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 basic definitions |
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20 | #include "singularxx_defs.h" |
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21 | |
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22 | struct spolyrec; |
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23 | typedef struct spolyrec polyrec; |
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24 | typedef polyrec * poly; |
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25 | |
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26 | struct ip_sring; |
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27 | typedef struct ip_sring * ring; |
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28 | |
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29 | struct sip_sideal; |
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30 | typedef struct sip_sideal * ideal; |
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31 | |
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32 | |
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33 | BEGIN_NAMESPACE_SINGULARXX BEGIN_NAMESPACE(SYZEXTRA) |
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34 | |
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35 | poly leadmonom(const poly p, const ring r); |
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36 | |
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37 | /// return the tail of a given polynomial or vector |
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38 | /// returns NULL if input is NULL, otherwise |
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39 | /// the result is a new polynomial/vector in the ring r |
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40 | poly p_Tail(const poly p, const ring r); |
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41 | |
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42 | |
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43 | /// return the tail of a given ideal or module |
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44 | /// returns NULL if input is NULL, otherwise |
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45 | /// the result is a new ideal/module in the ring r |
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46 | /// NOTE: the resulting rank is autocorrected |
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47 | ideal id_Tail(const ideal id, const ring r); |
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48 | |
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49 | /// inplace sorting of the module (ideal) id wrt <_(c,ds) |
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50 | void Sort_c_ds(const ideal id, const ring r); |
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51 | |
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52 | |
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53 | /** @class SchreyerSyzygyComputation syzextra.h |
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54 | * |
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55 | * Computing syzygies after Schreyer |
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56 | * |
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57 | * Storing/accumulating data during the computation requires some global |
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58 | * object, like this class. Ideally the above global functions should not |
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59 | * be used in favour of this class. |
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60 | * |
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61 | * @sa Schreyer Syzygy Computation Paper & Talk & Python prototype |
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62 | */ |
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63 | class SchreyerSyzygyComputation |
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64 | { |
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65 | public: |
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66 | /// Construct a global object for given input data (separated into leads & tails) |
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67 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const ring rBaseRing): |
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68 | m_idLeads(idLeads), m_idTails(idTails), m_rBaseRing(rBaseRing), |
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69 | m_syzLeads(NULL), m_syzTails(NULL), m_LS(NULL) {} |
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70 | |
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71 | |
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72 | /// Construct a global object for given input data (separated into leads & tails) |
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73 | SchreyerSyzygyComputation(const ideal idLeads, const ideal idTails, const ideal syzLeads, const ring rBaseRing): |
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74 | m_idLeads(idLeads), m_idTails(idTails), m_rBaseRing(rBaseRing), |
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75 | m_syzLeads(NULL), m_syzTails(NULL), m_LS(syzLeads) {} |
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76 | |
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77 | |
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78 | /// Destructor should not destruct the resulting m_syzLeads, m_syzTails. |
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79 | ~SchreyerSyzygyComputation(){ CleanUp(); } |
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80 | |
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81 | /// Read off the results while detaching them from this object |
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82 | /// NOTE: no copy! |
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83 | inline void ReadOffResult(ideal& syzL, ideal& syzT) |
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84 | { |
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85 | syzL = m_syzLeads; syzT = m_syzTails; |
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86 | |
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87 | m_syzLeads = m_syzTails = NULL; // m_LS ? |
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88 | } |
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89 | |
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90 | /// The main driver function: computes |
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91 | void ComputeSyzygy(); |
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92 | |
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93 | /// Computes Syz(leads) or only LEAD of it. |
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94 | /// The result is stored into m_syzLeads |
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95 | void ComputeLeadingSyzygyTerms(bool bComputeSecondTerms = true); |
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96 | |
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97 | // TODO: save shortcut (syz: |-.->) LM(LM(m) * "t") -> syz? |
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98 | poly FindReducer(poly product, poly syzterm); |
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99 | |
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100 | poly SchreyerSyzygyNF(poly syz_lead, poly syz_2); |
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101 | |
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102 | // TODO: store m * @tail -.-^-.-^-.--> ? |
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103 | poly TraverseTail(poly multiplier, poly tail); |
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104 | |
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105 | // TODO: save shortcut (syz: |-.->) LM(m) * "t" -> ? |
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106 | poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck); |
