[35aab3] | 1 | // emacs edit mode for this file is -*- C++ -*- |
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[bdaa5d] | 2 | // $Id: fglm.cc,v 1.3 2005-05-03 07:29:01 Singular Exp $ |
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[35aab3] | 3 | |
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| 4 | /**************************************** |
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| 5 | * Computer Algebra System SINGULAR * |
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| 6 | ****************************************/ |
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| 7 | /* |
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| 8 | * ABSTRACT - The FGLM-Algorithm plus extension |
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| 9 | * Calculate a reduced groebner basis for one ordering, given a |
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| 10 | * reduced groebner basis for another ordering. |
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| 11 | * In this file the input is checked. Furthermore we decide, if |
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| 12 | * the input is 0-dimensional ( then fglmzero.cc is used ) or |
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| 13 | * if the input is homogeneous ( then fglmhom.cc is used. Yet |
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| 14 | * not implemented ). |
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| 15 | * The extension (finduni) finds minimal univariate Polynomials |
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| 16 | * lying in a 0-dimensional ideal. |
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| 17 | */ |
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| 18 | |
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| 19 | #include "mod2.h" |
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| 20 | |
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| 21 | #ifdef HAVE_FGLM |
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| 22 | #include "tok.h" |
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| 23 | #include "structs.h" |
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| 24 | #include "polys.h" |
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| 25 | #include "ideals.h" |
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| 26 | #include "ring.h" |
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| 27 | #include "ipid.h" |
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| 28 | #include "ipshell.h" |
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| 29 | #include "febase.h" |
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| 30 | #include "maps.h" |
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| 31 | #include "omalloc.h" |
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| 32 | #include "kstd1.h" |
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| 33 | #include "fglm.h" |
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| 34 | |
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| 35 | // internal Version: 1.18.1.6 |
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| 36 | // enumeration to handle the various errors to occour. |
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| 37 | enum FglmState{ |
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| 38 | FglmOk, |
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| 39 | FglmHasOne, |
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| 40 | FglmNoIdeal, |
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| 41 | FglmNotReduced, |
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| 42 | FglmNotZeroDim, |
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| 43 | FglmIncompatibleRings, |
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| 44 | // for fglmquot: |
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| 45 | FglmPolyIsOne, |
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| 46 | FglmPolyIsZero |
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| 47 | }; |
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| 48 | |
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| 49 | // Has to be called, if currQuotient != NULL. ( i.e. qring-case ) |
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| 50 | // Then a new ideal is build, consisting of the generators of sourceIdeal |
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| 51 | // and the generators of currQuotient, which are completely reduced by |
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| 52 | // the sourceIdeal. This means: If sourceIdeal is reduced, then the new |
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| 53 | // ideal will be reduced as well. |
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| 54 | // Assumes that currRing == sourceRing |
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| 55 | ideal fglmUpdatesource( const ideal sourceIdeal ) |
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| 56 | { |
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| 57 | int k, l, offset; |
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| 58 | BOOLEAN found; |
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| 59 | ideal newSource= idInit( IDELEMS( sourceIdeal ) + IDELEMS( currQuotient ), 1 ); |
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| 60 | for ( k= IDELEMS( sourceIdeal )-1; k >=0; k-- ) |
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| 61 | (newSource->m)[k]= pCopy( (sourceIdeal->m)[k] ); |
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| 62 | offset= IDELEMS( sourceIdeal ); |
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| 63 | for ( l= IDELEMS( currQuotient )-1; l >= 0; l-- ) { |
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| 64 | if ( (currQuotient->m)[l] != NULL ) { |
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| 65 | found= FALSE; |
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| 66 | for ( k= IDELEMS( sourceIdeal )-1; (k >= 0) && (found == FALSE); k-- ) |
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| 67 | if ( pDivisibleBy( (sourceIdeal->m)[k], (currQuotient->m)[l] ) ) |
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| 68 | found= TRUE; |
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| 69 | if ( ! found ) { |
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| 70 | (newSource->m)[offset]= pCopy( (currQuotient->m)[l] ); |
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| 71 | offset++; |
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| 72 | } |
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| 73 | } |
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| 74 | } |
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| 75 | idSkipZeroes( newSource ); |
