[7885020] | 1 | // ---------------------------------------------------------------------------- |
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| 2 | // semic.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 SEMIC_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 SEMIC_PRINT |
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| 15 | #ifndef SEMIC_IOSTREAM |
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| 16 | #include<stdio.h> |
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| 17 | #else |
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| 18 | #include<iostream.h> |
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| 19 | #endif |
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| 20 | #endif |
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| 21 | |
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| 22 | #include<string.h> |
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| 23 | #include<values.h> |
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| 24 | |
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| 25 | #include"intvec.h" |
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| 26 | #include"lists.h" |
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| 27 | #include"GMPrat.h" |
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| 28 | #include"semic.h" |
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| 29 | |
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| 30 | // ---------------------------------------------------------------------------- |
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| 31 | // Delete the memory of a spectrum |
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| 32 | // ---------------------------------------------------------------------------- |
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| 33 | |
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| 34 | inline void spectrum::copy_delete( void ) |
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| 35 | { |
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| 36 | if( s != (Rational*)NULL && n > 0 ) delete [] s; |
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| 37 | if( w != (int*)NULL && n > 0 ) delete [] w; |
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| 38 | copy_zero( ); |
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| 39 | } |
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| 40 | |
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| 41 | // ---------------------------------------------------------------------------- |
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| 42 | // Allocate memory for a spectrum of k numbers |
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| 43 | // ---------------------------------------------------------------------------- |
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| 44 | |
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| 45 | void spectrum::copy_new( int k ) |
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| 46 | { |
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| 47 | if( k > 0 ) |
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| 48 | { |
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| 49 | s = new Rational[k]; |
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| 50 | w = new int[k]; |
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| 51 | |
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| 52 | #ifndef NDEBUG |
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| 53 | if( s == (Rational*)NULL || w == (int*)NULL ) |
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| 54 | { |
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| 55 | #ifdef SEMIC_PRINT |
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| 56 | #ifdef SEMIC_IOSTREAM |
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| 57 | cerr << "spectrum::copy_new(" << k << ")" << endl; |
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| 58 | cerr << " returned ZERO!!!" << endl; |
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| 59 | cerr << " exit..." << endl; |
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| 60 | #else |
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| 61 | fprintf( stderr,"spectrum::copy_new( %d )\n",k ); |
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| 62 | fprintf( stderr," returned ZERO!!!\n" ); |
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| 63 | fprintf( stderr," exit...\n" ); |
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| 64 | #endif |
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| 65 | #endif |
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| 66 | } |
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| 67 | #endif |
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| 68 | } |
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| 69 | else if( k == 0 ) |
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| 70 | { |
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| 71 | s = (Rational*)NULL; |
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| 72 | w = (int*)NULL; |
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| 73 | } |
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| 74 | else if( k < 0 ) |
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| 75 | { |
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| 76 | #ifdef SEMIC_PRINT |
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| 77 | #ifdef SEMIC_IOSTREAM |
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| 78 | cerr << "spectrum::copy_new(" << k << ")"; |
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| 79 | cerr << ": k < 0 ..." << endl; |
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| 80 | #else |
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| 81 | fprintf( stderr,"spectrum::copy_new( %d )",k ); |
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| 82 | fprintf( stderr,": k < 0 ...\n" ); |
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| 83 | #endif |
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| 84 | #endif |
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| 85 | |
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| 86 | exit( 1 ); |
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| 87 | } |
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| 88 | } |
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| 89 | |
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| 90 | // ---------------------------------------------------------------------------- |
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| 91 | // Initialize a spectrum deep from another spectrum |
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| 92 | // ---------------------------------------------------------------------------- |
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| 93 | |
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| 94 | void spectrum::copy_deep( const spectrum &spec ) |
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| 95 | { |
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| 96 | mu = spec.mu; |
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| 97 | pg = spec.pg; |
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| 98 | n = spec.n; |
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| 99 | |
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| 100 | copy_new( n ); |
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| 101 | |
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| 102 | for( int i=0; i<n; i++ ) |
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| 103 | { |
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| 104 | s[i] = spec.s[i]; |
