1 | // Buchberger.cc |
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2 | |
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3 | // implementation of Buchberger's Algorithm. |
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4 | |
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5 | #ifndef BUCHBERGER_CC |
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6 | #define BUCHBERGER_CC |
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7 | |
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8 | #include "ideal.h" |
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9 | |
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10 | ///////////////////////////////////////////////////////////////////////////// |
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11 | /////////////// S-pair computation ////////////////////////////////////////// |
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12 | ///////////////////////////////////////////////////////////////////////////// |
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13 | |
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14 | BOOLEAN ideal::unnecessary_S_pair(list_iterator& first_iter, |
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15 | list_iterator& second_iter) const |
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16 | { |
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17 | // This function checks several criteria to discard th S-pair of the |
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18 | // binomials referenced by the iterators. The criteria depend on the |
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19 | // settings of the idealŽs S-pair flags. |
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20 | |
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21 | // The arguments are iterators instead of the referenced binomials |
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22 | // because we have to do some equality tests. These are more efficient on |
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23 | // iterators than on binomials. |
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24 | |
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25 | ///////////// criterion of relatively prime leading terms /////////////////// |
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26 | |
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27 | // An S-pair can discarded if the leading terms of the two binomials are |
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28 | // relatively prime. |
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29 | |
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30 | if(rel_primeness) |
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31 | if(relatively_prime(first_iter.get_element(),second_iter.get_element()) |
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32 | ==TRUE) |
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33 | return TRUE; |
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34 | |
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35 | //////////// criterion M /////////////////////////////////////////////////// |
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36 | |
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37 | if(M_criterion) |
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38 | { |
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39 | |
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40 | list_iterator iter; |
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41 | binomial& bin1=first_iter.get_element(); |
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42 | binomial& bin2=second_iter.get_element(); |
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43 | |
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44 | // The M-criterion of Gebauer/Moeller checks binomial triples as |
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45 | // explained in binomial.h; these are built of the elements referenced |
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46 | // by the argument iterators and a third element appearing before the |
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47 | // element referenced by second_iter in the generator lists. |
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48 | |
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49 | |
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50 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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51 | |
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52 | iter.set_to_list(generators); |
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53 | |
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54 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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55 | |
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56 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
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57 | |
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58 | // The support of the lcm of two monomials is the union of their supports. |
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59 | // To test criterion M, we then only have to consider lists whose support |
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60 | // is a subset of the union of (first_iter.get_element()).head_support and |
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61 | // (second_iter.get_element()).head_support. As only elements before |
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62 | // second_iter.get_element() are tested, we can stop iteraton as soon as |
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63 | // we reach this element. |
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64 | |
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65 | short supp2=bin2.head_support%Number_of_Lists; |
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66 | short supp_union=(bin1.head_support%Number_of_Lists)|supp2; |
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67 | // supp_union (read as binary vector) is the union of the supports of |
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68 | // first_iter.get_element() and second_iter.get_element() |
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69 | // (restricted to List_Support_Variables variables). |
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70 | |
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71 | for(short i=0;i<S.number_of_subsets[supp_union];i++) |
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72 | // Go through the lists that contain elements whose support is a |
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73 | // subset of supp_union. |
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74 | { |
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75 | short actual_list=S.subsets_of_support[supp_union][i]; |
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76 | iter.set_to_list(generators[actual_list]); |
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77 | // This is the i-th list among the generator list with elements |
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78 | // whose support is a subset of supp_union. |
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79 | |
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80 | if(actual_list==supp2) |
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81 | break; |
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82 | // The iteration has reached the list referenced by second_iter, |
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83 | // this is handled alone to avoid unnecessary checks. |
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84 | // Before breakin the loop, iter has to be set to this list. |
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85 | |
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86 | while(iter.is_at_end()==FALSE) |
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87 | // Iterate over the list with three iterators according to the |
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88 | // description of criterion M. |
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89 | { |
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90 | if(M(iter.get_element(),bin1,bin2)==TRUE) |
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91 | return TRUE; |
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92 | iter.next(); |
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93 | } |
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94 | } |
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95 | |
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96 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
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97 | |
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98 | |
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99 | // Now, iter references second_iter's list, |
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100 | // if SUPPORT_DRIVEN_METHODS_EXTENDED are enabled or not. |
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101 | |
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102 | while(iter!=second_iter) |
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103 | { |
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104 | if(M(iter.get_element(),bin1,bin2)==TRUE) |
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105 | return TRUE; |
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106 | iter.next(); |
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107 | } |
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108 | } |
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109 | |
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110 | /////////////////////// criterion F //////////////////////////////////////// |
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111 | |
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112 | if(F_criterion) |
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113 | { |
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114 | |
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115 | list_iterator iter; |
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116 | binomial& bin1=first_iter.get_element(); |
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117 | binomial& bin2=second_iter.get_element(); |
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118 | |
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119 | // The F-criterion of Gebauer/Moeller checks binomial triples as |
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120 | // explained in binomial.h; these are built of the elements referenced |
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121 | // by the argument iterators and a third element appearing before the |
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122 | // element referenced by first_iter in the generator lists. |
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123 | |
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124 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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125 | |
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126 | iter.set_to_list(generators); |
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127 | |
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128 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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129 | |
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130 | |
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131 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
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132 | |
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133 | // Again, we only have to consider lists whose support is a subset of the |
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134 | // union of (first_iter.get_element()).head_support and |
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135 | // (second_iter.get_element()).head_support. |
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136 | // Additionally,we can override lists whose support is to small. |
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137 | |
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138 | short supp1=bin1.head_support%Number_of_Lists; |
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139 | short supp2=bin2.head_support%Number_of_Lists; |
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140 | short supp_union=supp1|supp2; |
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141 | // supp_union (read as binary vector) is the union of the supports of |
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142 | // first_iter.get_element() and second_iter.get_element() |
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143 | // (restricted to List_Support_Variables variables). |
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144 | |
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145 | for(short i=0;i<S.number_of_subsets[supp_union];i++) |
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146 | // Go through the lists that contain elements whose support is a |
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147 | // subset of supp_union. |
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148 | { |
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149 | short actual_list=S.subsets_of_support[supp_union][i]; |
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150 | |
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151 | if((actual_list|supp2) != supp_union) |
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152 | continue; |
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153 | // The support of the actual list is too small, so its elements cannot |
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154 | // satisfie criterion F. |
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155 | |
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156 | iter.set_to_list(generators[actual_list]); |
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157 | // This is the i-th list among the generator list with elements |
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158 | // whose support is a subset of supp_union. |
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159 | |
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160 | if(actual_list==supp1) |
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161 | break; |
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162 | // The iteration has reached the list referenced by first_iter; |
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163 | // this is handled alone to avoid unnecessary checks. |
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164 | // iter has to be set to that list before breaking the loop. |
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165 | |
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166 | while(iter.is_at_end()==FALSE) |
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167 | // Iterate over the list with three iterators according to the |
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168 | // description of criterion F. |
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169 | { |
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170 | if(F(iter.get_element(),bin1,bin2)==TRUE) |
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171 | return TRUE; |
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172 | iter.next(); |
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173 | } |
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174 | } |
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175 | |
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176 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
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177 | |
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178 | // Now, iter references first_iter's list, |
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179 | // if SUPPORT_DRIVEN_METHODS_EXTENDED are enabled or not. |
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180 | |
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181 | while(iter!=first_iter) |
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182 | { |
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183 | if(F(iter.get_element(),bin1,bin2)==TRUE) |
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184 | return TRUE; |
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185 | iter.next(); |
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186 | } |
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187 | } |
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188 | |
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189 | /////////////////////// criterion B ///////////////////////////////////////// |
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190 | |
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191 | if(B_criterion) |
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192 | { |
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193 | |
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194 | list_iterator iter; |
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195 | binomial& bin1=first_iter.get_element(); |
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196 | binomial& bin2=second_iter.get_element(); |
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197 | |
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198 | // The B-criterion of Gebauer/Moeller checks binomial triples as |
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199 | // explained in binomial.h; these are built of the elements referenced |
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200 | // by the argument iterators and a third element appearing after the |
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201 | // element referenced by second_iter in the generator lists. |
