[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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[16f511] | 10 | #ifdef HAVE_CONFIG_H |
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[762407] | 11 | #include "config.h" |
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[16f511] | 12 | #endif /* HAVE_CONFIG_H */ |
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[599326] | 13 | #include <kernel/mod2.h> |
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[35aab3] | 14 | |
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| 15 | #ifdef HAVE_SPECTRUM |
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| 16 | |
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| 17 | #ifdef SPECTRUM_PRINT |
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| 18 | #include <iostream.h> |
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| 19 | #ifndef SPECTRUM_IOSTREAM |
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| 20 | #include <stdio.h> |
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| 21 | #endif |
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| 22 | #endif |
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| 23 | |
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[e7d5ef] | 24 | #include <misc/mylimits.h> |
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[35aab3] | 25 | |
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[0f401f] | 26 | #include <coeffs/numbers.h> |
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[3835a88] | 27 | #include <polys/monomials/p_polys.h> |
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| 28 | #include <polys/simpleideals.h> |
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[210e07] | 29 | #include <misc/intvec.h> |
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| 30 | #include <polys/monomials/ring.h> |
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[3835a88] | 31 | //extern ring currRing; |
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[599326] | 32 | |
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[3835a88] | 33 | #include <kernel/kstd1.h> |
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| 34 | #include <kernel/stairc.h> |
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[599326] | 35 | #include <kernel/multicnt.h> |
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| 36 | #include <kernel/GMPrat.h> |
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| 37 | #include <kernel/kmatrix.h> |
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| 38 | #include <kernel/npolygon.h> |
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| 39 | #include <kernel/splist.h> |
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| 40 | #include <kernel/semic.h> |
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[35aab3] | 41 | |
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| 42 | // ---------------------------------------------------------------------------- |
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| 43 | // test if the polynomial h has a term of total degree d |
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| 44 | // ---------------------------------------------------------------------------- |
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| 45 | |
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[3835a88] | 46 | BOOLEAN hasTermOfDegree( poly h, int d, const ring r ) |
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[35aab3] | 47 | { |
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| 48 | do |
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| 49 | { |
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[3835a88] | 50 | if( p_Totaldegree( h,r )== d ) |
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[35aab3] | 51 | return TRUE; |
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| 52 | pIter(h); |
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| 53 | } |
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[beef52] | 54 | while( h!=NULL ); |
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[35aab3] | 55 | |
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| 56 | return FALSE; |
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| 57 | } |
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| 58 | |
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| 59 | // ---------------------------------------------------------------------------- |
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| 60 | // test if the polynomial h has a constant term |
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| 61 | // ---------------------------------------------------------------------------- |
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| 62 | |
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[3835a88] | 63 | static BOOLEAN inline hasConstTerm( poly h, const ring r ) |
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[35aab3] | 64 | { |
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[3835a88] | 65 | return hasTermOfDegree(h,0,r); |
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[35aab3] | 66 | } |
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| 67 | |
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| 68 | // ---------------------------------------------------------------------------- |
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| 69 | // test if the polynomial h has a linear term |
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| 70 | // ---------------------------------------------------------------------------- |
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| 71 | |
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[3835a88] | 72 | static BOOLEAN inline hasLinearTerm( poly h, const ring r ) |
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[35aab3] | 73 | { |
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[3835a88] | 74 | return hasTermOfDegree(h,1,r); |
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[35aab3] | 75 | } |
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| 76 | |
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| 77 | // ---------------------------------------------------------------------------- |
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| 78 | // test if the ideal J has a lead monomial on the axis number k |
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| 79 | // ---------------------------------------------------------------------------- |
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| 80 | |
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[3835a88] | 81 | BOOLEAN hasAxis( ideal J,int k, const ring r ) |
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[35aab3] | 82 | { |
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| 83 | int i; |
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| 84 | |
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| 85 | for( i=0; i<IDELEMS(J); i++ ) |
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| 86 | { |
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[3835a88] | 87 | if (p_IsPurePower( J->m[i],r ) == k) return TRUE; |
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[35aab3] | 88 | } |
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| 89 | return FALSE; |
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| 90 | } |
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| 91 | |
