1 | |
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2 | |
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3 | |
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4 | #include <kernel/mod2.h> |
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5 | |
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6 | // include before anything to avoid clashes with stdio.h included elsewhere |
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7 | // #include <cstdio> |
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8 | |
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9 | #include <kernel/linear_algebra/MinorInterface.h> |
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10 | #include <kernel/linear_algebra/MinorProcessor.h> |
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11 | |
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12 | #include <polys/simpleideals.h> |
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13 | #include <coeffs/modulop.h> // for NV_MAX_PRIME |
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14 | |
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15 | #include <kernel/polys.h> |
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16 | #include <kernel/structs.h> |
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17 | #include <kernel/GBEngine/kstd1.h> |
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18 | #include <kernel/ideals.h> |
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19 | |
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20 | using namespace std; |
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21 | |
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22 | bool currRingIsOverIntegralDomain () |
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23 | { |
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24 | if (rField_is_Ring_PtoM(currRing)) return false; |
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25 | if (rField_is_Ring_2toM(currRing)) return false; |
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26 | if (rField_is_Ring_ModN(currRing)) return false; |
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27 | return true; |
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28 | } |
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29 | |
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30 | bool currRingIsOverField () |
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31 | { |
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32 | if (rField_is_Ring_PtoM(currRing)) return false; |
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33 | if (rField_is_Ring_2toM(currRing)) return false; |
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34 | if (rField_is_Ring_ModN(currRing)) return false; |
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35 | if (rField_is_Ring_Z(currRing)) return false; |
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36 | return true; |
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37 | } |
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38 | |
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39 | /* returns true iff the given polyArray has only number entries; |
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40 | if so, the int's corresponding to these numbers will be written |
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41 | into intArray[0..(length-1)]; |
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42 | the method assumes that both polyArray and intArray have valid |
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43 | entries for the indices 0..(length-1); |
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44 | after the call, zeroCounter contains the number of zero entries |
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45 | in the matrix */ |
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46 | bool arrayIsNumberArray (const poly* polyArray, const ideal iSB, |
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47 | const int length, int* intArray, |
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48 | poly* nfPolyArray, int& zeroCounter) |
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49 | { |
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50 | int n = 0; if (currRing != 0) n = currRing->N; |
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51 | int characteristic = 0; if (currRing != 0) characteristic = rChar(currRing); |
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52 | zeroCounter = 0; |
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53 | bool result = true; |
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54 | |
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55 | for (int i = 0; i < length; i++) |
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56 | { |
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57 | nfPolyArray[i] = pCopy(polyArray[i]); |
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58 | if (iSB != 0) nfPolyArray[i] = kNF(iSB, currRing->qideal, nfPolyArray[i]); |
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59 | if (nfPolyArray[i] == NULL) |
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60 | { |
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61 | intArray[i] = 0; |
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62 | zeroCounter++; |
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63 | } |
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64 | else |
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65 | { |
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66 | bool isConstant = true; |
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67 | for (int j = 1; j <= n; j++) |
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68 | if (pGetExp(nfPolyArray[i], j) > 0) |
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69 | isConstant = false; |
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70 | if (!isConstant) result = false; |
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71 | else |
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72 | { |
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73 | intArray[i] = n_Int(pGetCoeff(nfPolyArray[i]), currRing->cf); |
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74 | if (characteristic != 0) intArray[i] = intArray[i] % characteristic; |
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75 | if (intArray[i] == 0) zeroCounter++; |
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76 | } |
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77 | } |
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78 | } |
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79 | return result; |
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80 | } |
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81 | |
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82 | /* special implementation for the case that the matrix has only number entries; |
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83 | if i is not the zero pointer, then it is assumed to contain a std basis, and |
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84 | the number entries of the matrix are then assumed to be reduced w.r.t. i and |
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85 | modulo the characteristic of the gound field/ring; |
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86 | this method should also work when currRing == null, i.e. when no ring has |
