1 | // emacs edit mode for this file is -*- C++ -*- |
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2 | |
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3 | /**************************************** |
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4 | * Computer Algebra System SINGULAR * |
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5 | ****************************************/ |
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6 | /* |
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7 | * ABSTRACT - The FGLM-Algorithm plus extension |
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8 | * Calculate a reduced groebner basis for one ordering, given a |
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9 | * reduced groebner basis for another ordering. |
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10 | * In this file the input is checked. Furthermore we decide, if |
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11 | * the input is 0-dimensional ( then fglmzero.cc is used ) or |
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12 | * if the input is homogeneous ( then fglmhom.cc is used. Yet |
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13 | * not implemented ). |
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14 | * The extension (finduni) finds minimal univariate Polynomials |
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15 | * lying in a 0-dimensional ideal. |
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16 | */ |
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17 | |
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18 | #ifdef HAVE_CONFIG_H |
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19 | #include "singularconfig.h" |
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20 | #endif /* HAVE_CONFIG_H */ |
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21 | #include <kernel/mod2.h> |
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22 | |
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23 | #ifdef HAVE_FACTORY |
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24 | |
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25 | |
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26 | #include <omalloc/omalloc.h> |
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27 | #include <misc/options.h> |
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28 | |
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29 | #include <polys/monomials/ring.h> |
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30 | #include <polys/monomials/maps.h> |
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31 | |
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32 | #include <kernel/febase.h> |
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33 | #include <kernel/polys.h> |
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34 | #include <kernel/ideals.h> |
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35 | |
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36 | #include <kernel/kstd1.h> |
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37 | #include <kernel/fglm.h> |
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38 | |
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39 | #include <Singular/fglm.h> |
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40 | #include <Singular/ipid.h> |
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41 | #include <Singular/ipshell.h> |
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42 | #include <Singular/tok.h> |
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43 | |
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44 | |
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45 | // internal Version: 1.18.1.6 |
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46 | // enumeration to handle the various errors to occour. |
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47 | enum FglmState{ |
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48 | FglmOk, |
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49 | FglmHasOne, |
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50 | FglmNoIdeal, |
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51 | FglmNotReduced, |
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52 | FglmNotZeroDim, |
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53 | FglmIncompatibleRings, |
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54 | // for fglmquot: |
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55 | FglmPolyIsOne, |
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56 | FglmPolyIsZero |
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57 | }; |
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58 | |
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59 | // Has to be called, if currQuotient != NULL. ( i.e. qring-case ) |
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60 | // Then a new ideal is build, consisting of the generators of sourceIdeal |
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61 | // and the generators of currQuotient, which are completely reduced by |
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62 | // the sourceIdeal. This means: If sourceIdeal is reduced, then the new |
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63 | // ideal will be reduced as well. |
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64 | // Assumes that currRing == sourceRing |
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65 | ideal fglmUpdatesource( const ideal sourceIdeal ) |
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66 | { |
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67 | int k, l, offset; |
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68 | BOOLEAN found; |
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69 | ideal newSource= idInit( IDELEMS( sourceIdeal ) + IDELEMS( currQuotient ), 1 ); |
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70 | for ( k= IDELEMS( sourceIdeal )-1; k >=0; k-- ) |
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71 | (newSource->m)[k]= pCopy( (sourceIdeal->m)[k] ); |
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72 | offset= IDELEMS( sourceIdeal ); |
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73 | for ( l= IDELEMS( currQuotient )-1; l >= 0; l-- ) |
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74 | { |
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75 | if ( (currQuotient->m)[l] != NULL ) |
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76 | { |
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77 | found= FALSE; |
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78 | for ( k= IDELEMS( sourceIdeal )-1; (k >= 0) && (found == FALSE); k-- ) |
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79 | if ( pDivisibleBy( (sourceIdeal->m)[k], (currQuotient->m)[l] ) ) |
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80 | found= TRUE; |
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81 | if ( ! found ) |
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82 | { |
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83 | (newSource->m)[offset]= pCopy( (currQuotient->m)[l] ); |
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84 | offset++; |
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85 | } |
