[35aab3] | 1 | // ---------------------------------------------------------------------------- |
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| 2 | // npolygon.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 NPOLYGON_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 NPOLYGON_PRINT |
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| 15 | #include <iostream.h> |
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| 16 | #ifndef NPOLYGON_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 "polys.h" |
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| 22 | #include "GMPrat.h" |
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| 23 | #include "kmatrix.h" |
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| 24 | #include "npolygon.h" |
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| 25 | |
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| 26 | // ---------------------------------------------------------------------------- |
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| 27 | // Allocate memory for a linear form of k terms |
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| 28 | // ---------------------------------------------------------------------------- |
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| 29 | |
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| 30 | void linearForm::copy_new( int k ) |
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| 31 | { |
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| 32 | if( k > 0 ) |
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| 33 | { |
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| 34 | c = new Rational[k]; |
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| 35 | |
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| 36 | #ifndef NBDEBUG |
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| 37 | if( c == (Rational*)NULL ) |
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| 38 | { |
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| 39 | #ifdef NPOLYGON_PRINT |
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| 40 | #ifdef NPOLYGON_IOSTREAM |
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| 41 | cerr << |
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| 42 | "void linearForm::copy_new( int k ): no memory left ...\n" ; |
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| 43 | #else |
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| 44 | fprintf( stderr, |
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| 45 | "void linearForm::copy_new( int k ): no memory left ...\n"); |
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| 46 | #endif |
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| 47 | #endif |
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| 48 | HALT(); |
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| 49 | } |
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| 50 | #endif |
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| 51 | } |
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| 52 | else if( k == 0 ) |
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| 53 | { |
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| 54 | c = (Rational*)NULL; |
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| 55 | } |
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| 56 | else if( k < 0 ) |
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| 57 | { |
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| 58 | #ifdef NPOLYGON_PRINT |
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| 59 | #ifdef NPOLYGON_IOSTREAM |
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| 60 | cerr << |
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| 61 | "void linearForm::copy_new( int k ): k < 0 ...\n"; |
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| 62 | #else |
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| 63 | fprintf( stderr, |
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| 64 | "void linearForm::copy_new( int k ): k < 0 ...\n" ); |
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| 65 | #endif |
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| 66 | #endif |
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| 67 | |
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| 68 | HALT(); |
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| 69 | } |
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| 70 | } |
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| 71 | |
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| 72 | // ---------------------------------------------------------------------------- |
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| 73 | // Delete the memory of a linear form |
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| 74 | // ---------------------------------------------------------------------------- |
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| 75 | |
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| 76 | void linearForm::copy_delete( void ) |
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| 77 | { |
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| 78 | if( c != (Rational*)NULL && N > 0 ) |
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| 79 | delete [] c; |
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| 80 | copy_zero( ); |
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| 81 | } |
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| 82 | |
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| 83 | // ---------------------------------------------------------------------------- |
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| 84 | // Initialize deep from another linear form |
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| 85 | // ---------------------------------------------------------------------------- |
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| 86 | |
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| 87 | void linearForm::copy_deep( const linearForm &l ) |
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| 88 | { |
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| 89 | copy_new( l.N ); |
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| 90 | for( int i=l.N-1; i>=0; i-- ) |
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| 91 | { |
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| 92 | c[i] = l.c[i]; |
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| 93 | } |
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| 94 | N = l.N; |
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| 95 | } |
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| 96 | |
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| 97 | // ---------------------------------------------------------------------------- |
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| 98 | // Copy constructor |
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| 99 | // ---------------------------------------------------------------------------- |
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| 100 | |
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| 101 | linearForm::linearForm( const linearForm &l ) |
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| 102 | { |
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| 103 | copy_deep( l ); |
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| 104 | } |
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| 105 | |
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| 106 | // ---------------------------------------------------------------------------- |
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| 107 | // Destructor |
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| 108 | // ---------------------------------------------------------------------------- |
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| 109 | |
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| 110 | linearForm::~linearForm( ) |
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| 111 | { |
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| 112 | copy_delete( ); |
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| 113 | } |
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| 114 | |
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| 115 | // ---------------------------------------------------------------------------- |
