |
---|
3716 | if (inextension) |
---|
3717 | random_element= randomElement (m, V_buf, l, fail); |
---|
3718 | else |
---|
3719 | random_element= FpRandomElement (m, l, fail); |
---|
3720 | if (random_element == 0 && !fail) |
---|
3721 | { |
---|
3722 | if (!find (l, random_element)) |
---|
3723 | l.append (random_element); |
---|
3724 | continue; |
---|
3725 | } |
---|
3726 | |
---|
3727 | if (!fail && !inextension) |
---|
3728 | { |
---|
3729 | CFList list; |
---|
3730 | TIMING_START (gcd_recursion); |
---|
3731 | G_random_element= |
---|
3732 | sparseGCDFp (ppA (random_element,x), ppB (random_element,x), topLevel, |
---|
3733 | list); |
---|
3734 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3735 | "time for recursive call: "); |
---|
3736 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3737 | } |
---|
3738 | else if (!fail && inextension) |
---|
3739 | { |
---|
3740 | CFList list; |
---|
3741 | TIMING_START (gcd_recursion); |
---|
3742 | G_random_element= |
---|
3743 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
3744 | list, topLevel); |
---|
3745 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3746 | "time for recursive call: "); |
---|
3747 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3748 | } |
---|
3749 | else if (fail && !inextension) |
---|
3750 | { |
---|
3751 | source= CFList(); |
---|
3752 | dest= CFList(); |
---|
3753 | CFList list; |
---|
3754 | CanonicalForm mipo; |
---|
3755 | int deg= 2; |
---|
3756 | do |
---|
3757 | { |
---|
3758 | mipo= randomIrredpoly (deg, x); |
---|
3759 | alpha= rootOf (mipo); |
---|
3760 | inextension= true; |
---|
3761 | fail= false; |
---|
3762 | random_element= randomElement (m, alpha, l, fail); |
---|
3763 | deg++; |
---|
3764 | } while (fail); |
---|
3765 | V_buf= alpha; |
---|
3766 | list= CFList(); |
---|
3767 | TIMING_START (gcd_recursion); |
---|
3768 | G_random_element= |
---|
3769 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
3770 | list, topLevel); |
---|
3771 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3772 | "time for recursive call: "); |
---|
3773 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3774 | } |
---|
3775 | else if (fail && inextension) |
---|
3776 | { |
---|
3777 | source= CFList(); |
---|
3778 | dest= CFList(); |
---|
3779 | |
---|
3780 | Variable V_buf3= V_buf; |
---|
3781 | V_buf= chooseExtension (V_buf); |
---|
3782 | bool prim_fail= false; |
---|
3783 | Variable V_buf2; |
---|
3784 | CanonicalForm prim_elem, im_prim_elem; |
---|
3785 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3786 | |
---|
3787 | if (V_buf3 != alpha) |
---|
3788 | { |
---|
3789 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3790 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3791 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, source, |
---|
3792 | dest); |
---|
3793 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3794 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3795 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
3796 | dest); |
---|
3797 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3798 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3799 | source, dest); |
---|
3800 | } |
---|
3801 | |
---|
3802 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3803 | if (prim_fail) |
---|
3804 | ; //ERROR |
---|
3805 | else |
---|
3806 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3807 | |
---|
3808 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3809 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
3810 | |
---|
3811 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3812 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3813 | im_prim_elem, source, dest); |
---|
3814 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3815 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3816 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3817 | source, dest); |
---|
3818 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3819 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3820 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3821 | source, dest); |
---|
3822 | fail= false; |
---|
3823 | random_element= randomElement (m, V_buf, l, fail ); |
---|
3824 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3825 | CFList list; |
---|
3826 | TIMING_START (gcd_recursion); |
---|
3827 | G_random_element= |
---|
3828 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
3829 | list, topLevel); |
---|
3830 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3831 | "time for recursive call: "); |
---|
3832 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3833 | } |
---|
3834 | |
---|
3835 | if (!G_random_element.inCoeffDomain()) |
---|
3836 | d0= totaldegree (G_random_element, Variable(2), |
---|
3837 | Variable (G_random_element.level())); |
---|
3838 | else |
---|
3839 | d0= 0; |
---|
3840 | |
---|
3841 | if (d0 == 0) |
---|
3842 | return N(gcdcAcB); |
---|
3843 | if (d0 > d) |
---|
3844 | { |
---|
3845 | if (!find (l, random_element)) |
---|
3846 | l.append (random_element); |
---|
3847 | continue; |
---|
3848 | } |
---|
3849 | |
---|
3850 | G_random_element= |
---|
3851 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3852 | * G_random_element; |
---|
3853 | |
---|
3854 | skeleton= G_random_element; |
---|
3855 | |
---|
3856 | if (!G_random_element.inCoeffDomain()) |
---|
3857 | d0= totaldegree (G_random_element, Variable(2), |