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202 | |
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203 | iter=second_iter; |
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204 | iter.next(); |
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205 | |
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206 | // First test second_iter's list. |
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207 | // This is the only list if NO_SUPPORT_DRIVEN_METHODS are enabled. |
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208 | |
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209 | while(iter.is_at_end()==FALSE) |
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210 | { |
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211 | if(B(iter.get_element(),bin1,bin2)==TRUE) |
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212 | return(TRUE); |
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213 | iter.next(); |
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214 | } |
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215 | |
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216 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
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217 | |
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218 | // Now consider the other lists. |
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219 | // Again, we only have to consider lists whose support is a subset of the |
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220 | // union of (first_iter.get_element()).head_support and |
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221 | // (second_iter.get_element()).head_support. |
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222 | |
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223 | short supp2=bin2.head_support%Number_of_Lists; |
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224 | short supp_union=(bin1.head_support%Number_of_Lists)|supp2; |
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225 | // supp_union (read as binary vector) is the union of the supports of |
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226 | // first_iter.get_element() and second_iter.get_element() |
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227 | // (restricted to List_Support_Variables variables). |
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228 | |
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229 | for(int i=0;i<S.number_of_subsets[supp_union];i++) |
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230 | // Go through the lists that contain elements whose support is a |
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231 | // subset of supp_union. |
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232 | { |
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233 | short actual_list=S.subsets_of_support[supp_union][i]; |
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234 | |
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235 | if(actual_list<=supp2) |
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236 | continue; |
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237 | // Only lists after second_iter's list have to be considered. |
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238 | |
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239 | iter.set_to_list(generators[actual_list]); |
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240 | // This is the i-th list among the generator list with elements |
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241 | // whose support is a subset of supp_union. |
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242 | |
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243 | while(iter.is_at_end()==FALSE) |
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244 | { |
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245 | // Iterate over the list with three iterators according to the |
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246 | // description of criterion B. |
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247 | if(B(iter.get_element(),bin1,bin2)==TRUE) |
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248 | return TRUE; |
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249 | iter.next(); |
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250 | } |
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251 | } |
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252 | |
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253 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
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254 | } |
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255 | |
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256 | ////////////////////// BuchbergerŽs second criterion //////////////////////// |
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257 | |
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258 | if(second_criterion) |
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259 | { |
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260 | list_iterator iter; |
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261 | binomial& bin1=first_iter.get_element(); |
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262 | binomial& bin2=second_iter.get_element(); |
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263 | |
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264 | // The BuchbergerŽs second criterion checks binomial triples as |
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265 | // explained in binomial.h; these are built of the elements referenced |
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266 | // by the argument iterators and a third element appearing anywhere |
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267 | // in the generator lists. |
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268 | |
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269 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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270 | |
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271 | iter.set_to_list(generators); |
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272 | |
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273 | while(iter.is_at_end()==FALSE) |
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274 | // Iterate over the list with three iterators according to the |
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275 | // description of the second criterion. |
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276 | { |
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277 | if((iter!=first_iter) && (iter!=second_iter)) |
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278 | // Else the second criterion must not be applied |
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279 | // (lcm(a,b) is, of course, divisible by a and by b). |
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280 | if(second_crit(iter.get_element(),bin1,bin2)==TRUE) |
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281 | return TRUE; |
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282 | iter.next(); |
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283 | } |
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284 | |
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285 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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286 | |
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287 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
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288 | |
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289 | // Again, we only have to consider lists whose support is a subset of |
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290 | // the union of (first_iter.get_element()).head_support |
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291 | // and (second_iter.get_element()).head_support. |
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292 | |
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293 | short supp1=bin1.head_support%Number_of_Lists; |
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294 | short supp2=bin2.head_support%Number_of_Lists; |
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295 | short supp_union=supp1|supp2; |
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296 | // supp_union (read as binary vector) is the union of the supports of |
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297 | // first_iter.get_element() and second_iter.get_element() |
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298 | // (restricted to List_Support_Variables variables) |
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299 | |
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300 | for(short i=0;i<S.number_of_subsets[supp_union];i++) |
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301 | // Go through the lists that contain elements whose support is a |
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302 | // subset of supp_union. |
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303 | { |
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304 | short actual_list=S.subsets_of_support[supp_union][i]; |
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305 | |
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306 | if((actual_list==supp1) || (actual_list==supp2)) |
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307 | continue; |
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308 | // The lists containing the elements referenced by the argument |
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309 | // iterators are tested separately to avoid unnecessary checks for |
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310 | // equality. |
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311 | |
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312 | iter.set_to_list(generators[actual_list]); |
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313 | // This is the i-th list among the generator list with elements |
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314 | // whose support is a subset of supp_union. |
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315 | |
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316 | while(iter.is_at_end()==FALSE) |
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317 | // Iterate over the list with three iterators according to the |
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318 | // description of the second criterion. |
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319 | { |
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320 | if(second_crit(iter.get_element(),bin1,bin2)==TRUE) |
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321 | return TRUE; |
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322 | iter.next(); |
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323 | } |
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324 | } |
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325 | |
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326 | if(supp1==supp2) |
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327 | // The elements referenced by first_iter and second_iter appear in the |
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328 | // same list. |
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329 | { |
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330 | iter.set_to_list(generators[supp1]); |
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331 | while(iter.is_at_end()==FALSE) |
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332 | { |
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333 | if((iter!=first_iter) && (iter!=second_iter)) |
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334 | // Else the second criterion must not be applied |
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335 | // (lcm(a,b) is, of course, divisible by a and by b). |
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336 | if(second_crit(iter.get_element(),bin1,bin2)==TRUE) |
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337 | return TRUE; |
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338 | iter.next(); |
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339 | } |
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340 | } |
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341 | else |
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342 | // The elements referenced by first_iter and second_iter appear in |
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343 | // different lists. |
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344 | { |
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345 | |
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346 | // Test first_iterŽs list. |
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347 | iter.set_to_list(generators[supp1]); |
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348 | while(iter.is_at_end()==FALSE) |
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349 | { |
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350 | if(iter!=first_iter) |
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351 | // Else the second criterion must not be applied |
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352 | // (lcm(a,b) is, of course, divisible by a and by b). |
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353 | if(second_crit(iter.get_element(),bin1,bin2)==TRUE) |
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354 | return TRUE; |
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355 | iter.next(); |
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356 | } |
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357 | |
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358 | // Test second_iterŽs list. |
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359 | iter.set_to_list(generators[supp2]); |
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360 | while(iter.is_at_end()==FALSE) |
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361 | { |
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362 | if(iter!=second_iter) |
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363 | // Else the second criterion must not be applied |
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364 | // (lcm(a,b) is, of course, divisible by a and by b). |
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365 | if(second_crit(iter.get_element(),bin1,bin2)==TRUE) |
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366 | return TRUE; |
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367 | iter.next(); |
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368 | } |
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369 | } |
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370 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
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371 | } |
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372 | |
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373 | // no criterion found to discard the S-Pair to compute |
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374 | return FALSE; |
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375 | } |
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376 | |
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377 | ideal& ideal::compute_actual_S_pairs_1() |
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378 | { |
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379 | // This routine implements the simplest method for the S-pair computation |
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380 | // (and one of the most efficient methods). We simply iterate over the |
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381 | // generator list(s) with two pointers to look at each binomial pair. |
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382 | // The "done"-mark of each list element tells us if this element was |
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383 | // already considered in a previous S-pair computation; pairs of such |
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384 | // "old" binomials do not have to be computed anymore (but pairs of an old |
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385 | // and a new one have to be computed, of course). As the generator list are |
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386 | // ordered with respect to the "done"-flag (all undone elements preceed all |
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387 | // done elements), we can avoid unnecessary iteration steps by breaking |
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388 | // the iteration at the right point. |
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389 | |
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390 | // The computed S-pairs are stored in the aux_list for further computations. |
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391 | |
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392 | // For a better overview, the code for NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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393 | // and SUPPORT_DRIVEN_METHODS_EXTENDED is completetly separated in this |
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394 | // function. |
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395 | |
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396 | // Note that the "next()"-operations in the following routine do not reach a |
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397 | // NULL pointer because of the implementation of the "is_at_end()"-function |
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398 | // and because the "done"-component of the dummy element is set to zero. |
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399 | |