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| 116 | // Define `=` to be a deep copy |
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| 117 | // ---------------------------------------------------------------------------- |
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| 118 | |
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| 119 | linearForm & linearForm::operator = ( const linearForm &l ) |
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| 120 | { |
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| 121 | copy_delete( ); |
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| 122 | copy_deep( l ); |
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| 123 | |
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| 124 | return *this; |
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| 125 | } |
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| 126 | |
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| 127 | // ---------------------------------------------------------------------------- |
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| 128 | // ostream for linear form |
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| 129 | // ---------------------------------------------------------------------------- |
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| 130 | |
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| 131 | #ifdef NPOLYGON_PRINT |
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| 132 | |
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| 133 | ostream & operator << ( ostream &s,const linearForm &l ) |
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| 134 | { |
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| 135 | for( int i=0; i<l.N; i++ ) |
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| 136 | { |
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| 137 | if( l.c[i] != (Rational)0 ) |
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| 138 | { |
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| 139 | if( i > 0 && l.c[i] >= (Rational)0 ) |
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| 140 | { |
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| 141 | #ifdef NPOLYGON_IOSTREAM |
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| 142 | s << "+"; |
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| 143 | #else |
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| 144 | fprintf( stdout,"+" ); |
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| 145 | #endif |
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| 146 | } |
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| 147 | |
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| 148 | s << l.c[i]; |
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| 149 | |
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| 150 | #ifdef NPOLYGON_IOSTREAM |
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| 151 | s << "*x" << i+1; |
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| 152 | #else |
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| 153 | fprintf( stdout,"*x%d",i+1 ); |
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| 154 | #endif |
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| 155 | } |
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| 156 | } |
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| 157 | return s; |
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| 158 | } |
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| 159 | |
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| 160 | #endif |
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| 161 | |
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| 162 | // ---------------------------------------------------------------------------- |
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| 163 | // Equality of linear forms |
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| 164 | // ---------------------------------------------------------------------------- |
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| 165 | |
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| 166 | int operator == ( const linearForm &l1,const linearForm &l2 ) |
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| 167 | { |
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| 168 | if( l1.N!=l2.N ) |
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| 169 | return FALSE; |
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| 170 | for( int i=l1.N-1; i >=0 ; i-- ) |
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| 171 | { |
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| 172 | if( l1.c[i]!=l2.c[i] ) |
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| 173 | return FALSE; |
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| 174 | } |
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| 175 | return TRUE; |
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| 176 | } |
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| 177 | |
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| 178 | |
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| 179 | // ---------------------------------------------------------------------------- |
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| 180 | // Newton weight of a monomial |
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| 181 | // ---------------------------------------------------------------------------- |
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| 182 | |
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| 183 | Rational linearForm::weight( poly m ) const |
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| 184 | { |
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| 185 | Rational ret=(Rational)0; |
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| 186 | |
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| 187 | for( int i=0,j=1; i<N; i++,j++ ) |
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| 188 | { |
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| 189 | ret += c[i]*(Rational)pGetExp( m,j ); |
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| 190 | } |
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| 191 | |
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| 192 | return ret; |
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| 193 | } |
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| 194 | |
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| 195 | // ---------------------------------------------------------------------------- |
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| 196 | // Newton weight of a polynomial |
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| 197 | // ---------------------------------------------------------------------------- |
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| 198 | |
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| 199 | Rational linearForm::pweight( poly m ) const |
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| 200 | { |
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| 201 | if( m==(poly)NULL ) |
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| 202 | return (Rational)0; |
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| 203 | |
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| 204 | Rational ret = weight( m ); |
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| 205 | Rational tmp; |
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| 206 | |
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| 207 | for( m=pNext(m); m!=(poly)NULL; pIter(m) ) |
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| 208 | { |
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| 209 | tmp = weight( m ); |
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| 210 | if( tmp<ret ) |
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| 211 | { |
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| 212 | ret = tmp; |
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| 213 | } |
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| 214 | } |
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| 215 | |
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| 216 | return ret; |
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| 217 | } |
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| 218 | |
