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 "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 "cf_map.h" |
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29 | #include "cf_util.h" |
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30 | #include "ftmpl_functions.h" |
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31 | #include "cf_random.h" |
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32 | |
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33 | // iinline helper functions: |
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34 | #include "cf_map_ext.h" |
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35 | |
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36 | #ifdef HAVE_NTL |
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37 | #include <NTL/ZZ_pEX.h> |
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38 | #include <NTLconvert.h> |
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39 | #endif |
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40 | |
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41 | #include "cf_gcd_smallp.h" |
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42 | |
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43 | #ifdef HAVE_NTL |
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44 | |
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45 | TIMING_DEFINE_PRINT(gcd_recursion); |
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46 | TIMING_DEFINE_PRINT(newton_interpolation); |
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47 | |
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48 | /// compressing two polynomials F and G, M is used for compressing, |
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49 | /// N to reverse the compression |
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50 | static inline |
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51 | int myCompress (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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52 | CFMap & N, bool& topLevel) |
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53 | { |
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54 | int n= tmax (F.level(), G.level()); |
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55 | int * degsf= new int [n + 1]; |
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56 | int * degsg= new int [n + 1]; |
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57 | |
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58 | for (int i = 0; i <= n; i++) |
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59 | degsf[i]= degsg[i]= 0; |
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60 | |
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61 | degsf= degrees (F, degsf); |
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62 | degsg= degrees (G, degsg); |
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63 | |
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64 | int both_non_zero= 0; |
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65 | int f_zero= 0; |
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66 | int g_zero= 0; |
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67 | int both_zero= 0; |
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68 | |
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69 | if (topLevel) |
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70 | { |
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71 | for (int i= 1; i <= n; i++) |
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72 | { |
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73 | if (degsf[i] != 0 && degsg[i] != 0) |
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74 | { |
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75 | both_non_zero++; |
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76 | continue; |
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77 | } |
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78 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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79 | { |
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80 | f_zero++; |
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81 | continue; |
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82 | } |
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83 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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84 | { |
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85 | g_zero++; |
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86 | continue; |
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87 | } |
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88 | } |
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89 | |
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90 | if (both_non_zero == 0) |
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91 | { |
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92 | delete [] degsf; |
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93 | delete [] degsg; |
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94 | return 0; |
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95 | } |
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96 | |
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97 | // map Variables which do not occur in both polynomials to higher levels |
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98 | int k= 1; |
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99 | int l= 1; |
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100 | for (int i= 1; i <= n; i++) |
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101 | { |
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102 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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103 | { |
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104 | if (k + both_non_zero != i) |
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105 | { |
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106 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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107 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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108 | } |
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109 | k++; |
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110 | } |
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111 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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112 | { |
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113 | if (l + g_zero + both_non_zero != i) |
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114 | { |
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115 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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116 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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117 | } |
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118 | l++; |
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119 | } |
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120 | } |
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121 | |
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122 | // sort Variables x_{i} in increasing order of |
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123 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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124 | int m= tmin (F.level(), G.level()); |
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125 | int max_min_deg; |
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126 | k= both_non_zero; |
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127 | l= 0; |
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128 | int i= 1; |
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129 | while (k > 0) |
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130 | { |
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131 | max_min_deg= tmin (degsf[i], degsg[i]); |
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132 | while (max_min_deg == 0) |
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133 | { |
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134 | i++; |
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135 | max_min_deg= tmin (degsf[i], degsg[i]); |
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136 | } |