---|
3858 | Variable (G_random_element.level())); |
---|
3859 | else |
---|
3860 | d0= 0; |
---|
3861 | |
---|
3862 | if (d0 < d) |
---|
3863 | { |
---|
3864 | m= gcdlcAlcB; |
---|
3865 | newtonPoly= 1; |
---|
3866 | G_m= 0; |
---|
3867 | d= d0; |
---|
3868 | } |
---|
3869 | |
---|
3870 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3871 | |
---|
3872 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3873 | { |
---|
3874 | cH= uni_content (H); |
---|
3875 | ppH= H/cH; |
---|
3876 | ppH /= Lc (ppH); |
---|
3877 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
3878 | |
---|
3879 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3880 | return N(gcdcAcB*ppH); |
---|
3881 | } |
---|
3882 | G_m= H; |
---|
3883 | newtonPoly= newtonPoly*(x - random_element); |
---|
3884 | m= m*(x - random_element); |
---|
3885 | if (!find (l, random_element)) |
---|
3886 | l.append (random_element); |
---|
3887 | |
---|
3888 | if ((getCharacteristic() > 3 && size (skeleton) < 100)) |
---|
3889 | { |
---|
3890 | CFArray Monoms; |
---|
3891 | CFArray* coeffMonoms= NULL; |
---|
3892 | |
---|
3893 | do //second do |
---|
3894 | { |
---|
3895 | if (inextension) |
---|
3896 | random_element= randomElement (m, alpha, l, fail); |
---|
3897 | else |
---|
3898 | random_element= FpRandomElement (m, l, fail); |
---|
3899 | if (random_element == 0 && !fail) |
---|
3900 | { |
---|
3901 | if (!find (l, random_element)) |
---|
3902 | l.append (random_element); |
---|
3903 | continue; |
---|
3904 | } |
---|
3905 | |
---|
3906 | bool sparseFail= false; |
---|
3907 | if (!fail && !inextension) |
---|
3908 | { |
---|
3909 | CFList list; |
---|
3910 | TIMING_START (gcd_recursion); |
---|
3911 | if (LC (skeleton).inCoeffDomain()) |
---|
3912 | G_random_element= |
---|
3913 | monicSparseInterpol(ppA(random_element, x), ppB (random_element, x), |
---|
3914 | skeleton, Variable(1), sparseFail, coeffMonoms, |
---|
3915 | Monoms); |
---|
3916 | else |
---|
3917 | G_random_element= |
---|
3918 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3919 | skeleton, Variable (1), sparseFail, |
---|
3920 | coeffMonoms, Monoms); |
---|
3921 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3922 | "time for recursive call: "); |
---|
3923 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3924 | } |
---|
3925 | else if (!fail && inextension) |
---|
3926 | { |
---|
3927 | CFList list; |
---|
3928 | TIMING_START (gcd_recursion); |
---|
3929 | if (LC (skeleton).inCoeffDomain()) |
---|
3930 | G_random_element= |
---|
3931 | monicSparseInterpol(ppA (random_element,x), ppB (random_element, x), |
---|
3932 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3933 | Monoms); |
---|
3934 | else |
---|
3935 | G_random_element= |
---|
3936 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3937 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3938 | Monoms); |
---|
3939 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3940 | "time for recursive call: "); |
---|
3941 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3942 | } |
---|
3943 | else if (fail && !inextension) |
---|
3944 | { |
---|
3945 | source= CFList(); |
---|
3946 | dest= CFList(); |
---|
3947 | CFList list; |
---|
3948 | CanonicalForm mipo; |
---|
3949 | int deg= 2; |
---|
3950 | do |
---|
3951 | { |
---|
3952 | mipo= randomIrredpoly (deg, x); |
---|
3953 | alpha= rootOf (mipo); |
---|
3954 | inextension= true; |
---|
3955 | fail= false; |
---|
3956 | random_element= randomElement (m, alpha, l, fail); |
---|
3957 | deg++; |
---|
3958 | } while (fail); |
---|
3959 | V_buf= alpha; |
---|
3960 | list= CFList(); |
---|
3961 | TIMING_START (gcd_recursion); |
---|
3962 | if (LC (skeleton).inCoeffDomain()) |
---|
3963 | G_random_element= |
---|
3964 | monicSparseInterpol (ppA (random_element,x), ppB (random_element,x), |
---|
3965 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3966 | Monoms); |
---|
3967 | else |
---|
3968 | G_random_element= |
---|
3969 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3970 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3971 | Monoms); |
---|
3972 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3973 | "time for recursive call: "); |
---|
3974 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3975 | } |
---|
3976 | else if (fail && inextension) |
---|
3977 | { |
---|
3978 | source= CFList(); |
---|
3979 | dest= CFList(); |
---|
3980 | |
---|
3981 | Variable V_buf3= V_buf; |
---|
3982 | V_buf= chooseExtension (V_buf); |
---|
3983 | bool prim_fail= false; |
---|
3984 | Variable V_buf2; |
---|
3985 | CanonicalForm prim_elem, im_prim_elem; |
---|
3986 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3987 | |
---|
3988 | if (V_buf3 != alpha) |
---|
3989 | { |
---|
3990 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3991 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3992 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3993 | source, dest); |
---|
3994 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3995 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3996 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
3997 | source, dest); |
---|
3998 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3999 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
4000 | source, dest); |
---|
4001 | } |
---|
4002 | |
---|
4003 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
