1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file fac_ezgcd.cc |
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5 | * |
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6 | * This file implements the GCD of two multivariate polynomials over Q using |
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7 | * EZ-GCD as described in "Algorithms for Computer Algebra" by Geddes, Czapor, |
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8 | * Labahnn |
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9 | * |
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10 | * @author Martin Lee |
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11 | * |
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12 | **/ |
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13 | /*****************************************************************************/ |
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14 | |
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15 | #include "config.h" |
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16 | |
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17 | #include "timing.h" |
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18 | #include "cf_assert.h" |
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19 | #include "debug.h" |
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20 | |
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21 | #include "cf_defs.h" |
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22 | #include "canonicalform.h" |
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23 | #include "fac_util.h" // HEADER for this file |
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24 | #include "cf_algorithm.h" |
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25 | #include "cf_reval.h" |
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26 | #include "cf_random.h" |
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27 | #include "cf_primes.h" |
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28 | #include "templates/ftmpl_functions.h" |
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29 | #include "cf_map.h" |
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30 | #include "facHensel.h" |
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31 | |
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32 | #ifdef HAVE_NTL |
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33 | |
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34 | TIMING_DEFINE_PRINT(ez_eval) |
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35 | TIMING_DEFINE_PRINT(ez_compress) |
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36 | TIMING_DEFINE_PRINT(ez_hensel_lift) |
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37 | TIMING_DEFINE_PRINT(ez_content) |
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38 | TIMING_DEFINE_PRINT(ez_termination) |
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39 | |
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40 | static |
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41 | int compress4EZGCD (const CanonicalForm& F, const CanonicalForm& G, CFMap & M, |
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42 | CFMap & N, int& both_non_zero) |
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43 | { |
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44 | int n= tmax (F.level(), G.level()); |
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45 | int * degsf= new int [n + 1]; |
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46 | int * degsg= new int [n + 1]; |
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47 | |
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48 | for (int i = 0; i <= n; i++) |
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49 | degsf[i]= degsg[i]= 0; |
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50 | |
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51 | degsf= degrees (F, degsf); |
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52 | degsg= degrees (G, degsg); |
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53 | |
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54 | both_non_zero= 0; |
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55 | int f_zero= 0; |
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56 | int g_zero= 0; |
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57 | |
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58 | for (int i= 1; i <= n; i++) |
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59 | { |
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60 | if (degsf[i] != 0 && degsg[i] != 0) |
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61 | { |
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62 | both_non_zero++; |
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63 | continue; |
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64 | } |
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65 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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66 | { |
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67 | f_zero++; |
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68 | continue; |
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69 | } |
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70 | if (degsg[i] == 0 && degsf[i] && i <= F.level()) |
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71 | { |
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72 | g_zero++; |
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73 | continue; |
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74 | } |
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75 | } |
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76 | |
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77 | if (both_non_zero == 0) |
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78 | { |
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79 | delete [] degsf; |
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80 | delete [] degsg; |
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81 | return 0; |
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82 | } |
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83 | |
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84 | // map Variables which do not occur in both polynomials to higher levels |
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85 | int k= 1; |
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86 | int l= 1; |
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87 | for (int i= 1; i <= n; i++) |
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88 | { |
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89 | if (degsf[i] != 0 && degsg[i] == 0 && i <= F.level()) |
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90 | { |
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91 | if (k + both_non_zero != i) |
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92 | { |
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93 | M.newpair (Variable (i), Variable (k + both_non_zero)); |
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94 | N.newpair (Variable (k + both_non_zero), Variable (i)); |
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95 | } |
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96 | k++; |
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97 | } |
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98 | if (degsf[i] == 0 && degsg[i] != 0 && i <= G.level()) |
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99 | { |
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100 | if (l + g_zero + both_non_zero != i) |
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101 | { |
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102 | M.newpair (Variable (i), Variable (l + g_zero + both_non_zero)); |
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103 | N.newpair (Variable (l + g_zero + both_non_zero), Variable (i)); |
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104 | } |
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105 | l++; |
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106 | } |