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137 | for (int j= i + 1; j <= m; j++) |
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138 | { |
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139 | if (tmin (degsf[j],degsg[j]) >= max_min_deg) |
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140 | { |
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141 | max_min_deg= tmin (degsf[j], degsg[j]); |
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142 | l= j; |
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143 | } |
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144 | } |
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145 | if (l != 0) |
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146 | { |
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147 | if (l != k) |
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148 | { |
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149 | M.newpair (Variable (l), Variable(k)); |
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150 | N.newpair (Variable (k), Variable(l)); |
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151 | degsf[l]= 0; |
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152 | degsg[l]= 0; |
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153 | l= 0; |
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154 | } |
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155 | else |
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156 | { |
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157 | degsf[l]= 0; |
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158 | degsg[l]= 0; |
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159 | l= 0; |
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160 | } |
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161 | } |
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162 | else if (l == 0) |
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163 | { |
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164 | if (i != k) |
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165 | { |
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166 | M.newpair (Variable (i), Variable (k)); |
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167 | N.newpair (Variable (k), Variable (i)); |
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168 | degsf[i]= 0; |
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169 | degsg[i]= 0; |
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170 | } |
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171 | else |
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172 | { |
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173 | degsf[i]= 0; |
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174 | degsg[i]= 0; |
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175 | } |
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176 | i++; |
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177 | } |
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178 | k--; |
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179 | } |
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180 | } |
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181 | else |
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182 | { |
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183 | //arrange Variables such that no gaps occur |
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184 | for (int i= 1; i <= n; i++) |
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185 | { |
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186 | if (degsf[i] == 0 && degsg[i] == 0) |
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187 | { |
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188 | both_zero++; |
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189 | continue; |
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190 | } |
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191 | else |
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192 | { |
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193 | if (both_zero != 0) |
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194 | { |
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195 | M.newpair (Variable (i), Variable (i - both_zero)); |
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196 | N.newpair (Variable (i - both_zero), Variable (i)); |
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197 | } |
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198 | } |
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199 | } |
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200 | } |
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201 | |
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202 | delete [] degsf; |
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203 | delete [] degsg; |
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204 | |
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205 | return 1; |
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206 | } |
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207 | |
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208 | int |
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209 | substituteCheck (const CanonicalForm& F, const CanonicalForm& G) |
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210 | { |
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211 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
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212 | return 0; |
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213 | Variable x= Variable (1); |
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214 | if (degree (F, x) <= 1 || degree (G, x) <= 1) |
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215 | return 0; |
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216 | CanonicalForm f= swapvar (F, F.mvar(), x); //TODO swapping seems to be pretty expensive |
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217 | CanonicalForm g= swapvar (G, G.mvar(), x); |
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218 | int sizef= 0; |
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219 | int sizeg= 0; |
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220 | for (CFIterator i= f; i.hasTerms(); i++, sizef++) |
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221 | { |
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222 | if (i.exp() == 1) |
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223 | return 0; |
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224 | } |
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225 | for (CFIterator i= g; i.hasTerms(); i++, sizeg++) |
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226 | { |
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227 | if (i.exp() == 1) |
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228 | return 0; |
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229 | } |
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230 | int * expf= new int [sizef]; |
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231 | int * expg= new int [sizeg]; |
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232 | int j= 0; |
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233 | for (CFIterator i= f; i.hasTerms(); i++, j++) |
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234 | { |
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235 | expf [j]= i.exp(); |
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236 | } |
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237 | j= 0; |
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238 | for (CFIterator i= g; i.hasTerms(); i++, j++) |
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239 | { |
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240 | expg [j]= i.exp(); |
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241 | } |
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242 | |
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243 | int indf= sizef - 1; |
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244 | int indg= sizeg - 1; |
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245 | if (expf[indf] == 0) |
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246 | indf--; |
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247 | if (expg[indg] == 0) |
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248 | indg--; |
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249 | |
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250 | if (expg[indg] != expf [indf] || (expg[indg] == 1 && expf[indf] == 1)) |