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400 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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401 | |
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402 | list_iterator first_iter(generators); |
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403 | |
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404 | while(first_iter.element_is_marked_done()==FALSE) |
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405 | // new generator, compute S-pairs with all following generators |
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406 | // Notice that the new generators are always at the beginning, |
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407 | // the old generators at the end of the generator list. |
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408 | { |
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409 | binomial& bin=first_iter.get_element(); |
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410 | first_iter.mark_element_done(); |
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411 | |
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412 | list_iterator second_iter(first_iter); |
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413 | second_iter.next(); |
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414 | // This may be the dummy element. |
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415 | |
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416 | while(second_iter.is_at_end()==FALSE) |
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417 | { |
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418 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
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419 | aux_list._insert(S_binomial(bin,second_iter.get_element(),w)); |
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420 | second_iter.next(); |
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421 | } |
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422 | |
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423 | first_iter.next(); |
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424 | } |
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425 | |
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426 | // Now, first_iter references an old generator or the end of the generator |
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427 | // list. As all following generators are old ones, we are done. |
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428 | |
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429 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
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430 | |
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431 | |
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432 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
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433 | |
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434 | list_iterator first_iter; |
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435 | |
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436 | for(short i=0;i<Number_of_Lists;i++) |
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437 | { |
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438 | first_iter.set_to_list(generators[i]); |
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439 | |
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440 | while(first_iter.element_is_marked_done()==FALSE) |
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441 | // new generator, compute S-pairs with all following elements |
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442 | // Notice that the new generators are always at the beginning, |
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443 | // the old generators at the end of the generator lists. |
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444 | { |
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445 | binomial& bin=first_iter.get_element(); |
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446 | first_iter.mark_element_done(); |
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447 | |
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448 | // First search over the actual list with the second iterator. |
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449 | |
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450 | list_iterator second_iter(first_iter); |
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451 | second_iter.next(); |
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452 | |
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453 | while(second_iter.is_at_end()==FALSE) |
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454 | { |
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455 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
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456 | aux_list._insert(S_binomial(bin,second_iter.get_element(),w)); |
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457 | second_iter.next(); |
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458 | } |
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459 | |
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460 | // Then search over the remaining lists. |
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461 | |
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462 | for(short j=i+1;j<Number_of_Lists;j++) |
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463 | { |
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464 | second_iter.set_to_list(generators[j]); |
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465 | |
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466 | while(second_iter.is_at_end()==FALSE) |
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467 | { |
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468 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
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469 | aux_list._insert(S_binomial(bin,second_iter.get_element(),w)); |
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470 | second_iter.next(); |
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471 | } |
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472 | } |
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473 | first_iter.next(); |
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474 | } |
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475 | |
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476 | while(first_iter.is_at_end()==FALSE) |
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477 | // old generator, compute only S-pairs with the following new generators |
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478 | // (S-pairs with the following old generators were already computed |
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479 | // before, first_iter.element_is_marked_done()==TRUE) |
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480 | // As all generators in the actual list are old ones, we can |
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481 | // start iteration with the next list. |
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482 | { |
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483 | binomial& bin=first_iter.get_element(); |
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484 | |
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485 | list_iterator second_iter; |
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486 | |
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487 | for(short j=i+1;j<Number_of_Lists;j++) |
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488 | // search over remaining lists |
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489 | { |
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490 | second_iter.set_to_list(generators[j]); |
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491 | |
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492 | while(second_iter.element_is_marked_done()==FALSE) |
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493 | // consider only new generators |
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494 | { |
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495 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
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496 | aux_list._insert(S_binomial(bin,second_iter.get_element(),w)); |
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497 | second_iter.next(); |
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498 | } |
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499 | } |
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500 | first_iter.next(); |
---|
501 | } |
---|
502 | |
---|
503 | } |
---|
504 | |
---|
505 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
506 | return(*this); |
---|
507 | } |
---|
508 | |
---|
509 | ideal& ideal::compute_actual_S_pairs_1a() |
---|
510 | { |
---|
511 | // The only difference to the previous routine is that the aux_list is kept |
---|
512 | // ordered with respect to the idealŽs term ordering, i.e. the inserts are |
---|
513 | // replaced by ordered inserts. |
---|
514 | |
---|
515 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
516 | |
---|
517 | list_iterator first_iter(generators); |
---|
518 | |
---|
519 | while(first_iter.element_is_marked_done()==FALSE) |
---|
520 | // new generator, compute S-pairs with all following generators |
---|
521 | // Notice that the new generators are always at the beginning, |
---|
522 | // the old generators at the end of the generator list. |
---|
523 | { |
---|
524 | binomial& bin=first_iter.get_element(); |
---|
525 | first_iter.mark_element_done(); |
---|
526 | |
---|
527 | list_iterator second_iter(first_iter); |
---|
528 | second_iter.next(); |
---|
529 | // This may be the dummy element. |
---|
530 | |
---|
531 | while(second_iter.is_at_end()==FALSE) |
---|
532 | { |
---|
533 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
534 | aux_list._ordered_insert |
---|
535 | (S_binomial(bin,second_iter.get_element(),w),w); |
---|
536 | second_iter.next(); |
---|
537 | } |
---|
538 | first_iter.next(); |
---|
539 | } |
---|
540 | |
---|
541 | // Now, first_iter references an old generator or the end of the generator |
---|
542 | // list. As all following generators are old ones, we are done. |
---|
543 | |
---|
544 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
545 | |
---|
546 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
547 | |
---|
548 | list_iterator first_iter; |
---|
549 | |
---|
550 | for(short i=0;i<Number_of_Lists;i++) |
---|
551 | { |
---|
552 | first_iter.set_to_list(generators[i]); |
---|
553 | |
---|
554 | while(first_iter.element_is_marked_done()==FALSE) |
---|
555 | // new generator, compute S-pairs with all following elements |
---|
556 | // Notice that the new generators are always at the beginning, |
---|
557 | // the old generators at the end of the generator lists. |
---|
558 | { |
---|
559 | binomial& bin=first_iter.get_element(); |
---|
560 | first_iter.mark_element_done(); |
---|
561 | |
---|
562 | // First search over the actual list with the second iterator. |
---|
563 | |
---|
564 | list_iterator second_iter(first_iter); |
---|
565 | second_iter.next(); |
---|
566 | |
---|
567 | while(second_iter.is_at_end()==FALSE) |
---|
568 | { |
---|
569 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
570 | aux_list._ordered_insert |
---|
571 | (S_binomial(bin,second_iter.get_element(),w),w); |
---|
572 | second_iter.next(); |
---|
573 | } |
---|
574 | |
---|
575 | // Then search over the remaining lists. |
---|
576 | |
---|
577 | for(short j=i+1;j<Number_of_Lists;j++) |
---|
578 | { |
---|
579 | second_iter.set_to_list(generators[j]); |
---|
580 | |
---|
581 | while(second_iter.is_at_end()==FALSE) |
---|
582 | { |
---|
583 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
584 | aux_list._ordered_insert |
---|
585 | (S_binomial(bin,second_iter.get_element(),w),w); |
---|
586 | second_iter.next(); |
---|
587 | } |
---|
588 | } |
---|
589 | first_iter.next(); |
---|
590 | } |
---|
591 | |
---|
592 | while(first_iter.is_at_end()==FALSE) |
---|
593 | // old generator, compute only S-pairs with the following new generators |
---|
594 | // (S-pairs with the following old generators were already computed |
---|
595 | // before, first_iter.element_is_marked_done()==TRUE) |
---|
596 | // As all generators in the actual list are old ones, we can |
---|
597 | // start iteration with the next list. |
---|
598 | { |
---|
599 | binomial& bin=first_iter.get_element(); |
---|
600 | |
---|
601 | list_iterator second_iter; |
---|
602 | |
---|
603 | for(short j=i+1;j<Number_of_Lists;j++) |
---|
604 | // search over remaining lists |
---|
605 | { |
---|
606 | second_iter.set_to_list(generators[j]); |
---|
607 | |
---|
608 | while(second_iter.element_is_marked_done()==FALSE) |
---|
609 | // consider only new generators |
---|
610 | { |
---|
611 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
612 | aux_list._ordered_insert |
---|
613 | (S_binomial(bin,second_iter.get_element(),w),w); |
---|
614 | second_iter.next(); |
---|
615 | } |
---|
616 | } |
---|
617 | first_iter.next(); |
---|
618 | } |
---|
619 | |
---|
620 | } |
---|
621 | |
---|
622 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
623 | |
---|
624 | return(*this); |
---|
625 | } |
---|
626 | |
---|
627 | ideal& ideal::compute_actual_S_pairs_2() |
---|
628 | { |
---|
629 | // This routine implements are mor dynamic S-pair-computation. As in the |
---|
630 | // previous routines, we iterate over the generator list(s) with two |
---|
631 | // iterators, forming pairs under the consideration of the "done"-flags. |
---|
632 | |
---|
633 | // But before inserting into the aux_list, these S-pairs are reduced by |
---|
634 | // the ideal generators. This seems to be clever, but shows to be a |
---|
635 | // disadvantage: |
---|
636 | // In the previous S-pair routines, the computed S-bionomials are not reduced |
---|
637 | // at all. This is done in the appropriate Groebner basis routine |
---|
638 | // (reduced_Groebner_basis_1 or ..._1a) when moving them from the aux_list |
---|
639 | // to the generator lists. This meens that S-binomials cannot only be reduced |
---|
640 | // by the generators known at the time of their computation, but also by |
---|
641 | // the S-pairs that where already treated. |
---|
642 | |
---|
643 | // The advantage of the current routine is that the immediately reduced |
---|
644 | // S-binomial can be used to reduce the ideal itself. This strategy keeps |
---|
645 | // the ideal almost reduced, so the minimalization will be faster. |
---|
646 | // Furthermore, the computation of S-pairs with unreduced generators is |
---|
647 | // avoided. |
---|
648 | // To provide a possibility to compensate the mentionned disadvantage, |
---|
649 | // I have written the routine minimalize_S_pairs() that interreduces the |
---|
650 | // binomials stored in aux_list. |
---|
651 | |
---|
652 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
653 | |
---|
654 | list_iterator first_iter(generators); |
---|
655 | |
---|
656 | Integer first_reduced=0; |
---|
657 | Integer second_reduced=0; |
---|
658 | // When reducing the ideal immediately by newly found generators, it |
---|
659 | // can happen that the binomials referenced by the iterators are |
---|
660 | // reduced to zero and then deleted. We need to make sure that the |
---|
661 | // iterators do not reference freed memory in such a case. These two |
---|
662 | // flags help us with this task. |
---|
663 | |
---|
664 | while(first_iter.element_is_marked_done()==FALSE) |
---|
665 | // new generator, compute S-pairs with all following generators |
---|
666 | { |
---|
667 | binomial& bin1=first_iter.get_element(); |
---|
668 | first_iter.mark_element_done(); |
---|
669 | |
---|
670 | list_iterator second_iter(first_iter); |
---|
671 | second_iter.next(); |
---|
672 | // This may be the dummy element. |
---|
673 | |
---|
674 | while((second_iter.is_at_end()==FALSE) && (first_reduced<=0)) |
---|
675 | { |
---|
676 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
677 | { |
---|
678 | binomial& bin2=second_iter.get_element(); |
---|
679 | |
---|
680 | // compute S-binomial |
---|
681 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
682 | |
---|
683 | // reduce S-binomial by the actual ideal generators |
---|
684 | reduce(S_bin,FALSE); |
---|
685 | |
---|
686 | if(S_bin!=0) |
---|
687 | { |
---|
688 | // reduce the ideal generators by the S-binomial |
---|
689 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
690 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
691 | reduce_by(S_bin,first_iter,second_iter); |
---|
692 | aux_list._insert(S_bin); |
---|
693 | } |
---|
694 | else |
---|
695 | delete &S_bin; |
---|
696 | |
---|
697 | } |
---|
698 | |
---|
699 | // Move second_iter to the next element if its referenced binomial |
---|
700 | // has not changed (if it has changed, the binomial was moved to the |
---|
701 | // aux_list during the reduce_by(...)-procedure, and second_iter |
---|
702 | // already references a new binomial). |
---|
703 | if(second_reduced<=0) |
---|
704 | second_iter.next(); |
---|
705 | else |
---|
706 | second_reduced=0; |
---|
707 | |
---|
708 | } |
---|
709 | |
---|
710 | // same procedure for first_iter |
---|
711 | if(first_reduced<=0) |
---|
712 | first_iter.next(); |
---|
713 | else |
---|
714 | first_reduced=0; |
---|
715 | } |
---|
716 | |
---|
717 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
718 | |
---|
719 | |
---|
720 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
721 | |
---|
722 | list_iterator first_iter; |
---|
723 | |
---|
724 | Integer first_reduced=0; |
---|
725 | Integer second_reduced=0; |
---|
726 | // When reducing the ideal immediately by newly found generators, it |
---|
727 | // can happen that the binomials referenced by the iterators are |
---|
728 | // changed (including their support!) or even reduced to zero and then |
---|
729 | // deleted. We need to make sure that the iterators do not reference |
---|
