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 | * @internal |
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16 | * @version \$Id$ |
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17 | * |
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18 | **/ |
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19 | //***************************************************************************** |
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20 | |
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21 | #include "config.h" |
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22 | |
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23 | #include "cf_assert.h" |
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24 | #include "debug.h" |
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25 | #include "timing.h" |
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26 | |
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27 | #include "canonicalform.h" |
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28 | #include "algext.h" |
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29 | #include "cf_map.h" |
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30 | #include "cf_util.h" |
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31 | #include "templates/ftmpl_functions.h" |
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32 | #include "cf_random.h" |
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33 | #include "cf_reval.h" |
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34 | #include "facHensel.h" |
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35 | #include "cf_iter.h" |
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36 | #include "cfNewtonPolygon.h" |
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37 | |
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38 | // iinline helper functions: |
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39 | #include "cf_map_ext.h" |
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40 | |
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41 | #ifdef HAVE_NTL |
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42 | #include <NTL/ZZ_pEX.h> |
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43 | #include <NTLconvert.h> |
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44 | #endif |
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45 | |
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46 | #include "cf_gcd_smallp.h" |
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47 | |
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48 | #ifdef HAVE_NTL |
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49 | |
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50 | TIMING_DEFINE_PRINT(gcd_recursion) |
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51 | TIMING_DEFINE_PRINT(newton_interpolation) |
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52 | |
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53 | static const double log2exp= 1.442695041; |
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54 | |
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55 | /// compressing two polynomials F and G, M is used for compressing, |
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56 | /// N to reverse the compression |
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57 | int myCompress (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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58 | CFMap & N, bool topLevel) |
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59 | { |
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60 | int n= tmax (F.level(), G.level()); |
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61 | int * degsf= new int [n + 1]; |
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62 | int * degsg= new int [n + 1]; |
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63 | |
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64 | for (int i = 0; i <= n; i++) |
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65 | degsf[i]= degsg[i]= 0; |
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66 | |
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67 | degsf= degrees (F, degsf); |
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68 | degsg= degrees (G, degsg); |
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69 | |
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70 | int both_non_zero= 0; |
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71 | int f_zero= 0; |
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72 | int g_zero= 0; |
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73 | int both_zero= 0; |
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74 | |
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75 | if (topLevel) |
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76 | { |
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77 | for (int i= 1; i <= n; i++) |
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78 | { |
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79 | if (degsf[i] != 0 && degsg[i] != 0) |
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80 | { |
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81 | both_non_zero++; |
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82 | continue; |
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83 | } |
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84 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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85 | { |
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86 | f_zero++; |
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87 | continue; |
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88 | } |
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89 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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90 | { |
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91 | g_zero++; |
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92 | continue; |
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93 | } |
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94 | } |
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95 | |
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96 | if (both_non_zero == 0) |
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97 | { |
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98 | delete [] degsf; |
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99 | delete [] degsg; |
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100 | return 0; |
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101 | } |
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102 | |
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103 | // map Variables which do not occur in both polynomials to higher levels |
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104 | int k= 1; |
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105 | int l= 1; |
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106 | for (int i= 1; i <= n; i++) |
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107 | { |
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108 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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109 | { |
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110 | if (k + both_non_zero != i) |
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111 | { |
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112 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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113 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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114 | } |
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115 | k++; |
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116 | } |
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117 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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118 | { |
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119 | if (l + g_zero + both_non_zero != i) |
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120 | { |
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121 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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122 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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123 | } |
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124 | l++; |
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125 | } |
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126 | } |
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127 | |
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128 | // sort Variables x_{i} in increasing order of |
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129 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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130 | int m= tmax (F.level(), G.level()); |
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131 | int min_max_deg; |
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132 | k= both_non_zero; |
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133 | l= 0; |
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134 | int i= 1; |
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135 | while (k > 0) |
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136 | { |
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137 | if (degsf [i] != 0 && degsg [i] != 0) |
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138 | min_max_deg= tmax (degsf[i], degsg[i]); |
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139 | else |
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140 | min_max_deg= 0; |
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141 | while (min_max_deg == 0) |
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142 | { |
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143 | i++; |
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144 | if (degsf [i] != 0 && degsg [i] != 0) |
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145 | min_max_deg= tmax (degsf[i], degsg[i]); |
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146 | else |
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147 | min_max_deg= 0; |
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148 | } |
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149 | for (int j= i + 1; j <= m; j++) |
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150 | { |
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151 | if (degsf[j] != 0 && degsg [j] != 0 && |
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152 | tmax (degsf[j],degsg[j]) <= min_max_deg) |
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153 | { |
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154 | min_max_deg= tmax (degsf[j], degsg[j]); |
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155 | l= j; |
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156 | } |
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157 | } |
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158 | if (l != 0) |
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159 | { |
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160 | if (l != k) |
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161 | { |
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162 | M.newpair (Variable (l), Variable(k)); |
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163 | N.newpair (Variable (k), Variable(l)); |
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164 | degsf[l]= 0; |
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165 | degsg[l]= 0; |
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166 | l= 0; |
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167 | } |
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168 | else |
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169 | { |
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170 | degsf[l]= 0; |
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171 | degsg[l]= 0; |
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172 | l= 0; |
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173 | } |
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174 | } |
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175 | else if (l == 0) |
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176 | { |
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177 | if (i != k) |
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178 | { |
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179 | M.newpair (Variable (i), Variable (k)); |
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180 | N.newpair (Variable (k), Variable (i)); |
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181 | degsf[i]= 0; |
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182 | degsg[i]= 0; |
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183 | } |
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184 | else |
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185 | { |
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186 | degsf[i]= 0; |
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187 | degsg[i]= 0; |
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188 | } |
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189 | i++; |
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190 | } |
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191 | k--; |
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192 | } |
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193 | } |
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194 | else |
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195 | { |
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196 | //arrange Variables such that no gaps occur |
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197 | for (int i= 1; i <= n; i++) |
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198 | { |
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199 | if (degsf[i] == 0 && degsg[i] == 0) |
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200 | { |
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201 | both_zero++; |
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202 | continue; |
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203 | } |
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204 | else |
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205 | { |
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206 | if (both_zero != 0) |
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207 | { |
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208 | M.newpair (Variable (i), Variable (i - both_zero)); |
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209 | N.newpair (Variable (i - both_zero), Variable (i)); |
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210 | } |
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211 | } |
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212 | } |
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213 | } |
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214 | |
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215 | delete [] degsf; |
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216 | delete [] degsg; |
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217 | |
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218 | return 1; |
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219 | } |
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220 | |
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221 | static inline CanonicalForm |
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222 | uni_content (const CanonicalForm & F); |
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223 | |
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224 | CanonicalForm |
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225 | uni_content (const CanonicalForm& F, const Variable& x) |
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226 | { |
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227 | if (F.inCoeffDomain()) |
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228 | return F.genOne(); |
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229 | if (F.level() == x.level() && F.isUnivariate()) |
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230 | return F; |
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231 | if (F.level() != x.level() && F.isUnivariate()) |
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232 | return F.genOne(); |
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233 | |
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234 | if (x.level() != 1) |
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235 | { |
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236 | CanonicalForm f= swapvar (F, x, Variable (1)); |
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237 | CanonicalForm result= uni_content (f); |
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238 | return swapvar (result, x, Variable (1)); |
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239 | } |
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240 | else |
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241 | return uni_content (F); |
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242 | } |
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243 | |
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244 | /// compute the content of F, where F is considered as an element of |
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245 | /// \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$ |
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246 | static inline CanonicalForm |
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247 | uni_content (const CanonicalForm & F) |
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248 | { |
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249 | if (F.inBaseDomain()) |
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250 | return F.genOne(); |
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251 | if (F.level() == 1 && F.isUnivariate()) |
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252 | return F; |
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253 | if (F.level() != 1 && F.isUnivariate()) |
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254 | return F.genOne(); |
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255 | if (degree (F,1) == 0) return F.genOne(); |
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256 | |
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257 | int l= F.level(); |
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258 | if (l == 2) |
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259 | return content(F); |
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260 | else |
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261 | { |
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262 | CanonicalForm pol, c = 0; |
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263 | CFIterator i = F; |
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264 | for (; i.hasTerms(); i++) |
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265 | { |
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266 | pol= i.coeff(); |
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267 | pol= uni_content (pol); |
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268 | c= gcd (c, pol); |
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269 | if (c.isOne()) |
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270 | return c; |
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271 | } |
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272 | return c; |
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273 | } |
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274 | } |
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275 | |
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276 | CanonicalForm |
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277 | extractContents (const CanonicalForm& F, const CanonicalForm& G, |
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278 | CanonicalForm& contentF, CanonicalForm& contentG, |
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279 | CanonicalForm& ppF, CanonicalForm& ppG, const int d) |
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280 | { |
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281 | CanonicalForm uniContentF, uniContentG, gcdcFcG; |
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282 | contentF= 1; |
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283 | contentG= 1; |
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284 | ppF= F; |
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285 | ppG= G; |
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286 | CanonicalForm result= 1; |
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287 | for (int i= 1; i <= d; i++) |
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288 | { |
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289 | uniContentF= uni_content (F, Variable (i)); |
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290 | uniContentG= uni_content (G, Variable (i)); |
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291 | gcdcFcG= gcd (uniContentF, uniContentG); |
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292 | contentF *= uniContentF; |
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293 | contentG *= uniContentG; |
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294 | ppF /= uniContentF; |
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295 | ppG /= uniContentG; |
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296 | result *= gcdcFcG; |
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297 | } |
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298 | return result; |
