1 | // -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- |
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2 | /*****************************************************************************\ |
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3 | * Computer Algebra System SINGULAR |
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4 | \*****************************************************************************/ |
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5 | /** @file syzextra.h |
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6 | * |
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7 | * Computation of Syzygies |
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8 | * |
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9 | * ABSTRACT: Computation of Syzygies due to Schreyer |
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10 | * |
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11 | * @author Oleksandr Motsak |
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12 | * |
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13 | **/ |
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14 | /*****************************************************************************/ |
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15 | |
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16 | #ifndef SYZEXTRA_H |
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17 | #define SYZEXTRA_H |
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18 | |
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19 | #include <vector> |
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20 | #include <map> |
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21 | #include <string.h> |
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22 | #include <stack> |
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23 | |
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24 | // include basic definitions |
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25 | #include "kernel/ideals.h" |
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26 | |
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27 | class idrec; typedef idrec * idhdl; |
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28 | |
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29 | class kBucket; typedef kBucket* kBucket_pt; |
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30 | |
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31 | #ifndef NOPRODUCT |
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32 | # define NOPRODUCT 1 |
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33 | #endif |
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34 | |
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35 | // set to 1 if all leading coeffs are assumed to be all =1... |
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36 | // note the use of simplify on input in SSinit! |
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37 | #ifndef NODIVISION |
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38 | # define NODIVISION 1 |
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39 | #endif |
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40 | |
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41 | poly leadmonom(const poly p, const ring r, const bool bSetZeroComp = true); |
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42 | |
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43 | /// inplace sorting of the module (ideal) id wrt <_(c,ds) |
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44 | void Sort_c_ds(const ideal id, const ring r); |
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45 | |
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46 | |
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47 | class sBucket; typedef sBucket* sBucket_pt; |
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48 | |
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49 | /** @class SBucketFactory syzextra.h |
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50 | * |
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51 | * sBucket Factory |
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52 | * |
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53 | * Cleate/store/reuse buckets |
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54 | * |
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55 | */ |
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56 | class SBucketFactory: private std::stack <sBucket_pt> |
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57 | { |
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58 | private: |
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59 | typedef std::stack <sBucket_pt> Base; |
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60 | |
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61 | public: |
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62 | typedef Base::value_type Bucket; |
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63 | |
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64 | SBucketFactory(const ring r) |
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65 | { |
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66 | push ( _CreateBucket(r) ); // start with at least one sBucket...? |
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67 | assume( top() != NULL ); |
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68 | }; |
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69 | |
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70 | ~SBucketFactory() |
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71 | { |
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72 | while( !empty() ) |
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73 | { |
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74 | _DestroyBucket( top() ); |
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75 | pop(); |
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76 | } |
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77 | } |
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78 | |
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79 | Bucket getBucket(const ring r, const bool remove = true) |
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80 | { |
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81 | Bucket bt = NULL; |
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82 | |
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83 | if( !empty() ) |
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84 | { |
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85 | bt = top(); |
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86 | |
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87 | if( remove ) |
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88 | pop(); |
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89 | } |
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90 | else |
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91 | { |
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92 | bt = _CreateBucket(r); |
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93 | |
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94 | if( !remove ) |
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95 | { |
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96 | push(bt); |
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97 | assume( bt == top() ); |
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98 | } |
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99 | } |
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100 | |