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251 | { |
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252 | delete [] expg; |
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253 | delete [] expf; |
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254 | return 0; |
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255 | } |
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256 | // expf[indg] == expf[indf] after here |
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257 | int result= expg[indg]; |
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258 | for (int i= indf - 1; i >= 0; i--) |
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259 | { |
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260 | if (expf [i]%result != 0) |
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261 | { |
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262 | delete [] expg; |
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263 | delete [] expf; |
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264 | return 0; |
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265 | } |
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266 | } |
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267 | |
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268 | for (int i= indg - 1; i >= 0; i--) |
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269 | { |
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270 | if (expg [i]%result != 0) |
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271 | { |
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272 | delete [] expg; |
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273 | delete [] expf; |
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274 | return 0; |
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275 | } |
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276 | } |
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277 | |
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278 | delete [] expg; |
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279 | delete [] expf; |
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280 | return result; |
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281 | } |
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282 | |
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283 | // substiution |
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284 | void |
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285 | subst (const CanonicalForm& F, const CanonicalForm& G, CanonicalForm& A, |
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286 | CanonicalForm& B, const int d |
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287 | ) |
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288 | { |
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289 | if (d == 1) |
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290 | { |
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291 | A= F; |
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292 | B= G; |
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293 | return; |
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294 | } |
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295 | |
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296 | CanonicalForm C= 0; |
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297 | CanonicalForm D= 0; |
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298 | Variable x= Variable (1); |
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299 | CanonicalForm f= swapvar (F, x, F.mvar()); |
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300 | CanonicalForm g= swapvar (G, x, G.mvar()); |
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301 | for (CFIterator i= f; i.hasTerms(); i++) |
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302 | C += i.coeff()*power (f.mvar(), i.exp()/ d); |
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303 | for (CFIterator i= g; i.hasTerms(); i++) |
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304 | D += i.coeff()*power (g.mvar(), i.exp()/ d); |
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305 | A= swapvar (C, x, F.mvar()); |
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306 | B= swapvar (D, x, G.mvar()); |
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307 | } |
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308 | |
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309 | CanonicalForm |
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310 | reverseSubst (const CanonicalForm& F, const int d) |
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311 | { |
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312 | if (d == 1) |
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313 | return F; |
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314 | |
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315 | Variable x= Variable (1); |
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316 | if (degree (F, x) <= 0) |
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317 | return F; |
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318 | CanonicalForm f= swapvar (F, x, F.mvar()); |
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319 | CanonicalForm result= 0; |
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320 | for (CFIterator i= f; i.hasTerms(); i++) |
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321 | result += i.coeff()*power (f.mvar(), d*i.exp()); |
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322 | return swapvar (result, x, F.mvar()); |
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323 | } |
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324 | |
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325 | static inline CanonicalForm |
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326 | uni_content (const CanonicalForm & F); |
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327 | |
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328 | CanonicalForm |
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329 | uni_content (const CanonicalForm& F, const Variable& x) |
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330 | { |
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331 | if (F.inCoeffDomain()) |
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332 | return F.genOne(); |
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333 | if (F.level() == x.level() && F.isUnivariate()) |
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334 | return F; |
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335 | if (F.level() != x.level() && F.isUnivariate()) |
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336 | return F.genOne(); |
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337 | |
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338 | if (x.level() != 1) |
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339 | { |
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340 | CanonicalForm f= swapvar (F, x, Variable (1)); |
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341 | CanonicalForm result= uni_content (f); |
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342 | return swapvar (result, x, Variable (1)); |
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343 | } |
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344 | else |
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345 | return uni_content (F); |
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346 | } |
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347 | |
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348 | /// compute the content of F, where F is considered as an element of |
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349 | /// \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$ |
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350 | static inline CanonicalForm |
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351 | uni_content (const CanonicalForm & F) |
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352 | { |
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353 | if (F.inBaseDomain()) |
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354 | return F.genOne(); |
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355 | if (F.level() == 1 && F.isUnivariate()) |
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356 | return F; |
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357 | if (F.level() != 1 && F.isUnivariate()) |