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107 | } |
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108 | |
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109 | // sort Variables x_{i} in decreasing order of |
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110 | // min(deg_{x_{i}}(f),deg_{x_{i}}(g)) |
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111 | int m= tmin (F.level(), G.level()); |
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112 | int max_min_deg; |
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113 | k= both_non_zero; |
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114 | l= 0; |
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115 | int i= 1; |
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116 | while (k > 0) |
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117 | { |
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118 | max_min_deg= tmin (degsf[i], degsg[i]); |
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119 | while (max_min_deg == 0) |
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120 | { |
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121 | i++; |
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122 | max_min_deg= tmin (degsf[i], degsg[i]); |
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123 | } |
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124 | for (int j= i + 1; j <= m; j++) |
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125 | { |
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126 | if ((tmin (degsf[j],degsg[j]) < max_min_deg) && |
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127 | (tmin (degsf[j], degsg[j]) != 0)) |
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128 | { |
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129 | max_min_deg= tmin (degsf[j], degsg[j]); |
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130 | l= j; |
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131 | } |
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132 | } |
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133 | |
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134 | if (l != 0) |
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135 | { |
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136 | if (l != k) |
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137 | { |
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138 | M.newpair (Variable (l), Variable(k)); |
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139 | N.newpair (Variable (k), Variable(l)); |
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140 | degsf[l]= 0; |
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141 | degsg[l]= 0; |
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142 | l= 0; |
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143 | } |
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144 | else |
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145 | { |
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146 | degsf[l]= 0; |
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147 | degsg[l]= 0; |
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148 | l= 0; |
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149 | } |
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150 | } |
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151 | else if (l == 0) |
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152 | { |
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153 | if (i != k) |
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154 | { |
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155 | M.newpair (Variable (i), Variable (k)); |
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156 | N.newpair (Variable (k), Variable (i)); |
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157 | degsf[i]= 0; |
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158 | degsg[i]= 0; |
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159 | } |
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160 | else |
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161 | { |
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162 | degsf[i]= 0; |
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163 | degsg[i]= 0; |
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164 | } |
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165 | i++; |
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166 | } |
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167 | k--; |
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168 | } |
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169 | |
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170 | delete [] degsf; |
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171 | delete [] degsg; |
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172 | |
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173 | return both_non_zero; |
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174 | } |
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175 | |
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176 | static inline |
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177 | CanonicalForm myShift2Zero (const CanonicalForm& F, CFList& Feval, |
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178 | const CFList& evaluation) |
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179 | { |
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180 | CanonicalForm A= F; |
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181 | int k= 2; |
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182 | for (CFListIterator i= evaluation; i.hasItem(); i++, k++) |
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183 | A= A (Variable (k) + i.getItem(), k); |
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184 | |
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185 | CanonicalForm buf= A; |
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186 | Feval= CFList(); |
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187 | Feval.append (buf); |
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188 | for (k= evaluation.length() + 1; k > 2; k--) |
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189 | { |
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190 | buf= mod (buf, Variable (k)); |
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191 | Feval.insert (buf); |
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192 | } |
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193 | return A; |
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194 | } |
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195 | |
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196 | static inline |
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197 | CanonicalForm myReverseShift (const CanonicalForm& F, const CFList& evaluation) |
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198 | { |
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199 | int l= evaluation.length() + 1; |
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200 | CanonicalForm result= F; |
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201 | CFListIterator j= evaluation; |
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202 | for (int i= 2; i < l + 1; i++, j++) |
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203 | { |
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204 | if (F.level() < i) |
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205 | continue; |
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206 | result= result (Variable (i) - j.getItem(), i); |
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207 | } |
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208 | return result; |
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209 | } |
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210 | |
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211 | static inline |
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212 | Evaluation optimize4Lift (const CanonicalForm& F, CFMap & M, |
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213 | CFMap & N, const Evaluation& A) |
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214 | { |
