1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facFqBivarUtil.cc |
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5 | * |
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6 | * This file provides utility functions for bivariate factorization |
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7 | * |
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8 | * @author Martin Lee |
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9 | * |
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10 | **/ |
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11 | /*****************************************************************************/ |
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12 | |
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13 | |
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14 | #include "config.h" |
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15 | |
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16 | |
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17 | #include "timing.h" |
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18 | |
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19 | #include "cf_map.h" |
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20 | #include "cf_map_ext.h" |
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21 | #include "templates/ftmpl_functions.h" |
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22 | #include "ExtensionInfo.h" |
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23 | #include "cf_algorithm.h" |
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24 | #include "cf_factory.h" |
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25 | #include "cf_util.h" |
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26 | #include "imm.h" |
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27 | #include "cf_iter.h" |
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28 | #include "facFqBivarUtil.h" |
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29 | #include "cfNewtonPolygon.h" |
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30 | #include "facHensel.h" |
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31 | #include "facMul.h" |
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32 | |
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33 | #ifdef HAVE_FLINT |
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34 | #include "FLINTconvert.h" |
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35 | #endif |
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36 | |
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37 | TIMING_DEFINE_PRINT(fac_log_deriv_div) |
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38 | TIMING_DEFINE_PRINT(fac_log_deriv_mul) |
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39 | TIMING_DEFINE_PRINT(fac_log_deriv_pre) |
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40 | |
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41 | void append (CFList& factors1, const CFList& factors2) |
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42 | { |
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43 | for (CFListIterator i= factors2; i.hasItem(); i++) |
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44 | { |
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45 | if (!i.getItem().inCoeffDomain()) |
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46 | factors1.append (i.getItem()); |
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47 | } |
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48 | return; |
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49 | } |
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50 | |
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51 | void decompress (CFList& factors, const CFMap& N) |
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52 | { |
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53 | for (CFListIterator i= factors; i.hasItem(); i++) |
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54 | i.getItem()= N (i.getItem()); |
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55 | } |
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56 | |
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57 | void decompress (CFFList& factors, const CFMap& N) |
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58 | { |
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59 | for (CFFListIterator i= factors; i.hasItem(); i++) |
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60 | i.getItem()= CFFactor (N (i.getItem().factor()), i.getItem().exp()); |
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61 | } |
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62 | |
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63 | void decompress (CFAFList& factors, const CFMap& N) |
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64 | { |
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65 | for (CFAFListIterator i= factors; i.hasItem(); i++) |
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66 | i.getItem()= CFAFactor (N (i.getItem().factor()), i.getItem().minpoly(), |
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67 | i.getItem().exp()); |
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68 | } |
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69 | |
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70 | void appendSwapDecompress (CFList& factors1, const CFList& factors2, |
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71 | const CFList& factors3, const bool swap1, |
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72 | const bool swap2, const CFMap& N) |
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73 | { |
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74 | Variable x= Variable (1); |
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75 | Variable y= Variable (2); |
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76 | for (CFListIterator i= factors1; i.hasItem(); i++) |
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77 | { |
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78 | if (swap1) |
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79 | { |
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80 | if (!swap2) |
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81 | i.getItem()= swapvar (i.getItem(), x, y); |
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82 | } |
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83 | else |
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84 | { |
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85 | if (swap2) |
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86 | i.getItem()= swapvar (i.getItem(), y, x); |
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87 | } |
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88 | i.getItem()= N (i.getItem()); |
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89 | } |
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90 | for (CFListIterator i= factors2; i.hasItem(); i++) |
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91 | factors1.append (N (i.getItem())); |
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92 | for (CFListIterator i= factors3; i.hasItem(); i++) |
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93 | factors1.append (N (i.getItem())); |
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94 | return; |
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95 | } |
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96 | |
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97 | void swapDecompress (CFList& factors, const bool swap, const CFMap& N) |
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98 | { |
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99 | Variable x= Variable (1); |
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100 | Variable y= Variable (2); |
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101 | for (CFListIterator i= factors; i.hasItem(); i++) |
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102 | { |
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103 | if (swap) |
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104 | i.getItem()= swapvar (i.getItem(), x, y); |
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105 | i.getItem()= N (i.getItem()); |
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106 | } |
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107 | return; |
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108 | } |
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109 | |