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358 | return F.genOne(); |
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359 | if (degree (F,1) == 0) return F.genOne(); |
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360 | |
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361 | int l= F.level(); |
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362 | if (l == 2) |
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363 | return content(F); |
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364 | else |
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365 | { |
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366 | CanonicalForm pol, c = 0; |
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367 | CFIterator i = F; |
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368 | for (; i.hasTerms(); i++) |
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369 | { |
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370 | pol= i.coeff(); |
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371 | pol= uni_content (pol); |
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372 | c= gcd (c, pol); |
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373 | if (c.isOne()) |
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374 | return c; |
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375 | } |
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376 | return c; |
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377 | } |
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378 | } |
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379 | |
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380 | CanonicalForm |
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381 | extractContents (const CanonicalForm& F, const CanonicalForm& G, |
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382 | CanonicalForm& contentF, CanonicalForm& contentG, |
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383 | CanonicalForm& ppF, CanonicalForm& ppG, const int d) |
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384 | { |
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385 | CanonicalForm uniContentF, uniContentG, gcdcFcG; |
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386 | contentF= 1; |
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387 | contentG= 1; |
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388 | ppF= F; |
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389 | ppG= G; |
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390 | CanonicalForm result= 1; |
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391 | for (int i= 1; i <= d; i++) |
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392 | { |
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393 | uniContentF= uni_content (F, Variable (i)); |
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394 | uniContentG= uni_content (G, Variable (i)); |
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395 | gcdcFcG= gcd (uniContentF, uniContentG); |
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396 | contentF *= uniContentF; |
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397 | contentG *= uniContentG; |
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398 | ppF /= uniContentF; |
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399 | ppG /= uniContentG; |
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400 | result *= gcdcFcG; |
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401 | } |
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402 | return result; |
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403 | } |
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404 | |
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405 | /// compute the leading coefficient of F, where F is considered as an element |
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406 | /// of \f$ R[x_{1}][x_{2},\ldots ,x_{n}] \f$, order on Mon (x_{2},\ldots ,x_{n}) |
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407 | /// is dp. |
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408 | static inline |
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409 | CanonicalForm uni_lcoeff (const CanonicalForm& F) |
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410 | { |
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411 | if (F.level() <= 1) |
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412 | return F; |
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413 | else |
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414 | { |
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415 | Variable x= Variable (2); |
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416 | int deg= totaldegree (F, x, F.mvar()); |
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417 | for (CFIterator i= F; i.hasTerms(); i++) |
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418 | { |
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419 | if (i.exp() + totaldegree (i.coeff(), x, i.coeff().mvar()) == deg) |
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420 | return uni_lcoeff (i.coeff()); |
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421 | } |
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422 | } |
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423 | } |
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424 | |
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425 | /// Newton interpolation - Incremental algorithm. |
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426 | /// Given a list of values alpha_i and a list of polynomials u_i, 1 <= i <= n, |
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427 | /// computes the interpolation polynomial assuming that |
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428 | /// the polynomials in u are the results of evaluating the variabe x |
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429 | /// of the unknown polynomial at the alpha values. |
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430 | /// This incremental version receives only the values of alpha_n and u_n and |
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431 | /// the previous interpolation polynomial for points 1 <= i <= n-1, and computes |
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432 | /// the polynomial interpolating in all the points. |
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433 | /// newtonPoly must be equal to (x - alpha_1) * ... * (x - alpha_{n-1}) |
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434 | static inline CanonicalForm |
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435 | newtonInterp(const CanonicalForm alpha, const CanonicalForm u, const CanonicalForm newtonPoly, const CanonicalForm oldInterPoly, const Variable & x) |
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436 | { |
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437 | CanonicalForm interPoly; |
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438 | |
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439 | interPoly = oldInterPoly + ((u - oldInterPoly(alpha, x)) / newtonPoly(alpha, x)) * newtonPoly; |
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440 | return interPoly; |
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441 | } |
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442 | |
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443 | /// compute a random element a of \f$ F_{p}(\alpha ) \f$ , |
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444 | /// s.t. F(a) \f$ \neq 0 \f$ , F is a univariate polynomial, returns |
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445 | /// fail if there are no field elements left which have not been used before |
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446 | static inline CanonicalForm |
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447 | randomElement (const CanonicalForm & F, const Variable & alpha, CFList & list, |
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448 | bool & fail) |
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449 | { |
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450 | fail= false; |
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451 | Variable x= F.mvar(); |
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452 | AlgExtRandomF genAlgExt (alpha); |
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453 | FFRandom genFF; |
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454 | CanonicalForm random, mipo; |