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| 105 | w[i] = spec.w[i]; |
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| 106 | } |
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| 107 | } |
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| 108 | |
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| 109 | // ---------------------------------------------------------------------------- |
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| 110 | // Initialize a spectrum deep from a singular lists |
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| 111 | // ---------------------------------------------------------------------------- |
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| 112 | |
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| 113 | void spectrum::copy_deep( lists l ) |
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| 114 | { |
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| 115 | mu = (int)(l->m[0].Data( )); |
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| 116 | pg = (int)(l->m[1].Data( )); |
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| 117 | n = (int)(l->m[2].Data( )); |
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| 118 | |
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| 119 | copy_new( n ); |
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| 120 | |
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| 121 | intvec *num = (intvec*)l->m[3].Data( ); |
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| 122 | intvec *den = (intvec*)l->m[4].Data( ); |
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| 123 | intvec *mul = (intvec*)l->m[5].Data( ); |
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| 124 | |
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| 125 | for( int i=0; i<n; i++ ) |
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| 126 | { |
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| 127 | s[i] = (Rational)((*num)[i])/(Rational)((*den)[i]); |
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| 128 | w[i] = (*mul)[i]; |
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| 129 | } |
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| 130 | } |
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| 131 | |
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| 132 | // ---------------------------------------------------------------------------- |
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| 133 | // Copy constructor for spectrum |
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| 134 | // ---------------------------------------------------------------------------- |
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| 135 | |
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| 136 | spectrum::spectrum( const spectrum &spec ) |
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| 137 | { |
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| 138 | copy_deep( spec ); |
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| 139 | } |
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| 140 | |
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| 141 | // ---------------------------------------------------------------------------- |
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| 142 | // singular lists constructor for spectrum |
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| 143 | // ---------------------------------------------------------------------------- |
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| 144 | |
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| 145 | spectrum::spectrum( lists l ) |
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| 146 | { |
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| 147 | copy_deep( l ); |
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| 148 | } |
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| 149 | |
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| 150 | // ---------------------------------------------------------------------------- |
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| 151 | // Destructor for spectrum |
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| 152 | // ---------------------------------------------------------------------------- |
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| 153 | |
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| 154 | spectrum::~spectrum( ) |
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| 155 | { |
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| 156 | copy_delete( ); |
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| 157 | } |
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| 158 | |
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| 159 | |
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| 160 | // ---------------------------------------------------------------------------- |
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| 161 | // operator = for spectrum |
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| 162 | // ---------------------------------------------------------------------------- |
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| 163 | |
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| 164 | spectrum spectrum::operator = ( const spectrum &spec ) |
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| 165 | { |
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| 166 | copy_delete( ); |
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| 167 | copy_deep( spec ); |
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| 168 | |
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| 169 | return *this; |
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| 170 | } |
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| 171 | |
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| 172 | // ---------------------------------------------------------------------------- |
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| 173 | // generate a Singular lists from a spectrum |
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| 174 | // ---------------------------------------------------------------------------- |
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| 175 | |
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| 176 | lists spectrum::thelist( void ) |
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| 177 | { |
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[b7b08c] | 178 | lists L = (lists)AllocSizeOf( slists ); |
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[7885020] | 179 | |
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| 180 | L->Init( 6 ); |
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| 181 | |
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[477993] | 182 | intvec *num = NewIntvec1( n ); |
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| 183 | intvec *den = NewIntvec1( n ); |
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| 184 | intvec *mult = NewIntvec1( n ); |
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[7885020] | 185 | |
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| 186 | for( int i=0; i<n; i++ ) |
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| 187 | { |
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| 188 | (*num) [i] = s[i].get_num_si( ); |
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| 189 | (*den) [i] = s[i].get_den_si( ); |
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| 190 | (*mult)[i] = w[i]; |
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| 191 | } |
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| 192 | |
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| 193 | L->m[0].rtyp = INT_CMD; // milnor number |