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87 | been declared */ |
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88 | ideal getMinorIdeal_Int (const int* intMatrix, const int rowCount, |
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89 | const int columnCount, const int minorSize, |
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90 | const int k, const char* algorithm, |
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91 | const ideal i, const bool allDifferent) |
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92 | { |
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93 | /* setting up a MinorProcessor for matrices with integer entries: */ |
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94 | IntMinorProcessor mp; |
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95 | mp.defineMatrix(rowCount, columnCount, intMatrix); |
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96 | int *myRowIndices=new int[rowCount]; |
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97 | for (int j = 0; j < rowCount; j++) myRowIndices[j] = j; |
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98 | int *myColumnIndices=new int[columnCount]; |
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99 | for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j; |
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100 | mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices); |
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101 | mp.setMinorSize(minorSize); |
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102 | |
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103 | /* containers for all upcoming results: */ |
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104 | IntMinorValue theMinor; |
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105 | // int value = 0; |
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106 | int collectedMinors = 0; |
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107 | int characteristic = 0; if (currRing != 0) characteristic = rChar(currRing); |
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108 | |
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109 | /* the ideal to be returned: */ |
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110 | ideal iii = idInit(1); |
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111 | |
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112 | bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are requested, |
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113 | omitting zero minors */ |
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114 | bool duplicatesOk = (allDifferent ? false : true); |
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115 | int kk = ((k < 0) ? -k : k); /* absolute value of k */ |
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116 | |
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117 | /* looping over all minors: */ |
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118 | while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk))) |
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119 | { |
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120 | /* retrieving the next minor: */ |
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121 | theMinor = mp.getNextMinor(characteristic, i, algorithm); |
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122 | poly f = NULL; |
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123 | if (theMinor.getResult() != 0) f = pISet(theMinor.getResult()); |
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124 | if (idInsertPolyWithTests(iii, collectedMinors, f, zeroOk, duplicatesOk)) |
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125 | collectedMinors++; |
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126 | } |
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127 | |
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128 | /* before we return the result, let's omit zero generators |
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129 | in iii which come after the computed minors */ |
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130 | ideal jjj; |
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131 | if (collectedMinors == 0) jjj = idInit(1); |
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132 | else jjj = idCopyFirstK(iii, collectedMinors); |
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133 | idDelete(&iii); |
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134 | delete[] myColumnIndices; |
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135 | delete[] myRowIndices; |
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136 | return jjj; |
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137 | } |
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138 | |
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139 | /* special implementation for the case that the matrix has non-number, |
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140 | i.e., actual polynomial entries; |
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141 | if i is not the zero pointer than it is assumed to be a std basis (ideal), |
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142 | and the poly matrix is assumed to be already reduced w.r.t. i */ |
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143 | ideal getMinorIdeal_Poly (const poly* polyMatrix, const int rowCount, |
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144 | const int columnCount, const int minorSize, |
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145 | const int k, const char* algorithm, |
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146 | const ideal i, const bool allDifferent) |
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147 | { |
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148 | /* setting up a MinorProcessor for matrices with polynomial entries: */ |
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149 | PolyMinorProcessor mp; |
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150 | mp.defineMatrix(rowCount, columnCount, polyMatrix); |
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151 | int *myRowIndices=new int[rowCount]; |
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152 | for (int j = 0; j < rowCount; j++) myRowIndices[j] = j; |
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153 | int *myColumnIndices=new int[columnCount]; |
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154 | for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j; |
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155 | mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices); |
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156 | mp.setMinorSize(minorSize); |
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157 | |
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158 | /* containers for all upcoming results: */ |
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159 | PolyMinorValue theMinor; |
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160 | poly f = NULL; |
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161 | int collectedMinors = 0; |
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162 | |
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163 | /* the ideal to be returned: */ |
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164 | ideal iii = idInit(1); |
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165 | |