730 | // freed memory in such a case. These two flags help us with this task. |
---|
731 | |
---|
732 | |
---|
733 | for(short i=0;i<Number_of_Lists;i++) |
---|
734 | { |
---|
735 | first_iter.set_to_list(generators[i]); |
---|
736 | |
---|
737 | while(first_iter.element_is_marked_done()==FALSE) |
---|
738 | // new generator, compute S-pairs with all following elements |
---|
739 | { |
---|
740 | binomial& bin1=first_iter.get_element(); |
---|
741 | first_iter.mark_element_done(); |
---|
742 | |
---|
743 | list_iterator second_iter(first_iter); |
---|
744 | second_iter.next(); |
---|
745 | |
---|
746 | // First search over the actual list. |
---|
747 | |
---|
748 | while((second_iter.is_at_end()==FALSE) && (first_reduced<=0)) |
---|
749 | { |
---|
750 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
751 | { |
---|
752 | binomial& bin2=second_iter.get_element(); |
---|
753 | |
---|
754 | // compute S-binomial |
---|
755 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
756 | |
---|
757 | // reduce S-binomial by the actual ideal generators |
---|
758 | reduce(S_bin,FALSE); |
---|
759 | |
---|
760 | if((S_bin)!=0) |
---|
761 | { |
---|
762 | // reduce the ideal generators by the S-binomial |
---|
763 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
764 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
765 | reduce_by(S_bin,first_iter,second_iter); |
---|
766 | aux_list._insert(S_bin); |
---|
767 | } |
---|
768 | else |
---|
769 | delete &S_bin; |
---|
770 | |
---|
771 | } |
---|
772 | |
---|
773 | // Move second_iter to the next element if its referenced binomial |
---|
774 | // has not changed (if it has changed, the binomial was moved to the |
---|
775 | // aux_list during the reduce_by(...)-procedure, and second_iter |
---|
776 | // already references a new binomial). |
---|
777 | if(second_reduced<=0) |
---|
778 | second_iter.next(); |
---|
779 | else |
---|
780 | second_reduced=0; |
---|
781 | |
---|
782 | } |
---|
783 | |
---|
784 | // Then search over the remaining lists. |
---|
785 | |
---|
786 | for(short j=i+1;(j<Number_of_Lists) && (first_reduced<=0);j++) |
---|
787 | { |
---|
788 | second_iter.set_to_list(generators[j]); |
---|
789 | |
---|
790 | while((second_iter.is_at_end()==FALSE) && (first_reduced<=0)) |
---|
791 | { |
---|
792 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
793 | { |
---|
794 | binomial& bin2=second_iter.get_element(); |
---|
795 | |
---|
796 | // compute S-binomial |
---|
797 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
798 | |
---|
799 | // reduce S-binomial by the actual ideal generators |
---|
800 | reduce(S_bin,FALSE); |
---|
801 | |
---|
802 | if((S_bin)!=0) |
---|
803 | { |
---|
804 | // reduce the ideal generators by the S-binomial |
---|
805 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
806 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
807 | reduce_by(S_bin,first_iter,second_iter); |
---|
808 | aux_list._insert(S_bin); |
---|
809 | } |
---|
810 | else |
---|
811 | delete& S_bin; |
---|
812 | |
---|
813 | } |
---|
814 | |
---|
815 | // Move second_iter to the next element if its referenced binomial |
---|
816 | // has not changed. |
---|
817 | if(second_reduced<=0) |
---|
818 | second_iter.next(); |
---|
819 | else |
---|
820 | second_reduced=0; |
---|
821 | } |
---|
822 | } |
---|
823 | |
---|
824 | // same procedure for first_iter |
---|
825 | if(first_reduced<=0) |
---|
826 | first_iter.next(); |
---|
827 | else |
---|
828 | first_reduced=0; |
---|
829 | |
---|
830 | } |
---|
831 | |
---|
832 | |
---|
833 | while(first_iter.is_at_end()==FALSE) |
---|
834 | // old generator, compute only S-pairs with the following new generators |
---|
835 | // As all generators in the actual list are old ones, we can |
---|
836 | // start iteration with the next list. |
---|
837 | { |
---|
838 | binomial& bin1=first_iter.get_element(); |
---|
839 | |
---|
840 | list_iterator second_iter(first_iter); |
---|
841 | second_iter.next(); |
---|
842 | |
---|
843 | for(short j=i+1;(j<Number_of_Lists) && (first_reduced<=0);j++) |
---|
844 | { |
---|
845 | second_iter.set_to_list(generators[j]); |
---|
846 | |
---|
847 | while((second_iter.element_is_marked_done()==FALSE) && |
---|
848 | (first_reduced<=0)) |
---|
849 | // consider only new generators |
---|
850 | { |
---|
851 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
852 | { |
---|
853 | binomial& bin2=second_iter.get_element(); |
---|
854 | |
---|
855 | // compute S-binomial |
---|
856 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
857 | |
---|
858 | // reduce S-binomial by the actual ideal generators |
---|
859 | reduce(S_bin,FALSE); |
---|
860 | |
---|
861 | if((S_bin)!=0) |
---|
862 | { |
---|
863 | // reduce the ideal generators by the S-binomial |
---|
864 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
865 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
866 | reduce_by(S_bin,first_iter,second_iter); |
---|
867 | aux_list._insert(S_bin); |
---|
868 | } |
---|
869 | else |
---|
870 | delete& S_bin; |
---|
871 | |
---|
872 | } |
---|
873 | |
---|
874 | // Move second_iter to the next element if its referenced binomial |
---|
875 | // has not changed. |
---|
876 | if(second_reduced<=0) |
---|
877 | second_iter.next(); |
---|
878 | else |
---|
879 | second_reduced=0; |
---|
880 | } |
---|
881 | } |
---|
882 | |
---|
883 | // same procedure for first_iter |
---|
884 | if(first_reduced<=0) |
---|
885 | first_iter.next(); |
---|
886 | else |
---|
887 | first_reduced=0; |
---|
888 | |
---|
889 | } |
---|
890 | } |
---|
891 | |
---|
892 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
893 | |
---|
894 | |
---|
895 | return(*this); |
---|
896 | } |
---|
897 | |
---|
898 | |
---|
899 | |
---|
900 | |
---|
901 | |
---|
902 | ideal& ideal::compute_actual_S_pairs_3() |
---|
903 | { |
---|
904 | // This routine is quite similar to the preceeding. |
---|
905 | // The main difference is that the computed S-binomials are not stored in the |
---|
906 | // aux_list, but in new_generators. This makes a difference when minimalizing |
---|
907 | // the S-binomials in the appropriate Groebner basis routine |
---|
908 | // (reduced_Groebner_basis_3) with the help of the procedure |
---|
909 | // minimalize_new_generators(...). |
---|
910 | // If NO_SUPPORT_DRIVEN_METHODS_EXTENDED are enabled, only the organization |
---|
911 | // of the minimalization is different. |
---|
912 | // If SUPPORT_DRIVEN_METHODS_EXTENDED are enabled, the minimalization can |
---|
913 | // use the support information. |
---|
914 | |
---|
915 | |
---|
916 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
917 | |
---|
918 | list_iterator first_iter(generators); |
---|
919 | |
---|
920 | Integer first_reduced=0; |
---|
921 | Integer second_reduced=0; |
---|
922 | // When reducing the ideal immediately by newly found generators, it |
---|
923 | // can happen that the binomials referenced by the iterators are |
---|
924 | // reduced to zero and then deleted. We need to make sure that the |
---|
925 | // iterators do not reference freed memory in such a case. These two |
---|
926 | // flags help us with this task. |
---|
927 | |
---|
928 | while(first_iter.element_is_marked_done()==FALSE) |
---|
929 | // new generator, compute S-pairs with all following generators |
---|
930 | { |
---|
931 | binomial& bin1=first_iter.get_element(); |
---|
932 | first_iter.mark_element_done(); |
---|
933 | |
---|
934 | list_iterator second_iter(first_iter); |
---|
935 | second_iter.next(); |
---|
936 | // This may be the dummy element. |
---|
937 | |
---|
938 | while((second_iter.is_at_end()==FALSE) && (first_reduced<=0)) |
---|
939 | { |
---|
940 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
941 | { |
---|
942 | binomial& bin2=second_iter.get_element(); |
---|
943 | |
---|
944 | // compute S-binomial |
---|
945 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
946 | |
---|
947 | // reduce S-binomial by the actual ideal generators |
---|
948 | reduce(S_bin,FALSE); |
---|
949 | |
---|
950 | if(S_bin!=0) |
---|
951 | { |
---|
952 | // reduce the ideal generators by the S-binomial |
---|
953 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
954 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
955 | reduce_by(S_bin,first_iter,second_iter); |
---|
956 | add_new_generator(S_bin); |
---|
957 | } |
---|
958 | else |
---|
959 | delete &S_bin; |
---|
960 | |
---|
961 | } |
---|
962 | |
---|
963 | // Move second_iter to the next element if its referenced binomial |
---|
964 | // has not changed (if it has changed, the binomial was moved to the |
---|
965 | // aux_list during the reduce_by(...)-procedure, and second_iter |
---|
966 | // already references a new binomial). |
---|
967 | if(second_reduced<=0) |
---|
968 | second_iter.next(); |
---|
969 | else |
---|
970 | second_reduced=0; |
---|
971 | |
---|
972 | } |
---|
973 | |
---|
974 | // same procedure for first_iter |
---|
975 | if(first_reduced<=0) |
---|
976 | first_iter.next(); |
---|
977 | else |
---|
978 | first_reduced=0; |
---|
979 | } |
---|
980 | |
---|
981 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
982 | |
---|
983 | |
---|
984 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
985 | |
---|
986 | list_iterator first_iter; |
---|
987 | |
---|
988 | Integer first_reduced=0; |
---|
989 | Integer second_reduced=0; |
---|
990 | // When reducing the ideal immediately by newly found generators, it |
---|
991 | // can happen that the binomials referenced by the iterators are |
---|
992 | // changed (including their support!) or even reduced to zero and then |
---|
993 | // deleted. We need to make sure that the iterators do not reference |
---|
994 | // freed memory in such a case. These two flags help us with this task. |
---|
995 | |
---|
996 | |
---|
997 | for(short i=0;i<Number_of_Lists;i++) |
---|
998 | { |
---|
999 | first_iter.set_to_list(generators[i]); |
---|
1000 | |
---|
1001 | while(first_iter.element_is_marked_done()==FALSE) |
---|
1002 | // new generator, compute S-pairs with all following elements |
---|
1003 | { |
---|
1004 | binomial& bin1=first_iter.get_element(); |
---|
1005 | first_iter.mark_element_done(); |
---|
1006 | |
---|
1007 | list_iterator second_iter(first_iter); |
---|
1008 | second_iter.next(); |
---|
1009 | |
---|
1010 | // First search over the actual list. |
---|
1011 | |
---|
1012 | while((second_iter.is_at_end()==FALSE) && (first_reduced<=0)) |
---|
1013 | { |
---|
1014 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
1015 | { |
---|
1016 | binomial& bin2=second_iter.get_element(); |
---|
1017 | |
---|
1018 | // compute S-binomial |
---|
1019 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
1020 | |
---|
1021 | // reduce S-binomial by the actual ideal generators |
---|
1022 | reduce(S_bin,FALSE); |
---|
1023 | |
---|
1024 | if((S_bin)!=0) |
---|
1025 | { |
---|
1026 | // reduce the ideal generators by the S-binomial |
---|
1027 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
1028 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
1029 | reduce_by(S_bin,first_iter,second_iter); |
---|
1030 | add_new_generator(S_bin); |
---|
1031 | } |
---|
1032 | else |
---|
1033 | delete &S_bin; |
---|
1034 | |
---|
1035 | } |
---|
1036 | |
---|
1037 | // Move second_iter to the next element if its referenced binomial |
---|
1038 | // has not changed (if it has changed, the binomial was moved to the |
---|
1039 | // aux_list during the reduce_by(...)-procedure, and second_iter |
---|
1040 | // already references a new binomial). |
---|
1041 | if(second_reduced<=0) |
---|
1042 | second_iter.next(); |
---|
1043 | else |
---|
1044 | second_reduced=0; |
---|
1045 | |
---|
1046 | } |
---|
1047 | |
---|
1048 | // Then search over the remaining lists. |
---|
1049 | |
---|
1050 | for(short j=i+1;(j<Number_of_Lists) && (first_reduced<=0);j++) |
---|
1051 | { |
---|
1052 | second_iter.set_to_list(generators[j]); |
---|
1053 | |
---|
1054 | while((second_iter.is_at_end()==FALSE) && (first_reduced<=0)) |
---|
1055 | { |
---|
1056 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
1057 | { |
---|
1058 | binomial& bin2=second_iter.get_element(); |
---|
1059 | |
---|
1060 | // compute S-binomial |
---|
1061 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
1062 | |
---|
1063 | // reduce S-binomial by the actual ideal generators |
---|
1064 | reduce(S_bin,FALSE); |
---|
1065 | |
---|
1066 | if((S_bin)!=0) |
---|
1067 | { |
---|
1068 | // reduce the ideal generators by the S-binomial |
---|
1069 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
1070 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
1071 | reduce_by(S_bin,first_iter,second_iter); |
---|
1072 | add_new_generator(S_bin); |
---|
1073 | } |
---|
1074 | else |
---|
1075 | delete& S_bin; |
---|
1076 | |
---|
1077 | } |
---|
1078 | |
---|
1079 | // Move second_iter to the next element if its referenced binomial |
---|
1080 | // has not changed. |
---|
1081 | if(second_reduced<=0) |
---|
1082 | second_iter.next(); |
---|
1083 | else |
---|
1084 | second_reduced=0; |
---|
1085 | } |
---|
1086 | } |
---|
1087 | |
---|
1088 | // same procedure for first_iter |
---|
1089 | if(first_reduced<=0) |
---|
1090 | first_iter.next(); |
---|
1091 | else |
---|
1092 | first_reduced=0; |
---|
1093 | |
---|
1094 | } |
---|
1095 | |
---|
1096 | |
---|
1097 | while(first_iter.is_at_end()==FALSE) |
---|
1098 | // old generator, compute only S-pairs with the following new generators |
---|
1099 | // As all generators in the actual list are old ones, we can |
---|
1100 | // start iteration with the next list. |
---|
1101 | { |
---|
1102 | binomial& bin1=first_iter.get_element(); |
---|
1103 | |
---|
1104 | list_iterator second_iter(first_iter); |
---|
1105 | second_iter.next(); |
---|
1106 | |
---|
1107 | for(short j=i+1;(j<Number_of_Lists) && (first_reduced<=0);j++) |
---|
1108 | { |
---|
1109 | second_iter.set_to_list(generators[j]); |
---|
1110 | |
---|
1111 | while((second_iter.element_is_marked_done()==FALSE) && |
---|
1112 | (first_reduced<=0)) |
---|
1113 | // consider only new generators |
---|
1114 | { |
---|
1115 | if(unnecessary_S_pair(first_iter,second_iter)==FALSE) |
---|
1116 | { |
---|
1117 | binomial& bin2=second_iter.get_element(); |
---|
1118 | |
---|
1119 | // compute S-binomial |
---|
1120 | binomial& S_bin=S_binomial(bin1,bin2,w); |
---|
1121 | |
---|
1122 | // reduce S-binomial by the actual ideal generators |
---|
1123 | reduce(S_bin,FALSE); |
---|
1124 | |
---|
1125 | if((S_bin)!=0) |
---|
1126 | { |
---|
1127 | // reduce the ideal generators by the S-binomial |
---|
1128 | first_reduced=bin1.head_reductions_by(S_bin); |
---|
1129 | second_reduced=bin2.head_reductions_by(S_bin); |
---|
1130 | reduce_by(S_bin,first_iter,second_iter); |
---|
1131 | add_new_generator(S_bin); |
---|
1132 | } |
---|
1133 | else |
---|
1134 | delete& S_bin; |
---|
1135 | |
---|
1136 | } |
---|
1137 | |
---|
1138 | // Move second_iter to the next element if its referenced binomial |
---|
1139 | // has not changed. |
---|
1140 | if(second_reduced<=0) |
---|
1141 | second_iter.next(); |
---|
1142 | else |
---|
1143 | second_reduced=0; |
---|
1144 | } |
---|
1145 | } |
---|
1146 | |
---|
1147 | // same procedure for first_iter |
---|
1148 | if(first_reduced<=0) |
---|
1149 | first_iter.next(); |
---|
1150 | else |
---|
1151 | first_reduced=0; |
---|
1152 | |
---|
1153 | } |
---|
1154 | } |
---|
1155 | |
---|
1156 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
1157 | |
---|
1158 | |
---|
1159 | // During the reduce_by(...)-routines, some reduced generators were |
---|
1160 | // perhaps moved to the aux_list. This list is emptied now: Like the |
---|
1161 | // computed S-pairs, its elements are moved to the list(s) new_generators. |
---|
1162 | // To avoid this construction, we would have to write a second version |
---|
1163 | // of the reduce_by(...)-procedure. The efficiency gains would however |
---|
1164 | // not be considerable. |
---|
1165 | |
---|
1166 | list_iterator iter(aux_list); |
---|
1167 | |
---|
1168 | while(iter.is_at_end()==FALSE) |
---|
1169 | { |
---|
1170 | add_new_generator(iter.get_element()); |
---|
1171 | iter.extract_element(); |
---|
1172 | } |
---|
1173 | |
---|
1174 | |
---|
1175 | return(*this); |
---|
1176 | } |
---|
1177 | |
---|
1178 | |
---|
1179 | |
---|
1180 | |
---|
1181 | |
---|
1182 | ////////////////////////////////////////////////////////////////////////////// |
---|
1183 | //////////// minimalization / autoreduction ////////////////////////////////// |
---|
1184 | ////////////////////////////////////////////////////////////////////////////// |
---|
1185 | |
---|
1186 | |
---|
1187 | |
---|
1188 | |
---|
1189 | |
---|
1190 | ideal& ideal::reduce_by(const binomial& bin, list_iterator& first_iter, |
---|
1191 | list_iterator& second_iter) |
---|
1192 | { |
---|
1193 | // This routine reduces the ideal by the argument binomial and takes |
---|
1194 | // care that the argument list iterators are not corrupted. |
---|
1195 | // Only head reductions are performed. |
---|
1196 | |
---|
1197 | |
---|
1198 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
1199 | |
---|
1200 | list_iterator iter(generators); |
---|
1201 | Integer reduced; |
---|
1202 | |
---|
1203 | while(iter.is_at_end()==FALSE) |
---|
1204 | { |
---|
1205 | binomial& actual=iter.get_element(); |
---|
1206 | |
---|
1207 | // reduce actual binomial by bin |
---|
1208 | reduced=actual.head_reductions_by(bin); |
---|
1209 | |
---|
1210 | if(reduced<=0) |
---|
1211 | iter.next(); |
---|
1212 | |
---|
1213 | else |
---|
1214 | // the actual binomial has changed and will be removed or |
---|
1215 | // moved to the aux_list |
---|
1216 | { |
---|
1217 | |
---|
1218 | #ifdef SL_LIST |
---|
1219 | |
---|
1220 | // If we use a simply linked list, we have to take care of the |
---|
1221 | // following binomial. |
---|
1222 | if(iter.next_is(first_iter)==TRUE) |
---|
1223 | first_iter=iter; |
---|
1224 | if(iter.next_is(second_iter)==TRUE) |
---|
1225 | second_iter=iter; |
---|
1226 | |
---|
1227 | #endif // SL_LIST |
---|
1228 | |
---|
1229 | |
---|
1230 | #ifdef DL_LIST |
---|
1231 | |
---|
1232 | // If we use a doubly linked list, we have to take care of the |
---|
1233 | // binomial itself. |
---|