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299 | } |
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300 | |
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301 | /// compute the leading coefficient of F, where F is considered as an element |
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302 | /// of \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$, order on Mon (x_{2},\ldots ,x_{n}) |
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303 | /// is dp. |
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304 | static inline |
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305 | CanonicalForm uni_lcoeff (const CanonicalForm& F) |
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306 | { |
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307 | if (F.level() > 1) |
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308 | { |
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309 | Variable x= Variable (2); |
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310 | int deg= totaldegree (F, x, F.mvar()); |
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311 | for (CFIterator i= F; i.hasTerms(); i++) |
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312 | { |
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313 | if (i.exp() + totaldegree (i.coeff(), x, i.coeff().mvar()) == deg) |
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314 | return uni_lcoeff (i.coeff()); |
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315 | } |
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316 | } |
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317 | return F; |
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318 | } |
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319 | |
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320 | /// Newton interpolation - Incremental algorithm. |
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321 | /// Given a list of values alpha_i and a list of polynomials u_i, 1 <= i <= n, |
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322 | /// computes the interpolation polynomial assuming that |
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323 | /// the polynomials in u are the results of evaluating the variabe x |
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324 | /// of the unknown polynomial at the alpha values. |
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325 | /// This incremental version receives only the values of alpha_n and u_n and |
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326 | /// the previous interpolation polynomial for points 1 <= i <= n-1, and computes |
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327 | /// the polynomial interpolating in all the points. |
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328 | /// newtonPoly must be equal to (x - alpha_1) * ... * (x - alpha_{n-1}) |
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329 | static inline CanonicalForm |
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330 | newtonInterp(const CanonicalForm alpha, const CanonicalForm u, |
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331 | const CanonicalForm newtonPoly, const CanonicalForm oldInterPoly, |
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332 | const Variable & x) |
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333 | { |
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334 | CanonicalForm interPoly; |
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335 | |
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336 | interPoly= oldInterPoly + ((u - oldInterPoly(alpha, x))/newtonPoly(alpha, x)) |
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337 | *newtonPoly; |
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338 | return interPoly; |
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339 | } |
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340 | |
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341 | /// compute a random element a of \f$ F_{p}(\alpha ) \f$ , |
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342 | /// s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns |
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343 | /// fail if there are no field elements left which have not been used before |
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344 | static inline CanonicalForm |
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345 | randomElement (const CanonicalForm & F, const Variable & alpha, CFList & list, |
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346 | bool & fail) |
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347 | { |
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348 | fail= false; |
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349 | Variable x= F.mvar(); |
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350 | AlgExtRandomF genAlgExt (alpha); |
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351 | FFRandom genFF; |
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352 | CanonicalForm random, mipo; |
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353 | mipo= getMipo (alpha); |
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354 | int p= getCharacteristic (); |
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355 | int d= degree (mipo); |
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356 | int bound= ipower (p, d); |
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357 | do |
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358 | { |
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359 | if (list.length() == bound) |
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360 | { |
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361 | fail= true; |
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362 | break; |
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363 | } |
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364 | if (list.length() < p) |
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365 | { |
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366 | random= genFF.generate(); |
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367 | while (find (list, random)) |
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368 | random= genFF.generate(); |
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369 | } |
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370 | else |
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371 | { |
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372 | random= genAlgExt.generate(); |
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373 | while (find (list, random)) |
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374 | random= genAlgExt.generate(); |
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375 | } |
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376 | if (F (random, x) == 0) |
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377 | { |
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378 | list.append (random); |
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379 | continue; |
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380 | } |
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381 | } while (find (list, random)); |
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382 | return random; |
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383 | } |
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384 | |
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385 | static inline |
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386 | Variable chooseExtension (const Variable & alpha) |
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387 | { |
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388 | zz_p::init (getCharacteristic()); |
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389 | zz_pX NTLIrredpoly; |
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390 | int i, m; |
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391 | // extension of F_p needed |
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392 | if (alpha.level() == 1) |
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393 | { |
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394 | i= 1; |
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395 | m= 2; |
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396 | } //extension of F_p(alpha) |
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397 | if (alpha.level() != 1) |
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398 | { |
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399 | i= 4; |
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400 | m= degree (getMipo (alpha)); |
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401 | } |
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402 | BuildIrred (NTLIrredpoly, i*m); |
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403 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
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404 | return rootOf (newMipo); |
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405 | } |
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406 | |
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407 | /// chooses a suitable extension of \f$ F_{p}(\alpha ) \f$ |
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408 | /// we do not extend \f$ F_{p}(\alpha ) \f$ itself but extend \f$ F_{p} \f$ , |
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409 | /// s.t. \f$ F_{p}(\alpha ) \subset F_{p}(\beta ) \f$ |
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410 | static inline |
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411 | void choose_extension (const int& d, const int& num_vars, Variable& beta) |
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412 | { |
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413 | int p= getCharacteristic(); |
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414 | ZZ NTLp= to_ZZ (p); |
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415 | ZZ_p::init (NTLp); |
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416 | ZZ_pX NTLirredpoly; |
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417 | //TODO: replace d by max_{i} (deg_x{i}(f)) |
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418 | int i= (int) (log ((double) ipower (d + 1, num_vars))/log ((double) p)); |
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419 | int m= degree (getMipo (beta)); |
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420 | if (i <= 1) |
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421 | i= 2; |
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422 | BuildIrred (NTLirredpoly, i*m); |
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423 | CanonicalForm mipo= convertNTLZZpX2CF (NTLirredpoly, Variable(1)); |
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424 | beta= rootOf (mipo); |
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425 | } |
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426 | |
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427 | /// GCD of F and G over \f$ F_{p}(\alpha ) \f$ , |
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428 | /// l and topLevel are only used internally, output is monic |
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429 | /// based on Alg. 7.2. as described in "Algorithms for |
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430 | /// Computer Algebra" by Geddes, Czapor, Labahn |
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431 | CanonicalForm |
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432 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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433 | Variable & alpha, CFList& l, bool& topLevel) |
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434 | { |
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435 | CanonicalForm A= F; |
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436 | CanonicalForm B= G; |
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437 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
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438 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
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439 | else if (F.isZero() && G.isZero()) return F.genOne(); |
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440 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
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441 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
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442 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
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443 | if (F == G) return F/Lc(F); |
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444 | |
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445 | CFMap M,N; |
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446 | int best_level= myCompress (A, B, M, N, topLevel); |
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447 | |
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448 | if (best_level == 0) return B.genOne(); |
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449 | |
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450 | A= M(A); |
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451 | B= M(B); |
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452 | |
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453 | Variable x= Variable(1); |
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454 | |
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455 | //univariate case |
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456 | if (A.isUnivariate() && B.isUnivariate()) |
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457 | return N (gcd(A,B)); |
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458 | |
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459 | CanonicalForm cA, cB; // content of A and B |
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460 | CanonicalForm ppA, ppB; // primitive part of A and B |
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461 | CanonicalForm gcdcAcB; |
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462 | |
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463 | if (topLevel) |
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464 | { |
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465 | if (best_level <= 2) |
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466 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
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467 | else |
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468 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
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469 | } |
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470 | else |
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471 | { |
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472 | cA = uni_content (A); |
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473 | cB = uni_content (B); |
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474 | gcdcAcB= gcd (cA, cB); |
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475 | ppA= A/cA; |
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476 | ppB= B/cB; |
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477 | } |
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478 | |
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479 | int sizeNewtonPolyg; |
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480 | int ** newtonPolyg= NULL; |
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481 | mat_ZZ MM; |
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482 | vec_ZZ V; |
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483 | bool compressConvexDense= (ppA.level() == 2 && ppB.level() == 2); |
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484 | if (compressConvexDense) |
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485 | { |
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486 | cA= content (ppA, 1); |
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487 | cB= content (ppB, 1); |
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488 | ppA /= cA; |
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489 | ppB /= cB; |
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490 | gcdcAcB *= gcd (cA, cB); |
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491 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
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492 | { |
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493 | if (ppA.level() == ppB.level()) |
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494 | return N (gcd (ppA, ppB)*gcdcAcB); |
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495 | else |
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496 | return N (gcdcAcB); |
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497 | } |
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498 | |
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499 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
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500 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
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501 | |
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502 | for (int i= 0; i < sizeNewtonPolyg; i++) |
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503 | delete [] newtonPolyg[i]; |
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504 | delete [] newtonPolyg; |
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505 | |
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506 | ppA= compress (ppA, MM, V, false); |
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507 | ppB= compress (ppB, MM, V, false); |
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508 | MM= inv (MM); |
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509 | |
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510 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
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511 | { |
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512 | if (ppA.level() == ppB.level()) |
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513 | return N (decompress (gcd (ppA, ppB), MM, V)*gcdcAcB); |
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514 | else |
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515 | return N (gcdcAcB); |
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516 | } |
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517 | } |
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518 | |
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519 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
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520 | CanonicalForm gcdlcAlcB; |
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521 | |
---|
522 | lcA= uni_lcoeff (ppA); |
---|
523 | lcB= uni_lcoeff (ppB); |
---|
524 | |
---|
525 | if (fdivides (lcA, lcB)) |
---|
526 | { |
---|
527 | if (fdivides (A, B)) |
---|
528 | return F/Lc(F); |
---|
529 | } |
---|
530 | if (fdivides (lcB, lcA)) |
---|
531 | { |
---|
532 | if (fdivides (B, A)) |
---|
533 | return G/Lc(G); |
---|
534 | } |
---|
535 | |
---|
536 | gcdlcAlcB= gcd (lcA, lcB); |
---|
537 | |
---|
538 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
539 | |
---|
540 | if (d == 0) |
---|
541 | return N(gcdcAcB); |
---|
542 | |
---|
543 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
544 | if (d0 < d) |
---|
545 | d= d0; |
---|
546 | if (d == 0) |
---|
547 | return N(gcdcAcB); |
---|
548 | |
---|
549 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
550 | CanonicalForm newtonPoly; |
---|
551 | |
---|
552 | newtonPoly= 1; |
---|
553 | m= gcdlcAlcB; |
---|
554 | G_m= 0; |
---|
555 | H= 0; |
---|
556 | bool fail= false; |
---|
557 | topLevel= false; |
---|
558 | bool inextension= false; |
---|
559 | Variable V_buf= alpha; |
---|
560 | CanonicalForm prim_elem, im_prim_elem; |
---|
561 | CFList source, dest; |
---|
562 | do |
---|
563 | { |
---|
564 | random_element= randomElement (m, V_buf, l, fail); |
---|
565 | if (fail) |
---|
566 | { |
---|
567 | source= CFList(); |
---|
568 | dest= CFList(); |
---|
569 | |
---|
570 | Variable V_buf3= V_buf; |
---|
571 | V_buf= chooseExtension (V_buf); |
---|
572 | bool prim_fail= false; |
---|
573 | Variable V_buf2; |
---|
574 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
575 | |
---|
576 | if (V_buf3 != alpha) |
---|
577 | { |
---|
578 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
579 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
580 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
581 | source, dest); |
---|
582 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
583 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
584 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
585 | source, dest); |
---|
586 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
587 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
588 | source, dest); |
---|
589 | } |
---|
590 | |
---|
591 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
592 | if (prim_fail) |
---|
593 | ; //ERROR |
---|
594 | else |
---|
595 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
596 | |
---|
597 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
598 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
599 | inextension= true; |
---|
600 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
601 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
602 | im_prim_elem, source, dest); |
---|
603 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
604 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
605 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
606 | source, dest); |
---|
607 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
608 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
609 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
610 | source, dest); |
---|
611 | |
---|