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| 76 | return newSource; |
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| 77 | } |
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| 78 | |
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| 79 | // Has to be called, if currQuotient != NULL, i.e. in qring-case. |
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| 80 | // Gets rid of the elements of result which are contained in |
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| 81 | // currQuotient and skips Zeroes. |
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| 82 | // Assumes that currRing == destRing |
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| 83 | void |
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| 84 | fglmUpdateresult( ideal & result ) |
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| 85 | { |
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| 86 | int k, l; |
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| 87 | BOOLEAN found; |
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| 88 | for ( k= IDELEMS( result )-1; k >=0; k-- ) { |
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| 89 | if ( (result->m)[k] != NULL ) { |
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| 90 | found= FALSE; |
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| 91 | for ( l= IDELEMS( currQuotient )-1; (l >= 0) && ( found == FALSE ); l-- ) |
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| 92 | if ( pDivisibleBy( (currQuotient->m)[l], (result->m)[k] ) ) |
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| 93 | found= TRUE; |
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| 94 | if ( found ) pDelete( & ((result->m)[k]) ); |
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| 95 | } |
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| 96 | } |
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| 97 | idSkipZeroes( result ); |
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| 98 | } |
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| 99 | |
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| 100 | // Checks if the two rings sringHdl and dringHdl are compatible enough to |
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| 101 | // be used for the fglm. This means: |
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| 102 | // 1) Same Characteristic, 2) globalOrderings in both rings, |
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| 103 | // 3) Same number of variables, 4) same number of parameters |
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| 104 | // 5) variables in one ring are permutated variables of the other one |
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| 105 | // 6) parameters in one ring are permutated parameters of the other one |
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| 106 | // 7) either both rings are rings or both rings are qrings |
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| 107 | // 8) if they are qrings, the quotientIdeals of both must coincide. |
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| 108 | // vperm must be a vector of length pVariables+1, initialized by 0. |
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| 109 | // If both rings are compatible, it stores the permutation of the |
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| 110 | // variables if mapped from sringHdl to dringHdl. |
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| 111 | // if the rings are compatible, it returns FglmOk. |
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| 112 | // Should be called with currRing= IDRING( sringHdl ); |
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| 113 | FglmState |
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| 114 | fglmConsistency( idhdl sringHdl, idhdl dringHdl, int * vperm ) |
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| 115 | { |
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| 116 | int k; |
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| 117 | FglmState state= FglmOk; |
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| 118 | ring dring = IDRING( dringHdl ); |
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| 119 | ring sring = IDRING( sringHdl ); |
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| 120 | |
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| 121 | if ( rChar(sring) != rChar(dring) ) { |
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| 122 | WerrorS( "rings must have same characteristic" ); |
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| 123 | state= FglmIncompatibleRings; |
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| 124 | } |
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| 125 | if ( (sring->OrdSgn != 1) || (dring->OrdSgn != 1) ) { |
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| 126 | WerrorS( "only works for global orderings" ); |
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| 127 | state= FglmIncompatibleRings; |
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| 128 | } |
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| 129 | if ( sring->N != dring->N ) |
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| 130 | { |
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| 131 | WerrorS( "rings must have same number of variables" ); |
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| 132 | state= FglmIncompatibleRings; |
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| 133 | } |
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| 134 | if ( rPar(sring) != rPar(dring) ) |
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| 135 | { |
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| 136 | WerrorS( "rings must have same number of parameters" ); |
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| 137 | state= FglmIncompatibleRings; |
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| 138 | } |
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| 139 | if ( state != FglmOk ) return state; |
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| 140 | // now the rings have the same number of variables resp. parameters. |
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| 141 | // check if the names of the variables resp. parameters do agree: |
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| 142 | int nvar = sring->N; |
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| 143 | int npar = rPar(sring); |
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| 144 | int * pperm; |
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| 145 | if ( npar > 0 ) |
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| 146 | pperm= (int *)omAlloc0( (npar+1)*sizeof( int ) ); |