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| 92 | // ---------------------------------------------------------------------------- |
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| 93 | // test if the ideal J has 1 as a lead monomial |
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| 94 | // ---------------------------------------------------------------------------- |
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| 95 | |
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[3835a88] | 96 | int hasOne( ideal J, const ring r ) |
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[35aab3] | 97 | { |
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| 98 | int i; |
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| 99 | |
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| 100 | for( i=0; i<IDELEMS(J); i++ ) |
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| 101 | { |
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[3835a88] | 102 | if (p_IsConstant(J->m[i],r)) return TRUE; |
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[35aab3] | 103 | } |
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| 104 | return FALSE; |
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| 105 | } |
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| 106 | // ---------------------------------------------------------------------------- |
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| 107 | // test if m is a multiple of one of the monomials of f |
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| 108 | // ---------------------------------------------------------------------------- |
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| 109 | |
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[3835a88] | 110 | int isMultiple( poly f,poly m, const ring r ) |
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[35aab3] | 111 | { |
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[beef52] | 112 | while( f!=NULL ) |
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[35aab3] | 113 | { |
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| 114 | // --------------------------------------------------- |
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| 115 | // for a local order f|m is only possible if f>=m |
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| 116 | // --------------------------------------------------- |
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| 117 | |
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[3835a88] | 118 | if( p_LmCmp( f,m,r )>=0 ) |
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[35aab3] | 119 | { |
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[3835a88] | 120 | if( p_LmDivisibleByNoComp( f,m,r ) ) |
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[35aab3] | 121 | { |
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| 122 | return TRUE; |
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| 123 | } |
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| 124 | else |
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| 125 | { |
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| 126 | pIter( f ); |
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| 127 | } |
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| 128 | } |
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| 129 | else |
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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 | return FALSE; |
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| 136 | } |
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| 137 | |
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| 138 | // ---------------------------------------------------------------------------- |
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| 139 | // compute the minimal monomial of minimmal weight>=max_weight |
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| 140 | // ---------------------------------------------------------------------------- |
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| 141 | |
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[3835a88] | 142 | poly computeWC( const newtonPolygon &np,Rational max_weight, const ring r ) |
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[35aab3] | 143 | { |
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[3835a88] | 144 | poly m = p_One(r); |
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[beef52] | 145 | poly wc = NULL; |
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[35aab3] | 146 | int mdegree; |
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| 147 | |
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[3835a88] | 148 | for( int i=1; i<=r->N; i++ ) |
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[35aab3] | 149 | { |
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| 150 | mdegree = 1; |
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[3835a88] | 151 | p_SetExp( m,i,mdegree,r ); |
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[35aab3] | 152 | // pSetm( m ); |
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| 153 | // np.weight_shift does not need pSetm( m ), postpone it |
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| 154 | |
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[3835a88] | 155 | while( np.weight_shift( m,r )<max_weight ) |
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[35aab3] | 156 | { |
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| 157 | mdegree++; |
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[3835a88] | 158 | p_SetExp( m,i,mdegree,r ); |
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[35aab3] | 159 | // pSetm( m ); |
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| 160 | // np.weight_shift does not need pSetm( m ), postpone it |
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| 161 | } |
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[3835a88] | 162 | p_Setm( m,r ); |
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[35aab3] | 163 | |
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[3835a88] | 164 | if( i==1 || p_Cmp( m,wc,r )<0 ) |
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[35aab3] | 165 | { |
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[3835a88] | 166 | p_Delete( &wc,r ); |
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| 167 | wc = p_Head( m,r ); |
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[35aab3] | 168 | } |
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| 169 | |
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[3835a88] | 170 | p_SetExp( m,i,0,r ); |
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[35aab3] | 171 | } |
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| 172 | |
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[3835a88] | 173 | p_Delete( &m,r ); |
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[35aab3] | 174 | |
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| 175 | return wc; |
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| 176 | } |
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| 177 | |
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| 178 | // ---------------------------------------------------------------------------- |
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| 179 | // deletes all monomials of f which are less than hc |