612 | fail= false; |
---|
613 | random_element= randomElement (m, V_buf, l, fail ); |
---|
614 | DEBOUTLN (cerr, "fail= " << fail); |
---|
615 | CFList list; |
---|
616 | TIMING_START (gcd_recursion); |
---|
617 | G_random_element= |
---|
618 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
619 | list, topLevel); |
---|
620 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
621 | "time for recursive call: "); |
---|
622 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
623 | } |
---|
624 | else |
---|
625 | { |
---|
626 | CFList list; |
---|
627 | TIMING_START (gcd_recursion); |
---|
628 | G_random_element= |
---|
629 | GCD_Fp_extension (ppA(random_element, x), ppB(random_element, x), V_buf, |
---|
630 | list, topLevel); |
---|
631 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
632 | "time for recursive call: "); |
---|
633 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
634 | } |
---|
635 | |
---|
636 | if (!G_random_element.inCoeffDomain()) |
---|
637 | d0= totaldegree (G_random_element, Variable(2), |
---|
638 | Variable (G_random_element.level())); |
---|
639 | else |
---|
640 | d0= 0; |
---|
641 | |
---|
642 | if (d0 == 0) |
---|
643 | return N(gcdcAcB); |
---|
644 | if (d0 > d) |
---|
645 | { |
---|
646 | if (!find (l, random_element)) |
---|
647 | l.append (random_element); |
---|
648 | continue; |
---|
649 | } |
---|
650 | |
---|
651 | G_random_element= |
---|
652 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
653 | * G_random_element; |
---|
654 | |
---|
655 | if (!G_random_element.inCoeffDomain()) |
---|
656 | d0= totaldegree (G_random_element, Variable(2), |
---|
657 | Variable (G_random_element.level())); |
---|
658 | else |
---|
659 | d0= 0; |
---|
660 | |
---|
661 | if (d0 < d) |
---|
662 | { |
---|
663 | m= gcdlcAlcB; |
---|
664 | newtonPoly= 1; |
---|
665 | G_m= 0; |
---|
666 | d= d0; |
---|
667 | } |
---|
668 | |
---|
669 | TIMING_START (newton_interpolation); |
---|
670 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
671 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
672 | "time for newton interpolation: "); |
---|
673 | |
---|
674 | //termination test |
---|
675 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
676 | { |
---|
677 | cH= uni_content (H); |
---|
678 | ppH= H/cH; |
---|
679 | if (inextension) |
---|
680 | { |
---|
681 | CFList u, v; |
---|
682 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
683 | //mapping down |
---|
684 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
685 | { |
---|
686 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
687 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
688 | ppH /= Lc(ppH); |
---|
689 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
690 | if (compressConvexDense) |
---|
691 | ppH= decompress (ppH, MM, V); |
---|
692 | return N(gcdcAcB*ppH); |
---|
693 | } |
---|
694 | } |
---|
695 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
696 | { |
---|
697 | if (compressConvexDense) |
---|
698 | ppH= decompress (ppH, MM, V); |
---|
699 | return N(gcdcAcB*ppH); |
---|
700 | } |
---|
701 | } |
---|
702 | |
---|
703 | G_m= H; |
---|
704 | newtonPoly= newtonPoly*(x - random_element); |
---|
705 | m= m*(x - random_element); |
---|
706 | if (!find (l, random_element)) |
---|
707 | l.append (random_element); |
---|
708 | } while (1); |
---|
709 | } |
---|
710 | |
---|
711 | /// compute a random element a of GF, s.t. F(a) \f$ \neq 0 \f$ , F is a |
---|
712 | /// univariate polynomial, returns fail if there are no field elements left |
---|
713 | /// which have not been used before |
---|
714 | static inline |
---|
715 | CanonicalForm |
---|
716 | GFRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
717 | { |
---|
718 | fail= false; |
---|
719 | Variable x= F.mvar(); |
---|
720 | GFRandom genGF; |
---|
721 | CanonicalForm random; |
---|
722 | int p= getCharacteristic(); |
---|
723 | int d= getGFDegree(); |
---|
724 | int bound= ipower (p, d); |
---|
725 | do |
---|
726 | { |
---|
727 | if (list.length() == bound) |
---|
728 | { |
---|
729 | fail= true; |
---|
730 | break; |
---|
731 | } |
---|
732 | if (list.length() < 1) |
---|
733 | random= 0; |
---|
734 | else |
---|
735 | { |
---|
736 | random= genGF.generate(); |
---|
737 | while (find (list, random)) |
---|
738 | random= genGF.generate(); |
---|
739 | } |
---|
740 | if (F (random, x) == 0) |
---|
741 | { |
---|
742 | list.append (random); |
---|
743 | continue; |
---|
744 | } |
---|
745 | } while (find (list, random)); |
---|
746 | return random; |
---|
747 | } |
---|
748 | |
---|
749 | /// GCD of F and G over GF, based on Alg. 7.2. as described in "Algorithms for |
---|
750 | /// Computer Algebra" by Geddes, Czapor, Labahn |
---|
751 | /// Usually this algorithm will be faster than GCD_Fp_extension since GF has |
---|
752 | /// faster field arithmetics, however it might fail if the input is large since |
---|
753 | /// the size of the base field is bounded by 2^16, output is monic |
---|
754 | CanonicalForm GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
755 | CFList& l, bool& topLevel) |
---|
756 | { |
---|
757 | CanonicalForm A= F; |
---|
758 | CanonicalForm B= G; |
---|
759 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
760 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
761 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
762 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
763 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
764 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
765 | if (F == G) return F/Lc(F); |
---|
766 | |
---|
767 | CFMap M,N; |
---|
768 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
769 | |
---|
770 | if (best_level == 0) return B.genOne(); |
---|
771 | |
---|
772 | A= M(A); |
---|
773 | B= M(B); |
---|
774 | |
---|
775 | Variable x= Variable(1); |
---|
776 | |
---|
777 | //univariate case |
---|
778 | if (A.isUnivariate() && B.isUnivariate()) |
---|
779 | return N (gcd (A, B)); |
---|
780 | |
---|
781 | CanonicalForm cA, cB; // content of A and B |
---|
782 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
783 | CanonicalForm gcdcAcB; |
---|
784 | |
---|
785 | if (topLevel) |
---|
786 | { |
---|
787 | if (best_level <= 2) |
---|
788 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
---|
789 | else |
---|
790 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
---|
791 | } |
---|
792 | else |
---|
793 | { |
---|
794 | cA = uni_content (A); |
---|
795 | cB = uni_content (B); |
---|
796 | gcdcAcB= gcd (cA, cB); |
---|
797 | ppA= A/cA; |
---|
798 | ppB= B/cB; |
---|
799 | } |
---|
800 | |
---|
801 | int sizeNewtonPolyg; |
---|
802 | int ** newtonPolyg= NULL; |
---|
803 | mat_ZZ MM; |
---|
804 | vec_ZZ V; |
---|
805 | bool compressConvexDense= (ppA.level() == 2 && ppB.level() == 2); |
---|
806 | if (compressConvexDense) |
---|
807 | { |
---|
808 | cA= content (ppA, 1); |
---|
809 | cB= content (ppB, 1); |
---|
810 | ppA /= cA; |
---|
811 | ppB /= cB; |
---|
812 | gcdcAcB *= gcd (cA, cB); |
---|
813 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
814 | { |
---|
815 | if (ppA.level() == ppB.level()) |
---|
816 | return N (gcd (ppA, ppB)*gcdcAcB); |
---|
817 | else |
---|
818 | return N (gcdcAcB); |
---|
819 | } |
---|
820 | |
---|
821 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
822 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
823 | |
---|
824 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
825 | delete [] newtonPolyg[i]; |
---|
826 | delete [] newtonPolyg; |
---|
827 | |
---|
828 | ppA= compress (ppA, MM, V, false); |
---|
829 | ppB= compress (ppB, MM, V, false); |
---|
830 | MM= inv (MM); |
---|
831 | |
---|
832 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
833 | { |
---|
834 | if (ppA.level() == ppB.level()) |
---|
835 | return N (decompress (gcd (ppA, ppB), MM, V)*gcdcAcB); |
---|
836 | else |
---|
837 | return N (gcdcAcB); |
---|
838 | } |
---|
839 | } |
---|
840 | |
---|
841 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
842 | CanonicalForm gcdlcAlcB; |
---|
843 | |
---|
844 | lcA= uni_lcoeff (ppA); |
---|
845 | lcB= uni_lcoeff (ppB); |
---|
846 | |
---|
847 | if (fdivides (lcA, lcB)) |
---|
848 | { |
---|
849 | if (fdivides (A, B)) |
---|
850 | return F; |
---|
851 | } |
---|
852 | if (fdivides (lcB, lcA)) |
---|
853 | { |
---|
854 | if (fdivides (B, A)) |
---|
855 | return G; |
---|
856 | } |
---|
857 | |
---|
858 | gcdlcAlcB= gcd (lcA, lcB); |
---|
859 | |
---|
860 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
861 | if (d == 0) |
---|
862 | return N(gcdcAcB); |
---|
863 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
864 | if (d0 < d) |
---|
865 | d= d0; |
---|
866 | if (d == 0) |
---|
867 | return N(gcdcAcB); |
---|
868 | |
---|
869 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
870 | CanonicalForm newtonPoly; |
---|
871 | |
---|
872 | newtonPoly= 1; |
---|
873 | m= gcdlcAlcB; |
---|
874 | G_m= 0; |
---|
875 | H= 0; |
---|
876 | bool fail= false; |
---|
877 | topLevel= false; |
---|
878 | bool inextension= false; |
---|
879 | int p=-1; |
---|
880 | int k= getGFDegree(); |
---|
881 | int kk; |
---|
882 | int expon; |
---|
883 | char gf_name_buf= gf_name; |
---|
884 | do |
---|
885 | { |
---|
886 | random_element= GFRandomElement (m, l, fail); |
---|
887 | if (fail) |
---|
888 | { |
---|
889 | p= getCharacteristic(); |
---|
890 | expon= 2; |
---|
891 | kk= getGFDegree(); |
---|
892 | if (ipower (p, kk*expon) < (1 << 16)) |
---|
893 | setCharacteristic (p, kk*(int)expon, 'b'); |
---|
894 | else |
---|
895 | { |
---|
896 | expon= (int) floor((log ((double)((1<<16) - 1)))/(log((double)p)*kk)); |
---|
897 | ASSERT (expon >= 2, "not enough points in GCD_GF"); |
---|
898 | setCharacteristic (p, (int)(kk*expon), 'b'); |
---|
899 | } |
---|
900 | inextension= true; |
---|
901 | fail= false; |
---|
902 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
903 | i.getItem()= GFMapUp (i.getItem(), kk); |
---|
904 | m= GFMapUp (m, kk); |
---|
905 | G_m= GFMapUp (G_m, kk); |
---|
906 | newtonPoly= GFMapUp (newtonPoly, kk); |
---|
907 | ppA= GFMapUp (ppA, kk); |
---|
908 | ppB= GFMapUp (ppB, kk); |
---|
909 | gcdlcAlcB= GFMapUp (gcdlcAlcB, kk); |
---|
910 | random_element= GFRandomElement (m, l, fail); |
---|
911 | DEBOUTLN (cerr, "fail= " << fail); |
---|
912 | CFList list; |
---|
913 | TIMING_START (gcd_recursion); |
---|
914 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
915 | list, topLevel); |
---|
916 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
917 | "time for recursive call: "); |
---|
918 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
919 | } |
---|
920 | else |
---|
921 | { |
---|
922 | CFList list; |
---|
923 | TIMING_START (gcd_recursion); |
---|
924 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
925 | list, topLevel); |
---|
926 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
927 | "time for recursive call: "); |
---|
928 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
929 | } |
---|
930 | |
---|
931 | if (!G_random_element.inCoeffDomain()) |
---|
932 | d0= totaldegree (G_random_element, Variable(2), |
---|
933 | Variable (G_random_element.level())); |
---|
934 | else |
---|
935 | d0= 0; |
---|
936 | |
---|
937 | if (d0 == 0) |
---|
938 | { |
---|
939 | if (inextension) |
---|
940 | setCharacteristic (p, k, gf_name_buf); |
---|
941 | return N(gcdcAcB); |
---|
942 | } |
---|
943 | if (d0 > d) |
---|
944 | { |
---|
945 | if (!find (l, random_element)) |
---|
946 | l.append (random_element); |
---|
947 | continue; |
---|
948 | } |
---|
949 | |
---|
950 | G_random_element= |
---|
951 | (gcdlcAlcB(random_element, x)/uni_lcoeff(G_random_element)) * |
---|
952 | G_random_element; |
---|
953 | if (!G_random_element.inCoeffDomain()) |
---|
954 | d0= totaldegree (G_random_element, Variable(2), |
---|
955 | Variable (G_random_element.level())); |
---|
956 | else |
---|
957 | d0= 0; |
---|
958 | |
---|
959 | if (d0 < d) |
---|
960 | { |
---|
961 | m= gcdlcAlcB; |
---|
962 | newtonPoly= 1; |
---|
963 | G_m= 0; |
---|
964 | d= d0; |
---|
965 | } |
---|
966 | |
---|
967 | TIMING_START (newton_interpolation); |
---|
968 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
969 | TIMING_END_AND_PRINT (newton_interpolation, "time for newton interpolation: "); |
---|
970 | |
---|
971 | //termination test |
---|
972 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
973 | { |
---|
974 | cH= uni_content (H); |
---|
975 | ppH= H/cH; |
---|
976 | if (inextension) |
---|
977 | { |
---|
978 | if (fdivides(ppH, ppA) && fdivides(ppH, ppB)) |
---|
979 | { |
---|
980 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
981 | ppH= GFMapDown (ppH, k); |
---|
982 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
983 | if (compressConvexDense) |
---|
984 | ppH= decompress (ppH, MM, V); |
---|
985 | setCharacteristic (p, k, gf_name_buf); |
---|
986 | return N(gcdcAcB*ppH); |
---|
987 | } |
---|
988 | } |
---|
989 | else |
---|
990 | { |
---|
991 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
992 | { |
---|
993 | if (compressConvexDense) |
---|
994 | ppH= decompress (ppH, MM, V); |
---|
995 | return N(gcdcAcB*ppH); |
---|
996 | } |
---|
997 | } |
---|
998 | } |
---|
999 | |
---|
1000 | G_m= H; |
---|
1001 | newtonPoly= newtonPoly*(x - random_element); |
---|
1002 | m= m*(x - random_element); |
---|
1003 | if (!find (l, random_element)) |
---|
1004 | l.append (random_element); |
---|
1005 | } while (1); |
---|
1006 | } |
---|
1007 | |
---|
1008 | /// F is assumed to be an univariate polynomial in x, |
---|
1009 | /// computes a random monic irreducible univariate polynomial of random |
---|
1010 | /// degree < i in x which does not divide F |
---|
1011 | CanonicalForm |
---|
1012 | randomIrredpoly (int i, const Variable & x) |
---|
1013 | { |
---|
1014 | int p= getCharacteristic(); |
---|
1015 | ZZ NTLp= to_ZZ (p); |
---|
1016 | ZZ_p::init (NTLp); |
---|
1017 | ZZ_pX NTLirredpoly; |
---|
1018 | CanonicalForm CFirredpoly; |
---|
1019 | BuildIrred (NTLirredpoly, i + 1); |
---|
1020 | CFirredpoly= convertNTLZZpX2CF (NTLirredpoly, x); |
---|
1021 | return CFirredpoly; |
---|
1022 | } |
---|
1023 | |
---|
1024 | static inline |
---|
1025 | CanonicalForm |
---|
1026 | FpRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
1027 | { |
---|
1028 | fail= false; |
---|
1029 | Variable x= F.mvar(); |
---|
1030 | FFRandom genFF; |
---|
1031 | CanonicalForm random; |
---|
1032 | int p= getCharacteristic(); |
---|
1033 | int bound= p; |
---|
1034 | do |
---|
1035 | { |
---|
1036 | if (list.length() == bound) |
---|
1037 | { |
---|
1038 | fail= true; |
---|
1039 | break; |
---|
1040 | } |
---|
1041 | if (list.length() < 1) |
---|
1042 | random= 0; |
---|
1043 | else |
---|
1044 | { |
---|
1045 | random= genFF.generate(); |
---|
1046 | while (find (list, random)) |
---|
1047 | random= genFF.generate(); |
---|
1048 | } |
---|
1049 | if (F (random, x) == 0) |
---|
1050 | { |
---|
1051 | list.append (random); |
---|
1052 | continue; |
---|
1053 | } |
---|
1054 | } while (find (list, random)); |
---|
1055 | return random; |
---|
1056 | } |
---|
1057 | |
---|
1058 | CanonicalForm GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1059 | bool& topLevel, CFList& l) |
---|
1060 | { |
---|
1061 | CanonicalForm A= F; |
---|
1062 | CanonicalForm B= G; |
---|
1063 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
1064 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
1065 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
1066 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
1067 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
1068 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
1069 | if (F == G) return F/Lc(F); |
---|
1070 | |
---|
1071 | CFMap M,N; |
---|
1072 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
1073 | |
---|
1074 | if (best_level == 0) return B.genOne(); |
---|
1075 | |
---|
1076 | A= M(A); |
---|
1077 | B= M(B); |
---|
1078 | |
---|
1079 | Variable x= Variable (1); |
---|
1080 | |
---|
1081 | //univariate case |
---|
1082 | if (A.isUnivariate() && B.isUnivariate()) |
---|
1083 | return N (gcd (A, B)); |
---|
1084 | |
---|
1085 | CanonicalForm cA, cB; // content of A and B |
---|
1086 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
1087 | CanonicalForm gcdcAcB; |
---|
1088 | |
---|
1089 | if (topLevel) |
---|
1090 | { |
---|
1091 | if (best_level <= 2) |
---|
1092 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
---|
1093 | else |
---|
1094 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
---|
1095 | } |
---|
1096 | else |
---|
1097 | { |
---|
1098 | cA = uni_content (A); |
---|
1099 | cB = uni_content (B); |
---|
1100 | gcdcAcB= gcd (cA, cB); |
---|
1101 | ppA= A/cA; |
---|
1102 | ppB= B/cB; |
---|
1103 | } |
---|
1104 | |
---|
1105 | int sizeNewtonPolyg; |
---|
1106 | int ** newtonPolyg= NULL; |
---|
1107 | mat_ZZ MM; |
---|
1108 | vec_ZZ V; |
---|
1109 | bool compressConvexDense= (ppA.level() == 2 && ppB.level() == 2); |
---|
1110 | if (compressConvexDense) |
---|
1111 | { |
---|
1112 | cA= content (ppA, 1); |
---|
1113 | cB= content (ppB, 1); |
---|
1114 | ppA /= cA; |
---|
1115 | ppB /= cB; |
---|
1116 | gcdcAcB *= gcd (cA, cB); |
---|
1117 | if (ppA.isUnivariate() || ppB.isUnivariate()) |
---|
1118 | { |
---|
1119 | if (ppA.level() == ppB.level()) |
---|
1120 | return N (gcd (ppA, ppB)*gcdcAcB); |
---|
1121 | else |
---|
1122 | return N (gcdcAcB); |
---|
1123 | } |
---|
1124 | |
---|
1125 | newtonPolyg= newtonPolygon (ppA,ppB, sizeNewtonPolyg); |
---|
1126 | convexDense (newtonPolyg, sizeNewtonPolyg, MM, V); |
---|
1127 | |
---|
1128 | for (int i= 0; i < sizeNewtonPolyg; i++) |
---|
1129 | delete [] newtonPolyg[i]; |
---|
1130 | delete [] newtonPolyg; |
---|
1131 | |
---|
1132 | ppA= compress (ppA, MM, V, false); |
---|
1133 | ppB= compress (ppB, MM, V, false); |
---|
1134 | MM= inv (MM); |
---|
1135 | |
---|
1136 | if (ppA.isUnivariate() && ppB.isUnivariate()) |
---|
1137 | { |
---|
1138 | if (ppA.level() == ppB.level()) |
---|
1139 | return N (decompress (gcd (ppA, ppB), MM, V)*gcdcAcB); |
---|
1140 | else |
---|
1141 | return N (gcdcAcB); |
---|
1142 | } |
---|
1143 | } |
---|
1144 | |
---|
1145 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
1146 | CanonicalForm gcdlcAlcB; |
---|
1147 | lcA= uni_lcoeff (ppA); |
---|
1148 | lcB= uni_lcoeff (ppB); |
---|
1149 | |
---|
1150 | if (fdivides (lcA, lcB)) |
---|
1151 | { |
---|
1152 | if (fdivides (A, B)) |
---|
1153 | return F/Lc(F); |
---|
1154 | } |
---|
1155 | if (fdivides (lcB, lcA)) |
---|
1156 | { |
---|
1157 | if (fdivides (B, A)) |
---|
1158 | return G/Lc(G); |
---|
1159 | } |
---|
1160 | |
---|
1161 | gcdlcAlcB= gcd (lcA, lcB); |
---|
1162 | |
---|
1163 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
1164 | int d0; |
---|
1165 | |
---|
1166 | if (d == 0) |
---|
1167 | return N(gcdcAcB); |
---|
1168 | |
---|
1169 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
1170 | |
---|
1171 | if (d0 < d) |
---|
1172 | d= d0; |
---|
1173 | |
---|
1174 | if (d == 0) |
---|
1175 | return N(gcdcAcB); |
---|
1176 | |
---|
1177 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
1178 | CanonicalForm newtonPoly= 1; |
---|
1179 | m= gcdlcAlcB; |
---|
1180 | H= 0; |
---|
1181 | G_m= 0; |
---|
1182 | Variable alpha, V_buf; |
---|
1183 | bool fail= false; |
---|
1184 | bool inextension= false; |
---|
1185 | bool inextensionextension= false; |
---|
1186 | topLevel= false; |
---|
1187 | CFList source, dest; |
---|
1188 | do |
---|
1189 | { |
---|
1190 | if (inextension) |
---|
1191 | random_element= randomElement (m, V_buf, l, fail); |
---|
1192 | else |
---|
1193 | random_element= FpRandomElement (m, l, fail); |
---|
1194 | |
---|
1195 | if (!fail && !inextension) |
---|
1196 | { |
---|
1197 | CFList list; |
---|
1198 | TIMING_START (gcd_recursion); |
---|
1199 | G_random_element= |
---|
1200 | GCD_small_p (ppA (random_element,x), ppB (random_element,x), topLevel, |
---|
1201 | list); |
---|
1202 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1203 | "time for recursive call: "); |
---|
1204 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1205 | } |
---|
1206 | else if (!fail && inextension) |
---|
1207 | { |
---|
1208 | CFList list; |
---|
1209 | TIMING_START (gcd_recursion); |
---|
1210 | G_random_element= |
---|
1211 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
1212 | list, topLevel); |
---|
1213 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1214 | "time for recursive call: "); |
---|
1215 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1216 | } |
---|
1217 | else if (fail && !inextension) |
---|
1218 | { |
---|
1219 | source= CFList(); |
---|
1220 | dest= CFList(); |
---|
1221 | CFList list; |
---|
1222 | CanonicalForm mipo; |
---|
1223 | int deg= 2; |
---|
1224 | do { |
---|
1225 | mipo= randomIrredpoly (deg, x); |
---|
1226 | alpha= rootOf (mipo); |
---|
1227 | inextension= true; |
---|
1228 | fail= false; |
---|
1229 | random_element= randomElement (m, alpha, l, fail); |
---|
1230 | deg++; |
---|
1231 | } while (fail); |
---|
1232 | list= CFList(); |
---|
1233 | V_buf= alpha; |
---|
1234 | TIMING_START (gcd_recursion); |
---|
1235 | G_random_element= |
---|
1236 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
1237 | list, topLevel); |
---|
1238 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1239 | "time for recursive call: "); |
---|
1240 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1241 | } |
---|
1242 | else if (fail && inextension) |
---|
1243 | { |
---|
1244 | source= CFList(); |
---|
1245 | dest= CFList(); |
---|
1246 | |
---|
1247 | Variable V_buf3= V_buf; |
---|
1248 | V_buf= chooseExtension (V_buf); |
---|
1249 | bool prim_fail= false; |
---|
1250 | Variable V_buf2; |
---|
1251 | CanonicalForm prim_elem, im_prim_elem; |
---|
1252 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
1253 | |
---|
1254 | if (V_buf3 != alpha) |
---|
1255 | { |
---|
1256 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1257 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1258 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
1259 | source, dest); |
---|
1260 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1261 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
1262 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
