[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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[599326] | 10 | #include <kernel/mod2.h> |
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[35aab3] | 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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[b1dfaf] | 21 | #include <omalloc/mylimits.h> |
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[35aab3] | 22 | |
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[0f401f] | 23 | #include <coeffs/numbers.h> |
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[3835a88] | 24 | #include <polys/monomials/p_polys.h> |
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| 25 | #include <polys/simpleideals.h> |
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[210e07] | 26 | #include <misc/intvec.h> |
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| 27 | #include <polys/monomials/ring.h> |
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[3835a88] | 28 | //extern ring currRing; |
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[599326] | 29 | |
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[3835a88] | 30 | #include <kernel/kstd1.h> |
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| 31 | #include <kernel/stairc.h> |
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[599326] | 32 | #include <kernel/multicnt.h> |
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| 33 | #include <kernel/GMPrat.h> |
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| 34 | #include <kernel/kmatrix.h> |
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| 35 | #include <kernel/npolygon.h> |
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| 36 | #include <kernel/splist.h> |
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| 37 | #include <kernel/semic.h> |
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[35aab3] | 38 | |
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| 39 | // ---------------------------------------------------------------------------- |
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| 40 | // test if the polynomial h has a term of total degree d |
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| 41 | // ---------------------------------------------------------------------------- |
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| 42 | |
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[3835a88] | 43 | BOOLEAN hasTermOfDegree( poly h, int d, const ring r ) |
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[35aab3] | 44 | { |
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| 45 | do |
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| 46 | { |
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[3835a88] | 47 | if( p_Totaldegree( h,r )== d ) |
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[35aab3] | 48 | return TRUE; |
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| 49 | pIter(h); |
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| 50 | } |
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[beef52] | 51 | while( h!=NULL ); |
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[35aab3] | 52 | |
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| 53 | return FALSE; |
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| 54 | } |
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| 55 | |
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| 56 | // ---------------------------------------------------------------------------- |
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| 57 | // test if the polynomial h has a constant term |
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| 58 | // ---------------------------------------------------------------------------- |
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| 59 | |
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[3835a88] | 60 | static BOOLEAN inline hasConstTerm( poly h, const ring r ) |
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[35aab3] | 61 | { |
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[3835a88] | 62 | return hasTermOfDegree(h,0,r); |
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[35aab3] | 63 | } |
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| 64 | |
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| 65 | // ---------------------------------------------------------------------------- |
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| 66 | // test if the polynomial h has a linear term |
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| 67 | // ---------------------------------------------------------------------------- |
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| 68 | |
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[3835a88] | 69 | static BOOLEAN inline hasLinearTerm( poly h, const ring r ) |
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[35aab3] | 70 | { |
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[3835a88] | 71 | return hasTermOfDegree(h,1,r); |
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[35aab3] | 72 | } |
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| 73 | |
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| 74 | // ---------------------------------------------------------------------------- |
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| 75 | // test if the ideal J has a lead monomial on the axis number k |
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| 76 | // ---------------------------------------------------------------------------- |
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| 77 | |
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[3835a88] | 78 | BOOLEAN hasAxis( ideal J,int k, const ring r ) |
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[35aab3] | 79 | { |
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| 80 | int i; |
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| 81 | |
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| 82 | for( i=0; i<IDELEMS(J); i++ ) |
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| 83 | { |
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[3835a88] | 84 | if (p_IsPurePower( J->m[i],r ) == k) return TRUE; |
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[35aab3] | 85 | } |
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| 86 | return FALSE; |
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| 87 | } |
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| 88 | |
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| 89 | // ---------------------------------------------------------------------------- |
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| 90 | // test if the ideal J has 1 as a lead monomial |
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| 91 | // ---------------------------------------------------------------------------- |
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| 92 | |
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[3835a88] | 93 | int hasOne( ideal J, const ring r ) |
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[35aab3] | 94 | { |
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| 95 | int i; |