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| 194 | L->m[1].rtyp = INT_CMD; // geometrical genus |
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| 195 | L->m[2].rtyp = INT_CMD; // # of spectrum numbers |
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| 196 | L->m[3].rtyp = INTVEC_CMD; // numerators |
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| 197 | L->m[4].rtyp = INTVEC_CMD; // denomiantors |
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| 198 | L->m[5].rtyp = INTVEC_CMD; // multiplicities |
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| 199 | |
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| 200 | L->m[0].data = (void*)mu; |
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| 201 | L->m[1].data = (void*)pg; |
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| 202 | L->m[2].data = (void*)n; |
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| 203 | L->m[3].data = (void*)num; |
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| 204 | L->m[4].data = (void*)den; |
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| 205 | L->m[5].data = (void*)mult; |
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| 206 | |
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| 207 | return L; |
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| 208 | } |
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| 209 | |
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| 210 | // ---------------------------------------------------------------------------- |
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| 211 | // add the two spectra s1 and s2 and return their sum |
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| 212 | // ---------------------------------------------------------------------------- |
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| 213 | |
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| 214 | spectrum operator + ( const spectrum &s1,const spectrum &s2 ) |
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| 215 | { |
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| 216 | int i1=0, i2=0, i3=0; |
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| 217 | |
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| 218 | spectrum result; |
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| 219 | |
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| 220 | do |
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| 221 | { |
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| 222 | if( i1 >= s1.n ) |
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| 223 | { |
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| 224 | i2++; |
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| 225 | } |
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| 226 | else if( i2 >= s2.n ) |
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| 227 | { |
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| 228 | i1++; |
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| 229 | } |
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| 230 | else if( s1.s[i1] < s2.s[i2] ) |
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| 231 | { |
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| 232 | i1++; |
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| 233 | } |
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| 234 | else if( s1.s[i1] == s2.s[i2] ) |
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| 235 | { |
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| 236 | i1++; |
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| 237 | i2++; |
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| 238 | } |
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| 239 | else |
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| 240 | { |
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| 241 | i2++; |
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| 242 | } |
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| 243 | i3++; |
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| 244 | } |
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| 245 | while( i1 < s1.n || i2 < s2.n ); |
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| 246 | |
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| 247 | result.copy_new( i3 ); |
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| 248 | result.n = i3; |
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| 249 | |
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| 250 | i1 = i2 = i3 = 0; |
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| 251 | |
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| 252 | do |
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| 253 | { |
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| 254 | if( i1 >= s1.n ) |
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| 255 | { |
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| 256 | result.s[i3] = s2.s[i2]; |
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| 257 | result.w[i3] = s2.w[i2]; |
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| 258 | i2++; |
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| 259 | } |
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| 260 | else if( i2 >= s2.n ) |
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| 261 | { |
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| 262 | result.s[i3] = s1.s[i1]; |
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| 263 | result.w[i3] = s1.w[i1]; |
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| 264 | i1++; |
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| 265 | } |
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| 266 | else if( s1.s[i1] < s2.s[i2] ) |
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| 267 | { |
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| 268 | result.s[i3] = s1.s[i1]; |
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| 269 | result.w[i3] = s1.w[i1]; |
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| 270 | i1++; |
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| 271 | } |
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| 272 | else if( s1.s[i1] == s2.s[i2] ) |
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| 273 | { |
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| 274 | result.s[i3] = s1.s[i1]; |
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| 275 | result.w[i3] = s1.w[i1] + s2.w[i2]; |
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| 276 | i1++; |
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| 277 | i2++; |
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| 278 | } |
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| 279 | else |
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| 280 | { |
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| 281 | result.s[i3] = s2.s[i2]; |
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| 282 | result.w[i3] = s2.w[i2]; |
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| 283 | i2++; |
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| 284 | } |
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| 285 | i3++; |
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| 286 | } |
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| 287 | while( i1 < s1.n || i2 < s2.n ); |
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| 288 | |
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| 289 | result.mu = s1.mu + s2.mu; |
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| 290 | result.pg = s1.pg + s2.pg; |
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| 291 | |
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| 292 | return result; |
