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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206 | pCmp( root->mon,newnode->mon )<0 ) ) |
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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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235 | pCmp( newnode->mon,next->mon )<0 ) ) ) |
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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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273 | if( pCmp( m,(*node)->mon )>=0 && pLmDivisibleByNoComp( m,(*node)->mon ) ) |
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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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283 | if( pCmp( m,*f )>=0 && pLmDivisibleByNoComp( m,*f ) ) |
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284 | { |
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285 | pDeleteLm(f); |
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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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357 | cmp = pCmp( (*node)->mon,f ); |
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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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374 | pMult_nn( search->nf,inv ); |
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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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424 | cmp = pCmp( (*node)->mon,f ); |
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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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433 | ppMult_nn( (*node)->nf,pGetCoeff( f ) ) ); |
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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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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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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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527 | *L = (lists)omAllocBin( slists_bin); |
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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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536 | *L = (lists)omAllocBin( slists_bin); |
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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 | |
---|
619 | return s; |
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620 | } |
---|
621 | #endif |
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622 | |
---|
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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