[35aab3] | 1 | // ---------------------------------------------------------------------------- |
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| 2 | // spectrum.cc |
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| 3 | // begin of file |
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| 4 | // Stephan Endrass, endrass@mathematik.uni-mainz.de |
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| 5 | // 23.7.99 |
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| 6 | // ---------------------------------------------------------------------------- |
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| 7 | |
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| 8 | #define SPECTRUM_CC |
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| 9 | |
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| 10 | #include "mod2.h" |
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| 11 | |
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| 12 | #ifdef HAVE_SPECTRUM |
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| 13 | |
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| 14 | #ifdef SPECTRUM_PRINT |
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| 15 | #include <iostream.h> |
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| 16 | #ifndef SPECTRUM_IOSTREAM |
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| 17 | #include <stdio.h> |
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| 18 | #endif |
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| 19 | #endif |
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| 20 | |
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| 21 | #include <mylimits.h> |
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| 22 | |
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| 23 | #include "numbers.h" |
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| 24 | #include "polys.h" |
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| 25 | #include "ideals.h" |
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| 26 | #include "kstd1.h" |
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| 27 | #include "stairc.h" |
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| 28 | #include "intvec.h" |
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| 29 | #include "ring.h" |
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| 30 | |
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| 31 | #include "multicnt.h" |
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| 32 | #include "GMPrat.h" |
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| 33 | #include "kmatrix.h" |
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| 34 | #include "npolygon.h" |
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| 35 | #include "splist.h" |
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| 36 | #include "semic.h" |
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| 37 | |
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| 38 | // ---------------------------------------------------------------------------- |
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| 39 | // test if the polynomial h has a term of total degree d |
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| 40 | // ---------------------------------------------------------------------------- |
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| 41 | |
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| 42 | BOOLEAN hasTermOfDegree( poly h, int d ) |
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| 43 | { |
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| 44 | do |
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| 45 | { |
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| 46 | if( pTotaldegree( h )== d ) |
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| 47 | return TRUE; |
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| 48 | pIter(h); |
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| 49 | } |
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| 50 | while( h!=(poly)NULL ); |
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| 51 | |
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| 52 | return FALSE; |
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| 53 | } |
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| 54 | |
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| 55 | // ---------------------------------------------------------------------------- |
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| 56 | // test if the polynomial h has a constant term |
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| 57 | // ---------------------------------------------------------------------------- |
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| 58 | |
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| 59 | static BOOLEAN inline hasConstTerm( poly h ) |
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| 60 | { |
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| 61 | return hasTermOfDegree(h,0); |
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| 62 | } |
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| 63 | |
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| 64 | // ---------------------------------------------------------------------------- |
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| 65 | // test if the polynomial h has a linear term |
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| 66 | // ---------------------------------------------------------------------------- |
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| 67 | |
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| 68 | static BOOLEAN inline hasLinearTerm( poly h ) |
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| 69 | { |
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| 70 | return hasTermOfDegree(h,1); |
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| 71 | } |
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| 72 | |
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| 73 | // ---------------------------------------------------------------------------- |
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| 74 | // test if the ideal J has a lead monomial on the axis number k |
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| 75 | // ---------------------------------------------------------------------------- |
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| 76 | |
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| 77 | BOOLEAN hasAxis( ideal J,int k ) |
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| 78 | { |
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| 79 | int i; |
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| 80 | |
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| 81 | for( i=0; i<IDELEMS(J); i++ ) |
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| 82 | { |
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| 83 | if (pIsPurePower( J->m[i] ) == k) return TRUE; |
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| 84 | } |
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| 85 | return FALSE; |
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| 86 | } |
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| 87 | |
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| 88 | // ---------------------------------------------------------------------------- |
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| 89 | // test if the ideal J has 1 as a lead monomial |
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| 90 | // ---------------------------------------------------------------------------- |
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| 91 | |
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| 92 | int hasOne( ideal J ) |
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| 93 | { |
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| 94 | int i; |
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| 95 | |
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| 96 | for( i=0; i<IDELEMS(J); i++ ) |
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| 97 | { |
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| 98 | if (pIsConstant(J->m[i])) return TRUE; |
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| 99 | } |
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| 100 | return FALSE; |
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| 101 | } |
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| 102 | // ---------------------------------------------------------------------------- |