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| 293 | } |
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| 294 | |
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| 295 | // ---------------------------------------------------------------------------- |
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| 296 | // multiply the multiplicities of the spectrum numbers of a with m |
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| 297 | // ---------------------------------------------------------------------------- |
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| 298 | |
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| 299 | spectrum operator * ( int k,const spectrum &spec ) |
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| 300 | { |
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| 301 | if( k == 0 ) |
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| 302 | { |
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| 303 | spectrum result; |
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| 304 | |
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| 305 | return result; |
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| 306 | } |
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| 307 | else |
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| 308 | { |
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| 309 | spectrum result( spec ); |
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| 310 | |
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| 311 | result.mu *= k; |
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| 312 | result.pg *= k; |
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| 313 | |
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| 314 | for( int i=0; i<result.n; i++ ) |
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| 315 | { |
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| 316 | result.w[i] *= k; |
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| 317 | } |
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| 318 | |
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| 319 | return result; |
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| 320 | } |
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| 321 | } |
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| 322 | |
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| 323 | // ---------------------------------------------------------------------------- |
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| 324 | // Print a spectrum |
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| 325 | // ---------------------------------------------------------------------------- |
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| 326 | |
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| 327 | #ifdef SEMIC_PRINT |
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| 328 | |
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| 329 | ostream & operator << ( ostream &s,const spectrum &spec ) |
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| 330 | { |
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| 331 | for( int i=0; i<spec.n; i++ ) |
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| 332 | { |
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| 333 | if( i>0 ) |
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| 334 | { |
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| 335 | #ifdef SEMIC_STDOUT |
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| 336 | s << "+"; |
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| 337 | #else |
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| 338 | fprintf( stdout,"+" ); |
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| 339 | #endif |
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| 340 | } |
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| 341 | |
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| 342 | #ifdef SEMIC_STDOUT |
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| 343 | s << spec.w[i] << "*t^"; |
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| 344 | #else |
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| 345 | fprintf( stdout,"%d*t^",spec.w[i] ); |
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| 346 | #endif |
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| 347 | |
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| 348 | s << spec.s[i]; |
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| 349 | } |
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| 350 | |
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| 351 | return s; |
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| 352 | } |
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| 353 | #endif |
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| 354 | |
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| 355 | // ---------------------------------------------------------------------------- |
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| 356 | // Add a subspectrum with multiplicity k (faster than '+') |
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| 357 | // ---------------------------------------------------------------------------- |
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| 358 | |
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| 359 | int spectrum::add_subspectrum( spectrum &a,int k ) |
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| 360 | { |
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| 361 | int i,j; |
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| 362 | for( i=0, j=0; i<n; i++ ) |
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| 363 | { |
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| 364 | if( s[i] == a.s[j] ) |
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| 365 | { |
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| 366 | w[i] += k*a.w[j]; |
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| 367 | j++; |
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| 368 | } |
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| 369 | } |
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| 370 | |
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| 371 | return ( j == a.n ? TRUE : FALSE ); |
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| 372 | } |
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| 373 | |
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| 374 | // ---------------------------------------------------------------------------- |
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| 375 | // set *alpha to the next spectrum number strictly bigger than *alpha |
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| 376 | // returns: TRUE, if such a spectrum number exists |
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| 377 | // FALSE otherwise |
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| 378 | // ---------------------------------------------------------------------------- |
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| 379 | |
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| 380 | int spectrum::next_number( Rational *alpha ) |
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| 381 | { |
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| 382 | int i=0; |
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| 383 | |
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| 384 | while( i < n && *alpha >= s[i] ) |
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| 385 | { |
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| 386 | i++; |
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| 387 | } |