1234 | if(iter==first_iter) |
---|
1235 | first_iter.next(); |
---|
1236 | if(iter==second_iter) |
---|
1237 | second_iter.next(); |
---|
1238 | |
---|
1239 | #endif // DL_LIST |
---|
1240 | |
---|
1241 | |
---|
1242 | // move changed generator to the aux_list or delete it |
---|
1243 | if(actual==0) |
---|
1244 | iter.delete_element(); |
---|
1245 | else |
---|
1246 | { |
---|
1247 | aux_list._insert(actual); |
---|
1248 | iter.extract_element(); |
---|
1249 | } |
---|
1250 | |
---|
1251 | size--; |
---|
1252 | } |
---|
1253 | } |
---|
1254 | |
---|
1255 | #endif // NO_SUPPORT_DRIVEN_METHOD_EXTENDED |
---|
1256 | |
---|
1257 | |
---|
1258 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
1259 | |
---|
1260 | short supp1=(first_iter.get_element()).head_support%Number_of_Lists; |
---|
1261 | short supp2=(second_iter.get_element()).head_support%Number_of_Lists; |
---|
1262 | |
---|
1263 | // Determine the lists over which we have to iterate. |
---|
1264 | // These are the lists with elements whose support contains the support |
---|
1265 | // of bin. |
---|
1266 | // List i has to be checked iff the set of bits in i that are 1 contains |
---|
1267 | // the set of bits in supp that are 1. |
---|
1268 | // Equivalent: List i has to be checked iff the set of bits in i |
---|
1269 | // that are 0 is contained in the set of bits of supp that are 0. |
---|
1270 | // With this formulation, we can use the subset tree as follows: |
---|
1271 | |
---|
1272 | short supp=bin.head_support%Number_of_Lists; |
---|
1273 | short inv_supp=Number_of_Lists-supp-1; |
---|
1274 | // This bit vector is the bitwise inverse of bin.head_support (restricted |
---|
1275 | // to the variables considered in the list indices. |
---|
1276 | |
---|
1277 | list_iterator iter; |
---|
1278 | Integer reduced; |
---|
1279 | |
---|
1280 | |
---|
1281 | for(short i=0;i<S.number_of_subsets[inv_supp];i++) |
---|
1282 | { |
---|
1283 | short actual_list=Number_of_Lists-S.subsets_of_support[inv_supp][i]-1; |
---|
1284 | // the actual list for iteration |
---|
1285 | // The support of S.subsets_of_support[inv_supp][i] as a bit vector |
---|
1286 | // is contained in that of inv_supp. |
---|
1287 | // I.e. the support of |
---|
1288 | // Number_of_Lists-S.subsets_of_support[inv_supp][i]-1 |
---|
1289 | // - which is the bitwise inverse of S.subsets_of_support[inv_supp][i] - |
---|
1290 | // contains the support of the bitwise inverse of inv_supp, hence the |
---|
1291 | // support of supp. |
---|
1292 | |
---|
1293 | if((actual_list==supp1) || (actual_list==supp2)) |
---|
1294 | // The lists referenced by first_iter and second_iter are tested |
---|
1295 | // separately to avoid unnecessary checks. |
---|
1296 | continue; |
---|
1297 | |
---|
1298 | iter.set_to_list(generators[actual_list]); |
---|
1299 | |
---|
1300 | while(iter.is_at_end()==FALSE) |
---|
1301 | { |
---|
1302 | binomial& actual=iter.get_element(); |
---|
1303 | |
---|
1304 | // reduce actual binomial by bin |
---|
1305 | reduced=actual.head_reductions_by(bin); |
---|
1306 | |
---|
1307 | if(reduced<=0) |
---|
1308 | iter.next(); |
---|
1309 | |
---|
1310 | else |
---|
1311 | // the actual binomial has changed and will be removed or |
---|
1312 | { |
---|
1313 | if(actual==0) |
---|
1314 | iter.delete_element(); |
---|
1315 | |
---|
1316 | else |
---|
1317 | { |
---|
1318 | aux_list._insert(actual); |
---|
1319 | iter.extract_element(); |
---|
1320 | } |
---|
1321 | |
---|
1322 | size--; |
---|
1323 | } |
---|
1324 | } |
---|
1325 | } |
---|
1326 | |
---|
1327 | // Now test the lists referenced by first_iter and second_iter. |
---|
1328 | |
---|
1329 | if(supp1==supp2) |
---|
1330 | // first_iter and second_iter reference the same list |
---|
1331 | { |
---|
1332 | if((supp1|supp)==supp1) |
---|
1333 | // support of bin contained in that of the element referenced by |
---|
1334 | // first_iter, else this list has not to be tested |
---|
1335 | { |
---|
1336 | iter.set_to_list(generators[supp1]); |
---|
1337 | |
---|
1338 | while(iter.is_at_end()==FALSE) |
---|
1339 | { |
---|
1340 | binomial& actual=iter.get_element(); |
---|
1341 | reduced=actual.head_reductions_by(bin); |
---|
1342 | if(reduced<=0) |
---|
1343 | iter.next(); |
---|
1344 | else |
---|
1345 | { |
---|
1346 | |
---|
1347 | #ifdef SL_LIST |
---|
1348 | |
---|
1349 | if(iter.next_is(first_iter)==TRUE) |
---|
1350 | first_iter=iter; |
---|
1351 | if(iter.next_is(second_iter)==TRUE) |
---|
1352 | second_iter=iter; |
---|
1353 | |
---|
1354 | #endif // SL_LIST |
---|
1355 | |
---|
1356 | #ifdef DL_LIST |
---|
1357 | |
---|
1358 | if(iter==first_iter) |
---|
1359 | first_iter.next(); |
---|
1360 | if(iter==second_iter) |
---|
1361 | second_iter.next(); |
---|
1362 | |
---|
1363 | #endif // DL_LIST |
---|
1364 | |
---|
1365 | if(actual==0) |
---|
1366 | iter.delete_element(); |
---|
1367 | else |
---|
1368 | { |
---|
1369 | aux_list._insert(actual); |
---|
1370 | iter.extract_element(); |
---|
1371 | } |
---|
1372 | |
---|
1373 | size--; |
---|
1374 | } |
---|
1375 | } |
---|
1376 | } |
---|
1377 | } |
---|
1378 | |
---|
1379 | else |
---|
1380 | // first_iter and second_iter reference different lists |
---|
1381 | { |
---|
1382 | if((supp1|supp)==supp1) |
---|
1383 | // support of bin contained in that of the element referenced by |
---|
1384 | // first_iter, else this list has not to be tested |
---|
1385 | { |
---|
1386 | iter.set_to_list(generators[supp1]); |
---|
1387 | |
---|
1388 | while(iter.is_at_end()==FALSE) |
---|
1389 | { |
---|
1390 | binomial& actual=iter.get_element(); |
---|
1391 | reduced=actual.head_reductions_by(bin); |
---|
1392 | if(reduced<=0) |
---|
1393 | iter.next(); |
---|
1394 | else |
---|
1395 | { |
---|
1396 | |
---|
1397 | #ifdef SL_LIST |
---|
1398 | |
---|
1399 | if(iter.next_is(first_iter)==TRUE) |
---|
1400 | first_iter=iter; |
---|
1401 | |
---|
1402 | #endif // SL_LIST |
---|
1403 | |
---|
1404 | #ifdef DL_LIST |
---|
1405 | |
---|
1406 | if(iter==first_iter) |
---|
1407 | first_iter.next(); |
---|
1408 | |
---|
1409 | #endif // DL_LIST |
---|
1410 | |
---|
1411 | if(actual==0) |
---|
1412 | iter.delete_element(); |
---|
1413 | else |
---|
1414 | { |
---|
1415 | aux_list._insert(actual); |
---|
1416 | iter.extract_element(); |
---|
1417 | } |
---|
1418 | |
---|
1419 | size--; |
---|
1420 | } |
---|
1421 | } |
---|
1422 | } |
---|
1423 | |
---|
1424 | if((supp2|supp)==supp2) |
---|
1425 | // support of bin contained in that of the element referenced by |
---|
1426 | // second_iter, else this list has not to be tested |
---|
1427 | { |
---|
1428 | iter.set_to_list(generators[supp2]); |
---|
1429 | |
---|
1430 | while(iter.is_at_end()==FALSE) |
---|
1431 | { |
---|
1432 | binomial& actual=iter.get_element(); |
---|
1433 | reduced=actual.head_reductions_by(bin); |
---|
1434 | if(reduced<=0) |
---|
1435 | iter.next(); |
---|
1436 | else |
---|
1437 | { |
---|
1438 | |
---|
1439 | #ifdef SL_LIST |
---|
1440 | |
---|
1441 | if(iter.next_is(second_iter)==TRUE) |
---|
1442 | second_iter=iter; |
---|
1443 | |
---|
1444 | #endif // SL_LIST |
---|
1445 | |
---|
1446 | #ifdef DL_LIST |
---|
1447 | |
---|
1448 | if(iter==second_iter) |
---|
1449 | second_iter.next(); |
---|
1450 | |
---|
1451 | #endif // DL_LIST |
---|
1452 | |
---|
1453 | if(actual==0) |
---|
1454 | iter.delete_element(); |
---|
1455 | else |
---|
1456 | { |
---|
1457 | aux_list._insert(actual); |
---|
1458 | iter.extract_element(); |
---|
1459 | } |
---|
1460 | |
---|
1461 | size--; |
---|
1462 | } |
---|
1463 | } |
---|
1464 | } |
---|
1465 | } |
---|
1466 | |
---|
1467 | #endif |
---|
1468 | |
---|
1469 | return *this; |
---|
1470 | |
---|
1471 | } |
---|
1472 | |
---|
1473 | |
---|
1474 | |
---|
1475 | |
---|
1476 | |
---|
1477 | ideal& ideal::minimalize_S_pairs() |
---|
1478 | { |
---|
1479 | // This routine implements a very simple minimalization method. We iterate |
---|
1480 | // over the S-pair lists with two iterators, interreducing the two referenced |
---|
1481 | // binomials. Remember that the S-pair list does not use the "head_reduced"- |
---|
1482 | // flags. The iteration is repeated as long as some interreduction is done. |
---|
1483 | |
---|
1484 | list_iterator first_iter; |
---|
1485 | short found; |
---|
1486 | // to control if a reduction has occurred during the actual iteration |
---|
1487 | |
---|
1488 | do |
---|
1489 | { |
---|
1490 | |
---|
1491 | first_iter.set_to_list(aux_list); |
---|
1492 | found=0; |
---|
1493 | // no reduction occured yet |
---|
1494 | |
---|
1495 | while(first_iter.is_at_end()==FALSE) |
---|
1496 | { |
---|
1497 | |
---|
1498 | binomial& bin1=first_iter.get_element(); |
---|
1499 | short first_changed=0; |
---|
1500 | // to control if the first element has been reduced |
---|
1501 | |
---|
1502 | // look at all following binomials |
---|
1503 | list_iterator second_iter(first_iter); |
---|
1504 | second_iter.next(); |
---|
1505 | // this may be the dummy element |
---|
1506 | |
---|
1507 | while(second_iter.is_at_end()==FALSE) |
---|
1508 | { |
---|
1509 | binomial& bin2=second_iter.get_element(); |
---|
1510 | short second_changed=0; |
---|
1511 | |
---|
1512 | if(bin1.reduce_head_by(bin2,w)!=0) |
---|
1513 | // head of first binomial can be reduced by second |
---|
1514 | { |
---|
1515 | |
---|
1516 | if(bin1!=0) |
---|
1517 | found=1; |
---|
1518 | // found has not to be set if a binomial is reduced to zero |
---|
1519 | // (then there are no new binomials) |
---|
1520 | |
---|
1521 | else |
---|
1522 | // the binomial referenced by bin1 is zero |
---|
1523 | { |
---|
1524 | |
---|
1525 | #ifdef SL_LIST |
---|
1526 | |
---|
1527 | if(first_iter.next_is(second_iter)) |
---|
1528 | second_iter.next(); |
---|
1529 | |
---|
1530 | #endif // SL_LIST |
---|
1531 | |
---|
1532 | first_iter.delete_element(); |
---|
1533 | first_changed=1; |
---|
1534 | } |
---|
1535 | |
---|
1536 | break; |
---|
1537 | // Breaks the while-loop. |
---|
1538 | // As the element referenced by first_iter has changed, |
---|
1539 | // the iteration with the second iterator can be restarted. |
---|
1540 | // (We try to reduce as many elements as possible in one iteration.) |
---|
1541 | } |
---|
1542 | |
---|
1543 | |
---|
1544 | if(bin2.reduce_head_by(bin1,w)!=0) |
---|
1545 | // head of second binomial can be reduced by first |
---|
1546 | { |
---|
1547 | |
---|
1548 | if(bin2!=0) |
---|
1549 | found=1; |
---|
1550 | // found has not to be set if a binomial is reduced to zero |
---|
1551 | // (then there are no new binomials) |
---|
1552 | |
---|
1553 | else |
---|
1554 | // binomial referenced by bin2 is zero |
---|
1555 | { |
---|
1556 | second_iter.delete_element(); |
---|
1557 | second_changed=1; |
---|
1558 | } |
---|
1559 | |
---|
1560 | // As the second iterator always references an element coming |
---|
1561 | // after first_iter's element in the generator list, we do not |
---|
1562 | // pay attention to the deletion... |
---|
1563 | } |
---|
1564 | |
---|
1565 | if(second_changed==0) |
---|
1566 | second_iter.next(); |
---|
1567 | } |
---|
1568 | |
---|
1569 | |
---|
1570 | // Now second_iter has reached the end of the generator list or the |
---|
1571 | // element referenced by first_iter has been reduced...The iteration |
---|
1572 | // is continued with a new (or changed) first binomial. |
---|
1573 | |
---|
1574 | if(first_changed==0) |
---|
1575 | first_iter.next(); |
---|
1576 | } |
---|
1577 | |
---|
1578 | } |
---|
1579 | while(found==1); |
---|
1580 | |
---|
1581 | // When leaving the loop, no generators have been interreduced during |
---|
1582 | // the last iteration. |
---|
1583 | |
---|
1584 | return *this; |
---|
1585 | } |
---|
1586 | |
---|
1587 | |
---|
1588 | |
---|
1589 | |
---|
1590 | |
---|
1591 | ideal& ideal::minimalize_new_generators() |
---|
1592 | { |
---|
1593 | // This routine is very similar to the following one, minimalize(). |
---|
1594 | // The only difference is that we interreduce the elements stored in |
---|
1595 | // new_generators instead of those stored in generators. |
---|
1596 | // The size of the ideal has not to be manipulated hereby. |
---|
1597 | |
---|
1598 | |
---|
1599 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
1600 | |
---|
1601 | list_iterator first_iter; |
---|
1602 | short found; |
---|
1603 | // to control if a reduction has occurred during the actual iteration |
---|
1604 | |
---|
1605 | do |
---|
1606 | { |
---|
1607 | first_iter.set_to_list(new_generators); |
---|
1608 | found=0; |
---|
1609 | // no reduction occured yet |
---|
1610 | |
---|
1611 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
1612 | // only the first element is tested for this flag |
---|
1613 | // the second may be an old one |
---|
1614 | { |
---|
1615 | binomial& bin1=first_iter.get_element(); |
---|
1616 | short first_changed=0; |
---|
1617 | // to control if the first element has been reduced |
---|
1618 | |
---|
1619 | // look at all following binomials |
---|
1620 | list_iterator second_iter(first_iter); |
---|
1621 | second_iter.next(); |
---|
1622 | // this may be the dummy element |
---|
1623 | |
---|
1624 | while(second_iter.is_at_end()==FALSE) |
---|
1625 | { |
---|
1626 | binomial& bin2=second_iter.get_element(); |
---|
1627 | |
---|
1628 | if(bin1.reduce_head_by(bin2,w)!=0) |
---|
1629 | // head of first binomial can be reduced by second |
---|
1630 | { |
---|
1631 | |
---|
1632 | #ifdef SL_LIST |
---|
1633 | |
---|
1634 | // The binomial referenced by first_iter will be deleted or |
---|
1635 | // extracted. When using a simply linked list, this also affects |
---|
1636 | // the following element. We need to assure that this element does |
---|
1637 | // not reference freed memory. |
---|
1638 | if(first_iter.next_is(second_iter)) |
---|
1639 | second_iter.next(); |
---|
1640 | |
---|
1641 | #endif // SL_LIST |
---|
1642 | |
---|
1643 | if(bin1!=0) |
---|
1644 | { |
---|
1645 | found=1; |
---|
1646 | // found has not to be set if a binomial is reduced to zero |
---|
1647 | // (then there are no new binomials to insert) |
---|
1648 | |
---|
1649 | aux_list._insert(bin1); |
---|
1650 | first_iter.extract_element(); |
---|
1651 | // moved changed binomial to aux_list |
---|
1652 | } |
---|
1653 | |
---|
1654 | else |
---|
1655 | first_iter.delete_element(); |
---|
1656 | |
---|
1657 | |
---|
1658 | first_changed=1; |
---|
1659 | break; |
---|
1660 | // As the binomial referenced by first_iter has changed, |
---|
1661 | // the iteration with the second iterator can be restarted. |
---|
1662 | // (We try to reduce as many elements as possible in one iteration.) |
---|
1663 | } |
---|
1664 | |
---|
1665 | |
---|
1666 | if(bin2.reduce_head_by(bin1,w)!=0) |
---|
1667 | // head of second binomial can be reduced by first |
---|
1668 | { |
---|
1669 | // Here we do not have to pay attention to the deletion or the |
---|
1670 | // extraction of the element referenced by second_iter because |
---|
1671 | // the element referenced by second_iter always comes after the |
---|
1672 | // element referenced by first_iter in new_generators. |
---|
1673 | |
---|
1674 | if(bin2!=0) |
---|
1675 | { |
---|
1676 | found=1; |
---|
1677 | // found has not to be set if a binomial is reduced to zero |
---|
1678 | // (then there are no new binomials to insert) |
---|
1679 | |
---|
1680 | aux_list._insert(bin2); |
---|
1681 | second_iter.extract_element(); |
---|
1682 | // move the element referenced by second_iter to aux_list |
---|
1683 | } |
---|
1684 | |
---|
1685 | else |
---|
1686 | second_iter.delete_element(); |
---|
1687 | |
---|
1688 | // Here it makes not sense to restart iteration because the |
---|
1689 | // deletion sets the pointers as desired. |
---|
1690 | } |
---|
1691 | |
---|
1692 | else |
---|
1693 | // no reduction possible |
---|
1694 | second_iter.next(); |
---|
1695 | |
---|
1696 | } |
---|
1697 | |
---|
1698 | // Now second_iter has reached the end of the list new_generators or the |
---|
1699 | // binomial referenced first_iter has been reduced...The iteration |
---|
1700 | // is continued with a new (or changed) first binomial. |
---|
1701 | |
---|
1702 | if(first_changed==0) |
---|
1703 | first_iter.next(); |
---|
1704 | } |
---|
1705 | |
---|
1706 | |
---|
1707 | // Now we have found all currently possible reductions. |
---|
1708 | // The elements remaining in new_generators cannot be interreduced |
---|
1709 | // and are marked head_reduced. |
---|
1710 | |
---|
1711 | first_iter.set_to_list(new_generators); |
---|
1712 | // if(first_iter.is_at_end()==FALSE) |
---|
1713 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
1714 | { |
---|
1715 | first_iter.mark_element_head_reduced(); |
---|
1716 | first_iter.next(); |
---|
1717 | } |
---|
1718 | |
---|
1719 | |
---|
1720 | // Now reinsert reduced elements. |
---|
1721 | |
---|
1722 | first_iter.set_to_list(aux_list); |
---|
1723 | |
---|
1724 | while(first_iter.is_at_end()==FALSE) |
---|
1725 | { |
---|
1726 | binomial& bin=first_iter.get_element(); |
---|
1727 | |
---|
1728 | reduce(bin,FALSE); |
---|
1729 | // The binomial was only reduced by one other binomial before it was |
---|
1730 | // moved to aux_list. To reduce it by all other binomials now can |
---|
1731 | // diminish the number of iterations (do-while-loop). |
---|
1732 | |
---|
1733 | if(bin==0) |
---|
1734 | first_iter.delete_element(); |
---|
1735 | else |
---|
1736 | { |
---|
1737 | add_new_generator(bin); |
---|
1738 | first_iter.extract_element(); |
---|
1739 | } |
---|
1740 | |
---|
1741 | } |
---|
1742 | |
---|
1743 | } |
---|
1744 | while(found==1); |
---|
1745 | |
---|
1746 | // When leaving the loop, no generators have been interreduced during |
---|
1747 | // the last iteration; we are done. |
---|
1748 | |
---|
1749 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
1750 | |
---|
1751 | |
---|
1752 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
1753 | |
---|
1754 | list_iterator first_iter; |
---|
1755 | list_iterator second_iter; |
---|
1756 | short found; |
---|
1757 | // to control if a reduction has occurred during the actual iteration |
---|
1758 | |
---|
1759 | do |
---|
1760 | { |
---|
1761 | found=0; |
---|
1762 | // no reduction occurred yet |
---|
1763 | |
---|
1764 | for(short i=0;i<Number_of_Lists;i++) |
---|
1765 | { |
---|