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| 147 | else |
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| 148 | pperm= NULL; |
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| 149 | maFindPerm( sring->names, nvar, sring->parameter, npar, |
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| 150 | dring->names, nvar, dring->parameter, npar, vperm, pperm, |
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| 151 | dring->ch); |
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| 152 | for ( k= nvar; (k > 0) && (state == FglmOk); k-- ) |
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| 153 | if ( vperm[k] <= 0 ) { |
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| 154 | WerrorS( "variable names do not agree" ); |
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| 155 | state= FglmIncompatibleRings; |
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| 156 | } |
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| 157 | for ( k= npar-1; (k >= 0) && (state == FglmOk); k-- ) |
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| 158 | if ( pperm[k] >= 0 ) { |
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| 159 | WerrorS( "paramater names do not agree" ); |
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| 160 | state= FglmIncompatibleRings; |
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| 161 | } |
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| 162 | if (pperm != NULL) // OB: ???? |
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| 163 | omFreeSize( (ADDRESS)pperm, (npar+1)*sizeof( int ) ); |
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| 164 | if ( state != FglmOk ) return state; |
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| 165 | // check if both rings are qrings or not |
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| 166 | if ( sring->qideal != NULL ) { |
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| 167 | if ( dring->qideal == NULL ) { |
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| 168 | Werror( "%s is a qring, current ring not", sringHdl->id ); |
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| 169 | return FglmIncompatibleRings; |
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| 170 | } |
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| 171 | // both rings are qrings, now check if both quotients define the same ideal. |
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| 172 | // check if sring->qideal is contained in dring->qideal: |
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| 173 | rSetHdl( dringHdl ); |
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| 174 | nMapFunc nMap=nSetMap( sring ); |
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| 175 | ideal sqind = idInit( IDELEMS( sring->qideal ), 1 ); |
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| 176 | for ( k= IDELEMS( sring->qideal )-1; k >= 0; k-- ) |
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| 177 | (sqind->m)[k]= pPermPoly( (sring->qideal->m)[k], vperm, sring, nMap); |
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| 178 | ideal sqindred = kNF( dring->qideal, NULL, sqind ); |
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| 179 | if ( ! idIs0( sqindred ) ) { |
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| 180 | WerrorS( "the quotients do not agree" ); |
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| 181 | state= FglmIncompatibleRings; |
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| 182 | } |
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| 183 | idDelete( & sqind ); |
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| 184 | idDelete( & sqindred ); |
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| 185 | rSetHdl( sringHdl ); |
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| 186 | if ( state != FglmOk ) return state; |
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| 187 | // check if dring->qideal is contained in sring->qideal: |
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| 188 | int * dsvperm = (int *)omAlloc0( (nvar+1)*sizeof( int ) ); |
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| 189 | maFindPerm( dring->names, nvar, NULL, 0, sring->names, nvar, NULL, 0, |
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| 190 | dsvperm, NULL, sring->ch); |
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| 191 | nMap=nSetMap(dring); |
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| 192 | ideal dqins = idInit( IDELEMS( dring->qideal ), 1 ); |
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| 193 | for ( k= IDELEMS( dring->qideal )-1; k >= 0; k-- ) |
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| 194 | (dqins->m)[k]=pPermPoly( (dring->qideal->m)[k], dsvperm, sring, nMap); |
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| 195 | ideal dqinsred = kNF( sring->qideal, NULL, dqins ); |
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| 196 | if ( ! idIs0( dqinsred ) ) { |
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| 197 | WerrorS( "the quotients do not agree" ); |
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| 198 | state= FglmIncompatibleRings; |
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| 199 | } |
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| 200 | idDelete( & dqins ); |
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| 201 | idDelete( & dqinsred ); |
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| 202 | omFreeSize( (ADDRESS)dsvperm, (nvar+1)*sizeof( int ) ); |
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| 203 | if ( state != FglmOk ) return state; |
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| 204 | } |
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| 205 | else { |
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| 206 | if ( dring->qideal != NULL ) { |
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| 207 | Werror( "current ring is a qring, %s not", sringHdl->id ); |
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| 208 | return FglmIncompatibleRings; |
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| 209 | } |
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| 210 | } |
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| 211 | return FglmOk; |
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| 212 | } |
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| 213 | |
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| 214 | // Checks if the ideal "theIdeal" is zero-dimensional and minimal. It does |
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| 215 | // not check, if it is reduced. |
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| 216 | // returns FglmOk if we can use theIdeal for CalculateFunctionals (this |