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101 | assume( bt != NULL ); |
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102 | |
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103 | return bt; |
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104 | } |
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105 | |
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106 | // TODO: this may be spared if we give-out a smart Bucket (which returns here upon its destructor!) |
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107 | void putBucket(const Bucket & bt, const bool replace = false) |
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108 | { |
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109 | assume( bt != NULL ); |
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110 | |
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111 | if( empty() ) |
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112 | push( bt ); |
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113 | else |
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114 | { |
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115 | if( replace ) |
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116 | top() = bt; |
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117 | else |
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118 | { |
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119 | if( bt != top() ) |
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120 | push( bt ); |
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121 | } |
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122 | } |
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123 | |
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124 | assume( bt == top() ); |
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125 | } |
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126 | |
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127 | private: |
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128 | /// inital allocation for new buckets |
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129 | static Bucket _CreateBucket(const ring r); |
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130 | |
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131 | /// we only expect empty buckets to be left at the end for destructor |
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132 | /// bt will be set to NULL |
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133 | static void _DestroyBucket(Bucket & bt); |
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134 | |
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135 | private: |
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136 | SBucketFactory(); |
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137 | SBucketFactory(const SBucketFactory&); |
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138 | void operator=(const SBucketFactory&); |
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139 | |
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140 | }; |
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141 | |
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142 | /// Computation attribute storage |
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143 | struct SchreyerSyzygyComputationFlags |
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144 | { |
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145 | SchreyerSyzygyComputationFlags(idhdl rootRingHdl); |
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146 | |
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147 | SchreyerSyzygyComputationFlags(const SchreyerSyzygyComputationFlags& attr): |
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148 | OPT__DEBUG(attr.OPT__DEBUG), |
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149 | OPT__LEAD2SYZ(attr.OPT__LEAD2SYZ), OPT__TAILREDSYZ(attr.OPT__TAILREDSYZ), |
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150 | OPT__HYBRIDNF(attr.OPT__HYBRIDNF), OPT__IGNORETAILS(attr.OPT__IGNORETAILS), |
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151 | OPT__SYZNUMBER(attr.OPT__SYZNUMBER), OPT__TREEOUTPUT(attr.OPT__TREEOUTPUT), |
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152 | OPT__SYZCHECK(attr.OPT__SYZCHECK), OPT__PROT(attr.OPT__PROT), |
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153 | OPT__NOCACHING(attr.OPT__NOCACHING), |
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154 | m_rBaseRing(attr.m_rBaseRing) |
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155 | {} |
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156 | |
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157 | /// output all the intermediate states |
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158 | const int OPT__DEBUG; // DebugOutput; |
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159 | |
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160 | /// ? |
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161 | const int OPT__LEAD2SYZ; // TwoLeadingSyzygyTerms; |
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162 | |
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163 | /// Reduce syzygy tails wrt the leading syzygy terms |
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164 | const int OPT__TAILREDSYZ; // TailReducedSyzygies; |
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165 | |
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166 | /// Use the usual NF's S-poly reduction while dropping lower order terms |
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167 | /// 2 means - smart selection! |
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168 | const int OPT__HYBRIDNF; // UseHybridNF |
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169 | |
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170 | |
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171 | /// ignore tails and compute the pure Schreyer frame |
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172 | const int OPT__IGNORETAILS; // @IGNORETAILS |
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173 | |
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174 | /// Syzygy level (within a resolution) |
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175 | mutable int OPT__SYZNUMBER; |
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176 | |
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177 | inline void nextSyzygyLayer() const |
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178 | { |
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179 | OPT__SYZNUMBER++; |
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180 | } |
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181 | |
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182 | /// output lifting tree |
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183 | const int OPT__TREEOUTPUT; |
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184 | |
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185 | /// CheckSyzygyProperty: TODO |
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186 | const int OPT__SYZCHECK; |
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187 | |
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188 | /// TEST_OPT_PROT |
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189 | const bool OPT__PROT; |
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190 | |
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191 | /// no caching/stores/lookups |
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192 | const int OPT__NOCACHING; |
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193 | |