1263 | dest); |
---|
1264 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1265 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
1266 | source, dest); |
---|
1267 | } |
---|
1268 | |
---|
1269 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
1270 | if (prim_fail) |
---|
1271 | ; //ERROR |
---|
1272 | else |
---|
1273 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
1274 | |
---|
1275 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
1276 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
1277 | |
---|
1278 | inextensionextension= true; |
---|
1279 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1280 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
1281 | im_prim_elem, source, dest); |
---|
1282 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1283 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1284 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1285 | source, dest); |
---|
1286 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1287 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1288 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1289 | source, dest); |
---|
1290 | fail= false; |
---|
1291 | random_element= randomElement (m, V_buf, l, fail ); |
---|
1292 | DEBOUTLN (cerr, "fail= " << fail); |
---|
1293 | CFList list; |
---|
1294 | TIMING_START (gcd_recursion); |
---|
1295 | G_random_element= |
---|
1296 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
1297 | list, topLevel); |
---|
1298 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1299 | "time for recursive call: "); |
---|
1300 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1301 | } |
---|
1302 | |
---|
1303 | if (!G_random_element.inCoeffDomain()) |
---|
1304 | d0= totaldegree (G_random_element, Variable(2), |
---|
1305 | Variable (G_random_element.level())); |
---|
1306 | else |
---|
1307 | d0= 0; |
---|
1308 | |
---|
1309 | if (d0 == 0) |
---|
1310 | return N(gcdcAcB); |
---|
1311 | if (d0 > d) |
---|
1312 | { |
---|
1313 | if (!find (l, random_element)) |
---|
1314 | l.append (random_element); |
---|
1315 | continue; |
---|
1316 | } |
---|
1317 | |
---|
1318 | G_random_element= (gcdlcAlcB(random_element,x)/uni_lcoeff(G_random_element)) |
---|
1319 | *G_random_element; |
---|
1320 | |
---|
1321 | |
---|
1322 | if (!G_random_element.inCoeffDomain()) |
---|
1323 | d0= totaldegree (G_random_element, Variable(2), |
---|
1324 | Variable (G_random_element.level())); |
---|
1325 | else |
---|
1326 | d0= 0; |
---|
1327 | |
---|
1328 | if (d0 < d) |
---|
1329 | { |
---|
1330 | m= gcdlcAlcB; |
---|
1331 | newtonPoly= 1; |
---|
1332 | G_m= 0; |
---|
1333 | d= d0; |
---|
1334 | } |
---|
1335 | |
---|
1336 | TIMING_START (newton_interpolation); |
---|
1337 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
1338 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
1339 | "time for newton_interpolation: "); |
---|
1340 | |
---|
1341 | //termination test |
---|
1342 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
1343 | { |
---|
1344 | cH= uni_content (H); |
---|
1345 | ppH= H/cH; |
---|
1346 | ppH /= Lc (ppH); |
---|
1347 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
1348 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
1349 | { |
---|
1350 | if (compressConvexDense) |
---|
1351 | ppH= decompress (ppH, MM, V); |
---|
1352 | return N(gcdcAcB*ppH); |
---|
1353 | } |
---|
1354 | } |
---|
1355 | |
---|
1356 | G_m= H; |
---|
1357 | newtonPoly= newtonPoly*(x - random_element); |
---|
1358 | m= m*(x - random_element); |
---|
1359 | if (!find (l, random_element)) |
---|
1360 | l.append (random_element); |
---|
1361 | } while (1); |
---|
1362 | } |
---|
1363 | |
---|
1364 | CFArray |
---|
1365 | solveVandermonde (const CFArray& M, const CFArray& A) |
---|
1366 | { |
---|
1367 | int r= M.size(); |
---|
1368 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
1369 | |
---|
1370 | if (r == 1) |
---|
1371 | { |
---|
1372 | CFArray result= CFArray (1); |
---|
1373 | result [0]= A [0] / M [0]; |
---|
1374 | return result; |
---|
1375 | } |
---|
1376 | // check solvability |
---|
1377 | bool notDistinct= false; |
---|
1378 | for (int i= 0; i < r - 1; i++) |
---|
1379 | { |
---|
1380 | for (int j= i + 1; j < r; j++) |
---|
1381 | { |
---|
1382 | if (M [i] == M [j]) |
---|
1383 | { |
---|
1384 | notDistinct= true; |
---|
1385 | break; |
---|
1386 | } |
---|
1387 | } |
---|
1388 | } |
---|
1389 | if (notDistinct) |
---|
1390 | return CFArray(); |
---|
1391 | |
---|
1392 | CanonicalForm master= 1; |
---|
1393 | Variable x= Variable (1); |
---|
1394 | for (int i= 0; i < r; i++) |
---|
1395 | master *= x - M [i]; |
---|
1396 | CFList Pj; |
---|
1397 | CanonicalForm tmp; |
---|
1398 | for (int i= 0; i < r; i++) |
---|
1399 | { |
---|
1400 | tmp= master/(x - M [i]); |
---|
1401 | tmp /= tmp (M [i], 1); |
---|
1402 | Pj.append (tmp); |
---|
1403 | } |
---|
1404 | CFArray result= CFArray (r); |
---|
1405 | |
---|
1406 | CFListIterator j= Pj; |
---|
1407 | for (int i= 1; i <= r; i++, j++) |
---|
1408 | { |
---|
1409 | tmp= 0; |
---|
1410 | for (int l= 0; l < A.size(); l++) |
---|
1411 | tmp += A[l]*j.getItem()[l]; |
---|
1412 | result[i - 1]= tmp; |
---|
1413 | } |
---|
1414 | return result; |
---|
1415 | } |
---|
1416 | |
---|
1417 | CFArray |
---|
1418 | solveGeneralVandermonde (const CFArray& M, const CFArray& A) |
---|
1419 | { |
---|
1420 | int r= M.size(); |
---|
1421 | ASSERT (A.size() == r, "vector does not have right size"); |
---|
1422 | if (r == 1) |
---|
1423 | { |
---|
1424 | CFArray result= CFArray (1); |
---|
1425 | result [0]= A[0] / M [0]; |
---|
1426 | return result; |
---|
1427 | } |
---|
1428 | // check solvability |
---|
1429 | bool notDistinct= false; |
---|
1430 | for (int i= 0; i < r - 1; i++) |
---|
1431 | { |
---|
1432 | for (int j= i + 1; j < r; j++) |
---|
1433 | { |
---|
1434 | if (M [i] == M [j]) |
---|
1435 | { |
---|
1436 | notDistinct= true; |
---|
1437 | break; |
---|
1438 | } |
---|
1439 | } |
---|
1440 | } |
---|
1441 | if (notDistinct) |
---|
1442 | return CFArray(); |
---|
1443 | |
---|
1444 | CanonicalForm master= 1; |
---|
1445 | Variable x= Variable (1); |
---|
1446 | for (int i= 0; i < r; i++) |
---|
1447 | master *= x - M [i]; |
---|
1448 | master *= x; |
---|
1449 | CFList Pj; |
---|
1450 | CanonicalForm tmp; |
---|
1451 | for (int i= 0; i < r; i++) |
---|
1452 | { |
---|
1453 | tmp= master/(x - M [i]); |
---|
1454 | tmp /= tmp (M [i], 1); |
---|
1455 | Pj.append (tmp); |
---|
1456 | } |
---|
1457 | |
---|
1458 | CFArray result= CFArray (r); |
---|
1459 | |
---|
1460 | CFListIterator j= Pj; |
---|
1461 | for (int i= 1; i <= r; i++, j++) |
---|
1462 | { |
---|
1463 | tmp= 0; |
---|
1464 | |
---|
1465 | for (int l= 1; l <= A.size(); l++) |
---|
1466 | tmp += A[l - 1]*j.getItem()[l]; |
---|
1467 | result[i - 1]= tmp; |
---|
1468 | } |
---|
1469 | return result; |
---|
1470 | } |
---|
1471 | |
---|
1472 | /// M in row echolon form, rk rank of M |
---|
1473 | CFArray |
---|
1474 | readOffSolution (const CFMatrix& M, const long rk) |
---|
1475 | { |
---|
1476 | CFArray result= CFArray (rk); |
---|
1477 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1478 | for (int i= rk; i >= 1; i--) |
---|
1479 | { |
---|
1480 | tmp3= 0; |
---|
1481 | tmp1= M (i, M.columns()); |
---|
1482 | for (int j= M.columns() - 1; j >= 1; j--) |
---|
1483 | { |
---|
1484 | tmp2= M (i, j); |
---|
1485 | if (j == i) |
---|
1486 | break; |
---|
1487 | else |
---|
1488 | tmp3 += tmp2*result[j - 1]; |
---|
1489 | } |
---|
1490 | result[i - 1]= (tmp1 - tmp3)/tmp2; |
---|
1491 | } |
---|
1492 | return result; |
---|
1493 | } |
---|
1494 | |
---|
1495 | CFArray |
---|
1496 | readOffSolution (const CFMatrix& M, const CFArray& L, const CFArray& partialSol) |
---|
1497 | { |
---|
1498 | CFArray result= CFArray (M.rows()); |
---|
1499 | CanonicalForm tmp1, tmp2, tmp3; |
---|
1500 | int k; |
---|
1501 | for (int i= M.rows(); i >= 1; i--) |
---|
1502 | { |
---|
1503 | tmp3= 0; |
---|
1504 | tmp1= L[i - 1]; |
---|
1505 | k= 0; |
---|
1506 | for (int j= M.columns(); j >= 1; j--, k++) |
---|
1507 | { |
---|
1508 | tmp2= M (i, j); |
---|
1509 | if (j == i) |
---|
1510 | break; |
---|
1511 | else |
---|
1512 | { |
---|
1513 | if (k > partialSol.size() - 1) |
---|
1514 | tmp3 += tmp2*result[j - 1]; |
---|
1515 | else |
---|
1516 | tmp3 += tmp2*partialSol[partialSol.size() - k - 1]; |
---|
1517 | } |
---|
1518 | } |
---|
1519 | result [i - 1]= (tmp1 - tmp3)/tmp2; |
---|
1520 | } |
---|
1521 | return result; |
---|
1522 | } |
---|
1523 | |
---|
1524 | long |
---|
1525 | gaussianElimFp (CFMatrix& M, CFArray& L) |
---|
1526 | { |
---|
1527 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1528 | CFMatrix *N; |
---|
1529 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1530 | |
---|
1531 | for (int i= 1; i <= M.rows(); i++) |
---|
1532 | for (int j= 1; j <= M.columns(); j++) |
---|
1533 | (*N) (i, j)= M (i, j); |
---|
1534 | |
---|
1535 | int j= 1; |
---|
1536 | for (int i= 0; i < L.size(); i++, j++) |
---|
1537 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1538 | int p= getCharacteristic (); |
---|
1539 | zz_p::init (p); |
---|
1540 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
1541 | long rk= gauss (*NTLN); |
---|
1542 | |
---|
1543 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
1544 | |
---|
1545 | L= CFArray (M.rows()); |
---|
1546 | for (int i= 0; i < M.rows(); i++) |
---|
1547 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
1548 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
1549 | delete N; |
---|
1550 | return rk; |
---|
1551 | } |
---|
1552 | |
---|
1553 | long |
---|
1554 | gaussianElimFq (CFMatrix& M, CFArray& L, const Variable& alpha) |
---|
1555 | { |
---|
1556 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1557 | CFMatrix *N; |
---|
1558 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1559 | |
---|
1560 | for (int i= 1; i <= M.rows(); i++) |
---|
1561 | for (int j= 1; j <= M.columns(); j++) |
---|
1562 | (*N) (i, j)= M (i, j); |
---|
1563 | |
---|
1564 | int j= 1; |
---|
1565 | for (int i= 0; i < L.size(); i++, j++) |
---|
1566 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1567 | int p= getCharacteristic (); |
---|
1568 | zz_p::init (p); |
---|
1569 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1570 | zz_pE::init (NTLMipo); |
---|
1571 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
1572 | long rk= gauss (*NTLN); |
---|
1573 | |
---|
1574 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
1575 | |
---|
1576 | M= (*N) (1, M.rows(), 1, M.columns()); |
---|
1577 | L= CFArray (M.rows()); |
---|
1578 | for (int i= 0; i < M.rows(); i++) |
---|
1579 | L[i]= (*N) (i + 1, M.columns() + 1); |
---|
1580 | |
---|
1581 | delete N; |
---|
1582 | return rk; |
---|
1583 | } |
---|
1584 | |
---|
1585 | CFArray |
---|
1586 | solveSystemFp (const CFMatrix& M, const CFArray& L) |
---|
1587 | { |
---|
1588 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1589 | CFMatrix *N; |
---|
1590 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1591 | |
---|
1592 | for (int i= 1; i <= M.rows(); i++) |
---|
1593 | for (int j= 1; j <= M.columns(); j++) |
---|
1594 | (*N) (i, j)= M (i, j); |
---|
1595 | |
---|
1596 | int j= 1; |
---|
1597 | for (int i= 0; i < L.size(); i++, j++) |
---|
1598 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1599 | int p= getCharacteristic (); |
---|
1600 | zz_p::init (p); |
---|
1601 | mat_zz_p *NTLN= convertFacCFMatrix2NTLmat_zz_p(*N); |
---|
1602 | long rk= gauss (*NTLN); |
---|
1603 | if (rk != M.columns()) |
---|
1604 | { |
---|
1605 | delete N; |
---|
1606 | return CFArray(); |
---|
1607 | } |
---|
1608 | N= convertNTLmat_zz_p2FacCFMatrix (*NTLN); |
---|
1609 | |
---|
1610 | CFArray A= readOffSolution (*N, rk); |
---|
1611 | |
---|
1612 | delete N; |
---|
1613 | return A; |
---|
1614 | } |
---|
1615 | |
---|
1616 | CFArray |
---|
1617 | solveSystemFq (const CFMatrix& M, const CFArray& L, const Variable& alpha) |
---|
1618 | { |
---|
1619 | ASSERT (L.size() <= M.rows(), "dimension exceeded"); |
---|
1620 | CFMatrix *N; |
---|
1621 | N= new CFMatrix (M.rows(), M.columns() + 1); |
---|
1622 | |
---|
1623 | for (int i= 1; i <= M.rows(); i++) |
---|
1624 | for (int j= 1; j <= M.columns(); j++) |
---|
1625 | (*N) (i, j)= M (i, j); |
---|
1626 | int j= 1; |
---|
1627 | for (int i= 0; i < L.size(); i++, j++) |
---|
1628 | (*N) (j, M.columns() + 1)= L[i]; |
---|
1629 | int p= getCharacteristic (); |
---|
1630 | zz_p::init (p); |
---|
1631 | zz_pX NTLMipo= convertFacCF2NTLzzpX (getMipo (alpha)); |
---|
1632 | zz_pE::init (NTLMipo); |
---|
1633 | mat_zz_pE *NTLN= convertFacCFMatrix2NTLmat_zz_pE(*N); |
---|
1634 | long rk= gauss (*NTLN); |
---|
1635 | if (rk != M.columns()) |
---|
1636 | { |
---|
1637 | delete N; |
---|
1638 | return CFArray(); |
---|
1639 | } |
---|
1640 | N= convertNTLmat_zz_pE2FacCFMatrix (*NTLN, alpha); |
---|
1641 | |
---|
1642 | CFArray A= readOffSolution (*N, rk); |
---|
1643 | |
---|
1644 | delete N; |
---|
1645 | return A; |
---|
1646 | } |
---|
1647 | #endif |
---|
1648 | |
---|
1649 | CFArray |
---|
1650 | getMonoms (const CanonicalForm& F) |
---|
1651 | { |
---|
1652 | if (F.inCoeffDomain()) |
---|
1653 | { |
---|
1654 | CFArray result= CFArray (1); |
---|
1655 | result [0]= 1; |
---|
1656 | return result; |
---|
1657 | } |
---|
1658 | if (F.isUnivariate()) |
---|
1659 | { |
---|
1660 | CFArray result= CFArray (size(F)); |
---|
1661 | int j= 0; |
---|
1662 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
1663 | result[j]= power (F.mvar(), i.exp()); |
---|
1664 | return result; |
---|
1665 | } |
---|
1666 | int numMon= size (F); |
---|
1667 | CFArray result= CFArray (numMon); |
---|
1668 | int j= 0; |
---|
1669 | CFArray recResult; |
---|
1670 | Variable x= F.mvar(); |
---|
1671 | CanonicalForm powX; |
---|
1672 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
1673 | { |
---|
1674 | powX= power (x, i.exp()); |
---|
1675 | recResult= getMonoms (i.coeff()); |
---|
1676 | for (int k= 0; k < recResult.size(); k++) |
---|
1677 | result[j+k]= powX*recResult[k]; |
---|
1678 | j += recResult.size(); |
---|
1679 | } |
---|
1680 | return result; |
---|
1681 | } |
---|
1682 | |
---|
1683 | #ifdef HAVE_NTL |
---|
1684 | CFArray |
---|
1685 | evaluateMonom (const CanonicalForm& F, const CFList& evalPoints) |
---|
1686 | { |
---|
1687 | if (F.inCoeffDomain()) |
---|
1688 | { |
---|
1689 | CFArray result= CFArray (1); |
---|
1690 | result [0]= F; |
---|
1691 | return result; |
---|
1692 | } |
---|
1693 | if (F.isUnivariate()) |
---|
1694 | { |
---|
1695 | ASSERT (evalPoints.length() == 1, |
---|
1696 | "expected an eval point with only one component"); |
---|
1697 | CFArray result= CFArray (size(F)); |
---|
1698 | int j= 0; |
---|
1699 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
1700 | for (CFIterator i= F; i.hasTerms(); i++, j++) |
---|
1701 | result[j]= power (evalPoint, i.exp()); |
---|
1702 | return result; |
---|
1703 | } |
---|
1704 | int numMon= size (F); |
---|
1705 | CFArray result= CFArray (numMon); |
---|
1706 | int j= 0; |
---|
1707 | CanonicalForm evalPoint= evalPoints.getLast(); |
---|
1708 | CFList buf= evalPoints; |
---|
1709 | buf.removeLast(); |
---|
1710 | CFArray recResult; |
---|
1711 | CanonicalForm powEvalPoint; |
---|
1712 | for (CFIterator i= F; i.hasTerms(); i++) |
---|
1713 | { |
---|
1714 | powEvalPoint= power (evalPoint, i.exp()); |
---|
1715 | recResult= evaluateMonom (i.coeff(), buf); |
---|
1716 | for (int k= 0; k < recResult.size(); k++) |
---|
1717 | result[j+k]= powEvalPoint*recResult[k]; |
---|
1718 | j += recResult.size(); |
---|
1719 | } |
---|
1720 | return result; |
---|
1721 | } |
---|
1722 | |
---|
1723 | CFArray |
---|
1724 | evaluate (const CFArray& A, const CFList& evalPoints) |
---|
1725 | { |
---|
1726 | CFArray result= A.size(); |
---|
1727 | CanonicalForm tmp; |
---|
1728 | int k; |
---|
1729 | for (int i= 0; i < A.size(); i++) |
---|
1730 | { |
---|
1731 | tmp= A[i]; |
---|
1732 | k= 1; |
---|
1733 | for (CFListIterator j= evalPoints; j.hasItem(); j++, k++) |
---|
1734 | tmp= tmp (j.getItem(), k); |
---|
1735 | result[i]= tmp; |
---|
1736 | } |
---|
1737 | return result; |
---|
1738 | } |
---|
1739 | |
---|
1740 | CFList |
---|
1741 | evaluationPoints (const CanonicalForm& F, const CanonicalForm& G, |
---|
1742 | CanonicalForm& Feval, CanonicalForm& Geval, |
---|
1743 | const CanonicalForm& LCF, const bool& GF, |
---|
1744 | const Variable& alpha, bool& fail, CFList& list |
---|
1745 | ) |
---|
1746 | { |
---|
1747 | int k= tmax (F.level(), G.level()) - 1; |
---|
1748 | Variable x= Variable (1); |
---|
1749 | CFList result; |
---|
1750 | FFRandom genFF; |
---|
1751 | GFRandom genGF; |
---|
1752 | int p= getCharacteristic (); |
---|
1753 | int bound; |
---|
1754 | if (alpha != Variable (1)) |
---|
1755 | { |
---|
1756 | bound= ipower (p, degree (getMipo(alpha))); |
---|
1757 | bound= ipower (bound, k); |
---|
1758 | } |
---|
1759 | else if (GF) |
---|
1760 | { |
---|
1761 | bound= ipower (p, getGFDegree()); |
---|
1762 | bound= ipower (bound, k); |
---|
1763 | } |
---|
1764 | else |
---|
1765 | bound= ipower (p, k); |
---|
1766 | |
---|
1767 | CanonicalForm random; |
---|
1768 | int j; |
---|
1769 | bool zeroOneOccured= false; |
---|
1770 | bool allEqual= false; |
---|
1771 | CanonicalForm buf; |
---|
1772 | do |
---|
1773 | { |
---|
1774 | random= 0; |
---|
1775 | // possible overflow if list.length() does not fit into a int |
---|
1776 | if (list.length() >= bound) |
---|
1777 | { |
---|
1778 | fail= true; |
---|
1779 | break; |
---|
1780 | } |
---|
1781 | for (int i= 0; i < k; i++) |
---|
1782 | { |
---|
1783 | if (GF) |
---|
1784 | { |
---|
1785 | result.append (genGF.generate()); |
---|
1786 | random += result.getLast()*power (x, i); |
---|
1787 | } |
---|
1788 | else if (alpha.level() != 1) |
---|
1789 | { |
---|
1790 | AlgExtRandomF genAlgExt (alpha); |
---|
1791 | result.append (genAlgExt.generate()); |
---|
1792 | random += result.getLast()*power (x, i); |
---|
1793 | } |
---|
1794 | else |
---|
1795 | { |
---|
1796 | result.append (genFF.generate()); |
---|
1797 | random += result.getLast()*power (x, i); |
---|
1798 | } |
---|
1799 | if (result.getLast().isOne() || result.getLast().isZero()) |
---|
1800 | zeroOneOccured= true; |
---|
1801 | } |
---|
1802 | if (find (list, random)) |
---|
1803 | { |
---|
1804 | zeroOneOccured= false; |
---|
1805 | allEqual= false; |
---|
1806 | result= CFList(); |
---|
1807 | continue; |
---|
1808 | } |
---|
1809 | if (zeroOneOccured) |
---|
1810 | { |
---|
1811 | list.append (random); |
---|
1812 | zeroOneOccured= false; |
---|
1813 | allEqual= false; |
---|
1814 | result= CFList(); |
---|
1815 | continue; |
---|
1816 | } |
---|
1817 | // no zero at this point |
---|
1818 | if (k > 1) |
---|
1819 | { |
---|
1820 | allEqual= true; |
---|
1821 | CFIterator iter= random; |
---|
1822 | buf= iter.coeff(); |
---|
1823 | iter++; |
---|
1824 | for (; iter.hasTerms(); iter++) |
---|
1825 | if (buf != iter.coeff()) |
---|
1826 | allEqual= false; |
---|
1827 | } |
---|
1828 | if (allEqual) |
---|
1829 | { |
---|
1830 | list.append (random); |
---|
1831 | allEqual= false; |
---|
1832 | zeroOneOccured= false; |
---|
1833 | result= CFList(); |
---|
1834 | continue; |
---|
1835 | } |
---|
1836 | |
---|
1837 | Feval= F; |
---|
1838 | Geval= G; |
---|
1839 | CanonicalForm LCeval= LCF; |
---|
1840 | j= 1; |
---|
1841 | for (CFListIterator i= result; i.hasItem(); i++, j++) |
---|
1842 | { |
---|
1843 | Feval= Feval (i.getItem(), j); |
---|
1844 | Geval= Geval (i.getItem(), j); |
---|
1845 | LCeval= LCeval (i.getItem(), j); |
---|
1846 | } |
---|
1847 | |
---|
1848 | if (LCeval.isZero()) |
---|
1849 | { |
---|
1850 | if (!find (list, random)) |
---|
1851 | list.append (random); |
---|
1852 | zeroOneOccured= false; |
---|
1853 | allEqual= false; |
---|
1854 | result= CFList(); |
---|
1855 | continue; |
---|
1856 | } |
---|
1857 | |
---|
1858 | if (list.length() >= bound) |
---|
1859 | { |
---|
1860 | fail= true; |
---|
1861 | break; |
---|
1862 | } |
---|
1863 | } while (find (list, random)); |
---|
1864 | |
---|
1865 | return result; |
---|
1866 | } |
---|
1867 | |
---|
1868 | /// multiply two lists componentwise |
---|
1869 | void mult (CFList& L1, const CFList& L2) |
---|
1870 | { |
---|
1871 | ASSERT (L1.length() == L2.length(), "lists of the same size expected"); |
---|
1872 | |
---|
1873 | CFListIterator j= L2; |
---|
1874 | for (CFListIterator i= L1; i.hasItem(); i++, j++) |
---|
1875 | i.getItem() *= j.getItem(); |
---|
1876 | } |
---|
1877 | |
---|
1878 | void eval (const CanonicalForm& A, const CanonicalForm& B, CanonicalForm& Aeval, |
---|
1879 | CanonicalForm& Beval, const CFList& L) |
---|
1880 | { |
---|
1881 | Aeval= A; |
---|
1882 | Beval= B; |
---|
1883 | int j= 1; |
---|
1884 | for (CFListIterator i= L; i.hasItem(); i++, j++) |
---|
1885 | { |
---|
1886 | Aeval= Aeval (i.getItem(), j); |
---|
1887 | Beval= Beval (i.getItem(), j); |
---|
1888 | } |
---|
1889 | } |
---|
1890 | |
---|
1891 | CanonicalForm |
---|
1892 | monicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
1893 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
1894 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
1895 | ) |
---|
1896 | { |
---|
1897 | CanonicalForm A= F; |
---|
1898 | CanonicalForm B= G; |
---|
1899 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
1900 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
1901 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
1902 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
1903 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
1904 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
1905 | if (F == G) return F/Lc(F); |
---|
1906 | |
---|
1907 | CFMap M,N; |
---|
1908 | int best_level= myCompress (A, B, M, N, false); |
---|
1909 | |
---|
1910 | if (best_level == 0) |
---|
1911 | return B.genOne(); |
---|
1912 | |
---|
1913 | A= M(A); |
---|
1914 | B= M(B); |
---|
1915 | |
---|
1916 | Variable x= Variable (1); |
---|
1917 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
1918 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
1919 | |
---|
1920 | //univariate case |
---|
1921 | if (A.isUnivariate() && B.isUnivariate()) |
---|
1922 | return N (gcd (A, B)); |
---|
1923 | |