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| 96 | |
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| 97 | for( i=0; i<IDELEMS(J); i++ ) |
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| 98 | { |
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[3835a88] | 99 | if (p_IsConstant(J->m[i],r)) return TRUE; |
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[35aab3] | 100 | } |
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| 101 | return FALSE; |
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| 102 | } |
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| 103 | // ---------------------------------------------------------------------------- |
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| 104 | // test if m is a multiple of one of the monomials of f |
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| 105 | // ---------------------------------------------------------------------------- |
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| 106 | |
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[3835a88] | 107 | int isMultiple( poly f,poly m, const ring r ) |
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[35aab3] | 108 | { |
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[beef52] | 109 | while( f!=NULL ) |
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[35aab3] | 110 | { |
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| 111 | // --------------------------------------------------- |
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| 112 | // for a local order f|m is only possible if f>=m |
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| 113 | // --------------------------------------------------- |
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| 114 | |
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[3835a88] | 115 | if( p_LmCmp( f,m,r )>=0 ) |
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[35aab3] | 116 | { |
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[3835a88] | 117 | if( p_LmDivisibleByNoComp( f,m,r ) ) |
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[35aab3] | 118 | { |
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| 119 | return TRUE; |
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| 120 | } |
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| 121 | else |
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| 122 | { |
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| 123 | pIter( f ); |
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| 124 | } |
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| 125 | } |
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| 126 | else |
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| 127 | { |
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| 128 | return FALSE; |
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| 129 | } |
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| 130 | } |
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| 131 | |
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| 132 | return FALSE; |
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| 133 | } |
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| 134 | |
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| 135 | // ---------------------------------------------------------------------------- |
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| 136 | // compute the minimal monomial of minimmal weight>=max_weight |
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| 137 | // ---------------------------------------------------------------------------- |
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| 138 | |
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[3835a88] | 139 | poly computeWC( const newtonPolygon &np,Rational max_weight, const ring r ) |
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[35aab3] | 140 | { |
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[3835a88] | 141 | poly m = p_One(r); |
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[beef52] | 142 | poly wc = NULL; |
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[35aab3] | 143 | int mdegree; |
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| 144 | |
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[3835a88] | 145 | for( int i=1; i<=r->N; i++ ) |
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[35aab3] | 146 | { |
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| 147 | mdegree = 1; |
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[3835a88] | 148 | p_SetExp( m,i,mdegree,r ); |
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[35aab3] | 149 | // pSetm( m ); |
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| 150 | // np.weight_shift does not need pSetm( m ), postpone it |
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| 151 | |
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[3835a88] | 152 | while( np.weight_shift( m,r )<max_weight ) |
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[35aab3] | 153 | { |
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| 154 | mdegree++; |
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[3835a88] | 155 | p_SetExp( m,i,mdegree,r ); |
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[35aab3] | 156 | // pSetm( m ); |
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| 157 | // np.weight_shift does not need pSetm( m ), postpone it |
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| 158 | } |
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[3835a88] | 159 | p_Setm( m,r ); |
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[35aab3] | 160 | |
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[3835a88] | 161 | if( i==1 || p_Cmp( m,wc,r )<0 ) |
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[35aab3] | 162 | { |
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[3835a88] | 163 | p_Delete( &wc,r ); |
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| 164 | wc = p_Head( m,r ); |
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[35aab3] | 165 | } |
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| 166 | |
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[3835a88] | 167 | p_SetExp( m,i,0,r ); |
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[35aab3] | 168 | } |
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| 169 | |
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[3835a88] | 170 | p_Delete( &m,r ); |
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[35aab3] | 171 | |
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| 172 | return wc; |
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| 173 | } |
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| 174 | |
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| 175 | // ---------------------------------------------------------------------------- |
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| 176 | // deletes all monomials of f which are less than hc |
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| 177 | // ---------------------------------------------------------------------------- |
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| 178 | |