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| 217 | // function reports an error if theIdeal is not reduced, |
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| 218 | // so this need not to be tested here) |
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| 219 | // FglmNotReduced if theIdeal is not minimal |
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| 220 | // FglmNotZeroDim if it is not zero-dimensional |
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| 221 | // FglmHasOne if 1 belongs to theIdeal |
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| 222 | FglmState |
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| 223 | fglmIdealcheck( const ideal theIdeal ) |
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| 224 | { |
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| 225 | FglmState state = FglmOk; |
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| 226 | int power; |
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| 227 | int k; |
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| 228 | BOOLEAN * purePowers = (BOOLEAN *)omAlloc( pVariables*sizeof( BOOLEAN ) ); |
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| 229 | for ( k= pVariables-1; k >= 0; k-- ) |
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| 230 | purePowers[k]= FALSE; |
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| 231 | |
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| 232 | for ( k= IDELEMS( theIdeal ) - 1; (state == FglmOk) && (k >= 0); k-- ) { |
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| 233 | poly p = (theIdeal->m)[k]; |
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| 234 | if ( pIsConstant( p ) ) state= FglmHasOne; |
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| 235 | else if ( (power= pIsPurePower( p )) > 0 ) { |
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| 236 | fglmASSERT( 0 < power && power <= pVariables, "illegal power" ); |
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| 237 | if ( purePowers[power-1] == TRUE ) state= FglmNotReduced; |
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| 238 | else purePowers[power-1]= TRUE; |
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| 239 | } |
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| 240 | for ( int l = IDELEMS( theIdeal ) - 1; state == FglmOk && l >= 0; l-- ) |
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| 241 | if ( (k != l) && pDivisibleBy( p, (theIdeal->m)[l] ) ) |
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| 242 | state= FglmNotReduced; |
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| 243 | } |
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| 244 | if ( state == FglmOk ) { |
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| 245 | for ( k= pVariables-1 ; (state == FglmOk) && (k >= 0); k-- ) |
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| 246 | if ( purePowers[k] == FALSE ) state= FglmNotZeroDim; |
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| 247 | } |
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| 248 | omFreeSize( (ADDRESS)purePowers, pVariables*sizeof( BOOLEAN ) ); |
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| 249 | return state; |
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| 250 | } |
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| 251 | |
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| 252 | // The main function for the fglm-Algorithm. |
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| 253 | // Checks the input-data, and calls fglmzero (see fglmzero.cc). |
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| 254 | // Returns the new groebnerbasis or 0 if an error occoured. |
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| 255 | BOOLEAN |
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| 256 | fglmProc( leftv result, leftv first, leftv second ) |
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| 257 | { |
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| 258 | FglmState state = FglmOk; |
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| 259 | |
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| 260 | idhdl destRingHdl = currRingHdl; |
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| 261 | ring destRing = currRing; |
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| 262 | ideal destIdeal = NULL; |
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| 263 | idhdl sourceRingHdl = (idhdl)first->data; |
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| 264 | rSetHdl( sourceRingHdl ); |
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| 265 | ring sourceRing = currRing; |
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| 266 | |
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| 267 | int * vperm = (int *)omAlloc0( (pVariables+1)*sizeof( int ) ); |
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| 268 | state= fglmConsistency( sourceRingHdl, destRingHdl, vperm ); |
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| 269 | omFreeSize( (ADDRESS)vperm, (pVariables+1)*sizeof(int) ); |
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| 270 | |
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| 271 | if ( state == FglmOk ) { |
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| 272 | idhdl ih = currRing->idroot->get( second->Name(), myynest ); |
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| 273 | if ( (ih != NULL) && (IDTYP(ih)==IDEAL_CMD) ) { |
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| 274 | ideal sourceIdeal; |
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| 275 | if ( currQuotient != NULL ) |
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| 276 | sourceIdeal= fglmUpdatesource( IDIDEAL( ih ) ); |
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| 277 | else |
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| 278 | sourceIdeal = IDIDEAL( ih ); |
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| 279 | state= fglmIdealcheck( sourceIdeal ); |
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| 280 | if ( state == FglmOk ) { |
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| 281 | // Now the settings are compatible with FGLM |
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| 282 | assumeStdFlag( (leftv)ih ); |
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| 283 | if ( fglmzero( sourceRingHdl, sourceIdeal, destRingHdl, destIdeal, FALSE, (currQuotient != NULL) ) == FALSE ) |
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| 284 | state= FglmNotReduced; |
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| 285 | } |
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| 286 | } else state= FglmNoIdeal; |