4004 | if (prim_fail) |
---|
4005 | ; //ERROR |
---|
4006 | else |
---|
4007 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
4008 | |
---|
4009 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
4010 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
4011 | |
---|
4012 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
4013 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
4014 | im_prim_elem, source, dest); |
---|
4015 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
4016 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
4017 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
4018 | source, dest); |
---|
4019 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
4020 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
4021 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
4022 | source, dest); |
---|
4023 | fail= false; |
---|
4024 | random_element= randomElement (m, V_buf, l, fail ); |
---|
4025 | DEBOUTLN (cerr, "fail= " << fail); |
---|
4026 | CFList list; |
---|
4027 | TIMING_START (gcd_recursion); |
---|
4028 | if (LC (skeleton).inCoeffDomain()) |
---|
4029 | G_random_element= |
---|
4030 | monicSparseInterpol (ppA (random_element, x), ppB (random_element, x), |
---|
4031 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
4032 | Monoms); |
---|
4033 | else |
---|
4034 | G_random_element= |
---|
4035 | nonMonicSparseInterpol (ppA(random_element,x), ppB(random_element,x), |
---|
4036 | skeleton, V_buf, sparseFail, |
---|
4037 | coeffMonoms, Monoms); |
---|
4038 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
4039 | "time for recursive call: "); |
---|
4040 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
4041 | } |
---|
4042 | |
---|
4043 | if (sparseFail) |
---|
4044 | break; |
---|
4045 | |
---|
4046 | if (!G_random_element.inCoeffDomain()) |
---|
4047 | d0= totaldegree (G_random_element, Variable(2), |
---|
4048 | Variable (G_random_element.level())); |
---|
4049 | else |
---|
4050 | d0= 0; |
---|
4051 | |
---|
4052 | if (d0 == 0) |
---|
4053 | return N(gcdcAcB); |
---|
4054 | if (d0 > d) |
---|
4055 | { |
---|
4056 | if (!find (l, random_element)) |
---|
4057 | l.append (random_element); |
---|
4058 | continue; |
---|
4059 | } |
---|
4060 | |
---|
4061 | G_random_element= |
---|
4062 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
4063 | * G_random_element; |
---|
4064 | |
---|
4065 | if (!G_random_element.inCoeffDomain()) |
---|
4066 | d0= totaldegree (G_random_element, Variable(2), |
---|
4067 | Variable (G_random_element.level())); |
---|
4068 | else |
---|
4069 | d0= 0; |
---|
4070 | |
---|
4071 | if (d0 < d) |
---|
4072 | { |
---|
4073 | m= gcdlcAlcB; |
---|
4074 | newtonPoly= 1; |
---|
4075 | G_m= 0; |
---|
4076 | d= d0; |
---|
4077 | } |
---|
4078 | |
---|
4079 | TIMING_START (newton_interpolation); |
---|
4080 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
4081 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
4082 | "time for newton interpolation: "); |
---|
4083 | |
---|
4084 | //termination test |
---|
4085 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
4086 | { |
---|
4087 | cH= uni_content (H); |
---|
4088 | ppH= H/cH; |
---|
4089 | ppH /= Lc (ppH); |
---|
4090 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
4091 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
4092 | return N(gcdcAcB*ppH); |
---|
4093 | } |
---|
4094 | |
---|
4095 | G_m= H; |
---|
4096 | newtonPoly= newtonPoly*(x - random_element); |
---|
4097 | m= m*(x - random_element); |
---|
4098 | if (!find (l, random_element)) |
---|
4099 | l.append (random_element); |
---|
4100 | |
---|
4101 | } while (1); //end of second do |
---|
4102 | } |
---|
4103 | } while (1); //end of first do |
---|
4104 | } |
---|
4105 | |
---|
4106 | static inline |
---|
4107 | int compress4EZGCD (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
---|
4108 | CFMap & N, int& both_non_zero) |
---|
4109 | { |
---|
4110 | int n= tmax (F.level(), G.level()); |
---|
4111 | int * degsf= new int [n + 1]; |
---|
4112 | int * degsg= new int [n + 1]; |
---|
4113 | |
---|
4114 | for (int i = 0; i <= n; i++) |
---|
4115 | degsf[i]= degsg[i]= 0; |
---|
4116 | |
---|
4117 | degsf= degrees (F, degsf); |
---|
4118 | degsg= degrees (G, degsg); |
---|
4119 | |
---|
4120 | both_non_zero= 0; |
---|
4121 | int f_zero= 0; |
---|
4122 | int g_zero= 0; |
---|
4123 | |
---|
4124 | for (int i= 1; i <= n; i++) |
---|
4125 | { |
---|
4126 | if (degsf[i] != 0 && degsg[i] != 0) |
---|
4127 | { |
---|
4128 | both_non_zero++; |
---|
4129 | continue; |
---|
4130 | } |
---|
4131 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
4132 | { |
---|
4133 | f_zero++; |
---|
4134 | continue; |
---|
4135 | } |
---|
4136 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
---|
4137 | { |
---|
4138 | g_zero++; |
---|
4139 | continue; |
---|
4140 | } |
---|
4141 | } |
---|
4142 | |
---|
4143 | if (both_non_zero == 0) |
---|
4144 | { |
---|
4145 | delete [] degsf; |
---|
4146 | delete [] degsg; |
---|
4147 | return 0; |
---|
4148 | } |
---|
4149 | |
---|
4150 | // map Variables which do not occur in both polynomials to higher levels |
---|
4151 | int k= 1; |
---|
4152 | int l= 1; |
---|
4153 | for (int i= 1; i <= n; i++) |
---|
4154 | { |
---|
4155 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
---|
4156 | { |
---|
4157 | if (k + both_non_zero != i) |
---|
4158 | { |
---|