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| 219 | // ---------------------------------------------------------------------------- |
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| 220 | // Newton weight of a monomial shifted by the product of the variables |
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| 221 | // ---------------------------------------------------------------------------- |
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| 222 | |
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| 223 | Rational linearForm::weight_shift( poly m ) const |
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| 224 | { |
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| 225 | Rational ret=(Rational)0; |
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| 226 | |
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| 227 | for( int i=0,j=1; i<N; i++,j++ ) |
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| 228 | { |
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| 229 | ret += c[i]*(Rational)( pGetExp( m,j ) + 1 ); |
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| 230 | } |
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| 231 | |
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| 232 | return ret; |
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| 233 | } |
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| 234 | |
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| 235 | // ---------------------------------------------------------------------------- |
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| 236 | // Newton weight of a monomial (forgetting the first variable) |
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| 237 | // ---------------------------------------------------------------------------- |
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| 238 | |
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| 239 | Rational linearForm::weight1( poly m ) const |
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| 240 | { |
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| 241 | Rational ret=(Rational)0; |
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| 242 | |
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| 243 | for( int i=0,j=2; i<N; i++,j++ ) |
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| 244 | { |
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| 245 | ret += c[i]*(Rational)pGetExp( m,j ); |
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| 246 | } |
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| 247 | |
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| 248 | return ret; |
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| 249 | } |
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| 250 | |
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| 251 | // ---------------------------------------------------------------------------- |
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| 252 | // Newton weight of a monomial shifted by the product of the variables |
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| 253 | // (forgetting the first variable) |
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| 254 | // ---------------------------------------------------------------------------- |
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| 255 | |
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| 256 | Rational linearForm::weight_shift1( poly m ) const |
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| 257 | { |
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| 258 | Rational ret=(Rational)0; |
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| 259 | |
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| 260 | for( int i=0,j=2; i<N; i++,j++ ) |
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| 261 | { |
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| 262 | ret += c[i]*(Rational)( pGetExp( m,j ) + 1 ); |
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| 263 | } |
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| 264 | |
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| 265 | return ret; |
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| 266 | } |
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| 267 | |
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| 268 | |
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| 269 | // ---------------------------------------------------------------------------- |
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| 270 | // Test if all coefficients of a linear form are positive |
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| 271 | // ---------------------------------------------------------------------------- |
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| 272 | |
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| 273 | int linearForm::positive( void ) |
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| 274 | { |
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| 275 | for( int i=0; i<N; i++ ) |
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| 276 | { |
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| 277 | if( c[i] <= (Rational)0 ) |
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| 278 | { |
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| 279 | return FALSE; |
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| 280 | } |
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| 281 | } |
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| 282 | return TRUE; |
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| 283 | } |
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| 284 | |
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| 285 | |
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| 286 | // ---------------------------------------------------------------------------- |
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| 287 | // Allocate memory for a newton polygon of k linear forms |
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| 288 | // ---------------------------------------------------------------------------- |
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| 289 | |
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| 290 | void newtonPolygon::copy_new( int k ) |
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| 291 | { |
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| 292 | if( k > 0 ) |
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| 293 | { |
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| 294 | l = new linearForm[k]; |
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| 295 | |
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| 296 | #ifndef NDEBUG |
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| 297 | if( l == (linearForm*)NULL ) |
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| 298 | { |
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| 299 | #ifdef NPOLYGON_PRINT |
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| 300 | #ifdef NPOLYGON_IOSTREAM |
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| 301 | cerr << |
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| 302 | "void newtonPolygon::copy_new( int k ): no memory left ...\n"; |
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| 303 | #else |
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| 304 | fprintf( stderr, |
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| 305 | "void newtonPolygon::copy_new( int k ): no memory left ...\n" ); |
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| 306 | #endif |
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| 307 | #endif |
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| 308 | |
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| 309 | HALT(); |
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| 310 | } |
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| 311 | #endif |
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| 312 | } |
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| 313 | else if( k == 0 ) |
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| 314 | { |
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| 315 | l = (linearForm*)NULL; |
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| 316 | } |
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| 317 | else if( k < 0 ) |
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| 318 | { |