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194 | /// global base ring |
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195 | const ring m_rBaseRing; |
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196 | }; |
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197 | |
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198 | class SchreyerSyzygyComputation; |
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199 | |
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200 | class CLCM: public SchreyerSyzygyComputationFlags, public std::vector<bool> |
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201 | { |
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202 | public: |
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203 | CLCM(const ideal& L, const SchreyerSyzygyComputationFlags& flags); |
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204 | |
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205 | bool Check(const poly m) const; |
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206 | |
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207 | private: |
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208 | bool m_compute; |
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209 | |
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210 | const unsigned int m_N; ///< number of ring variables |
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211 | }; |
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212 | |
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213 | |
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214 | class CLeadingTerm |
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215 | { |
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216 | public: |
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217 | CLeadingTerm(unsigned int label, const poly lt, const ring); |
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218 | |
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219 | #if NOPRODUCT |
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220 | bool DivisibilityCheck(const poly multiplier, const poly t, const unsigned long not_sev, const ring r) const; |
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221 | #endif |
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222 | bool DivisibilityCheck(const poly product, const unsigned long not_sev, const ring r) const; |
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223 | |
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224 | bool CheckLT( const ideal & L ) const; |
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225 | |
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226 | inline poly lt() const { return m_lt; }; |
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227 | inline unsigned long sev() const { return m_sev; }; |
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228 | inline unsigned int label() const { return m_label; }; |
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229 | private: |
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230 | const unsigned long m_sev; ///< not short exp. vector |
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231 | |
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232 | // NOTE/TODO: either of the following should be enough: |
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233 | const unsigned int m_label; ///< index in the main L[] + 1 |
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234 | |
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235 | const poly m_lt; ///< the leading term itself L[label-1] |
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236 | |
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237 | // disable the following: |
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238 | CLeadingTerm(); |
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239 | CLeadingTerm(const CLeadingTerm&); |
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240 | void operator=(const CLeadingTerm&); |
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241 | }; |
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242 | |
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243 | |
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244 | // TODO: needs a specialized variant without a component (hash!) |
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245 | class CReducerFinder: public SchreyerSyzygyComputationFlags |
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246 | { |
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247 | #if NOPRODUCT |
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248 | friend class CDivisorEnumerator2; |
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249 | #endif |
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250 | friend class CDivisorEnumerator; |
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251 | |
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252 | public: |
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253 | typedef long TComponentKey; |
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254 | typedef std::vector<const CLeadingTerm*> TReducers; |
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255 | |
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256 | private: |
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257 | typedef std::map< TComponentKey, TReducers> CReducersHash; |
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258 | |
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259 | public: |
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260 | /// goes over all leading terms |
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261 | CReducerFinder(const ideal L, const SchreyerSyzygyComputationFlags& flags); |
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262 | |
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263 | void Initialize(const ideal L); |
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264 | |
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265 | ~CReducerFinder(); |
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266 | |
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267 | |
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268 | #if NOPRODUCT |
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269 | poly |
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270 | FindReducer(const poly multiplier, const poly monom, const poly syzterm, const CReducerFinder& checker) const; |
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271 | |
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272 | #endif |
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273 | // TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz? |
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274 | poly // const_iterator // TODO: return const_iterator it, s.th: it->m_lt is the needed |
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275 | FindReducer(const poly product, const poly syzterm, const CReducerFinder& checker) const; |
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276 | |
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277 | bool IsDivisible(const poly q) const; |
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278 | |
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279 | |
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280 | inline bool IsNonempty() const { return !m_hash.empty(); } |
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281 | |
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282 | /// is the term to be "preprocessed" as lower order term or lead to only reducible syzygies... |