4159 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
---|
4160 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
---|
4161 | } |
---|
4162 | k++; |
---|
4163 | } |
---|
4164 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
4165 | { |
---|
4166 | if (l + g_zero + both_non_zero != i) |
---|
4167 | { |
---|
4168 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
---|
4169 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
---|
4170 | } |
---|
4171 | l++; |
---|
4172 | } |
---|
4173 | } |
---|
4174 | |
---|
4175 | // sort Variables x_{i} in decreasing order of |
---|
4176 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
---|
4177 | int m= tmin (F.level(), G.level()); |
---|
4178 | int max_min_deg; |
---|
4179 | k= both_non_zero; |
---|
4180 | l= 0; |
---|
4181 | int i= 1; |
---|
4182 | while (k > 0) |
---|
4183 | { |
---|
4184 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
4185 | while (max_min_deg == 0) |
---|
4186 | { |
---|
4187 | i++; |
---|
4188 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
4189 | } |
---|
4190 | for (int j= i + 1; j <= m; j++) |
---|
4191 | { |
---|
4192 | if ((tmin (degsf[j],degsg[j]) < max_min_deg) && |
---|
4193 | (tmin (degsf[j], degsg[j]) != 0)) |
---|
4194 | { |
---|
4195 | max_min_deg= tmin (degsf[j], degsg[j]); |
---|
4196 | l= j; |
---|
4197 | } |
---|
4198 | } |
---|
4199 | |
---|
4200 | if (l != 0) |
---|
4201 | { |
---|
4202 | if (l != k) |
---|
4203 | { |
---|
4204 | M.newpair (Variable (l), Variable(k)); |
---|
4205 | N.newpair (Variable (k), Variable(l)); |
---|
4206 | degsf[l]= 0; |
---|
4207 | degsg[l]= 0; |
---|
4208 | l= 0; |
---|
4209 | } |
---|
4210 | else |
---|
4211 | { |
---|
4212 | degsf[l]= 0; |
---|
4213 | degsg[l]= 0; |
---|
4214 | l= 0; |
---|
4215 | } |
---|
4216 | } |
---|
4217 | else if (l == 0) |
---|
4218 | { |
---|
4219 | if (i != k) |
---|
4220 | { |
---|
4221 | M.newpair (Variable (i), Variable (k)); |
---|
4222 | N.newpair (Variable (k), Variable (i)); |
---|
4223 | degsf[i]= 0; |
---|
4224 | degsg[i]= 0; |
---|
4225 | } |
---|
4226 | else |
---|
4227 | { |
---|
4228 | degsf[i]= 0; |
---|
4229 | degsg[i]= 0; |
---|
4230 | } |
---|
4231 | i++; |
---|
4232 | } |
---|
4233 | k--; |
---|
4234 | } |
---|
4235 | |
---|
4236 | delete [] degsf; |
---|
4237 | delete [] degsg; |
---|
4238 | |
---|
4239 | return both_non_zero; |
---|
4240 | } |
---|
4241 | |
---|
4242 | static inline |
---|
4243 | CanonicalForm myShift2Zero (const CanonicalForm& F, CFList& Feval, |
---|
4244 | const CFList& evaluation) |
---|
4245 | { |
---|
4246 | CanonicalForm A= F; |
---|
4247 | int k= 2; |
---|
4248 | for (CFListIterator i= evaluation; i.hasItem(); i++, k++) |
---|
4249 | A= A (Variable (k) + i.getItem(), k); |
---|
4250 | |
---|
4251 | CanonicalForm buf= A; |
---|
4252 | Feval= CFList(); |
---|
4253 | Feval.append (buf); |
---|
4254 | for (k= evaluation.length() + 1; k > 2; k--) |
---|
4255 | { |
---|
4256 | buf= mod (buf, Variable (k)); |
---|
4257 | Feval.insert (buf); |
---|
4258 | } |
---|
4259 | return A; |
---|
4260 | } |
---|
4261 | |
---|
4262 | static inline |
---|
4263 | CanonicalForm myReverseShift (const CanonicalForm& F, const CFList& evaluation) |
---|
4264 | { |
---|
4265 | int l= evaluation.length() + 1; |
---|
4266 | CanonicalForm result= F; |
---|
4267 | CFListIterator j= evaluation; |
---|
4268 | for (int i= 2; i < l + 1; i++, j++) |
---|
4269 | { |
---|
4270 | if (F.level() < i) |
---|
4271 | continue; |
---|
4272 | result= result (Variable (i) - j.getItem(), i); |
---|
4273 | } |
---|
4274 | return result; |
---|
4275 | } |
---|
4276 | |
---|
4277 | static inline |
---|
4278 | Evaluation optimize4Lift (const CanonicalForm& F, CFMap & M, |
---|
4279 | CFMap & N, const Evaluation& A) |
---|
4280 | { |
---|
4281 | int n= F.level(); |
---|
4282 | int * degsf= new int [n + 1]; |
---|
4283 | |
---|
4284 | for (int i = 0; i <= n; i++) |
---|
4285 | degsf[i]= 0; |
---|
4286 | |
---|
4287 | degsf= degrees (F, degsf); |
---|
4288 | |
---|
4289 | Evaluation result= Evaluation (A.min(), A.max()); |
---|
4290 | ASSERT (A.min() == 2, "expected A.min() == 2"); |
---|
4291 | int max_deg; |
---|
4292 | int k= n; |
---|
4293 | int l= 1; |
---|
4294 | int i= 2; |
---|
4295 | int pos= 2; |
---|
4296 | while (k > 1) |
---|
4297 | { |
---|
4298 | max_deg= degsf [i]; |
---|
4299 | while (max_deg == 0) |
---|
4300 | { |
---|
4301 | i++; |
---|
4302 | max_deg= degsf [i]; |
---|
4303 | } |
---|
4304 | l= i; |
---|
4305 | for (int j= i + 1; j <= n; j++) |
---|
4306 | { |
---|
4307 | if (degsf[j] > max_deg) |
---|
4308 | { |
---|
4309 | max_deg= degsf[j]; |
---|
4310 | l= j; |
---|
4311 | } |
---|
4312 | } |
---|
4313 | |
---|
4314 | if (l <= n) |
---|
4315 | { |
---|
4316 | if (l != pos) |
---|
4317 | { |
---|
4318 | result.setValue (pos, A [l]); |
---|
4319 | M.newpair (Variable (l), Variable (pos)); |
---|
4320 | N.newpair (Variable (pos), Variable (l)); |
---|
4321 | degsf[l]= 0; |
---|
4322 | l= 2; |
---|
4323 | if (k == 2 && n == 3) |
---|
4324 | { |
---|
4325 | result.setValue (l, A [pos]); |
---|
4326 | M.newpair (Variable (pos), Variable (l)); |
---|
4327 | N.newpair (Variable (l), Variable (pos)); |
---|
4328 | degsf[pos]= 0; |
---|
4329 | } |
---|
4330 | } |
---|
4331 | else |
---|
4332 | { |
---|
4333 | result.setValue (l, A [l]); |
---|
4334 | degsf [l]= 0; |
---|
4335 | } |
---|
4336 | } |
---|
4337 | pos++; |
---|