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| 103 | // test if m is a multiple of one of the monomials of f |
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| 104 | // ---------------------------------------------------------------------------- |
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| 105 | |
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| 106 | int isMultiple( poly f,poly m ) |
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| 107 | { |
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| 108 | while( f!=(poly)NULL ) |
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| 109 | { |
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| 110 | // --------------------------------------------------- |
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| 111 | // for a local order f|m is only possible if f>=m |
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| 112 | // --------------------------------------------------- |
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| 113 | |
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| 114 | if( pLmCmp( f,m )>=0 ) |
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| 115 | { |
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| 116 | if( pLmDivisibleByNoComp( f,m ) ) |
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| 117 | { |
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| 118 | return TRUE; |
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| 119 | } |
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| 120 | else |
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| 121 | { |
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| 122 | pIter( f ); |
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| 123 | } |
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| 124 | } |
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| 125 | else |
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| 126 | { |
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| 127 | return FALSE; |
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| 128 | } |
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| 129 | } |
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| 130 | |
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| 131 | return FALSE; |
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| 132 | } |
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| 133 | |
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| 134 | // ---------------------------------------------------------------------------- |
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| 135 | // compute the minimal monomial of minimmal weight>=max_weight |
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| 136 | // ---------------------------------------------------------------------------- |
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| 137 | |
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| 138 | poly computeWC( const newtonPolygon &np,Rational max_weight ) |
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| 139 | { |
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| 140 | poly m = pOne(); |
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| 141 | poly wc = (poly)NULL; |
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| 142 | int mdegree; |
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| 143 | |
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| 144 | for( int i=1; i<=pVariables; i++ ) |
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| 145 | { |
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| 146 | mdegree = 1; |
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| 147 | pSetExp( m,i,mdegree ); |
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| 148 | // pSetm( m ); |
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| 149 | // np.weight_shift does not need pSetm( m ), postpone it |
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| 150 | |
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| 151 | while( np.weight_shift( m )<max_weight ) |
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| 152 | { |
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| 153 | mdegree++; |
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| 154 | pSetExp( m,i,mdegree ); |
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| 155 | // pSetm( m ); |
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| 156 | // np.weight_shift does not need pSetm( m ), postpone it |
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| 157 | } |
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| 158 | pSetm( m ); |
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| 159 | |
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| 160 | if( i==1 || pCmp( m,wc )<0 ) |
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| 161 | { |
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| 162 | pDelete( &wc ); |
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| 163 | wc = pHead( m ); |
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| 164 | } |
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| 165 | |
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| 166 | pSetExp( m,i,0 ); |
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| 167 | } |
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| 168 | |
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| 169 | pDelete( &m ); |
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| 170 | |
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| 171 | return wc; |
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| 172 | } |
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| 173 | |
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| 174 | // ---------------------------------------------------------------------------- |
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| 175 | // deletes all monomials of f which are less than hc |
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| 176 | // ---------------------------------------------------------------------------- |
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| 177 | |
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| 178 | static inline poly normalFormHC( poly f,poly hc ) |
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| 179 | { |
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| 180 | poly *ptr = &f; |
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| 181 | |
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| 182 | while( (*ptr)!=(poly)NULL ) |
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| 183 | { |
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| 184 | if( pLmCmp( *ptr,hc )>=0 ) |
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| 185 | { |
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| 186 | ptr = &(pNext( *ptr )); |
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| 187 | } |
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| 188 | else |
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| 189 | { |
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| 190 | pDelete( ptr ); |
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| 191 | return f; |
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| 192 | } |
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| 193 | } |
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| 194 | |
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| 195 | return f; |
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| 196 | } |
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| 197 | |
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| 198 | // ---------------------------------------------------------------------------- |
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| 199 | // deletes all monomials of f which are multiples of monomials of Z |
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| 200 | // ---------------------------------------------------------------------------- |
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| 201 | |
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| 202 | static inline poly normalFormZ( poly f,poly Z ) |
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| 203 | { |
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| 204 | poly *ptr = &f; |
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| 205 | |
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| 206 | while( (*ptr)!=(poly)NULL ) |