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86 | } |
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87 | } |
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88 | idSkipZeroes( newSource ); |
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89 | return newSource; |
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90 | } |
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91 | |
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92 | // Has to be called, if currQuotient != NULL, i.e. in qring-case. |
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93 | // Gets rid of the elements of result which are contained in |
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94 | // currQuotient and skips Zeroes. |
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95 | // Assumes that currRing == destRing |
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96 | void |
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97 | fglmUpdateresult( ideal & result ) |
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98 | { |
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99 | int k, l; |
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100 | BOOLEAN found; |
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101 | for ( k= IDELEMS( result )-1; k >=0; k-- ) |
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102 | { |
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103 | if ( (result->m)[k] != NULL ) |
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104 | { |
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105 | found= FALSE; |
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106 | for ( l= IDELEMS( currQuotient )-1; (l >= 0) && ( found == FALSE ); l-- ) |
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107 | if ( pDivisibleBy( (currQuotient->m)[l], (result->m)[k] ) ) |
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108 | found= TRUE; |
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109 | if ( found ) pDelete( & ((result->m)[k]) ); |
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110 | } |
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111 | } |
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112 | idSkipZeroes( result ); |
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113 | } |
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114 | |
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115 | // Checks if the two rings sringHdl and dringHdl are compatible enough to |
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116 | // be used for the fglm. This means: |
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117 | // 1) Same Characteristic, 2) globalOrderings in both rings, |
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118 | // 3) Same number of variables, 4) same number of parameters |
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119 | // 5) variables in one ring are permutated variables of the other one |
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120 | // 6) parameters in one ring are permutated parameters of the other one |
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121 | // 7) either both rings are rings or both rings are qrings |
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122 | // 8) if they are qrings, the quotientIdeals of both must coincide. |
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123 | // vperm must be a vector of length pVariables+1, initialized by 0. |
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124 | // If both rings are compatible, it stores the permutation of the |
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125 | // variables if mapped from sringHdl to dringHdl. |
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126 | // if the rings are compatible, it returns FglmOk. |
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127 | // Should be called with currRing= IDRING( sringHdl ); |
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128 | FglmState |
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129 | fglmConsistency( idhdl sringHdl, idhdl dringHdl, int * vperm ) |
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130 | { |
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131 | int k; |
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132 | FglmState state= FglmOk; |
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133 | ring dring = IDRING( dringHdl ); |
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134 | ring sring = IDRING( sringHdl ); |
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135 | |
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136 | if ( rChar(sring) != rChar(dring) ) |
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137 | { |
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138 | WerrorS( "rings must have same characteristic" ); |
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139 | state= FglmIncompatibleRings; |
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140 | } |
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141 | if ( (sring->OrdSgn != 1) || (dring->OrdSgn != 1) ) |
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142 | { |
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143 | WerrorS( "only works for global orderings" ); |
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144 | state= FglmIncompatibleRings; |
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145 | } |
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146 | if ( sring->N != dring->N ) |
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147 | { |
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148 | WerrorS( "rings must have same number of variables" ); |
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149 | state= FglmIncompatibleRings; |
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150 | } |
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151 | if ( rPar(sring) != rPar(dring) ) |
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152 | { |
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153 | WerrorS( "rings must have same number of parameters" ); |
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154 | state= FglmIncompatibleRings; |
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155 | } |
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156 | if ( state != FglmOk ) return state; |
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157 | // now the rings have the same number of variables resp. parameters. |
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158 | // check if the names of the variables resp. parameters do agree: |
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159 | int nvar = sring->N; |
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160 | int npar = rPar(sring); |
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161 | int * pperm; |
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162 | if ( npar > 0 ) |
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163 | pperm= (int *)omAlloc0( (npar+1)*sizeof( int ) ); |
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164 | else |
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165 | pperm= NULL; |
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166 | maFindPerm( sring->names, nvar, rParameter(sring), npar, |