4338 | k--; |
---|
4339 | l= 2; |
---|
4340 | } |
---|
4341 | |
---|
4342 | delete [] degsf; |
---|
4343 | |
---|
4344 | return result; |
---|
4345 | } |
---|
4346 | |
---|
4347 | static inline |
---|
4348 | int Hensel_P (const CanonicalForm & UU, CFArray & G, const Evaluation & AA, |
---|
4349 | const CFArray& LeadCoeffs ) |
---|
4350 | { |
---|
4351 | CFList factors; |
---|
4352 | factors.append (G[1]); |
---|
4353 | factors.append (G[2]); |
---|
4354 | |
---|
4355 | CFMap NN, MM; |
---|
4356 | Evaluation A= optimize4Lift (UU, MM, NN, AA); |
---|
4357 | |
---|
4358 | CanonicalForm U= MM (UU); |
---|
4359 | CFArray LCs= CFArray (1,2); |
---|
4360 | LCs [1]= MM (LeadCoeffs [1]); |
---|
4361 | LCs [2]= MM (LeadCoeffs [2]); |
---|
4362 | |
---|
4363 | CFList evaluation; |
---|
4364 | for (int i= A.min(); i <= A.max(); i++) |
---|
4365 | evaluation.append (A [i]); |
---|
4366 | CFList UEval; |
---|
4367 | CanonicalForm shiftedU= myShift2Zero (U, UEval, evaluation); |
---|
4368 | |
---|
4369 | if (size (shiftedU)/getNumVars (U) > 500) |
---|
4370 | return -1; |
---|
4371 | |
---|
4372 | CFArray shiftedLCs= CFArray (2); |
---|
4373 | CFList shiftedLCsEval1, shiftedLCsEval2; |
---|
4374 | shiftedLCs[0]= myShift2Zero (LCs[1], shiftedLCsEval1, evaluation); |
---|
4375 | shiftedLCs[1]= myShift2Zero (LCs[2], shiftedLCsEval2, evaluation); |
---|
4376 | factors.insert (1); |
---|
4377 | int liftBound= degree (UEval.getLast(), 2) + 1; |
---|
4378 | CFArray Pi; |
---|
4379 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
4380 | CFList diophant; |
---|
4381 | CFArray lcs= CFArray (2); |
---|
4382 | lcs [0]= shiftedLCsEval1.getFirst(); |
---|
4383 | lcs [1]= shiftedLCsEval2.getFirst(); |
---|
4384 | nonMonicHenselLift12 (UEval.getFirst(), factors, liftBound, Pi, diophant, M, |
---|
4385 | lcs, false); |
---|
4386 | |
---|
4387 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
4388 | { |
---|
4389 | if (!fdivides (i.getItem(), UEval.getFirst())) |
---|
4390 | return 0; |
---|
4391 | } |
---|
4392 | |
---|
4393 | int * liftBounds; |
---|
4394 | bool noOneToOne= false; |
---|
4395 | if (U.level() > 2) |
---|
4396 | { |
---|
4397 | liftBounds= new int [U.level() - 1]; /* index: 0.. U.level()-2 */ |
---|
4398 | liftBounds[0]= liftBound; |
---|
4399 | for (int i= 1; i < U.level() - 1; i++) |
---|
4400 | liftBounds[i]= degree (shiftedU, Variable (i + 2)) + 1; |
---|
4401 | factors= nonMonicHenselLift2 (UEval, factors, liftBounds, U.level() - 1, |
---|
4402 | false, shiftedLCsEval1, shiftedLCsEval2, Pi, |
---|
4403 | diophant, noOneToOne); |
---|
4404 | delete [] liftBounds; |
---|
4405 | if (noOneToOne) |
---|
4406 | return 0; |
---|
4407 | } |
---|
4408 | G[1]= factors.getFirst(); |
---|
4409 | G[2]= factors.getLast(); |
---|
4410 | G[1]= myReverseShift (G[1], evaluation); |
---|
4411 | G[2]= myReverseShift (G[2], evaluation); |
---|
4412 | G[1]= NN (G[1]); |
---|
4413 | G[2]= NN (G[2]); |
---|
4414 | return 1; |
---|
4415 | } |
---|
4416 | |
---|
4417 | static inline |
---|
4418 | bool findeval_P (const CanonicalForm & F, const CanonicalForm & G, |
---|
4419 | CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, |
---|
4420 | REvaluation & b, int delta, int degF, int degG, int maxeval, |
---|
4421 | int & count, int& k, int bound, int& l) |
---|
4422 | { |
---|
4423 | if( count == 0 && delta != 0) |
---|
4424 | { |
---|
4425 | if( count++ > maxeval ) |
---|
4426 | return false; |
---|
4427 | } |
---|
4428 | if (count > 0) |
---|
4429 | { |
---|
4430 | b.nextpoint(k); |
---|
4431 | if (k == 0) |
---|
4432 | k++; |
---|
4433 | l++; |
---|
4434 | if (l > bound) |
---|
4435 | { |
---|
4436 | l= 1; |
---|
4437 | k++; |
---|
4438 | if (k > tmax (F.level(), G.level()) - 1) |
---|
4439 | return false; |
---|
4440 | b.nextpoint (k); |
---|
4441 | } |
---|
4442 | if (count++ > maxeval) |
---|
4443 | return false; |
---|
4444 | } |
---|
4445 | while( true ) |
---|
4446 | { |
---|
4447 | Fb = b( F ); |
---|
4448 | if( degree( Fb, 1 ) == degF ) |
---|
4449 | { |
---|
4450 | Gb = b( G ); |
---|
4451 | if( degree( Gb, 1 ) == degG ) |
---|
4452 | { |
---|
4453 | Db = gcd( Fb, Gb ); |
---|
4454 | if( delta > 0 ) |
---|
4455 | { |
---|
4456 | if( degree( Db, 1 ) <= delta ) |
---|
4457 | return true; |
---|
4458 | } |
---|
4459 | else |
---|
4460 | return true; |
---|
4461 | } |
---|
4462 | } |
---|
4463 | if (k == 0) |
---|
4464 | k++; |
---|
4465 | b.nextpoint(k); |
---|
4466 | l++; |
---|
4467 | if (l > bound) |
---|
4468 | { |
---|
4469 | l= 1; |
---|
4470 | k++; |
---|
4471 | if (k > tmax (F.level(), G.level()) - 1) |
---|
4472 | return false; |
---|
4473 | b.nextpoint (k); |
---|
4474 | } |
---|
4475 | if( count++ > maxeval ) |
---|
4476 | return false; |
---|
4477 | } |
---|
4478 | } |
---|
4479 | |
---|
4480 | // parameters for heuristic |
---|
4481 | static int maxNumEval= 200; |
---|
4482 | static int sizePerVars1= 500; //try dense gcd if size/#variables is bigger |
---|
4483 | |
---|
4484 | /// Extended Zassenhaus GCD for finite fields |
---|
4485 | CanonicalForm EZGCD_P( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
4486 | { |
---|
4487 | if (FF.isZero() && degree(GG) > 0) return GG/Lc(GG); |
---|
4488 | else if (GG.isZero() && degree (FF) > 0) return FF/Lc(FF); |
---|
4489 | else if (FF.isZero() && GG.isZero()) return FF.genOne(); |
---|
4490 | if (FF.inBaseDomain() || GG.inBaseDomain()) return FF.genOne(); |