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215 | int n= F.level(); |
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216 | int * degsf= new int [n + 1]; |
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217 | |
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218 | for (int i = 0; i <= n; i++) |
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219 | degsf[i]= 0; |
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220 | |
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221 | degsf= degrees (F, degsf); |
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222 | |
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223 | Evaluation result= Evaluation (A.min(), A.max()); |
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224 | ASSERT (A.min() == 2, "expected A.min() == 2"); |
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225 | int max_deg; |
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226 | int k= n; |
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227 | int l= 1; |
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228 | int i= 2; |
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229 | int pos= 2; |
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230 | while (k > 1) |
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231 | { |
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232 | max_deg= degsf [i]; |
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233 | while (max_deg == 0) |
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234 | { |
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235 | i++; |
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236 | max_deg= degsf [i]; |
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237 | } |
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238 | l= i; |
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239 | for (int j= i + 1; j <= n; j++) |
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240 | { |
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241 | if (degsf[j] > max_deg) |
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242 | { |
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243 | max_deg= degsf[j]; |
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244 | l= j; |
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245 | } |
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246 | } |
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247 | |
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248 | if (l <= n) |
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249 | { |
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250 | if (l != pos) |
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251 | { |
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252 | result.setValue (pos, A [l]); |
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253 | M.newpair (Variable (l), Variable (pos)); |
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254 | N.newpair (Variable (pos), Variable (l)); |
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255 | degsf[l]= 0; |
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256 | l= 2; |
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257 | if (k == 2 && n == 3) |
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258 | { |
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259 | result.setValue (l, A [pos]); |
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260 | M.newpair (Variable (pos), Variable (l)); |
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261 | N.newpair (Variable (l), Variable (pos)); |
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262 | degsf[pos]= 0; |
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263 | } |
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264 | } |
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265 | else |
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266 | { |
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267 | result.setValue (l, A [l]); |
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268 | degsf [l]= 0; |
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269 | } |
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270 | } |
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271 | pos++; |
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272 | k--; |
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273 | l= 2; |
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274 | } |
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275 | |
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276 | delete [] degsf; |
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277 | |
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278 | return result; |
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279 | } |
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280 | |
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281 | static inline |
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282 | int Hensel (const CanonicalForm & UU, CFArray & G, const Evaluation & AA, |
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283 | const CFArray& LeadCoeffs ) |
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284 | { |
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285 | CFList factors; |
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286 | factors.append (G[1]); |
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287 | factors.append (G[2]); |
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288 | |
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289 | CFMap NN, MM; |
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290 | Evaluation A= optimize4Lift (UU, MM, NN, AA); |
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291 | |
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292 | CanonicalForm U= MM (UU); |
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293 | CFArray LCs= CFArray (1,2); |
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294 | LCs [1]= MM (LeadCoeffs [1]); |
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295 | LCs [2]= MM (LeadCoeffs [2]); |
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296 | |
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297 | CFList evaluation; |
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298 | long termEstimate= size (U); |
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299 | for (int i= A.min(); i <= A.max(); i++) |
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300 | { |
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301 | if (!A[i].isZero()) |
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302 | { |
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303 | termEstimate *= degree (U,i)*2; |
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304 | termEstimate /= 3; |
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305 | } |
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306 | evaluation.append (A [i]); |
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307 | } |
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308 | if (termEstimate/getNumVars(U) > 500) |
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309 | return -1; |
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310 | CFList UEval; |
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311 | CanonicalForm shiftedU= myShift2Zero (U, UEval, evaluation); |
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312 | |
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313 | if (size (shiftedU)/getNumVars (U) > 500) |
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314 | return -1; |
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315 | |
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316 | CFArray shiftedLCs= CFArray (2); |
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317 | CFList shiftedLCsEval1, shiftedLCsEval2; |
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318 | shiftedLCs[0]= myShift2Zero (LCs[1], shiftedLCsEval1, evaluation); |
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319 | shiftedLCs[1]= myShift2Zero (LCs[2], shiftedLCsEval2, evaluation); |