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| 388 | |
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| 389 | if( i < n ) |
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| 390 | { |
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| 391 | *alpha = s[i]; |
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| 392 | return TRUE; |
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| 393 | } |
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| 394 | else |
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| 395 | { |
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| 396 | return FALSE; |
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| 397 | } |
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| 398 | } |
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| 399 | |
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| 400 | // ---------------------------------------------------------------------------- |
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| 401 | // find the next interval on the real line of same length as |
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| 402 | // [*alpha1,*alpha2] having a spectrum number as interval border |
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| 403 | // ---------------------------------------------------------------------------- |
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| 404 | |
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| 405 | int spectrum::next_interval( Rational *alpha1,Rational *alpha2 ) |
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| 406 | { |
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| 407 | Rational zero( 0,1 ); |
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| 408 | Rational a1 = *alpha1; |
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| 409 | Rational a2 = *alpha2; |
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| 410 | Rational d = *alpha2 - *alpha1; |
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| 411 | |
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| 412 | int e1 = this->next_number( &a1 ); |
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| 413 | int e2 = this->next_number( &a2 ); |
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| 414 | |
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| 415 | if( e1 || e2 ) |
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| 416 | { |
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| 417 | Rational d1 = a1 - *alpha1; |
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| 418 | Rational d2 = a2 - *alpha2; |
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| 419 | |
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| 420 | if( d1 < d2 || d2 == zero ) |
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| 421 | { |
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| 422 | *alpha1 = a1; |
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| 423 | *alpha2 = a1 + d; |
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| 424 | } |
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| 425 | else |
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| 426 | { |
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| 427 | *alpha1 = a2 - d; |
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| 428 | *alpha2 = a2; |
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| 429 | } |
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| 430 | return TRUE; |
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| 431 | } |
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| 432 | else |
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| 433 | { |
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| 434 | return FALSE; |
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| 435 | } |
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| 436 | } |
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| 437 | |
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| 438 | // ---------------------------------------------------------------------------- |
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| 439 | // compute the numver of spectrum numbers in the inverval [*alpha1,*alpha2] |
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| 440 | // ---------------------------------------------------------------------------- |
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| 441 | |
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| 442 | int spectrum::numbers_in_interval( Rational &alpha1, |
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| 443 | Rational &alpha2,interval_status status ) |
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| 444 | { |
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| 445 | int count = 0; |
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| 446 | |
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| 447 | for( int i=0; i<n; i++ ) |
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| 448 | { |
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| 449 | if( ( ( status == OPEN || status == LEFTOPEN ) && |
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| 450 | s[i] > alpha1 ) || |
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| 451 | ( ( status == CLOSED || status == RIGHTOPEN ) && |
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| 452 | s[i] >= alpha1 ) ) |
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| 453 | { |
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| 454 | if( ( ( status == OPEN || status == RIGHTOPEN ) && |
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| 455 | s[i] < alpha2 ) || |
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| 456 | ( ( status == CLOSED || status == LEFTOPEN ) && |
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| 457 | s[i] <= alpha2 ) ) |
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| 458 | { |
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| 459 | count += w[i]; |
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| 460 | } |
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| 461 | else |
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| 462 | { |
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| 463 | break; |
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| 464 | } |
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| 465 | } |
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| 466 | } |
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| 467 | |
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| 468 | return count; |
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| 469 | } |
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| 470 | |
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| 471 | // ---------------------------------------------------------------------------- |
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| 472 | // find the maximal integer k such that k*t is semicontinous |
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| 473 | // for the spectrum |
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| 474 | // ---------------------------------------------------------------------------- |
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| 475 | |
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| 476 | int spectrum::mult_spectrum( spectrum &t ) |
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| 477 | { |
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| 478 | spectrum u = *this + t; |
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| 479 | |
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| 480 | Rational alpha1 = -2; |
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| 481 | Rational alpha2 = -1; |