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| 287 | } |
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| 288 | if ( currRingHdl != destRingHdl ) |
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| 289 | rSetHdl( destRingHdl ); |
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| 290 | switch (state) { |
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| 291 | case FglmOk: |
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| 292 | if ( currQuotient != NULL ) fglmUpdateresult( destIdeal ); |
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| 293 | break; |
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| 294 | case FglmHasOne: |
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| 295 | destIdeal= idInit(1,1); |
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| 296 | (destIdeal->m)[0]= pOne(); |
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| 297 | state= FglmOk; |
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| 298 | break; |
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| 299 | case FglmIncompatibleRings: |
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| 300 | Werror( "ring %s and current ring are incompatible", first->Name() ); |
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| 301 | destIdeal= idInit(0,0); |
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| 302 | break; |
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| 303 | case FglmNoIdeal: |
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| 304 | Werror( "Can't find ideal %s in ring %s", second->Name(), first->Name() ); |
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| 305 | destIdeal= idInit(0,0); |
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| 306 | break; |
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| 307 | case FglmNotZeroDim: |
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| 308 | Werror( "The ideal %s has to be 0-dimensional", second->Name() ); |
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| 309 | destIdeal= idInit(0,0); |
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| 310 | break; |
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| 311 | case FglmNotReduced: |
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[6fdd4a] | 312 | Werror( "The ideal %s has to be given by a reduced SB", second->Name() ); |
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[35aab3] | 313 | destIdeal= idInit(0,0); |
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| 314 | break; |
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| 315 | default: |
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| 316 | destIdeal= idInit(1,1); |
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| 317 | } |
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| 318 | |
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| 319 | result->rtyp = IDEAL_CMD; |
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| 320 | result->data= (void *)destIdeal; |
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| 321 | setFlag( result, FLAG_STD ); |
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| 322 | return (state != FglmOk); |
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| 323 | } |
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| 324 | |
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| 325 | // fglmQuotProc: Calculate I:f with FGLM methods. |
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| 326 | // Checks the input-data, and calls fglmquot (see fglmzero.cc). |
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| 327 | // Returns the new groebnerbasis if I:f or 0 if an error occoured. |
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| 328 | BOOLEAN |
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| 329 | fglmQuotProc( leftv result, leftv first, leftv second ) |
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| 330 | { |
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| 331 | FglmState state = FglmOk; |
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| 332 | |
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| 333 | // STICKYPROT("quotstart\n"); |
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| 334 | ideal sourceIdeal = (ideal)first->Data(); |
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| 335 | poly quot = (poly)second->Data(); |
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| 336 | ideal destIdeal = NULL; |
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| 337 | |
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| 338 | state = fglmIdealcheck( sourceIdeal ); |
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| 339 | if ( state == FglmOk ) { |
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| 340 | if ( quot == NULL ) state= FglmPolyIsZero; |
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| 341 | else if ( pIsConstant( quot ) ) state= FglmPolyIsOne; |
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| 342 | } |
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| 343 | |
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| 344 | if ( state == FglmOk ) { |
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| 345 | assumeStdFlag( first ); |
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| 346 | if ( fglmquot( sourceIdeal, quot, destIdeal ) == FALSE ) |
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| 347 | state= FglmNotReduced; |
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| 348 | } |
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| 349 | |
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| 350 | switch (state) { |
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| 351 | case FglmOk: |
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| 352 | break; |
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| 353 | case FglmHasOne: |
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| 354 | destIdeal= idInit(1,1); |
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| 355 | (destIdeal->m)[0]= pOne(); |
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| 356 | state= FglmOk; |
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| 357 | break; |
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| 358 | case FglmNotZeroDim: |
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| 359 | Werror( "The ideal %s has to be 0-dimensional", first->Name() ); |
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| 360 | destIdeal= idInit(0,0); |
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| 361 | break; |
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| 362 | case FglmNotReduced: |
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| 363 | Werror( "The poly %s has to be reduced", second->Name() ); |