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166 | bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are |
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167 | requested, omitting zero minors */ |
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168 | bool duplicatesOk = (allDifferent ? false : true); |
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169 | int kk = ((k < 0) ? -k : k); /* absolute value of k */ |
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170 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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171 | printCounters ("starting", true); |
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172 | int qqq = 0; |
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173 | #endif |
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174 | /* looping over all minors: */ |
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175 | while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk))) |
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176 | { |
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177 | /* retrieving the next minor: */ |
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178 | theMinor = mp.getNextMinor(algorithm, i); |
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179 | #if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 1) |
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180 | qqq++; |
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181 | Print("after %d", qqq); |
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182 | printCounters ("-th minor", false); |
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183 | #endif |
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184 | f = theMinor.getResult(); |
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185 | if (idInsertPolyWithTests(iii, collectedMinors, pCopy(f), |
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186 | zeroOk, duplicatesOk)) |
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187 | collectedMinors++; |
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188 | } |
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189 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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190 | printCounters ("ending", true); |
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191 | #endif |
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192 | |
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193 | /* before we return the result, let's omit zero generators |
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194 | in iii which come after the computed minors */ |
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195 | idKeepFirstK(iii, collectedMinors); |
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196 | delete[] myColumnIndices; |
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197 | delete[] myRowIndices; |
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198 | return(iii); |
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199 | } |
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200 | |
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201 | ideal getMinorIdeal_toBeDone (const matrix mat, const int minorSize, |
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202 | const int k, const char* algorithm, |
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203 | const ideal i, const bool allDifferent) |
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204 | { |
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205 | int rowCount = mat->nrows; |
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206 | int columnCount = mat->ncols; |
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207 | poly* myPolyMatrix = (poly*)(mat->m); |
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208 | ideal iii; /* the ideal to be filled and returned */ |
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209 | int zz = 0; |
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210 | |
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211 | /* divert to special implementations for pure number matrices and actual |
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212 | polynomial matrices: */ |
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213 | int* myIntMatrix = new int [rowCount * columnCount]; |
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214 | poly* nfPolyMatrix = new poly[rowCount * columnCount]; |
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215 | if (arrayIsNumberArray(myPolyMatrix, i, rowCount * columnCount, |
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216 | myIntMatrix, nfPolyMatrix, zz)) |
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217 | iii = getMinorIdeal_Int(myIntMatrix, rowCount, columnCount, minorSize, k, |
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218 | algorithm, i, allDifferent); |
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219 | else |
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220 | { |
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221 | if ((k == 0) && (strcmp(algorithm, "Bareiss") == 0) |
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222 | && (!rField_is_Ring_Z(currRing)) && (!allDifferent)) |
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223 | { |
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224 | /* In this case, we call an optimized procedure, dating back to |
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225 | Wilfried Pohl. It may be used whenever |
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226 | - all minors are requested, |
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227 | - requested minors need not be mutually distinct, and |
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228 | - coefficients come from a field (i.e., Z is also not allowed |
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229 | for this implementation). */ |
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230 | iii = (i == 0 ? idMinors(mat, minorSize) : idMinors(mat, minorSize, i)); |
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231 | } |
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232 | else |
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233 | { |
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234 | iii = getMinorIdeal_Poly(nfPolyMatrix, rowCount, columnCount, minorSize, |
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235 | k, algorithm, i, allDifferent); |
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236 | } |
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237 | } |
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238 | |
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239 | /* clean up */ |
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240 | delete [] myIntMatrix; |
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241 | for (int j = 0; j < rowCount * columnCount; j++) pDelete(&nfPolyMatrix[j]); |
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242 | delete [] nfPolyMatrix; |
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243 | |
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244 | return iii; |
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245 | } |
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246 | |
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247 | /* When called with algorithm == "Bareiss", the coefficients are assumed |