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320 | factors.insert (1); |
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321 | int liftBound= degree (UEval.getLast(), 2) + 1; |
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322 | CFArray Pi; |
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323 | CFMatrix M= CFMatrix (liftBound, factors.length() - 1); |
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324 | CFList diophant; |
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325 | CFArray lcs= CFArray (2); |
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326 | lcs [0]= shiftedLCsEval1.getFirst(); |
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327 | lcs [1]= shiftedLCsEval2.getFirst(); |
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328 | nonMonicHenselLift12 (UEval.getFirst(), factors, liftBound, Pi, diophant, M, |
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329 | lcs, false); |
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330 | |
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331 | for (CFListIterator i= factors; i.hasItem(); i++) |
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332 | { |
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333 | if (!fdivides (i.getItem(), UEval.getFirst())) |
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334 | return 0; |
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335 | } |
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336 | |
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337 | int * liftBounds; |
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338 | bool noOneToOne= false; |
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339 | if (U.level() > 2) |
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340 | { |
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341 | liftBounds= new int [U.level() - 1]; /* index: 0.. U.level()-2 */ |
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342 | liftBounds[0]= liftBound; |
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343 | for (int i= 1; i < U.level() - 1; i++) |
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344 | liftBounds[i]= degree (shiftedU, Variable (i + 2)) + 1; |
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345 | factors= nonMonicHenselLift2 (UEval, factors, liftBounds, U.level() - 1, |
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346 | false, shiftedLCsEval1, shiftedLCsEval2, Pi, |
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347 | diophant, noOneToOne); |
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348 | delete [] liftBounds; |
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349 | if (noOneToOne) |
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350 | return 0; |
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351 | } |
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352 | G[1]= factors.getFirst(); |
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353 | G[2]= factors.getLast(); |
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354 | G[1]= myReverseShift (G[1], evaluation); |
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355 | G[2]= myReverseShift (G[2], evaluation); |
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356 | G[1]= NN (G[1]); |
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357 | G[2]= NN (G[2]); |
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358 | return 1; |
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359 | } |
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360 | |
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361 | static |
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362 | bool findeval (const CanonicalForm & F, const CanonicalForm & G, |
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363 | CanonicalForm & Fb, CanonicalForm & Gb, CanonicalForm & Db, |
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364 | REvaluation & b, int delta, int degF, int degG, int maxeval, |
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365 | int & count, int& k, int bound, int& l) |
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366 | { |
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367 | if( count == 0 && delta != 0) |
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368 | { |
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369 | if( count++ > maxeval ) |
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370 | return false; |
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371 | } |
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372 | if (count > 0) |
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373 | { |
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374 | b.nextpoint(k); |
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375 | if (k == 0) |
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376 | k++; |
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377 | l++; |
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378 | if (l > bound) |
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379 | { |
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380 | l= 1; |
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381 | k++; |
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382 | if (k > tmax (F.level(), G.level()) - 1) |
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383 | return false; |
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384 | b.nextpoint (k); |
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385 | } |
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386 | if (count++ > maxeval) |
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387 | return false; |
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388 | } |
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389 | while( true ) |
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390 | { |
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391 | Fb = b( F ); |
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392 | if( degree( Fb, 1 ) == degF ) |
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393 | { |
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394 | Gb = b( G ); |
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395 | if( degree( Gb, 1 ) == degG ) |
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396 | { |
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397 | Db = gcd( Fb, Gb ); |
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398 | if( delta > 0 ) |
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399 | { |
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400 | if( degree( Db, 1 ) <= delta ) |
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401 | return true; |
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402 | } |
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403 | else |
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404 | { |
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405 | k++; |
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406 | return true; |
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407 | } |
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408 | } |
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409 | } |
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410 | if (k == 0) |
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411 | k++; |
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412 | b.nextpoint(k); |
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413 | l++; |
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414 | if (l > bound) |
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415 | { |
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416 | l= 1; |
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417 | k++; |
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418 | if (k > tmax (F.level(), G.level()) - 1) |
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419 | return false; |
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420 | b.nextpoint (k); |
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421 | } |
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422 | if( count++ > maxeval ) |
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423 | return false; |