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110 | static inline |
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111 | bool GFInExtensionHelper (const CanonicalForm& F, const int number) |
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112 | { |
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113 | if (F.isOne()) return false; |
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114 | InternalCF* buf; |
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115 | int exp; |
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116 | bool result= false; |
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117 | if (F.inBaseDomain()) |
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118 | { |
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119 | buf= F.getval(); |
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120 | exp= imm2int (buf); |
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121 | if (exp%number != 0) |
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122 | return true; |
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123 | else |
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124 | return result; |
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125 | } |
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126 | else |
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127 | { |
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128 | for (CFIterator i= F; i.hasTerms(); i++) |
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129 | { |
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130 | result= GFInExtensionHelper (i.coeff(), number); |
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131 | if (result == true) |
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132 | return result; |
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133 | } |
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134 | } |
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135 | return result; |
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136 | } |
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137 | |
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138 | static inline |
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139 | bool FqInExtensionHelper (const CanonicalForm& F, const CanonicalForm& gamma, |
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140 | const CanonicalForm& delta, CFList& source, |
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141 | CFList& dest) |
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142 | { |
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143 | bool result= false; |
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144 | if (F.inBaseDomain()) |
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145 | return result; |
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146 | else if (F.inCoeffDomain()) |
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147 | { |
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148 | if (!fdivides (gamma, F)) |
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149 | return true; |
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150 | else |
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151 | { |
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152 | int pos= findItem (source, F); |
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153 | if (pos > 0) |
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154 | return false; |
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155 | Variable a; |
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156 | hasFirstAlgVar (F, a); |
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157 | int bound= ipower (getCharacteristic(), degree (getMipo (a))); |
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158 | CanonicalForm buf= 1; |
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159 | for (int i= 1; i < bound; i++) |
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160 | { |
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161 | buf *= gamma; |
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162 | if (buf == F) |
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163 | { |
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164 | source.append (buf); |
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165 | dest.append (power (delta, i)); |
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166 | return false; |
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167 | } |
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168 | } |
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169 | return true; |
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170 | } |
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171 | } |
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172 | else |
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173 | { |
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174 | for (CFIterator i= F; i.hasTerms(); i++) |
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175 | { |
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176 | result= FqInExtensionHelper (i.coeff(), gamma, delta, source, dest); |
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177 | if (result == true) |
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178 | return result; |
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179 | } |
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180 | } |
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181 | return result; |
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182 | } |
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183 | |
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184 | bool isInExtension (const CanonicalForm& F, const CanonicalForm& gamma, |
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185 | const int k, const CanonicalForm& delta, |
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186 | CFList& source, CFList& dest) |
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187 | { |
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188 | bool result; |
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189 | if (CFFactory::gettype() == GaloisFieldDomain) |
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190 | { |
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191 | int p= getCharacteristic(); |
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192 | int orderFieldExtension= ipower (p, getGFDegree()) - 1; |
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193 | int order= ipower (p, k) - 1; |
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194 | int number= orderFieldExtension/order; |
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195 | result= GFInExtensionHelper (F, number); |
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196 | return result; |
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197 | } |
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198 | else |
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199 | { |
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200 | result= FqInExtensionHelper (F, gamma, delta, source, dest); |
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201 | return result; |
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202 | } |
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203 | } |
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204 | |
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205 | CanonicalForm |
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206 | mapDown (const CanonicalForm& F, const ExtensionInfo& info, CFList& source, |
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207 | CFList& dest) |
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208 | { |
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209 | int k= info.getGFDegree(); |
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210 | Variable beta= info.getAlpha(); |
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211 | CanonicalForm primElem= info.getGamma(); |
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212 | CanonicalForm imPrimElem= info.getDelta(); |
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213 | if (k > 1) |
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214 | return GFMapDown (F, k); |
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215 | else if (k == 1) |
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216 | return F; |
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217 | if (/*k==0 &&*/ beta == Variable (1)) |
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218 | return F; |