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| 207 | { |
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| 208 | if( !isMultiple( Z,*ptr ) ) |
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| 209 | { |
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| 210 | ptr = &(pNext( *ptr )); |
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| 211 | } |
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| 212 | else |
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| 213 | { |
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| 214 | pDeleteLm(ptr); |
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| 215 | } |
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| 216 | } |
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| 217 | |
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| 218 | return f; |
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| 219 | } |
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| 220 | |
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| 221 | // ?? HS: |
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| 222 | // Looks for the shortest polynomial f in stdJ which is divisible |
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| 223 | // by the monimial m, return its index in stdJ |
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| 224 | // ---------------------------------------------------------------------------- |
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| 225 | // Looks for the first polynomial f in stdJ which satisfies m=LT(f)*eta |
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| 226 | // for a monomial eta. The return eta*f-m and cancel all monomials |
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| 227 | // which are smaller than the highest corner hc |
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| 228 | // ---------------------------------------------------------------------------- |
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| 229 | |
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| 230 | static inline int isLeadMonomial( poly m,ideal stdJ ) |
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| 231 | { |
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| 232 | int length = INT_MAX; |
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| 233 | int result = -1; |
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| 234 | |
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| 235 | for( int i=0; i<IDELEMS(stdJ); i++ ) |
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| 236 | { |
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| 237 | if( pCmp( stdJ->m[i],m )>=0 && pDivisibleBy( stdJ->m[i],m ) ) |
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| 238 | { |
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| 239 | int tmp = pLength( stdJ->m[i] ); |
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| 240 | |
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| 241 | if( tmp < length ) |
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| 242 | { |
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| 243 | length = tmp; |
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| 244 | result = i; |
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| 245 | } |
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| 246 | } |
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| 247 | } |
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| 248 | |
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| 249 | return result; |
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| 250 | } |
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| 251 | |
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| 252 | // ---------------------------------------------------------------------------- |
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| 253 | // set the exponent of a monomial t an integer array |
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| 254 | // ---------------------------------------------------------------------------- |
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| 255 | |
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| 256 | static void setExp( poly m,int *r ) |
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| 257 | { |
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| 258 | for( int i=pVariables; i>0; i-- ) |
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| 259 | { |
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| 260 | pSetExp( m,i,r[i-1] ); |
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| 261 | } |
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| 262 | pSetm( m ); |
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| 263 | } |
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| 264 | |
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| 265 | // ---------------------------------------------------------------------------- |
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| 266 | // check if the ordering is a reverse wellordering, i.e. every monomial |
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| 267 | // is smaller than only finitely monomials |
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| 268 | // ---------------------------------------------------------------------------- |
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| 269 | |
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| 270 | static BOOLEAN isWell( void ) |
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| 271 | { |
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| 272 | int b = rBlocks( currRing ); |
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| 273 | |
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| 274 | if( b==3 && |
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| 275 | ( currRing->order[0] == ringorder_ds || |
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| 276 | currRing->order[0] == ringorder_Ds || |
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| 277 | currRing->order[0] == ringorder_ws || |
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| 278 | currRing->order[0] == ringorder_Ws ) ) |
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| 279 | { |
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| 280 | return TRUE; |
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| 281 | } |
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| 282 | else if( b>=3 |
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| 283 | && (( currRing->order[0] ==ringorder_a |
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| 284 | && currRing->block1[0]==pVariables ) |
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| 285 | || (currRing->order[0]==ringorder_M |
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| 286 | && currRing->block1[0]==pVariables*pVariables ))) |
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| 287 | { |
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| 288 | for( int i=pVariables-1; i>=0; i-- ) |
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| 289 | { |
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| 290 | if( currRing->wvhdl[0][i]>=0 ) |
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| 291 | { |
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| 292 | return FALSE; |
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| 293 | } |
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| 294 | } |
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| 295 | return TRUE; |
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| 296 | } |
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| 297 | |
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| 298 | return FALSE; |
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| 299 | } |
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| 300 | |
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| 301 | // ---------------------------------------------------------------------------- |
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| 302 | // compute all monomials not in stdJ and their normal forms |
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| 303 | // ---------------------------------------------------------------------------- |
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| 304 | |
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| 305 | void computeNF( ideal stdJ,poly hc,poly wc,spectrumPolyList *NF ) |
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| 306 | { |