1766 | first_iter.set_to_list(new_generators[i]); |
---|
1767 | |
---|
1768 | // First try to reduce the binomials that are marked unreduced. |
---|
1769 | |
---|
1770 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
1771 | // all other elements have to be tested for interreduction |
---|
1772 | { |
---|
1773 | |
---|
1774 | binomial& bin=first_iter.get_element(); |
---|
1775 | Integer changed=0; |
---|
1776 | // binomial referenced by bin not yet reduced |
---|
1777 | |
---|
1778 | // Look for head reductions: |
---|
1779 | // Iterate over the lists that could contain reducers for the head of bin. |
---|
1780 | // The list containing bin is tested separately to avoid an interreduction |
---|
1781 | // of a binomial by itself respectively unnecessary checks for this when the |
---|
1782 | // two iterators reference different lists. |
---|
1783 | |
---|
1784 | for(short j=0;(j<S.number_of_subsets[i]-1)&&(changed==0);j++) |
---|
1785 | { |
---|
1786 | second_iter.set_to_list(new_generators[S.subsets_of_support[i][j]]); |
---|
1787 | // This is the j-th list among the new_generator lists with elements |
---|
1788 | // whose support is a subset of that of i. |
---|
1789 | // The support of i is just the head support of bin (restricted |
---|
1790 | // to the corresponding variables). |
---|
1791 | |
---|
1792 | while((second_iter.is_at_end()==FALSE)&&(changed==0)) |
---|
1793 | { |
---|
1794 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
1795 | |
---|
1796 | if(changed!=0) |
---|
1797 | // bin has been reduced |
---|
1798 | { |
---|
1799 | if(bin!=0) |
---|
1800 | { |
---|
1801 | found=1; |
---|
1802 | // found has only to be set if the binomial has not been |
---|
1803 | // reduced to zero (else there are no new binomials) |
---|
1804 | |
---|
1805 | aux_list._insert(bin); |
---|
1806 | first_iter.extract_element(); |
---|
1807 | } |
---|
1808 | else |
---|
1809 | first_iter.delete_element(); |
---|
1810 | } |
---|
1811 | second_iter.next(); |
---|
1812 | } |
---|
1813 | } |
---|
1814 | |
---|
1815 | // The list new_generators[i] |
---|
1816 | // =new_generators[S.subsets_of_support[i][S.number_of_subsets[i]-1]] |
---|
1817 | // has to be tested separately to avoid a reduction of the actual |
---|
1818 | // binomial by itself. |
---|
1819 | |
---|
1820 | if(changed==0) |
---|
1821 | // binomial referenced by first_iter has not yet been reduced |
---|
1822 | { |
---|
1823 | second_iter.set_to_list(new_generators[i]); |
---|
1824 | |
---|
1825 | while((second_iter.is_at_end()==FALSE) && (changed==0)) |
---|
1826 | { |
---|
1827 | if(second_iter!=first_iter) |
---|
1828 | // the two iterators do not reference the same element |
---|
1829 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
1830 | |
---|
1831 | if(changed!=0) |
---|
1832 | // bin has been reduced |
---|
1833 | { |
---|
1834 | |
---|
1835 | #ifdef SL_LIST |
---|
1836 | |
---|
1837 | // bin will be deleted ar extracted - maybe dangerous for |
---|
1838 | // second_iter |
---|
1839 | if(first_iter.next_is(second_iter)) |
---|
1840 | second_iter.next(); |
---|
1841 | |
---|
1842 | #endif // SL_LIST |
---|
1843 | |
---|
1844 | if(bin!=0) |
---|
1845 | { |
---|
1846 | found=1; |
---|
1847 | aux_list._insert(bin); |
---|
1848 | first_iter.extract_element(); |
---|
1849 | } |
---|
1850 | else |
---|
1851 | first_iter.delete_element(); |
---|
1852 | } |
---|
1853 | |
---|
1854 | else |
---|
1855 | // bin has not been reduced |
---|
1856 | second_iter.next(); |
---|
1857 | } |
---|
1858 | } |
---|
1859 | |
---|
1860 | if(changed==0) |
---|
1861 | first_iter.next(); |
---|
1862 | // Else first_iter has already been set to the next element by deletion |
---|
1863 | // or extraction. |
---|
1864 | } |
---|
1865 | |
---|
1866 | |
---|
1867 | // Now try to reduce the binomials that are marked reduced. |
---|
1868 | |
---|
1869 | while(first_iter.is_at_end()==FALSE) |
---|
1870 | // only unreduced elements have to be tested for interreduction |
---|
1871 | { |
---|
1872 | binomial& bin=first_iter.get_element(); |
---|
1873 | Integer changed=0; |
---|
1874 | // binomial referenced by bin not yet reduced |
---|
1875 | |
---|
1876 | // Look for head reductions: |
---|
1877 | // Iterate over the lists that could contain reducers for the head of bin. |
---|
1878 | // The list containing bin is tested separately to avoid an interreduction |
---|
1879 | // of a binomial by itself respectively unnecessary checks for this when the |
---|
1880 | // two iterators reference different lists. |
---|
1881 | |
---|
1882 | for(short j=0;(j<S.number_of_subsets[i]-1)&&(changed==0);j++) |
---|
1883 | { |
---|
1884 | second_iter.set_to_list(new_generators[S.subsets_of_support[i][j]]); |
---|
1885 | // This is the j-th list among the new_generators lists with elements |
---|
1886 | // whose support is a subset of that of i. |
---|
1887 | // The support of i is just the head support of bin (restricted |
---|
1888 | // to the corresponding variables). |
---|
1889 | |
---|
1890 | while((second_iter.element_is_marked_head_reduced()==FALSE) && |
---|
1891 | (changed==0)) |
---|
1892 | { |
---|
1893 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
1894 | |
---|
1895 | if(changed!=0) |
---|
1896 | // bin has been reduced |
---|
1897 | { |
---|
1898 | if(bin!=0) |
---|
1899 | { |
---|
1900 | found=1; |
---|
1901 | // found has only to be set if the binomial has not been |
---|
1902 | // reduced to zero (else there are no new binomials) |
---|
1903 | aux_list._insert(bin); |
---|
1904 | first_iter.extract_element(); |
---|
1905 | } |
---|
1906 | else |
---|
1907 | first_iter.delete_element(); |
---|
1908 | } |
---|
1909 | second_iter.next(); |
---|
1910 | } |
---|
1911 | } |
---|
1912 | |
---|
1913 | // The list new_generators[i] |
---|
1914 | // =new_generators[S.subsets_of_support[i][S.number_of_subsets[i]-1]] |
---|
1915 | // has to be tested separately to avoid a reduction of the actual |
---|
1916 | // binomial by itself. |
---|
1917 | |
---|
1918 | if(changed==0) |
---|
1919 | // binomial referenced by first_iter has not yet been reduced |
---|
1920 | { |
---|
1921 | second_iter.set_to_list(new_generators[i]); |
---|
1922 | |
---|
1923 | while((second_iter.element_is_marked_head_reduced()==FALSE) && |
---|
1924 | (changed==0)) |
---|
1925 | { |
---|
1926 | if(second_iter!=first_iter) |
---|
1927 | // the two iterators do not reference the same element |
---|
1928 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
1929 | |
---|
1930 | if(changed!=0) |
---|
1931 | // bin has been reduced |
---|
1932 | { |
---|
1933 | |
---|
1934 | #ifdef SL_LIST |
---|
1935 | |
---|
1936 | // bin will be deleted ar extracted - maybe dangerous for |
---|
1937 | // second_iter |
---|
1938 | if(first_iter.next_is(second_iter)) |
---|
1939 | second_iter.next(); |
---|
1940 | |
---|
1941 | #endif // SL_LIST |
---|
1942 | |
---|
1943 | if(bin!=0) |
---|
1944 | { |
---|
1945 | found=1; |
---|
1946 | aux_list._insert(bin); |
---|
1947 | first_iter.extract_element(); |
---|
1948 | } |
---|
1949 | else |
---|
1950 | first_iter.delete_element(); |
---|
1951 | } |
---|
1952 | |
---|
1953 | else |
---|
1954 | // bin has not been reduced |
---|
1955 | second_iter.next(); |
---|
1956 | } |
---|
1957 | } |
---|
1958 | |
---|
1959 | if(changed==0) |
---|
1960 | first_iter.next(); |
---|
1961 | // Else first_iter has already been set to the next element by deletion |
---|
1962 | // or extraction. |
---|
1963 | } |
---|
1964 | |
---|
1965 | } |
---|
1966 | |
---|
1967 | |
---|
1968 | // Now we have found all currently possible reductions. |
---|
1969 | // The elements remaining in the new_generator lists cannot be interreduced |
---|
1970 | // and are marked reduced. |
---|
1971 | |
---|
1972 | for(int i=0;i<Number_of_Lists;i++) |
---|
1973 | { |
---|
1974 | first_iter.set_to_list(new_generators[i]); |
---|
1975 | if(first_iter.is_at_end()==FALSE) |
---|
1976 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
1977 | { |
---|
1978 | first_iter.mark_element_head_reduced(); |
---|
1979 | first_iter.next(); |
---|
1980 | } |
---|
1981 | } |
---|
1982 | |
---|
1983 | |
---|
1984 | // Now reinsert reduced elements |
---|
1985 | // It seems to be quite unimportant for the performance if an element is |
---|
1986 | // completely reduced before reinsertion or not. |
---|
1987 | |
---|
1988 | first_iter.set_to_list(aux_list); |
---|
1989 | while(first_iter.is_at_end()==FALSE) |
---|
1990 | { |
---|
1991 | binomial& bin=first_iter.get_element(); |
---|
1992 | reduce(bin,FALSE); |
---|
1993 | |
---|
1994 | if(bin==0) |
---|
1995 | first_iter.delete_element(); |
---|
1996 | else |
---|
1997 | { |
---|
1998 | add_new_generator(bin); |
---|
1999 | first_iter.extract_element(); |
---|
2000 | } |
---|
2001 | } |
---|
2002 | |
---|
2003 | } |
---|
2004 | while(found==1); |
---|
2005 | |
---|
2006 | // When leaving the loop, no generators have been interreduced during |
---|
2007 | // the last iteration; we are done. |
---|
2008 | |
---|
2009 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2010 | |
---|
2011 | |
---|
2012 | return(*this); |
---|
2013 | |
---|
2014 | } |
---|
2015 | |
---|
2016 | |
---|
2017 | |
---|
2018 | |
---|
2019 | |
---|
2020 | ideal& ideal::minimalize() |
---|
2021 | { |
---|
2022 | // For a better overview, the code for NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2023 | // and SUPPORT_DRIVEN_METHODS_EXTENDED is completetly separated in this |
---|
2024 | // function. Note that th iteration methods are quite different for those |
---|
2025 | // two possibilities. |
---|
2026 | |
---|
2027 | |
---|
2028 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2029 | |
---|
2030 | // For technical simplicity, the interreduction is done as follows: |
---|
2031 | // We iterate over the generators with two iterators. |
---|
2032 | // For each binomial pair, we examine if one binomialŽs head can be |
---|
2033 | // reduced by the other. If this is the case, the reducible binomial is |
---|
2034 | // reduced and moved to the aux_list if it is not 0, else deleted. |
---|
2035 | // After one iteration, the elements of the aux_list are reinserted; |
---|
2036 | // then the interreduction is restarted until no new elements are found. |
---|
2037 | |
---|
2038 | // The above method of deleting and inserting is chosen for the following |
---|
2039 | // reasons: |
---|
2040 | // - The order undone elements - done elements in the generator lists |
---|
2041 | // is not destroyed. Newly found elements are automatically marked |
---|
2042 | // undone when they are reinserted. |
---|
2043 | // The S-pair computation can as usually make use of this fact. |
---|
2044 | // - In analogy, the order head_unreduced elements - head_reduced elements |
---|
2045 | // is not destroyed. Remark that an undone element can never be reduced, as |
---|
2046 | // reduction is only done after an S-pair computation. Newly found |
---|
2047 | // elements are automatically marked unreduced. With the "head_reduced"- |
---|
2048 | // flag we make sure that any binomial pair is tested only once for |
---|
2049 | // interreduction during the whole algorithm. |
---|
2050 | |
---|
2051 | list_iterator first_iter; |
---|
2052 | short found; |
---|
2053 | // to control if a reduction has occurred during the actual iteration |
---|
2054 | |
---|
2055 | do |
---|
2056 | { |
---|
2057 | first_iter.set_to_list(generators); |
---|
2058 | found=0; |
---|
2059 | // no reduction occured yet |
---|
2060 | |
---|
2061 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
2062 | // only the first element is tested for this flag |
---|
2063 | // the second may be an old one |
---|
2064 | { |
---|
2065 | binomial& bin1=first_iter.get_element(); |
---|
2066 | short first_changed=0; |
---|
2067 | // to control if the first element has been reduced |
---|
2068 | |
---|
2069 | // look at all following binomials |
---|
2070 | list_iterator second_iter(first_iter); |
---|
2071 | second_iter.next(); |
---|
2072 | // this may be the dummy element |
---|
2073 | |
---|
2074 | while(second_iter.is_at_end()==FALSE) |
---|
2075 | { |
---|
2076 | binomial& bin2=second_iter.get_element(); |
---|
2077 | |
---|
2078 | if(bin1.reduce_head_by(bin2,w)!=0) |
---|
2079 | // head of first binomial can be reduced by second |
---|
2080 | { |
---|
2081 | |
---|
2082 | #ifdef SL_LIST |
---|
2083 | |
---|
2084 | // The binomial referenced by first_iter will be deleted or |
---|
2085 | // extracted. When using a simply linked list, this also affects |
---|
2086 | // the following element. We need to assure that this element does |
---|
2087 | // not reference freed memory. |
---|
2088 | if(first_iter.next_is(second_iter)) |
---|
2089 | second_iter.next(); |
---|
2090 | |
---|
2091 | #endif // SL_LIST |
---|
2092 | |
---|
2093 | if(bin1!=0) |
---|
2094 | { |
---|
2095 | found=1; |
---|
2096 | // found has not to be set if a binomial is reduced to zero |
---|
2097 | // (then there are no new binomials to insert) |
---|
2098 | |
---|
2099 | aux_list._insert(bin1); |
---|
2100 | first_iter.extract_element(); |
---|
2101 | // moved changed binomial to aux_list |
---|
2102 | } |
---|
2103 | |
---|
2104 | else |
---|
2105 | first_iter.delete_element(); |
---|
2106 | |
---|
2107 | |
---|
2108 | first_changed=1; |
---|
2109 | size--; |
---|
2110 | break; |
---|
2111 | // As the binomial referenced by first_iter has changed, |
---|
2112 | // the iteration with the second iterator can be restarted. |
---|
2113 | // (We try to reduce as many elements as possible in one iteration.) |
---|
2114 | } |
---|
2115 | |
---|
2116 | |
---|
2117 | if(bin2.reduce_head_by(bin1,w)!=0) |
---|
2118 | // head of second binomial can be reduced by first |
---|
2119 | { |
---|
2120 | // Here we do not have to pay attention to the deletion or the |
---|
2121 | // extraction of the element referenced by second_iter because |
---|
2122 | // the element referenced by second_iter always comes after the |
---|
2123 | // element referenced by first_iter in the generator list. |
---|
2124 | |
---|
2125 | if(bin2!=0) |
---|
2126 | { |
---|
2127 | found=1; |
---|
2128 | // found has not to be set if a binomial is reduced to zero |
---|
2129 | // (then there are no new binomials to insert) |
---|
2130 | |
---|
2131 | aux_list._insert(bin2); |
---|
2132 | second_iter.extract_element(); |
---|
2133 | // move the element referenced by second_iter to aux_list |
---|
2134 | } |
---|
2135 | |
---|
2136 | else |
---|
2137 | second_iter.delete_element(); |
---|
2138 | |
---|
2139 | size--; |
---|
2140 | // Here it makes not sense to restart iteration because the |
---|
2141 | // deletion sets the pointers as desired. |
---|
2142 | } |
---|
2143 | |
---|
2144 | else |
---|
2145 | // no reduction possible |
---|
2146 | second_iter.next(); |
---|
2147 | |
---|
2148 | } |
---|
2149 | |
---|
2150 | // Now second_iter has reached the end of the generator list or the |
---|
2151 | // binomial referenced first_iter has been reduced...The iteration |
---|
2152 | // is continued with a new (or changed) first binomial. |
---|
2153 | |
---|
2154 | if(first_changed==0) |
---|
2155 | first_iter.next(); |
---|
2156 | } |
---|
2157 | |
---|
2158 | |
---|
2159 | // Now we have found all currently possible reductions. |
---|
2160 | // The elements remaining in the generator list cannot be interreduced |
---|
2161 | // and are marked head_reduced. |
---|
2162 | |
---|
2163 | first_iter.set_to_list(generators); |
---|
2164 | // if(first_iter.is_at_end()==FALSE) |
---|
2165 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
2166 | { |
---|
2167 | first_iter.mark_element_head_reduced(); |
---|
2168 | first_iter.next(); |
---|
2169 | } |
---|
2170 | |
---|
2171 | |
---|
2172 | // Now reinsert reduced elements. |
---|
2173 | |
---|
2174 | first_iter.set_to_list(aux_list); |
---|
2175 | |
---|
2176 | while(first_iter.is_at_end()==FALSE) |
---|
2177 | { |
---|
2178 | binomial& bin=first_iter.get_element(); |
---|
2179 | |
---|
2180 | reduce(bin,FALSE); |
---|
2181 | // The binomial was only reduced by one other generator before it was |
---|
2182 | // moved to aux_list. To reduce it by all other generators now can |
---|
2183 | // diminish the number of iterations (do-while-loop). |
---|
2184 | |
---|
2185 | if(bin==0) |
---|
2186 | first_iter.delete_element(); |
---|
2187 | else |
---|
2188 | { |
---|
2189 | generators.insert(bin); |
---|
2190 | // We do not call the add_generator(...)-routine because we do not |
---|
2191 | // want number_of_new_binomials to be incremented. |
---|
2192 | size++; |
---|
2193 | first_iter.extract_element(); |
---|
2194 | } |
---|
2195 | |
---|
2196 | } |
---|
2197 | |
---|
2198 | } |
---|
2199 | while(found==1); |
---|
2200 | |
---|
2201 | // When leaving the loop, no generators have been interreduced during |
---|
2202 | // the last iteration; we are done. |
---|
2203 | |
---|
2204 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2205 | |
---|
2206 | |
---|
2207 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2208 | |
---|
2209 | // In this case, the reduction has to be organized in a different way to |
---|
2210 | // use the support information to its full extend. Without the support |
---|
2211 | // methods, we test interreduction symmetrically: if we have a pair of |
---|
2212 | // generators, we test if generator 1 can be reduced by generator 2 AND |
---|
2213 | // if generator 2 can be reduced by generator 1. So each unordered pair is |
---|
2214 | // considered only once. |
---|
2215 | // If we would implement the same for the support methods, the second head |
---|
2216 | // reduction could not use the support information. |
---|
2217 | // For this reason, we test ordered pairs: For a given generator, we |
---|
2218 | // try to reduce his head by all other generators, considering its head |
---|
2219 | // support vector. |
---|
2220 | |
---|
2221 | // The method of moving changed binomials to aux_list and later reinserting |
---|
2222 | // them is kept. When using SUPPORT_DRIVEN_METHODS_EXTENDED, it is even |
---|
2223 | // necessary to choose such a method because the head support of some |
---|
2224 | // binomials may change, too, a fact that requires the list structure to be |
---|
2225 | // rebuilt. |
---|
2226 | |
---|
2227 | list_iterator first_iter; |