---|
4491 | if (FF.isUnivariate() && fdivides(FF, GG)) return FF/Lc(FF); |
---|
4492 | if (GG.isUnivariate() && fdivides(GG, FF)) return GG/Lc(GG); |
---|
4493 | if (FF == GG) return FF/Lc(FF); |
---|
4494 | |
---|
4495 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, |
---|
4496 | lcD; |
---|
4497 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
---|
4498 | int degF, degG, delta, count; |
---|
4499 | int maxeval; |
---|
4500 | maxeval= tmin((getCharacteristic()/ |
---|
4501 | (int)(ilog2(getCharacteristic())*log2exp))*2, maxNumEval); |
---|
4502 | count= 0; // number of eval. used |
---|
4503 | REvaluation b, bt; |
---|
4504 | int gcdfound = 0; |
---|
4505 | Variable x = Variable(1); |
---|
4506 | |
---|
4507 | F= FF; |
---|
4508 | G= GG; |
---|
4509 | |
---|
4510 | CFMap M,N; |
---|
4511 | int smallestDegLev; |
---|
4512 | TIMING_START (ez_p_compress) |
---|
4513 | int best_level= compress4EZGCD (F, G, M, N, smallestDegLev); |
---|
4514 | |
---|
4515 | if (best_level == 0) return G.genOne(); |
---|
4516 | |
---|
4517 | F= M (F); |
---|
4518 | G= M (G); |
---|
4519 | TIMING_END_AND_PRINT (ez_p_compress, "time for compression in EZ_P: ") |
---|
4520 | |
---|
4521 | TIMING_START (ez_p_content) |
---|
4522 | f = content( F, x ); g = content( G, x ); |
---|
4523 | d = gcd( f, g ); |
---|
4524 | F /= f; G /= g; |
---|
4525 | TIMING_END_AND_PRINT (ez_p_content, "time to extract content in EZ_P: ") |
---|
4526 | |
---|
4527 | if( F.isUnivariate() && G.isUnivariate() ) |
---|
4528 | { |
---|
4529 | if( F.mvar() == G.mvar() ) |
---|
4530 | d *= gcd( F, G ); |
---|
4531 | return N (d); |
---|
4532 | } |
---|
4533 | |
---|
4534 | int maxNumVars= tmax (getNumVars (F), getNumVars (G)); |
---|
4535 | Variable a, oldA; |
---|
4536 | int sizeF= size (F); |
---|
4537 | int sizeG= size (G); |
---|
4538 | |
---|
4539 | if (sizeF/maxNumVars > sizePerVars1 && sizeG/maxNumVars > sizePerVars1) |
---|
4540 | { |
---|
4541 | if (hasFirstAlgVar (F, a) || hasFirstAlgVar (G, a)) |
---|
4542 | return N (d*GCD_Fp_extension (F, G, a)); |
---|
4543 | else if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4544 | return N (d*GCD_GF (F, G)); |
---|
4545 | else |
---|
4546 | return N (d*GCD_small_p (F, G)); |
---|
4547 | } |
---|
4548 | |
---|
4549 | int dummy= 0; |
---|
4550 | if( gcd_test_one( F, G, false, dummy ) ) |
---|
4551 | { |
---|
4552 | return N (d); |
---|
4553 | } |
---|
4554 | |
---|
4555 | bool passToGF= false; |
---|
4556 | bool extOfExt= false; |
---|
4557 | int p= getCharacteristic(); |
---|
4558 | bool algExtension= (hasFirstAlgVar(F,a) || hasFirstAlgVar(G,a)); |
---|
4559 | int k= 1; |
---|
4560 | CanonicalForm primElem, imPrimElem; |
---|
4561 | CFList source, dest; |
---|
4562 | if (p < 50 && CFFactory::gettype() != GaloisFieldDomain && !algExtension) |
---|
4563 | { |
---|
4564 | if (p == 2) |
---|
4565 | setCharacteristic (2, 12, 'Z'); |
---|
4566 | else if (p == 3) |
---|
4567 | setCharacteristic (3, 4, 'Z'); |
---|
4568 | else if (p == 5 || p == 7) |
---|
4569 | setCharacteristic (p, 3, 'Z'); |
---|
4570 | else |
---|
4571 | setCharacteristic (p, 2, 'Z'); |
---|
4572 | passToGF= true; |
---|
4573 | F= F.mapinto(); |
---|
4574 | G= G.mapinto(); |
---|
4575 | maxeval= 2*ipower (p, getGFDegree()); |
---|
4576 | } |
---|
4577 | else if (CFFactory::gettype() == GaloisFieldDomain && |
---|
4578 | ipower (p , getGFDegree()) < 50) |
---|
4579 | { |
---|
4580 | k= getGFDegree(); |
---|
4581 | if (ipower (p, 2*k) > 50) |
---|
4582 | setCharacteristic (p, 2*k, gf_name); |
---|
4583 | else |
---|
4584 | setCharacteristic (p, 3*k, gf_name); |
---|
4585 | F= GFMapUp (F, k); |
---|
4586 | G= GFMapUp (G, k); |
---|
4587 | maxeval= tmin (2*ipower (p, getGFDegree()), maxNumEval); |
---|
4588 | } |
---|
4589 | else if (p < 50 && algExtension && !CFFactory::gettype() == GaloisFieldDomain) |
---|
4590 | { |
---|
4591 | int d= degree (getMipo (a)); |
---|
4592 | oldA= a; |
---|
4593 | Variable v2; |
---|
4594 | if (p == 2 && d < 6) |
---|
4595 | { |
---|
4596 | zz_p::init (p); |
---|
4597 | bool primFail= false; |
---|
4598 | Variable vBuf; |
---|
4599 | primElem= primitiveElement (a, vBuf, primFail); |
---|
4600 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
4601 | if (d < 3) |
---|
4602 | { |
---|
4603 | zz_pX NTLIrredpoly; |
---|
4604 | BuildIrred (NTLIrredpoly, d*3); |
---|
4605 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4606 | v2= rootOf (newMipo); |
---|
4607 | } |
---|
4608 | else |
---|
4609 | { |
---|
4610 | zz_pX NTLIrredpoly; |
---|
4611 | BuildIrred (NTLIrredpoly, d*2); |
---|
4612 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4613 | v2= rootOf (newMipo); |
---|
4614 | } |
---|
4615 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
4616 | extOfExt= true; |
---|
4617 | } |
---|
4618 | else if ((p == 3 && d < 4) || ((p == 5 || p == 7) && d < 3)) |
---|
4619 | { |
---|
4620 | zz_p::init (p); |
---|
4621 | bool primFail= false; |
---|
4622 | Variable vBuf; |
---|
4623 | primElem= primitiveElement (a, vBuf, primFail); |
---|
4624 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
4625 | zz_pX NTLIrredpoly; |
---|
4626 | BuildIrred (NTLIrredpoly, d*2); |
---|
4627 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4628 | v2= rootOf (newMipo); |
---|
4629 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
4630 | extOfExt= true; |
---|
4631 | } |
---|