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| 307 | int carry,k; |
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| 308 | multiCnt C( pVariables,0 ); |
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| 309 | poly Z = (poly)NULL; |
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| 310 | |
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| 311 | int well = isWell( ); |
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| 312 | |
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| 313 | do |
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| 314 | { |
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| 315 | poly m = pOne(); |
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| 316 | setExp( m,C.cnt ); |
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| 317 | |
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| 318 | carry = FALSE; |
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| 319 | |
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| 320 | k = isLeadMonomial( m,stdJ ); |
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| 321 | |
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| 322 | if( k < 0 ) |
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| 323 | { |
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| 324 | // --------------------------- |
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| 325 | // m is not a lead monomial |
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| 326 | // --------------------------- |
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| 327 | |
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| 328 | NF->insert_node( m,(poly)NULL ); |
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| 329 | } |
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| 330 | else if( isMultiple( Z,m ) ) |
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| 331 | { |
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| 332 | // ------------------------------------ |
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| 333 | // m is trivially in the ideal stdJ |
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| 334 | // ------------------------------------ |
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| 335 | |
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| 336 | pDelete( &m ); |
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| 337 | carry = TRUE; |
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| 338 | } |
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| 339 | else if( pCmp( m,hc ) < 0 || pCmp( m,wc ) < 0 ) |
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| 340 | { |
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| 341 | // ------------------- |
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| 342 | // we do not need m |
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| 343 | // ------------------- |
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| 344 | |
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| 345 | pDelete( &m ); |
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| 346 | carry = TRUE; |
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| 347 | } |
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| 348 | else |
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| 349 | { |
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| 350 | // -------------------------- |
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| 351 | // compute lazy normal form |
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| 352 | // -------------------------- |
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| 353 | |
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| 354 | poly multiplicant = pDivide( m,stdJ->m[k] ); |
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| 355 | pGetCoeff( multiplicant ) = nInit(1); |
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| 356 | |
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| 357 | poly nf = pMult_mm( pCopy( stdJ->m[k] ), multiplicant ); |
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| 358 | |
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| 359 | pDelete( &multiplicant ); |
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| 360 | |
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| 361 | nf = normalFormHC( nf,hc ); |
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| 362 | |
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| 363 | if( pNext( nf )==(poly)NULL ) |
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| 364 | { |
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| 365 | // ---------------------------------- |
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| 366 | // normal form of m is m itself |
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| 367 | // ---------------------------------- |
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| 368 | |
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| 369 | pDelete( &nf ); |
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| 370 | NF->delete_monomial( m ); |
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| 371 | Z = pAdd( Z,m ); |
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| 372 | carry = TRUE; |
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| 373 | } |
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| 374 | else |
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| 375 | { |
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| 376 | nf = normalFormZ( nf,Z ); |
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| 377 | |
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| 378 | if( pNext( nf )==(poly)NULL ) |
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| 379 | { |
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| 380 | // ---------------------------------- |
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| 381 | // normal form of m is m itself |
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| 382 | // ---------------------------------- |
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| 383 | |
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| 384 | pDelete( &nf ); |
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| 385 | NF->delete_monomial( m ); |
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| 386 | Z = pAdd( Z,m ); |
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| 387 | carry = TRUE; |
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| 388 | } |
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| 389 | else |
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| 390 | { |
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| 391 | // ------------------------------------ |
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| 392 | // normal form of m is a polynomial |
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| 393 | // ------------------------------------ |
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| 394 | |
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| 395 | pNorm( nf ); |
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| 396 | if( well==TRUE ) |
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| 397 | { |
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| 398 | NF->insert_node( m,nf ); |
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| 399 | } |
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| 400 | else |
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| 401 | { |
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| 402 | poly nfhard = kNF( stdJ,(ideal)NULL,pNext( nf ),0,0 ); |
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| 403 | nfhard = normalFormHC( nfhard,hc ); |
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| 404 | nfhard = normalFormZ ( nfhard,Z ); |
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| 405 | |
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| 406 | if( nfhard==(poly)NULL ) |
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| 407 | { |
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| 408 | NF->delete_monomial( m ); |
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| 409 | Z = pAdd( Z,m ); |
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| 410 | carry = TRUE; |
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| 411 | } |
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| 412 | else |
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| 413 | { |
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| 414 | pDelete( &pNext( nf ) ); |