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167 | dring->names, nvar, rParameter(dring), npar, vperm, pperm, |
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168 | dring->cf->type); |
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169 | for ( k= nvar; (k > 0) && (state == FglmOk); k-- ) |
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170 | if ( vperm[k] <= 0 ) |
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171 | { |
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172 | WerrorS( "variable names do not agree" ); |
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173 | state= FglmIncompatibleRings; |
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174 | } |
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175 | for ( k= npar-1; (k >= 0) && (state == FglmOk); k-- ) |
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176 | if ( pperm[k] >= 0 ) |
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177 | { |
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178 | WerrorS( "paramater names do not agree" ); |
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179 | state= FglmIncompatibleRings; |
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180 | } |
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181 | if (pperm != NULL) // OB: ???? |
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182 | omFreeSize( (ADDRESS)pperm, (npar+1)*sizeof( int ) ); |
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183 | if ( state != FglmOk ) return state; |
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184 | // check if both rings are qrings or not |
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185 | if ( sring->qideal != NULL ) |
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186 | { |
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187 | if ( dring->qideal == NULL ) |
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188 | { |
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189 | Werror( "%s is a qring, current ring not", sringHdl->id ); |
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190 | return FglmIncompatibleRings; |
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191 | } |
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192 | // both rings are qrings, now check if both quotients define the same ideal. |
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193 | // check if sring->qideal is contained in dring->qideal: |
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194 | rSetHdl( dringHdl ); |
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195 | nMapFunc nMap=n_SetMap(currRing->cf, sring->cf ); |
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196 | ideal sqind = idInit( IDELEMS( sring->qideal ), 1 ); |
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197 | for ( k= IDELEMS( sring->qideal )-1; k >= 0; k-- ) |
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198 | (sqind->m)[k]= p_PermPoly( (sring->qideal->m)[k], vperm, sring, |
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199 | currRing, nMap); |
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200 | ideal sqindred = kNF( dring->qideal, NULL, sqind ); |
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201 | if ( ! idIs0( sqindred ) ) |
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202 | { |
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203 | WerrorS( "the quotients do not agree" ); |
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204 | state= FglmIncompatibleRings; |
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205 | } |
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206 | idDelete( & sqind ); |
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207 | idDelete( & sqindred ); |
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208 | rSetHdl( sringHdl ); |
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209 | if ( state != FglmOk ) return state; |
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210 | // check if dring->qideal is contained in sring->qideal: |
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211 | int * dsvperm = (int *)omAlloc0( (nvar+1)*sizeof( int ) ); |
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212 | maFindPerm( dring->names, nvar, NULL, 0, sring->names, nvar, NULL, 0, |
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213 | dsvperm, NULL, sring->cf->type); |
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214 | nMap=n_SetMap(currRing->cf, dring->cf); |
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215 | ideal dqins = idInit( IDELEMS( dring->qideal ), 1 ); |
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216 | for ( k= IDELEMS( dring->qideal )-1; k >= 0; k-- ) |
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217 | (dqins->m)[k]=p_PermPoly( (dring->qideal->m)[k], dsvperm, sring, |
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218 | currRing, nMap); |
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219 | ideal dqinsred = kNF( sring->qideal, NULL, dqins ); |
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220 | if ( ! idIs0( dqinsred ) ) |
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221 | { |
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222 | WerrorS( "the quotients do not agree" ); |
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223 | state= FglmIncompatibleRings; |
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224 | } |
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225 | idDelete( & dqins ); |
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226 | idDelete( & dqinsred ); |
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227 | omFreeSize( (ADDRESS)dsvperm, (nvar+1)*sizeof( int ) ); |
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228 | if ( state != FglmOk ) return state; |
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229 | } |
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230 | else |
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231 | { |
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232 | if ( dring->qideal != NULL ) |
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233 | { |
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234 | Werror( "current ring is a qring, %s not", sringHdl->id ); |
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235 | return FglmIncompatibleRings; |
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236 | } |
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237 | } |
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238 | return FglmOk; |
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239 | } |
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240 | |
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241 | // Checks if the ideal "theIdeal" is zero-dimensional and minimal. It does |
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242 | // not check, if it is reduced. |
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243 | // returns FglmOk if we can use theIdeal for CalculateFunctionals (this |
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244 | // function reports an error if theIdeal is not reduced, |
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245 | // so this need not to be tested here) |
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246 | // FglmNotReduced if theIdeal is not minimal |