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219 | else /*if (k==0 && beta != Variable (1))*/ |
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220 | return mapDown (F, imPrimElem, primElem, beta, source, dest); |
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221 | } |
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222 | |
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223 | void appendTestMapDown (CFList& factors, const CanonicalForm& f, |
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224 | const ExtensionInfo& info, CFList& source, CFList& dest) |
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225 | { |
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226 | int k= info.getGFDegree(); |
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227 | Variable beta= info.getBeta(); |
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228 | Variable alpha= info.getAlpha(); |
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229 | CanonicalForm delta= info.getDelta(); |
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230 | CanonicalForm gamma= info.getGamma(); |
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231 | CanonicalForm g= f; |
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232 | int degMipoBeta=0; |
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233 | if (!k && beta.level() == 1) |
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234 | degMipoBeta= 1; |
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235 | else if (!k && beta.level() != 1) |
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236 | degMipoBeta= degree (getMipo (beta)); |
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237 | if (k > 1) |
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238 | { |
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239 | if (!isInExtension (g, gamma, k, delta, source, dest)) |
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240 | { |
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241 | g= GFMapDown (g, k); |
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242 | factors.append (g); |
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243 | } |
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244 | } |
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245 | else if (k == 1) |
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246 | { |
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247 | if (!isInExtension (g, gamma, k, delta, source, dest)) |
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248 | factors.append (g); |
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249 | } |
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250 | else if (!k && beta == Variable (1)) |
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251 | { |
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252 | if (degree (g, alpha) < degMipoBeta) |
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253 | factors.append (g); |
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254 | } |
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255 | else if (!k && beta != Variable (1)) |
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256 | { |
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257 | if (!isInExtension (g, gamma, k, delta, source, dest)) |
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258 | { |
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259 | g= mapDown (g, delta, gamma, alpha, source, dest); |
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260 | factors.append (g); |
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261 | } |
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262 | } |
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263 | return; |
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264 | } |
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265 | |
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266 | void |
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267 | appendMapDown (CFList& factors, const CanonicalForm& g, |
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268 | const ExtensionInfo& info, CFList& source, CFList& dest) |
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269 | { |
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270 | int k= info.getGFDegree(); |
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271 | Variable beta= info.getBeta(); |
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272 | Variable alpha= info.getAlpha(); |
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273 | CanonicalForm gamma= info.getGamma(); |
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274 | CanonicalForm delta= info.getDelta(); |
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275 | if (k > 1) |
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276 | factors.append (GFMapDown (g, k)); |
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277 | else if (k == 1) |
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278 | factors.append (g); |
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279 | else if (!k && beta == Variable (1)) |
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280 | factors.append (g); |
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281 | else if (!k && beta != Variable (1)) |
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282 | factors.append (mapDown (g, delta, gamma, alpha, source, dest)); |
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283 | return; |
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284 | } |
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285 | |
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286 | void normalize (CFList& factors) |
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287 | { |
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288 | CanonicalForm lcinv; |
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289 | for (CFListIterator i= factors; i.hasItem(); i++) |
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290 | { |
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291 | lcinv= 1/Lc (i.getItem()); |
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292 | i.getItem() *= lcinv; |
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293 | } |
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294 | return; |
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295 | } |
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296 | |
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297 | void normalize (CFFList& factors) |
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298 | { |
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299 | CanonicalForm lcinv; |
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300 | for (CFFListIterator i= factors; i.hasItem(); i++) |
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301 | { |
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302 | lcinv= 1/ Lc (i.getItem().factor()); |
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303 | i.getItem()= CFFactor (i.getItem().factor()*lcinv, |
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304 | i.getItem().exp()); |
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305 | } |
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306 | return; |
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307 | } |
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308 | |
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309 | CFList subset (int index [], const int& s, const CFArray& elements, |
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310 | bool& noSubset) |
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311 | { |
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312 | int r= elements.size(); |
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313 | int i= 0; |
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314 | CFList result; |
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315 | noSubset= false; |
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316 | if (index[s - 1] == 0) |
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317 | { |
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318 | while (i < s) |
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319 | { |
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320 | index[i]= i + 1; |
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321 | result.append (elements[i]); |
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322 | i++; |
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323 | } |
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324 | return result; |