---|
1924 | CanonicalForm skel= M(skeleton); |
---|
1925 | CanonicalForm cA, cB; // content of A and B |
---|
1926 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
1927 | CanonicalForm gcdcAcB; |
---|
1928 | cA = uni_content (A); |
---|
1929 | cB = uni_content (B); |
---|
1930 | gcdcAcB= gcd (cA, cB); |
---|
1931 | ppA= A/cA; |
---|
1932 | ppB= B/cB; |
---|
1933 | |
---|
1934 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
1935 | CanonicalForm gcdlcAlcB; |
---|
1936 | lcA= uni_lcoeff (ppA); |
---|
1937 | lcB= uni_lcoeff (ppB); |
---|
1938 | |
---|
1939 | if (fdivides (lcA, lcB)) |
---|
1940 | { |
---|
1941 | if (fdivides (A, B)) |
---|
1942 | return F/Lc(F); |
---|
1943 | } |
---|
1944 | if (fdivides (lcB, lcA)) |
---|
1945 | { |
---|
1946 | if (fdivides (B, A)) |
---|
1947 | return G/Lc(G); |
---|
1948 | } |
---|
1949 | |
---|
1950 | gcdlcAlcB= gcd (lcA, lcB); |
---|
1951 | int skelSize= size (skel, skel.mvar()); |
---|
1952 | |
---|
1953 | int j= 0; |
---|
1954 | int biggestSize= 0; |
---|
1955 | |
---|
1956 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
1957 | biggestSize= tmax (biggestSize, size (i.coeff())); |
---|
1958 | |
---|
1959 | CanonicalForm g, Aeval, Beval; |
---|
1960 | |
---|
1961 | CFList evalPoints; |
---|
1962 | bool evalFail= false; |
---|
1963 | CFList list; |
---|
1964 | bool GF= false; |
---|
1965 | CanonicalForm LCA= LC (A); |
---|
1966 | CanonicalForm tmp; |
---|
1967 | CFArray gcds= CFArray (biggestSize); |
---|
1968 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
1969 | Variable V_buf= alpha; |
---|
1970 | CFList source, dest; |
---|
1971 | CanonicalForm prim_elem, im_prim_elem; |
---|
1972 | for (int i= 0; i < biggestSize; i++) |
---|
1973 | { |
---|
1974 | if (i == 0) |
---|
1975 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, evalFail, |
---|
1976 | list); |
---|
1977 | else |
---|
1978 | { |
---|
1979 | mult (evalPoints, pEvalPoints [0]); |
---|
1980 | eval (A, B, Aeval, Beval, evalPoints); |
---|
1981 | } |
---|
1982 | |
---|
1983 | if (evalFail) |
---|
1984 | { |
---|
1985 | if (V_buf.level() != 1) |
---|
1986 | { |
---|
1987 | do |
---|
1988 | { |
---|
1989 | Variable V_buf2= chooseExtension (V_buf); |
---|
1990 | source= CFList(); |
---|
1991 | dest= CFList(); |
---|
1992 | |
---|
1993 | bool prim_fail= false; |
---|
1994 | Variable V_buf3; |
---|
1995 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
1996 | |
---|
1997 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
1998 | if (prim_fail) |
---|
1999 | ; //ERROR |
---|
2000 | else |
---|
2001 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
2002 | |
---|
2003 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
2004 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
2005 | |
---|
2006 | for (CFListIterator j= list; j.hasItem(); j++) |
---|
2007 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
2008 | im_prim_elem, source, dest); |
---|
2009 | for (int k= 0; k < i; k++) |
---|
2010 | { |
---|
2011 | for (CFListIterator j= pEvalPoints[k]; j.hasItem(); j++) |
---|
2012 | j.getItem()= mapUp (j.getItem(), V_buf, V_buf2, prim_elem, |
---|
2013 | im_prim_elem, source, dest); |
---|
2014 | gcds[k]= mapUp (gcds[k], V_buf, V_buf2, prim_elem, im_prim_elem, |
---|
2015 | source, dest); |
---|
2016 | } |
---|
2017 | |
---|
2018 | if (alpha.level() != 1) |
---|
2019 | { |
---|
2020 | A= mapUp (A, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
2021 | B= mapUp (B, V_buf, V_buf2, prim_elem, im_prim_elem, source,dest); |
---|
2022 | } |
---|
2023 | evalFail= false; |
---|
2024 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2025 | evalFail, list); |
---|
2026 | } while (evalFail); |
---|
2027 | } |
---|
2028 | else |
---|
2029 | { |
---|
2030 | CanonicalForm mipo; |
---|
2031 | int deg= 2; |
---|
2032 | do { |
---|
2033 | mipo= randomIrredpoly (deg, x); |
---|
2034 | V_buf= rootOf (mipo); |
---|
2035 | evalFail= false; |
---|
2036 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2037 | evalFail, list); |
---|
2038 | deg++; |
---|
2039 | } while (evalFail); |
---|
2040 | } |
---|
2041 | } |
---|
2042 | |
---|
2043 | g= gcd (Aeval, Beval); |
---|
2044 | g /= Lc (g); |
---|
2045 | |
---|
2046 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2047 | { |
---|
2048 | delete[] pEvalPoints; |
---|
2049 | fail= true; |
---|
2050 | return 0; |
---|
2051 | } |
---|
2052 | CFIterator l= skel; |
---|
2053 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2054 | { |
---|
2055 | if (k.exp() != l.exp()) |
---|
2056 | { |
---|
2057 | delete[] pEvalPoints; |
---|
2058 | fail= true; |
---|
2059 | return 0; |
---|
2060 | } |
---|
2061 | } |
---|
2062 | pEvalPoints[i]= evalPoints; |
---|
2063 | gcds[i]= g; |
---|
2064 | |
---|
2065 | tmp= 0; |
---|
2066 | int j= 0; |
---|
2067 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
2068 | tmp += k.getItem()*power (x, j); |
---|
2069 | list.append (tmp); |
---|
2070 | } |
---|
2071 | |
---|
2072 | if (Monoms.size() == 0) |
---|
2073 | Monoms= getMonoms (skel); |
---|
2074 | if (coeffMonoms == NULL) |
---|
2075 | coeffMonoms= new CFArray [skelSize]; |
---|
2076 | j= 0; |
---|
2077 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2078 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
2079 | |
---|
2080 | CFArray* pL= new CFArray [skelSize]; |
---|
2081 | CFArray* pM= new CFArray [skelSize]; |
---|
2082 | for (int i= 0; i < biggestSize; i++) |
---|
2083 | { |
---|
2084 | CFIterator l= gcds [i]; |
---|
2085 | evalPoints= pEvalPoints [i]; |
---|
2086 | for (int k= 0; k < skelSize; k++, l++) |
---|
2087 | { |
---|
2088 | if (i == 0) |
---|
2089 | pL[k]= CFArray (biggestSize); |
---|
2090 | pL[k] [i]= l.coeff(); |
---|
2091 | |
---|
2092 | if (i == 0) |
---|
2093 | pM[k]= evaluate (coeffMonoms [k], evalPoints); |
---|
2094 | } |
---|
2095 | } |
---|
2096 | |
---|
2097 | CFArray solution; |
---|
2098 | CanonicalForm result= 0; |
---|
2099 | int ind= 0; |
---|
2100 | CFArray bufArray; |
---|
2101 | CFMatrix Mat; |
---|
2102 | for (int k= 0; k < skelSize; k++) |
---|
2103 | { |
---|
2104 | if (biggestSize != coeffMonoms[k].size()) |
---|
2105 | { |
---|
2106 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
2107 | for (int i= 0; i < coeffMonoms[k].size(); i++) |
---|
2108 | bufArray [i]= pL[k] [i]; |
---|
2109 | solution= solveGeneralVandermonde (pM [k], bufArray); |
---|
2110 | } |
---|
2111 | else |
---|
2112 | solution= solveGeneralVandermonde (pM [k], pL[k]); |
---|
2113 | |
---|
2114 | if (solution.size() == 0) |
---|
2115 | { |
---|
2116 | delete[] pEvalPoints; |
---|
2117 | delete[] pM; |
---|
2118 | delete[] pL; |
---|
2119 | delete[] coeffMonoms; |
---|
2120 | fail= true; |
---|
2121 | return 0; |
---|
2122 | } |
---|
2123 | for (int l= 0; l < solution.size(); l++) |
---|
2124 | result += solution[l]*Monoms [ind + l]; |
---|
2125 | ind += solution.size(); |
---|
2126 | } |
---|
2127 | |
---|
2128 | delete[] pEvalPoints; |
---|
2129 | delete[] pM; |
---|
2130 | delete[] pL; |
---|
2131 | |
---|
2132 | if (alpha.level() != 1 && V_buf != alpha) |
---|
2133 | { |
---|
2134 | CFList u, v; |
---|
2135 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
2136 | } |
---|
2137 | |
---|
2138 | result= N(result); |
---|
2139 | if (fdivides (result, F) && fdivides (result, G)) |
---|
2140 | return result; |
---|
2141 | else |
---|
2142 | { |
---|
2143 | delete[] coeffMonoms; |
---|
2144 | fail= true; |
---|
2145 | return 0; |
---|
2146 | } |
---|
2147 | } |
---|
2148 | |
---|
2149 | CanonicalForm |
---|
2150 | nonMonicSparseInterpol (const CanonicalForm& F, const CanonicalForm& G, |
---|
2151 | const CanonicalForm& skeleton, const Variable& alpha, |
---|
2152 | bool& fail, CFArray*& coeffMonoms, CFArray& Monoms |
---|
2153 | ) |
---|
2154 | { |
---|
2155 | CanonicalForm A= F; |
---|
2156 | CanonicalForm B= G; |
---|
2157 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
2158 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
2159 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
2160 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
2161 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
2162 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
2163 | if (F == G) return F/Lc(F); |
---|
2164 | |
---|
2165 | CFMap M,N; |
---|
2166 | int best_level= myCompress (A, B, M, N, false); |
---|
2167 | |
---|
2168 | if (best_level == 0) |
---|
2169 | return B.genOne(); |
---|
2170 | |
---|
2171 | A= M(A); |
---|
2172 | B= M(B); |
---|
2173 | |
---|
2174 | Variable x= Variable (1); |
---|
2175 | ASSERT (degree (A, x) == 0, "expected degree (F, 1) == 0"); |
---|
2176 | ASSERT (degree (B, x) == 0, "expected degree (G, 1) == 0"); |
---|
2177 | |
---|
2178 | //univariate case |
---|
2179 | if (A.isUnivariate() && B.isUnivariate()) |
---|
2180 | return N (gcd (A, B)); |
---|
2181 | |
---|
2182 | CanonicalForm skel= M(skeleton); |
---|
2183 | |
---|
2184 | CanonicalForm cA, cB; // content of A and B |
---|
2185 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
2186 | CanonicalForm gcdcAcB; |
---|
2187 | cA = uni_content (A); |
---|
2188 | cB = uni_content (B); |
---|
2189 | gcdcAcB= gcd (cA, cB); |
---|
2190 | ppA= A/cA; |
---|
2191 | ppB= B/cB; |
---|
2192 | |
---|
2193 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
2194 | CanonicalForm gcdlcAlcB; |
---|
2195 | lcA= uni_lcoeff (ppA); |
---|
2196 | lcB= uni_lcoeff (ppB); |
---|
2197 | |
---|
2198 | if (fdivides (lcA, lcB)) |
---|
2199 | { |
---|
2200 | if (fdivides (A, B)) |
---|
2201 | return F/Lc(F); |
---|
2202 | } |
---|
2203 | if (fdivides (lcB, lcA)) |
---|
2204 | { |
---|
2205 | if (fdivides (B, A)) |
---|
2206 | return G/Lc(G); |
---|
2207 | } |
---|
2208 | |
---|
2209 | gcdlcAlcB= gcd (lcA, lcB); |
---|
2210 | int skelSize= size (skel, skel.mvar()); |
---|
2211 | |
---|
2212 | int j= 0; |
---|
2213 | int biggestSize= 0; |
---|
2214 | int bufSize; |
---|
2215 | int numberUni= 0; |
---|
2216 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2217 | { |
---|
2218 | bufSize= size (i.coeff()); |
---|
2219 | biggestSize= tmax (biggestSize, bufSize); |
---|
2220 | numberUni += bufSize; |
---|
2221 | } |
---|
2222 | numberUni--; |
---|
2223 | numberUni= (int) ceil ( (double) numberUni / (skelSize - 1)); |
---|
2224 | biggestSize= tmax (biggestSize , numberUni); |
---|
2225 | |
---|
2226 | numberUni= biggestSize + size (LC(skel)) - 1; |
---|
2227 | int biggestSize2= tmax (numberUni, biggestSize); |
---|
2228 | |
---|
2229 | CanonicalForm g, Aeval, Beval; |
---|
2230 | |
---|
2231 | CFList evalPoints; |
---|
2232 | CFArray coeffEval; |
---|
2233 | bool evalFail= false; |
---|
2234 | CFList list; |
---|
2235 | bool GF= false; |
---|
2236 | CanonicalForm LCA= LC (A); |
---|
2237 | CanonicalForm tmp; |
---|
2238 | CFArray gcds= CFArray (biggestSize); |
---|
2239 | CFList * pEvalPoints= new CFList [biggestSize]; |
---|
2240 | Variable V_buf= alpha; |
---|
2241 | CFList source, dest; |
---|
2242 | CanonicalForm prim_elem, im_prim_elem; |
---|
2243 | for (int i= 0; i < biggestSize; i++) |
---|
2244 | { |
---|
2245 | if (i == 0) |
---|
2246 | { |
---|
2247 | if (getCharacteristic() > 3) |
---|
2248 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2249 | evalFail, list); |
---|
2250 | else |
---|
2251 | evalFail= true; |
---|
2252 | |
---|
2253 | if (evalFail) |
---|
2254 | { |
---|
2255 | if (V_buf.level() != 1) |
---|
2256 | { |
---|
2257 | do |
---|
2258 | { |
---|
2259 | Variable V_buf2= chooseExtension (V_buf); |
---|
2260 | source= CFList(); |
---|
2261 | dest= CFList(); |
---|
2262 | |
---|
2263 | bool prim_fail= false; |
---|
2264 | Variable V_buf3; |
---|
2265 | prim_elem= primitiveElement (V_buf, V_buf3, prim_fail); |
---|
2266 | |
---|
2267 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
2268 | if (prim_fail) |
---|
2269 | ; //ERROR |
---|
2270 | else |
---|
2271 | im_prim_elem= mapPrimElem (prim_elem, V_buf, V_buf2); |
---|
2272 | |
---|
2273 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf)); |
---|
2274 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
2275 | |
---|
2276 | for (CFListIterator i= list; i.hasItem(); i++) |
---|
2277 | i.getItem()= mapUp (i.getItem(), V_buf, V_buf2, prim_elem, |
---|
2278 | im_prim_elem, source, dest); |
---|
2279 | evalFail= false; |
---|
2280 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2281 | evalFail, list); |
---|
2282 | } while (evalFail); |
---|
2283 | } |
---|
2284 | else |
---|
2285 | { |
---|
2286 | CanonicalForm mipo; |
---|
2287 | int deg= 2; |
---|
2288 | do { |
---|
2289 | mipo= randomIrredpoly (deg, x); |
---|
2290 | V_buf= rootOf (mipo); |
---|
2291 | evalFail= false; |
---|
2292 | evalPoints= evaluationPoints (A, B, Aeval, Beval, LCA, GF, V_buf, |
---|
2293 | evalFail, list); |
---|
2294 | deg++; |
---|
2295 | } while (evalFail); |
---|
2296 | } |
---|
2297 | } |
---|
2298 | } |
---|
2299 | else |
---|
2300 | { |
---|
2301 | mult (evalPoints, pEvalPoints[0]); |
---|
2302 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2303 | } |
---|
2304 | |
---|
2305 | g= gcd (Aeval, Beval); |
---|
2306 | g /= Lc (g); |
---|
2307 | |
---|
2308 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2309 | { |
---|
2310 | delete[] pEvalPoints; |
---|
2311 | fail= true; |
---|
2312 | return 0; |
---|
2313 | } |
---|
2314 | CFIterator l= skel; |
---|
2315 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2316 | { |
---|
2317 | if (k.exp() != l.exp()) |
---|
2318 | { |
---|
2319 | delete[] pEvalPoints; |
---|
2320 | fail= true; |
---|
2321 | return 0; |
---|
2322 | } |
---|
2323 | } |
---|
2324 | pEvalPoints[i]= evalPoints; |
---|
2325 | gcds[i]= g; |
---|
2326 | |
---|
2327 | tmp= 0; |
---|
2328 | int j= 0; |
---|
2329 | for (CFListIterator k= evalPoints; k.hasItem(); k++, j++) |
---|
2330 | tmp += k.getItem()*power (x, j); |
---|
2331 | list.append (tmp); |
---|
2332 | } |
---|
2333 | |
---|
2334 | if (Monoms.size() == 0) |
---|
2335 | Monoms= getMonoms (skel); |
---|
2336 | |
---|
2337 | if (coeffMonoms == NULL) |
---|
2338 | coeffMonoms= new CFArray [skelSize]; |
---|
2339 | |
---|
2340 | j= 0; |
---|
2341 | for (CFIterator i= skel; i.hasTerms(); i++, j++) |
---|
2342 | coeffMonoms[j]= getMonoms (i.coeff()); |
---|
2343 | |
---|
2344 | int minimalColumnsIndex; |
---|
2345 | if (skelSize > 1) |
---|
2346 | minimalColumnsIndex= 1; |
---|
2347 | else |
---|
2348 | minimalColumnsIndex= 0; |
---|
2349 | int minimalColumns=-1; |
---|
2350 | |
---|
2351 | CFArray* pM= new CFArray [skelSize]; |
---|
2352 | CFMatrix Mat; |
---|
2353 | // find the Matrix with minimal number of columns |
---|
2354 | for (int i= 0; i < skelSize; i++) |
---|
2355 | { |
---|
2356 | pM[i]= CFArray (coeffMonoms[i].size()); |
---|
2357 | if (i == 1) |
---|
2358 | minimalColumns= coeffMonoms[i].size(); |
---|
2359 | if (i > 1) |
---|
2360 | { |
---|
2361 | if (minimalColumns > coeffMonoms[i].size()) |
---|
2362 | { |
---|
2363 | minimalColumns= coeffMonoms[i].size(); |
---|
2364 | minimalColumnsIndex= i; |
---|
2365 | } |
---|
2366 | } |
---|
2367 | } |
---|
2368 | CFMatrix* pMat= new CFMatrix [2]; |
---|
2369 | pMat[0]= CFMatrix (biggestSize, coeffMonoms[0].size()); |
---|
2370 | pMat[1]= CFMatrix (biggestSize, coeffMonoms[minimalColumnsIndex].size()); |
---|
2371 | CFArray* pL= new CFArray [skelSize]; |
---|
2372 | for (int i= 0; i < biggestSize; i++) |
---|
2373 | { |
---|
2374 | CFIterator l= gcds [i]; |
---|
2375 | evalPoints= pEvalPoints [i]; |
---|
2376 | for (int k= 0; k < skelSize; k++, l++) |
---|
2377 | { |
---|
2378 | if (i == 0) |
---|
2379 | pL[k]= CFArray (biggestSize); |
---|
2380 | pL[k] [i]= l.coeff(); |
---|
2381 | |
---|
2382 | if (i == 0 && k != 0 && k != minimalColumnsIndex) |
---|
2383 | pM[k]= evaluate (coeffMonoms[k], evalPoints); |
---|
2384 | else if (i == 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
2385 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2386 | if (i > 0 && (k == 0 || k == minimalColumnsIndex)) |
---|
2387 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2388 | |
---|
2389 | if (k == 0) |
---|
2390 | { |
---|
2391 | if (pMat[k].rows() >= i + 1) |
---|
2392 | { |
---|
2393 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2394 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2395 | } |
---|
2396 | } |
---|
2397 | if (k == minimalColumnsIndex) |
---|
2398 | { |
---|
2399 | if (pMat[1].rows() >= i + 1) |
---|
2400 | { |
---|
2401 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2402 | pMat[1] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2403 | } |
---|
2404 | } |
---|
2405 | } |
---|
2406 | } |
---|
2407 | |
---|
2408 | CFArray solution; |
---|
2409 | CanonicalForm result= 0; |
---|
2410 | int ind= 1; |
---|
2411 | int matRows, matColumns; |
---|
2412 | matRows= pMat[1].rows(); |
---|
2413 | matColumns= pMat[0].columns() - 1; |
---|
2414 | matColumns += pMat[1].columns(); |
---|
2415 | |
---|
2416 | Mat= CFMatrix (matRows, matColumns); |
---|
2417 | for (int i= 1; i <= matRows; i++) |
---|
2418 | for (int j= 1; j <= pMat[1].columns(); j++) |
---|
2419 | Mat (i, j)= pMat[1] (i, j); |
---|
2420 | |
---|
2421 | for (int j= pMat[1].columns() + 1; j <= matColumns; |
---|
2422 | j++, ind++) |
---|
2423 | { |
---|
2424 | for (int i= 1; i <= matRows; i++) |
---|
2425 | Mat (i, j)= (-pMat [0] (i, ind + 1))*pL[minimalColumnsIndex] [i - 1]; |
---|
2426 | } |
---|
2427 | |
---|
2428 | CFArray firstColumn= CFArray (pMat[0].rows()); |
---|
2429 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
2430 | firstColumn [i]= pMat[0] (i + 1, 1); |
---|
2431 | |
---|
2432 | CFArray bufArray= pL[minimalColumnsIndex]; |
---|
2433 | |
---|
2434 | for (int i= 0; i < biggestSize; i++) |
---|
2435 | pL[minimalColumnsIndex] [i] *= firstColumn[i]; |
---|
2436 | |
---|
2437 | CFMatrix bufMat= pMat[1]; |
---|
2438 | pMat[1]= Mat; |
---|
2439 | |
---|
2440 | if (V_buf.level() != 1) |
---|
2441 | solution= solveSystemFq (pMat[1], |
---|
2442 | pL[minimalColumnsIndex], V_buf); |
---|
2443 | else |
---|
2444 | solution= solveSystemFp (pMat[1], |
---|
2445 | pL[minimalColumnsIndex]); |
---|
2446 | |
---|
2447 | if (solution.size() == 0) |
---|
2448 | { //Javadi's method failed, try deKleine, Monagan, Wittkopf instead |
---|
2449 | CFMatrix bufMat0= pMat[0]; |
---|
2450 | delete [] pMat; |
---|
2451 | pMat= new CFMatrix [skelSize]; |
---|
2452 | pL[minimalColumnsIndex]= bufArray; |
---|
2453 | CFList* bufpEvalPoints= NULL; |
---|
2454 | CFArray bufGcds; |
---|
2455 | if (biggestSize != biggestSize2) |
---|
2456 | { |
---|
2457 | bufpEvalPoints= pEvalPoints; |
---|
2458 | pEvalPoints= new CFList [biggestSize2]; |
---|
2459 | bufGcds= gcds; |
---|
2460 | gcds= CFArray (biggestSize2); |
---|
2461 | for (int i= 0; i < biggestSize; i++) |
---|
2462 | { |
---|
2463 | pEvalPoints[i]= bufpEvalPoints [i]; |
---|
2464 | gcds[i]= bufGcds[i]; |
---|
2465 | } |
---|
2466 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
2467 | { |
---|
2468 | mult (evalPoints, pEvalPoints[0]); |
---|
2469 | eval (A, B, Aeval, Beval, evalPoints); |
---|
2470 | g= gcd (Aeval, Beval); |
---|
2471 | g /= Lc (g); |
---|
2472 | if (degree (g) != degree (skel) || (skelSize != size (g))) |
---|
2473 | { |
---|
2474 | delete[] pEvalPoints; |
---|
2475 | delete[] pMat; |
---|
2476 | delete[] pL; |
---|
2477 | delete[] coeffMonoms; |
---|
2478 | delete[] pM; |
---|
2479 | if (bufpEvalPoints != NULL) |
---|
2480 | delete [] bufpEvalPoints; |
---|
2481 | fail= true; |
---|
2482 | return 0; |
---|
2483 | } |
---|
2484 | CFIterator l= skel; |
---|
2485 | for (CFIterator k= g; k.hasTerms(); k++, l++) |
---|
2486 | { |
---|
2487 | if (k.exp() != l.exp()) |
---|
2488 | { |
---|
2489 | delete[] pEvalPoints; |
---|
2490 | delete[] pMat; |
---|
2491 | delete[] pL; |
---|
2492 | delete[] coeffMonoms; |
---|
2493 | delete[] pM; |
---|
2494 | if (bufpEvalPoints != NULL) |
---|
2495 | delete [] bufpEvalPoints; |
---|
2496 | fail= true; |
---|
2497 | return 0; |
---|
2498 | } |
---|
2499 | } |
---|
2500 | pEvalPoints[i + biggestSize]= evalPoints; |
---|
2501 | gcds[i + biggestSize]= g; |
---|
2502 | } |
---|
2503 | } |
---|
2504 | for (int i= 0; i < biggestSize; i++) |
---|
2505 | { |
---|
2506 | CFIterator l= gcds [i]; |
---|
2507 | evalPoints= pEvalPoints [i]; |
---|
2508 | for (int k= 1; k < skelSize; k++, l++) |
---|
2509 | { |
---|
2510 | if (i == 0) |
---|
2511 | pMat[k]= CFMatrix (biggestSize2,coeffMonoms[k].size()+biggestSize2-1); |
---|
2512 | if (k == minimalColumnsIndex) |
---|
2513 | continue; |
---|
2514 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2515 | if (pMat[k].rows() >= i + 1) |
---|
2516 | { |
---|
2517 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2518 | pMat[k] (i + 1, ind)= coeffEval[ind - 1]; |
---|
2519 | } |
---|
2520 | } |
---|
2521 | } |
---|
2522 | Mat= bufMat0; |
---|
2523 | pMat[0]= CFMatrix (biggestSize2, coeffMonoms[0].size() + biggestSize2 - 1); |
---|
2524 | for (int j= 1; j <= Mat.rows(); j++) |
---|
2525 | for (int k= 1; k <= Mat.columns(); k++) |
---|
2526 | pMat [0] (j,k)= Mat (j,k); |
---|
2527 | Mat= bufMat; |
---|
2528 | for (int j= 1; j <= Mat.rows(); j++) |
---|
2529 | for (int k= 1; k <= Mat.columns(); k++) |
---|
2530 | pMat [minimalColumnsIndex] (j,k)= Mat (j,k); |
---|
2531 | // write old matrix entries into new matrices |
---|
2532 | for (int i= 0; i < skelSize; i++) |
---|
2533 | { |
---|
2534 | bufArray= pL[i]; |
---|
2535 | pL[i]= CFArray (biggestSize2); |
---|
2536 | for (int j= 0; j < bufArray.size(); j++) |
---|
2537 | pL[i] [j]= bufArray [j]; |
---|
2538 | } |
---|
2539 | //write old vector entries into new and add new entries to old matrices |
---|
2540 | for (int i= 0; i < biggestSize2 - biggestSize; i++) |
---|
2541 | { |
---|
2542 | CFIterator l= gcds [i + biggestSize]; |
---|
2543 | evalPoints= pEvalPoints [i + biggestSize]; |
---|
2544 | for (int k= 0; k < skelSize; k++, l++) |
---|
2545 | { |
---|
2546 | pL[k] [i + biggestSize]= l.coeff(); |
---|
2547 | coeffEval= evaluate (coeffMonoms[k], evalPoints); |
---|
2548 | if (pMat[k].rows() >= i + biggestSize + 1) |
---|
2549 | { |
---|
2550 | for (int ind= 1; ind < coeffEval.size() + 1; ind++) |
---|
2551 | pMat[k] (i + biggestSize + 1, ind)= coeffEval[ind - 1]; |
---|
2552 | } |
---|
2553 | } |
---|
2554 | } |
---|
2555 | // begin new |
---|
2556 | for (int i= 0; i < skelSize; i++) |