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[3835a88] | 179 | static inline poly normalFormHC( poly f,poly hc, const ring r ) |
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[35aab3] | 180 | { |
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| 181 | poly *ptr = &f; |
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| 182 | |
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[beef52] | 183 | while( (*ptr)!=NULL ) |
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[35aab3] | 184 | { |
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[3835a88] | 185 | if( p_LmCmp( *ptr,hc,r )>=0 ) |
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[35aab3] | 186 | { |
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| 187 | ptr = &(pNext( *ptr )); |
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| 188 | } |
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| 189 | else |
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| 190 | { |
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[3835a88] | 191 | p_Delete( ptr,r ); |
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[35aab3] | 192 | return f; |
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| 193 | } |
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| 194 | } |
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| 195 | |
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| 196 | return f; |
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| 197 | } |
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| 198 | |
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| 199 | // ---------------------------------------------------------------------------- |
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| 200 | // deletes all monomials of f which are multiples of monomials of Z |
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| 201 | // ---------------------------------------------------------------------------- |
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| 202 | |
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[3835a88] | 203 | static inline poly normalFormZ( poly f,poly Z, const ring r ) |
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[35aab3] | 204 | { |
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| 205 | poly *ptr = &f; |
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| 206 | |
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[beef52] | 207 | while( (*ptr)!=NULL ) |
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[35aab3] | 208 | { |
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[3835a88] | 209 | if( !isMultiple( Z,*ptr,r ) ) |
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[35aab3] | 210 | { |
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| 211 | ptr = &(pNext( *ptr )); |
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| 212 | } |
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| 213 | else |
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| 214 | { |
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[3835a88] | 215 | p_LmDelete(ptr,r); |
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[35aab3] | 216 | } |
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| 217 | } |
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| 218 | |
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| 219 | return f; |
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| 220 | } |
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| 221 | |
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| 222 | // ?? HS: |
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| 223 | // Looks for the shortest polynomial f in stdJ which is divisible |
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| 224 | // by the monimial m, return its index in stdJ |
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| 225 | // ---------------------------------------------------------------------------- |
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| 226 | // Looks for the first polynomial f in stdJ which satisfies m=LT(f)*eta |
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| 227 | // for a monomial eta. The return eta*f-m and cancel all monomials |
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| 228 | // which are smaller than the highest corner hc |
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| 229 | // ---------------------------------------------------------------------------- |
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| 230 | |
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[3835a88] | 231 | static inline int isLeadMonomial( poly m,ideal stdJ, const ring r ) |
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[35aab3] | 232 | { |
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| 233 | int length = INT_MAX; |
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| 234 | int result = -1; |
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| 235 | |
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| 236 | for( int i=0; i<IDELEMS(stdJ); i++ ) |
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| 237 | { |
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[3835a88] | 238 | if( p_Cmp( stdJ->m[i],m,r )>=0 && p_DivisibleBy( stdJ->m[i],m,r ) ) |
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[35aab3] | 239 | { |
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| 240 | int tmp = pLength( stdJ->m[i] ); |
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| 241 | |
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| 242 | if( tmp < length ) |
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| 243 | { |
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| 244 | length = tmp; |
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| 245 | result = i; |
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| 246 | } |
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| 247 | } |
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| 248 | } |
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| 249 | |
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| 250 | return result; |
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| 251 | } |
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| 252 | |
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| 253 | // ---------------------------------------------------------------------------- |
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| 254 | // set the exponent of a monomial t an integer array |
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| 255 | // ---------------------------------------------------------------------------- |
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| 256 | |
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[3835a88] | 257 | static void setExp( poly m,int *r, const ring s ) |
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[35aab3] | 258 | { |
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[3835a88] | 259 | for( int i=s->N; i>0; i-- ) |
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[35aab3] | 260 | { |
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[3835a88] | 261 | p_SetExp( m,i,r[i-1],s ); |