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325 | } |
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326 | int buf; |
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327 | int k; |
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328 | bool found= false; |
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329 | if (index[s - 1] == r) |
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330 | { |
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331 | if (index[0] == r - s + 1) |
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332 | { |
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333 | noSubset= true; |
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334 | return result; |
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335 | } |
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336 | else { |
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337 | while (found == false) |
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338 | { |
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339 | if (index[s - 2 - i] < r - i - 1) |
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340 | found= true; |
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341 | i++; |
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342 | } |
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343 | buf= index[s - i - 1]; |
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344 | k= 0; |
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345 | while (s - i - 1 + k < s) |
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346 | { |
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347 | index[s - i - 1 + k]= buf + k + 1; |
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348 | k++; |
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349 | } |
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350 | } |
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351 | for (int j= 0; j < s; j++) |
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352 | result.append (elements[index[j] - 1]); |
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353 | return result; |
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354 | } |
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355 | else |
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356 | { |
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357 | index[s - 1] += 1; |
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358 | for (int j= 0; j < s; j++) |
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359 | result.append (elements[index[j] - 1]); |
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360 | return result; |
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361 | } |
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362 | } |
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363 | |
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364 | CFArray copy (const CFList& list) |
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365 | { |
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366 | CFArray array= CFArray (list.length()); |
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367 | int j= 0; |
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368 | for (CFListIterator i= list; i.hasItem(); i++, j++) |
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369 | array[j]= i.getItem(); |
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370 | return array; |
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371 | } |
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372 | |
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373 | void indexUpdate (int index [], const int& subsetSize, const int& setSize, |
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374 | bool& noSubset) |
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375 | { |
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376 | noSubset= false; |
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377 | if (subsetSize > setSize) |
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378 | { |
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379 | noSubset= true; |
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380 | return; |
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381 | } |
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382 | int * v= new int [setSize]; |
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383 | for (int i= 0; i < setSize; i++) |
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384 | v[i]= index[i]; |
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385 | if (subsetSize == 1) |
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386 | { |
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387 | v[0]= v[0] - 1; |
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388 | if (v[0] >= setSize) |
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389 | { |
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390 | noSubset= true; |
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391 | delete [] v; |
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392 | return; |
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393 | } |
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394 | } |
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395 | else |
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396 | { |
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397 | if (v[subsetSize - 1] - v[0] + 1 == subsetSize && v[0] > 1) |
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398 | { |
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399 | if (v[0] + subsetSize - 1 > setSize) |
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400 | { |
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401 | noSubset= true; |
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402 | delete [] v; |
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403 | return; |
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404 | } |
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405 | v[0]= v[0] - 1; |
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406 | for (int i= 1; i < subsetSize - 1; i++) |
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407 | v[i]= v[i - 1] + 1; |
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408 | v[subsetSize - 1]= v[subsetSize - 2]; |
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409 | } |
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410 | else |
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411 | { |
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412 | if (v[0] + subsetSize - 1 > setSize) |
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413 | { |
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414 | noSubset= true; |
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415 | delete [] v; |
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416 | return; |
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417 | } |
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418 | for (int i= 1; i < subsetSize - 1; i++) |
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419 | v[i]= v[i - 1] + 1; |
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420 | v[subsetSize - 1]= v[subsetSize - 2]; |
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421 | } |
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422 | } |
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423 | for (int i= 0; i < setSize; i++) |
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424 | index[i]= v[i]; |
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425 | delete [] v; |
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426 | } |
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427 | |
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428 | int subsetDegree (const CFList& S) |
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429 | { |
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430 | int result= 0; |
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431 | for (CFListIterator i= S; i.hasItem(); i++) |
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432 | result += degree (i.getItem(), Variable (1)); |
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433 | return result; |
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434 | } |
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435 | |
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436 | CFFList multiplicity (CanonicalForm& F, const CFList& factors) |
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437 | { |