---|
2557 | { |
---|
2558 | if (pL[i].size() > 1) |
---|
2559 | { |
---|
2560 | for (int j= 2; j <= pMat[i].rows(); j++) |
---|
2561 | pMat[i] (j, coeffMonoms[i].size() + j - 1)= |
---|
2562 | -pL[i] [j - 1]; |
---|
2563 | } |
---|
2564 | } |
---|
2565 | |
---|
2566 | long rk; |
---|
2567 | matColumns= biggestSize2 - 1; |
---|
2568 | matRows= 0; |
---|
2569 | for (int i= 0; i < skelSize; i++) |
---|
2570 | { |
---|
2571 | if (V_buf.level() == 1) |
---|
2572 | rk= gaussianElimFp (pMat[i], pL[i]); |
---|
2573 | else |
---|
2574 | rk= gaussianElimFq (pMat[i], pL[i], V_buf); |
---|
2575 | |
---|
2576 | if (pMat[i] (coeffMonoms[i].size(), coeffMonoms[i].size()) == 0) |
---|
2577 | { |
---|
2578 | delete[] pEvalPoints; |
---|
2579 | delete[] pMat; |
---|
2580 | delete[] pL; |
---|
2581 | delete[] coeffMonoms; |
---|
2582 | delete[] pM; |
---|
2583 | if (bufpEvalPoints != NULL) |
---|
2584 | delete [] bufpEvalPoints; |
---|
2585 | fail= true; |
---|
2586 | return 0; |
---|
2587 | } |
---|
2588 | matRows += pMat[i].rows() - coeffMonoms[i].size(); |
---|
2589 | } |
---|
2590 | |
---|
2591 | CFMatrix bufMat; |
---|
2592 | Mat= CFMatrix (matRows, matColumns); |
---|
2593 | ind= 0; |
---|
2594 | bufArray= CFArray (matRows); |
---|
2595 | CFArray bufArray2; |
---|
2596 | for (int i= 0; i < skelSize; i++) |
---|
2597 | { |
---|
2598 | bufMat= pMat[i] (coeffMonoms[i].size() + 1, pMat[i].rows(), |
---|
2599 | coeffMonoms[i].size() + 1, pMat[i].columns()); |
---|
2600 | |
---|
2601 | for (int j= 1; j <= bufMat.rows(); j++) |
---|
2602 | for (int k= 1; k <= bufMat.columns(); k++) |
---|
2603 | Mat (j + ind, k)= bufMat(j, k); |
---|
2604 | bufArray2= coeffMonoms[i].size(); |
---|
2605 | for (int j= 1; j <= pMat[i].rows(); j++) |
---|
2606 | { |
---|
2607 | if (j > coeffMonoms[i].size()) |
---|
2608 | bufArray [j-coeffMonoms[i].size() + ind - 1]= pL[i] [j - 1]; |
---|
2609 | else |
---|
2610 | bufArray2 [j - 1]= pL[i] [j - 1]; |
---|
2611 | } |
---|
2612 | pL[i]= bufArray2; |
---|
2613 | ind += bufMat.rows(); |
---|
2614 | pMat[i]= pMat[i] (1, coeffMonoms[i].size(), 1, pMat[i].columns()); |
---|
2615 | } |
---|
2616 | |
---|
2617 | if (V_buf.level() != 1) |
---|
2618 | solution= solveSystemFq (Mat, bufArray, V_buf); |
---|
2619 | else |
---|
2620 | solution= solveSystemFp (Mat, bufArray); |
---|
2621 | |
---|
2622 | if (solution.size() == 0) |
---|
2623 | { |
---|
2624 | delete[] pEvalPoints; |
---|
2625 | delete[] pMat; |
---|
2626 | delete[] pL; |
---|
2627 | delete[] coeffMonoms; |
---|
2628 | delete[] pM; |
---|
2629 | if (bufpEvalPoints != NULL) |
---|
2630 | delete [] bufpEvalPoints; |
---|
2631 | fail= true; |
---|
2632 | return 0; |
---|
2633 | } |
---|
2634 | |
---|
2635 | ind= 0; |
---|
2636 | result= 0; |
---|
2637 | CFArray bufSolution; |
---|
2638 | for (int i= 0; i < skelSize; i++) |
---|
2639 | { |
---|
2640 | bufSolution= readOffSolution (pMat[i], pL[i], solution); |
---|
2641 | for (int i= 0; i < bufSolution.size(); i++, ind++) |
---|
2642 | result += Monoms [ind]*bufSolution[i]; |
---|
2643 | } |
---|
2644 | if (alpha.level() != 1 && V_buf != alpha) |
---|
2645 | { |
---|
2646 | CFList u, v; |
---|
2647 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
2648 | } |
---|
2649 | result= N(result); |
---|
2650 | if (fdivides (result, F) && fdivides (result, G)) |
---|
2651 | { |
---|
2652 | delete[] pEvalPoints; |
---|
2653 | delete[] pMat; |
---|
2654 | delete[] pL; |
---|
2655 | delete[] pM; |
---|
2656 | if (bufpEvalPoints != NULL) |
---|
2657 | delete [] bufpEvalPoints; |
---|
2658 | return result; |
---|
2659 | } |
---|
2660 | else |
---|
2661 | { |
---|
2662 | delete[] pEvalPoints; |
---|
2663 | delete[] pMat; |
---|
2664 | delete[] pL; |
---|
2665 | delete[] coeffMonoms; |
---|
2666 | delete[] pM; |
---|
2667 | if (bufpEvalPoints != NULL) |
---|
2668 | delete [] bufpEvalPoints; |
---|
2669 | fail= true; |
---|
2670 | return 0; |
---|
2671 | } |
---|
2672 | } // end of deKleine, Monagan & Wittkopf |
---|
2673 | |
---|
2674 | result += Monoms[0]; |
---|
2675 | int ind2= 0, ind3= 2; |
---|
2676 | ind= 0; |
---|
2677 | for (int l= 0; l < minimalColumnsIndex; l++) |
---|
2678 | ind += coeffMonoms[l].size(); |
---|
2679 | for (int l= solution.size() - pMat[0].columns() + 1; l < solution.size(); |
---|
2680 | l++, ind2++, ind3++) |
---|
2681 | { |
---|
2682 | result += solution[l]*Monoms [1 + ind2]; |
---|
2683 | for (int i= 0; i < pMat[0].rows(); i++) |
---|
2684 | firstColumn[i] += solution[l]*pMat[0] (i + 1, ind3); |
---|
2685 | } |
---|
2686 | for (int l= 0; l < solution.size() + 1 - pMat[0].columns(); l++) |
---|
2687 | result += solution[l]*Monoms [ind + l]; |
---|
2688 | ind= coeffMonoms[0].size(); |
---|
2689 | for (int k= 1; k < skelSize; k++) |
---|
2690 | { |
---|
2691 | if (k == minimalColumnsIndex) |
---|
2692 | { |
---|
2693 | ind += coeffMonoms[k].size(); |
---|
2694 | continue; |
---|
2695 | } |
---|
2696 | if (k != minimalColumnsIndex) |
---|
2697 | { |
---|
2698 | for (int i= 0; i < biggestSize; i++) |
---|
2699 | pL[k] [i] *= firstColumn [i]; |
---|
2700 | } |
---|
2701 | |
---|
2702 | if (biggestSize != coeffMonoms[k].size() && k != minimalColumnsIndex) |
---|
2703 | { |
---|
2704 | bufArray= CFArray (coeffMonoms[k].size()); |
---|
2705 | for (int i= 0; i < bufArray.size(); i++) |
---|
2706 | bufArray [i]= pL[k] [i]; |
---|
2707 | solution= solveGeneralVandermonde (pM[k], bufArray); |
---|
2708 | } |
---|
2709 | else |
---|
2710 | solution= solveGeneralVandermonde (pM[k], pL[k]); |
---|
2711 | |
---|
2712 | if (solution.size() == 0) |
---|
2713 | { |
---|
2714 | delete[] pEvalPoints; |
---|
2715 | delete[] pMat; |
---|
2716 | delete[] pL; |
---|
2717 | delete[] coeffMonoms; |
---|
2718 | delete[] pM; |
---|
2719 | fail= true; |
---|
2720 | return 0; |
---|
2721 | } |
---|
2722 | if (k != minimalColumnsIndex) |
---|
2723 | { |
---|
2724 | for (int l= 0; l < solution.size(); l++) |
---|
2725 | result += solution[l]*Monoms [ind + l]; |
---|
2726 | ind += solution.size(); |
---|
2727 | } |
---|
2728 | } |
---|
2729 | |
---|
2730 | delete[] pEvalPoints; |
---|
2731 | delete[] pMat; |
---|
2732 | delete[] pL; |
---|
2733 | delete[] pM; |
---|
2734 | |
---|
2735 | if (alpha.level() != 1 && V_buf != alpha) |
---|
2736 | { |
---|
2737 | CFList u, v; |
---|
2738 | result= mapDown (result, prim_elem, im_prim_elem, alpha, u, v); |
---|
2739 | } |
---|
2740 | result= N(result); |
---|
2741 | |
---|
2742 | if (fdivides (result, F) && fdivides (result, G)) |
---|
2743 | return result; |
---|
2744 | else |
---|
2745 | { |
---|
2746 | delete[] coeffMonoms; |
---|
2747 | fail= true; |
---|
2748 | return 0; |
---|
2749 | } |
---|
2750 | } |
---|
2751 | |
---|
2752 | CanonicalForm sparseGCDFq (const CanonicalForm& F, const CanonicalForm& G, |
---|
2753 | const Variable & alpha, CFList& l, bool& topLevel) |
---|
2754 | { |
---|
2755 | CanonicalForm A= F; |
---|
2756 | CanonicalForm B= G; |
---|
2757 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
2758 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
2759 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
2760 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
2761 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
2762 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
2763 | if (F == G) return F/Lc(F); |
---|
2764 | |
---|
2765 | CFMap M,N; |
---|
2766 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
2767 | |
---|
2768 | if (best_level == 0) return B.genOne(); |
---|
2769 | |
---|
2770 | A= M(A); |
---|
2771 | B= M(B); |
---|
2772 | |
---|
2773 | Variable x= Variable (1); |
---|
2774 | |
---|
2775 | //univariate case |
---|
2776 | if (A.isUnivariate() && B.isUnivariate()) |
---|
2777 | return N (gcd (A, B)); |
---|
2778 | |
---|
2779 | CanonicalForm cA, cB; // content of A and B |
---|
2780 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
2781 | CanonicalForm gcdcAcB; |
---|
2782 | if (topLevel) |
---|
2783 | { |
---|
2784 | if (best_level <= 2) |
---|
2785 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
---|
2786 | else |
---|
2787 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
---|
2788 | } |
---|
2789 | else |
---|
2790 | { |
---|
2791 | cA = uni_content (A); |
---|
2792 | cB = uni_content (B); |
---|
2793 | gcdcAcB= gcd (cA, cB); |
---|
2794 | ppA= A/cA; |
---|
2795 | ppB= B/cB; |
---|
2796 | } |
---|
2797 | |
---|
2798 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
2799 | CanonicalForm gcdlcAlcB; |
---|
2800 | lcA= uni_lcoeff (ppA); |
---|
2801 | lcB= uni_lcoeff (ppB); |
---|
2802 | |
---|
2803 | if (fdivides (lcA, lcB)) |
---|
2804 | { |
---|
2805 | if (fdivides (A, B)) |
---|
2806 | return F/Lc(F); |
---|
2807 | } |
---|
2808 | if (fdivides (lcB, lcA)) |
---|
2809 | { |
---|
2810 | if (fdivides (B, A)) |
---|
2811 | return G/Lc(G); |
---|
2812 | } |
---|
2813 | |
---|
2814 | gcdlcAlcB= gcd (lcA, lcB); |
---|
2815 | |
---|
2816 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
2817 | int d0; |
---|
2818 | |
---|
2819 | if (d == 0) |
---|
2820 | return N(gcdcAcB); |
---|
2821 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
2822 | |
---|
2823 | if (d0 < d) |
---|
2824 | d= d0; |
---|
2825 | |
---|
2826 | if (d == 0) |
---|
2827 | return N(gcdcAcB); |
---|
2828 | |
---|
2829 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
2830 | CanonicalForm newtonPoly= 1; |
---|
2831 | m= gcdlcAlcB; |
---|
2832 | G_m= 0; |
---|
2833 | H= 0; |
---|
2834 | bool fail= false; |
---|
2835 | topLevel= false; |
---|
2836 | bool inextension= false; |
---|
2837 | Variable V_buf= alpha; |
---|
2838 | CanonicalForm prim_elem, im_prim_elem; |
---|
2839 | CFList source, dest; |
---|
2840 | do // first do |
---|
2841 | { |
---|
2842 | random_element= randomElement (m, V_buf, l, fail); |
---|
2843 | if (random_element == 0 && !fail) |
---|
2844 | { |
---|
2845 | if (!find (l, random_element)) |
---|
2846 | l.append (random_element); |
---|
2847 | continue; |
---|
2848 | } |
---|
2849 | if (fail) |
---|
2850 | { |
---|
2851 | source= CFList(); |
---|
2852 | dest= CFList(); |
---|
2853 | |
---|
2854 | Variable V_buf3= V_buf; |
---|
2855 | V_buf= chooseExtension (V_buf); |
---|
2856 | bool prim_fail= false; |
---|
2857 | Variable V_buf2; |
---|
2858 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
2859 | |
---|
2860 | if (V_buf3 != alpha) |
---|
2861 | { |
---|
2862 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
2863 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
2864 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
2865 | source, dest); |
---|
2866 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
2867 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
2868 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
2869 | dest); |
---|
2870 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
2871 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
2872 | source, dest); |
---|
2873 | } |
---|
2874 | |
---|
2875 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
2876 | if (prim_fail) |
---|
2877 | ; //ERROR |
---|
2878 | else |
---|
2879 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
2880 | |
---|
2881 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
2882 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
2883 | inextension= true; |
---|
2884 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
2885 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
2886 | im_prim_elem, source, dest); |
---|
2887 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
2888 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
2889 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
2890 | source, dest); |
---|
2891 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
2892 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
2893 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
2894 | source, dest); |
---|
2895 | |
---|
2896 | fail= false; |
---|
2897 | random_element= randomElement (m, V_buf, l, fail ); |
---|
2898 | DEBOUTLN (cerr, "fail= " << fail); |
---|
2899 | CFList list; |
---|
2900 | TIMING_START (gcd_recursion); |
---|
2901 | G_random_element= |
---|
2902 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
2903 | list, topLevel); |
---|
2904 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
2905 | "time for recursive call: "); |
---|
2906 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
2907 | } |
---|
2908 | else |
---|
2909 | { |
---|
2910 | CFList list; |
---|
2911 | TIMING_START (gcd_recursion); |
---|
2912 | G_random_element= |
---|
2913 | sparseGCDFq (ppA(random_element, x), ppB(random_element, x), V_buf, |
---|
2914 | list, topLevel); |
---|
2915 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
2916 | "time for recursive call: "); |
---|
2917 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
2918 | } |
---|
2919 | |
---|
2920 | if (!G_random_element.inCoeffDomain()) |
---|
2921 | d0= totaldegree (G_random_element, Variable(2), |
---|
2922 | Variable (G_random_element.level())); |
---|
2923 | else |
---|
2924 | d0= 0; |
---|
2925 | |
---|
2926 | if (d0 == 0) |
---|
2927 | return N(gcdcAcB); |
---|
2928 | if (d0 > d) |
---|
2929 | { |
---|
2930 | if (!find (l, random_element)) |
---|
2931 | l.append (random_element); |
---|
2932 | continue; |
---|
2933 | } |
---|
2934 | |
---|
2935 | G_random_element= |
---|
2936 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
2937 | * G_random_element; |
---|
2938 | |
---|
2939 | skeleton= G_random_element; |
---|
2940 | if (!G_random_element.inCoeffDomain()) |
---|
2941 | d0= totaldegree (G_random_element, Variable(2), |
---|
2942 | Variable (G_random_element.level())); |
---|
2943 | else |
---|
2944 | d0= 0; |
---|
2945 | |
---|
2946 | if (d0 < d) |
---|
2947 | { |
---|
2948 | m= gcdlcAlcB; |
---|
2949 | newtonPoly= 1; |
---|
2950 | G_m= 0; |
---|
2951 | d= d0; |
---|
2952 | } |
---|
2953 | |
---|
2954 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
2955 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
2956 | { |
---|
2957 | cH= uni_content (H); |
---|
2958 | ppH= H/cH; |
---|
2959 | if (inextension) |
---|
2960 | { |
---|
2961 | CFList u, v; |
---|
2962 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
2963 | //mapping down |
---|
2964 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
2965 | { |
---|
2966 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
2967 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
2968 | ppH /= Lc(ppH); |
---|
2969 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
2970 | return N(gcdcAcB*ppH); |
---|
2971 | } |
---|
2972 | } |
---|
2973 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
2974 | return N(gcdcAcB*ppH); |
---|
2975 | } |
---|
2976 | G_m= H; |
---|
2977 | newtonPoly= newtonPoly*(x - random_element); |
---|
2978 | m= m*(x - random_element); |
---|
2979 | if (!find (l, random_element)) |
---|
2980 | l.append (random_element); |
---|
2981 | |
---|
2982 | if (getCharacteristic () > 3 && size (skeleton) < 100) |
---|
2983 | { |
---|
2984 | CFArray Monoms; |
---|
2985 | CFArray *coeffMonoms= NULL; |
---|
2986 | do //second do |
---|
2987 | { |
---|
2988 | random_element= randomElement (m, V_buf, l, fail); |
---|
2989 | if (random_element == 0 && !fail) |
---|
2990 | { |
---|
2991 | if (!find (l, random_element)) |
---|
2992 | l.append (random_element); |
---|
2993 | continue; |
---|
2994 | } |
---|
2995 | if (fail) |
---|
2996 | { |
---|
2997 | source= CFList(); |
---|
2998 | dest= CFList(); |
---|
2999 | |
---|
3000 | Variable V_buf3= V_buf; |
---|
3001 | V_buf= chooseExtension (V_buf); |
---|
3002 | bool prim_fail= false; |
---|
3003 | Variable V_buf2; |
---|
3004 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3005 | |
---|
3006 | if (V_buf3 != alpha) |
---|
3007 | { |
---|
3008 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3009 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3010 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3011 | source, dest); |
---|
3012 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3013 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3014 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
3015 | source, dest); |
---|
3016 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3017 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3018 | source, dest); |
---|
3019 | } |
---|
3020 | |
---|
3021 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3022 | if (prim_fail) |
---|
3023 | ; //ERROR |
---|
3024 | else |
---|
3025 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3026 | |
---|
3027 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3028 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
3029 | inextension= true; |
---|
3030 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3031 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3032 | im_prim_elem, source, dest); |
---|
3033 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3034 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3035 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3036 | source, dest); |
---|
3037 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3038 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3039 | |
---|
3040 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3041 | source, dest); |
---|
3042 | |
---|
3043 | fail= false; |
---|
3044 | random_element= randomElement (m, V_buf, l, fail); |
---|
3045 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3046 | CFList list; |
---|
3047 | TIMING_START (gcd_recursion); |
---|
3048 | |
---|
3049 | //sparseInterpolation |
---|
3050 | bool sparseFail= false; |
---|
3051 | if (LC (skeleton).inCoeffDomain()) |
---|
3052 | G_random_element= |
---|
3053 | monicSparseInterpol (ppA (random_element, x), ppB(random_element,x), |
---|
3054 | skeleton,V_buf, sparseFail, coeffMonoms,Monoms); |
---|
3055 | else |
---|
3056 | G_random_element= |
---|
3057 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
3058 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3059 | Monoms); |
---|
3060 | if (sparseFail) |
---|
3061 | break; |
---|
3062 | |
---|
3063 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3064 | "time for recursive call: "); |
---|
3065 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3066 | } |
---|
3067 | else |
---|
3068 | { |
---|
3069 | CFList list; |
---|
3070 | TIMING_START (gcd_recursion); |
---|
3071 | bool sparseFail= false; |
---|
3072 | if (LC (skeleton).inCoeffDomain()) |
---|
3073 | G_random_element= |
---|
3074 | monicSparseInterpol (ppA (random_element, x),ppB(random_element, x), |
---|
3075 | skeleton,V_buf, sparseFail,coeffMonoms, Monoms); |
---|
3076 | else |
---|
3077 | G_random_element= |
---|
3078 | nonMonicSparseInterpol (ppA(random_element,x),ppB(random_element,x), |
---|
3079 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3080 | Monoms); |
---|
3081 | if (sparseFail) |
---|
3082 | break; |
---|
3083 | |
---|
3084 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3085 | "time for recursive call: "); |
---|
3086 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3087 | } |
---|
3088 | |
---|
3089 | if (!G_random_element.inCoeffDomain()) |
---|
3090 | d0= totaldegree (G_random_element, Variable(2), |
---|
3091 | Variable (G_random_element.level())); |
---|
3092 | else |
---|
3093 | d0= 0; |
---|
3094 | |
---|
3095 | if (d0 == 0) |
---|
3096 | return N(gcdcAcB); |
---|
3097 | if (d0 > d) |
---|
3098 | { |
---|
3099 | if (!find (l, random_element)) |
---|
3100 | l.append (random_element); |
---|
3101 | continue; |
---|
3102 | } |
---|
3103 | |
---|
3104 | G_random_element= |
---|
3105 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3106 | * G_random_element; |
---|
3107 | |
---|
3108 | if (!G_random_element.inCoeffDomain()) |
---|
3109 | d0= totaldegree (G_random_element, Variable(2), |
---|
3110 | Variable (G_random_element.level())); |
---|
3111 | else |
---|
3112 | d0= 0; |
---|
3113 | |
---|
3114 | if (d0 < d) |
---|
3115 | { |
---|
3116 | m= gcdlcAlcB; |
---|
3117 | newtonPoly= 1; |
---|
3118 | G_m= 0; |
---|
3119 | d= d0; |
---|
3120 | } |
---|
3121 | |
---|
3122 | TIMING_START (newton_interpolation); |
---|
3123 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3124 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
3125 | "time for newton interpolation: "); |
---|
3126 | |
---|
3127 | //termination test |
---|
3128 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3129 | { |
---|
3130 | cH= uni_content (H); |
---|
3131 | ppH= H/cH; |
---|
3132 | if (inextension) |
---|
3133 | { |
---|
3134 | CFList u, v; |
---|
3135 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
3136 | //mapping down |
---|
3137 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3138 | { |
---|
3139 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
3140 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
3141 | ppH /= Lc(ppH); |
---|
3142 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
3143 | return N(gcdcAcB*ppH); |
---|
3144 | } |
---|
3145 | } |
---|
3146 | else if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3147 | { |
---|
3148 | return N(gcdcAcB*ppH); |
---|
3149 | } |
---|
3150 | } |
---|
3151 | |
---|
3152 | G_m= H; |
---|
3153 | newtonPoly= newtonPoly*(x - random_element); |
---|
3154 | m= m*(x - random_element); |
---|
3155 | if (!find (l, random_element)) |
---|
3156 | l.append (random_element); |
---|
3157 | |
---|
3158 | } while (1); |
---|
3159 | } |
---|
3160 | } while (1); |
---|
3161 | } |
---|
3162 | |
---|
3163 | CanonicalForm sparseGCDFp (const CanonicalForm& F, const CanonicalForm& G, |
---|
3164 | bool& topLevel, CFList& l) |
---|
3165 | { |
---|
3166 | CanonicalForm A= F; |
---|
3167 | CanonicalForm B= G; |
---|
3168 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
3169 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
3170 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
3171 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
3172 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
3173 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
3174 | if (F == G) return F/Lc(F); |
---|
3175 | |
---|
3176 | CFMap M,N; |
---|
3177 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
3178 | |
---|
3179 | if (best_level == 0) return B.genOne(); |