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| 364 | destIdeal= idInit(0,0); |
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| 365 | break; |
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| 366 | case FglmPolyIsOne: |
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| 367 | int k; |
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| 368 | destIdeal= idInit( IDELEMS(sourceIdeal), 1 ); |
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| 369 | for ( k= IDELEMS( sourceIdeal )-1; k >=0; k-- ) |
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| 370 | (destIdeal->m)[k]= pCopy( (sourceIdeal->m)[k] ); |
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| 371 | state= FglmOk; |
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| 372 | break; |
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| 373 | case FglmPolyIsZero: |
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| 374 | destIdeal= idInit(1,1); |
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| 375 | (destIdeal->m)[0]= pOne(); |
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| 376 | state= FglmOk; |
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| 377 | break; |
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| 378 | default: |
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| 379 | destIdeal= idInit(1,1); |
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| 380 | } |
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| 381 | |
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| 382 | result->rtyp = IDEAL_CMD; |
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| 383 | result->data= (void *)destIdeal; |
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| 384 | setFlag( result, FLAG_STD ); |
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| 385 | // STICKYPROT("quotend\n"); |
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| 386 | return (state != FglmOk); |
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| 387 | } // fglmQuotProt |
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| 388 | |
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| 389 | // The main function for finduni(). |
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| 390 | // Checks the input-data, and calls FindUnivariateWrapper (see fglmzero.cc). |
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| 391 | // Returns an ideal containing the univariate Polynomials or 0 if an error |
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| 392 | // has occoured. |
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| 393 | BOOLEAN |
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| 394 | findUniProc( leftv result, leftv first ) |
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| 395 | { |
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| 396 | ideal sourceIdeal; |
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| 397 | ideal destIdeal = NULL; |
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| 398 | FglmState state; |
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| 399 | |
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| 400 | idhdl sourceIdealHdl = (idhdl)first->data; |
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| 401 | sourceIdeal= IDIDEAL(sourceIdealHdl); |
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| 402 | |
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| 403 | assumeStdFlag( first ); |
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| 404 | state= fglmIdealcheck( sourceIdeal ); |
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| 405 | if ( state == FglmOk ) { |
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| 406 | if ( FindUnivariateWrapper( sourceIdeal, destIdeal ) == FALSE ) |
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| 407 | state = FglmNotReduced; |
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| 408 | } |
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| 409 | switch (state) { |
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| 410 | case FglmOk: |
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| 411 | break; |
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| 412 | case FglmHasOne: |
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| 413 | destIdeal= idInit(1,1); |
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| 414 | (destIdeal->m)[0]= pOne(); |
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| 415 | state= FglmOk; |
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| 416 | break; |
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| 417 | case FglmNotZeroDim: |
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| 418 | Werror( "The ideal %s has to be 0-dimensional", first->Name() ); |
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| 419 | destIdeal= idInit(0,0); |
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| 420 | break; |
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| 421 | case FglmNotReduced: |
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[bdaa5d] | 422 | Werror( "The ideal %s has to be given by a reduced SB", |
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| 423 | first->Name() ); |
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[35aab3] | 424 | destIdeal= idInit(0,0); |
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| 425 | break; |
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| 426 | default: |
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| 427 | destIdeal= idInit(1,1); |
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| 428 | } |
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| 429 | |
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| 430 | result->rtyp = IDEAL_CMD; |
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| 431 | result->data= (void *)destIdeal; |
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| 432 | |
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| 433 | return FALSE; |
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| 434 | } |
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| 435 | #endif |
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| 436 | // ---------------------------------------------------------------------------- |
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| 437 | // Local Variables: *** |
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| 438 | // compile-command: "make Singular" *** |
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| 439 | // page-delimiter: "^\\(\\|//!\\)" *** |
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| 440 | // fold-internal-margins: nil *** |
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| 441 | // End: *** |
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