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438 | if (F.inCoeffDomain()) |
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439 | return CFFList (CFFactor (F, 1)); |
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440 | CFFList result; |
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441 | int multi= 0; |
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442 | CanonicalForm quot; |
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443 | for (CFListIterator i= factors; i.hasItem(); i++) |
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444 | { |
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445 | while (fdivides (i.getItem(), F, quot)) |
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446 | { |
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447 | multi++; |
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448 | F= quot; |
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449 | } |
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450 | if (multi > 0) |
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451 | result.append (CFFactor (i.getItem(), multi)); |
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452 | multi= 0; |
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453 | } |
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454 | return result; |
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455 | } |
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456 | |
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457 | #ifdef HAVE_NTL |
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458 | CFArray |
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459 | logarithmicDerivative (const CanonicalForm& F, const CanonicalForm& G, int l, |
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460 | CanonicalForm& Q |
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461 | ) |
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462 | { |
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463 | Variable x= Variable (2); |
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464 | Variable y= Variable (1); |
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465 | CanonicalForm xToL= power (x, l); |
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466 | CanonicalForm q,r; |
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467 | CanonicalForm logDeriv; |
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468 | |
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469 | TIMING_START (fac_log_deriv_div); |
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470 | q= newtonDiv (F, G, xToL); |
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471 | TIMING_END_AND_PRINT (fac_log_deriv_div, "time for division in logderiv1: "); |
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472 | |
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473 | TIMING_START (fac_log_deriv_mul); |
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474 | logDeriv= mulMod2 (q, deriv (G, y), xToL); |
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475 | TIMING_END_AND_PRINT (fac_log_deriv_mul, "time to multiply in logderiv1: "); |
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476 | |
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477 | if (degree (logDeriv, x) == 0) |
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478 | { |
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479 | Q= q; |
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480 | return CFArray(); |
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481 | } |
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482 | |
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483 | int j= degree (logDeriv, y) + 1; |
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484 | CFArray result= CFArray (j); |
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485 | CFIterator ii; |
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486 | for (CFIterator i= logDeriv; i.hasTerms() && !logDeriv.isZero(); i++) |
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487 | { |
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488 | if (i.coeff().inCoeffDomain()) |
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489 | result[0] += i.coeff()*power (x,i.exp()); |
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490 | else |
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491 | { |
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492 | for (ii= i.coeff(); ii.hasTerms(); ii++) |
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493 | result[ii.exp()] += ii.coeff()*power (x,i.exp()); |
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494 | } |
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495 | } |
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496 | Q= q; |
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497 | return result; |
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498 | } |
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499 | |
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500 | CFArray |
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501 | logarithmicDerivative (const CanonicalForm& F, const CanonicalForm& G, int l, |
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502 | int oldL, const CanonicalForm& oldQ, CanonicalForm& Q |
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503 | ) |
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504 | { |
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505 | Variable x= Variable (2); |
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506 | Variable y= Variable (1); |
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507 | CanonicalForm xToL= power (x, l); |
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508 | CanonicalForm xToOldL= power (x, oldL); |
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509 | CanonicalForm xToLOldL= power (x, l-oldL); |
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510 | CanonicalForm q,r; |
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511 | CanonicalForm logDeriv; |
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512 | |
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513 | CanonicalForm bufF; |
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514 | TIMING_START (fac_log_deriv_pre); |
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515 | if ((oldL > 100 && l - oldL < 50) || (oldL < 100 && l - oldL < 30)) |
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516 | { |
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517 | bufF= F; |
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518 | CanonicalForm oldF= mulMod2 (G, oldQ, xToL); |
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519 | bufF -= oldF; |
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520 | bufF= div (bufF, xToOldL); |
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521 | } |
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522 | else |
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523 | { |
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524 | //middle product style computation of [G*oldQ]^{l}_{oldL} |
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525 | CanonicalForm G3= div (G, xToOldL); |
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526 | CanonicalForm Up= mulMod2 (G3, oldQ, xToLOldL); |
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527 | CanonicalForm xToOldL2= power (x, (oldL+1)/2); |
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528 | CanonicalForm G2= mod (G, xToOldL); |
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529 | CanonicalForm G1= div (G2, xToOldL2); |
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530 | CanonicalForm G0= mod (G2, xToOldL2); |
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531 | CanonicalForm oldQ1= div (oldQ, xToOldL2); |
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532 | CanonicalForm oldQ0= mod (oldQ, xToOldL2); |
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533 | CanonicalForm Mid; |
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534 | if (oldL % 2 == 1) |
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535 | Mid= mulMod2 (G1, oldQ1*x, xToLOldL); |
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536 | else |
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537 | Mid= mulMod2 (G1, oldQ1, xToLOldL); |
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538 | //computation of Low might be faster using a real middle product? |
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539 | CanonicalForm Low= mulMod2 (G0, oldQ1, xToOldL)+mulMod2 (G1, oldQ0, xToOldL); |
