1 | /*****************************************************************************\ |
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2 | * Computer Algebra System SINGULAR |
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3 | \*****************************************************************************/ |
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4 | /** @file facFqBivarUtil.h |
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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 | * @internal @version \$Id$ |
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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 | #ifndef FAC_FQ_BIVAR_UTIL_H |
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16 | #define FAC_FQ_BIVAR_UTIL_H |
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17 | |
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18 | // #include "config.h" |
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19 | |
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20 | #include "cf_map.h" |
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21 | #include "ExtensionInfo.h" |
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22 | |
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23 | #ifdef HAVE_NTL |
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24 | #include "NTLconvert.h" |
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25 | #endif |
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26 | |
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27 | /// append @a factors2 on @a factors1 |
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28 | void append (CFList& factors1, ///< [in,out] a list of polys |
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29 | const CFList& factors2 ///< [in] a list of polys |
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30 | ); |
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31 | |
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32 | /// decompress a list of polys @a factors using the map @a N |
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33 | void decompress (CFList& factors, ///< [in,out] a list of polys |
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34 | const CFMap& N ///< [in] a map |
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35 | ); |
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36 | |
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37 | /// as above |
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38 | void decompress (CFFList& factors, ///< [in,out] a list of factors |
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39 | const CFMap& N ///< [in] a map |
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40 | ); |
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41 | |
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42 | /// first swap Variables in @a factors1 if necessary, then append @a factors2 |
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43 | /// and @a factors3 on @a factors1 and finally decompress @a factors1 |
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44 | void appendSwapDecompress (CFList& factors1, ///< [in,out] a list of polys |
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45 | const CFList& factors2, ///< [in] a list of polys |
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46 | const CFList& factors3, ///< [in] a list of polys |
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47 | const bool swap1, ///< [in] indicates the need |
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48 | ///< to swap |
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49 | const bool swap2, ///< [in] indicates the need |
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50 | ///< to swap |
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51 | const CFMap& N ///< [in] a map |
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52 | ); |
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53 | |
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54 | /// swap Variables in @a factors, then decompress @a factors |
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55 | void swapDecompress (CFList& factors, ///< [in,out] a list of polys |
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56 | const bool swap, ///< [in] indicates the need to swap |
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57 | const CFMap& N ///< [in] a map |
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58 | ); |
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59 | |
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60 | /// tests if F is not contained in a subfield defined by @a gamma (Fq case) or |
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61 | /// @a k (GF case) |
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62 | /// |
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63 | /// @return @a isInExtension returns true if @a F is not contained in a subfield |
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64 | /// defined by @a gamma (Fq case) or @a k (GF case), false else |
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65 | /// @sa appendTestMapDown() |
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66 | bool isInExtension (const CanonicalForm& F, ///< [in] a poly over |
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67 | ///< F_p (alpha)=Fq or GF(p^l) |
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68 | const CanonicalForm& gamma, ///< [in] a primitive element |
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69 | ///< defining a subfield of |
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70 | ///< Fq if we are not over some |
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71 | ///< GF |
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72 | const int k, ///< some int k such that k |
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73 | ///< divides l if we are not |
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74 | ///< over some Fq |
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75 | const CanonicalForm& delta, ///< [in] image of gamma |
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76 | CFList& source, ///< [in,out] list of preimages |
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77 | CFList& dest ///< [in,out] list of images |
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78 | ); |
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79 | |
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80 | /// map a poly into a subfield of the current field, no testing is performed! |
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81 | /// |
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82 | /// @return @a mapDown returns @a F mapped into a subfield of the current field |
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83 | /// @sa appendTestMapDown(), appendMapDown() |
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84 | CanonicalForm |
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85 | mapDown (const CanonicalForm& F, ///< [in] a poly |
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86 | const ExtensionInfo& info, ///< [in] information about the sub- and |
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87 | ///< current field |
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88 | CFList& source, ///< [in,out] in case we are over some |
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89 | ///< F_p (alpha) and want to map down into |
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90 | ///< F_p (beta) source contains powers of |
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91 | ///< the primitive element of F_p (alpha) |
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92 | CFList& dest ///< [in,out] as source but contains |
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93 | ///< the corresponding powers of the |
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94 | ///< primitive element of F_p (beta) |
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95 | ); |
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96 | |
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97 | /// test if @a g is in a subfield of the current field, if so map it down and |
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98 | /// append it to @a factors |
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99 | /// |
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100 | /// @sa mapDown(), isInExtension() |
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101 | void appendTestMapDown (CFList& factors, ///< [in,out] a list of polys |
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102 | const CanonicalForm& f, ///< [in] a poly |
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103 | const ExtensionInfo& info,///< [in] information about |
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104 | ///< extension |
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105 | CFList& source, ///< [in,out] @sa mapDown() |
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106 | CFList& dest ///< [in,out] @sa mapDown() |
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107 | ); |
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108 | |
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109 | /// map @a g down into a subfield of the current field and append it to @a |