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248 | to come from a field or from a ring which does not have zero-divisors |
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249 | (other than 0), i.e. from an integral domain. |
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250 | E.g. Bareiss may be used over fields or over Z but not over |
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251 | Z/6 (which has non-zero zero divisors, namely 2 and 3). */ |
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252 | ideal getMinorIdeal (const matrix mat, const int minorSize, const int k, |
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253 | const char* algorithm, const ideal iSB, |
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254 | const bool allDifferent) |
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255 | { |
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256 | /* Note that this method should be replaced by getMinorIdeal_toBeDone, |
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257 | to enable faster computations in the case of matrices which contain |
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258 | only numbers. But so far, this method is not yet usable as it replaces |
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259 | the numbers by ints which may result in overflows during computations |
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260 | of minors. */ |
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261 | int rowCount = mat->nrows; |
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262 | int columnCount = mat->ncols; |
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263 | poly* myPolyMatrix = (poly*)(mat->m); |
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264 | int length = rowCount * columnCount; |
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265 | poly* nfPolyMatrix = new poly[length]; |
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266 | ideal iii; /* the ideal to be filled and returned */ |
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267 | |
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268 | /* copy all polynomials and reduce them w.r.t. iSB |
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269 | (if iSB is present, i.e., not the NULL pointer) */ |
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270 | if (iSB != NULL) |
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271 | { |
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272 | for (int i = 0; i < length; i++) |
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273 | { |
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274 | nfPolyMatrix[i] = kNF(iSB, currRing->qideal,myPolyMatrix[i]); |
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275 | } |
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276 | } |
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277 | else |
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278 | { |
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279 | for (int i = 0; i < length; i++) |
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280 | { |
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281 | nfPolyMatrix[i] = pCopy(myPolyMatrix[i]); |
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282 | } |
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283 | } |
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284 | |
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285 | if ((k == 0) && (strcmp(algorithm, "Bareiss") == 0) |
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286 | && (!rField_is_Ring_Z(currRing)) && (!allDifferent)) |
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287 | { |
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288 | /* In this case, we call an optimized procedure, dating back to |
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289 | Wilfried Pohl. It may be used whenever |
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290 | - all minors are requested, |
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291 | - requested minors need not be mutually distinct, and |
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292 | - coefficients come from a field (i.e., the ring Z is not |
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293 | allowed for this implementation). */ |
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294 | iii = (iSB == 0 ? idMinors(mat, minorSize) : idMinors(mat, minorSize, |
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295 | iSB)); |
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296 | } |
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297 | else |
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298 | { |
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299 | iii = getMinorIdeal_Poly(nfPolyMatrix, rowCount, columnCount, minorSize, |
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300 | k, algorithm, iSB, allDifferent); |
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301 | } |
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302 | |
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303 | /* clean up */ |
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304 | for (int j = 0; j < length; j++) pDelete(&nfPolyMatrix[j]); |
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305 | delete [] nfPolyMatrix; |
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306 | |
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307 | return iii; |
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308 | } |
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309 | |
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310 | /* special implementation for the case that the matrix has only number entries; |
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311 | if i is not the zero pointer, then it is assumed to contain a std basis, and |
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312 | the number entries of the matrix are then assumed to be reduced w.r.t. i and |
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313 | modulo the characteristic of the gound field/ring; |
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314 | this method should also work when currRing == null, i.e. when no ring has |
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315 | been declared */ |
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316 | ideal getMinorIdealCache_Int(const int* intMatrix, const int rowCount, |
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317 | const int columnCount, const int minorSize, |
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318 | const int k, const ideal i, |
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319 | const int cacheStrategy, const int cacheN, |
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320 | const int cacheW, const bool allDifferent) |
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321 | { |
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322 | /* setting up a MinorProcessor for matrices with integer entries: */ |
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323 | IntMinorProcessor mp; |
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324 | mp.defineMatrix(rowCount, columnCount, intMatrix); |
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325 | int *myRowIndices=new int[rowCount]; |
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326 | for (int j = 0; j < rowCount; j++) myRowIndices[j] = j; |