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247 | // FglmNotZeroDim if it is not zero-dimensional |
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248 | // FglmHasOne if 1 belongs to theIdeal |
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249 | FglmState |
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250 | fglmIdealcheck( const ideal theIdeal ) |
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251 | { |
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252 | FglmState state = FglmOk; |
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253 | int power; |
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254 | int k; |
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255 | BOOLEAN * purePowers = (BOOLEAN *)omAlloc0( currRing->N*sizeof( BOOLEAN ) ); |
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256 | |
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257 | for ( k= IDELEMS( theIdeal ) - 1; (state == FglmOk) && (k >= 0); k-- ) |
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258 | { |
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259 | poly p = (theIdeal->m)[k]; |
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260 | if (p!=NULL) |
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261 | { |
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262 | if( pIsConstant( p ) ) state= FglmHasOne; |
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263 | else if ( (power= pIsPurePower( p )) > 0 ) |
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264 | { |
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265 | fglmASSERT( 0 < power && power <= currRing->N, "illegal power" ); |
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266 | if ( purePowers[power-1] == TRUE ) state= FglmNotReduced; |
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267 | else purePowers[power-1]= TRUE; |
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268 | } |
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269 | for ( int l = IDELEMS( theIdeal ) - 1; state == FglmOk && l >= 0; l-- ) |
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270 | if ( (k != l) && pDivisibleBy( p, (theIdeal->m)[l] ) ) |
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271 | state= FglmNotReduced; |
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272 | } |
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273 | } |
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274 | if ( state == FglmOk ) |
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275 | { |
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276 | for ( k= currRing->N-1 ; (state == FglmOk) && (k >= 0); k-- ) |
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277 | if ( purePowers[k] == FALSE ) state= FglmNotZeroDim; |
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278 | } |
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279 | omFreeSize( (ADDRESS)purePowers, currRing->N*sizeof( BOOLEAN ) ); |
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280 | return state; |
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281 | } |
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282 | |
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283 | // The main function for the fglm-Algorithm. |
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284 | // Checks the input-data, and calls fglmzero (see fglmzero.cc). |
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285 | // Returns the new groebnerbasis or 0 if an error occoured. |
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286 | BOOLEAN |
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287 | fglmProc( leftv result, leftv first, leftv second ) |
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288 | { |
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289 | FglmState state = FglmOk; |
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290 | |
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291 | idhdl destRingHdl = currRingHdl; |
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292 | // ring destRing = currRing; |
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293 | ideal destIdeal = NULL; |
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294 | idhdl sourceRingHdl = (idhdl)first->data; |
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295 | rSetHdl( sourceRingHdl ); |
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296 | // ring sourceRing = currRing; |
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297 | |
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298 | int * vperm = (int *)omAlloc0( (currRing->N+1)*sizeof( int ) ); |
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299 | state= fglmConsistency( sourceRingHdl, destRingHdl, vperm ); |
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300 | omFreeSize( (ADDRESS)vperm, (currRing->N+1)*sizeof(int) ); |
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301 | |
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302 | if ( state == FglmOk ) |
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303 | { |
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304 | idhdl ih = currRing->idroot->get( second->Name(), myynest ); |
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305 | if ( (ih != NULL) && (IDTYP(ih)==IDEAL_CMD) ) |
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306 | { |
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307 | ideal sourceIdeal; |
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308 | if ( currQuotient != NULL ) |
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309 | sourceIdeal= fglmUpdatesource( IDIDEAL( ih ) ); |
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310 | else |
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311 | sourceIdeal = IDIDEAL( ih ); |
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312 | state= fglmIdealcheck( sourceIdeal ); |
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313 | if ( state == FglmOk ) |
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314 | { |
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315 | // Now the settings are compatible with FGLM |
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316 | assumeStdFlag( (leftv)ih ); |
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317 | if ( fglmzero( IDRING(sourceRingHdl), sourceIdeal, IDRING(destRingHdl), destIdeal, FALSE, (currQuotient != NULL) ) == FALSE ) |
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318 | state= FglmNotReduced; |
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319 | } |
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320 | } else state= FglmNoIdeal; |
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321 | } |
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322 | if ( currRingHdl != destRingHdl ) |
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323 | rSetHdl( destRingHdl ); |
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324 | switch (state) |
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325 | { |
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326 | case FglmOk: |
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327 | if ( currQuotient != NULL ) fglmUpdateresult( destIdeal ); |
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328 | break; |
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329 | case FglmHasOne: |