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110 | /// factors |
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111 | /// |
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112 | /// @sa mapDown(), appendTestMapDown() |
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113 | void |
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114 | appendMapDown (CFList& factors, ///< [in,out] a list of polys |
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115 | const CanonicalForm& g, ///< [in] a poly |
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116 | const ExtensionInfo& info,///< [in] information about extension |
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117 | CFList& source, ///< [in,out] @sa mapDown() |
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118 | CFList& dest ///< [in,out] @sa mapDown() |
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119 | ); |
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120 | |
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121 | /// normalize factors, i.e. make factors monic |
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122 | void normalize (CFList& factors ///< [in,out] a list of polys |
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123 | ); |
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124 | |
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125 | /// as above |
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126 | void normalize (CFFList& factors ///< [in,out] a list of factors |
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127 | ); |
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128 | |
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129 | /// extract a subset given by @a index of size @a s from @a elements, if there |
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130 | /// is no subset we have not yet considered noSubset is set to true. @a index |
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131 | /// encodes the next subset, e.g. if s= 3, elements= {a,b,c,d}, |
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132 | /// index= {1, 2, 4, 0}, then subset= {a,c,d}. @a index is of size |
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133 | /// @a elements.size(). |
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134 | /// |
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135 | /// @return @a subset returns a list of polys of length @a s if there is a |
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136 | /// subset we have not yet considered. |
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137 | CFList subset (int index [], ///< [in,out] an array encoding the next |
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138 | ///< subset |
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139 | const int& s, ///< [in] size of the subset |
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140 | const CFArray& elements, ///< [in] an array of polys |
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141 | bool& noSubset ///< [in,out] if there is no subset we |
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142 | ///< have not yet considered @a noSubset |
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143 | ///< is true |
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144 | ); |
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145 | |
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146 | /// write elements of @a list into an array |
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147 | /// |
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148 | /// @return an array of polys |
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149 | CFArray copy (const CFList& list ///< [in] a list of polys |
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150 | ); |
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151 | |
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152 | /// update @a index |
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153 | void indexUpdate (int index [], ///< [in,out] an array encoding a |
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154 | ///< subset of size subsetSize |
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155 | const int& subsetSize, ///< [in] size of the subset |
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156 | const int& setSize, ///< [in] size of the given set |
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157 | bool& noSubset ///< [in,out] if there is no subset we |
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158 | ///< have not yet considered @a |
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159 | ///< noSubset is true |
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160 | ); |
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161 | |
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162 | /// compute the sum of degrees in Variable(1) of elements in S |
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163 | /// |
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164 | /// @return @a subsetDegree returns the sum of degrees in Variable(1) of |
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165 | /// elements in S |
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166 | int subsetDegree (const CFList& S ///< [in] a list of polys |
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167 | ); |
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168 | |
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169 | /// determine multiplicity of the factors |
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170 | /// |
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171 | /// @return a list of factors of F with their multiplicity |
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172 | CFFList multiplicity (CanonicalForm& F, ///< [in] a poly |
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173 | const CFList& factors ///< [in] a list of factors of F |
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174 | ); |
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175 | |
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176 | /// compute the coefficients of the logarithmic derivative of G mod |
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177 | /// Variable (2)^l over Fq |
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178 | /// |
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179 | /// @return an array of coefficients of the logarithmic derivative of G mod |
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180 | /// Variable (2)^l |
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181 | CFArray logarithmicDerivative (const CanonicalForm& F,///<[in] a bivariate poly |
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182 | const CanonicalForm& G, ///<[in] a factor of F |
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183 | int l, ///<[in] lifting precision |
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184 | CanonicalForm& Q ///<[in,out] F/G |
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185 | ); |
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186 | |
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187 | /// compute the coefficients of the logarithmic derivative of G mod |
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188 | /// Variable (2)^l over Fq with oldQ= F/G mod Variable (2)^oldL |
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189 | /// |
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190 | /// @return an array of coefficients of the logarithmic derivative of G mod |
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191 | /// Variable (2)^l |
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192 | CFArray |
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193 | logarithmicDerivative (const CanonicalForm& F, ///< [in] bivariate poly |
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194 | const CanonicalForm& G, ///< [in] a factor of F |
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195 | int l, ///< [in] lifting precision |
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196 | int oldL, ///< [in] old precision |
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197 | const CanonicalForm& oldQ,///< [in] F/G mod |
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198 | ///< Variable(2)^oldL |
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199 | CanonicalForm& Q ///< [in, out] F/G |
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200 | ); |
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201 | |
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202 | /// compute bounds for logarithmic derivative as described in K. Belabas, |
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203 | /// M. van Hoeij, J. KlÃŒners, and A. Steel, Factoring polynomials over global |
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204 | /// fields |
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205 | /// |
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206 | /// @return @a computeBounds returns bounds as described above |
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207 | int * |
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208 | computeBounds (const CanonicalForm& F,///< [in] compressed bivariate polynomial |