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[35aab3] | 262 | } |
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[3835a88] | 263 | p_Setm( m,s ); |
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[35aab3] | 264 | } |
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| 265 | |
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| 266 | // ---------------------------------------------------------------------------- |
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| 267 | // check if the ordering is a reverse wellordering, i.e. every monomial |
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| 268 | // is smaller than only finitely monomials |
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| 269 | // ---------------------------------------------------------------------------- |
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| 270 | |
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[3835a88] | 271 | static BOOLEAN isWell( const ring r ) |
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[35aab3] | 272 | { |
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[3835a88] | 273 | int b = rBlocks( r ); |
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[35aab3] | 274 | |
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| 275 | if( b==3 && |
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[3835a88] | 276 | ( r->order[0] == ringorder_ds || |
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| 277 | r->order[0] == ringorder_Ds || |
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| 278 | r->order[0] == ringorder_ws || |
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| 279 | r->order[0] == ringorder_Ws ) ) |
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[35aab3] | 280 | { |
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| 281 | return TRUE; |
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| 282 | } |
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| 283 | else if( b>=3 |
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[3835a88] | 284 | && (( r->order[0] ==ringorder_a |
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| 285 | && r->block1[0]==r->N ) |
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| 286 | || (r->order[0]==ringorder_M |
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| 287 | && r->block1[0]==r->N*r->N ))) |
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[35aab3] | 288 | { |
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[3835a88] | 289 | for( int i=r->N-1; i>=0; i-- ) |
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[35aab3] | 290 | { |
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[3835a88] | 291 | if( r->wvhdl[0][i]>=0 ) |
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[35aab3] | 292 | { |
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| 293 | return FALSE; |
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| 294 | } |
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| 295 | } |
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| 296 | return TRUE; |
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| 297 | } |
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| 298 | |
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| 299 | return FALSE; |
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| 300 | } |
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| 301 | |
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| 302 | // ---------------------------------------------------------------------------- |
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| 303 | // compute all monomials not in stdJ and their normal forms |
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| 304 | // ---------------------------------------------------------------------------- |
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| 305 | |
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[3835a88] | 306 | void computeNF( ideal stdJ,poly hc,poly wc,spectrumPolyList *NF, const ring r ) |
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[35aab3] | 307 | { |
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| 308 | int carry,k; |
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[3835a88] | 309 | multiCnt C( r->N,0 ); |
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[beef52] | 310 | poly Z = NULL; |
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[35aab3] | 311 | |
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[3835a88] | 312 | int well = isWell(r); |
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[35aab3] | 313 | |
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| 314 | do |
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| 315 | { |
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[3835a88] | 316 | poly m = p_One(r); |
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| 317 | setExp( m,C.cnt,r ); |
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[35aab3] | 318 | |
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| 319 | carry = FALSE; |
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| 320 | |
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[3835a88] | 321 | k = isLeadMonomial( m,stdJ,r ); |
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[35aab3] | 322 | |
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| 323 | if( k < 0 ) |
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| 324 | { |
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| 325 | // --------------------------- |
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| 326 | // m is not a lead monomial |
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| 327 | // --------------------------- |
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| 328 | |
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[beef52] | 329 | NF->insert_node( m,NULL ); |
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[35aab3] | 330 | } |
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[3835a88] | 331 | else if( isMultiple( Z,m,r ) ) |
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[35aab3] | 332 | { |
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| 333 | // ------------------------------------ |
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| 334 | // m is trivially in the ideal stdJ |
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| 335 | // ------------------------------------ |
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| 336 | |
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[3835a88] | 337 | p_Delete( &m,r ); |
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[35aab3] | 338 | carry = TRUE; |
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| 339 | } |
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[3835a88] | 340 | else if( p_Cmp( m,hc,r ) < 0 || p_Cmp( m,wc,r ) < 0 ) |
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[35aab3] | 341 | { |
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| 342 | // ------------------- |
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| 343 | // we do not need m |
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| 344 | // ------------------- |
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| 345 | |
