[7885020] | 1 | // ---------------------------------------------------------------------------- |
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| 2 | // splist.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 SPLIST_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 SPLIST_PRINT |
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| 15 | #include <iostream.h> |
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| 16 | #ifndef SPLIST_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 "tok.h" |
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| 22 | #include "GMPrat.h" |
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| 23 | #include "numbers.h" |
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| 24 | #include "polys.h" |
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| 25 | #include "npolygon.h" |
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| 26 | #include "splist.h" |
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| 27 | #include "intvec.h" |
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| 28 | #include "lists.h" |
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| 29 | |
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| 30 | // ------------------------ |
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| 31 | // class spectrumPolyNode |
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| 32 | // ------------------------ |
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| 33 | |
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| 34 | // ---------------------------------------------------------------------------- |
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| 35 | // Initialize a spectrumPolyNode with zero |
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| 36 | // ---------------------------------------------------------------------------- |
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| 37 | |
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| 38 | void spectrumPolyNode::copy_zero( void ) |
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| 39 | { |
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| 40 | next = (spectrumPolyNode*)NULL; |
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| 41 | mon = (poly)NULL; |
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| 42 | weight = (Rational)0; |
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| 43 | nf = (poly)NULL; |
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| 44 | } |
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| 45 | |
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| 46 | // ---------------------------------------------------------------------------- |
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| 47 | // Inizialize a spectrumPolyNode shallow from data |
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| 48 | // ---------------------------------------------------------------------------- |
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| 49 | |
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| 50 | void spectrumPolyNode::copy_shallow( |
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| 51 | spectrumPolyNode *pnode,poly m,const Rational &w,poly f ) |
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| 52 | { |
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| 53 | next = pnode; |
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| 54 | mon = m; |
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| 55 | weight = w; |
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| 56 | nf = f; |
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| 57 | } |
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| 58 | |
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| 59 | // ---------------------------------------------------------------------------- |
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| 60 | // Inizialize a spectrumPolyNode shallow from another spectrumPolyNode |
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| 61 | // ---------------------------------------------------------------------------- |
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| 62 | |
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| 63 | void spectrumPolyNode::copy_shallow( spectrumPolyNode &node ) |
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| 64 | { |
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| 65 | next = node.next; |
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| 66 | mon = node.mon; |
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| 67 | weight = node.weight; |
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| 68 | nf = node.nf; |
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| 69 | } |
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| 70 | |
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| 71 | // ---------------------------------------------------------------------------- |
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| 72 | // Zero constructor for spectrumPolyNode |
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| 73 | // ---------------------------------------------------------------------------- |
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| 74 | |
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| 75 | spectrumPolyNode::spectrumPolyNode( ) |
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| 76 | { |
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| 77 | copy_zero( ); |
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| 78 | } |
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| 79 | |
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| 80 | // ---------------------------------------------------------------------------- |
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| 81 | // Data constructor for spectrumPolyNode is shallow |
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| 82 | // ---------------------------------------------------------------------------- |
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| 83 | |
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| 84 | spectrumPolyNode::spectrumPolyNode( |
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| 85 | spectrumPolyNode *pnode,poly m,const Rational &w,poly f ) |
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| 86 | { |
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| 87 | copy_shallow( pnode,m,w,f ); |
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| 88 | } |
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| 89 | |
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| 90 | // ---------------------------------------------------------------------------- |
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| 91 | // Destructor is empty since we construct our objects shallow |
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| 92 | // ---------------------------------------------------------------------------- |
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| 93 | |
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| 94 | spectrumPolyNode::~spectrumPolyNode( ) |
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| 95 | { |
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| 96 | if( mon!=(poly)NULL ) pDelete( &mon ); |
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| 97 | if( nf !=(poly)NULL ) pDelete( &nf ); |
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| 98 | copy_zero( ); |
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| 99 | } |
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| 100 | |
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| 101 | // ------------------------ |
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| 102 | // class spectrumPolyList |
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| 103 | // ------------------------ |
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| 104 | |
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| 105 | // ---------------------------------------------------------------------------- |
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| 106 | // Initialize a spectrumPolyList with zero |
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| 107 | // ---------------------------------------------------------------------------- |
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| 108 | |
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| 109 | void spectrumPolyList::copy_zero( void ) |
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| 110 | { |
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| 111 | root = (spectrumPolyNode*)NULL; |
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| 112 | N = 0; |