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327 | int *myColumnIndices=new int[columnCount]; |
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328 | for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j; |
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329 | mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices); |
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330 | mp.setMinorSize(minorSize); |
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331 | MinorValue::SetRankingStrategy(cacheStrategy); |
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332 | Cache<MinorKey, IntMinorValue> cch(cacheN, cacheW); |
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333 | |
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334 | /* containers for all upcoming results: */ |
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335 | IntMinorValue theMinor; |
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336 | // int value = 0; |
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337 | int collectedMinors = 0; |
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338 | int characteristic = 0; if (currRing != 0) characteristic = rChar(currRing); |
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339 | |
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340 | /* the ideal to be returned: */ |
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341 | ideal iii = idInit(1); |
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342 | |
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343 | bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are |
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344 | requested, omitting zero minors */ |
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345 | bool duplicatesOk = (allDifferent ? false : true); |
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346 | int kk = ((k < 0) ? -k : k); /* absolute value of k */ |
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347 | |
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348 | /* looping over all minors: */ |
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349 | while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk))) |
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350 | { |
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351 | /* retrieving the next minor: */ |
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352 | theMinor = mp.getNextMinor(cch, characteristic, i); |
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353 | poly f = NULL; |
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354 | if (theMinor.getResult() != 0) f = pISet(theMinor.getResult()); |
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355 | if (idInsertPolyWithTests(iii, collectedMinors, f, zeroOk, duplicatesOk)) |
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356 | collectedMinors++; |
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357 | } |
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358 | |
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359 | /* before we return the result, let's omit zero generators |
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360 | in iii which come after the computed minors */ |
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361 | ideal jjj; |
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362 | if (collectedMinors == 0) jjj = idInit(1); |
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363 | else jjj = idCopyFirstK(iii, collectedMinors); |
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364 | idDelete(&iii); |
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365 | delete[] myColumnIndices; |
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366 | delete[] myRowIndices; |
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367 | return jjj; |
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368 | } |
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369 | |
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370 | /* special implementation for the case that the matrix has non-number, |
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371 | i.e. real poly entries; |
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372 | if i is not the zero pointer, then it is assumed to contain a std basis, |
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373 | and the entries of the matrix are then assumed to be reduced w.r.t. i */ |
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374 | ideal getMinorIdealCache_Poly(const poly* polyMatrix, const int rowCount, |
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375 | const int columnCount, const int minorSize, |
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376 | const int k, const ideal i, |
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377 | const int cacheStrategy, const int cacheN, |
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378 | const int cacheW, const bool allDifferent) |
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379 | { |
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380 | /* setting up a MinorProcessor for matrices with polynomial entries: */ |
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381 | PolyMinorProcessor mp; |
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382 | mp.defineMatrix(rowCount, columnCount, polyMatrix); |
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383 | int *myRowIndices=new int[rowCount]; |
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384 | for (int j = 0; j < rowCount; j++) myRowIndices[j] = j; |
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385 | int *myColumnIndices=new int[columnCount]; |
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386 | for (int j = 0; j < columnCount; j++) myColumnIndices[j] = j; |
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387 | mp.defineSubMatrix(rowCount, myRowIndices, columnCount, myColumnIndices); |
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388 | mp.setMinorSize(minorSize); |
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389 | MinorValue::SetRankingStrategy(cacheStrategy); |
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390 | Cache<MinorKey, PolyMinorValue> cch(cacheN, cacheW); |
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391 | |
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392 | /* containers for all upcoming results: */ |
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393 | PolyMinorValue theMinor; |
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394 | poly f = NULL; |
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395 | int collectedMinors = 0; |
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396 | |
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397 | /* the ideal to be returned: */ |
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398 | ideal iii = idInit(1); |
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399 | |
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400 | bool zeroOk = ((k < 0) ? true : false); /* for k = 0, all minors are |
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401 | requested, omitting zero minors */ |
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402 | bool duplicatesOk = (allDifferent ? false : true); |
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403 | int kk = ((k < 0) ? -k : k); /* absolute value of k */ |