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[3835a88] | 346 | p_Delete( &m,r ); |
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[35aab3] | 347 | carry = TRUE; |
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| 348 | } |
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| 349 | else |
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| 350 | { |
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| 351 | // -------------------------- |
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| 352 | // compute lazy normal form |
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| 353 | // -------------------------- |
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| 354 | |
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[3835a88] | 355 | poly multiplicant = p_Divide( m,stdJ->m[k],r ); |
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| 356 | pGetCoeff( multiplicant ) = n_Init(1,r->cf); |
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[35aab3] | 357 | |
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[3835a88] | 358 | poly nf = p_Mult_mm( p_Copy( stdJ->m[k],r ), multiplicant,r ); |
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[35aab3] | 359 | |
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[3835a88] | 360 | p_Delete( &multiplicant,r ); |
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[35aab3] | 361 | |
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[3835a88] | 362 | nf = normalFormHC( nf,hc,r ); |
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[35aab3] | 363 | |
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[beef52] | 364 | if( pNext( nf )==NULL ) |
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[35aab3] | 365 | { |
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| 366 | // ---------------------------------- |
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| 367 | // normal form of m is m itself |
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| 368 | // ---------------------------------- |
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| 369 | |
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[3835a88] | 370 | p_Delete( &nf,r ); |
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[35aab3] | 371 | NF->delete_monomial( m ); |
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[3835a88] | 372 | Z = p_Add_q( Z,m,r ); |
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[35aab3] | 373 | carry = TRUE; |
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| 374 | } |
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| 375 | else |
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| 376 | { |
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[3835a88] | 377 | nf = normalFormZ( nf,Z,r ); |
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[35aab3] | 378 | |
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[beef52] | 379 | if( pNext( nf )==NULL ) |
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[35aab3] | 380 | { |
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| 381 | // ---------------------------------- |
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| 382 | // normal form of m is m itself |
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| 383 | // ---------------------------------- |
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| 384 | |
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[3835a88] | 385 | p_Delete( &nf,r ); |
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[35aab3] | 386 | NF->delete_monomial( m ); |
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[3835a88] | 387 | Z = p_Add_q( Z,m,r ); |
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[35aab3] | 388 | carry = TRUE; |
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| 389 | } |
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| 390 | else |
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| 391 | { |
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| 392 | // ------------------------------------ |
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| 393 | // normal form of m is a polynomial |
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| 394 | // ------------------------------------ |
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| 395 | |
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[3835a88] | 396 | p_Norm( nf,r ); |
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[35aab3] | 397 | if( well==TRUE ) |
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| 398 | { |
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| 399 | NF->insert_node( m,nf ); |
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| 400 | } |
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| 401 | else |
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| 402 | { |
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| 403 | poly nfhard = kNF( stdJ,(ideal)NULL,pNext( nf ),0,0 ); |
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[3835a88] | 404 | nfhard = normalFormHC( nfhard,hc,r ); |
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| 405 | nfhard = normalFormZ ( nfhard,Z,r ); |
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[35aab3] | 406 | |
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[beef52] | 407 | if( nfhard==NULL ) |
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[35aab3] | 408 | { |
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| 409 | NF->delete_monomial( m ); |
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[3835a88] | 410 | Z = p_Add_q( Z,m,r ); |
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[35aab3] | 411 | carry = TRUE; |
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| 412 | } |
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| 413 | else |
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| 414 | { |
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[3835a88] | 415 | p_Delete( &pNext( nf ),r ); |
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[35aab3] | 416 | pNext( nf ) = nfhard; |
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| 417 | NF->insert_node( m,nf ); |
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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 | } |
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| 424 | while( C.inc( carry ) ); |
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| 425 | |
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| 426 | // delete single monomials |
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| 427 | |
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| 428 | BOOLEAN not_finished; |
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| 429 | |
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| 430 | do |
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| 431 | { |
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| 432 | not_finished = FALSE; |
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| 433 | |
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| 434 | spectrumPolyNode *node = NF->root; |
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| 435 | |
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| 436 | while( node!=(spectrumPolyNode*)NULL ) |