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107 | |
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108 | |
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109 | protected: |
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110 | |
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111 | /// Clean up all the accumulated data |
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112 | void CleanUp() {} |
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113 | |
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114 | private: |
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115 | /// global base ring |
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116 | const ring m_rBaseRing; |
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117 | |
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118 | /// input leading terms |
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119 | const ideal m_idLeads; |
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120 | |
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121 | /// input tails |
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122 | const ideal m_idTails; |
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123 | |
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124 | /// output (syzygy) leading terms (+2nd terms?) |
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125 | ideal m_syzLeads; |
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126 | |
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127 | /// output (syzygy) tails |
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128 | ideal m_syzTails; |
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129 | |
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130 | /*mutable?*/ ideal m_LS; ///< leading syzygy terms used for reducing syzygy tails |
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131 | }; |
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132 | |
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133 | |
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134 | // The following wrappers are just for testing separate functions on highest level (within schreyer.lib) |
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135 | |
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136 | static inline void ComputeSyzygy(const ideal L, const ideal T, ideal& LL, ideal& TT, const ring R) |
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137 | { |
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138 | SchreyerSyzygyComputation syz(L, T, R); |
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139 | syz.ComputeSyzygy(); |
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140 | syz.ReadOffResult(LL, TT); |
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141 | } |
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142 | |
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143 | static inline ideal ComputeLeadingSyzygyTerms(const ideal& L, const ring R) |
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144 | { |
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145 | SchreyerSyzygyComputation syz(L, NULL, R); |
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146 | syz.ComputeLeadingSyzygyTerms(false); |
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147 | ideal LL, TT; |
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148 | syz.ReadOffResult(LL, TT); |
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149 | return LL; // assume TT is NULL! |
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150 | } |
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151 | |
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152 | static inline ideal Compute2LeadingSyzygyTerms(const ideal& L, const ring R) |
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153 | { |
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154 | SchreyerSyzygyComputation syz(L, NULL, R); |
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155 | syz.ComputeLeadingSyzygyTerms(true); |
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156 | ideal LL, TT; |
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157 | syz.ReadOffResult(LL, TT); |
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158 | return LL; // assume TT is NULL! |
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159 | } |
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160 | |
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161 | static inline poly FindReducer(poly product, poly syzterm, |
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162 | ideal L, ideal LS, const ring R) |
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163 | { |
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164 | SchreyerSyzygyComputation syz(L, NULL, LS, R); |
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165 | return syz.FindReducer(product, syzterm); |
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166 | } |
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167 | |
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168 | static inline poly TraverseTail(poly multiplier, poly tail, |
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169 | ideal L, ideal T, ideal LS, const ring R) |
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170 | { |
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171 | SchreyerSyzygyComputation syz(L, T, LS, R); |
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172 | return syz.TraverseTail(multiplier, tail); |
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173 | } |
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174 | |
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175 | static inline poly ReduceTerm(poly multiplier, poly term4reduction, poly syztermCheck, |
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176 | ideal L, ideal T, ideal LS, const ring R) |
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177 | { |
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178 | SchreyerSyzygyComputation syz(L, T, LS, R); |
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179 | return syz.ReduceTerm(multiplier, term4reduction, syztermCheck); |
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180 | } |
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181 | |
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182 | |
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183 | static inline poly SchreyerSyzygyNF(poly syz_lead, poly syz_2, |
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184 | ideal L, ideal T, ideal LS, const ring R) |
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185 | { |
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186 | SchreyerSyzygyComputation syz(L, T, LS, R); |
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187 | return syz.SchreyerSyzygyNF(syz_lead, syz_2); |
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188 | } |
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189 | |
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190 | |
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191 | |
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192 | END_NAMESPACE |
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193 | |
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194 | END_NAMESPACE_SINGULARXX |
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195 | |
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196 | #endif |
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197 | /* #ifndef SYZEXTRA_H */ |
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198 | |
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199 | // Vi-modeline: vim: filetype=c:syntax:shiftwidth=2:tabstop=8:textwidth=0:expandtab |
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200 | |
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