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| 113 | np = (newtonPolygon*)NULL; |
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| 114 | } |
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| 115 | |
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| 116 | // ---------------------------------------------------------------------------- |
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| 117 | // Inizialize a spectrumPolyList shallow from data |
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| 118 | // ---------------------------------------------------------------------------- |
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| 119 | |
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| 120 | void spectrumPolyList::copy_shallow( |
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| 121 | spectrumPolyNode *node,int k,newtonPolygon *npolygon ) |
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| 122 | { |
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| 123 | root = node; |
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| 124 | N = k; |
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| 125 | np = npolygon; |
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| 126 | } |
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| 127 | |
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| 128 | // ---------------------------------------------------------------------------- |
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| 129 | // Inizialize a spectrumPolyList shallow from another spectrumPolyList |
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| 130 | // ---------------------------------------------------------------------------- |
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| 131 | |
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| 132 | void spectrumPolyList::copy_shallow( spectrumPolyList &splist ) |
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| 133 | { |
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| 134 | copy_shallow( splist.root,splist.N,splist.np ); |
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| 135 | } |
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| 136 | |
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| 137 | // ---------------------------------------------------------------------------- |
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| 138 | // Zero constructor for spectrumPolyList |
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| 139 | // ---------------------------------------------------------------------------- |
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| 140 | |
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| 141 | spectrumPolyList::spectrumPolyList( ) |
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| 142 | { |
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| 143 | copy_zero( ); |
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| 144 | } |
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| 145 | |
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| 146 | // ---------------------------------------------------------------------------- |
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| 147 | // Data constructor for spectrumPolyList |
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| 148 | // ---------------------------------------------------------------------------- |
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| 149 | |
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| 150 | spectrumPolyList::spectrumPolyList( newtonPolygon *npolygon ) |
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| 151 | { |
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| 152 | copy_shallow( (spectrumPolyNode*)NULL,0,npolygon ); |
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| 153 | } |
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| 154 | |
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| 155 | // ---------------------------------------------------------------------------- |
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| 156 | // Destuctor for spectrumPolyList |
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| 157 | // ---------------------------------------------------------------------------- |
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| 158 | |
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| 159 | spectrumPolyList::~spectrumPolyList( ) |
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| 160 | { |
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| 161 | spectrumPolyNode *node; |
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| 162 | |
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| 163 | while( root!=(spectrumPolyNode*)NULL ) |
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| 164 | { |
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| 165 | node = root->next; |
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| 166 | delete root; |
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| 167 | root = node; |
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| 168 | } |
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| 169 | |
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| 170 | copy_zero( ); |
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| 171 | } |
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| 172 | |
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| 173 | // ---------------------------------------------------------------------------- |
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| 174 | // Insert a new node into a spectrumPolyList at position k |
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| 175 | // If the list is sorted, then |
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| 176 | // the new node ist inserted such that the list remains sorted. |
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| 177 | // ---------------------------------------------------------------------------- |
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| 178 | |
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| 179 | void spectrumPolyList::insert_node( poly m,poly f ) |
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| 180 | { |
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| 181 | #ifdef SPLIST_DEBUG |
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| 182 | if( np==(newtonPolygon*)NULL ) |
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| 183 | { |
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| 184 | #ifdef SPLIST_PRINT |
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| 185 | #ifdef SPLIST_IOSTREAM |
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| 186 | cerr << "void spectrumPolyList::insert_node( poly f )" << endl; |
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| 187 | cerr << " no Newton polygon" << endl; |
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| 188 | cerr << " exiting..." << endl; |
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| 189 | #else |
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| 190 | fprintf( stderr,"void spectrumPolyList::insert_node( poly f )\n" ); |
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| 191 | fprintf( stderr," no Newton polygon\n" ); |
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| 192 | fprintf( stderr," exiting...\n" ); |
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| 193 | #endif |
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| 194 | #endif |
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| 195 | |
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| 196 | exit( 1 ); |
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| 197 | } |
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| 198 | #endif |
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| 199 | |
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| 200 | spectrumPolyNode *newnode = new spectrumPolyNode( |
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| 201 | (spectrumPolyNode*)NULL,m,np->weight_shift( m ),f ); |
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| 202 | |
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| 203 | if( N==0 || |
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| 204 | root->weight>newnode->weight || |
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| 205 | ( root->weight==newnode->weight && |
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[a6a239] | 206 | pCmp( root->mon,newnode->mon )<0 ) ) |
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[7885020] | 207 | { |
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| 208 | // ---------------------- |