---|
2228 | list_iterator second_iter; |
---|
2229 | short found; |
---|
2230 | // to control if a reduction has occurred during the actual iteration |
---|
2231 | |
---|
2232 | do |
---|
2233 | { |
---|
2234 | found=0; |
---|
2235 | // no reduction occurred yet |
---|
2236 | |
---|
2237 | for(short i=0;i<Number_of_Lists;i++) |
---|
2238 | { |
---|
2239 | first_iter.set_to_list(generators[i]); |
---|
2240 | |
---|
2241 | // First try to reduce the binomials that are marked unreduced. |
---|
2242 | |
---|
2243 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
2244 | // all other elements have to be tested for interreduction |
---|
2245 | { |
---|
2246 | |
---|
2247 | binomial& bin=first_iter.get_element(); |
---|
2248 | Integer changed=0; |
---|
2249 | // binomial referenced by bin not yet reduced |
---|
2250 | |
---|
2251 | // Look for head reductions: |
---|
2252 | // Iterate over the lists that could contain reducers for the head of bin. |
---|
2253 | // The list containing bin is tested separately to avoid an interreduction |
---|
2254 | // of a binomial by itself respectively unnecessary checks for this when the |
---|
2255 | // two iterators reference different lists. |
---|
2256 | |
---|
2257 | for(short j=0;(j<S.number_of_subsets[i]-1)&&(changed==0);j++) |
---|
2258 | { |
---|
2259 | second_iter.set_to_list(generators[S.subsets_of_support[i][j]]); |
---|
2260 | // This is the j-th list among the generator lists with elements |
---|
2261 | // whose support is a subset of that of i. |
---|
2262 | // The support of i is just the head support of bin (restricted |
---|
2263 | // to the corresponding variables). |
---|
2264 | |
---|
2265 | while((second_iter.is_at_end()==FALSE)&&(changed==0)) |
---|
2266 | { |
---|
2267 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
2268 | |
---|
2269 | if(changed!=0) |
---|
2270 | // bin has been reduced |
---|
2271 | { |
---|
2272 | if(bin!=0) |
---|
2273 | { |
---|
2274 | found=1; |
---|
2275 | // found has only to be set if the binomial has not been |
---|
2276 | // reduced to zero (else there are no new binomials) |
---|
2277 | |
---|
2278 | aux_list._insert(bin); |
---|
2279 | first_iter.extract_element(); |
---|
2280 | } |
---|
2281 | else |
---|
2282 | first_iter.delete_element(); |
---|
2283 | |
---|
2284 | size--; |
---|
2285 | } |
---|
2286 | second_iter.next(); |
---|
2287 | } |
---|
2288 | } |
---|
2289 | |
---|
2290 | // The list generators[i] |
---|
2291 | // =generators[S.subsets_of_support[i][S.number_of_subsets[i]-1]] |
---|
2292 | // has to be tested separately to avoid a reduction of the actual |
---|
2293 | // binomial by itself. |
---|
2294 | |
---|
2295 | if(changed==0) |
---|
2296 | // binomial referenced by first_iter has not yet been reduced |
---|
2297 | { |
---|
2298 | second_iter.set_to_list(generators[i]); |
---|
2299 | |
---|
2300 | while((second_iter.is_at_end()==FALSE) && (changed==0)) |
---|
2301 | { |
---|
2302 | if(second_iter!=first_iter) |
---|
2303 | // the two iterators do not reference the same element |
---|
2304 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
2305 | |
---|
2306 | if(changed!=0) |
---|
2307 | // bin has been reduced |
---|
2308 | { |
---|
2309 | |
---|
2310 | #ifdef SL_LIST |
---|
2311 | |
---|
2312 | // bin will be deleted ar extracted - maybe dangerous for |
---|
2313 | // second_iter |
---|
2314 | if(first_iter.next_is(second_iter)) |
---|
2315 | second_iter.next(); |
---|
2316 | |
---|
2317 | #endif // SL_LIST |
---|
2318 | |
---|
2319 | if(bin!=0) |
---|
2320 | { |
---|
2321 | found=1; |
---|
2322 | aux_list._insert(bin); |
---|
2323 | first_iter.extract_element(); |
---|
2324 | } |
---|
2325 | else |
---|
2326 | first_iter.delete_element(); |
---|
2327 | |
---|
2328 | size--; |
---|
2329 | } |
---|
2330 | |
---|
2331 | else |
---|
2332 | // bin has not been reduced |
---|
2333 | second_iter.next(); |
---|
2334 | } |
---|
2335 | } |
---|
2336 | |
---|
2337 | if(changed==0) |
---|
2338 | first_iter.next(); |
---|
2339 | // Else first_iter has already been set to the next element by deletion |
---|
2340 | // or extraction. |
---|
2341 | } |
---|
2342 | |
---|
2343 | |
---|
2344 | // Now try to reduce the binomials that are marked reduced. |
---|
2345 | |
---|
2346 | while(first_iter.is_at_end()==FALSE) |
---|
2347 | // only unreduced elements have to be tested for interreduction |
---|
2348 | { |
---|
2349 | binomial& bin=first_iter.get_element(); |
---|
2350 | Integer changed=0; |
---|
2351 | // binomial referenced by bin not yet reduced |
---|
2352 | |
---|
2353 | // Look for head reductions: |
---|
2354 | // Iterate over the lists that could contain reducers for the head of bin. |
---|
2355 | // The list containing bin is tested separately to avoid an interreduction |
---|
2356 | // of a binomial by itself respectively unnecessary checks for this when the |
---|
2357 | // two iterators reference different lists. |
---|
2358 | |
---|
2359 | for(short j=0;(j<S.number_of_subsets[i]-1)&&(changed==0);j++) |
---|
2360 | { |
---|
2361 | second_iter.set_to_list(generators[S.subsets_of_support[i][j]]); |
---|
2362 | // This is the j-th list among the generator lists with elements |
---|
2363 | // whose support is a subset of that of i. |
---|
2364 | // The support of i is just the head support of bin (restricted |
---|
2365 | // to the corresponding variables). |
---|
2366 | |
---|
2367 | while((second_iter.element_is_marked_head_reduced()==FALSE) && |
---|
2368 | (changed==0)) |
---|
2369 | { |
---|
2370 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
2371 | |
---|
2372 | if(changed!=0) |
---|
2373 | // bin has been reduced |
---|
2374 | { |
---|
2375 | if(bin!=0) |
---|
2376 | { |
---|
2377 | found=1; |
---|
2378 | // found has only to be set if the binomial has not been |
---|
2379 | // reduced to zero (else there are no new binomials) |
---|
2380 | aux_list._insert(bin); |
---|
2381 | first_iter.extract_element(); |
---|
2382 | } |
---|
2383 | else |
---|
2384 | first_iter.delete_element(); |
---|
2385 | |
---|
2386 | size--; |
---|
2387 | } |
---|
2388 | second_iter.next(); |
---|
2389 | } |
---|
2390 | } |
---|
2391 | |
---|
2392 | // The list generators[i] |
---|
2393 | // =generators[S.subsets_of_support[i][S.number_of_subsets[i]-1]] |
---|
2394 | // has to be tested separately to avoid a reduction of the actual |
---|
2395 | // binomial by itself. |
---|
2396 | |
---|
2397 | if(changed==0) |
---|
2398 | // binomial referenced by first_iter has not yet been reduced |
---|
2399 | { |
---|
2400 | second_iter.set_to_list(generators[i]); |
---|
2401 | |
---|
2402 | while((second_iter.element_is_marked_head_reduced()==FALSE) && |
---|
2403 | (changed==0)) |
---|
2404 | { |
---|
2405 | if(second_iter!=first_iter) |
---|
2406 | // the two iterators do not reference the same element |
---|
2407 | changed=bin.reduce_head_by(second_iter.get_element(),w); |
---|
2408 | |
---|
2409 | if(changed!=0) |
---|
2410 | // bin has been reduced |
---|
2411 | { |
---|
2412 | |
---|
2413 | #ifdef SL_LIST |
---|
2414 | |
---|
2415 | // bin will be deleted ar extracted - maybe dangerous for |
---|
2416 | // second_iter |
---|
2417 | if(first_iter.next_is(second_iter)) |
---|
2418 | second_iter.next(); |
---|
2419 | |
---|
2420 | #endif // SL_LIST |
---|
2421 | |
---|
2422 | if(bin!=0) |
---|
2423 | { |
---|
2424 | found=1; |
---|
2425 | aux_list._insert(bin); |
---|
2426 | first_iter.extract_element(); |
---|
2427 | } |
---|
2428 | else |
---|
2429 | first_iter.delete_element(); |
---|
2430 | |
---|
2431 | size--; |
---|
2432 | } |
---|
2433 | |
---|
2434 | else |
---|
2435 | // bin has not been reduced |
---|
2436 | second_iter.next(); |
---|
2437 | } |
---|
2438 | } |
---|
2439 | |
---|
2440 | if(changed==0) |
---|
2441 | first_iter.next(); |
---|
2442 | // Else first_iter has already been set to the next element by deletion |
---|
2443 | // or extraction. |
---|
2444 | } |
---|
2445 | |
---|
2446 | } |
---|
2447 | |
---|
2448 | |
---|
2449 | // Now we have found all currently possible reductions. |
---|
2450 | // The elements remaining in the generator lists cannot be interreduced |
---|
2451 | // and are marked reduced. |
---|
2452 | |
---|
2453 | for(int i=0;i<Number_of_Lists;i++) |
---|
2454 | { |
---|
2455 | first_iter.set_to_list(generators[i]); |
---|
2456 | if(first_iter.is_at_end()==FALSE) |
---|
2457 | while(first_iter.element_is_marked_head_reduced()==FALSE) |
---|
2458 | { |
---|
2459 | first_iter.mark_element_head_reduced(); |
---|
2460 | first_iter.next(); |
---|
2461 | } |
---|
2462 | } |
---|
2463 | |
---|
2464 | |
---|
2465 | // Now reinsert reduced elements |
---|
2466 | // It seems to be quite unimportant for the performance if an element is |
---|
2467 | // completely reduced before reinsertion or not. |
---|
2468 | |
---|
2469 | first_iter.set_to_list(aux_list); |
---|
2470 | while(first_iter.is_at_end()==FALSE) |
---|
2471 | { |
---|
2472 | binomial& bin=first_iter.get_element(); |
---|
2473 | reduce(bin,FALSE); |
---|
2474 | |
---|
2475 | if(bin==0) |
---|
2476 | first_iter.delete_element(); |
---|
2477 | else |
---|
2478 | { |
---|
2479 | generators[bin.head_support%Number_of_Lists].insert(bin); |
---|
2480 | size++; |
---|
2481 | // We do not call the add_generator(...)-routine because we do not |
---|
2482 | // want number_of_new_binomials to be incremented. |
---|
2483 | first_iter.extract_element(); |
---|
2484 | } |
---|
2485 | } |
---|
2486 | |
---|
2487 | } |
---|
2488 | while(found==1); |
---|
2489 | |
---|
2490 | // When leaving the loop, no generators have been interreduced during |
---|
2491 | // the last iteration; we are done. |
---|
2492 | |
---|
2493 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2494 | |
---|
2495 | |
---|
2496 | return(*this); |
---|
2497 | } |
---|
2498 | |
---|
2499 | |
---|
2500 | |
---|
2501 | |
---|
2502 | |
---|
2503 | ideal& ideal::final_reduce() |
---|
2504 | { |
---|
2505 | // During BuchbergerŽs algorithm, we perform only head reductions |
---|
2506 | // (minimalizations). This strategy showed to be a little more efficient |
---|
2507 | // than the strategy to do reduce the ideal always completely. |
---|
2508 | // This method leads to a minimal, but in general not to the reduced Groebner |
---|
2509 | // basis. The actual procedure reduces such a minimal basis at the end of |
---|
2510 | // BuchbergerŽs algorithm. It will probably cause problems when called |
---|
2511 | // in the course of the algorithm. For an explaination of this fact, see |
---|
2512 | // the following comment. |
---|
2513 | |
---|
2514 | minimalize(); |
---|
2515 | |
---|
2516 | // Now there remain only tail reductions. They are quite simple: Each |
---|
2517 | // binomial's tail is reduced as long as possible. As no binomial can be |
---|
2518 | // reduced to zero by that and a binomial cannot reduce its own tail, |
---|
2519 | // we do not have to pay special attention to that (under the assumption |
---|
2520 | // that a real term ordering (i.e. a well-ordering) is used and that |
---|
2521 | // the head and the tail of the binomial are coorect with respect to this |
---|
2522 | // ordering). |
---|
2523 | |
---|
2524 | // Notice that the head can change because of a tail reduction due to the |
---|
2525 | // trivial factors elimination (the new head will always divide the |
---|
2526 | // old one). This change is especially dangerous if |
---|
2527 | // SUPPORT_DRIVEN_METHODS_EXTENDED are enabled: It may happen that the |
---|
2528 | // binomial is in the wrong list after a tail reduction. |
---|
2529 | // Furthermore, if a head change occurs, it may happen that the generating |
---|
2530 | // set is no more minimalized after this. So the reduction has to be restarted |
---|
2531 | // after such a head change (and the respective binomial has to be marked |
---|
2532 | // head_unreduced before). |
---|
2533 | // This does not seem to be very efficient. |
---|
2534 | |
---|
2535 | // For this reason, the reduction routine is only written for a final |
---|
2536 | // reduction (having already computed a Groebner basis of the ideal). |
---|
2537 | // This Groebner basis is first minimalized. After that, a head change during |
---|
2538 | // tail reduction is impossible because the head is already a minimal |
---|
2539 | // generator of the initial ideal (and the new head would divide the old). |
---|
2540 | |
---|
2541 | // However, this argumentation is only valid if the input ideal is saturated. |
---|
2542 | // In some algorithms (Hosten_Sturmfels...) this is not the case in |
---|
2543 | // intermediate steps. The final reduction may cause inconsistencies here. |
---|
2544 | // But as the list structure is rebuild after each intermediate Groebner |
---|
2545 | // basis calculation (change of the term ordering) and as the last Groebner |
---|
2546 | // basis calculation deals with a saturated ideal, the final result will be |
---|
2547 | // correct. |
---|
2548 | // (For non-saturated input ideals, the computed Groebner basis is in general |
---|
2549 | // not a Groebner basis of the input ideal, but one for an ideal "between" |
---|
2550 | // the input ideal and its saturation.) |
---|
2551 | |
---|
2552 | |
---|
2553 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2554 | |
---|
2555 | list_iterator first_iter; |
---|
2556 | |
---|
2557 | first_iter.set_to_list(generators); |
---|
2558 | |
---|
2559 | while(first_iter.is_at_end()==FALSE) |
---|
2560 | { |
---|
2561 | binomial& bin=first_iter.get_element(); |
---|
2562 | short changed; |
---|
2563 | // to control if bin has been reduced |
---|
2564 | |
---|
2565 | do |
---|
2566 | { |
---|
2567 | changed=0; |
---|
2568 | list_iterator second_iter; |
---|
2569 | second_iter.set_to_list(generators); |
---|
2570 | |
---|
2571 | while(second_iter.is_at_end()==FALSE) |
---|
2572 | { |
---|
2573 | changed+=bin.reduce_tail_by(second_iter.get_element(),w); |
---|
2574 | // As soon as a reduction occurs, changed is set to a value !=0. |
---|
2575 | second_iter.next(); |
---|
2576 | } |
---|
2577 | |
---|
2578 | } |
---|
2579 | while(changed>0); |
---|
2580 | |
---|
2581 | first_iter.next(); |
---|
2582 | } |
---|
2583 | |
---|
2584 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2585 | |
---|
2586 | |
---|
2587 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2588 | |
---|
2589 | // In this case, the reduction has to be organized in a slightly different |
---|
2590 | // way to use the support information to its full extend. |
---|
2591 | // As soon as an reduction has taken place, the iteration over the reducer |
---|
2592 | // lists is restarted using the new tail support information. |
---|
2593 | |
---|
2594 | list_iterator first_iter; |
---|
2595 | |
---|
2596 | for(short i=0;i<Number_of_Lists;i++) |
---|
2597 | { |
---|
2598 | first_iter.set_to_list(generators[i]); |
---|
2599 | |
---|
2600 | while(first_iter.is_at_end()==FALSE) |
---|
2601 | { |
---|
2602 | binomial& bin=first_iter.get_element(); |
---|
2603 | short changed; |
---|
2604 | // to control if bin has been reduced |
---|
2605 | |
---|
2606 | do |
---|
2607 | { |
---|
2608 | changed=0; |
---|
2609 | list_iterator second_iter; |
---|
2610 | |
---|
2611 | short supp=bin.tail_support%Number_of_Lists; |
---|
2612 | // determine the lists over which we have to iterate |
---|
2613 | |
---|
2614 | for(short j=0;(j<S.number_of_subsets[supp]) && (changed==0);j++) |
---|
2615 | { |
---|
2616 | second_iter.set_to_list(generators[S.subsets_of_support[supp][j]]); |
---|
2617 | // This is the j-th list among the generator lists with elements |
---|
2618 | // whose support is a subset of supp. |
---|
2619 | |
---|
2620 | while((second_iter.is_at_end()==FALSE) && (changed==0)) |
---|
2621 | { |
---|
2622 | changed=bin.reduce_tail_by(second_iter.get_element(),w); |
---|
2623 | // Here we can do a simple assignment; as the iteration is stopped |
---|
2624 | // as soon as some reduction is done, reduced cannot be reset to |
---|
2625 | // zero in this assignment. |
---|
2626 | second_iter.next(); |
---|
2627 | } |
---|
2628 | } |
---|
2629 | |
---|
2630 | } |
---|
2631 | while(changed>0); |
---|
2632 | |
---|
2633 | first_iter.next(); |
---|
2634 | } |
---|
2635 | } |
---|
2636 | |
---|
2637 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2638 | |
---|
2639 | return(*this); |
---|
2640 | } |
---|
2641 | |
---|
2642 | |
---|
2643 | |
---|
2644 | |
---|
2645 | |
---|
2646 | ////////////////////////////////////////////////////////////////////////////// |
---|
2647 | ////////////////////// auxiliary stuff /////////////////////////////////////// |
---|
2648 | ////////////////////////////////////////////////////////////////////////////// |
---|
2649 | |
---|
2650 | |
---|
2651 | |
---|
2652 | |
---|
2653 | |
---|
2654 | short ideal::add_new_generators() |
---|
2655 | { |
---|
2656 | // Reduces the binomials in the "new_generators" list(s) by the generators |
---|
2657 | // and moves them to the "generators" list(s). |
---|
2658 | |
---|
2659 | |
---|
2660 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2661 | |
---|
2662 | short result=0; |
---|
2663 | // element inserted? |
---|
2664 | |
---|
2665 | list_iterator iter(new_generators); |
---|
2666 | |
---|
2667 | while(iter.is_at_end()==FALSE) |
---|
2668 | { |
---|
2669 | binomial& bin=iter.get_element(); |
---|
2670 | reduce(bin,FALSE); |
---|
2671 | |
---|
2672 | if(bin==0) |
---|
2673 | iter.delete_element(); |
---|
2674 | else |
---|
2675 | { |
---|
2676 | add_generator(bin); |
---|
2677 | iter.extract_element(); |
---|
2678 | result=1; |
---|
2679 | } |
---|
2680 | } |
---|
2681 | |
---|
2682 | |
---|
2683 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2684 | |
---|
2685 | |
---|
2686 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2687 | |
---|
2688 | short result=0; |
---|
2689 | // element inserted? |
---|
2690 | |
---|
2691 | list_iterator iter; |
---|
2692 | |
---|
2693 | for(short i=0;i<Number_of_Lists;i++) |
---|
2694 | { |
---|
2695 | iter.set_to_list(new_generators[i]); |
---|
2696 | |
---|
2697 | while(iter.is_at_end()==FALSE) |
---|
2698 | { |
---|
2699 | binomial& bin=iter.get_element(); |
---|
2700 | reduce(bin,FALSE); |
---|
2701 | |
---|
2702 | if(bin==0) |
---|
2703 | iter.delete_element(); |