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| 319 | #ifdef NPOLYGON_PRINT |
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| 320 | #ifdef NPOLYGON_IOSTREAM |
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| 321 | cerr << "void newtonPolygon::copy_new( int k ): k < 0 ...\n"; |
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| 322 | #else |
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| 323 | fprintf( stderr, |
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| 324 | "void newtonPolygon::copy_new( int k ): k < 0 ...\n" ); |
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| 325 | #endif |
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| 326 | #endif |
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| 327 | |
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| 328 | HALT(); |
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| 329 | } |
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| 330 | } |
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| 331 | |
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| 332 | // ---------------------------------------------------------------------------- |
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| 333 | // Delete the memory of a Newton polygon |
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| 334 | // ---------------------------------------------------------------------------- |
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| 335 | |
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| 336 | void newtonPolygon::copy_delete( void ) |
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| 337 | { |
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| 338 | if( l != (linearForm*)NULL && N > 0 ) |
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| 339 | delete [] l; |
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| 340 | copy_zero( ); |
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| 341 | } |
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| 342 | |
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| 343 | // ---------------------------------------------------------------------------- |
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| 344 | // Initialize deep from another Newton polygon |
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| 345 | // ---------------------------------------------------------------------------- |
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| 346 | |
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| 347 | void newtonPolygon::copy_deep( const newtonPolygon &np ) |
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| 348 | { |
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| 349 | copy_new( np.N ); |
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| 350 | for( int i=0; i<np.N; i++ ) |
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| 351 | { |
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| 352 | l[i] = np.l[i]; |
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| 353 | } |
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| 354 | N = np.N; |
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| 355 | } |
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| 356 | |
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| 357 | // ---------------------------------------------------------------------------- |
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| 358 | // Copy constructor |
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| 359 | // ---------------------------------------------------------------------------- |
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| 360 | |
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| 361 | newtonPolygon::newtonPolygon( const newtonPolygon &np ) |
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| 362 | { |
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| 363 | copy_deep( np ); |
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| 364 | } |
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| 365 | |
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| 366 | // ---------------------------------------------------------------------------- |
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| 367 | // Destructor |
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| 368 | // ---------------------------------------------------------------------------- |
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| 369 | |
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| 370 | newtonPolygon::~newtonPolygon( ) |
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| 371 | { |
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| 372 | copy_delete( ); |
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| 373 | } |
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| 374 | |
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| 375 | // ---------------------------------------------------------------------------- |
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| 376 | // We define `=` to be a deep copy |
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| 377 | // ---------------------------------------------------------------------------- |
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| 378 | |
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| 379 | newtonPolygon & newtonPolygon::operator = ( const newtonPolygon &np ) |
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| 380 | { |
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| 381 | copy_delete( ); |
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| 382 | copy_deep( np ); |
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| 383 | |
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| 384 | return *this; |
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| 385 | } |
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| 386 | |
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| 387 | // ---------------------------------------------------------------------------- |
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| 388 | // Initialize a Newton polygon from a polynomial |
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| 389 | // ---------------------------------------------------------------------------- |
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| 390 | |
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| 391 | newtonPolygon::newtonPolygon( poly f ) |
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| 392 | { |
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| 393 | copy_zero( ); |
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| 394 | |
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| 395 | int *r=new int[pVariables]; |
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| 396 | poly *m=new poly[pVariables]; |
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| 397 | |
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| 398 | |
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| 399 | KMatrix<Rational> mat( pVariables,pVariables+1 ); |
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| 400 | |
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| 401 | int i,j,stop=FALSE; |
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| 402 | linearForm sol; |
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| 403 | |
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| 404 | // --------------- |
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| 405 | // init counters |
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| 406 | // --------------- |
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| 407 | |
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| 408 | for( i=0; i<pVariables; i++ ) |
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| 409 | { |
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| 410 | r[i] = i; |
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| 411 | } |
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| 412 | |
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| 413 | m[0] = f; |
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| 414 | |
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| 415 | for( i=1; i<pVariables; i++ ) |
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| 416 | { |
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| 417 | m[i] = pNext(m[i-1]); |