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| 209 | // insert at position 0 |
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| 210 | // ---------------------- |
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| 211 | |
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| 212 | newnode->next = root; |
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| 213 | root = newnode; |
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| 214 | } |
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| 215 | else if( N==1 ) |
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| 216 | { |
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| 217 | // --------------- |
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| 218 | // insert at end |
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| 219 | // --------------- |
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| 220 | |
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| 221 | root->next = newnode; |
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| 222 | } |
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| 223 | else |
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| 224 | { |
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| 225 | // ---------------------------- |
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| 226 | // insert according to weight |
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| 227 | // ---------------------------- |
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| 228 | |
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| 229 | spectrumPolyNode *actual = root; |
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| 230 | spectrumPolyNode *next = root->next; |
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| 231 | |
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| 232 | while( next!=(spectrumPolyNode*)NULL && |
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| 233 | ( newnode->weight>next->weight || |
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| 234 | ( newnode->weight==next->weight && |
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[a6a239] | 235 | pCmp( newnode->mon,next->mon )<0 ) ) ) |
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[7885020] | 236 | { |
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| 237 | actual = next; |
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| 238 | next = next->next; |
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| 239 | } |
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| 240 | |
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| 241 | actual->next = newnode; |
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| 242 | newnode->next = next; |
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| 243 | } |
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| 244 | N++; |
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| 245 | } |
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| 246 | |
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| 247 | // ---------------------------------------------------------------------------- |
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| 248 | // Delete a node from a spectrumPolyList |
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| 249 | // ---------------------------------------------------------------------------- |
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| 250 | |
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| 251 | void spectrumPolyList::delete_node( spectrumPolyNode **node ) |
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| 252 | { |
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| 253 | spectrumPolyNode *foo = *node; |
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| 254 | *node = (*node)->next; |
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| 255 | delete foo; |
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| 256 | N--; |
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| 257 | } |
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| 258 | |
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| 259 | // ---------------------------------------------------------------------------- |
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| 260 | // Delete all nodes where node->mon is a multiple of m |
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| 261 | // In every node delete all instances of m in node->nf |
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| 262 | // ---------------------------------------------------------------------------- |
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| 263 | |
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| 264 | void spectrumPolyList::delete_monomial( poly m ) |
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| 265 | { |
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| 266 | spectrumPolyNode **node = &root; |
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| 267 | poly *f; |
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| 268 | |
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| 269 | m = pCopy( m ); |
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| 270 | |
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| 271 | while( *node!=(spectrumPolyNode*)NULL ) |
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| 272 | { |
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[512a2b] | 273 | if( pCmp( m,(*node)->mon )>=0 && pLmDivisibleByNoComp( m,(*node)->mon ) ) |
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[7885020] | 274 | { |
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| 275 | delete_node( node ); |
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| 276 | } |
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| 277 | else if( (*node)->nf!=(poly)NULL ) |
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| 278 | { |
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| 279 | f = &((*node)->nf); |
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| 280 | |
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| 281 | while( *f!=(poly)NULL ) |
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| 282 | { |
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[512a2b] | 283 | if( pCmp( m,*f )>=0 && pLmDivisibleByNoComp( m,*f ) ) |
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[7885020] | 284 | { |
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[512a2b] | 285 | pDeleteLm(f); |
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[7885020] | 286 | } |
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| 287 | else |
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| 288 | { |
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| 289 | f = &(pNext( *f )); |
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| 290 | } |
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| 291 | } |
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| 292 | |
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| 293 | if( (*node)->nf==(poly)NULL ) |
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| 294 | { |
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| 295 | delete_node( node ); |
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| 296 | } |
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| 297 | else |
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| 298 | { |
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| 299 | node = &((*node)->next); |
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| 300 | } |
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| 301 | } |
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| 302 | else |
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| 303 | { |
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| 304 | node = &((*node)->next); |
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| 305 | } |
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| 306 | } |
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| 307 | pDelete( &m ); |
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| 308 | } |
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| 309 | |
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| 310 | // ---------------------------------------------------------------------------- |
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| 311 | // Compute the spectrum of a spectrumPolyList |
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| 312 | // ---------------------------------------------------------------------------- |
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| 313 | |
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| 314 | spectrumState spectrumPolyList::spectrum( lists *L,int fast ) |