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455 | mipo= getMipo (alpha); |
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456 | int p= getCharacteristic (); |
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457 | int d= degree (mipo); |
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458 | int bound= ipower (p, d); |
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459 | do |
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460 | { |
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461 | if (list.length() == bound) |
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462 | { |
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463 | fail= true; |
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464 | break; |
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465 | } |
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466 | if (list.length() < p) |
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467 | { |
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468 | random= genFF.generate(); |
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469 | while (find (list, random)) |
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470 | random= genFF.generate(); |
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471 | } |
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472 | else |
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473 | { |
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474 | random= genAlgExt.generate(); |
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475 | while (find (list, random)) |
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476 | random= genAlgExt.generate(); |
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477 | } |
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478 | if (F (random, x) == 0) |
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479 | { |
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480 | list.append (random); |
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481 | continue; |
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482 | } |
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483 | } while (find (list, random)); |
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484 | return random; |
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485 | } |
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486 | |
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487 | /// chooses a suitable extension of \f$ F_{p}(\alpha ) \f$ |
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488 | /// we do not extend \f$ F_{p}(\alpha ) \f$ itself but extend \f$ F_{p} \f$ , |
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489 | /// s.t. \f$ F_{p}(\alpha ) \subset F_{p}(\beta ) \f$ |
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490 | static inline |
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491 | void choose_extension (const int& d, const int& num_vars, Variable& beta) |
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492 | { |
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493 | int p= getCharacteristic(); |
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494 | ZZ NTLp= to_ZZ (p); |
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495 | ZZ_p::init (NTLp); |
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496 | ZZ_pX NTLirredpoly; |
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497 | //TODO: replace d by max_{i} (deg_x{i}(f)) |
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498 | int i= (int) (log ((double) ipower (d + 1, num_vars))/log ((double) p)); |
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499 | int m= degree (getMipo (beta)); |
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500 | if (i <= 1) |
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501 | i= 2; |
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502 | BuildIrred (NTLirredpoly, i*m); |
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503 | CanonicalForm mipo= convertNTLZZpX2CF (NTLirredpoly, Variable(1)); |
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504 | beta= rootOf (mipo); |
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505 | } |
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506 | |
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507 | /// GCD of F and G over \f$ F_{p}(\alpha ) \f$ , |
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508 | /// l and topLevel are only used internally, output is monic |
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509 | /// based on Alg. 7.2. as described in "Algorithms for |
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510 | /// Computer Algebra" by Geddes, Czapor, Labahn |
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511 | CanonicalForm |
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512 | GCD_Fp_extension (const CanonicalForm& F, const CanonicalForm& G, |
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513 | Variable & alpha, CFList& l, bool& topLevel) |
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514 | { |
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515 | CanonicalForm A= F; |
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516 | CanonicalForm B= G; |
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517 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
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518 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
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519 | else if (F.isZero() && G.isZero()) return F.genOne(); |
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520 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
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521 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
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522 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
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523 | if (F == G) return F/Lc(F); |
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524 | |
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525 | CFMap M,N; |
---|
526 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
527 | |
---|
528 | if (best_level == 0) return B.genOne(); |
---|
529 | |
---|
530 | A= M(A); |
---|
531 | B= M(B); |
---|
532 | |
---|
533 | Variable x= Variable(1); |
---|
534 | |
---|
535 | //univariate case |
---|
536 | if (A.isUnivariate() && B.isUnivariate()) |
---|
537 | return N (gcd(A,B)); |
---|
538 | |
---|
539 | int substitute= substituteCheck (A, B); |
---|
540 | |
---|
541 | if (substitute > 1) |
---|
542 | subst (A, B, A, B, substitute); |
---|
543 | |
---|
544 | CanonicalForm cA, cB; // content of A and B |
---|
545 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
546 | CanonicalForm gcdcAcB; |
---|
547 | |
---|
548 | if (topLevel) |
---|
549 | { |
---|
550 | if (best_level <= 2) |
---|
551 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
---|
552 | else |
---|
553 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
---|
554 | } |
---|
555 | else |
---|
556 | { |
---|
557 | cA = uni_content (A); |
---|
558 | cB = uni_content (B); |
---|
559 | gcdcAcB= gcd (cA, cB); |
---|
560 | ppA= A/cA; |
---|
561 | ppB= B/cB; |
---|
562 | } |
---|
563 | |
---|
564 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
565 | CanonicalForm gcdlcAlcB; |
---|
566 | |
---|
567 | lcA= uni_lcoeff (ppA); |
---|
568 | lcB= uni_lcoeff (ppB); |
---|
569 | |
---|
570 | if (fdivides (lcA, lcB)) |
---|
571 | { |
---|
572 | if (fdivides (A, B)) |
---|
573 | return F/Lc(F); |
---|
574 | } |
---|
575 | if (fdivides (lcB, lcA)) |
---|
576 | { |
---|
577 | if (fdivides (B, A)) |
---|
578 | return G/Lc(G); |
---|
579 | } |
---|
580 | |
---|
581 | gcdlcAlcB= gcd (lcA, lcB); |
---|
582 | |
---|
583 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
584 | |
---|
585 | if (d == 0) |
---|
586 | { |
---|
587 | if (substitute > 1) |
---|
588 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
589 | else |
---|
590 | return N(gcdcAcB); |
---|
591 | } |
---|
592 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
593 | if (d0 < d) |
---|
594 | d= d0; |
---|
595 | if (d == 0) |
---|
596 | { |
---|
597 | if (substitute > 1) |
---|
598 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
599 | else |
---|
600 | return N(gcdcAcB); |
---|
601 | } |
---|
602 | |
---|
603 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
604 | CanonicalForm newtonPoly; |
---|
605 | |
---|
606 | newtonPoly= 1; |
---|
607 | m= gcdlcAlcB; |
---|
608 | G_m= 0; |
---|