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283 | int PreProcessTerm(const poly t, CReducerFinder& syzChecker) const; |
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284 | |
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285 | private: |
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286 | ideal m_L; ///< only for debug |
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287 | |
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288 | CReducersHash m_hash; // can also be replaced with a vector indexed by components |
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289 | |
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290 | private: |
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291 | CReducerFinder(const CReducerFinder&); |
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292 | void operator=(const CReducerFinder&); |
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293 | }; |
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294 | |
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295 | bool my_p_LmCmp (poly, poly, const ring); |
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296 | |
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297 | typedef poly TCacheKey; |
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298 | typedef poly TCacheValue; |
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299 | |
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300 | struct CCacheCompare |
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301 | { |
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302 | const ring & m_ring; |
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303 | |
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304 | CCacheCompare(); |
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305 | |
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306 | CCacheCompare(const ring& r): m_ring(r) { assume(r != NULL); } |
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307 | |
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308 | CCacheCompare(const CCacheCompare& lhs): m_ring(lhs.m_ring) { assume(m_ring != NULL); } |
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309 | CCacheCompare& operator=(const CCacheCompare& lhs) { assume(lhs.m_ring != NULL); return (const_cast<CCacheCompare&>(lhs)); } |
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310 | |
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311 | inline bool operator() (const TCacheKey& l, const TCacheKey& r) const { assume(m_ring != NULL); return my_p_LmCmp(l, r, m_ring); } |
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312 | }; |
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313 | |
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314 | typedef std::map<TCacheKey, TCacheValue, CCacheCompare> TP2PCache; // deallocation??? !!! |
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315 | typedef std::map<int, TP2PCache> TCache; |
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316 | |
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317 | |
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318 | /** @class SchreyerSyzygyComputation syzextra.h |
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319 | * |
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320 | * Computing syzygies after Schreyer |
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321 | * |
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322 | * Storing/accumulating data during the computation requires some global |
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323 | * object, like this class. Ideally the above global functions should not |
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324 | * be used in favour of this class. |
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325 | * |
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326 | * @sa Schreyer Syzygy Computation Paper & Talk & Python prototype |
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327 | */ |
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328 | class SchreyerSyzygyComputation: public SchreyerSyzygyComputationFlags |
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329 | { |
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330 | friend class CLCM; |
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331 | friend class CReducerFinder; |
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332 | |
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333 | public: |
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334 | /// Construct a global object for given input data (separated into leads & tails) |
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335 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const SchreyerSyzygyComputationFlags setting): |
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336 | SchreyerSyzygyComputationFlags(setting), |
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337 | m_idLeads(idLeads), m_idTails(id_Copy(idTails, setting.m_rBaseRing)), |
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338 | m_syzLeads(NULL), m_syzTails(NULL), |
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339 | m_LS(NULL), m_lcm(m_idLeads, setting), |
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340 | m_div(m_idLeads, setting), m_checker(NULL, setting), m_cache(), |
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341 | m_sum_bucket_factory(setting.m_rBaseRing), |
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342 | m_spoly_bucket(NULL) |
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343 | { |
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344 | if( UNLIKELY(OPT__PROT) ) memset( &m_stat, 0, sizeof(m_stat) ); |
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345 | } |
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346 | |
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347 | /// Construct a global object for given input data (separated into leads & tails) |
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348 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const ideal syzLeads, const SchreyerSyzygyComputationFlags setting): |
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349 | SchreyerSyzygyComputationFlags(setting), |
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350 | m_idLeads(idLeads), m_idTails(id_Copy(idTails, setting.m_rBaseRing)), |
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351 | m_syzLeads(syzLeads), m_syzTails(NULL), |
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352 | m_LS(syzLeads), m_lcm(m_idLeads, setting), |
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353 | m_div(m_idLeads, setting), m_checker(NULL, setting), m_cache(), |
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354 | m_sum_bucket_factory(setting.m_rBaseRing), |
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355 | m_spoly_bucket(NULL) |
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356 | { |
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357 | if( UNLIKELY(OPT__PROT) ) memset( &m_stat, 0, sizeof(m_stat) ); |
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358 | |
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359 | if( LIKELY(OPT__TAILREDSYZ && !OPT__IGNORETAILS) ) |
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360 | { |
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361 | if (syzLeads != NULL) |
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362 | m_checker.Initialize(syzLeads); |
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363 | // if( idTails != NULL ) |
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364 | // SetUpTailTerms(); |