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| 315 | { |
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| 316 | spectrumPolyNode **node = &root; |
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| 317 | spectrumPolyNode *search; |
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| 318 | |
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| 319 | poly f,tmp; |
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| 320 | int found,cmp; |
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| 321 | |
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| 322 | Rational smax( ( fast==0 ? 0 : pVariables ), |
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| 323 | ( fast==2 ? 2 : 1 ) ); |
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| 324 | |
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| 325 | Rational weight_prev( 0,1 ); |
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| 326 | |
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| 327 | int mu = 0; // the milnor number |
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| 328 | int pg = 0; // the geometrical genus |
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| 329 | int n = 0; // number of different spectral numbers |
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| 330 | int z = 0; // number of spectral number equal to smax |
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| 331 | |
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| 332 | int k = 0; |
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| 333 | |
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| 334 | while( (*node)!=(spectrumPolyNode*)NULL && |
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| 335 | ( fast==0 || (*node)->weight<=smax ) ) |
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| 336 | { |
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| 337 | // --------------------------------------- |
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| 338 | // determine the first normal form which |
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| 339 | // contains the monomial node->mon |
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| 340 | // --------------------------------------- |
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| 341 | |
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| 342 | found = FALSE; |
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| 343 | search = *node; |
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| 344 | |
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| 345 | while( search!=(spectrumPolyNode*)NULL && found==FALSE ) |
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| 346 | { |
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| 347 | if( search->nf!=(poly)NULL ) |
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| 348 | { |
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| 349 | f = search->nf; |
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| 350 | |
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| 351 | do |
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| 352 | { |
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| 353 | // -------------------------------- |
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| 354 | // look for (*node)->mon in f |
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| 355 | // -------------------------------- |
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| 356 | |
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[a6a239] | 357 | cmp = pCmp( (*node)->mon,f ); |
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[7885020] | 358 | |
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| 359 | if( cmp<0 ) |
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| 360 | { |
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| 361 | f = pNext( f ); |
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| 362 | } |
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| 363 | else if( cmp==0 ) |
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| 364 | { |
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| 365 | // ----------------------------- |
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| 366 | // we have found a normal form |
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| 367 | // ----------------------------- |
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| 368 | |
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| 369 | found = TRUE; |
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| 370 | |
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| 371 | // normalize coefficient |
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| 372 | |
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| 373 | number inv = nInvers( pGetCoeff( f ) ); |
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[a6a239] | 374 | pMult_nn( search->nf,inv ); |
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[7885020] | 375 | nDelete( &inv ); |
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| 376 | |
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| 377 | // exchange normal forms |
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| 378 | |
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| 379 | tmp = (*node)->nf; |
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| 380 | (*node)->nf = search->nf; |
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| 381 | search->nf = tmp; |
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| 382 | } |
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| 383 | } |
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| 384 | while( cmp<0 && f!=(poly)NULL ); |
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| 385 | } |
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| 386 | search = search->next; |
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| 387 | } |
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| 388 | |
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| 389 | if( found==FALSE ) |
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| 390 | { |
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| 391 | // ------------------------------------------------ |
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| 392 | // the weight of node->mon is a spectrum number |
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| 393 | // ------------------------------------------------ |
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| 394 | |
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| 395 | mu++; |
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| 396 | |
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| 397 | if( (*node)->weight<=(Rational)1 ) pg++; |
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| 398 | if( (*node)->weight==smax ) z++; |
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| 399 | if( (*node)->weight>weight_prev ) n++; |
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| 400 | |
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| 401 | weight_prev = (*node)->weight; |
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| 402 | node = &((*node)->next); |
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| 403 | } |
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| 404 | else |
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| 405 | { |
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| 406 | // ----------------------------------------------- |
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| 407 | // determine all other normal form which contain |
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| 408 | // the monomial node->mon |
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| 409 | // replace for node->mon its normal form |
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| 410 | // ----------------------------------------------- |
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| 411 | |
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| 412 | while( search!=(spectrumPolyNode*)NULL ) |
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| 413 | { |
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| 414 | if( search->nf!=(poly)NULL ) |
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| 415 | { |
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| 416 | f = search->nf; |
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| 417 | |
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| 418 | do |
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| 419 | { |
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| 420 | // -------------------------------- |