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| 482 | |
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| 483 | int mult=INT_MAX,nthis,nt; |
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| 484 | |
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| 485 | while( u.next_interval( &alpha1,&alpha2 ) ) |
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| 486 | { |
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| 487 | nt = t.numbers_in_interval( alpha1,alpha2,LEFTOPEN ); |
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| 488 | nthis = this->numbers_in_interval( alpha1,alpha2,LEFTOPEN ); |
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| 489 | |
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| 490 | if( nt != 0 ) |
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| 491 | { |
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| 492 | mult = (nthis/nt < mult ? nthis/nt: mult ); |
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| 493 | } |
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| 494 | |
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| 495 | } |
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| 496 | |
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| 497 | return mult; |
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| 498 | } |
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| 499 | |
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| 500 | // ---------------------------------------------------------------------------- |
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| 501 | // find the maximal integer k such that k*t is semicontinous |
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| 502 | // for the spectrum (in the homogeneous sense) |
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| 503 | // ---------------------------------------------------------------------------- |
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| 504 | |
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| 505 | int spectrum::mult_spectrumh( spectrum &t ) |
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| 506 | { |
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| 507 | spectrum u = *this + t; |
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| 508 | |
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| 509 | Rational alpha1 = -2; |
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| 510 | Rational alpha2 = -1; |
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| 511 | |
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| 512 | int mult=INT_MAX,nthis,nt; |
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| 513 | |
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| 514 | while( u.next_interval( &alpha1,&alpha2 ) ) |
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| 515 | { |
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| 516 | nt = t.numbers_in_interval( alpha1,alpha2,LEFTOPEN ); |
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| 517 | nthis = this->numbers_in_interval( alpha1,alpha2,LEFTOPEN ); |
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| 518 | |
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| 519 | if( nt != 0 ) |
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| 520 | { |
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| 521 | mult = (nthis/nt < mult ? nthis/nt: mult ); |
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| 522 | } |
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| 523 | |
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| 524 | nt = t.numbers_in_interval( alpha1,alpha2,OPEN ); |
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| 525 | nthis = this->numbers_in_interval( alpha1,alpha2,OPEN ); |
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| 526 | |
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| 527 | if( nt != 0 ) |
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| 528 | { |
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| 529 | mult = (nthis/nt < mult ? nthis/nt: mult ); |
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| 530 | } |
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| 531 | } |
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| 532 | |
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| 533 | return mult; |
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| 534 | } |
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| 535 | |
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| 536 | // ---------------------------------------------------------------------------- |
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| 537 | // Set the Milnor number |
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| 538 | // ---------------------------------------------------------------------------- |
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| 539 | |
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| 540 | /* |
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| 541 | int spectrum::set_milnor( void ) |
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| 542 | { |
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| 543 | mu = 0; |
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| 544 | |
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| 545 | for( int i=0; i<n; i++ ) |
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| 546 | { |
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| 547 | mu += w[i]; |
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| 548 | } |
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| 549 | |
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| 550 | return mu; |
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| 551 | } |
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| 552 | |
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| 553 | // ---------------------------------------------------------------------------- |
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| 554 | // Set the geometrical genus |
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| 555 | // ---------------------------------------------------------------------------- |
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| 556 | |
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| 557 | int spectrum::set_geometric_genus( void ) |
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| 558 | { |
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| 559 | pg = 0; |
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| 560 | |
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| 561 | for( int i=0; i<n && s[i]<=1; i++ ) |
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| 562 | { |
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| 563 | pg += w[i]; |
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| 564 | } |
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| 565 | return pg; |
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| 566 | } |
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| 567 | */ |
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| 568 | |
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| 569 | #endif /* HAVE_SPECTRUM */ |
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| 570 | // ---------------------------------------------------------------------------- |
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| 571 | // semic.cc |
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| 572 | // end of file |
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| 573 | // ---------------------------------------------------------------------------- |
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