609 | H= 0; |
---|
610 | bool fail= false; |
---|
611 | topLevel= false; |
---|
612 | bool inextension= false; |
---|
613 | Variable V_buf= alpha; |
---|
614 | CanonicalForm prim_elem, im_prim_elem; |
---|
615 | CFList source, dest; |
---|
616 | do |
---|
617 | { |
---|
618 | random_element= randomElement (m, V_buf, l, fail); |
---|
619 | if (fail) |
---|
620 | { |
---|
621 | source= CFList(); |
---|
622 | dest= CFList(); |
---|
623 | int num_vars= tmin (getNumVars(A), getNumVars(B)); |
---|
624 | num_vars--; |
---|
625 | |
---|
626 | choose_extension (d, num_vars, V_buf); |
---|
627 | bool prim_fail= false; |
---|
628 | Variable V_buf2; |
---|
629 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
630 | |
---|
631 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
632 | if (prim_fail) |
---|
633 | ; //ERROR |
---|
634 | else |
---|
635 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
636 | |
---|
637 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
638 | DEBOUTLN (cerr, "getMipo (V_buf2)= " << getMipo (V_buf2)); |
---|
639 | inextension= true; |
---|
640 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
641 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
642 | im_prim_elem, source, dest); |
---|
643 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
644 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
645 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
646 | source, dest); |
---|
647 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
648 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
649 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
650 | source, dest); |
---|
651 | |
---|
652 | fail= false; |
---|
653 | random_element= randomElement (m, V_buf, l, fail ); |
---|
654 | DEBOUTLN (cerr, "fail= " << fail); |
---|
655 | CFList list; |
---|
656 | TIMING_START (gcd_recursion); |
---|
657 | G_random_element= |
---|
658 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
659 | list, topLevel); |
---|
660 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
661 | "time for recursive call: "); |
---|
662 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
663 | } |
---|
664 | else |
---|
665 | { |
---|
666 | CFList list; |
---|
667 | TIMING_START (gcd_recursion); |
---|
668 | G_random_element= |
---|
669 | GCD_Fp_extension (ppA(random_element, x), ppB(random_element, x), V_buf, |
---|
670 | list, topLevel); |
---|
671 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
672 | "time for recursive call: "); |
---|
673 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
674 | } |
---|
675 | |
---|
676 | d0= totaldegree (G_random_element, Variable(2), |
---|
677 | Variable (G_random_element.level())); |
---|
678 | if (d0 == 0) |
---|
679 | { |
---|
680 | if (substitute > 1) |
---|
681 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
682 | else |
---|
683 | return N(gcdcAcB); |
---|
684 | } |
---|
685 | if (d0 > d) |
---|
686 | { |
---|
687 | if (!find (l, random_element)) |
---|
688 | l.append (random_element); |
---|
689 | continue; |
---|
690 | } |
---|
691 | |
---|
692 | G_random_element= |
---|
693 | (gcdlcAlcB(random_element, x)/uni_lcoeff (G_random_element)) |
---|
694 | * G_random_element; |
---|
695 | |
---|
696 | d0= totaldegree (G_random_element, Variable(2), |
---|
697 | Variable(G_random_element.level())); |
---|
698 | if (d0 < d) |
---|
699 | { |
---|
700 | m= gcdlcAlcB; |
---|
701 | newtonPoly= 1; |
---|
702 | G_m= 0; |
---|
703 | d= d0; |
---|
704 | } |
---|
705 | |
---|
706 | TIMING_START (newton_interpolation); |
---|
707 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
708 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
709 | "time for newton interpolation: "); |
---|
710 | |
---|
711 | //termination test |
---|
712 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
713 | { |
---|
714 | cH= uni_content (H); |
---|
715 | ppH= H/cH; |
---|
716 | if (inextension) |
---|
717 | { |
---|
718 | CFList u, v; |
---|
719 | //maybe it's better to test if ppH is an element of F(\alpha) before |
---|
720 | //mapping down |
---|
721 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
722 | ppH= mapDown (ppH, prim_elem, im_prim_elem, alpha, u, v); |
---|
723 | ppH /= Lc(ppH); |
---|
724 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
725 | if (fdivides (ppH, A) && fdivides (ppH, B)) |
---|
726 | { |
---|
727 | if (substitute > 1) |
---|
728 | { |
---|
729 | ppH= reverseSubst (ppH, substitute); |
---|
730 | gcdcAcB= reverseSubst (gcdcAcB, substitute); |
---|
731 | } |
---|
732 | return N(gcdcAcB*ppH); |
---|
733 | } |
---|
734 | } |
---|
735 | else if (fdivides (ppH, A) && fdivides (ppH, B)) |
---|
736 | { |
---|
737 | if (substitute > 1) |
---|
738 | { |
---|
739 | ppH= reverseSubst (ppH, substitute); |
---|
740 | gcdcAcB= reverseSubst (gcdcAcB, substitute); |
---|
741 | } |
---|
742 | return N(gcdcAcB*ppH); |
---|
743 | } |
---|
744 | } |
---|
745 | |
---|
746 | G_m= H; |
---|
747 | newtonPoly= newtonPoly*(x - random_element); |
---|
748 | m= m*(x - random_element); |
---|
749 | if (!find (l, random_element)) |
---|
750 | l.append (random_element); |
---|
751 | } while (1); |
---|
752 | } |
---|
753 | |
---|
754 | /// compute a random element a of GF, s.t. F(a) \f$ \neq 0 \f$ , F is a |
---|
755 | /// univariate polynomial, returns fail if there are no field elements left |
---|
756 | /// which have not been used before |
---|
757 | static inline |
---|
758 | CanonicalForm |
---|
759 | GFRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
760 | { |
---|
761 | fail= false; |
---|
762 | Variable x= F.mvar(); |
---|
763 | GFRandom genGF; |
---|
764 | CanonicalForm random; |
---|
765 | int p= getCharacteristic(); |
---|
766 | int d= getGFDegree(); |
---|
767 | int bound= ipower (p, d); |
---|
768 | do |
---|
769 | { |
---|
770 | if (list.length() == bound) |
---|
771 | { |
---|
772 | fail= true; |
---|
773 | break; |
---|
774 | } |
---|
775 | if (list.length() < 1) |
---|
776 | random= 0; |
---|
777 | else |
---|
778 | { |
---|
779 | random= genGF.generate(); |
---|
780 | while (find (list, random)) |
---|
781 | random= genGF.generate(); |
---|
782 | } |
---|
783 | if (F (random, x) == 0) |
---|
784 | { |
---|
785 | list.append (random); |
---|
786 | continue; |
---|
787 | } |
---|
788 | } while (find (list, random)); |
---|
789 | return random; |
---|
790 | } |
---|
791 | |
---|
792 | /// GCD of F and G over GF, based on Alg. 7.2. as described in "Algorithms for |
---|
793 | /// Computer Algebra" by Geddes, Czapor, Labahn |
---|
794 | /// Usually this algorithm will be faster than GCD_Fp_extension since GF has |
---|
795 | /// faster field arithmetics, however it might fail if the input is large since |
---|
796 | /// the size of the base field is bounded by 2^16, output is monic |
---|
797 | CanonicalForm GCD_GF (const CanonicalForm& F, const CanonicalForm& G, |
---|
798 | CFList& l, bool& topLevel) |
---|
799 | { |
---|
800 | CanonicalForm A= F; |
---|
801 | CanonicalForm B= G; |
---|
802 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
803 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
804 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
805 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
806 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
807 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
808 | if (F == G) return F/Lc(F); |
---|
809 | |
---|
810 | CFMap M,N; |
---|
811 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
812 | |
---|
813 | if (best_level == 0) return B.genOne(); |
---|
814 | |
---|
815 | A= M(A); |
---|
816 | B= M(B); |
---|
817 | |
---|
818 | Variable x= Variable(1); |
---|
819 | |
---|
820 | //univariate case |
---|
821 | if (A.isUnivariate() && B.isUnivariate()) |
---|
822 | return N (gcd (A, B)); |
---|
823 | |
---|
824 | int substitute= substituteCheck (A, B); |
---|
825 | |
---|
826 | if (substitute > 1) |
---|
827 | subst (A, B, A, B, substitute); |
---|
828 | |
---|
829 | CanonicalForm cA, cB; // content of A and B |
---|
830 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
831 | CanonicalForm gcdcAcB; |
---|
832 | |
---|
833 | if (topLevel) |
---|
834 | { |
---|
835 | if (best_level <= 2) |
---|
836 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
---|
837 | else |
---|
838 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
---|
839 | } |
---|
840 | else |
---|
841 | { |
---|
842 | cA = uni_content (A); |
---|
843 | cB = uni_content (B); |
---|
844 | gcdcAcB= gcd (cA, cB); |
---|
845 | ppA= A/cA; |
---|
846 | ppB= B/cB; |
---|
847 | } |
---|
848 | |
---|
849 | CanonicalForm lcA, lcB; // leading coefficients of A and B |