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540 | Low= div (Low, power (x, oldL/2)); |
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541 | Low= mod (Low, xToLOldL); |
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542 | Up += Mid + Low; |
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543 | bufF= div (F, xToOldL); |
---|
544 | bufF -= Up; |
---|
545 | } |
---|
546 | TIMING_END_AND_PRINT (fac_log_deriv_pre, "time to preprocess: "); |
---|
547 | |
---|
548 | TIMING_START (fac_log_deriv_div); |
---|
549 | if (l-oldL > 0) |
---|
550 | q= newtonDiv (bufF, G, xToLOldL); |
---|
551 | else |
---|
552 | q= 0; |
---|
553 | q *= xToOldL; |
---|
554 | q += oldQ; |
---|
555 | TIMING_END_AND_PRINT (fac_log_deriv_div, "time for div in logderiv2: "); |
---|
556 | |
---|
557 | TIMING_START (fac_log_deriv_mul); |
---|
558 | logDeriv= mulMod2 (q, deriv (G, y), xToL); |
---|
559 | TIMING_END_AND_PRINT (fac_log_deriv_mul, "time for mul in logderiv2: "); |
---|
560 | |
---|
561 | if (degree (logDeriv, x) == 0) |
---|
562 | { |
---|
563 | Q= q; |
---|
564 | return CFArray(); |
---|
565 | } |
---|
566 | |
---|
567 | int j= degree (logDeriv,y) + 1; |
---|
568 | CFArray result= CFArray (j); |
---|
569 | CFIterator ii; |
---|
570 | for (CFIterator i= logDeriv; i.hasTerms() && !logDeriv.isZero(); i++) |
---|
571 | { |
---|
572 | if (i.coeff().inCoeffDomain()) |
---|
573 | result[0] += i.coeff()*power (x,i.exp()); |
---|
574 | else |
---|
575 | { |
---|
576 | for (ii= i.coeff(); ii.hasTerms(); ii++) |
---|
577 | result[ii.exp()] += ii.coeff()*power (x,i.exp()); |
---|
578 | } |
---|
579 | } |
---|
580 | Q= q; |
---|
581 | return result; |
---|
582 | } |
---|
583 | #endif |
---|
584 | |
---|
585 | void |
---|
586 | writeInMatrix (CFMatrix& M, const CFArray& A, const int column, |
---|
587 | const int startIndex |
---|
588 | ) |
---|
589 | { |
---|
590 | ASSERT (A.size () - startIndex >= 0, "wrong starting index"); |
---|
591 | ASSERT (A.size () - startIndex <= M.rows(), "wrong starting index"); |
---|
592 | ASSERT (column > 0 && column <= M.columns(), "wrong column"); |
---|
593 | if (A.size() - startIndex <= 0) return; |
---|
594 | int j= 1; |
---|
595 | for (int i= startIndex; i < A.size(); i++, j++) |
---|
596 | M (j, column)= A [i]; |
---|
597 | } |
---|
598 | |
---|
599 | CFArray getCoeffs (const CanonicalForm& F, const int k) |
---|
600 | { |
---|
601 | ASSERT (F.isUnivariate() || F.inCoeffDomain(), "univariate input expected"); |
---|
602 | if (degree (F, 2) < k) |
---|
603 | return CFArray(); |
---|
604 | |
---|
605 | CFArray result= CFArray (degree (F) - k + 1); |
---|
606 | CFIterator j= F; |
---|
607 | for (int i= degree (F); i >= k; i--) |
---|
608 | { |
---|
609 | if (j.exp() == i) |
---|
610 | { |
---|
611 | result [i - k]= j.coeff(); |
---|
612 | j++; |
---|
613 | if (!j.hasTerms()) |
---|
614 | return result; |
---|
615 | } |
---|
616 | else |
---|
617 | result[i - k]= 0; |
---|
618 | } |
---|
619 | return result; |
---|
620 | } |
---|
621 | |
---|
622 | CFArray getCoeffs (const CanonicalForm& F, const int k, const Variable& alpha) |
---|
623 | { |
---|
624 | ASSERT (F.isUnivariate() || F.inCoeffDomain(), "univariate input expected"); |
---|
625 | if (degree (F, 2) < k) |
---|
626 | return CFArray (); |
---|
627 | |
---|
628 | int d= degree (getMipo (alpha)); |
---|
629 | CFArray result= CFArray ((degree (F) - k + 1)*d); |
---|
630 | CFIterator j= F; |
---|
631 | CanonicalForm buf; |
---|
632 | CFIterator iter; |
---|
633 | for (int i= degree (F); i >= k; i--) |
---|
634 | { |
---|
635 | if (j.exp() == i) |
---|
636 | { |
---|
637 | iter= j.coeff(); |
---|
638 | for (int l= degree (j.coeff(), alpha); l >= 0; l--) |
---|
639 | { |
---|
640 | if (iter.exp() == l) |
---|
641 | { |
---|
642 | result [(i - k)*d + l]= iter.coeff(); |
---|
643 | iter++; |
---|
644 | if (!iter.hasTerms()) |
---|
645 | break; |
---|
646 | } |
---|
647 | } |
---|
648 | j++; |
---|
649 | if (!j.hasTerms()) |
---|
650 | return result; |
---|
651 | } |
---|
652 | else |
---|
653 | { |
---|
654 | for (int l= 0; l < d; l++) |
---|
655 | result[(i - k)*d + l]= 0; |
---|
656 | } |
---|
657 | } |
---|
658 | return result; |
---|
659 | } |
---|
660 | |
---|
661 | #ifdef HAVE_NTL |
---|
662 | CFArray |
---|
663 | getCoeffs (const CanonicalForm& G, const int k, const int l, const int degMipo, |
---|
664 | const Variable& alpha, const CanonicalForm& evaluation, |
---|
665 | const mat_zz_p& M) |
---|
666 | { |
---|
667 | ASSERT (G.isUnivariate() || G.inCoeffDomain(), "univariate input expected"); |
---|
668 | CanonicalForm F= G (G.mvar() - evaluation, G.mvar()); |
---|
669 | if (F.isZero()) |
---|
670 | return CFArray (); |
---|
671 | |
---|
672 | Variable y= Variable (2); |
---|
673 | F= F (power (y, degMipo), y); |
---|
674 | F= F (y, alpha); |
---|
675 | zz_pX NTLF= convertFacCF2NTLzzpX (F); |
---|
676 | NTLF.rep.SetLength (l*degMipo); |
---|
677 | NTLF.rep= M*NTLF.rep; |
---|
678 | NTLF.normalize(); |
---|
679 | F= convertNTLzzpX2CF (NTLF, y); |
---|
680 | |
---|
681 | if (degree (F, 2) < k) |
---|
682 | return CFArray(); |
---|
683 | |
---|
684 | CFArray result= CFArray (degree (F) - k + 1); |
---|
685 | |
---|
686 | CFIterator j= F; |
---|
687 | for (int i= degree (F); i >= k; i--) |
---|
688 | { |
---|
689 | if (j.exp() == i) |
---|
690 | { |
---|
691 | result [i - k]= j.coeff(); |
---|
692 | j++; |
---|
693 | if (!j.hasTerms()) |
---|
694 | return result; |
---|
695 | } |
---|
696 | else |
---|
697 | result[i - k]= 0; |
---|
698 | } |
---|
699 | return result; |
---|
700 | } |
---|
701 | #endif |
---|
702 | |
---|
703 | #ifdef HAVE_FLINT |
---|
704 | CFArray |
---|
705 | getCoeffs (const CanonicalForm& G, const int k, const int l, const int degMipo, |
---|
706 | const Variable& alpha, const CanonicalForm& evaluation, |
---|
707 | const nmod_mat_t M) |
---|
708 | { |
---|
709 | ASSERT (G.isUnivariate() || G.inCoeffDomain(), "univariate input expected"); |
---|
710 | CanonicalForm F= G (G.mvar() - evaluation, G.mvar()); |
---|
711 | if (F.isZero()) |
---|
712 | return CFArray (); |
---|
713 | |
---|
714 | Variable y= Variable (2); |
---|
715 | F= F (power (y, degMipo), y); |
---|
716 | F= F (y, alpha); |
---|
717 | |
---|
718 | nmod_poly_t FLINTF; |
---|
719 | nmod_mat_t MFLINTF, mulResult; |
---|
720 | nmod_mat_init (MFLINTF, l*degMipo, 1, getCharacteristic()); |
---|
721 | nmod_mat_init (mulResult, l*degMipo, 1, getCharacteristic()); |
---|
722 | |
---|
723 | convertFacCF2nmod_poly_t (FLINTF, F); |
---|
724 | |
---|
725 | #ifndef slong |
---|
726 | #define slong long |
---|
727 | #endif |
---|
728 | slong i; |
---|
729 | |
---|
730 | for (i= 0; i < FLINTF->length; i++) |
---|
731 | nmod_mat_entry (MFLINTF, i, 0)= FLINTF->coeffs[i]; |
---|
732 | |
---|
733 | for (; i < MFLINTF->r; i++) |
---|
734 | nmod_mat_entry (MFLINTF, i, 0)= 0; |
---|
735 | |
---|
736 | nmod_mat_mul (mulResult, M, MFLINTF); |
---|
737 | |
---|
738 | F= 0; |
---|
739 | for (i= 0; i < mulResult->r; i++) |
---|
740 | F += CanonicalForm ((long) nmod_mat_entry (mulResult, i, 0))*power (y, i); |
---|
741 | |
---|
742 | nmod_mat_clear (MFLINTF); |
---|
743 | nmod_mat_clear (mulResult); |
---|
744 | nmod_poly_clear(FLINTF); |
---|
745 | |
---|
746 | if (degree (F, 2) < k) |
---|
747 | return CFArray(); |
---|
748 | |
---|
749 | CFArray result= CFArray (degree (F) - k + 1); |
---|
750 | |
---|
751 | CFIterator j= F; |
---|
752 | for (int i= degree (F); i >= k; i--) |
---|
753 | { |
---|
754 | if (j.exp() == i) |
---|
755 | { |
---|
756 | result [i - k]= j.coeff(); |
---|
757 | j++; |
---|
758 | if (!j.hasTerms()) |
---|
759 | return result; |
---|
760 | } |
---|
761 | else |
---|
762 | result[i - k]= 0; |
---|
763 | } |
---|
764 | return result; |
---|
765 | } |
---|
766 | #endif |
---|
767 | |
---|
768 | int * computeBounds (const CanonicalForm& F, int& n, bool& isIrreducible) |
---|
769 | { |
---|
770 | n= degree (F, 1); |
---|
771 | int* result= new int [n]; |
---|
772 | int sizeOfNewtonPolygon; |
---|
773 | int** newtonPolyg= newtonPolygon (F, sizeOfNewtonPolygon); |
---|
774 | |
---|
775 | isIrreducible= false; |
---|
776 | if (sizeOfNewtonPolygon == 3) |
---|
777 | { |
---|
778 | bool check1= |
---|
779 | (newtonPolyg[0][0]==0 || newtonPolyg[1][0]==0 || newtonPolyg[2][0]==0); |
---|
780 | if (check1) |
---|
781 | { |
---|
782 | bool check2= |
---|
783 | (newtonPolyg[0][1]==0 || newtonPolyg[1][1]==0 || newtonPolyg[2][0]==0); |
---|
784 | if (check2) |
---|
785 | { |
---|
786 | int p=getCharacteristic(); |
---|
787 | int d=1; |
---|
788 | char bufGFName='Z'; |
---|
789 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
790 | if (GF) |