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330 | destIdeal= idInit(1,1); |
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331 | (destIdeal->m)[0]= pOne(); |
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332 | state= FglmOk; |
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333 | break; |
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334 | case FglmIncompatibleRings: |
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335 | Werror( "ring %s and current ring are incompatible", first->Name() ); |
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336 | destIdeal= NULL; |
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337 | break; |
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338 | case FglmNoIdeal: |
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339 | Werror( "Can't find ideal %s in ring %s", second->Name(), first->Name() ); |
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340 | destIdeal= NULL; |
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341 | break; |
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342 | case FglmNotZeroDim: |
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343 | Werror( "The ideal %s has to be 0-dimensional", second->Name() ); |
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344 | destIdeal= NULL; |
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345 | break; |
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346 | case FglmNotReduced: |
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347 | Werror( "The ideal %s has to be given by a reduced SB", second->Name() ); |
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348 | destIdeal= NULL; |
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349 | break; |
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350 | default: |
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351 | destIdeal= idInit(1,1); |
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352 | } |
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353 | |
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354 | result->rtyp = IDEAL_CMD; |
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355 | result->data= (void *)destIdeal; |
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356 | setFlag( result, FLAG_STD ); |
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357 | return (state != FglmOk); |
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358 | } |
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359 | |
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360 | // fglmQuotProc: Calculate I:f with FGLM methods. |
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361 | // Checks the input-data, and calls fglmquot (see fglmzero.cc). |
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362 | // Returns the new groebnerbasis if I:f or 0 if an error occoured. |
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363 | BOOLEAN |
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364 | fglmQuotProc( leftv result, leftv first, leftv second ) |
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365 | { |
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366 | FglmState state = FglmOk; |
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367 | |
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368 | // STICKYPROT("quotstart\n"); |
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369 | ideal sourceIdeal = (ideal)first->Data(); |
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370 | poly quot = (poly)second->Data(); |
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371 | ideal destIdeal = NULL; |
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372 | |
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373 | state = fglmIdealcheck( sourceIdeal ); |
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374 | if ( state == FglmOk ) |
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375 | { |
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376 | if ( quot == NULL ) state= FglmPolyIsZero; |
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377 | else if ( pIsConstant( quot ) ) state= FglmPolyIsOne; |
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378 | } |
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379 | |
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380 | if ( state == FglmOk ) |
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381 | { |
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382 | assumeStdFlag( first ); |
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383 | if ( fglmquot( sourceIdeal, quot, destIdeal ) == FALSE ) |
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384 | state= FglmNotReduced; |
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385 | } |
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386 | |
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387 | switch (state) |
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388 | { |
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389 | case FglmOk: |
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390 | break; |
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391 | case FglmHasOne: |
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392 | destIdeal= idInit(1,1); |
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393 | (destIdeal->m)[0]= pOne(); |
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394 | state= FglmOk; |
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395 | break; |
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396 | case FglmNotZeroDim: |
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397 | Werror( "The ideal %s has to be 0-dimensional", first->Name() ); |
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398 | destIdeal= NULL; |
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399 | break; |
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400 | case FglmNotReduced: |
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401 | Werror( "The poly %s has to be reduced", second->Name() ); |
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402 | destIdeal= NULL; |
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403 | break; |
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404 | case FglmPolyIsOne: |
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405 | int k; |
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406 | destIdeal= idInit( IDELEMS(sourceIdeal), 1 ); |
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407 | for ( k= IDELEMS( sourceIdeal )-1; k >=0; k-- ) |
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408 | (destIdeal->m)[k]= pCopy( (sourceIdeal->m)[k] ); |
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409 | state= FglmOk; |
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410 | break; |
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411 | case FglmPolyIsZero: |
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412 | destIdeal= idInit(1,1); |
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413 | (destIdeal->m)[0]= pOne(); |
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414 | state= FglmOk; |
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415 | break; |
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416 | default: |
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417 | destIdeal= idInit(1,1); |