4632 | if (extOfExt) |
---|
4633 | { |
---|
4634 | maxeval= tmin (2*ipower (p, degree (getMipo (v2))), maxNumEval); |
---|
4635 | F= mapUp (F, a, v2, primElem, imPrimElem, source, dest); |
---|
4636 | G= mapUp (G, a, v2, primElem, imPrimElem, source, dest); |
---|
4637 | a= v2; |
---|
4638 | } |
---|
4639 | } |
---|
4640 | |
---|
4641 | lcF = LC( F, x ); lcG = LC( G, x ); |
---|
4642 | lcD = gcd( lcF, lcG ); |
---|
4643 | |
---|
4644 | delta = 0; |
---|
4645 | degF = degree( F, x ); degG = degree( G, x ); |
---|
4646 | |
---|
4647 | if(hasFirstAlgVar(G,a)) |
---|
4648 | b = REvaluation( 2, tmax(F.level(), G.level()), AlgExtRandomF( a ) ); |
---|
4649 | else |
---|
4650 | { // both not in extension given by algebraic variable |
---|
4651 | if (CFFactory::gettype() != GaloisFieldDomain) |
---|
4652 | b = REvaluation( 2, tmax(F.level(), G.level()), FFRandom() ); |
---|
4653 | else |
---|
4654 | b = REvaluation( 2, tmax(F.level(), G.level()), GFRandom() ); |
---|
4655 | } |
---|
4656 | |
---|
4657 | CanonicalForm cand, contcand; |
---|
4658 | CanonicalForm result; |
---|
4659 | int o, t; |
---|
4660 | o= 0; |
---|
4661 | t= 1; |
---|
4662 | int goodPointCount= 0; |
---|
4663 | while( !gcdfound ) |
---|
4664 | { |
---|
4665 | TIMING_START (ez_p_eval); |
---|
4666 | if( !findeval_P( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count, o, |
---|
4667 | maxeval/maxNumVars, t )) |
---|
4668 | { // too many eval. used --> try another method |
---|
4669 | Off (SW_USE_EZGCD_P); |
---|
4670 | result= gcd (F,G); |
---|
4671 | On (SW_USE_EZGCD_P); |
---|
4672 | if (passToGF) |
---|
4673 | { |
---|
4674 | CanonicalForm mipo= gf_mipo; |
---|
4675 | setCharacteristic (p); |
---|
4676 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4677 | result= GF2FalphaRep (result, alpha); |
---|
4678 | } |
---|
4679 | if (k > 1) |
---|
4680 | { |
---|
4681 | result= GFMapDown (result, k); |
---|
4682 | setCharacteristic (p, k, gf_name); |
---|
4683 | } |
---|
4684 | if (extOfExt) |
---|
4685 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4686 | return N (d*result); |
---|
4687 | } |
---|
4688 | TIMING_END_AND_PRINT (ez_p_eval, "time for eval point search in EZ_P1: "); |
---|
4689 | delta = degree( Db ); |
---|
4690 | if( delta == 0 ) |
---|
4691 | { |
---|
4692 | if (passToGF) |
---|
4693 | setCharacteristic (p); |
---|
4694 | if (k > 1) |
---|
4695 | setCharacteristic (p, k, gf_name); |
---|
4696 | return N (d); |
---|
4697 | } |
---|
4698 | while( true ) |
---|
4699 | { |
---|
4700 | bt = b; |
---|
4701 | TIMING_START (ez_p_eval); |
---|
4702 | if( !findeval_P(F,G,Fbt,Gbt,Dbt, bt, delta, degF, degG, maxeval, count, o, |
---|
4703 | maxeval/maxNumVars, t )) |
---|
4704 | { // too many eval. used --> try another method |
---|
4705 | Off (SW_USE_EZGCD_P); |
---|
4706 | result= gcd (F,G); |
---|
4707 | On (SW_USE_EZGCD_P); |
---|
4708 | if (passToGF) |
---|
4709 | { |
---|
4710 | CanonicalForm mipo= gf_mipo; |
---|
4711 | setCharacteristic (p); |
---|
4712 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4713 | result= GF2FalphaRep (result, alpha); |
---|
4714 | } |
---|
4715 | if (k > 1) |
---|
4716 | { |
---|
4717 | result= GFMapDown (result, k); |
---|
4718 | setCharacteristic (p, k, gf_name); |
---|
4719 | } |
---|
4720 | if (extOfExt) |
---|
4721 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4722 | return N (d*result); |
---|
4723 | } |
---|
4724 | TIMING_END_AND_PRINT (ez_p_eval, "time for eval point search in EZ_P2: "); |
---|
4725 | int dd = degree( Dbt ); |
---|
4726 | if( dd == 0 ) |
---|
4727 | { |
---|
4728 | if (passToGF) |
---|
4729 | setCharacteristic (p); |
---|
4730 | if (k > 1) |
---|
4731 | setCharacteristic (p, k, gf_name); |
---|
4732 | return N (d); |
---|
4733 | } |
---|
4734 | if( dd == delta ) |
---|
4735 | { |
---|
4736 | goodPointCount++; |
---|
4737 | if (goodPointCount == 5) |
---|
4738 | break; |
---|
4739 | } |
---|
4740 | if( dd < delta ) |
---|
4741 | { |
---|
4742 | goodPointCount= 0; |
---|
4743 | delta = dd; |
---|
4744 | b = bt; |
---|
4745 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
---|
4746 | } |
---|
4747 | if (delta == degF) |
---|
4748 | { |
---|
4749 | if (degF <= degG && fdivides (F, G)) |
---|
4750 | { |
---|
4751 | if (passToGF) |
---|
4752 | { |
---|
4753 | CanonicalForm mipo= gf_mipo; |
---|
4754 | setCharacteristic (p); |
---|
4755 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4756 | F= GF2FalphaRep (F, alpha); |
---|
4757 | } |
---|
4758 | if (k > 1) |
---|
4759 | { |
---|
4760 | F= GFMapDown (F, k); |
---|
4761 | setCharacteristic (p, k, gf_name); |
---|
4762 | } |
---|
4763 | if (extOfExt) |
---|
4764 | F= mapDown (F, primElem, imPrimElem, oldA, dest, source); |
---|
4765 | return N (d*F); |
---|
4766 | } |
---|
4767 | else |
---|
4768 | delta--; |
---|
4769 | } |
---|
4770 | else if (delta == degG) |
---|
4771 | { |
---|
4772 | if (degG <= degF && fdivides (G, F)) |
---|
4773 | { |
---|
4774 | if (passToGF) |
---|
4775 | { |
---|
4776 | CanonicalForm mipo= gf_mipo; |
---|
4777 | setCharacteristic (p); |
---|
4778 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4779 | G= GF2FalphaRep (G, alpha); |
---|
4780 | } |
---|
4781 | if (k > 1) |
---|
4782 | { |
---|
4783 | G= GFMapDown (G, k); |
---|
4784 | setCharacteristic (p, k, gf_name); |
---|
4785 | } |
---|
4786 | if (extOfExt) |
---|
4787 | G= mapDown (G, primElem, imPrimElem, oldA, dest, source); |