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| 180 | // ---------------------------------------------------------------------------- |
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| 181 | |
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[3835a88] | 182 | static inline poly normalFormHC( poly f,poly hc, const ring r ) |
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[35aab3] | 183 | { |
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| 184 | poly *ptr = &f; |
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| 185 | |
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[beef52] | 186 | while( (*ptr)!=NULL ) |
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[35aab3] | 187 | { |
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[3835a88] | 188 | if( p_LmCmp( *ptr,hc,r )>=0 ) |
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[35aab3] | 189 | { |
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| 190 | ptr = &(pNext( *ptr )); |
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| 191 | } |
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| 192 | else |
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| 193 | { |
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[3835a88] | 194 | p_Delete( ptr,r ); |
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[35aab3] | 195 | return f; |
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| 196 | } |
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| 197 | } |
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| 198 | |
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| 199 | return f; |
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| 200 | } |
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| 201 | |
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| 202 | // ---------------------------------------------------------------------------- |
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| 203 | // deletes all monomials of f which are multiples of monomials of Z |
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| 204 | // ---------------------------------------------------------------------------- |
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| 205 | |
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[3835a88] | 206 | static inline poly normalFormZ( poly f,poly Z, const ring r ) |
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[35aab3] | 207 | { |
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| 208 | poly *ptr = &f; |
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| 209 | |
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[beef52] | 210 | while( (*ptr)!=NULL ) |
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[35aab3] | 211 | { |
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[3835a88] | 212 | if( !isMultiple( Z,*ptr,r ) ) |
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[35aab3] | 213 | { |
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| 214 | ptr = &(pNext( *ptr )); |
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| 215 | } |
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| 216 | else |
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| 217 | { |
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[3835a88] | 218 | p_LmDelete(ptr,r); |
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[35aab3] | 219 | } |
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| 220 | } |
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| 221 | |
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| 222 | return f; |
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| 223 | } |
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| 224 | |
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| 225 | // ?? HS: |
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| 226 | // Looks for the shortest polynomial f in stdJ which is divisible |
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| 227 | // by the monimial m, return its index in stdJ |
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| 228 | // ---------------------------------------------------------------------------- |
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| 229 | // Looks for the first polynomial f in stdJ which satisfies m=LT(f)*eta |
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| 230 | // for a monomial eta. The return eta*f-m and cancel all monomials |
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| 231 | // which are smaller than the highest corner hc |
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| 232 | // ---------------------------------------------------------------------------- |
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| 233 | |
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[3835a88] | 234 | static inline int isLeadMonomial( poly m,ideal stdJ, const ring r ) |
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[35aab3] | 235 | { |
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[e554162] | 236 | int length = MAX_INT_VAL; |
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[35aab3] | 237 | int result = -1; |
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| 238 | |
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| 239 | for( int i=0; i<IDELEMS(stdJ); i++ ) |
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| 240 | { |
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[3835a88] | 241 | if( p_Cmp( stdJ->m[i],m,r )>=0 && p_DivisibleBy( stdJ->m[i],m,r ) ) |
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[35aab3] | 242 | { |
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| 243 | int tmp = pLength( stdJ->m[i] ); |
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| 244 | |
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| 245 | if( tmp < length ) |
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| 246 | { |
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| 247 | length = tmp; |
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| 248 | result = i; |
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| 249 | } |
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| 250 | } |
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| 251 | } |
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| 252 | |
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| 253 | return result; |
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| 254 | } |
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| 255 | |
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| 256 | // ---------------------------------------------------------------------------- |
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| 257 | // set the exponent of a monomial t an integer array |
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| 258 | // ---------------------------------------------------------------------------- |
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| 259 | |
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[3835a88] | 260 | static void setExp( poly m,int *r, const ring s ) |
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[35aab3] | 261 | { |
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[3835a88] | 262 | for( int i=s->N; i>0; i-- ) |
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[35aab3] | 263 | { |