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| 421 | // look for (*node)->mon in f |
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| 422 | // -------------------------------- |
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| 423 | |
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[a6a239] | 424 | cmp = pCmp( (*node)->mon,f ); |
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[7885020] | 425 | |
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| 426 | if( cmp<0 ) |
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| 427 | { |
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| 428 | f = pNext( f ); |
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| 429 | } |
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| 430 | else if( cmp==0 ) |
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| 431 | { |
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| 432 | search->nf = pSub( search->nf, |
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[a6a239] | 433 | ppMult_nn( (*node)->nf,pGetCoeff( f ) ) ); |
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[7885020] | 434 | pNorm( search->nf ); |
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| 435 | } |
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| 436 | } |
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| 437 | while( cmp<0 && f!=(poly)NULL ); |
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| 438 | } |
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| 439 | search = search->next; |
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| 440 | } |
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| 441 | delete_node( node ); |
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| 442 | } |
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| 443 | |
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| 444 | } |
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| 445 | |
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| 446 | // -------------------------------------------------------- |
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| 447 | // fast computation exploits the symmetry of the spectrum |
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| 448 | // -------------------------------------------------------- |
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| 449 | |
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| 450 | if( fast==2 ) |
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| 451 | { |
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| 452 | mu = 2*mu - z; |
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| 453 | n = ( z > 0 ? 2*n - 1 : 2*n ); |
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| 454 | } |
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| 455 | |
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| 456 | // -------------------------------------------------------- |
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| 457 | // compute the spectrum numbers with their multiplicities |
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| 458 | // -------------------------------------------------------- |
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| 459 | |
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[c232af] | 460 | intvec *nom = new intvec( n ); |
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| 461 | intvec *den = new intvec( n ); |
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| 462 | intvec *mult = new intvec( n ); |
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[7885020] | 463 | |
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| 464 | int count = 0; |
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| 465 | int multiplicity = 1; |
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| 466 | |
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| 467 | for( search=root; search!=(spectrumPolyNode*)NULL && |
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| 468 | ( fast==0 || search->weight<=smax ); |
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| 469 | search=search->next ) |
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| 470 | { |
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| 471 | if( search->next==(spectrumPolyNode*)NULL || |
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| 472 | search->weight<search->next->weight ) |
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| 473 | { |
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| 474 | (*nom) [count] = search->weight.get_num_si( ); |
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| 475 | (*den) [count] = search->weight.get_den_si( ); |
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| 476 | (*mult)[count] = multiplicity; |
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| 477 | |
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| 478 | multiplicity=1; |
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| 479 | count++; |
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| 480 | } |
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| 481 | else |
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| 482 | { |
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| 483 | multiplicity++; |
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| 484 | } |
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| 485 | } |
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| 486 | |
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| 487 | // -------------------------------------------------------- |
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| 488 | // fast computation exploits the symmetry of the spectrum |
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| 489 | // -------------------------------------------------------- |
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| 490 | |
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| 491 | if( fast==2 ) |
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| 492 | { |
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| 493 | int n1,n2; |
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| 494 | for( n1=0, n2=n-1; n1<n2; n1++, n2-- ) |
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| 495 | { |
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| 496 | (*nom) [n2] = pVariables*(*den)[n1]-(*nom)[n1]; |
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| 497 | (*den) [n2] = (*den)[n1]; |
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| 498 | (*mult)[n2] = (*mult)[n1]; |
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| 499 | } |
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| 500 | } |
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| 501 | |
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| 502 | // ----------------------------------- |
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| 503 | // test if the spectrum is symmetric |
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| 504 | // ----------------------------------- |
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| 505 | |
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| 506 | if( fast==0 || fast==1 ) |
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| 507 | { |
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| 508 | int symmetric=TRUE; |
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| 509 | |
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| 510 | for( int n1=0, n2=n-1 ; n1<n2 && symmetric==TRUE; n1++, n2-- ) |
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| 511 | { |
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| 512 | if( (*mult)[n1]!=(*mult)[n2] || |
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| 513 | (*den) [n1]!= (*den)[n2] || |
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| 514 | (*nom)[n1]+(*nom)[n2]!=pVariables*(*den) [n1] ) |
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| 515 | { |
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| 516 | symmetric = FALSE; |
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| 517 | } |
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| 518 | } |
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| 519 | |
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| 520 | if( symmetric==FALSE ) |
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| 521 | { |
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| 522 | // --------------------------------------------- |
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| 523 | // the spectrum is not symmetric => degenerate |
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| 524 | // principal part |
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| 525 | // --------------------------------------------- |