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| 418 | } |
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| 419 | |
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| 420 | // ----------------------------- |
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| 421 | // find faces (= linear forms) |
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| 422 | // ----------------------------- |
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| 423 | |
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| 424 | do |
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| 425 | { |
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| 426 | // --------------------------------------------------- |
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| 427 | // test if monomials p.m[r[0]]m,...,p.m[r[p.vars-1]] |
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| 428 | // are linearely independent |
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| 429 | // --------------------------------------------------- |
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| 430 | |
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| 431 | for( i=0; i<pVariables; i++ ) |
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| 432 | { |
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| 433 | for( j=0; j<pVariables; j++ ) |
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| 434 | { |
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| 435 | // mat.set( i,j,pGetExp( m[r[i]],j+1 ) ); |
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| 436 | mat.set( i,j,pGetExp( m[i],j+1 ) ); |
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| 437 | } |
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| 438 | mat.set( i,j,1 ); |
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| 439 | } |
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| 440 | |
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| 441 | if( mat.solve( &(sol.c),&(sol.N) ) == pVariables ) |
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| 442 | { |
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| 443 | // --------------------------------- |
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| 444 | // check if linearForm is positive |
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| 445 | // check if linearForm is extremal |
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| 446 | // --------------------------------- |
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| 447 | |
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| 448 | if( sol.positive( ) && sol.pweight( f ) >= (Rational)1 ) |
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| 449 | { |
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| 450 | // ---------------------------------- |
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| 451 | // this is a face or the polyhedron |
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| 452 | // ---------------------------------- |
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| 453 | |
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| 454 | add_linearForm( sol ); |
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| 455 | sol.c = (Rational*)NULL; |
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| 456 | sol.N = 0; |
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| 457 | } |
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| 458 | } |
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| 459 | |
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| 460 | // -------------------- |
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| 461 | // increment counters |
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| 462 | // -------------------- |
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| 463 | |
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| 464 | for( i=1; r[i-1] + 1 == r[i] && i < pVariables; i++ ); |
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| 465 | |
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| 466 | for( j=0; j<i-1; j++ ) |
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| 467 | { |
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| 468 | r[j]=j; |
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| 469 | } |
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| 470 | |
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| 471 | if( i>1 ) |
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| 472 | { |
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| 473 | m[0]=f; |
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| 474 | for( j=1; j<i-1; j++ ) |
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| 475 | { |
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| 476 | m[j]=pNext(m[j-1]); |
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| 477 | } |
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| 478 | } |
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| 479 | r[i-1]++; |
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| 480 | m[i-1]=pNext(m[i-1]); |
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| 481 | |
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| 482 | if( m[pVariables-1] == (poly)NULL ) |
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| 483 | { |
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| 484 | stop = TRUE; |
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| 485 | } |
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| 486 | } while( stop == FALSE ); |
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| 487 | } |
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| 488 | |
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| 489 | #ifdef NPOLYGON_PRINT |
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| 490 | |
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| 491 | ostream & operator << ( ostream &s,const newtonPolygon &a ) |
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| 492 | { |
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| 493 | #ifdef NPOLYGON_IOSTREAM |
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| 494 | s << "Newton polygon:" << endl; |
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| 495 | #else |
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| 496 | fprintf( stdout,"Newton polygon:\n" ); |
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| 497 | #endif |
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| 498 | |
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| 499 | for( int i=0; i<a.N; i++ ) |
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| 500 | { |
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| 501 | s << a.l[i]; |
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| 502 | |
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| 503 | #ifdef NPOLYGON_IOSTREAM |
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| 504 | s << endl; |
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| 505 | #else |
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| 506 | fprintf( stdout,"\n" ); |
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| 507 | #endif |
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| 508 | } |
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| 509 | |
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| 510 | return s; |
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| 511 | } |
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| 512 | |
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| 513 | #endif |
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| 514 | |
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| 515 | // ---------------------------------------------------------------------------- |
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| 516 | // Add a face to the newton polygon |
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| 517 | // ---------------------------------------------------------------------------- |
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| 518 | |
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| 519 | void newtonPolygon::add_linearForm( const linearForm &l0 ) |
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| 520 | { |
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| 521 | int i; |
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| 522 | newtonPolygon np; |