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[3835a88] | 264 | p_SetExp( m,i,r[i-1],s ); |
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[35aab3] | 265 | } |
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[3835a88] | 266 | p_Setm( m,s ); |
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[35aab3] | 267 | } |
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| 268 | |
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| 269 | // ---------------------------------------------------------------------------- |
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| 270 | // check if the ordering is a reverse wellordering, i.e. every monomial |
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| 271 | // is smaller than only finitely monomials |
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| 272 | // ---------------------------------------------------------------------------- |
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| 273 | |
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[3835a88] | 274 | static BOOLEAN isWell( const ring r ) |
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[35aab3] | 275 | { |
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[3835a88] | 276 | int b = rBlocks( r ); |
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[35aab3] | 277 | |
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| 278 | if( b==3 && |
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[3835a88] | 279 | ( r->order[0] == ringorder_ds || |
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| 280 | r->order[0] == ringorder_Ds || |
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| 281 | r->order[0] == ringorder_ws || |
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| 282 | r->order[0] == ringorder_Ws ) ) |
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[35aab3] | 283 | { |
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| 284 | return TRUE; |
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| 285 | } |
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| 286 | else if( b>=3 |
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[3835a88] | 287 | && (( r->order[0] ==ringorder_a |
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| 288 | && r->block1[0]==r->N ) |
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| 289 | || (r->order[0]==ringorder_M |
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| 290 | && r->block1[0]==r->N*r->N ))) |
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[35aab3] | 291 | { |
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[3835a88] | 292 | for( int i=r->N-1; i>=0; i-- ) |
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[35aab3] | 293 | { |
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[3835a88] | 294 | if( r->wvhdl[0][i]>=0 ) |
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[35aab3] | 295 | { |
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| 296 | return FALSE; |
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| 297 | } |
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| 298 | } |
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| 299 | return TRUE; |
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| 300 | } |
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| 301 | |
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| 302 | return FALSE; |
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| 303 | } |
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| 304 | |
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| 305 | // ---------------------------------------------------------------------------- |
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| 306 | // compute all monomials not in stdJ and their normal forms |
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| 307 | // ---------------------------------------------------------------------------- |
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| 308 | |
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[3835a88] | 309 | void computeNF( ideal stdJ,poly hc,poly wc,spectrumPolyList *NF, const ring r ) |
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[35aab3] | 310 | { |
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| 311 | int carry,k; |
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[3835a88] | 312 | multiCnt C( r->N,0 ); |
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[beef52] | 313 | poly Z = NULL; |
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[35aab3] | 314 | |
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[3835a88] | 315 | int well = isWell(r); |
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[35aab3] | 316 | |
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| 317 | do |
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| 318 | { |
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[3835a88] | 319 | poly m = p_One(r); |
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| 320 | setExp( m,C.cnt,r ); |
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[35aab3] | 321 | |
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| 322 | carry = FALSE; |
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| 323 | |
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[3835a88] | 324 | k = isLeadMonomial( m,stdJ,r ); |
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[35aab3] | 325 | |
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| 326 | if( k < 0 ) |
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| 327 | { |
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| 328 | // --------------------------- |
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| 329 | // m is not a lead monomial |
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| 330 | // --------------------------- |
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| 331 | |
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[660a68f] | 332 | NF->insert_node( m,NULL,r ); |
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[35aab3] | 333 | } |
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[3835a88] | 334 | else if( isMultiple( Z,m,r ) ) |
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[35aab3] | 335 | { |
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| 336 | // ------------------------------------ |
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| 337 | // m is trivially in the ideal stdJ |
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| 338 | // ------------------------------------ |
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| 339 | |
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[3835a88] | 340 | p_Delete( &m,r ); |
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[35aab3] | 341 | carry = TRUE; |
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| 342 | } |
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[3835a88] | 343 | else if( p_Cmp( m,hc,r ) < 0 || p_Cmp( m,wc,r ) < 0 ) |
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[35aab3] | 344 | { |
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| 345 | // ------------------- |
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| 346 | // we do not need m |
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| 347 | // ------------------- |
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| 348 | |
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[3835a88] | 349 | p_Delete( &m,r ); |