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365 | } |
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366 | } |
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367 | |
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368 | /// Destructor should not destruct the resulting m_syzLeads, m_syzTails. |
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369 | ~SchreyerSyzygyComputation(){ CleanUp(); } |
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370 | |
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371 | /// Convert the given ideal of tails into the internal representation (with reducers!) |
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372 | /// Preprocess m_idTails as well...? |
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373 | void SetUpTailTerms(); |
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374 | |
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375 | /// print statistics about the used heuristics |
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376 | void PrintStats() const; |
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377 | |
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378 | /// Read off the results while detaching them from this object |
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379 | /// NOTE: no copy! |
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380 | inline void ReadOffResult(ideal& syzL, ideal& syzT) |
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381 | { |
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382 | syzL = m_syzLeads; syzT = m_syzTails; |
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383 | |
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384 | m_syzLeads = m_syzTails = NULL; // m_LS ? |
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385 | |
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386 | if ( UNLIKELY(OPT__PROT) ) |
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387 | PrintStats(); |
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388 | } |
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389 | |
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390 | |
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391 | /// The main driver function: computes |
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392 | void ComputeSyzygy(); |
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393 | |
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394 | /// Computes Syz(leads) or only LEAD of it. |
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395 | /// The result is stored into m_syzLeads |
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396 | void ComputeLeadingSyzygyTerms(bool bComputeSecondTerms = true); |
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397 | |
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398 | |
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399 | |
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400 | /// Main HybridNF == 1: poly reduce + LOT + LCM? |
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401 | poly SchreyerSyzygyNF(const poly syz_lead, poly syz_2 = NULL) const; |
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402 | |
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403 | |
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404 | // Main (HybridNF == 0) Tree Travers + LOT + LCM? |
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405 | poly TraverseNF(const poly syz_lead, const poly syz_2 = NULL) const; |
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406 | |
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407 | /// High level caching function!!! |
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408 | poly TraverseTail(poly multiplier, const int tail) const; |
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409 | |
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410 | // REMOVE? |
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411 | /// called only from above and from outside (for testing) |
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412 | poly TraverseTail(poly multiplier, poly tail) const; |
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413 | |
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414 | /// TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? ??? |
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415 | poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck) const; |
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416 | |
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417 | /// low level computation... |
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418 | poly ComputeImage(poly multiplier, const int tail) const; |
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419 | |
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420 | public: |
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421 | /// just for testing via the wrapper below |
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422 | inline poly _FindReducer(const poly product, const poly syzterm) const |
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423 | { return m_div.FindReducer(product, syzterm, m_checker); } |
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424 | private: |
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425 | void CleanUp(); |
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426 | protected: |
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427 | |
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428 | |
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429 | /// just leading terms |
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430 | ideal Compute1LeadingSyzygyTerms(); |
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431 | |
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432 | /// leading + second terms |
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433 | ideal Compute2LeadingSyzygyTerms(); |
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434 | |
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435 | |
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436 | |
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437 | private: |
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438 | /// input leading terms |
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439 | const ideal m_idLeads; |
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440 | |
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441 | /// input tails |
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442 | const ideal m_idTails; |
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443 | |
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444 | /// output (syzygy) leading terms (+2nd terms?) |
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445 | ideal m_syzLeads; |
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446 | |
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447 | /// output (syzygy) tails |
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448 | ideal m_syzTails; |
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449 | |
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450 | /*mutable?*/ ideal m_LS; ///< leading syzygy terms used for reducing syzygy tails |
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451 | |
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452 | |
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453 | /// Bitmask for variables occuring in leading terms |
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454 | const CLCM m_lcm; |
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455 | |