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404 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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405 | printCounters ("starting", true); |
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406 | int qqq = 0; |
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407 | #endif |
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408 | /* looping over all minors: */ |
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409 | while (mp.hasNextMinor() && ((kk == 0) || (collectedMinors < kk))) |
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410 | { |
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411 | /* retrieving the next minor: */ |
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412 | theMinor = mp.getNextMinor(cch, i); |
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413 | #if (defined COUNT_AND_PRINT_OPERATIONS) && (COUNT_AND_PRINT_OPERATIONS > 1) |
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414 | qqq++; |
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415 | Print("after %d", qqq); |
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416 | printCounters ("-th minor", false); |
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417 | #endif |
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418 | f = theMinor.getResult(); |
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419 | if (idInsertPolyWithTests(iii, collectedMinors, pCopy(f), zeroOk, |
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420 | duplicatesOk)) |
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421 | collectedMinors++; |
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422 | } |
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423 | #ifdef COUNT_AND_PRINT_OPERATIONS |
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424 | printCounters ("ending", true); |
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425 | #endif |
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426 | |
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427 | /* before we return the result, let's omit zero generators |
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428 | in iii which come after the computed minors */ |
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429 | ideal jjj; |
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430 | if (collectedMinors == 0) jjj = idInit(1); |
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431 | else jjj = idCopyFirstK(iii, collectedMinors); |
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432 | idDelete(&iii); |
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433 | delete[] myColumnIndices; |
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434 | delete[] myRowIndices; |
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435 | return jjj; |
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436 | } |
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437 | |
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438 | ideal getMinorIdealCache_toBeDone (const matrix mat, const int minorSize, |
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439 | const int k, const ideal iSB, |
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440 | const int cacheStrategy, const int cacheN, |
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441 | const int cacheW, const bool allDifferent) |
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442 | { |
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443 | int rowCount = mat->nrows; |
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444 | int columnCount = mat->ncols; |
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445 | poly* myPolyMatrix = (poly*)(mat->m); |
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446 | ideal iii; /* the ideal to be filled and returned */ |
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447 | int zz = 0; |
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448 | |
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449 | /* divert to special implementation when myPolyMatrix has only number |
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450 | entries: */ |
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451 | int* myIntMatrix = new int [rowCount * columnCount]; |
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452 | poly* nfPolyMatrix = new poly[rowCount * columnCount]; |
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453 | if (arrayIsNumberArray(myPolyMatrix, iSB, rowCount * columnCount, |
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454 | myIntMatrix, nfPolyMatrix, zz)) |
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455 | iii = getMinorIdealCache_Int(myIntMatrix, rowCount, columnCount, |
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456 | minorSize, k, iSB, cacheStrategy, cacheN, |
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457 | cacheW, allDifferent); |
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458 | else |
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459 | iii = getMinorIdealCache_Poly(nfPolyMatrix, rowCount, columnCount, |
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460 | minorSize, k, iSB, cacheStrategy, cacheN, |
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461 | cacheW, allDifferent); |
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462 | |
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463 | /* clean up */ |
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464 | delete [] myIntMatrix; |
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465 | for (int j = 0; j < rowCount * columnCount; j++) pDelete(&nfPolyMatrix[j]); |
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466 | delete [] nfPolyMatrix; |
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467 | |
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468 | return iii; |
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469 | } |
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470 | |
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471 | ideal getMinorIdealCache (const matrix mat, const int minorSize, const int k, |
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472 | const ideal iSB, const int cacheStrategy, |
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473 | const int cacheN, const int cacheW, |
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474 | const bool allDifferent) |
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475 | { |
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476 | /* Note that this method should be replaced by getMinorIdealCache_toBeDone, |
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477 | to enable faster computations in the case of matrices which contain |
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478 | only numbers. But so far, this method is not yet usable as it replaces |
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479 | the numbers by ints which may result in overflows during computations |
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480 | of minors. */ |
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481 | int rowCount = mat->nrows; |
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482 | int columnCount = mat->ncols; |
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483 | poly* myPolyMatrix = (poly*)(mat->m); |
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484 | int length = rowCount * columnCount; |
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485 | poly* nfPolyMatrix = new poly[length]; |