---|
850 | CanonicalForm gcdlcAlcB; |
---|
851 | |
---|
852 | lcA= uni_lcoeff (ppA); |
---|
853 | lcB= uni_lcoeff (ppB); |
---|
854 | |
---|
855 | if (fdivides (lcA, lcB)) |
---|
856 | { |
---|
857 | if (fdivides (A, B)) |
---|
858 | return F; |
---|
859 | } |
---|
860 | if (fdivides (lcB, lcA)) |
---|
861 | { |
---|
862 | if (fdivides (B, A)) |
---|
863 | return G; |
---|
864 | } |
---|
865 | |
---|
866 | gcdlcAlcB= gcd (lcA, lcB); |
---|
867 | |
---|
868 | int d= totaldegree (ppA, Variable(2), Variable (ppA.level())); |
---|
869 | if (d == 0) |
---|
870 | { |
---|
871 | if (substitute > 1) |
---|
872 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
873 | else |
---|
874 | return N(gcdcAcB); |
---|
875 | } |
---|
876 | int d0= totaldegree (ppB, Variable(2), Variable (ppB.level())); |
---|
877 | if (d0 < d) |
---|
878 | d= d0; |
---|
879 | if (d == 0) |
---|
880 | { |
---|
881 | if (substitute > 1) |
---|
882 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
883 | else |
---|
884 | return N(gcdcAcB); |
---|
885 | } |
---|
886 | |
---|
887 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
888 | CanonicalForm newtonPoly; |
---|
889 | |
---|
890 | newtonPoly= 1; |
---|
891 | m= gcdlcAlcB; |
---|
892 | G_m= 0; |
---|
893 | H= 0; |
---|
894 | bool fail= false; |
---|
895 | topLevel= false; |
---|
896 | bool inextension= false; |
---|
897 | int p; |
---|
898 | int k= getGFDegree(); |
---|
899 | int kk; |
---|
900 | int expon; |
---|
901 | char gf_name_buf= gf_name; |
---|
902 | do |
---|
903 | { |
---|
904 | random_element= GFRandomElement (m, l, fail); |
---|
905 | if (fail) |
---|
906 | { |
---|
907 | int num_vars= tmin (getNumVars(A), getNumVars(B)); |
---|
908 | num_vars--; |
---|
909 | p= getCharacteristic(); |
---|
910 | expon= (int) floor ((log ((double) ipower (d + 1, num_vars))/log ((double) p))); |
---|
911 | if (expon < 2) |
---|
912 | expon= 2; |
---|
913 | kk= getGFDegree(); |
---|
914 | if (ipower (p, kk*expon) < (1 << 16)) |
---|
915 | setCharacteristic (p, kk*(int)expon, 'b'); |
---|
916 | else |
---|
917 | { |
---|
918 | expon= (int) floor((log ((double)((1<<16) - 1)))/(log((double)p)*kk)); |
---|
919 | ASSERT (expon >= 2, "not enough points in GCD_GF"); |
---|
920 | setCharacteristic (p, (int)(kk*expon), 'b'); |
---|
921 | } |
---|
922 | inextension= true; |
---|
923 | fail= false; |
---|
924 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
925 | i.getItem()= GFMapUp (i.getItem(), kk); |
---|
926 | m= GFMapUp (m, kk); |
---|
927 | G_m= GFMapUp (G_m, kk); |
---|
928 | newtonPoly= GFMapUp (newtonPoly, kk); |
---|
929 | ppA= GFMapUp (ppA, kk); |
---|
930 | ppB= GFMapUp (ppB, kk); |
---|
931 | gcdlcAlcB= GFMapUp (gcdlcAlcB, kk); |
---|
932 | random_element= GFRandomElement (m, l, fail); |
---|
933 | DEBOUTLN (cerr, "fail= " << fail); |
---|
934 | CFList list; |
---|
935 | TIMING_START (gcd_recursion); |
---|
936 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
937 | list, topLevel); |
---|
938 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
939 | "time for recursive call: "); |
---|
940 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
941 | } |
---|
942 | else |
---|
943 | { |
---|
944 | CFList list; |
---|
945 | TIMING_START (gcd_recursion); |
---|
946 | G_random_element= GCD_GF (ppA(random_element, x), ppB(random_element, x), |
---|
947 | list, topLevel); |
---|
948 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
949 | "time for recursive call: "); |
---|
950 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
951 | } |
---|
952 | |
---|
953 | d0= totaldegree (G_random_element, Variable(2), |
---|
954 | Variable (G_random_element.level())); |
---|
955 | if (d0 == 0) |
---|
956 | { |
---|
957 | if (inextension) |
---|
958 | { |
---|
959 | setCharacteristic (p, k, gf_name_buf); |
---|
960 | { |
---|
961 | if (substitute > 1) |
---|
962 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
963 | else |
---|
964 | return N(gcdcAcB); |
---|
965 | } |
---|
966 | } |
---|
967 | else |
---|
968 | { |
---|
969 | if (substitute > 1) |
---|
970 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
971 | else |
---|
972 | return N(gcdcAcB); |
---|
973 | } |
---|
974 | } |
---|
975 | if (d0 > d) |
---|
976 | { |
---|
977 | if (!find (l, random_element)) |
---|
978 | l.append (random_element); |
---|
979 | continue; |
---|
980 | } |
---|
981 | |
---|
982 | G_random_element= |
---|
983 | (gcdlcAlcB(random_element, x)/uni_lcoeff(G_random_element)) * |
---|
984 | G_random_element; |
---|
985 | d0= totaldegree (G_random_element, Variable(2), |
---|
986 | Variable (G_random_element.level())); |
---|
987 | |
---|
988 | if (d0 < d) |
---|
989 | { |
---|
990 | m= gcdlcAlcB; |
---|
991 | newtonPoly= 1; |
---|
992 | G_m= 0; |
---|
993 | d= d0; |
---|
994 | } |
---|
995 | |
---|
996 | TIMING_START (newton_interpolation); |
---|
997 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
998 | TIMING_END_AND_PRINT (newton_interpolation, "time for newton interpolation: "); |
---|
999 | |
---|
1000 | //termination test |
---|
1001 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
1002 | { |
---|
1003 | cH= uni_content (H); |
---|
1004 | ppH= H/cH; |
---|
1005 | if (inextension) |
---|
1006 | { |
---|
1007 | if (fdivides(ppH, GFMapUp(A, k)) && fdivides(ppH, GFMapUp(B,k))) |
---|
1008 | { |
---|
1009 | DEBOUTLN (cerr, "ppH before mapDown= " << ppH); |
---|
1010 | ppH= GFMapDown (ppH, k); |
---|
1011 | DEBOUTLN (cerr, "ppH after mapDown= " << ppH); |
---|
1012 | if (substitute > 1) |
---|
1013 | { |
---|
1014 | ppH= reverseSubst (ppH, substitute); |
---|
1015 | gcdcAcB= reverseSubst (gcdcAcB, substitute); |
---|
1016 | } |
---|
1017 | setCharacteristic (p, k, gf_name_buf); |
---|
1018 | return N(gcdcAcB*ppH); |
---|
1019 | } |
---|
1020 | } |
---|
1021 | else |
---|
1022 | { |
---|
1023 | if (fdivides (ppH, A) && fdivides (ppH, B)) |
---|
1024 | { |
---|
1025 | if (substitute > 1) |
---|
1026 | { |
---|
1027 | ppH= reverseSubst (ppH, substitute); |
---|
1028 | gcdcAcB= reverseSubst (gcdcAcB, substitute); |
---|
1029 | } |
---|
1030 | return N(gcdcAcB*ppH); |
---|
1031 | } |
---|
1032 | } |
---|
1033 | } |
---|
1034 | |
---|
1035 | G_m= H; |
---|
1036 | newtonPoly= newtonPoly*(x - random_element); |
---|
1037 | m= m*(x - random_element); |
---|
1038 | if (!find (l, random_element)) |
---|
1039 | l.append (random_element); |
---|
1040 | } while (1); |
---|
1041 | } |
---|
1042 | |
---|
1043 | /// F is assumed to be an univariate polynomial in x, |
---|
1044 | /// computes a random monic irreducible univariate polynomial of random |
---|
1045 | /// degree < i in x which does not divide F |
---|
1046 | CanonicalForm |
---|
1047 | randomIrredpoly (int i, const Variable & x) |
---|
1048 | { |
---|
1049 | int p= getCharacteristic(); |
---|
1050 | ZZ NTLp= to_ZZ (p); |
---|
1051 | ZZ_p::init (NTLp); |
---|
1052 | ZZ_pX NTLirredpoly; |
---|
1053 | CanonicalForm CFirredpoly; |
---|
1054 | BuildIrred (NTLirredpoly, i + 1); |
---|
1055 | CFirredpoly= convertNTLZZpX2CF (NTLirredpoly, x); |
---|
1056 | return CFirredpoly; |
---|
1057 | } |
---|
1058 | |
---|
1059 | static inline |
---|
1060 | CanonicalForm |
---|
1061 | FpRandomElement (const CanonicalForm& F, CFList& list, bool& fail) |
---|
1062 | { |
---|
1063 | fail= false; |
---|
1064 | Variable x= F.mvar(); |
---|
1065 | FFRandom genFF; |
---|
1066 | CanonicalForm random; |
---|
1067 | int p= getCharacteristic(); |
---|
1068 | int bound= p; |
---|
1069 | do |
---|
1070 | { |
---|
1071 | if (list.length() == bound) |
---|
1072 | { |
---|
1073 | fail= true; |
---|
1074 | break; |
---|
1075 | } |
---|
1076 | if (list.length() < 1) |
---|
1077 | random= 0; |
---|
1078 | else |
---|
1079 | { |
---|
1080 | random= genFF.generate(); |
---|
1081 | while (find (list, random)) |
---|
1082 | random= genFF.generate(); |
---|
1083 | } |
---|
1084 | if (F (random, x) == 0) |
---|
1085 | { |
---|
1086 | list.append (random); |
---|
1087 | continue; |
---|
1088 | } |
---|
1089 | } while (find (list, random)); |
---|
1090 | return random; |
---|
1091 | } |
---|
1092 | |
---|
1093 | CanonicalForm GCD_small_p (const CanonicalForm& F, const CanonicalForm& G, |
---|
1094 | bool& topLevel, CFList& l) |
---|
1095 | { |
---|
1096 | CanonicalForm A= F; |
---|
1097 | CanonicalForm B= G; |
---|
1098 | if (F.isZero() && degree(G) > 0) return G/Lc(G); |
---|
1099 | else if (G.isZero() && degree (F) > 0) return F/Lc(F); |
---|
1100 | else if (F.isZero() && G.isZero()) return F.genOne(); |
---|
1101 | if (F.inBaseDomain() || G.inBaseDomain()) return F.genOne(); |
---|
1102 | if (F.isUnivariate() && fdivides(F, G)) return F/Lc(F); |