---|
4788 | return N (d*G); |
---|
4789 | } |
---|
4790 | else |
---|
4791 | delta--; |
---|
4792 | } |
---|
4793 | } |
---|
4794 | if( delta != degF && delta != degG ) |
---|
4795 | { |
---|
4796 | bool B_is_F; |
---|
4797 | CanonicalForm xxx1, xxx2; |
---|
4798 | CanonicalForm buf; |
---|
4799 | DD[1] = Fb / Db; |
---|
4800 | buf= Gb/Db; |
---|
4801 | xxx1 = gcd( DD[1], Db ); |
---|
4802 | xxx2 = gcd( buf, Db ); |
---|
4803 | if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
4804 | (size (F) <= size (G))) |
---|
4805 | || (xxx1.inCoeffDomain() && !xxx2.inCoeffDomain())) |
---|
4806 | { |
---|
4807 | B = F; |
---|
4808 | DD[2] = Db; |
---|
4809 | lcDD[1] = lcF; |
---|
4810 | lcDD[2] = lcD; |
---|
4811 | B_is_F = true; |
---|
4812 | } |
---|
4813 | else if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
4814 | (size (G) < size (F))) |
---|
4815 | || (!xxx1.inCoeffDomain() && xxx2.inCoeffDomain())) |
---|
4816 | { |
---|
4817 | DD[1] = buf; |
---|
4818 | B = G; |
---|
4819 | DD[2] = Db; |
---|
4820 | lcDD[1] = lcG; |
---|
4821 | lcDD[2] = lcD; |
---|
4822 | B_is_F = false; |
---|
4823 | } |
---|
4824 | else // special case handling |
---|
4825 | { |
---|
4826 | Off (SW_USE_EZGCD_P); |
---|
4827 | result= gcd (F,G); |
---|
4828 | On (SW_USE_EZGCD_P); |
---|
4829 | if (passToGF) |
---|
4830 | { |
---|
4831 | CanonicalForm mipo= gf_mipo; |
---|
4832 | setCharacteristic (p); |
---|
4833 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4834 | result= GF2FalphaRep (result, alpha); |
---|
4835 | } |
---|
4836 | if (k > 1) |
---|
4837 | { |
---|
4838 | result= GFMapDown (result, k); |
---|
4839 | setCharacteristic (p, k, gf_name); |
---|
4840 | } |
---|
4841 | if (extOfExt) |
---|
4842 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4843 | return N (d*result); |
---|
4844 | } |
---|
4845 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
---|
4846 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
---|
4847 | |
---|
4848 | if (size (B*lcDD[2])/maxNumVars > sizePerVars1) |
---|
4849 | { |
---|
4850 | if (algExtension) |
---|
4851 | { |
---|
4852 | result= GCD_Fp_extension (F, G, a); |
---|
4853 | if (extOfExt) |
---|
4854 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4855 | return N (d*result); |
---|
4856 | } |
---|
4857 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4858 | { |
---|
4859 | result= GCD_GF (F, G); |
---|
4860 | if (passToGF) |
---|
4861 | { |
---|
4862 | CanonicalForm mipo= gf_mipo; |
---|
4863 | setCharacteristic (p); |
---|
4864 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4865 | result= GF2FalphaRep (result, alpha); |
---|
4866 | } |
---|
4867 | if (k > 1) |
---|
4868 | { |
---|
4869 | result= GFMapDown (result, k); |
---|
4870 | setCharacteristic (p, k, gf_name); |
---|
4871 | } |
---|
4872 | return N (d*result); |
---|
4873 | } |
---|
4874 | else |
---|
4875 | return N (d*GCD_small_p (F,G)); |
---|
4876 | } |
---|
4877 | |
---|
4878 | TIMING_START (ez_p_hensel_lift); |
---|
4879 | gcdfound= Hensel_P (B*lcD, DD, b, lcDD); |
---|
4880 | TIMING_END_AND_PRINT (ez_p_hensel_lift, "time for Hensel lift in EZ_P: "); |
---|
4881 | |
---|
4882 | if (gcdfound == -1) //things became dense |
---|
4883 | { |
---|
4884 | if (algExtension) |
---|
4885 | { |
---|
4886 | result= GCD_Fp_extension (F, G, a); |
---|
4887 | if (extOfExt) |
---|
4888 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4889 | return N (d*result); |
---|
4890 | } |
---|
4891 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4892 | { |
---|
4893 | result= GCD_GF (F, G); |
---|
4894 | if (passToGF) |
---|
4895 | { |
---|
4896 | CanonicalForm mipo= gf_mipo; |
---|
4897 | setCharacteristic (p); |
---|
4898 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4899 | result= GF2FalphaRep (result, alpha); |
---|
4900 | } |
---|
4901 | if (k > 1) |
---|
4902 | { |
---|
4903 | result= GFMapDown (result, k); |
---|
4904 | setCharacteristic (p, k, gf_name); |
---|
4905 | } |
---|
4906 | return N (d*result); |
---|
4907 | } |
---|
4908 | else |
---|
4909 | return N (d*GCD_small_p (F,G)); |
---|
4910 | } |
---|
4911 | |
---|
4912 | if (gcdfound == 1) |
---|
4913 | { |
---|
4914 | TIMING_START (termination_test); |
---|
4915 | contcand= content (DD[2], Variable (1)); |
---|
4916 | cand = DD[2] / contcand; |
---|
4917 | if (B_is_F) |
---|
4918 | gcdfound = fdivides( cand, G ) && cand*(DD[1]/(lcD/contcand)) == F; |
---|
4919 | else |
---|
4920 | gcdfound = fdivides( cand, F ) && cand*(DD[1]/(lcD/contcand)) == G; |
---|
4921 | TIMING_END_AND_PRINT (termination_test, |
---|
4922 | "time for termination test EZ_P: "); |
---|
4923 | |
---|
4924 | if (passToGF && gcdfound) |
---|
4925 | { |
---|
4926 | CanonicalForm mipo= gf_mipo; |
---|
4927 | setCharacteristic (p); |
---|
4928 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4929 | cand= GF2FalphaRep (cand, alpha); |
---|
4930 | } |
---|
4931 | if (k > 1 && gcdfound) |
---|
4932 | { |
---|
4933 | cand= GFMapDown (cand, k); |
---|
4934 | setCharacteristic (p, k, gf_name); |
---|
4935 | } |
---|
4936 | if (extOfExt && gcdfound) |
---|
4937 | cand= mapDown (cand, primElem, imPrimElem, oldA, dest, source); |
---|
4938 | } |
---|
4939 | } |
---|
4940 | delta--; |
---|
4941 | goodPointCount= 0; |
---|
4942 | } |
---|
4943 | return N (d*cand); |
---|
4944 | } |
---|
4945 | |
---|
4946 | |
---|
4947 | #endif |
---|