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| 415 | pNext( nf ) = nfhard; |
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| 416 | NF->insert_node( m,nf ); |
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| 417 | } |
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| 418 | } |
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| 419 | } |
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| 420 | } |
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| 421 | } |
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| 422 | } |
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| 423 | while( C.inc( carry ) ); |
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| 424 | |
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| 425 | // delete single monomials |
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| 426 | |
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| 427 | BOOLEAN not_finished; |
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| 428 | |
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| 429 | do |
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| 430 | { |
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| 431 | not_finished = FALSE; |
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| 432 | |
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| 433 | spectrumPolyNode *node = NF->root; |
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| 434 | |
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| 435 | while( node!=(spectrumPolyNode*)NULL ) |
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| 436 | { |
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| 437 | if( node->nf!=(poly)NULL && pNext( node->nf )==(poly)NULL ) |
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| 438 | { |
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| 439 | NF->delete_monomial( node->nf ); |
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| 440 | not_finished = TRUE; |
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| 441 | node = (spectrumPolyNode*)NULL; |
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| 442 | } |
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| 443 | else |
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| 444 | { |
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| 445 | node = node->next; |
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| 446 | } |
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| 447 | } |
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| 448 | } while( not_finished ); |
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| 449 | |
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| 450 | pDelete( &Z ); |
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| 451 | } |
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| 452 | |
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| 453 | // ---------------------------------------------------------------------------- |
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| 454 | // check if currRing is local |
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| 455 | // ---------------------------------------------------------------------------- |
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| 456 | |
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| 457 | BOOLEAN ringIsLocal( void ) |
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| 458 | { |
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| 459 | poly m = pOne(); |
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| 460 | poly one = pOne(); |
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| 461 | BOOLEAN res=TRUE; |
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| 462 | |
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| 463 | for( int i=pVariables; i>0; i-- ) |
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| 464 | { |
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| 465 | pSetExp( m,i,1 ); |
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| 466 | pSetm( m ); |
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| 467 | |
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| 468 | if( pCmp( m,one )>0 ) |
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| 469 | { |
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| 470 | res=FALSE; |
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| 471 | break; |
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| 472 | } |
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| 473 | pSetExp( m,i,0 ); |
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| 474 | } |
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| 475 | |
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| 476 | pDelete( &m ); |
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| 477 | pDelete( &one ); |
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| 478 | |
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| 479 | return res; |
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| 480 | } |
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| 481 | |
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| 482 | // ---------------------------------------------------------------------------- |
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| 483 | // print error message corresponding to spectrumState state: |
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| 484 | // ---------------------------------------------------------------------------- |
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| 485 | void spectrumPrintError(spectrumState state) |
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| 486 | { |
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| 487 | switch( state ) |
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| 488 | { |
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| 489 | case spectrumZero: |
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| 490 | WerrorS( "polynomial is zero" ); |
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| 491 | break; |
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| 492 | case spectrumBadPoly: |
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| 493 | WerrorS( "polynomial has constant term" ); |
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| 494 | break; |
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| 495 | case spectrumNoSingularity: |
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| 496 | WerrorS( "not a singularity" ); |
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| 497 | break; |
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| 498 | case spectrumNotIsolated: |
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| 499 | WerrorS( "the singularity is not isolated" ); |
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| 500 | break; |
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| 501 | case spectrumNoHC: |
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| 502 | WerrorS( "highest corner cannot be computed" ); |
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| 503 | break; |
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| 504 | case spectrumDegenerate: |
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| 505 | WerrorS( "principal part is degenerate" ); |
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| 506 | break; |
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| 507 | case spectrumOK: |
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| 508 | break; |
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| 509 | |
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| 510 | default: |
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| 511 | WerrorS( "unknown error occurred" ); |
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| 512 | break; |
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| 513 | } |
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| 514 | } |
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| 515 | #endif /* HAVE_SPECTRUM */ |
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| 516 | // ---------------------------------------------------------------------------- |
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| 517 | // spectrum.cc |
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| 518 | // end of file |
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| 519 | // ---------------------------------------------------------------------------- |
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