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486 | ideal iii; /* the ideal to be filled and returned */ |
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487 | |
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488 | /* copy all polynomials and reduce them w.r.t. iSB |
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489 | (if iSB is present, i.e., not the NULL pointer) */ |
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490 | for (int i = 0; i < length; i++) |
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491 | { |
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492 | nfPolyMatrix[i] = pCopy(myPolyMatrix[i]); |
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493 | if (iSB != 0) nfPolyMatrix[i] = kNF(iSB, currRing->qideal, |
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494 | nfPolyMatrix[i]); |
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495 | } |
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496 | |
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497 | iii = getMinorIdealCache_Poly(nfPolyMatrix, rowCount, columnCount, |
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498 | minorSize, k, iSB, cacheStrategy, |
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499 | cacheN, cacheW, allDifferent); |
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500 | |
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501 | /* clean up */ |
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502 | for (int j = 0; j < length; j++) pDelete(&nfPolyMatrix[j]); |
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503 | delete [] nfPolyMatrix; |
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504 | |
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505 | return iii; |
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506 | } |
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507 | |
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508 | ideal getMinorIdealHeuristic (const matrix mat, const int minorSize, |
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509 | const int k, const ideal iSB, |
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510 | const bool allDifferent) |
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511 | { |
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512 | int vars = 0; if (currRing != 0) vars = currRing->N; |
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513 | int rowCount = mat->nrows; |
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514 | int columnCount = mat->ncols; |
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515 | |
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516 | /* here comes the heuristic, as of 29 January 2010: |
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517 | |
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518 | integral domain and minorSize <= 2 -> Bareiss |
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519 | integral domain and minorSize >= 3 and vars <= 2 -> Bareiss |
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520 | field case and minorSize >= 3 and vars = 3 |
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521 | and c in {2, 3, ..., 32749} -> Bareiss |
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522 | |
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523 | otherwise: |
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524 | if not all minors are requested -> Laplace, no Caching |
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525 | otherwise: |
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526 | minorSize >= 3 and vars <= 4 and |
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527 | (rowCount over minorSize)*(columnCount over minorSize) >= 100 |
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528 | -> Laplace with Caching |
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529 | minorSize >= 3 and vars >= 5 and |
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530 | (rowCount over minorSize)*(columnCount over minorSize) >= 40 |
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531 | -> Laplace with Caching |
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532 | |
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533 | otherwise: -> Laplace, no Caching |
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534 | */ |
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535 | |
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536 | bool b = false; /* Bareiss */ |
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537 | bool l = false; /* Laplace without caching */ |
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538 | // bool c = false; /* Laplace with caching */ |
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539 | if (currRingIsOverIntegralDomain()) |
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540 | { /* the field case or ring Z */ |
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541 | if (minorSize <= 2) b = true; |
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542 | else if (vars <= 2) b = true; |
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543 | else if (currRingIsOverField() && (vars == 3) |
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544 | && (currRing->cf->ch >= 2) && (currRing->cf->ch <= NV_MAX_PRIME)) |
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545 | b = true; |
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546 | } |
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547 | if (!b) |
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548 | { /* the non-Bareiss cases */ |
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549 | if (k != 0) /* this means, not all minors are requested */ l = true; |
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550 | else |
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551 | { /* k == 0, i.e., all minors are requested */ |
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552 | int minorCount = binom(rowCount, minorSize); |
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553 | minorCount *= binom(columnCount, minorSize); |
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554 | // if ((minorSize >= 3) && (vars <= 4) |
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555 | // && (minorCount >= 100)) c = true; |
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556 | // else if ((minorSize >= 3) && (vars >= 5) |
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557 | // && (minorCount >= 40)) c = true; |
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558 | /*else*/ l = true; |
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559 | } |
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560 | } |
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561 | |
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562 | if (b) return getMinorIdeal(mat, minorSize, k, "Bareiss", iSB, |
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563 | allDifferent); |
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564 | else if (l) return getMinorIdeal(mat, minorSize, k, "Laplace", iSB, |
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565 | allDifferent); |
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566 | else /* (c) */ return getMinorIdealCache(mat, minorSize, k, iSB, |
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567 | 3, 200, 100000, allDifferent); |
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568 | } |
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