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[35aab3] | 350 | carry = TRUE; |
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| 351 | } |
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| 352 | else |
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| 353 | { |
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| 354 | // -------------------------- |
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| 355 | // compute lazy normal form |
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| 356 | // -------------------------- |
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| 357 | |
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[3835a88] | 358 | poly multiplicant = p_Divide( m,stdJ->m[k],r ); |
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| 359 | pGetCoeff( multiplicant ) = n_Init(1,r->cf); |
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[35aab3] | 360 | |
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[3835a88] | 361 | poly nf = p_Mult_mm( p_Copy( stdJ->m[k],r ), multiplicant,r ); |
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[35aab3] | 362 | |
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[3835a88] | 363 | p_Delete( &multiplicant,r ); |
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[35aab3] | 364 | |
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[3835a88] | 365 | nf = normalFormHC( nf,hc,r ); |
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[35aab3] | 366 | |
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[beef52] | 367 | if( pNext( nf )==NULL ) |
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[35aab3] | 368 | { |
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| 369 | // ---------------------------------- |
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| 370 | // normal form of m is m itself |
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| 371 | // ---------------------------------- |
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| 372 | |
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[3835a88] | 373 | p_Delete( &nf,r ); |
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[660a68f] | 374 | NF->delete_monomial( m,r ); |
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[3835a88] | 375 | Z = p_Add_q( Z,m,r ); |
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[35aab3] | 376 | carry = TRUE; |
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| 377 | } |
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| 378 | else |
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| 379 | { |
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[3835a88] | 380 | nf = normalFormZ( nf,Z,r ); |
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[35aab3] | 381 | |
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[beef52] | 382 | if( pNext( nf )==NULL ) |
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[35aab3] | 383 | { |
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| 384 | // ---------------------------------- |
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| 385 | // normal form of m is m itself |
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| 386 | // ---------------------------------- |
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| 387 | |
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[3835a88] | 388 | p_Delete( &nf,r ); |
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[660a68f] | 389 | NF->delete_monomial( m,r ); |
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[3835a88] | 390 | Z = p_Add_q( Z,m,r ); |
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[35aab3] | 391 | carry = TRUE; |
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| 392 | } |
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| 393 | else |
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| 394 | { |
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| 395 | // ------------------------------------ |
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| 396 | // normal form of m is a polynomial |
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| 397 | // ------------------------------------ |
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| 398 | |
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[3835a88] | 399 | p_Norm( nf,r ); |
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[35aab3] | 400 | if( well==TRUE ) |
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| 401 | { |
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[660a68f] | 402 | NF->insert_node( m,nf,r ); |
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[35aab3] | 403 | } |
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| 404 | else |
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| 405 | { |
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| 406 | poly nfhard = kNF( stdJ,(ideal)NULL,pNext( nf ),0,0 ); |
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[3835a88] | 407 | nfhard = normalFormHC( nfhard,hc,r ); |
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| 408 | nfhard = normalFormZ ( nfhard,Z,r ); |
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[35aab3] | 409 | |
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[beef52] | 410 | if( nfhard==NULL ) |
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[35aab3] | 411 | { |
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[660a68f] | 412 | NF->delete_monomial( m,r ); |
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[3835a88] | 413 | Z = p_Add_q( Z,m,r ); |
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[35aab3] | 414 | carry = TRUE; |
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| 415 | } |
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| 416 | else |
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| 417 | { |
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[3835a88] | 418 | p_Delete( &pNext( nf ),r ); |
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[35aab3] | 419 | pNext( nf ) = nfhard; |
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[660a68f] | 420 | NF->insert_node( m,nf,r ); |
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[35aab3] | 421 | } |
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| 422 | } |
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| 423 | } |
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| 424 | } |
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| 425 | } |
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| 426 | } |
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| 427 | while( C.inc( carry ) ); |
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| 428 | |
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| 429 | // delete single monomials |
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| 430 | |
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| 431 | BOOLEAN not_finished; |
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| 432 | |
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| 433 | do |
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| 434 | { |
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| 435 | not_finished = FALSE; |
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| 436 | |
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| 437 | spectrumPolyNode *node = NF->root; |