---|
3180 | |
---|
3181 | A= M(A); |
---|
3182 | B= M(B); |
---|
3183 | |
---|
3184 | Variable x= Variable (1); |
---|
3185 | |
---|
3186 | //univariate case |
---|
3187 | if (A.isUnivariate() && B.isUnivariate()) |
---|
3188 | return N (gcd (A, B)); |
---|
3189 | |
---|
3190 | CanonicalForm cA, cB; // content of A and B |
---|
3191 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
3192 | CanonicalForm gcdcAcB; |
---|
3193 | if (topLevel) |
---|
3194 | { |
---|
3195 | if (best_level <= 2) |
---|
3196 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
---|
3197 | else |
---|
3198 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
---|
3199 | } |
---|
3200 | else |
---|
3201 | { |
---|
3202 | cA = uni_content (A); |
---|
3203 | cB = uni_content (B); |
---|
3204 | gcdcAcB= gcd (cA, cB); |
---|
3205 | ppA= A/cA; |
---|
3206 | ppB= B/cB; |
---|
3207 | } |
---|
3208 | |
---|
3209 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
3210 | CanonicalForm gcdlcAlcB; |
---|
3211 | lcA= uni_lcoeff (ppA); |
---|
3212 | lcB= uni_lcoeff (ppB); |
---|
3213 | |
---|
3214 | if (fdivides (lcA, lcB)) |
---|
3215 | { |
---|
3216 | if (fdivides (A, B)) |
---|
3217 | return F/Lc(F); |
---|
3218 | } |
---|
3219 | if (fdivides (lcB, lcA)) |
---|
3220 | { |
---|
3221 | if (fdivides (B, A)) |
---|
3222 | return G/Lc(G); |
---|
3223 | } |
---|
3224 | |
---|
3225 | gcdlcAlcB= gcd (lcA, lcB); |
---|
3226 | |
---|
3227 | int d= totaldegree (ppA, Variable (2), Variable (ppA.level())); |
---|
3228 | int d0; |
---|
3229 | |
---|
3230 | if (d == 0) |
---|
3231 | return N(gcdcAcB); |
---|
3232 | |
---|
3233 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
3234 | |
---|
3235 | if (d0 < d) |
---|
3236 | d= d0; |
---|
3237 | |
---|
3238 | if (d == 0) |
---|
3239 | return N(gcdcAcB); |
---|
3240 | |
---|
3241 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH, skeleton; |
---|
3242 | CanonicalForm newtonPoly= 1; |
---|
3243 | m= gcdlcAlcB; |
---|
3244 | G_m= 0; |
---|
3245 | H= 0; |
---|
3246 | bool fail= false; |
---|
3247 | topLevel= false; |
---|
3248 | bool inextension= false; |
---|
3249 | bool inextensionextension= false; |
---|
3250 | Variable V_buf, alpha; |
---|
3251 | CanonicalForm prim_elem, im_prim_elem; |
---|
3252 | CFList source, dest; |
---|
3253 | do //first do |
---|
3254 | { |
---|
3255 | if (inextension) |
---|
3256 | random_element= randomElement (m, V_buf, l, fail); |
---|
3257 | else |
---|
3258 | random_element= FpRandomElement (m, l, fail); |
---|
3259 | if (random_element == 0 && !fail) |
---|
3260 | { |
---|
3261 | if (!find (l, random_element)) |
---|
3262 | l.append (random_element); |
---|
3263 | continue; |
---|
3264 | } |
---|
3265 | |
---|
3266 | if (!fail && !inextension) |
---|
3267 | { |
---|
3268 | CFList list; |
---|
3269 | TIMING_START (gcd_recursion); |
---|
3270 | G_random_element= |
---|
3271 | sparseGCDFp (ppA (random_element,x), ppB (random_element,x), topLevel, |
---|
3272 | list); |
---|
3273 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3274 | "time for recursive call: "); |
---|
3275 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3276 | } |
---|
3277 | else if (!fail && inextension) |
---|
3278 | { |
---|
3279 | CFList list; |
---|
3280 | TIMING_START (gcd_recursion); |
---|
3281 | G_random_element= |
---|
3282 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
3283 | list, topLevel); |
---|
3284 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3285 | "time for recursive call: "); |
---|
3286 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3287 | } |
---|
3288 | else if (fail && !inextension) |
---|
3289 | { |
---|
3290 | source= CFList(); |
---|
3291 | dest= CFList(); |
---|
3292 | CFList list; |
---|
3293 | CanonicalForm mipo; |
---|
3294 | int deg= 2; |
---|
3295 | do |
---|
3296 | { |
---|
3297 | mipo= randomIrredpoly (deg, x); |
---|
3298 | alpha= rootOf (mipo); |
---|
3299 | inextension= true; |
---|
3300 | fail= false; |
---|
3301 | random_element= randomElement (m, alpha, l, fail); |
---|
3302 | deg++; |
---|
3303 | } while (fail); |
---|
3304 | V_buf= alpha; |
---|
3305 | list= CFList(); |
---|
3306 | TIMING_START (gcd_recursion); |
---|
3307 | G_random_element= |
---|
3308 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
3309 | list, topLevel); |
---|
3310 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3311 | "time for recursive call: "); |
---|
3312 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3313 | } |
---|
3314 | else if (fail && inextension) |
---|
3315 | { |
---|
3316 | source= CFList(); |
---|
3317 | dest= CFList(); |
---|
3318 | |
---|
3319 | Variable V_buf3= V_buf; |
---|
3320 | V_buf= chooseExtension (V_buf); |
---|
3321 | bool prim_fail= false; |
---|
3322 | Variable V_buf2; |
---|
3323 | CanonicalForm prim_elem, im_prim_elem; |
---|
3324 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3325 | |
---|
3326 | if (V_buf3 != alpha) |
---|
3327 | { |
---|
3328 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3329 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3330 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, source, |
---|
3331 | dest); |
---|
3332 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3333 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3334 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, source, |
---|
3335 | dest); |
---|
3336 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3337 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3338 | source, dest); |
---|
3339 | } |
---|
3340 | |
---|
3341 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3342 | if (prim_fail) |
---|
3343 | ; //ERROR |
---|
3344 | else |
---|
3345 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3346 | |
---|
3347 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3348 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
3349 | |
---|
3350 | inextensionextension= true; |
---|
3351 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3352 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3353 | im_prim_elem, source, dest); |
---|
3354 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3355 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3356 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3357 | source, dest); |
---|
3358 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3359 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3360 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3361 | source, dest); |
---|
3362 | fail= false; |
---|
3363 | random_element= randomElement (m, V_buf, l, fail ); |
---|
3364 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3365 | CFList list; |
---|
3366 | TIMING_START (gcd_recursion); |
---|
3367 | G_random_element= |
---|
3368 | sparseGCDFq (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
3369 | list, topLevel); |
---|
3370 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3371 | "time for recursive call: "); |
---|
3372 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3373 | } |
---|
3374 | |
---|
3375 | if (!G_random_element.inCoeffDomain()) |
---|
3376 | d0= totaldegree (G_random_element, Variable(2), |
---|
3377 | Variable (G_random_element.level())); |
---|
3378 | else |
---|
3379 | d0= 0; |
---|
3380 | |
---|
3381 | if (d0 == 0) |
---|
3382 | return N(gcdcAcB); |
---|
3383 | if (d0 > d) |
---|
3384 | { |
---|
3385 | if (!find (l, random_element)) |
---|
3386 | l.append (random_element); |
---|
3387 | continue; |
---|
3388 | } |
---|
3389 | |
---|
3390 | G_random_element= |
---|
3391 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3392 | * G_random_element; |
---|
3393 | |
---|
3394 | skeleton= G_random_element; |
---|
3395 | |
---|
3396 | if (!G_random_element.inCoeffDomain()) |
---|
3397 | d0= totaldegree (G_random_element, Variable(2), |
---|
3398 | Variable (G_random_element.level())); |
---|
3399 | else |
---|
3400 | d0= 0; |
---|
3401 | |
---|
3402 | if (d0 < d) |
---|
3403 | { |
---|
3404 | m= gcdlcAlcB; |
---|
3405 | newtonPoly= 1; |
---|
3406 | G_m= 0; |
---|
3407 | d= d0; |
---|
3408 | } |
---|
3409 | |
---|
3410 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3411 | |
---|
3412 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3413 | { |
---|
3414 | cH= uni_content (H); |
---|
3415 | ppH= H/cH; |
---|
3416 | ppH /= Lc (ppH); |
---|
3417 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
3418 | |
---|
3419 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3420 | return N(gcdcAcB*ppH); |
---|
3421 | } |
---|
3422 | G_m= H; |
---|
3423 | newtonPoly= newtonPoly*(x - random_element); |
---|
3424 | m= m*(x - random_element); |
---|
3425 | if (!find (l, random_element)) |
---|
3426 | l.append (random_element); |
---|
3427 | |
---|
3428 | if ((getCharacteristic() > 3 && size (skeleton) < 100)) |
---|
3429 | { |
---|
3430 | CFArray Monoms; |
---|
3431 | CFArray* coeffMonoms= NULL; |
---|
3432 | |
---|
3433 | do //second do |
---|
3434 | { |
---|
3435 | if (inextension) |
---|
3436 | random_element= randomElement (m, alpha, l, fail); |
---|
3437 | else |
---|
3438 | random_element= FpRandomElement (m, l, fail); |
---|
3439 | if (random_element == 0 && !fail) |
---|
3440 | { |
---|
3441 | if (!find (l, random_element)) |
---|
3442 | l.append (random_element); |
---|
3443 | continue; |
---|
3444 | } |
---|
3445 | |
---|
3446 | bool sparseFail= false; |
---|
3447 | if (!fail && !inextension) |
---|
3448 | { |
---|
3449 | CFList list; |
---|
3450 | TIMING_START (gcd_recursion); |
---|
3451 | if (LC (skeleton).inCoeffDomain()) |
---|
3452 | G_random_element= |
---|
3453 | monicSparseInterpol(ppA(random_element, x), ppB (random_element, x), |
---|
3454 | skeleton, Variable(1), sparseFail, coeffMonoms, |
---|
3455 | Monoms); |
---|
3456 | else |
---|
3457 | G_random_element= |
---|
3458 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3459 | skeleton, Variable (1), sparseFail, |
---|
3460 | coeffMonoms, Monoms); |
---|
3461 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3462 | "time for recursive call: "); |
---|
3463 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3464 | } |
---|
3465 | else if (!fail && inextension) |
---|
3466 | { |
---|
3467 | CFList list; |
---|
3468 | TIMING_START (gcd_recursion); |
---|
3469 | if (LC (skeleton).inCoeffDomain()) |
---|
3470 | G_random_element= |
---|
3471 | monicSparseInterpol(ppA (random_element,x), ppB (random_element, x), |
---|
3472 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3473 | Monoms); |
---|
3474 | else |
---|
3475 | G_random_element= |
---|
3476 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3477 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3478 | Monoms); |
---|
3479 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3480 | "time for recursive call: "); |
---|
3481 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3482 | } |
---|
3483 | else if (fail && !inextension) |
---|
3484 | { |
---|
3485 | source= CFList(); |
---|
3486 | dest= CFList(); |
---|
3487 | CFList list; |
---|
3488 | CanonicalForm mipo; |
---|
3489 | int deg= 2; |
---|
3490 | do |
---|
3491 | { |
---|
3492 | mipo= randomIrredpoly (deg, x); |
---|
3493 | alpha= rootOf (mipo); |
---|
3494 | inextension= true; |
---|
3495 | fail= false; |
---|
3496 | random_element= randomElement (m, alpha, l, fail); |
---|
3497 | deg++; |
---|
3498 | } while (fail); |
---|
3499 | V_buf= alpha; |
---|
3500 | list= CFList(); |
---|
3501 | TIMING_START (gcd_recursion); |
---|
3502 | if (LC (skeleton).inCoeffDomain()) |
---|
3503 | G_random_element= |
---|
3504 | monicSparseInterpol (ppA (random_element,x), ppB (random_element,x), |
---|
3505 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3506 | Monoms); |
---|
3507 | else |
---|
3508 | G_random_element= |
---|
3509 | nonMonicSparseInterpol(ppA(random_element,x), ppB(random_element,x), |
---|
3510 | skeleton, alpha, sparseFail, coeffMonoms, |
---|
3511 | Monoms); |
---|
3512 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3513 | "time for recursive call: "); |
---|
3514 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3515 | } |
---|
3516 | else if (fail && inextension) |
---|
3517 | { |
---|
3518 | source= CFList(); |
---|
3519 | dest= CFList(); |
---|
3520 | |
---|
3521 | Variable V_buf3= V_buf; |
---|
3522 | V_buf= chooseExtension (V_buf); |
---|
3523 | bool prim_fail= false; |
---|
3524 | Variable V_buf2; |
---|
3525 | CanonicalForm prim_elem, im_prim_elem; |
---|
3526 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
3527 | |
---|
3528 | if (V_buf3 != alpha) |
---|
3529 | { |
---|
3530 | m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3531 | G_m= mapDown (m, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3532 | newtonPoly= mapDown (newtonPoly, prim_elem, im_prim_elem, alpha, |
---|
3533 | source, dest); |
---|
3534 | ppA= mapDown (ppA, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3535 | ppB= mapDown (ppB, prim_elem, im_prim_elem, alpha, source, dest); |
---|
3536 | gcdlcAlcB= mapDown (gcdlcAlcB, prim_elem, im_prim_elem, alpha, |
---|
3537 | source, dest); |
---|
3538 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3539 | i.getItem()= mapDown (i.getItem(), prim_elem, im_prim_elem, alpha, |
---|
3540 | source, dest); |
---|
3541 | } |
---|
3542 | |
---|
3543 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
3544 | if (prim_fail) |
---|
3545 | ; //ERROR |
---|
3546 | else |
---|
3547 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
3548 | |
---|
3549 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
3550 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
3551 | |
---|
3552 | inextensionextension= true; |
---|
3553 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
3554 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
3555 | im_prim_elem, source, dest); |
---|
3556 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3557 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3558 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3559 | source, dest); |
---|
3560 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3561 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
3562 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
3563 | source, dest); |
---|
3564 | fail= false; |
---|
3565 | random_element= randomElement (m, V_buf, l, fail ); |
---|
3566 | DEBOUTLN (cerr, "fail= " << fail); |
---|
3567 | CFList list; |
---|
3568 | TIMING_START (gcd_recursion); |
---|
3569 | if (LC (skeleton).inCoeffDomain()) |
---|
3570 | G_random_element= |
---|
3571 | monicSparseInterpol (ppA (random_element, x), ppB (random_element, x), |
---|
3572 | skeleton, V_buf, sparseFail, coeffMonoms, |
---|
3573 | Monoms); |
---|
3574 | else |
---|
3575 | G_random_element= |
---|
3576 | nonMonicSparseInterpol (ppA(random_element,x), ppB(random_element,x), |
---|
3577 | skeleton, V_buf, sparseFail, |
---|
3578 | coeffMonoms, Monoms); |
---|
3579 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
3580 | "time for recursive call: "); |
---|
3581 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
3582 | } |
---|
3583 | |
---|
3584 | if (sparseFail) |
---|
3585 | break; |
---|
3586 | |
---|
3587 | if (!G_random_element.inCoeffDomain()) |
---|
3588 | d0= totaldegree (G_random_element, Variable(2), |
---|
3589 | Variable (G_random_element.level())); |
---|
3590 | else |
---|
3591 | d0= 0; |
---|
3592 | |
---|
3593 | if (d0 == 0) |
---|
3594 | return N(gcdcAcB); |
---|
3595 | if (d0 > d) |
---|
3596 | { |
---|
3597 | if (!find (l, random_element)) |
---|
3598 | l.append (random_element); |
---|
3599 | continue; |
---|
3600 | } |
---|
3601 | |
---|
3602 | G_random_element= |
---|
3603 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
3604 | * G_random_element; |
---|
3605 | |
---|
3606 | if (!G_random_element.inCoeffDomain()) |
---|
3607 | d0= totaldegree (G_random_element, Variable(2), |
---|
3608 | Variable (G_random_element.level())); |
---|
3609 | else |
---|
3610 | d0= 0; |
---|
3611 | |
---|
3612 | if (d0 < d) |
---|
3613 | { |
---|
3614 | m= gcdlcAlcB; |
---|
3615 | newtonPoly= 1; |
---|
3616 | G_m= 0; |
---|
3617 | d= d0; |
---|
3618 | } |
---|
3619 | |
---|
3620 | TIMING_START (newton_interpolation); |
---|
3621 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
3622 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
3623 | "time for newton interpolation: "); |
---|
3624 | |
---|
3625 | //termination test |
---|
3626 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
3627 | { |
---|
3628 | cH= uni_content (H); |
---|
3629 | ppH= H/cH; |
---|
3630 | ppH /= Lc (ppH); |
---|
3631 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
3632 | if (fdivides (ppH, ppA) && fdivides (ppH, ppB)) |
---|
3633 | return N(gcdcAcB*ppH); |
---|
3634 | } |
---|
3635 | |
---|
3636 | G_m= H; |
---|
3637 | newtonPoly= newtonPoly*(x - random_element); |
---|
3638 | m= m*(x - random_element); |
---|
3639 | if (!find (l, random_element)) |
---|
3640 | l.append (random_element); |
---|
3641 | |
---|
3642 | } while (1); //end of second do |
---|
3643 | } |
---|
3644 | } while (1); //end of first do |
---|
3645 | } |
---|
3646 | |
---|
3647 | static inline |
---|
3648 | int compress4EZGCD (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
---|
3649 | CFMap & N, int& both_non_zero) |
---|
3650 | { |
---|
3651 | int n= tmax (F.level(), G.level()); |
---|
3652 | int * degsf= new int [n + 1]; |
---|
3653 | int * degsg= new int [n + 1]; |
---|
3654 | |
---|
3655 | for (int i = 0; i <= n; i++) |
---|
3656 | degsf[i]= degsg[i]= 0; |
---|
3657 | |
---|
3658 | degsf= degrees (F, degsf); |
---|
3659 | degsg= degrees (G, degsg); |
---|
3660 | |
---|
3661 | both_non_zero= 0; |
---|
3662 | int f_zero= 0; |
---|
3663 | int g_zero= 0; |
---|
3664 | |
---|
3665 | for (int i= 1; i <= n; i++) |
---|
3666 | { |
---|
3667 | if (degsf[i] != 0 && degsg[i] != 0) |
---|
3668 | { |
---|
3669 | both_non_zero++; |
---|
3670 | continue; |
---|
3671 | } |
---|
3672 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
3673 | { |
---|
3674 | f_zero++; |
---|
3675 | continue; |
---|
3676 | } |
---|
3677 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
---|
3678 | { |
---|
3679 | g_zero++; |
---|
3680 | continue; |
---|
3681 | } |
---|
3682 | } |
---|
3683 | |
---|
3684 | if (both_non_zero == 0) |
---|
3685 | { |
---|
3686 | delete [] degsf; |
---|
3687 | delete [] degsg; |
---|
3688 | return 0; |
---|
3689 | } |
---|
3690 | |
---|
3691 | // map Variables which do not occur in both polynomials to higher levels |
---|
3692 | int k= 1; |
---|
3693 | int l= 1; |
---|
3694 | for (int i= 1; i <= n; i++) |
---|
3695 | { |
---|
3696 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
---|
3697 | { |
---|
3698 | if (k + both_non_zero != i) |
---|
3699 | { |
---|
3700 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
---|
3701 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
---|
3702 | } |
---|
3703 | k++; |
---|
3704 | } |
---|
3705 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
---|
3706 | { |
---|
3707 | if (l + g_zero + both_non_zero != i) |
---|
3708 | { |
---|
3709 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
---|
3710 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
---|
3711 | } |
---|
3712 | l++; |
---|
3713 | } |
---|
3714 | } |
---|
3715 | |
---|
3716 | // sort Variables x_{i} in decreasing order of |
---|
3717 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
---|
3718 | int m= tmin (F.level(), G.level()); |
---|
3719 | int max_min_deg; |
---|
3720 | k= both_non_zero; |
---|
3721 | l= 0; |
---|
3722 | int i= 1; |
---|
3723 | while (k > 0) |
---|
3724 | { |
---|
3725 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
3726 | while (max_min_deg == 0) |
---|
3727 | { |
---|
3728 | i++; |
---|
3729 | max_min_deg= tmin (degsf[i], degsg[i]); |
---|
3730 | } |
---|
3731 | for (int j= i + 1; j <= m; j++) |
---|
3732 | { |
---|
3733 | if ((tmin (degsf[j],degsg[j]) < max_min_deg) && |
---|
3734 | (tmin (degsf[j], degsg[j]) != 0)) |
---|
3735 | { |
---|
3736 | max_min_deg= tmin (degsf[j], degsg[j]); |
---|
3737 | l= j; |
---|
3738 | } |
---|
3739 | } |
---|
3740 | |
---|
3741 | if (l != 0) |
---|
3742 | { |
---|
3743 | if (l != k) |
---|
3744 | { |
---|
3745 | M.newpair (Variable (l), Variable(k)); |
---|
3746 | N.newpair (Variable (k), Variable(l)); |
---|
3747 | degsf[l]= 0; |
---|
3748 | degsg[l]= 0; |
---|
3749 | l= 0; |
---|
3750 | } |
---|
3751 | else |
---|
3752 | { |
---|
3753 | degsf[l]= 0; |
---|
3754 | degsg[l]= 0; |
---|
3755 | l= 0; |
---|
3756 | } |
---|
3757 | } |
---|
3758 | else if (l == 0) |
---|
3759 | { |
---|
3760 | if (i != k) |
---|
3761 | { |
---|
3762 | M.newpair (Variable (i), Variable (k)); |
---|
3763 | N.newpair (Variable (k), Variable (i)); |
---|
3764 | degsf[i]= 0; |
---|
3765 | degsg[i]= 0; |
---|
3766 | } |
---|
3767 | else |
---|
3768 | { |
---|
3769 | degsf[i]= 0; |
---|
3770 | degsg[i]= 0; |
---|
3771 | } |
---|
3772 | i++; |
---|
3773 | } |
---|
3774 | k--; |
---|
3775 | } |
---|
3776 | |
---|
3777 | delete [] degsf; |
---|
3778 | delete [] degsg; |
---|
3779 | |
---|
3780 | return both_non_zero; |
---|
3781 | } |
---|
3782 | |
---|
3783 | static inline |
---|
3784 | CanonicalForm myShift2Zero (const CanonicalForm& F, CFList& Feval, |
---|
3785 | const CFList& evaluation) |
---|
3786 | { |
---|
3787 | CanonicalForm A= F; |
---|
3788 | int k= 2; |
---|
3789 | for (CFListIterator i= evaluation; i.hasItem(); i++, k++) |
---|
3790 | A= A (Variable (k) + i.getItem(), k); |
---|
3791 | |
---|
3792 | CanonicalForm buf= A; |
---|
3793 | Feval= CFList(); |
---|
3794 | Feval.append (buf); |
---|
3795 | for (k= evaluation.length() + 1; k > 2; k--) |
---|
3796 | { |
---|
3797 | buf= mod (buf, Variable (k)); |
---|
3798 | Feval.insert (buf); |
---|
3799 | } |
---|
3800 | return A; |
---|
3801 | } |
---|
3802 | |
---|
3803 | static inline |
---|
3804 | CanonicalForm myReverseShift (const CanonicalForm& F, const CFList& evaluation) |
---|
3805 | { |
---|
3806 | int l= evaluation.length() + 1; |
---|
3807 | CanonicalForm result= F; |
---|
3808 | CFListIterator j= evaluation; |
---|
3809 | for (int i= 2; i < l + 1; i++, j++) |
---|
3810 | { |
---|
3811 | if (F.level() < i) |
---|
3812 | continue; |
---|
3813 | result= result (Variable (i) - j.getItem(), i); |
---|
3814 | } |
---|