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| 523 | |
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| 524 | // ------------------------------------- |
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| 525 | // test if linear form is already here |
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| 526 | // ------------------------------------- |
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| 527 | |
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| 528 | for( i=0; i<N; i++ ) |
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| 529 | { |
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| 530 | if( l0==l[i] ) |
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| 531 | { |
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| 532 | return; |
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| 533 | } |
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| 534 | } |
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| 535 | |
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| 536 | np.copy_new( N+1 ); |
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| 537 | np.N = N+1; |
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| 538 | |
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| 539 | for( i=0; i<N; i++ ) |
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| 540 | { |
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| 541 | np.l[i].copy_shallow( l[i] ); |
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| 542 | l[i].copy_zero( ); |
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| 543 | } |
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| 544 | |
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| 545 | np.l[N] = l0; |
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| 546 | |
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| 547 | copy_delete( ); |
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| 548 | copy_shallow( np ); |
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| 549 | np.copy_zero( ); |
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| 550 | |
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| 551 | return; |
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| 552 | } |
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| 553 | |
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| 554 | // ---------------------------------------------------------------------------- |
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| 555 | // Newton weight of a monomial |
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| 556 | // ---------------------------------------------------------------------------- |
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| 557 | |
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| 558 | Rational newtonPolygon::weight( poly m ) const |
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| 559 | { |
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| 560 | Rational ret = l[0].weight( m ); |
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| 561 | Rational tmp; |
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| 562 | |
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| 563 | for( int i=1; i<N; i++ ) |
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| 564 | { |
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| 565 | tmp = l[i].weight( m ); |
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| 566 | |
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| 567 | if( tmp < ret ) |
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| 568 | { |
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| 569 | ret = tmp; |
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| 570 | } |
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| 571 | } |
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| 572 | return ret; |
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| 573 | } |
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| 574 | |
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| 575 | // ---------------------------------------------------------------------------- |
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| 576 | // Newton weight of a monomial shifted by the product of the variables |
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| 577 | // ---------------------------------------------------------------------------- |
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| 578 | |
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| 579 | Rational newtonPolygon::weight_shift( poly m ) const |
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| 580 | { |
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| 581 | Rational ret = l[0].weight_shift( m ); |
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| 582 | Rational tmp; |
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| 583 | |
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| 584 | for( int i=1; i<N; i++ ) |
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| 585 | { |
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| 586 | tmp = l[i].weight_shift( m ); |
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| 587 | |
---|
| 588 | if( tmp < ret ) |
---|
| 589 | { |
---|
| 590 | ret = tmp; |
---|
| 591 | } |
---|
| 592 | } |
---|
| 593 | return ret; |
---|
| 594 | } |
---|
| 595 | |
---|
| 596 | // ---------------------------------------------------------------------------- |
---|
| 597 | // Newton weight of a monomial (forgetting the first variable) |
---|
| 598 | // ---------------------------------------------------------------------------- |
---|
| 599 | |
---|
| 600 | Rational newtonPolygon::weight1( poly m ) const |
---|
| 601 | { |
---|
| 602 | Rational ret = l[0].weight1( m ); |
---|
| 603 | Rational tmp; |
---|
| 604 | |
---|
| 605 | for( int i=1; i<N; i++ ) |
---|
| 606 | { |
---|
| 607 | tmp = l[i].weight1( m ); |
---|
| 608 | |
---|
| 609 | if( tmp < ret ) |
---|
| 610 | { |
---|
| 611 | ret = tmp; |
---|
| 612 | } |
---|
| 613 | } |
---|
| 614 | return ret; |
---|
| 615 | } |
---|
| 616 | |
---|
| 617 | // ---------------------------------------------------------------------------- |
---|
| 618 | // Newton weight of a monomial shifted by the product of the variables |
---|
| 619 | // (forgetting the first variable) |
---|
| 620 | // ---------------------------------------------------------------------------- |
---|
| 621 | |
---|
| 622 | Rational newtonPolygon::weight_shift1( poly m ) const |
---|
| 623 | { |
---|
| 624 | Rational ret = l[0].weight_shift1( m ); |
---|
| 625 | Rational tmp; |
---|
| 626 | |
---|
| 627 | for( int i=1; i<N; i++ ) |
---|
| 628 | { |
---|
| 629 | tmp = l[i].weight_shift1( m ); |
---|
| 630 | |
---|
| 631 | if( tmp < ret ) |
---|
| 632 | { |
---|
| 633 | ret = tmp; |
---|
| 634 | } |
---|
| 635 | } |
---|
| 636 | return ret; |
---|
| 637 | } |
---|
| 638 | |
---|
| 639 | /* |
---|
| 640 | // ---------------------------------------------------------------------------- |
---|
| 641 | // Chcek if the polynomial belonging to the Newton polygon |
---|
| 642 | // is semiquasihomogeneous (sqh) |
---|
| 643 | // ---------------------------------------------------------------------------- |
---|
| 644 | |
---|
| 645 | int newtonPolygon::is_sqh( void ) const |
---|
| 646 | { |
---|
| 647 | return ( N==1 ? TRUE : FALSE ); |
---|
| 648 | } |
---|
| 649 | |
---|
| 650 | // ---------------------------------------------------------------------------- |
---|
| 651 | // If the polynomial belonging to the Newton polygon is sqh, |
---|
| 652 | // return its weights vector |
---|
| 653 | // ---------------------------------------------------------------------------- |
---|
| 654 | |
---|
| 655 | Rational* newtonPolygon::sqh_weights( void ) const |
---|
| 656 | { |
---|
| 657 | return ( N==1 ? l[0].c : (Rational*)NULL ); |
---|
| 658 | } |
---|
| 659 | |
---|
| 660 | int newtonPolygon::sqh_N( void ) const |
---|
| 661 | { |
---|
| 662 | return ( N==1 ? l[0].N : 0 ); |
---|
| 663 | } |
---|
| 664 | */ |
---|
| 665 | |
---|
| 666 | #endif /* HAVE_SPECTRUM */ |
---|
| 667 | // ---------------------------------------------------------------------------- |
---|
| 668 | // npolygon.cc |
---|
| 669 | // end of file |
---|
| 670 | // ---------------------------------------------------------------------------- |
---|
| 671 | |
---|