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| 438 | |
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| 439 | while( node!=(spectrumPolyNode*)NULL ) |
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| 440 | { |
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[beef52] | 441 | if( node->nf!=NULL && pNext( node->nf )==NULL ) |
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[35aab3] | 442 | { |
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[660a68f] | 443 | NF->delete_monomial( node->nf,r ); |
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[35aab3] | 444 | not_finished = TRUE; |
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| 445 | node = (spectrumPolyNode*)NULL; |
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| 446 | } |
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| 447 | else |
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| 448 | { |
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| 449 | node = node->next; |
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| 450 | } |
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| 451 | } |
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| 452 | } while( not_finished ); |
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| 453 | |
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[3835a88] | 454 | p_Delete( &Z,r ); |
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[35aab3] | 455 | } |
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| 456 | |
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| 457 | // ---------------------------------------------------------------------------- |
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| 458 | // check if currRing is local |
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| 459 | // ---------------------------------------------------------------------------- |
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| 460 | |
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[3835a88] | 461 | BOOLEAN ringIsLocal( const ring r ) |
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[35aab3] | 462 | { |
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[3835a88] | 463 | poly m = p_One(r); |
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| 464 | poly one = p_One(r); |
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[35aab3] | 465 | BOOLEAN res=TRUE; |
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| 466 | |
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[3835a88] | 467 | for( int i=r->N; i>0; i-- ) |
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[35aab3] | 468 | { |
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[3835a88] | 469 | p_SetExp( m,i,1,r ); |
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| 470 | p_Setm( m,r ); |
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[35aab3] | 471 | |
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[3835a88] | 472 | if( p_Cmp( m,one,r )>0 ) |
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[35aab3] | 473 | { |
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| 474 | res=FALSE; |
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| 475 | break; |
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| 476 | } |
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[3835a88] | 477 | p_SetExp( m,i,0,r ); |
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[35aab3] | 478 | } |
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| 479 | |
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[3835a88] | 480 | p_Delete( &m,r ); |
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| 481 | p_Delete( &one,r ); |
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[35aab3] | 482 | |
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| 483 | return res; |
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| 484 | } |
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| 485 | |
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| 486 | // ---------------------------------------------------------------------------- |
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| 487 | // print error message corresponding to spectrumState state: |
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| 488 | // ---------------------------------------------------------------------------- |
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[f599a46] | 489 | /*void spectrumPrintError(spectrumState state) |
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[35aab3] | 490 | { |
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| 491 | switch( state ) |
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| 492 | { |
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| 493 | case spectrumZero: |
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| 494 | WerrorS( "polynomial is zero" ); |
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| 495 | break; |
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| 496 | case spectrumBadPoly: |
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| 497 | WerrorS( "polynomial has constant term" ); |
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| 498 | break; |
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| 499 | case spectrumNoSingularity: |
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| 500 | WerrorS( "not a singularity" ); |
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| 501 | break; |
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| 502 | case spectrumNotIsolated: |
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| 503 | WerrorS( "the singularity is not isolated" ); |
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| 504 | break; |
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| 505 | case spectrumNoHC: |
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| 506 | WerrorS( "highest corner cannot be computed" ); |
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| 507 | break; |
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| 508 | case spectrumDegenerate: |
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| 509 | WerrorS( "principal part is degenerate" ); |
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| 510 | break; |
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| 511 | case spectrumOK: |
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| 512 | break; |
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| 513 | |
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| 514 | default: |
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| 515 | WerrorS( "unknown error occurred" ); |
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| 516 | break; |
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| 517 | } |
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[f599a46] | 518 | }*/ |
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[35aab3] | 519 | #endif /* HAVE_SPECTRUM */ |
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| 520 | // ---------------------------------------------------------------------------- |
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| 521 | // spectrum.cc |
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| 522 | // end of file |
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| 523 | // ---------------------------------------------------------------------------- |
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