---|
2704 | else |
---|
2705 | { |
---|
2706 | add_generator(bin); |
---|
2707 | iter.extract_element(); |
---|
2708 | result=1; |
---|
2709 | } |
---|
2710 | } |
---|
2711 | } |
---|
2712 | |
---|
2713 | |
---|
2714 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2715 | |
---|
2716 | |
---|
2717 | return result; |
---|
2718 | } |
---|
2719 | |
---|
2720 | |
---|
2721 | |
---|
2722 | |
---|
2723 | |
---|
2724 | ///////////////////////////////////////////////////////////////////////////// |
---|
2725 | ///////////////////// binomial reduction //////////////////////////////////// |
---|
2726 | ///////////////////////////////////////////////////////////////////////////// |
---|
2727 | |
---|
2728 | |
---|
2729 | |
---|
2730 | |
---|
2731 | |
---|
2732 | binomial& ideal::reduce(binomial& bin, BOOLEAN complete=TRUE) const |
---|
2733 | { |
---|
2734 | // As bin is reduced by a fixed set of binomials, it is sufficient to do |
---|
2735 | // head reductions first, then tail reductions (cf. Pottier). |
---|
2736 | |
---|
2737 | list_iterator iter; |
---|
2738 | Integer reduced; |
---|
2739 | // to control if the binomial has been reduced during the actual iteration |
---|
2740 | |
---|
2741 | |
---|
2742 | #ifdef NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2743 | |
---|
2744 | do |
---|
2745 | { |
---|
2746 | iter.set_to_list(generators); |
---|
2747 | reduced=0; |
---|
2748 | // not yet reduced |
---|
2749 | |
---|
2750 | while(iter.is_at_end()==FALSE) |
---|
2751 | { |
---|
2752 | reduced+=bin.reduce_head_by(iter.get_element(),w); |
---|
2753 | // reduced is incremented (and so set to a value >0) as soon as bin |
---|
2754 | // is really reduced |
---|
2755 | iter.next(); |
---|
2756 | } |
---|
2757 | } |
---|
2758 | while((reduced>0) && (bin!=0)); |
---|
2759 | |
---|
2760 | if(complete==TRUE) |
---|
2761 | do |
---|
2762 | { |
---|
2763 | iter.set_to_list(generators); |
---|
2764 | reduced=0; |
---|
2765 | // not yet reduced |
---|
2766 | |
---|
2767 | while(iter.is_at_end()==FALSE) |
---|
2768 | { |
---|
2769 | reduced+=bin.reduce_tail_by(iter.get_element(),w); |
---|
2770 | // reduced is incremented (and so set to a value >0) as soon as bin |
---|
2771 | // is really reduced |
---|
2772 | iter.next(); |
---|
2773 | } |
---|
2774 | } |
---|
2775 | while((reduced>0) && (bin!=0)); |
---|
2776 | |
---|
2777 | #endif // NO_SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2778 | |
---|
2779 | |
---|
2780 | #ifdef SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2781 | |
---|
2782 | do |
---|
2783 | { |
---|
2784 | reduced=0; |
---|
2785 | // not yet reduced |
---|
2786 | |
---|
2787 | short supp=bin.head_support%Number_of_Lists; |
---|
2788 | // determine the lists over which we have to iterate |
---|
2789 | |
---|
2790 | // As soon as some reduction is done, the iteration is started with |
---|
2791 | // the new support information; so we do not finish iterations over lists |
---|
2792 | // that cannot contain reducers any more. |
---|
2793 | |
---|
2794 | for(short i=0;(i<S.number_of_subsets[supp]) && (reduced==0);i++) |
---|
2795 | { |
---|
2796 | iter.set_to_list(generators[S.subsets_of_support[supp][i]]); |
---|
2797 | // This is the i-th list among the generator lists with elements |
---|
2798 | // whose support is a subset of that of supp. |
---|
2799 | |
---|
2800 | while((iter.is_at_end()==FALSE)&&(reduced==0)) |
---|
2801 | { |
---|
2802 | reduced=bin.reduce_head_by(iter.get_element(),w); |
---|
2803 | // Here we can do a simple assignment; as the iteration is stopped |
---|
2804 | // as soon as some reduction is done, reduced cannot be reset to zero |
---|
2805 | // in this assignment. |
---|
2806 | iter.next(); |
---|
2807 | } |
---|
2808 | } |
---|
2809 | } |
---|
2810 | while((reduced>0) && (bin!=0)); |
---|
2811 | |
---|
2812 | if(complete==TRUE) |
---|
2813 | do |
---|
2814 | { |
---|
2815 | reduced=0; |
---|
2816 | // not yet reduced |
---|
2817 | |
---|
2818 | short supp=bin.tail_support%Number_of_Lists; |
---|
2819 | // determine the lists over which we have to iterate |
---|
2820 | |
---|
2821 | // As soon as some reduction is done, the iteration is started with |
---|
2822 | // the new support information; so we do not finish iterations over |
---|
2823 | // lists that cannot contain reducers any more. |
---|
2824 | |
---|
2825 | for(short i=0;(i<S.number_of_subsets[supp]) && (reduced==0);i++) |
---|
2826 | { |
---|
2827 | iter.set_to_list(generators[S.subsets_of_support[supp][i]]); |
---|
2828 | // This is the i-th list among the generator lists with elements |
---|
2829 | // whose support is a subset of that of supp. |
---|
2830 | |
---|
2831 | while((iter.is_at_end()==FALSE)&&(reduced==0)) |
---|
2832 | { |
---|
2833 | reduced=bin.reduce_tail_by(iter.get_element(),w); |
---|
2834 | // Here we can do a simple assignment; as the iteration is stopped |
---|
2835 | // as soon as some reduction is done, reduced cannot be reset to |
---|
2836 | // zero in this assignment |
---|
2837 | iter.next(); |
---|
2838 | } |
---|
2839 | } |
---|
2840 | } |
---|
2841 | while(reduced>0); |
---|
2842 | // bin cannot be reduced to zero by a tail reduction |
---|
2843 | |
---|
2844 | #endif // SUPPORT_DRIVEN_METHODS_EXTENDED |
---|
2845 | |
---|
2846 | return(bin); |
---|
2847 | } |
---|
2848 | |
---|
2849 | |
---|
2850 | |
---|
2851 | |
---|
2852 | |
---|
2853 | ////////////////////////////////////////////////////////////////////////////// |
---|
2854 | /////////// variants of BuchbergerŽs algorithm /////////////////////////////// |
---|
2855 | ////////////////////////////////////////////////////////////////////////////// |
---|
2856 | |
---|
2857 | |
---|
2858 | |
---|
2859 | |
---|
2860 | |
---|
2861 | ideal& ideal::reduced_Groebner_basis_1(const short& S_pair_criteria=11, |
---|
2862 | const float& interred_percentage=12.0) |
---|
2863 | { |
---|
2864 | // set flags for the use of the S-pair criteria |
---|
2865 | // for an explaination see in globals.h |
---|
2866 | rel_primeness=(S_pair_criteria & 1); |
---|
2867 | M_criterion=(S_pair_criteria & 2); |
---|
2868 | F_criterion=(S_pair_criteria & 4); |
---|
2869 | B_criterion=(S_pair_criteria & 8); |
---|
2870 | second_criterion=(S_pair_criteria & 16); |
---|
2871 | |
---|
2872 | interreduction_percentage=interred_percentage; |
---|
2873 | |
---|
2874 | short done; |
---|
2875 | // control variable for recognizing when Buchberger's algorithm has reached |
---|
2876 | // his end |
---|
2877 | |
---|
2878 | // first minimalize the initial generating system |
---|
2879 | minimalize(); |
---|
2880 | |
---|
2881 | do |
---|
2882 | { |
---|
2883 | done=1; |
---|
2884 | // no new generators found yet |
---|
2885 | |
---|
2886 | compute_actual_S_pairs_1(); |
---|
2887 | // compute the S-pairs of the actual generators |
---|
2888 | // These are stored in a unreduced form in aux_list. |
---|
2889 | |
---|
2890 | list_iterator S_pair_iter(aux_list); |
---|
2891 | // now reduce and insert the computed S-pairs |
---|
2892 | |
---|
2893 | while(S_pair_iter.is_at_end()==FALSE) |
---|
2894 | { |
---|
2895 | binomial& S_bin=S_pair_iter.get_element(); |
---|
2896 | reduce(S_bin,FALSE); |
---|
2897 | |
---|
2898 | if(S_bin!=0) |
---|
2899 | // new generator found |
---|
2900 | { |
---|
2901 | add_generator(S_bin); |
---|
2902 | S_pair_iter.extract_element(); |
---|
2903 | done=0; |
---|
2904 | // algorithm does not terminate when a new generator is found |
---|
2905 | } |
---|
2906 | else |
---|
2907 | S_pair_iter.delete_element(); |
---|
2908 | } |
---|
2909 | |
---|
2910 | // now all computed S-pairs are inserted as generators |
---|
2911 | // enough for a minimalization? |
---|
2912 | |
---|
2913 | if(interreduction_percentage>=0) |
---|
2914 | // intermediate interreductions allowed |
---|
2915 | { |
---|
2916 | if(number_of_new_binomials>=size*interreduction_percentage/100) |
---|
2917 | // enough new generators since last minimalization |
---|
2918 | { |
---|
2919 | minimalize(); |
---|
2920 | number_of_new_binomials=0; |
---|
2921 | } |
---|
2922 | } |
---|
2923 | |
---|
2924 | // now we restart the algorithm with the new generating system |
---|
2925 | // if the generating system has changed during the last iteration |
---|
2926 | |
---|
2927 | } |
---|
2928 | while(done==0); |
---|
2929 | // if done==1, all computed S-pairs reduced to zero |
---|
2930 | |
---|
2931 | // compute reduced from minimal Groebner basis |
---|
2932 | final_reduce(); |
---|
2933 | |
---|
2934 | return(*this); |
---|
2935 | } |
---|
2936 | |
---|
2937 | |
---|
2938 | |
---|
2939 | |
---|
2940 | |
---|
2941 | |
---|
2942 | ideal& ideal::reduced_Groebner_basis_1a(const short& S_pair_criteria=11, |
---|
2943 | const float& interred_percentage=12.0) |
---|
2944 | { |
---|
2945 | // set flags for the use of the S-pair criteria |
---|
2946 | // for an explaination see in globals.h |
---|
2947 | rel_primeness=(S_pair_criteria & 1); |
---|
2948 | M_criterion=(S_pair_criteria & 2); |
---|
2949 | F_criterion=(S_pair_criteria & 4); |
---|
2950 | B_criterion=(S_pair_criteria & 8); |
---|
2951 | second_criterion=(S_pair_criteria & 16); |
---|
2952 | |
---|
2953 | interreduction_percentage=interred_percentage; |
---|
2954 | |
---|
2955 | short done; |
---|
2956 | // control variable for recognizing when Buchberger's algorithm has reached |
---|
2957 | // his end |
---|
2958 | |
---|
2959 | // first minimalize the initial generating system |
---|
2960 | minimalize(); |
---|
2961 | |
---|
2962 | do |
---|
2963 | { |
---|
2964 | done=1; |
---|
2965 | // no new generators found yet |
---|
2966 | |
---|
2967 | compute_actual_S_pairs_1a(); |
---|
2968 | // compute the S-pairs of the actual generators |
---|
2969 | // These are stored in a unreduced form in aux_list. |
---|
2970 | // aux_list is ordered according to the idealŽs term ordering. |
---|
2971 | |
---|
2972 | list_iterator S_pair_iter(aux_list); |
---|
2973 | // now reduce and insert the computed S-pairs |
---|
2974 | |
---|
2975 | while(S_pair_iter.is_at_end()==FALSE) |
---|
2976 | { |
---|
2977 | binomial& S_bin=S_pair_iter.get_element(); |
---|
2978 | reduce(S_bin,FALSE); |
---|
2979 | |
---|
2980 | if(S_pair_iter.get_element()!=0) |
---|
2981 | // new generator found |
---|
2982 | { |
---|
2983 | add_generator(S_bin); |
---|
2984 | S_pair_iter.extract_element(); |
---|
2985 | done=0; |
---|
2986 | // algorithm does not terminate when a new generator is found |
---|
2987 | } |
---|
2988 | else |
---|
2989 | S_pair_iter.delete_element(); |
---|
2990 | } |
---|
2991 | |
---|
2992 | // now all computed S-pairs are inserted as generators |
---|
2993 | // enough for a minimalization? |
---|
2994 | |
---|
2995 | if(interreduction_percentage>=0) |
---|
2996 | // intermediate interreductions allowed |
---|
2997 | { |
---|
2998 | if(number_of_new_binomials>=size*interreduction_percentage/100) |
---|
2999 | // enough new generators since last minimalization |
---|
3000 | { |
---|
3001 | minimalize(); |
---|
3002 | number_of_new_binomials=0; |
---|
3003 | } |
---|
3004 | } |
---|
3005 | |
---|
3006 | // now we restart the algorithm with the new generating system |
---|
3007 | // if the generating system has changed during the last iteration |
---|
3008 | |
---|
3009 | } |
---|
3010 | while(done==0); |
---|
3011 | // if done==1, all computed S-pairs reduced to zero |
---|
3012 | |
---|
3013 | // compute reduced from minimal Groebner basis |
---|
3014 | final_reduce(); |
---|
3015 | |
---|
3016 | return(*this); |
---|
3017 | } |
---|
3018 | |
---|
3019 | |
---|
3020 | |
---|
3021 | |
---|
3022 | |
---|
3023 | ideal& ideal::reduced_Groebner_basis_2(const short& S_pair_criteria=11, |
---|
3024 | const float& interred_percentage=12.0) |
---|
3025 | { |
---|
3026 | // set flags for the use of the S-pair criteria |
---|
3027 | // for an explaination see in globals.h |
---|
3028 | rel_primeness=(S_pair_criteria & 1); |
---|
3029 | M_criterion=(S_pair_criteria & 2); |
---|
3030 | F_criterion=(S_pair_criteria & 4); |
---|
3031 | B_criterion=(S_pair_criteria & 8); |
---|
3032 | second_criterion=(S_pair_criteria & 16); |
---|
3033 | |
---|
3034 | interreduction_percentage=interred_percentage; |
---|
3035 | |
---|
3036 | short done; |
---|
3037 | // control variable for recognizing when Buchberger's algorithm has reached |
---|
3038 | // his end |
---|
3039 | |
---|
3040 | // first minimalize the initial generating system |
---|
3041 | minimalize(); |
---|
3042 | |
---|
3043 | do |
---|
3044 | { |
---|
3045 | done=1; |
---|
3046 | // no new generators found yet |
---|
3047 | |
---|
3048 | compute_actual_S_pairs_2(); |
---|
3049 | // compute the S-pairs of the actual generators |
---|
3050 | // These are stored in a reduced version in aux_list. |
---|
3051 | |
---|
3052 | minimalize_S_pairs(); |
---|
3053 | // minimalize the binomials in aux_list |
---|
3054 | // These are not only S-pairs, but also ideal generators that were |
---|
3055 | // reduced by an S-pair during the S-pair computation. |
---|
3056 | |
---|
3057 | list_iterator S_pair_iter(aux_list); |
---|
3058 | |
---|
3059 | if(S_pair_iter.is_at_end()==FALSE) |
---|
3060 | // Zero binomials are not inserted in aux_list during the S-pair |
---|
3061 | // computation; i.e. if aux_list is not empty, a further iteration step |
---|
3062 | // has to be done. |
---|
3063 | done=0; |
---|
3064 | |
---|
3065 | // now insert the computed S-pairs |
---|
3066 | while(S_pair_iter.is_at_end()==FALSE) |
---|
3067 | // S_pairs remaining |
---|
3068 | { |
---|
3069 | add_generator(S_pair_iter.get_element()); |
---|
3070 | S_pair_iter.extract_element(); |
---|
3071 | } |
---|
3072 | |
---|
3073 | // now all computed S-pairs are inserted as generators |
---|
3074 | // enough for a minimalization? |
---|
3075 | |
---|
3076 | if(interreduction_percentage>=0) |
---|
3077 | // intermediate interreductions allowed |
---|
3078 | { |
---|
3079 | if(number_of_new_binomials>=size*interreduction_percentage/100) |
---|
3080 | // enough new generators since last minimalization |
---|
3081 | { |
---|
3082 | minimalize(); |
---|
3083 | number_of_new_binomials=0; |
---|
3084 | } |
---|
3085 | } |
---|
3086 | |
---|
3087 | // now we restart the algorithm with the new generating system |
---|
3088 | // if the generating system has changed during the last iteration |
---|
3089 | |
---|
3090 | } |
---|
3091 | while(done==0); |
---|
3092 | // if done==1, all computed S-pairs reduced to zero |
---|
3093 | |
---|
3094 | // compute reduced from minimal Groebner basis |
---|
3095 | final_reduce(); |
---|
3096 | |
---|
3097 | return(*this); |
---|
3098 | } |
---|
3099 | |
---|
3100 | |
---|
3101 | |
---|
3102 | |
---|
3103 | |
---|
3104 | ideal& ideal::reduced_Groebner_basis_3(const short& S_pair_criteria=11, |
---|
3105 | const float& interred_percentage=12.0) |
---|
3106 | { |
---|
3107 | // set flags for the use of the S-pair criteria |
---|
3108 | // for an explaination see in globals.h |
---|
3109 | rel_primeness=(S_pair_criteria & 1); |
---|
3110 | M_criterion=(S_pair_criteria & 2); |
---|
3111 | F_criterion=(S_pair_criteria & 4); |
---|
3112 | B_criterion=(S_pair_criteria & 8); |
---|
3113 | second_criterion=(S_pair_criteria & 16); |
---|
3114 | |
---|
3115 | interreduction_percentage=interred_percentage; |
---|
3116 | |
---|
3117 | short not_done; |
---|
3118 | // control variable for recognizing when Buchberger's algorithm has reached |
---|
3119 | // his end |
---|
3120 | |
---|
3121 | // first minimalize the initial generating system |
---|
3122 | minimalize(); |
---|
3123 | |
---|
3124 | do |
---|
3125 | { |
---|
3126 | |
---|
3127 | compute_actual_S_pairs_3(); |
---|
3128 | // compute the S-pairs of the actual generators |
---|
3129 | // These are stored in areduced version in the list(s) new_generators. |
---|
3130 | |
---|
3131 | minimalize_new_generators(); |
---|
3132 | // minimalize the binomials in aux_list |
---|
3133 | // These are not only S-pairs, but also ideal generators that were |
---|
3134 | // reduced by an S-pair during the S-pair computation. |
---|
3135 | |
---|
3136 | not_done=add_new_generators(); |
---|
3137 | // move binomials from new_generators to generators |
---|
3138 | |
---|
3139 | // now all computed S-pairs are inserted as generators |
---|
3140 | // enough for a minimalization? |
---|
3141 | |
---|
3142 | if(interreduction_percentage>=0) |
---|
3143 | // intermediate interreductions allowed |
---|
3144 | { |
---|
3145 | if(number_of_new_binomials>=size*interreduction_percentage/100) |
---|
3146 | // enough new generators since last reduction |
---|
3147 | { |
---|
3148 | minimalize(); |
---|
3149 | number_of_new_binomials=0; |
---|
3150 | } |
---|
3151 | } |
---|
3152 | |
---|
3153 | // now we restart the algorithm with the new generating system |
---|
3154 | // if the generating system has changed during the last iteration |
---|
3155 | |
---|
3156 | } |
---|
3157 | while(not_done==1); |
---|
3158 | // if not_done==0, all computed S-pairs reduced to zero |
---|
3159 | |
---|
3160 | // compute reduced from minimal Groebner basis |
---|
3161 | final_reduce(); |
---|
3162 | |
---|
3163 | return(*this); |
---|
3164 | } |
---|
3165 | |
---|
3166 | |
---|
3167 | |
---|
3168 | |
---|
3169 | |
---|
3170 | ideal& ideal::reduced_Groebner_basis(const short& version=1, |
---|
3171 | const short& S_pair_criteria=11, |
---|
3172 | const float& interred_percentage=12.0) |
---|
3173 | { |
---|
3174 | switch(version) |
---|
3175 | { |
---|
3176 | case 0: |
---|
3177 | return reduced_Groebner_basis_1a(S_pair_criteria, interred_percentage); |
---|
3178 | case 1: |
---|
3179 | return reduced_Groebner_basis_1(S_pair_criteria, interred_percentage); |
---|
3180 | case 2: |
---|
3181 | return reduced_Groebner_basis_2(S_pair_criteria, interred_percentage); |
---|
3182 | case 3: |
---|
3183 | return reduced_Groebner_basis_3(S_pair_criteria, interred_percentage); |
---|
3184 | default: |
---|
3185 | cerr<<"WARNING: ideal& ideal::reduced_Groebner_basis(const short&, " |
---|
3186 | "const short&, const float&):\n" |
---|
3187 | "version argument out of range, nothing done"<<endl; |
---|
3188 | return*this; |
---|
3189 | } |
---|
3190 | } |
---|
3191 | |
---|
3192 | |
---|
3193 | |
---|
3194 | |
---|
3195 | |
---|
3196 | #endif // BUCHBERGER_CC |
---|