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424 | } |
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425 | } |
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426 | |
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427 | static CanonicalForm |
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428 | ezgcd ( const CanonicalForm & FF, const CanonicalForm & GG, REvaluation & b, |
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429 | bool internal ) |
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430 | { |
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431 | bool isRat= isOn (SW_RATIONAL); |
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432 | CanonicalForm F, G, f, g, d, Fb, Gb, Db, Fbt, Gbt, Dbt, B0, B, D0, lcF, lcG, |
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433 | lcD, cand, contcand, result; |
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434 | CFArray DD( 1, 2 ), lcDD( 1, 2 ); |
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435 | int degF, degG, delta, t, count, maxeval; |
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436 | REvaluation bt; |
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437 | int gcdfound = 0; |
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438 | Variable x = Variable(1); |
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439 | count= 0; |
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440 | maxeval= 200; |
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441 | int o, l; |
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442 | o= 0; |
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443 | l= 1; |
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444 | |
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445 | if (!isRat) |
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446 | On (SW_RATIONAL); |
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447 | F= FF*bCommonDen (FF); |
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448 | G= GG*bCommonDen (GG); |
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449 | if (!isRat) |
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450 | Off (SW_RATIONAL); |
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451 | |
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452 | TIMING_START (ez_compress) |
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453 | CFMap M,N; |
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454 | int smallestDegLev; |
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455 | int best_level= compress4EZGCD (F, G, M, N, smallestDegLev); |
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456 | |
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457 | if (best_level == 0) |
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458 | { |
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459 | DEBDECLEVEL( cerr, "ezgcd" ); |
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460 | return G.genOne(); |
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461 | } |
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462 | |
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463 | F= M (F); |
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464 | G= M (G); |
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465 | TIMING_END_AND_PRINT (ez_compress, "time for compression in EZ: ") |
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466 | |
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467 | DEBINCLEVEL( cerr, "ezgcd" ); |
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468 | DEBOUTLN( cerr, "FF = " << FF ); |
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469 | DEBOUTLN( cerr, "GG = " << GG ); |
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470 | TIMING_START (ez_content) |
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471 | f = content( F, x ); g = content( G, x ); d = gcd( f, g ); |
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472 | d /= icontent (d); |
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473 | DEBOUTLN( cerr, "f = " << f ); |
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474 | DEBOUTLN( cerr, "g = " << g ); |
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475 | F /= f; G /= g; |
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476 | TIMING_END_AND_PRINT (ez_content, "time to extract content in EZ: ") |
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477 | if ( F.isUnivariate() && G.isUnivariate() ) |
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478 | { |
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479 | DEBDECLEVEL( cerr, "ezgcd" ); |
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480 | if(F.mvar()==G.mvar()) |
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481 | d*=gcd(F,G); |
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482 | else |
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483 | return N (d); |
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484 | return N (d); |
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485 | } |
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486 | if ( F.isUnivariate()) |
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487 | { |
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488 | g= content (G,G.mvar()); |
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489 | return N(d*gcd(F,g)); |
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490 | } |
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491 | if ( G.isUnivariate()) |
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492 | { |
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493 | f= content (F,F.mvar()); |
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494 | return N(d*gcd(G,f)); |
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495 | } |
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496 | |
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497 | int maxNumVars= tmax (getNumVars (F), getNumVars (G)); |
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498 | int sizeF= size (F); |
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499 | int sizeG= size (G); |
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500 | |
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501 | |
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502 | if (!isRat) |
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503 | On (SW_RATIONAL); |
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504 | if (sizeF/maxNumVars > 500 && sizeG/maxNumVars > 500) |
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505 | { |
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506 | Off(SW_USE_EZGCD); |
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507 | result=gcd( F, G ); |
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508 | On(SW_USE_EZGCD); |
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509 | if (!isRat) |
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510 | Off (SW_RATIONAL); |
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511 | result /= icontent (result); |
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512 | DEBDECLEVEL( cerr, "ezgcd" ); |
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513 | return N (d*result); |
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514 | } |
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515 | |
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516 | int dummy= 0; |
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517 | if ( gcd_test_one( F, G, false, dummy ) ) |
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518 | { |
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519 | DEBDECLEVEL( cerr, "ezgcd" ); |
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520 | if (!isRat) |
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521 | Off (SW_RATIONAL); |
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522 | return N (d); |
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523 | } |
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524 | lcF = LC( F, x ); lcG = LC( G, x ); |
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525 | lcD = gcd( lcF, lcG ); |