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209 | int& n ///< [in,out] length of output |
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210 | ); |
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211 | |
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212 | /// extract coefficients of \f$ x^i \f$ for \f$i\geq k\f$ where \f$ x \f$ is |
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213 | /// a variable of level 1 |
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214 | /// |
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215 | /// @return coefficients of \f$ x^i \f$ for \f$i\geq k\f$ |
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216 | /// @sa {getCoeffs (const CanonicalForm&, const int, const Variable&), |
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217 | /// getCoeffs (const CanonicalForm&, const int, const int, const int, |
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218 | /// const Variable&, const CanonicalForm&, const mat_zz_p&)} |
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219 | CFArray |
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220 | getCoeffs (const CanonicalForm& F,///< [in] compressed bivariate poly over F_p |
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221 | const int k ///< [in] some int |
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222 | ); |
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223 | |
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224 | /// extract coefficients of \f$ x^i \f$ for \f$i\geq k\f$ where \f$ x \f$ is |
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225 | /// a variable of level 1 |
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226 | /// |
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227 | /// @return coefficients of \f$ x^i \f$ for \f$i\geq k\f$ |
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228 | /// @sa {getCoeffs (const CanonicalForm&, const int), |
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229 | /// getCoeffs (const CanonicalForm&, const int, const int, const int, |
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230 | /// const Variable&, const CanonicalForm&, const mat_zz_p&)} |
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231 | CFArray |
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232 | getCoeffs (const CanonicalForm& F,///< [in] compressed bivariate poly over |
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233 | ///< F_p(alpha) |
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234 | const int k, ///< [in] some int |
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235 | const Variable& alpha ///< [in] algebraic variable |
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236 | ); |
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237 | |
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238 | #ifdef HAVE_NTL |
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239 | /// extract coefficients of \f$ x^i \f$ for \f$i\geq k\f$ where \f$ x \f$ is |
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240 | /// a variable of level 1 |
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241 | /// |
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242 | /// @return coefficients of \f$ x^i \f$ for \f$i\geq k\f$ |
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243 | /// @sa {getCoeffs (const CanonicalForm&, const int, const Variable& alpha), |
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244 | /// getCoeffs (const CanonicalForm&, const int)} |
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245 | CFArray |
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246 | getCoeffs (const CanonicalForm& F, ///< [in] compressed bivariate poly |
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247 | const int k, ///< [in] some int |
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248 | const int l, ///< [in] precision |
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249 | const int degMipo, ///< [in] degree of minimal poly |
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250 | const Variable& alpha, ///< [in] algebraic variable |
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251 | const CanonicalForm& evaluation,///< [in] evaluation point |
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252 | const mat_zz_p& M ///< [in] bases change matrix |
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253 | ); |
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254 | #endif |
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255 | |
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256 | /// write A into M starting at row startIndex |
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257 | void |
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258 | writeInMatrix (CFMatrix& M, ///< [in,out] some matrix |
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259 | const CFArray& A, ///< [in] array of polys |
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260 | const int column, ///< [in] column in which A is written |
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261 | const int startIndex///< [in] row in which to start |
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262 | ); |
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263 | |
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264 | /// checks if a substitution x^n->x is possible |
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265 | /// |
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266 | /// @return an integer n > 1, if a substitution described as above is possible |
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267 | /// else n <= 1 |
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268 | int substituteCheck (const CFList& L ///< [in] a list of univariate polys |
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269 | ); |
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270 | |
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271 | /// substitute x^d by x in F |
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272 | void |
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273 | subst (const CanonicalForm& F, ///< [in] a polynomial |
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274 | CanonicalForm& A, ///< [in,out] returns F with x^d replaced by x |
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275 | const int d, ///< d > 1 such that a substitution x^d -> x |
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276 | ///< [in] is possible |
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277 | const Variable& x ///< [in] a Variable |
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278 | ); |
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279 | |
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280 | /// reverse a substitution x^d->x |
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281 | /// |
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282 | /// @return a poly with x replaced by x^d |
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283 | CanonicalForm |
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284 | reverseSubst (const CanonicalForm& F, ///< [in] a poly |
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285 | const int d, ///< [in] an integer > 0 |
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286 | const Variable& x ///< [in] a Variable |
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287 | ); |
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288 | |
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289 | /// reverse a substitution x^d->x |
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290 | void |
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291 | reverseSubst (CFList& L, ///< [in,out] a list of polys, returns the |
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292 | ///< given list with x replaced by x^d |
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293 | const int d, ///< [in] an integer > 0 |
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294 | const Variable& x ///< [in] a Variable |
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295 | ); |
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296 | |
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297 | /// check if a substitution x^n->x is possible |
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298 | /// |
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299 | /// @return an integer n > 1, if a substitution described as above is possible |
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300 | /// else n <= 1 |
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301 | int |
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302 | substituteCheck (const CanonicalForm& F, ///<[in] a polynomial |
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303 | const Variable& x ///<[in] some variable |
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304 | ); |
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305 | |
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306 | #endif |
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307 | /* FAC_FQ_BIVAR_UTIL_H */ |
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308 | |
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