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418 | } |
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419 | |
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420 | result->rtyp = IDEAL_CMD; |
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421 | result->data= (void *)destIdeal; |
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422 | setFlag( result, FLAG_STD ); |
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423 | // STICKYPROT("quotend\n"); |
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424 | return (state != FglmOk); |
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425 | } // fglmQuotProt |
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426 | |
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427 | // The main function for finduni(). |
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428 | // Checks the input-data, and calls FindUnivariateWrapper (see fglmzero.cc). |
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429 | // Returns an ideal containing the univariate Polynomials or 0 if an error |
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430 | // has occoured. |
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431 | BOOLEAN |
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432 | findUniProc( leftv result, leftv first ) |
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433 | { |
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434 | ideal sourceIdeal; |
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435 | ideal destIdeal = NULL; |
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436 | FglmState state; |
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437 | |
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438 | sourceIdeal = (ideal)first->Data(); |
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439 | |
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440 | assumeStdFlag( first ); |
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441 | state= fglmIdealcheck( sourceIdeal ); |
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442 | if ( state == FglmOk ) |
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443 | { |
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444 | // check for special cases: if the input contains |
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445 | // univariate polys, try to reduce the problem |
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446 | int i,k; |
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447 | int count=0; |
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448 | BOOLEAN * purePowers = (BOOLEAN *)omAlloc0( currRing->N*sizeof( BOOLEAN ) ); |
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449 | for ( k= IDELEMS( sourceIdeal ) - 1; k >= 0; k-- ) |
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450 | { |
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451 | if((i=pIsUnivariate(sourceIdeal->m[k]))>0) |
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452 | { |
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453 | if (purePowers[i-1]==0) |
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454 | { |
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455 | purePowers[i-1]=k; |
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456 | count++; |
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457 | if (count==currRing->N) break; |
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458 | } |
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459 | } |
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460 | } |
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461 | if (count==currRing->N) |
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462 | { |
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463 | destIdeal=idInit(currRing->N,1); |
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464 | for(k=currRing->N-1; k>=0; k--) destIdeal->m[k]=pCopy(sourceIdeal->m[purePowers[k]]); |
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465 | } |
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466 | omFreeSize((ADDRESS)purePowers, currRing->N*sizeof( BOOLEAN ) ); |
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467 | if (destIdeal!=NULL) |
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468 | state = FglmOk; |
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469 | else if ( FindUnivariateWrapper( sourceIdeal, destIdeal ) == FALSE ) |
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470 | state = FglmNotReduced; |
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471 | } |
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472 | switch (state) |
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473 | { |
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474 | case FglmOk: |
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475 | break; |
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476 | case FglmHasOne: |
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477 | destIdeal= idInit(1,1); |
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478 | (destIdeal->m)[0]= pOne(); |
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479 | state= FglmOk; |
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480 | break; |
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481 | case FglmNotZeroDim: |
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482 | Werror( "The ideal %s has to be 0-dimensional", first->Name() ); |
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483 | destIdeal= NULL; |
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484 | break; |
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485 | case FglmNotReduced: |
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486 | Werror( "The ideal %s has to be reduced", first->Name() ); |
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487 | destIdeal= NULL; |
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488 | break; |
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489 | default: |
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490 | destIdeal= idInit(1,1); |
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491 | } |
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492 | |
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493 | result->rtyp = IDEAL_CMD; |
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494 | result->data= (void *)destIdeal; |
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495 | |
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496 | return FALSE; |
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497 | } |
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498 | #endif |
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499 | // ---------------------------------------------------------------------------- |
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500 | // Local Variables: *** |
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501 | // compile-command: "make Singular" *** |
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502 | // page-delimiter: "^\\(\\|//!\\)" *** |
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503 | // fold-internal-margins: nil *** |
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504 | // End: *** |
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