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526 | delta = 0; |
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527 | degF = degree( F, x ); degG = degree( G, x ); |
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528 | t = tmax( F.level(), G.level() ); |
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529 | if ( ! internal ) |
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530 | b = REvaluation( 2, t, IntRandom( 25 ) ); |
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531 | while ( ! gcdfound ) |
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532 | { |
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533 | /// ---> A2 |
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534 | DEBOUTLN( cerr, "search for evaluation, delta = " << delta ); |
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535 | DEBOUTLN( cerr, "F = " << F ); |
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536 | DEBOUTLN( cerr, "G = " << G ); |
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537 | TIMING_START (ez_eval) |
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538 | if (!findeval( F, G, Fb, Gb, Db, b, delta, degF, degG, maxeval, count, |
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539 | o, 25, l)) |
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540 | { |
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541 | Off(SW_USE_EZGCD); |
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542 | result=gcd( F, G ); |
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543 | On(SW_USE_EZGCD); |
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544 | if (!isRat) |
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545 | Off (SW_RATIONAL); |
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546 | DEBDECLEVEL( cerr, "ezgcd" ); |
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547 | result /= icontent (result); |
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548 | return N (d*result); |
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549 | } |
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550 | TIMING_END_AND_PRINT (ez_eval, "time to find eval point in EZ1: ") |
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551 | DEBOUTLN( cerr, "found evaluation b = " << b ); |
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552 | DEBOUTLN( cerr, "F(b) = " << Fb ); |
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553 | DEBOUTLN( cerr, "G(b) = " << Gb ); |
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554 | DEBOUTLN( cerr, "D(b) = " << Db ); |
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555 | delta = degree( Db ); |
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556 | /// ---> A3 |
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557 | if ( delta == 0 ) |
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558 | { |
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559 | DEBDECLEVEL( cerr, "ezgcd" ); |
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560 | if (!isRat) |
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561 | Off (SW_RATIONAL); |
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562 | return N (d); |
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563 | } |
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564 | /// ---> A4 |
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565 | //deltaold = delta; |
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566 | while ( 1 ) |
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567 | { |
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568 | bt = b; |
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569 | TIMING_START (ez_eval) |
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570 | if (!findeval( F, G, Fbt, Gbt, Dbt, bt, delta, degF, degG, maxeval, count, |
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571 | o, 25,l )) |
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572 | { |
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573 | Off(SW_USE_EZGCD); |
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574 | result=gcd( F, G ); |
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575 | On(SW_USE_EZGCD); |
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576 | if (!isRat) |
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577 | Off (SW_RATIONAL); |
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578 | DEBDECLEVEL( cerr, "ezgcd" ); |
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579 | result /= icontent (result); |
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580 | return N (d*result); |
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581 | } |
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582 | TIMING_END_AND_PRINT (ez_eval, "time to find eval point in EZ2: ") |
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583 | int dd=degree( Dbt ); |
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584 | if ( dd /*degree( Dbt )*/ == 0 ) |
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585 | { |
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586 | DEBDECLEVEL( cerr, "ezgcd" ); |
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587 | if (!isRat) |
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588 | Off (SW_RATIONAL); |
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589 | return N (d); |
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590 | } |
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591 | if ( dd /*degree( Dbt )*/ == delta ) |
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592 | break; |
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593 | else if ( dd /*degree( Dbt )*/ < delta ) |
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594 | { |
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595 | delta = dd /*degree( Dbt )*/; |
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596 | b = bt; |
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597 | Db = Dbt; Fb = Fbt; Gb = Gbt; |
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598 | } |
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599 | DEBOUTLN( cerr, "now after A4, delta = " << delta ); |
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600 | /// ---> A5 |
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601 | if (delta == degF) |
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602 | { |
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603 | if (degF <= degG && fdivides (F, G)) |
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604 | { |
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605 | DEBDECLEVEL( cerr, "ezgcd" ); |
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606 | if (!isRat) |
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607 | Off (SW_RATIONAL); |
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608 | return N (d*F); |
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609 | } |
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610 | else |
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611 | delta--; |
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612 | } |
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613 | else if (delta == degG) |
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614 | { |
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615 | if (degG <= degF && fdivides( G, F )) |
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616 | { |
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617 | DEBDECLEVEL( cerr, "ezgcd" ); |
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618 | if (!isRat) |
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619 | Off (SW_RATIONAL); |
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620 | return N (d*G); |
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621 | } |
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622 | else |
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623 | delta--; |
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624 | } |
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625 | } |
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626 | if ( delta != degF && delta != degG ) |
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627 | { |