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| 437 | { |
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[beef52] | 438 | if( node->nf!=NULL && pNext( node->nf )==NULL ) |
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[35aab3] | 439 | { |
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| 440 | NF->delete_monomial( node->nf ); |
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| 441 | not_finished = TRUE; |
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| 442 | node = (spectrumPolyNode*)NULL; |
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| 443 | } |
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| 444 | else |
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| 445 | { |
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| 446 | node = node->next; |
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| 447 | } |
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| 448 | } |
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| 449 | } while( not_finished ); |
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| 450 | |
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[3835a88] | 451 | p_Delete( &Z,r ); |
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[35aab3] | 452 | } |
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| 453 | |
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| 454 | // ---------------------------------------------------------------------------- |
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| 455 | // check if currRing is local |
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| 456 | // ---------------------------------------------------------------------------- |
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| 457 | |
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[3835a88] | 458 | BOOLEAN ringIsLocal( const ring r ) |
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[35aab3] | 459 | { |
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[3835a88] | 460 | poly m = p_One(r); |
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| 461 | poly one = p_One(r); |
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[35aab3] | 462 | BOOLEAN res=TRUE; |
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| 463 | |
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[3835a88] | 464 | for( int i=r->N; i>0; i-- ) |
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[35aab3] | 465 | { |
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[3835a88] | 466 | p_SetExp( m,i,1,r ); |
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| 467 | p_Setm( m,r ); |
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[35aab3] | 468 | |
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[3835a88] | 469 | if( p_Cmp( m,one,r )>0 ) |
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[35aab3] | 470 | { |
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| 471 | res=FALSE; |
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| 472 | break; |
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| 473 | } |
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[3835a88] | 474 | p_SetExp( m,i,0,r ); |
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[35aab3] | 475 | } |
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| 476 | |
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[3835a88] | 477 | p_Delete( &m,r ); |
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| 478 | p_Delete( &one,r ); |
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[35aab3] | 479 | |
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| 480 | return res; |
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| 481 | } |
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| 482 | |
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| 483 | // ---------------------------------------------------------------------------- |
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| 484 | // print error message corresponding to spectrumState state: |
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| 485 | // ---------------------------------------------------------------------------- |
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| 486 | void spectrumPrintError(spectrumState state) |
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| 487 | { |
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| 488 | switch( state ) |
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| 489 | { |
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| 490 | case spectrumZero: |
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| 491 | WerrorS( "polynomial is zero" ); |
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| 492 | break; |
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| 493 | case spectrumBadPoly: |
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| 494 | WerrorS( "polynomial has constant term" ); |
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| 495 | break; |
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| 496 | case spectrumNoSingularity: |
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| 497 | WerrorS( "not a singularity" ); |
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| 498 | break; |
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| 499 | case spectrumNotIsolated: |
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| 500 | WerrorS( "the singularity is not isolated" ); |
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| 501 | break; |
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| 502 | case spectrumNoHC: |
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| 503 | WerrorS( "highest corner cannot be computed" ); |
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| 504 | break; |
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| 505 | case spectrumDegenerate: |
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| 506 | WerrorS( "principal part is degenerate" ); |
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| 507 | break; |
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| 508 | case spectrumOK: |
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| 509 | break; |
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| 510 | |
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| 511 | default: |
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| 512 | WerrorS( "unknown error occurred" ); |
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| 513 | break; |
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| 514 | } |
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| 515 | } |
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| 516 | #endif /* HAVE_SPECTRUM */ |
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| 517 | // ---------------------------------------------------------------------------- |
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| 518 | // spectrum.cc |
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| 519 | // end of file |
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| 520 | // ---------------------------------------------------------------------------- |
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