3815 | return result; |
---|
3816 | } |
---|
3817 | |
---|
3818 | static inline |
---|
3819 | Evaluation optimize4Lift (const CanonicalForm& F, CFMap & M, |
---|
3820 | CFMap & N, const Evaluation& A) |
---|
3821 | { |
---|
3822 | int n= F.level(); |
---|
3823 | int * degsf= new int [n + 1]; |
---|
3824 | |
---|
3825 | for (int i = 0; i <= n; i++) |
---|
3826 | degsf[i]= 0; |
---|
3827 | |
---|
3828 | degsf= degrees (F, degsf); |
---|
3829 | |
---|
3830 | Evaluation result= Evaluation (A.min(), A.max()); |
---|
3831 | ASSERT (A.min() == 2, "expected A.min() == 2"); |
---|
3832 | ASSERT (A.max() >= n, "expected A.max() >= n"); |
---|
3833 | int max_deg; |
---|
3834 | int k= n; |
---|
3835 | int l= 1; |
---|
3836 | int i= 2; |
---|
3837 | int pos= 2; |
---|
3838 | while (k > 1) |
---|
3839 | { |
---|
3840 | max_deg= degsf [i]; |
---|
3841 | while (max_deg == 0) |
---|
3842 | { |
---|
3843 | i++; |
---|
3844 | max_deg= degsf [i]; |
---|
3845 | } |
---|
3846 | l= i; |
---|
3847 | for (int j= i + 1; j <= n; j++) |
---|
3848 | { |
---|
3849 | if (degsf[j] > max_deg) |
---|
3850 | { |
---|
3851 | max_deg= degsf[j]; |
---|
3852 | l= j; |
---|
3853 | } |
---|
3854 | } |
---|
3855 | |
---|
3856 | if (l <= n) |
---|
3857 | { |
---|
3858 | if (l != pos) |
---|
3859 | { |
---|
3860 | result.setValue (pos, A [l]); |
---|
3861 | M.newpair (Variable (l), Variable (pos)); |
---|
3862 | N.newpair (Variable (pos), Variable (l)); |
---|
3863 | degsf[l]= 0; |
---|
3864 | l= 2; |
---|
3865 | if (k == 2 && n == 3) |
---|
3866 | { |
---|
3867 | result.setValue (l, A [pos]); |
---|
3868 | M.newpair (Variable (pos), Variable (l)); |
---|
3869 | N.newpair (Variable (l), Variable (pos)); |
---|
3870 | degsf[pos]= 0; |
---|
3871 | } |
---|
3872 | } |
---|
3873 | else |
---|
3874 | { |
---|
3875 | result.setValue (l, A [l]); |
---|
3876 | degsf [l]= 0; |
---|
3877 | } |
---|
3878 | } |
---|
3879 | pos++; |
---|
3880 | k--; |
---|
3881 | l= 2; |
---|
3882 | } |
---|
3883 | |
---|
3884 | delete [] degsf; |
---|
3885 | |
---|
3886 | return result; |
---|
3887 | } |
---|
3888 | |
---|
3889 | static inline |
---|
3890 | int Hensel_P (const CanonicalForm & UU, CFArray & G, const Evaluation & AA, |
---|
3891 | const CFArray& LeadCoeffs ) |
---|
3892 | { |
---|
3893 | CFList factors; |
---|
3894 | factors.append (G[1]); |
---|
3895 | factors.append (G[2]); |
---|
3896 | |
---|
3897 | CFMap NN, MM; |
---|
3898 | Evaluation A= optimize4Lift (UU, MM, NN, AA); |
---|
3899 | |
---|
3900 | CanonicalForm U= MM (UU); |
---|
3901 | CFArray LCs= CFArray (1,2); |
---|
3902 | LCs [1]= MM (LeadCoeffs [1]); |
---|
3903 | LCs [2]= MM (LeadCoeffs [2]); |
---|
3904 | |
---|
3905 | CFList evaluation; |
---|
3906 | for (int i= A.min(); i <= A.max(); i++) |
---|
3907 | evaluation.append (A [i]); |
---|
3908 | CFList UEval; |
---|
3909 | CanonicalForm shiftedU= myShift2Zero (U, UEval, evaluation); |
---|
3910 | |
---|
3911 | if (size (shiftedU)/getNumVars (U) > 500) |
---|
3912 | return -1; |
---|
3913 | |
---|
3914 | CFArray shiftedLCs= CFArray (2); |
---|
3915 | CFList shiftedLCsEval1, shiftedLCsEval2; |
---|
3916 | shiftedLCs[0]= myShift2Zero (LCs[1], shiftedLCsEval1, evaluation); |
---|
3917 | shiftedLCs[1]= myShift2Zero (LCs[2], shiftedLCsEval2, evaluation); |
---|
3918 | factors.insert (1); |
---|
3919 | int liftBound= degree (UEval.getLast(), 2) + 1; |
---|
3920 | CFArray Pi; |
---|
3921 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
---|
3922 | CFList diophant; |
---|
3923 | CFArray lcs= CFArray (2); |
---|
3924 | lcs [0]= shiftedLCsEval1.getFirst(); |
---|
3925 | lcs [1]= shiftedLCsEval2.getFirst(); |
---|
3926 | nonMonicHenselLift12 (UEval.getFirst(), factors, liftBound, Pi, diophant, M, |
---|
3927 | lcs, false); |
---|
3928 | |
---|
3929 | for (CFListIterator i= factors; i.hasItem(); i++) |
---|
3930 | { |
---|
3931 | if (!fdivides (i.getItem(), UEval.getFirst())) |
---|
3932 | return 0; |
---|
3933 | } |
---|
3934 | |
---|
3935 | int * liftBounds; |
---|
3936 | bool noOneToOne= false; |
---|
3937 | if (U.level() > 2) |
---|
3938 | { |
---|
3939 | liftBounds= new int [U.level() - 1]; /* index: 0.. U.level()-2 */ |
---|
3940 | liftBounds[0]= liftBound; |
---|
3941 | for (int i= 1; i < U.level() - 1; i++) |
---|
3942 | liftBounds[i]= degree (shiftedU, Variable (i + 2)) + 1; |
---|
3943 | factors= nonMonicHenselLift2 (UEval, factors, liftBounds, U.level() - 1, |
---|
3944 | false, shiftedLCsEval1, shiftedLCsEval2, Pi, |
---|
3945 | diophant, noOneToOne); |
---|
3946 | delete [] liftBounds; |
---|
3947 | if (noOneToOne) |
---|
3948 | return 0; |
---|
3949 | } |
---|
3950 | G[1]= factors.getFirst(); |
---|
3951 | G[2]= factors.getLast(); |
---|
3952 | G[1]= myReverseShift (G[1], evaluation); |
---|
3953 | G[2]= myReverseShift (G[2], evaluation); |
---|
3954 | G[1]= NN (G[1]); |
---|
3955 | G[2]= NN (G[2]); |
---|
3956 | return 1; |
---|
3957 | } |
---|
3958 | |
---|
3959 | static inline |
---|
3960 | bool findeval_P (const CanonicalForm & F, const CanonicalForm & G, |
---|
3961 | CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, |
---|
3962 | REvaluation & b, int delta, int degF, int degG, int maxeval, |
---|
3963 | int & count, int& k, int bound, int& l) |
---|
3964 | { |
---|
3965 | if( count == 0 && delta != 0) |
---|
3966 | { |
---|
3967 | if( count++ > maxeval ) |
---|
3968 | return false; |
---|
3969 | } |
---|
3970 | if (count > 0) |
---|
3971 | { |
---|
3972 | b.nextpoint(k); |
---|
3973 | if (k == 0) |
---|
3974 | k++; |
---|
3975 | l++; |
---|
3976 | if (l > bound) |
---|
3977 | { |
---|
3978 | l= 1; |
---|
3979 | k++; |
---|
3980 | if (k > tmax (F.level(), G.level()) - 1) |
---|
3981 | return false; |
---|
3982 | b.nextpoint (k); |
---|
3983 | } |
---|
3984 | if (count++ > maxeval) |
---|
3985 | return false; |
---|
3986 | } |
---|
3987 | while( true ) |
---|
3988 | { |
---|
3989 | Fb = b( F ); |
---|
3990 | if( degree( Fb, 1 ) == degF ) |
---|
3991 | { |
---|
3992 | Gb = b( G ); |
---|
3993 | if( degree( Gb, 1 ) == degG ) |
---|
3994 | { |
---|
3995 | Db = gcd( Fb, Gb ); |
---|
3996 | if( delta > 0 ) |
---|
3997 | { |
---|
3998 | if( degree( Db, 1 ) <= delta ) |
---|
3999 | return true; |
---|
4000 | } |
---|
4001 | else |
---|
4002 | return true; |
---|
4003 | } |
---|
4004 | } |
---|
4005 | if (k == 0) |
---|
4006 | k++; |
---|
4007 | b.nextpoint(k); |
---|
4008 | l++; |
---|
4009 | if (l > bound) |
---|
4010 | { |
---|
4011 | l= 1; |
---|
4012 | k++; |
---|
4013 | if (k > tmax (F.level(), G.level()) - 1) |
---|
4014 | return false; |
---|
4015 | b.nextpoint (k); |
---|
4016 | } |
---|
4017 | if( count++ > maxeval ) |
---|
4018 | return false; |
---|
4019 | } |
---|
4020 | } |
---|
4021 | |
---|
4022 | // parameters for heuristic |
---|
4023 | static int maxNumEval= 200; |
---|
4024 | static int sizePerVars1= 500; //try dense gcd if size/#variables is bigger |
---|
4025 | |
---|
4026 | /// Extended Zassenhaus GCD for finite fields |
---|
4027 | CanonicalForm EZGCD_P( const CanonicalForm & FF, const CanonicalForm & GG ) |
---|
4028 | { |
---|
4029 | if (FF.isZero() && degree(GG) > 0) return GG/Lc(GG); |
---|
4030 | else if (GG.isZero() && degree (FF) > 0) return FF/Lc(FF); |
---|
4031 | else if (FF.isZero() && GG.isZero()) return FF.genOne(); |
---|
4032 | if (FF.inBaseDomain() || GG.inBaseDomain()) return FF.genOne(); |
---|
4033 | if (FF.isUnivariate() && fdivides(FF, GG)) return FF/Lc(FF); |
---|
4034 | if (GG.isUnivariate() && fdivides(GG, FF)) return GG/Lc(GG); |
---|
4035 | if (FF == GG) return FF/Lc(FF); |
---|
4036 | |
---|
4037 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, |
---|
4038 | lcD; |
---|
4039 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
---|
4040 | int degF, degG, delta, count; |
---|
4041 | int maxeval; |
---|
4042 | maxeval= tmin((getCharacteristic()/ |
---|
4043 | (int)(ilog2(getCharacteristic())*log2exp))*2, maxNumEval); |
---|
4044 | count= 0; // number of eval. used |
---|
4045 | REvaluation b, bt; |
---|
4046 | int gcdfound = 0; |
---|
4047 | Variable x = Variable(1); |
---|
4048 | |
---|
4049 | F= FF; |
---|
4050 | G= GG; |
---|
4051 | |
---|
4052 | CFMap M,N; |
---|
4053 | int smallestDegLev; |
---|
4054 | int best_level= compress4EZGCD (F, G, M, N, smallestDegLev); |
---|
4055 | |
---|
4056 | if (best_level == 0) return G.genOne(); |
---|
4057 | |
---|
4058 | F= M (F); |
---|
4059 | G= M (G); |
---|
4060 | |
---|
4061 | f = content( F, x ); g = content( G, x ); |
---|
4062 | d = gcd( f, g ); |
---|
4063 | F /= f; G /= g; |
---|
4064 | |
---|
4065 | if( F.isUnivariate() && G.isUnivariate() ) |
---|
4066 | { |
---|
4067 | if( F.mvar() == G.mvar() ) |
---|
4068 | d *= gcd( F, G ); |
---|
4069 | return N (d); |
---|
4070 | } |
---|
4071 | |
---|
4072 | int maxNumVars= tmax (getNumVars (F), getNumVars (G)); |
---|
4073 | Variable a, oldA; |
---|
4074 | int sizeF= size (F); |
---|
4075 | int sizeG= size (G); |
---|
4076 | |
---|
4077 | if (sizeF/maxNumVars > sizePerVars1 && sizeG/maxNumVars > sizePerVars1) |
---|
4078 | { |
---|
4079 | if (hasFirstAlgVar (F, a) || hasFirstAlgVar (G, a)) |
---|
4080 | return N (d*GCD_Fp_extension (F, G, a)); |
---|
4081 | else if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4082 | return N (d*GCD_GF (F, G)); |
---|
4083 | else |
---|
4084 | return N (d*GCD_small_p (F, G)); |
---|
4085 | } |
---|
4086 | |
---|
4087 | if( gcd_test_one( F, G, false ) ) |
---|
4088 | { |
---|
4089 | return N (d); |
---|
4090 | } |
---|
4091 | |
---|
4092 | bool passToGF= false; |
---|
4093 | bool extOfExt= false; |
---|
4094 | int p= getCharacteristic(); |
---|
4095 | bool algExtension= (hasFirstAlgVar(F,a) || hasFirstAlgVar(G,a)); |
---|
4096 | int k= 1; |
---|
4097 | CanonicalForm primElem, imPrimElem; |
---|
4098 | CFList source, dest; |
---|
4099 | if (p < 50 && CFFactory::gettype() != GaloisFieldDomain && !algExtension) |
---|
4100 | { |
---|
4101 | if (p == 2) |
---|
4102 | setCharacteristic (2, 6, 'Z'); |
---|
4103 | else if (p == 3) |
---|
4104 | setCharacteristic (3, 4, 'Z'); |
---|
4105 | else if (p == 5 || p == 7) |
---|
4106 | setCharacteristic (p, 3, 'Z'); |
---|
4107 | else |
---|
4108 | setCharacteristic (p, 2, 'Z'); |
---|
4109 | passToGF= true; |
---|
4110 | F= F.mapinto(); |
---|
4111 | G= G.mapinto(); |
---|
4112 | maxeval= 2*ipower (p, getGFDegree()); |
---|
4113 | } |
---|
4114 | else if (CFFactory::gettype() == GaloisFieldDomain && |
---|
4115 | ipower (p , getGFDegree()) < 50) |
---|
4116 | { |
---|
4117 | k= getGFDegree(); |
---|
4118 | if (ipower (p, 2*k) > 50) |
---|
4119 | setCharacteristic (p, 2*k, gf_name); |
---|
4120 | else |
---|
4121 | setCharacteristic (p, 3*k, gf_name); |
---|
4122 | F= GFMapUp (F, k); |
---|
4123 | G= GFMapUp (G, k); |
---|
4124 | maxeval= tmin (2*ipower (p, getGFDegree()), maxNumEval); |
---|
4125 | } |
---|
4126 | else if (p < 50 && algExtension && !CFFactory::gettype() == GaloisFieldDomain) |
---|
4127 | { |
---|
4128 | int d= degree (getMipo (a)); |
---|
4129 | oldA= a; |
---|
4130 | Variable v2; |
---|
4131 | if (p == 2 && d < 6) |
---|
4132 | { |
---|
4133 | zz_p::init (p); |
---|
4134 | bool primFail= false; |
---|
4135 | Variable vBuf; |
---|
4136 | primElem= primitiveElement (a, vBuf, primFail); |
---|
4137 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
4138 | if (d < 3) |
---|
4139 | { |
---|
4140 | zz_pX NTLIrredpoly; |
---|
4141 | BuildIrred (NTLIrredpoly, d*3); |
---|
4142 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4143 | v2= rootOf (newMipo); |
---|
4144 | } |
---|
4145 | else |
---|
4146 | { |
---|
4147 | zz_pX NTLIrredpoly; |
---|
4148 | BuildIrred (NTLIrredpoly, d*2); |
---|
4149 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4150 | v2= rootOf (newMipo); |
---|
4151 | } |
---|
4152 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
4153 | extOfExt= true; |
---|
4154 | } |
---|
4155 | else if ((p == 3 && d < 4) || ((p == 5 || p == 7) && d < 3)) |
---|
4156 | { |
---|
4157 | zz_p::init (p); |
---|
4158 | bool primFail= false; |
---|
4159 | Variable vBuf; |
---|
4160 | primElem= primitiveElement (a, vBuf, primFail); |
---|
4161 | ASSERT (!primFail, "failure in integer factorizer"); |
---|
4162 | zz_pX NTLIrredpoly; |
---|
4163 | BuildIrred (NTLIrredpoly, d*2); |
---|
4164 | CanonicalForm newMipo= convertNTLzzpX2CF (NTLIrredpoly, Variable (1)); |
---|
4165 | v2= rootOf (newMipo); |
---|
4166 | imPrimElem= mapPrimElem (primElem, a, v2); |
---|
4167 | extOfExt= true; |
---|
4168 | } |
---|
4169 | if (extOfExt) |
---|
4170 | { |
---|
4171 | maxeval= tmin (2*ipower (p, degree (getMipo (v2))), maxNumEval); |
---|
4172 | F= mapUp (F, a, v2, primElem, imPrimElem, source, dest); |
---|
4173 | G= mapUp (G, a, v2, primElem, imPrimElem, source, dest); |
---|
4174 | a= v2; |
---|
4175 | } |
---|
4176 | } |
---|
4177 | |
---|
4178 | lcF = LC( F, x ); lcG = LC( G, x ); |
---|
4179 | lcD = gcd( lcF, lcG ); |
---|
4180 | |
---|
4181 | delta = 0; |
---|
4182 | degF = degree( F, x ); degG = degree( G, x ); |
---|
4183 | |
---|
4184 | if(hasFirstAlgVar(G,a)) |
---|
4185 | b = REvaluation( 2, tmax(F.level(), G.level()), AlgExtRandomF( a ) ); |
---|
4186 | else |
---|
4187 | { // both not in extension given by algebraic variable |
---|
4188 | if (CFFactory::gettype() != GaloisFieldDomain) |
---|
4189 | b = REvaluation( 2, tmax(F.level(), G.level()), FFRandom() ); |
---|
4190 | else |
---|
4191 | b = REvaluation( 2, tmax(F.level(), G.level()), GFRandom() ); |
---|
4192 | } |
---|
4193 | |
---|
4194 | CanonicalForm cand; |
---|
4195 | CanonicalForm result; |
---|
4196 | int o, t; |
---|
4197 | o= 0; |
---|
4198 | t= 1; |
---|
4199 | int goodPointCount= 0; |
---|
4200 | while( !gcdfound ) |
---|
4201 | { |
---|
4202 | if( !findeval_P( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count, o, |
---|
4203 | maxeval/maxNumVars, t )) |
---|
4204 | { // too many eval. used --> try another method |
---|
4205 | Off (SW_USE_EZGCD_P); |
---|
4206 | result= gcd (F,G); |
---|
4207 | On (SW_USE_EZGCD_P); |
---|
4208 | if (passToGF) |
---|
4209 | { |
---|
4210 | CanonicalForm mipo= gf_mipo; |
---|
4211 | setCharacteristic (p); |
---|
4212 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4213 | result= GF2FalphaRep (result, alpha); |
---|
4214 | } |
---|
4215 | if (k > 1) |
---|
4216 | { |
---|
4217 | result= GFMapDown (result, k); |
---|
4218 | setCharacteristic (p, k, gf_name); |
---|
4219 | } |
---|
4220 | if (extOfExt) |
---|
4221 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4222 | return N (d*result); |
---|
4223 | } |
---|
4224 | delta = degree( Db ); |
---|
4225 | if( delta == 0 ) |
---|
4226 | { |
---|
4227 | if (passToGF) |
---|
4228 | setCharacteristic (p); |
---|
4229 | if (k > 1) |
---|
4230 | setCharacteristic (p, k, gf_name); |
---|
4231 | return N (d); |
---|
4232 | } |
---|
4233 | while( true ) |
---|
4234 | { |
---|
4235 | bt = b; |
---|
4236 | if( !findeval_P(F,G,Fbt,Gbt,Dbt, bt, delta, degF, degG, maxeval, count, o, |
---|
4237 | maxeval/maxNumVars, t )) |
---|
4238 | { // too many eval. used --> try another method |
---|
4239 | Off (SW_USE_EZGCD_P); |
---|
4240 | result= gcd (F,G); |
---|
4241 | On (SW_USE_EZGCD_P); |
---|
4242 | if (passToGF) |
---|
4243 | { |
---|
4244 | CanonicalForm mipo= gf_mipo; |
---|
4245 | setCharacteristic (p); |
---|
4246 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4247 | result= GF2FalphaRep (result, alpha); |
---|
4248 | } |
---|
4249 | if (k > 1) |
---|
4250 | { |
---|
4251 | result= GFMapDown (result, k); |
---|
4252 | setCharacteristic (p, k, gf_name); |
---|
4253 | } |
---|
4254 | if (extOfExt) |
---|
4255 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4256 | return N (d*result); |
---|
4257 | } |
---|
4258 | int dd = degree( Dbt ); |
---|
4259 | if( dd == 0 ) |
---|
4260 | { |
---|
4261 | if (passToGF) |
---|
4262 | setCharacteristic (p); |
---|
4263 | if (k > 1) |
---|
4264 | setCharacteristic (p, k, gf_name); |
---|
4265 | return N (d); |
---|
4266 | } |
---|
4267 | if( dd == delta ) |
---|
4268 | { |
---|
4269 | goodPointCount++; |
---|
4270 | if (goodPointCount == 5) |
---|
4271 | break; |
---|
4272 | } |
---|
4273 | if( dd < delta ) |
---|
4274 | { |
---|
4275 | goodPointCount= 0; |
---|
4276 | delta = dd; |
---|
4277 | b = bt; |
---|
4278 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
---|
4279 | } |
---|
4280 | if (delta == degF) |
---|
4281 | { |
---|
4282 | if (degF <= degG && fdivides (F, G)) |
---|
4283 | { |
---|
4284 | if (passToGF) |
---|
4285 | { |
---|
4286 | CanonicalForm mipo= gf_mipo; |
---|
4287 | setCharacteristic (p); |
---|
4288 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4289 | F= GF2FalphaRep (F, alpha); |
---|
4290 | } |
---|
4291 | if (k > 1) |
---|
4292 | { |
---|
4293 | F= GFMapDown (F, k); |
---|
4294 | setCharacteristic (p, k, gf_name); |
---|
4295 | } |
---|
4296 | if (extOfExt) |
---|
4297 | F= mapDown (F, primElem, imPrimElem, oldA, dest, source); |
---|
4298 | return N (d*F); |
---|
4299 | } |
---|
4300 | else |
---|
4301 | delta--; |
---|
4302 | } |
---|
4303 | else if (delta == degG) |
---|
4304 | { |
---|
4305 | if (degG <= degF && fdivides (G, F)) |
---|
4306 | { |
---|
4307 | if (passToGF) |
---|
4308 | { |
---|
4309 | CanonicalForm mipo= gf_mipo; |
---|
4310 | setCharacteristic (p); |
---|
4311 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4312 | G= GF2FalphaRep (G, alpha); |
---|
4313 | } |
---|
4314 | if (k > 1) |
---|
4315 | { |
---|
4316 | G= GFMapDown (G, k); |
---|
4317 | setCharacteristic (p, k, gf_name); |
---|
4318 | } |
---|
4319 | if (extOfExt) |
---|
4320 | G= mapDown (G, primElem, imPrimElem, oldA, dest, source); |
---|
4321 | return N (d*G); |
---|
4322 | } |
---|
4323 | else |
---|
4324 | delta--; |
---|
4325 | } |
---|
4326 | } |
---|
4327 | if( delta != degF && delta != degG ) |
---|
4328 | { |
---|
4329 | bool B_is_F; |
---|
4330 | CanonicalForm xxx1, xxx2; |
---|
4331 | CanonicalForm buf; |
---|
4332 | DD[1] = Fb / Db; |
---|
4333 | buf= Gb/Db; |
---|
4334 | xxx1 = gcd( DD[1], Db ); |
---|
4335 | xxx2 = gcd( buf, Db ); |
---|
4336 | if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
4337 | (size (F) <= size (G))) |
---|
4338 | || (xxx1.inCoeffDomain() && !xxx2.inCoeffDomain())) |
---|
4339 | { |
---|
4340 | B = F; |
---|
4341 | DD[2] = Db; |
---|
4342 | lcDD[1] = lcF; |
---|
4343 | lcDD[2] = lcD; |
---|
4344 | B_is_F = true; |
---|
4345 | } |
---|
4346 | else if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
---|
4347 | (size (G) < size (F))) |
---|
4348 | || (!xxx1.inCoeffDomain() && xxx2.inCoeffDomain())) |
---|
4349 | { |
---|
4350 | DD[1] = buf; |
---|
4351 | B = G; |
---|
4352 | DD[2] = Db; |
---|
4353 | lcDD[1] = lcG; |
---|
4354 | lcDD[2] = lcD; |
---|
4355 | B_is_F = false; |
---|
4356 | } |
---|
4357 | else // special case handling |
---|
4358 | { |
---|
4359 | Off (SW_USE_EZGCD_P); |
---|
4360 | result= gcd (F,G); |
---|
4361 | On (SW_USE_EZGCD_P); |
---|
4362 | if (passToGF) |
---|
4363 | { |
---|
4364 | CanonicalForm mipo= gf_mipo; |
---|
4365 | setCharacteristic (p); |
---|
4366 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4367 | result= GF2FalphaRep (result, alpha); |
---|
4368 | } |
---|
4369 | if (k > 1) |
---|
4370 | { |
---|
4371 | result= GFMapDown (result, k); |
---|
4372 | setCharacteristic (p, k, gf_name); |
---|
4373 | } |
---|
4374 | if (extOfExt) |
---|
4375 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4376 | return N (d*result); |
---|
4377 | } |
---|
4378 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
---|
4379 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
---|
4380 | |
---|
4381 | if (size (B*lcDD[2])/maxNumVars > sizePerVars1) |
---|
4382 | { |
---|
4383 | if (algExtension) |
---|
4384 | { |
---|
4385 | result= GCD_Fp_extension (F, G, a); |
---|
4386 | if (extOfExt) |
---|
4387 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4388 | return N (d*result); |
---|
4389 | } |
---|
4390 | if (CFFactory::gettype() == GaloisFieldDomain) |
---|
4391 | { |
---|
4392 | result= GCD_GF (F, G); |
---|
4393 | if (passToGF) |
---|
4394 | { |
---|
4395 | CanonicalForm mipo= gf_mipo; |
---|
4396 | setCharacteristic (p); |
---|
4397 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4398 | result= GF2FalphaRep (result, alpha); |
---|
4399 | } |
---|
4400 | if (k > 1) |
---|
4401 | { |
---|
4402 | result= GFMapDown (result, k); |
---|
4403 | setCharacteristic (p, k, gf_name); |
---|
4404 | } |
---|
4405 | return N (d*result); |
---|
4406 | } |
---|
4407 | else |
---|
4408 | return N (d*GCD_small_p (F,G)); |
---|
4409 | } |
---|
4410 | |
---|
4411 | gcdfound= Hensel_P (B*lcD, DD, b, lcDD); |
---|
4412 | |
---|
4413 | if (gcdfound == -1) |
---|
4414 | { |
---|
4415 | Off (SW_USE_EZGCD_P); |
---|
4416 | result= gcd (F,G); |
---|
4417 | On (SW_USE_EZGCD_P); |
---|
4418 | if (passToGF) |
---|
4419 | { |
---|
4420 | CanonicalForm mipo= gf_mipo; |
---|
4421 | setCharacteristic (p); |
---|
4422 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4423 | result= GF2FalphaRep (result, alpha); |
---|
4424 | } |
---|
4425 | if (k > 1) |
---|
4426 | { |
---|
4427 | result= GFMapDown (result, k); |
---|
4428 | setCharacteristic (p, k, gf_name); |
---|
4429 | } |
---|
4430 | if (extOfExt) |
---|
4431 | result= mapDown (result, primElem, imPrimElem, oldA, dest, source); |
---|
4432 | return N (d*result); |
---|
4433 | } |
---|
4434 | |
---|
4435 | if (gcdfound == 1) |
---|
4436 | { |
---|
4437 | cand = DD[2] / content( DD[2], Variable(1) ); |
---|
4438 | gcdfound = fdivides( cand, G ) && fdivides ( cand, F ); |
---|
4439 | |
---|
4440 | if (passToGF && gcdfound) |
---|
4441 | { |
---|
4442 | CanonicalForm mipo= gf_mipo; |
---|
4443 | setCharacteristic (p); |
---|
4444 | Variable alpha= rootOf (mipo.mapinto()); |
---|
4445 | cand= GF2FalphaRep (cand, alpha); |
---|
4446 | } |
---|
4447 | if (k > 1 && gcdfound) |
---|
4448 | { |
---|
4449 | cand= GFMapDown (cand, k); |
---|
4450 | setCharacteristic (p, k, gf_name); |
---|
4451 | } |
---|
4452 | if (extOfExt && gcdfound) |
---|
4453 | cand= mapDown (cand, primElem, imPrimElem, oldA, dest, source); |
---|
4454 | } |
---|
4455 | } |
---|
4456 | delta--; |
---|
4457 | goodPointCount= 0; |
---|
4458 | } |
---|
4459 | return N (d*cand); |
---|
4460 | } |
---|
4461 | |
---|
4462 | |
---|
4463 | #endif |
---|