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628 | /// ---> A6 |
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629 | bool B_is_F; |
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630 | CanonicalForm xxx1, xxx2; |
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631 | CanonicalForm buf; |
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632 | DD[1] = Fb / Db; |
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633 | buf= Gb/Db; |
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634 | xxx1 = gcd( DD[1], Db ); |
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635 | xxx2 = gcd( buf, Db ); |
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636 | if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
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637 | (size (F) <= size (G))) |
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638 | || (xxx1.inCoeffDomain() && !xxx2.inCoeffDomain())) |
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639 | { |
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640 | B = F; |
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641 | DD[2] = Db; |
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642 | lcDD[1] = lcF; |
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643 | lcDD[2] = lcD; |
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644 | B_is_F = true; |
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645 | } |
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646 | else if (((xxx1.inCoeffDomain() && xxx2.inCoeffDomain()) && |
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647 | (size (G) < size (F))) |
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648 | || (!xxx1.inCoeffDomain() && xxx2.inCoeffDomain())) |
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649 | { |
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650 | DD[1] = buf; |
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651 | B = G; |
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652 | DD[2] = Db; |
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653 | lcDD[1] = lcG; |
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654 | lcDD[2] = lcD; |
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655 | B_is_F = false; |
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656 | } |
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657 | else |
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658 | { |
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659 | //special case |
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660 | Off(SW_USE_EZGCD); |
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661 | result=gcd( F, G ); |
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662 | On(SW_USE_EZGCD); |
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663 | if (!isRat) |
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664 | Off (SW_RATIONAL); |
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665 | DEBDECLEVEL( cerr, "ezgcd" ); |
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666 | result /= icontent (result); |
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667 | return N (d*result); |
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668 | } |
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669 | /// ---> A7 |
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670 | DD[2] = DD[2] * ( b( lcDD[2] ) / lc( DD[2] ) ); |
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671 | DD[1] = DD[1] * ( b( lcDD[1] ) / lc( DD[1] ) ); |
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672 | DEBOUTLN( cerr, "(hensel) B = " << B ); |
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673 | DEBOUTLN( cerr, "(hensel) lcB = " << LC( B, Variable(1) ) ); |
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674 | DEBOUTLN( cerr, "(hensel) b(B) = " << b(B) ); |
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675 | DEBOUTLN( cerr, "(hensel) DD = " << DD ); |
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676 | DEBOUTLN( cerr, "(hensel) lcDD = " << lcDD ); |
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677 | TIMING_START (ez_hensel_lift) |
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678 | gcdfound= Hensel (B*lcD, DD, b, lcDD); |
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679 | TIMING_END_AND_PRINT (ez_hensel_lift, "time to hensel lift in EZ: ") |
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680 | DEBOUTLN( cerr, "(hensel finished) DD = " << DD ); |
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681 | |
---|
682 | if (gcdfound == -1) |
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683 | { |
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684 | Off (SW_USE_EZGCD); |
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685 | result= gcd (F,G); |
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686 | On (SW_USE_EZGCD); |
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687 | if (!isRat) |
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688 | Off (SW_RATIONAL); |
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689 | DEBDECLEVEL( cerr, "ezgcd" ); |
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690 | result /= icontent (result); |
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691 | return N (d*result); |
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692 | } |
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693 | |
---|
694 | if (gcdfound) |
---|
695 | { |
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696 | TIMING_START (ez_termination) |
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697 | contcand= content (DD[2], Variable (1)); |
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698 | cand = DD[2] / contcand; |
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699 | if (B_is_F) |
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700 | gcdfound = fdivides( cand, G ) && cand*(DD[1]/(lcD/contcand)) == F; |
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701 | else |
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702 | gcdfound = fdivides( cand, F ) && cand*(DD[1]/(lcD/contcand)) == G; |
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703 | TIMING_END_AND_PRINT (ez_termination, |
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704 | "time for termination test in EZ: ") |
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705 | } |
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706 | /// ---> A8 (gcdfound) |
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707 | } |
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708 | delta--; |
---|
709 | } |
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710 | /// ---> A9 |
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711 | DEBDECLEVEL( cerr, "ezgcd" ); |
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712 | cand *= bCommonDen (cand); |
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713 | if (!isRat) |
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714 | Off (SW_RATIONAL); |
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715 | cand /= icontent (cand); |
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716 | return N (d*cand); |
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717 | } |
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718 | #endif |
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719 | |
---|
720 | CanonicalForm |
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721 | ezgcd ( const CanonicalForm & FF, const CanonicalForm & GG ) |
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722 | { |
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723 | #ifdef HAVE_NTL |
---|
724 | REvaluation b; |
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725 | return ezgcd( FF, GG, b, false ); |
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726 | #else |
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727 | Off (SW_USE_EZGCD); |
---|
728 | return gcd (FF, GG); |
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729 | On (SW_USE_EZGCD); |
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730 | #endif |
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731 | } |
---|
732 | |
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