---|
791 | { |
---|
792 | d= getGFDegree(); |
---|
793 | bufGFName=gf_name; |
---|
794 | } |
---|
795 | setCharacteristic(0); |
---|
796 | CanonicalForm tmp= gcd (newtonPolyg[0][0],newtonPolyg[0][1]); // maybe it's better to use plain intgcd |
---|
797 | tmp= gcd (tmp, newtonPolyg[1][0]); |
---|
798 | tmp= gcd (tmp, newtonPolyg[1][1]); |
---|
799 | tmp= gcd (tmp, newtonPolyg[2][0]); |
---|
800 | tmp= gcd (tmp, newtonPolyg[2][1]); |
---|
801 | isIrreducible= (tmp==1); |
---|
802 | if (GF) |
---|
803 | setCharacteristic (p, d, bufGFName); |
---|
804 | else |
---|
805 | setCharacteristic(p); |
---|
806 | } |
---|
807 | } |
---|
808 | } |
---|
809 | |
---|
810 | int minX, minY, maxX, maxY; |
---|
811 | minX= newtonPolyg [0] [0]; |
---|
812 | minY= newtonPolyg [0] [1]; |
---|
813 | maxX= minX; |
---|
814 | maxY= minY; |
---|
815 | int indZero= 0; |
---|
816 | for (int i= 1; i < sizeOfNewtonPolygon; i++) |
---|
817 | { |
---|
818 | if (newtonPolyg[i][1] == 0) |
---|
819 | { |
---|
820 | if (newtonPolyg[indZero][1] == 0) |
---|
821 | { |
---|
822 | if (newtonPolyg[indZero][0] < newtonPolyg[i][0]) |
---|
823 | indZero= i; |
---|
824 | } |
---|
825 | else |
---|
826 | indZero= i; |
---|
827 | } |
---|
828 | if (minX > newtonPolyg [i] [0]) |
---|
829 | minX= newtonPolyg [i] [0]; |
---|
830 | if (maxX < newtonPolyg [i] [0]) |
---|
831 | maxX= newtonPolyg [i] [0]; |
---|
832 | if (minY > newtonPolyg [i] [1]) |
---|
833 | minY= newtonPolyg [i] [1]; |
---|
834 | if (maxY < newtonPolyg [i] [1]) |
---|
835 | maxY= newtonPolyg [i] [1]; |
---|
836 | } |
---|
837 | |
---|
838 | int slopeNum, slopeDen, constTerm; |
---|
839 | bool negativeSlope=false; |
---|
840 | if (indZero != sizeOfNewtonPolygon - 1) |
---|
841 | { |
---|
842 | slopeNum= newtonPolyg[indZero+1][0]-newtonPolyg[indZero][0]; |
---|
843 | slopeDen= newtonPolyg[indZero+1][1]; |
---|
844 | constTerm= newtonPolyg[indZero][0]; |
---|
845 | } |
---|
846 | else |
---|
847 | { |
---|
848 | slopeNum= newtonPolyg[0][0]-newtonPolyg[indZero][0]; |
---|
849 | slopeDen= newtonPolyg[0][1]; |
---|
850 | constTerm= newtonPolyg[indZero][0]; |
---|
851 | } |
---|
852 | if (slopeNum < 0) |
---|
853 | { |
---|
854 | slopeNum= -slopeNum; |
---|
855 | negativeSlope= true; |
---|
856 | } |
---|
857 | int k= 0; |
---|
858 | int* point= new int [2]; |
---|
859 | for (int i= 0; i < n; i++) |
---|
860 | { |
---|
861 | if (((indZero+1) < sizeOfNewtonPolygon && (i+1) > newtonPolyg[indZero+1][1]) |
---|
862 | || ((indZero+1) >= sizeOfNewtonPolygon && (i+1) > newtonPolyg[0][1])) |
---|
863 | { |
---|
864 | if (indZero + 1 != sizeOfNewtonPolygon) |
---|
865 | indZero++; |
---|
866 | else |
---|
867 | indZero= 0; |
---|
868 | if (indZero != sizeOfNewtonPolygon - 1) |
---|
869 | { |
---|
870 | slopeNum= newtonPolyg[indZero+1][0]-newtonPolyg[indZero][0]; |
---|
871 | slopeDen= newtonPolyg[indZero+1][1]-newtonPolyg[indZero][1]; |
---|
872 | constTerm= newtonPolyg[indZero][0]; |
---|
873 | } |
---|
874 | else |
---|
875 | { |
---|
876 | slopeNum= newtonPolyg[0][0]-newtonPolyg[indZero][0]; |
---|
877 | slopeDen= newtonPolyg[0][1]-newtonPolyg[indZero][1]; |
---|
878 | constTerm= newtonPolyg[indZero][0]; |
---|
879 | } |
---|
880 | if (slopeNum < 0) |
---|
881 | { |
---|
882 | negativeSlope= true; |
---|
883 | slopeNum= - slopeNum; |
---|
884 | k= (int) -(((long) slopeNum*((i+1)-newtonPolyg[indZero][1])+slopeDen-1)/ |
---|
885 | slopeDen) + constTerm; |
---|
886 | } |
---|
887 | else |
---|
888 | k= (int) (((long) slopeNum*((i+1)-newtonPolyg[indZero][1])) / slopeDen) |
---|
889 | + constTerm; |
---|
890 | } |
---|
891 | else |
---|
892 | { |
---|
893 | if (negativeSlope) |
---|
894 | k= (int) -(((long) slopeNum*((i+1)-newtonPolyg[indZero][1])+slopeDen-1)/ |
---|
895 | slopeDen) + constTerm; |
---|
896 | else |
---|
897 | k= (int) ((long) slopeNum*((i+1)-newtonPolyg[indZero][1])) / slopeDen |
---|
898 | + constTerm; |
---|
899 | } |
---|
900 | if (i + 1 > maxY || i + 1 < minY) |
---|
901 | { |
---|
902 | result [i]= 0; |
---|
903 | continue; |
---|
904 | } |
---|
905 | point [0]= k; |
---|
906 | point [1]= i + 1; |
---|
907 | if (!isInPolygon (newtonPolyg, sizeOfNewtonPolygon, point) && k > 0) |
---|
908 | k= 0; |
---|
909 | result [i]= k; |
---|
910 | } |
---|
911 | |
---|
912 | delete [] point; |
---|
913 | |
---|
914 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
915 | delete [] newtonPolyg[i]; |
---|
916 | delete [] newtonPolyg; |
---|
917 | |
---|
918 | return result; |
---|
919 | } |
---|
920 | |
---|
921 | int * |
---|
922 | computeBoundsWrtDiffMainvar (const CanonicalForm& F, int& n, |
---|
923 | bool& isIrreducible) |
---|
924 | { |
---|
925 | n= degree (F, 2); |
---|
926 | int* result= new int [n]; |
---|
927 | int sizeOfNewtonPolygon; |
---|
928 | int** newtonPolyg= newtonPolygon (F, sizeOfNewtonPolygon); |
---|
929 | |
---|
930 | isIrreducible= false; |
---|
931 | if (sizeOfNewtonPolygon == 3) |
---|
932 | { |
---|
933 | bool check1= |
---|
934 | (newtonPolyg[0][0]==0 || newtonPolyg[1][0]==0 || newtonPolyg[2][0]==0); |
---|
935 | if (check1) |
---|
936 | { |
---|
937 | bool check2= |
---|
938 | (newtonPolyg[0][1]==0 || newtonPolyg[1][1]==0 || newtonPolyg[2][0]==0); |
---|
939 | if (check2) |
---|
940 | { |
---|
941 | int p=getCharacteristic(); |
---|
942 | int d=1; |
---|
943 | char bufGFName='Z'; |
---|
944 | bool GF= (CFFactory::gettype()==GaloisFieldDomain); |
---|
945 | if (GF) |
---|
946 | { |
---|
947 | d= getGFDegree(); |
---|
948 | bufGFName=gf_name; |
---|
949 | } |
---|
950 | setCharacteristic(0); |
---|
951 | CanonicalForm tmp= gcd (newtonPolyg[0][0],newtonPolyg[0][1]); |
---|
952 | tmp= gcd (tmp, newtonPolyg[1][0]); |
---|
953 | tmp= gcd (tmp, newtonPolyg[1][1]); |
---|
954 | tmp= gcd (tmp, newtonPolyg[2][0]); |
---|
955 | tmp= gcd (tmp, newtonPolyg[2][1]); |
---|
956 | isIrreducible= (tmp==1); |
---|
957 | if (GF) |
---|
958 | setCharacteristic (p, d, bufGFName); |
---|
959 | else |
---|
960 | setCharacteristic(p); |
---|
961 | } |
---|
962 | } |
---|
963 | } |
---|
964 | |
---|
965 | int swap; |
---|
966 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
967 | { |
---|
968 | swap= newtonPolyg[i][1]; |
---|
969 | newtonPolyg[i][1]=newtonPolyg[i][0]; |
---|
970 | newtonPolyg[i][0]= swap; |
---|
971 | } |
---|
972 | |
---|
973 | sizeOfNewtonPolygon= polygon(newtonPolyg, sizeOfNewtonPolygon); |
---|
974 | |
---|
975 | int minX, minY, maxX, maxY; |
---|
976 | minX= newtonPolyg [0] [0]; |
---|
977 | minY= newtonPolyg [0] [1]; |
---|
978 | maxX= minX; |
---|
979 | maxY= minY; |
---|
980 | int indZero= 0; |
---|
981 | for (int i= 1; i < sizeOfNewtonPolygon; i++) |
---|
982 | { |
---|
983 | if (newtonPolyg[i][1] == 0) |
---|
984 | { |
---|
985 | if (newtonPolyg[indZero][1] == 0) |
---|
986 | { |
---|
987 | if (newtonPolyg[indZero][0] < newtonPolyg[i][0]) |
---|
988 | indZero= i; |
---|
989 | } |
---|
990 | else |
---|
991 | indZero= i; |
---|
992 | } |
---|
993 | if (minX > newtonPolyg [i] [0]) |
---|
994 | minX= newtonPolyg [i] [0]; |
---|
995 | if (maxX < newtonPolyg [i] [0]) |
---|
996 | maxX= newtonPolyg [i] [0]; |
---|
997 | if (minY > newtonPolyg [i] [1]) |
---|
998 | minY= newtonPolyg [i] [1]; |
---|
999 | if (maxY < newtonPolyg [i] [1]) |
---|
1000 | maxY= newtonPolyg [i] [1]; |
---|
1001 | } |
---|
1002 | |
---|
1003 | int slopeNum, slopeDen, constTerm; |
---|
1004 | bool negativeSlope=false; |
---|
1005 | if (indZero != sizeOfNewtonPolygon - 1) |
---|
1006 | { |
---|
1007 | slopeNum= newtonPolyg[indZero+1][0]-newtonPolyg[indZero][0]; |
---|
1008 | slopeDen= newtonPolyg[indZero+1][1]; |
---|
1009 | constTerm= newtonPolyg[indZero][0]; |
---|
1010 | } |
---|
1011 | else |
---|
1012 | { |
---|
1013 | slopeNum= newtonPolyg[0][0]-newtonPolyg[indZero][0]; |
---|
1014 | slopeDen= newtonPolyg[0][1]; |
---|
1015 | constTerm= newtonPolyg[indZero][0]; |
---|
1016 | } |
---|
1017 | if (slopeNum < 0) |
---|
1018 | { |
---|
1019 | slopeNum= -slopeNum; |
---|
1020 | negativeSlope= true; |
---|
1021 | } |
---|
1022 | int k= 0; |
---|
1023 | |
---|
1024 | int* point= new int [2]; |
---|
1025 | for (int i= 0; i < n; i++) |
---|
1026 | { |
---|
1027 | if (((indZero+1) < sizeOfNewtonPolygon && (i+1) > newtonPolyg[indZero+1][1]) |
---|
1028 | || ((indZero+1) >= sizeOfNewtonPolygon && (i+1) > newtonPolyg[0][1])) |
---|
1029 | { |
---|
1030 | if (indZero + 1 != sizeOfNewtonPolygon) |
---|
1031 | indZero++; |
---|
1032 | else |
---|
1033 | indZero= 0; |
---|
1034 | if (indZero != sizeOfNewtonPolygon - 1) |
---|
1035 | { |
---|
1036 | slopeNum= newtonPolyg[indZero+1][0]-newtonPolyg[indZero][0]; |
---|
1037 | slopeDen= newtonPolyg[indZero+1][1]-newtonPolyg[indZero][1]; |
---|
1038 | constTerm= newtonPolyg[indZero][0]; |