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| 526 | |
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[0bb212d] | 527 | *L = (lists)omAllocBin( slists_bin); |
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[7885020] | 528 | (*L)->Init( 1 ); |
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| 529 | (*L)->m[0].rtyp = INT_CMD; // milnor number |
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| 530 | (*L)->m[0].data = (void*)mu; |
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| 531 | |
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| 532 | return spectrumDegenerate; |
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| 533 | } |
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| 534 | } |
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| 535 | |
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[0bb212d] | 536 | *L = (lists)omAllocBin( slists_bin); |
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[7885020] | 537 | |
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| 538 | (*L)->Init( 6 ); |
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| 539 | |
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| 540 | (*L)->m[0].rtyp = INT_CMD; // milnor number |
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| 541 | (*L)->m[1].rtyp = INT_CMD; // geometrical genus |
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| 542 | (*L)->m[2].rtyp = INT_CMD; // number of spectrum values |
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| 543 | (*L)->m[3].rtyp = INTVEC_CMD; // nominators |
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| 544 | (*L)->m[4].rtyp = INTVEC_CMD; // denomiantors |
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| 545 | (*L)->m[5].rtyp = INTVEC_CMD; // multiplicities |
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| 546 | |
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| 547 | (*L)->m[0].data = (void*)mu; |
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| 548 | (*L)->m[1].data = (void*)pg; |
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| 549 | (*L)->m[2].data = (void*)n; |
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| 550 | (*L)->m[3].data = (void*)nom; |
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| 551 | (*L)->m[4].data = (void*)den; |
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| 552 | (*L)->m[5].data = (void*)mult; |
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| 553 | |
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| 554 | return spectrumOK; |
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| 555 | } |
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| 556 | |
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| 557 | // ---------------------------------------------------------------------------- |
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| 558 | // Print a spectrumPolyList |
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| 559 | // ---------------------------------------------------------------------------- |
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| 560 | |
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| 561 | #ifdef SPLIST_PRINT |
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| 562 | ostream & operator << ( ostream &s,const spectrumPolyList &l ) |
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| 563 | { |
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| 564 | #ifdef SPLIST_IOSTREAM |
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| 565 | s << "elements: " << l.N << endl; |
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| 566 | s << "{"; |
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| 567 | #else |
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| 568 | fprintf( stdout,"elements: %d\n",l.N ); |
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| 569 | fprintf( stdout,"{" ); |
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| 570 | #endif |
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| 571 | |
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| 572 | if( l.root!=(spectrumPolyNode*)NULL ) |
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| 573 | { |
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| 574 | #ifdef SPLIST_IOSTREAM |
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| 575 | s << "("; |
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| 576 | pWrite0( l.root->mon ); |
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| 577 | s << "=>"; |
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| 578 | pWrite0( l.root->nf ); |
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| 579 | cout << "," << l.root->weight << ")" << endl; |
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| 580 | #else |
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| 581 | fprintf( stdout,"(" ); |
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| 582 | pWrite0( l.root->mon ); |
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| 583 | fprintf( stdout,"=>" ); |
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| 584 | pWrite0( l.root->nf ); |
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| 585 | fprintf( stdout,"," ); |
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| 586 | cout << l.root->weight; |
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| 587 | fprintf( stdout,")\n" ); |
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| 588 | #endif |
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| 589 | |
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| 590 | spectrumPolyNode *node = l.root->next; |
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| 591 | |
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| 592 | while( node!=(spectrumPolyNode*)NULL ) |
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| 593 | { |
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| 594 | #ifdef SPLIST_IOSTREAM |
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| 595 | s << ",("; |
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| 596 | pWrite0( node->mon ); |
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| 597 | s << "=>"; |
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| 598 | pWrite0( node->nf ); |
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| 599 | cout << "," << node->weight << ")" << endl; |
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| 600 | #else |
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| 601 | fprintf( stdout,",(" ); |
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| 602 | pWrite0( node->mon ); |
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| 603 | fprintf( stdout,"=>" ); |
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| 604 | pWrite0( node->nf ); |
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| 605 | fprintf( stdout,"," ); |
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| 606 | cout << node->weight; |
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| 607 | fprintf( stdout,")\n" ); |
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| 608 | #endif |
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| 609 | |
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| 610 | node = node->next; |
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| 611 | } |
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| 612 | } |
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| 613 | #ifdef SPLIST_IOSTREAM |
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| 614 | s << "}"; |
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| 615 | #else |
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| 616 | fprintf( stdout,"}" ); |
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| 617 | #endif |
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| 618 | |
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| 619 | return s; |
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| 620 | } |
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| 621 | #endif |
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| 622 | |
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| 623 | #endif /* HAVE_SPECTRUM */ |
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| 624 | // ---------------------------------------------------------------------------- |
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| 625 | // splist.cc |
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| 626 | // end of file |
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| 627 | // ---------------------------------------------------------------------------- |
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| 628 | |
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