---|
1103 | if (G.isUnivariate() && fdivides(G, F)) return G/Lc(G); |
---|
1104 | if (F == G) return F/Lc(F); |
---|
1105 | |
---|
1106 | CFMap M,N; |
---|
1107 | int best_level= myCompress (A, B, M, N, topLevel); |
---|
1108 | |
---|
1109 | if (best_level == 0) return B.genOne(); |
---|
1110 | |
---|
1111 | A= M(A); |
---|
1112 | B= M(B); |
---|
1113 | |
---|
1114 | Variable x= Variable (1); |
---|
1115 | |
---|
1116 | //univariate case |
---|
1117 | if (A.isUnivariate() && B.isUnivariate()) |
---|
1118 | return N (gcd (A, B)); |
---|
1119 | |
---|
1120 | int substitute= substituteCheck (A, B); |
---|
1121 | |
---|
1122 | if (substitute > 1) |
---|
1123 | subst (A, B, A, B, substitute); |
---|
1124 | |
---|
1125 | CanonicalForm cA, cB; // content of A and B |
---|
1126 | CanonicalForm ppA, ppB; // primitive part of A and B |
---|
1127 | CanonicalForm gcdcAcB; |
---|
1128 | |
---|
1129 | if (topLevel) |
---|
1130 | { |
---|
1131 | if (best_level <= 2) |
---|
1132 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, best_level); |
---|
1133 | else |
---|
1134 | gcdcAcB= extractContents (A, B, cA, cB, ppA, ppB, 2); |
---|
1135 | } |
---|
1136 | else |
---|
1137 | { |
---|
1138 | cA = uni_content (A); |
---|
1139 | cB = uni_content (B); |
---|
1140 | gcdcAcB= gcd (cA, cB); |
---|
1141 | ppA= A/cA; |
---|
1142 | ppB= B/cB; |
---|
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 | { |
---|
1168 | if (substitute > 1) |
---|
1169 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
1170 | else |
---|
1171 | return N(gcdcAcB); |
---|
1172 | } |
---|
1173 | d0= totaldegree (ppB, Variable (2), Variable (ppB.level())); |
---|
1174 | |
---|
1175 | if (d0 < d) |
---|
1176 | d= d0; |
---|
1177 | |
---|
1178 | if (d == 0) |
---|
1179 | { |
---|
1180 | if (substitute > 1) |
---|
1181 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
1182 | else |
---|
1183 | return N(gcdcAcB); |
---|
1184 | } |
---|
1185 | |
---|
1186 | CanonicalForm m, random_element, G_m, G_random_element, H, cH, ppH; |
---|
1187 | CanonicalForm newtonPoly= 1; |
---|
1188 | m= gcdlcAlcB; |
---|
1189 | H= 0; |
---|
1190 | G_m= 0; |
---|
1191 | Variable alpha, V_buf; |
---|
1192 | bool fail= false; |
---|
1193 | bool inextension= false; |
---|
1194 | bool inextensionextension= false; |
---|
1195 | topLevel= false; |
---|
1196 | CFList source, dest; |
---|
1197 | do |
---|
1198 | { |
---|
1199 | if (inextension) |
---|
1200 | random_element= randomElement (m, alpha, l, fail); |
---|
1201 | else |
---|
1202 | random_element= FpRandomElement (m, l, fail); |
---|
1203 | |
---|
1204 | if (!fail && !inextension) |
---|
1205 | { |
---|
1206 | CFList list; |
---|
1207 | TIMING_START (gcd_recursion); |
---|
1208 | G_random_element= |
---|
1209 | GCD_small_p (ppA (random_element,x), ppB (random_element,x), topLevel, |
---|
1210 | list); |
---|
1211 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1212 | "time for recursive call: "); |
---|
1213 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1214 | } |
---|
1215 | else if (!fail && inextension) |
---|
1216 | { |
---|
1217 | CFList list; |
---|
1218 | TIMING_START (gcd_recursion); |
---|
1219 | G_random_element= |
---|
1220 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
1221 | list, topLevel); |
---|
1222 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1223 | "time for recursive call: "); |
---|
1224 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1225 | } |
---|
1226 | else if (fail && !inextension) |
---|
1227 | { |
---|
1228 | source= CFList(); |
---|
1229 | dest= CFList(); |
---|
1230 | CFList list; |
---|
1231 | CanonicalForm mipo; |
---|
1232 | int deg= 2; |
---|
1233 | do { |
---|
1234 | mipo= randomIrredpoly (deg, x); |
---|
1235 | alpha= rootOf (mipo); |
---|
1236 | inextension= true; |
---|
1237 | fail= false; |
---|
1238 | random_element= randomElement (m, alpha, l, fail); |
---|
1239 | deg++; |
---|
1240 | } while (fail); |
---|
1241 | list= CFList(); |
---|
1242 | TIMING_START (gcd_recursion); |
---|
1243 | G_random_element= |
---|
1244 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), alpha, |
---|
1245 | list, topLevel); |
---|
1246 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1247 | "time for recursive call: "); |
---|
1248 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1249 | } |
---|
1250 | else if (fail && inextension) |
---|
1251 | { |
---|
1252 | source= CFList(); |
---|
1253 | dest= CFList(); |
---|
1254 | int num_vars= tmin (getNumVars(A), getNumVars(B)); |
---|
1255 | num_vars--; |
---|
1256 | V_buf= alpha; |
---|
1257 | choose_extension (d, num_vars, V_buf); |
---|
1258 | bool prim_fail= false; |
---|
1259 | Variable V_buf2; |
---|
1260 | CanonicalForm prim_elem, im_prim_elem; |
---|
1261 | prim_elem= primitiveElement (alpha, V_buf2, prim_fail); |
---|
1262 | |
---|
1263 | ASSERT (!prim_fail, "failure in integer factorizer"); |
---|
1264 | if (prim_fail) |
---|
1265 | ; //ERROR |
---|
1266 | else |
---|
1267 | im_prim_elem= mapPrimElem (prim_elem, alpha, V_buf); |
---|
1268 | |
---|
1269 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (alpha)); |
---|
1270 | DEBOUTLN (cerr, "getMipo (alpha)= " << getMipo (V_buf2)); |
---|
1271 | |
---|
1272 | inextensionextension= true; |
---|
1273 | for (CFListIterator i= l; i.hasItem(); i++) |
---|
1274 | i.getItem()= mapUp (i.getItem(), alpha, V_buf, prim_elem, |
---|
1275 | im_prim_elem, source, dest); |
---|
1276 | m= mapUp (m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1277 | G_m= mapUp (G_m, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1278 | newtonPoly= mapUp (newtonPoly, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1279 | source, dest); |
---|
1280 | ppA= mapUp (ppA, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1281 | ppB= mapUp (ppB, alpha, V_buf, prim_elem, im_prim_elem, source, dest); |
---|
1282 | gcdlcAlcB= mapUp (gcdlcAlcB, alpha, V_buf, prim_elem, im_prim_elem, |
---|
1283 | source, dest); |
---|
1284 | fail= false; |
---|
1285 | random_element= randomElement (m, V_buf, l, fail ); |
---|
1286 | DEBOUTLN (cerr, "fail= " << fail); |
---|
1287 | CFList list; |
---|
1288 | TIMING_START (gcd_recursion); |
---|
1289 | G_random_element= |
---|
1290 | GCD_Fp_extension (ppA (random_element, x), ppB (random_element, x), V_buf, |
---|
1291 | list, topLevel); |
---|
1292 | TIMING_END_AND_PRINT (gcd_recursion, |
---|
1293 | "time for recursive call: "); |
---|
1294 | DEBOUTLN (cerr, "G_random_element= " << G_random_element); |
---|
1295 | alpha= V_buf; |
---|
1296 | } |
---|
1297 | |
---|
1298 | d0= totaldegree (G_random_element, Variable(2), |
---|
1299 | Variable (G_random_element.level())); |
---|
1300 | |
---|
1301 | if (d0 == 0) |
---|
1302 | { |
---|
1303 | if (substitute > 1) |
---|
1304 | return N (reverseSubst (gcdcAcB, substitute)); |
---|
1305 | else |
---|
1306 | return N(gcdcAcB); |
---|
1307 | } |
---|
1308 | if (d0 > d) |
---|
1309 | { |
---|
1310 | if (!find (l, random_element)) |
---|
1311 | l.append (random_element); |
---|
1312 | continue; |
---|
1313 | } |
---|
1314 | |
---|
1315 | G_random_element= (gcdlcAlcB(random_element,x)/uni_lcoeff(G_random_element)) |
---|
1316 | *G_random_element; |
---|
1317 | |
---|
1318 | |
---|
1319 | d0= totaldegree (G_random_element, Variable(2), |
---|
1320 | Variable(G_random_element.level())); |
---|
1321 | |
---|
1322 | if (d0 < d) |
---|
1323 | { |
---|
1324 | m= gcdlcAlcB; |
---|
1325 | newtonPoly= 1; |
---|
1326 | G_m= 0; |
---|
1327 | d= d0; |
---|
1328 | } |
---|
1329 | |
---|
1330 | TIMING_START (newton_interpolation); |
---|
1331 | H= newtonInterp (random_element, G_random_element, newtonPoly, G_m, x); |
---|
1332 | TIMING_END_AND_PRINT (newton_interpolation, |
---|
1333 | "time for newton_interpolation: "); |
---|
1334 | |
---|
1335 | //termination test |
---|
1336 | if (uni_lcoeff (H) == gcdlcAlcB) |
---|
1337 | { |
---|
1338 | cH= uni_content (H); |
---|
1339 | ppH= H/cH; |
---|
1340 | ppH /= Lc (ppH); |
---|
1341 | DEBOUTLN (cerr, "ppH= " << ppH); |
---|
1342 | if (fdivides (ppH, A) && fdivides (ppH, B)) |
---|
1343 | { |
---|
1344 | if (substitute > 1) |
---|
1345 | { |
---|
1346 | ppH= reverseSubst (ppH, substitute); |
---|
1347 | gcdcAcB= reverseSubst (gcdcAcB, substitute); |
---|
1348 | } |
---|
1349 | return N(gcdcAcB*ppH); |
---|
1350 | } |
---|
1351 | } |
---|
1352 | |
---|
1353 | G_m= H; |
---|
1354 | newtonPoly= newtonPoly*(x - random_element); |
---|
1355 | m= m*(x - random_element); |
---|
1356 | if (!find (l, random_element)) |
---|
1357 | l.append (random_element); |
---|
1358 | } while (1); |
---|
1359 | } |
---|
1360 | |
---|
1361 | #endif |
---|