---|
1039 | } |
---|
1040 | else |
---|
1041 | { |
---|
1042 | slopeNum= newtonPolyg[0][0]-newtonPolyg[indZero][0]; |
---|
1043 | slopeDen= newtonPolyg[0][1]-newtonPolyg[indZero][1]; |
---|
1044 | constTerm= newtonPolyg[indZero][0]; |
---|
1045 | } |
---|
1046 | if (slopeNum < 0) |
---|
1047 | { |
---|
1048 | negativeSlope= true; |
---|
1049 | slopeNum= - slopeNum; |
---|
1050 | k= (int) -(((long) slopeNum*((i+1)-newtonPolyg[indZero][1])+slopeDen-1)/ |
---|
1051 | slopeDen) + constTerm; |
---|
1052 | } |
---|
1053 | else |
---|
1054 | k= (int) (((long) slopeNum*((i+1)-newtonPolyg[indZero][1])) / slopeDen) |
---|
1055 | + constTerm; |
---|
1056 | } |
---|
1057 | else |
---|
1058 | { |
---|
1059 | if (negativeSlope) |
---|
1060 | k= (int) -(((long) slopeNum*((i+1)-newtonPolyg[indZero][1])+slopeDen-1)/ |
---|
1061 | slopeDen) + constTerm; |
---|
1062 | else |
---|
1063 | k= (int) ((long) slopeNum*((i+1)-newtonPolyg[indZero][1])) / slopeDen |
---|
1064 | + constTerm; |
---|
1065 | } |
---|
1066 | if (i + 1 > maxY || i + 1 < minY) |
---|
1067 | { |
---|
1068 | result [i]= 0; |
---|
1069 | continue; |
---|
1070 | } |
---|
1071 | |
---|
1072 | point [0]= k; |
---|
1073 | point [1]= i + 1; |
---|
1074 | if (!isInPolygon (newtonPolyg, sizeOfNewtonPolygon, point) && k > 0) |
---|
1075 | k= 0; |
---|
1076 | result [i]= k; |
---|
1077 | } |
---|
1078 | |
---|
1079 | delete [] point; |
---|
1080 | |
---|
1081 | for (int i= 0; i < sizeOfNewtonPolygon; i++) |
---|
1082 | delete [] newtonPolyg[i]; |
---|
1083 | delete [] newtonPolyg; |
---|
1084 | |
---|
1085 | return result; |
---|
1086 | } |
---|
1087 | |
---|
1088 | int |
---|
1089 | substituteCheck (const CanonicalForm& F, const Variable& x) |
---|
1090 | { |
---|
1091 | if (F.inCoeffDomain()) |
---|
1092 | return 0; |
---|
1093 | if (degree (F, x) < 0) |
---|
1094 | return 0; |
---|
1095 | CanonicalForm f= swapvar (F, F.mvar(), x); |
---|
1096 | int sizef= 0; |
---|
1097 | for (CFIterator i= f; i.hasTerms(); i++, sizef++) |
---|
1098 | { |
---|
1099 | if (i.exp() == 1) |
---|
1100 | return 0; |
---|
1101 | } |
---|
1102 | int * expf= new int [sizef]; |
---|
1103 | int j= 0; |
---|
1104 | for (CFIterator i= f; i.hasTerms(); i++, j++) |
---|
1105 | expf [j]= i.exp(); |
---|
1106 | |
---|
1107 | int indf= sizef - 1; |
---|
1108 | if (expf[indf] == 0) |
---|
1109 | indf--; |
---|
1110 | |
---|
1111 | int result= expf[indf]; |
---|
1112 | for (int i= indf - 1; i >= 0; i--) |
---|
1113 | { |
---|
1114 | if (expf [i]%result != 0) |
---|
1115 | { |
---|
1116 | delete [] expf; |
---|
1117 | return 0; |
---|
1118 | } |
---|
1119 | } |
---|
1120 | |
---|
1121 | delete [] expf; |
---|
1122 | return result; |
---|
1123 | } |
---|
1124 | |
---|
1125 | static int |
---|
1126 | substituteCheck (const CanonicalForm& F, const CanonicalForm& G) |
---|
1127 | { |
---|
1128 | if (F.inCoeffDomain() || G.inCoeffDomain()) |
---|
1129 | return 0; |
---|
1130 | Variable x= Variable (1); |
---|
1131 | if (degree (F, x) <= 1 || degree (G, x) <= 1) |
---|
1132 | return 0; |
---|
1133 | CanonicalForm f= swapvar (F, F.mvar(), x); |
---|
1134 | CanonicalForm g= swapvar (G, G.mvar(), x); |
---|
1135 | int sizef= 0; |
---|
1136 | int sizeg= 0; |
---|
1137 | for (CFIterator i= f; i.hasTerms(); i++, sizef++) |
---|
1138 | { |
---|
1139 | if (i.exp() == 1) |
---|
1140 | return 0; |
---|
1141 | } |
---|
1142 | for (CFIterator i= g; i.hasTerms(); i++, sizeg++) |
---|
1143 | { |
---|
1144 | if (i.exp() == 1) |
---|
1145 | return 0; |
---|
1146 | } |
---|
1147 | int * expf= new int [sizef]; |
---|
1148 | int * expg= new int [sizeg]; |
---|
1149 | int j= 0; |
---|
1150 | for (CFIterator i= f; i.hasTerms(); i++, j++) |
---|
1151 | { |
---|
1152 | expf [j]= i.exp(); |
---|
1153 | } |
---|
1154 | j= 0; |
---|
1155 | for (CFIterator i= g; i.hasTerms(); i++, j++) |
---|
1156 | { |
---|
1157 | expg [j]= i.exp(); |
---|
1158 | } |
---|
1159 | |
---|
1160 | int indf= sizef - 1; |
---|
1161 | int indg= sizeg - 1; |
---|
1162 | if (expf[indf] == 0) |
---|
1163 | indf--; |
---|
1164 | if (expg[indg] == 0) |
---|
1165 | indg--; |
---|
1166 | |
---|
1167 | if ((expg[indg]%expf [indf] != 0 && expf[indf]%expg[indg] != 0) || |
---|
1168 | (expg[indg] == 1 && expf[indf] == 1)) |
---|
1169 | { |
---|
1170 | delete [] expg; |
---|
1171 | delete [] expf; |
---|
1172 | return 0; |
---|
1173 | } |
---|
1174 | |
---|
1175 | int result; |
---|
1176 | if (expg [indg]%expf [indf] == 0) |
---|
1177 | result= expf[indf]; |
---|
1178 | else |
---|
1179 | result= expg[indg]; |
---|
1180 | for (int i= indf - 1; i >= 0; i--) |
---|
1181 | { |
---|
1182 | if (expf [i]%result != 0) |
---|
1183 | { |
---|
1184 | delete [] expf; |
---|
1185 | delete [] expg; |
---|
1186 | return 0; |
---|
1187 | } |
---|
1188 | } |
---|
1189 | |
---|
1190 | for (int i= indg - 1; i >= 0; i--) |
---|
1191 | { |
---|
1192 | if (expg [i]%result != 0) |
---|
1193 | { |
---|
1194 | delete [] expf; |
---|
1195 | delete [] expg; |
---|
1196 | return 0; |
---|
1197 | } |
---|
1198 | } |
---|
1199 | |
---|
1200 | delete [] expg; |
---|
1201 | delete [] expf; |
---|
1202 | return result; |
---|
1203 | } |
---|
1204 | |
---|
1205 | int recSubstituteCheck (const CanonicalForm& F, const int d) |
---|
1206 | { |
---|
1207 | if (F.inCoeffDomain()) |
---|
1208 | return 0; |
---|
1209 | Variable x= Variable (1); |
---|
1210 | if (degree (F, x) <= 1) |
---|
1211 | return 0; |
---|
1212 | CanonicalForm f= swapvar (F, F.mvar(), x); |
---|
1213 | int sizef= 0; |
---|
1214 | for (CFIterator i= f; i.hasTerms(); i++, sizef++) |
---|
1215 | { |
---|
1216 | if (i.exp() == 1) |
---|
1217 | return 0; |
---|
1218 | } |
---|
1219 | int * expf= new int [sizef]; |
---|
1220 | int j= 0; |
---|
1221 | for (CFIterator i= f; i.hasTerms(); i++, j++) |
---|
1222 | { |
---|
1223 | expf [j]= i.exp(); |
---|
1224 | } |
---|
1225 | |
---|
1226 | int indf= sizef - 1; |
---|
1227 | if (expf[indf] == 0) |
---|
1228 | indf--; |
---|
1229 | |
---|
1230 | if ((d%expf [indf] != 0 && expf[indf]%d != 0) || (expf[indf] == 1)) |
---|
1231 | { |
---|
1232 | delete [] expf; |
---|
1233 | return 0; |
---|
1234 | } |
---|
1235 | |
---|
1236 | int result; |
---|
1237 | if (d%expf [indf] == 0) |
---|
1238 | result= expf[indf]; |
---|
1239 | else |
---|
1240 | result= d; |
---|
1241 | for (int i= indf - 1; i >= 0; i--) |
---|
1242 | { |
---|
1243 | if (expf [i]%result != 0) |
---|
1244 | { |
---|
1245 | delete [] expf; |
---|
1246 | return 0; |
---|
1247 | } |
---|
1248 | } |
---|
1249 | |
---|
1250 | delete [] expf; |
---|
1251 | return result; |
---|
1252 | } |
---|
1253 | |
---|
1254 | int substituteCheck (const CFList& L) |
---|
1255 | { |
---|
1256 | ASSERT (L.length() > 1, "expected a list of at least two elements"); |
---|
1257 | if (L.length() < 2) |
---|
1258 | return 0; |
---|
1259 | CFListIterator i= L; |
---|
1260 | i++; |
---|
1261 | int result= substituteCheck (L.getFirst(), i.getItem()); |
---|
1262 | if (result <= 1) |
---|
1263 | return result; |
---|
1264 | i++; |
---|
1265 | for (;i.hasItem(); i++) |
---|
1266 | { |
---|
1267 | result= recSubstituteCheck (i.getItem(), result); |
---|
1268 | if (result <= 1) |
---|
1269 | return result; |
---|
1270 | } |
---|
1271 | return result; |
---|
1272 | } |
---|
1273 | |
---|
1274 | void |
---|
1275 | subst (const CanonicalForm& F, CanonicalForm& A, const int d, const Variable& x) |
---|
1276 | { |
---|
1277 | if (d <= 1) |
---|
1278 | { |
---|
1279 | A= F; |
---|
1280 | return; |
---|
1281 | } |
---|
1282 | if (degree (F, x) <= 0) |
---|
1283 | { |
---|
1284 | A= F; |
---|
1285 | return; |
---|
1286 | } |
---|
1287 | CanonicalForm C= 0; |
---|
1288 | CanonicalForm f= swapvar (F, x, F.mvar()); |
---|
1289 | for (CFIterator i= f; i.hasTerms(); i++) |
---|
1290 | C += i.coeff()*power (f.mvar(), i.exp()/ d); |
---|
1291 | A= swapvar (C, x, F.mvar()); |
---|
1292 | } |
---|
1293 | |
---|
1294 | CanonicalForm |
---|
1295 | reverseSubst (const CanonicalForm& F, const int d, const Variable& x) |
---|
1296 | { |
---|
1297 | if (d <= 1) |
---|
1298 | return F; |
---|
1299 | if (degree (F, x) <= 0) |
---|
1300 | return F; |
---|
1301 | CanonicalForm f= swapvar (F, x, F.mvar()); |
---|
1302 | CanonicalForm result= 0; |
---|
1303 | for (CFIterator i= f; i.hasTerms(); i++) |
---|
1304 | result += i.coeff()*power (f.mvar(), d*i.exp()); |
---|
1305 | return swapvar (result, x, F.mvar()); |
---|
1306 | } |
---|
1307 | |
---|
1308 | void |
---|
1309 | reverseSubst (CFList& L, const int d, const Variable& x) |
---|
1310 | { |
---|
1311 | for (CFListIterator i= L; i.hasItem(); i++) |
---|
1312 | i.getItem()= reverseSubst (i.getItem(), d, x); |
---|
1313 | } |
---|
1314 | |
---|