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456 | /// Divisor finder |
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457 | const CReducerFinder m_div; |
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458 | |
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459 | /// for checking tail-terms and makeing them irreducible (wrt m_LS!) |
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460 | CReducerFinder m_checker; |
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461 | |
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462 | mutable TCache m_cache; // cacher comp + poly -> poly! // mutable??? |
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463 | |
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464 | /// used for simple summing up |
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465 | mutable SBucketFactory m_sum_bucket_factory; // sBucket_pt |
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466 | |
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467 | /// for S-Polynomial reductions |
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468 | mutable kBucket_pt m_spoly_bucket; // only used inside of SchreyerSyzygyNF! destruction by CleanUp()! |
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469 | |
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470 | |
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471 | /// Statistics: |
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472 | /// 0..3: as in SetUpTailTerms()::PreProcessTerm() // TODO!!?? |
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473 | /// 4: number of terms discarded due to LOT heuristics |
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474 | /// 5: number of terms discarded due to LCM heuristics |
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475 | /// 6, 7: lookups without & with rescale, 8: stores |
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476 | mutable unsigned long m_stat[9]; |
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477 | }; |
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478 | |
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479 | // The following wrappers are just for testing separate functions on highest level (within schreyer.lib) |
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480 | |
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481 | static inline void ComputeSyzygy(const ideal L, const ideal T, ideal& LL, ideal& TT, const SchreyerSyzygyComputationFlags A) |
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482 | { |
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483 | SchreyerSyzygyComputation syz(L, T, A); |
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484 | syz.ComputeSyzygy(); |
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485 | syz.ReadOffResult(LL, TT); |
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486 | } |
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487 | |
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488 | static inline ideal ComputeLeadingSyzygyTerms(const ideal& L, const SchreyerSyzygyComputationFlags A) |
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489 | { |
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490 | SchreyerSyzygyComputation syz(L, NULL, A); |
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491 | syz.ComputeLeadingSyzygyTerms(false); |
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492 | ideal LL, TT; |
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493 | syz.ReadOffResult(LL, TT); |
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494 | return LL; // assume TT is NULL! |
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495 | } |
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496 | |
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497 | static inline ideal Compute2LeadingSyzygyTerms(const ideal& L, const SchreyerSyzygyComputationFlags A) |
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498 | { |
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499 | SchreyerSyzygyComputation syz(L, NULL, A); |
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500 | syz.ComputeLeadingSyzygyTerms(true); |
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501 | ideal LL, TT; |
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502 | syz.ReadOffResult(LL, TT); |
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503 | return LL; // assume TT is NULL! |
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504 | } |
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505 | |
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506 | static inline poly FindReducer(poly product, poly syzterm, |
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507 | ideal L, ideal LS, const SchreyerSyzygyComputationFlags A) |
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508 | { |
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509 | SchreyerSyzygyComputation syz(L, NULL, LS, A); |
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510 | return syz._FindReducer(product, syzterm); |
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511 | } |
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512 | |
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513 | static inline poly TraverseTail(poly multiplier, poly tail, |
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514 | ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A) |
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515 | { |
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516 | SchreyerSyzygyComputation syz(L, T, LS, A); |
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517 | return syz.TraverseTail(multiplier, tail); |
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518 | } |
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519 | |
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520 | static inline poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck, |
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521 | ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A) |
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522 | { |
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523 | SchreyerSyzygyComputation syz(L, T, LS, A); |
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524 | return syz.ReduceTerm(multiplier, term4reduction, syztermCheck); |
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525 | } |
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526 | |
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527 | |
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528 | static inline poly SchreyerSyzygyNF(poly syz_lead, poly syz_2, |
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529 | ideal L, ideal T, ideal LS, const SchreyerSyzygyComputationFlags A) |
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530 | { |
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531 | SchreyerSyzygyComputation syz(L, T, LS, A); |
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532 | return syz.SchreyerSyzygyNF(syz_lead, syz_2); |
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533 | } |
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534 | |
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535 | #endif |
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536 | /* #ifndef SYZEXTRA_H */ |
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537 | |
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538 | // Vi-modeline: vim: filetype=c:syntax:shiftwidth=2:tabstop=8:textwidth=0:expandtab |
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539 | |
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