1 | // ---------------------------------------------------------------------------- |
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2 | // npolygon.cc |
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3 | // begin of file |
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4 | // Stephan Endrass, endrass@mathematik.uni-mainz.de |
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5 | // 23.7.99 |
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6 | // ---------------------------------------------------------------------------- |
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7 | |
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8 | #define NPOLYGON_CC |
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9 | |
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10 | #include <kernel/mod2.h> |
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11 | |
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12 | #ifdef HAVE_SPECTRUM |
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13 | |
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14 | #ifdef NPOLYGON_PRINT |
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15 | #include <iostream.h> |
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16 | #ifndef NPOLYGON_IOSTREAM |
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17 | #include <stdio.h> |
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18 | #endif |
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19 | #endif |
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20 | |
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21 | //#include <polys/polys.h> |
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22 | #include <polys/monomials/p_polys.h> |
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23 | #include <polys/monomials/ring.h> |
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24 | |
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25 | #include <kernel/GMPrat.h> |
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26 | #include <kernel/kmatrix.h> |
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27 | #include <kernel/npolygon.h> |
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28 | #include <kernel/structs.h> |
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29 | |
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30 | // ---------------------------------------------------------------------------- |
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31 | // Allocate memory for a linear form of k terms |
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32 | // ---------------------------------------------------------------------------- |
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33 | |
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34 | void linearForm::copy_new( int k ) |
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35 | { |
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36 | if( k > 0 ) |
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37 | { |
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38 | c = new Rational[k]; |
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39 | |
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40 | #ifndef NBDEBUG |
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41 | if( c == (Rational*)NULL ) |
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42 | { |
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43 | #ifdef NPOLYGON_PRINT |
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44 | #ifdef NPOLYGON_IOSTREAM |
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45 | cerr << |
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46 | "void linearForm::copy_new( int k ): no memory left ...\n" ; |
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47 | #else |
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48 | fprintf( stderr, |
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49 | "void linearForm::copy_new( int k ): no memory left ...\n"); |
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50 | #endif |
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51 | #endif |
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52 | HALT(); |
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53 | } |
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54 | #endif |
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55 | } |
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56 | else if( k == 0 ) |
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57 | { |
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58 | c = (Rational*)NULL; |
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59 | } |
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60 | else if( k < 0 ) |
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61 | { |
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62 | #ifdef NPOLYGON_PRINT |
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63 | #ifdef NPOLYGON_IOSTREAM |
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64 | cerr << |
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65 | "void linearForm::copy_new( int k ): k < 0 ...\n"; |
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66 | #else |
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67 | fprintf( stderr, |
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68 | "void linearForm::copy_new( int k ): k < 0 ...\n" ); |
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69 | #endif |
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70 | #endif |
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71 | |
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72 | HALT(); |
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73 | } |
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74 | } |
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75 | |
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76 | // ---------------------------------------------------------------------------- |
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77 | // Delete the memory of a linear form |
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78 | // ---------------------------------------------------------------------------- |
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79 | |
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80 | void linearForm::copy_delete( void ) |
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81 | { |
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82 | if( c != (Rational*)NULL && N > 0 ) |
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83 | delete [] c; |
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84 | copy_zero( ); |
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85 | } |
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86 | |
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87 | // ---------------------------------------------------------------------------- |
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88 | // Initialize deep from another linear form |
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89 | // ---------------------------------------------------------------------------- |
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90 | |
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91 | void linearForm::copy_deep( const linearForm &l ) |
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92 | { |
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93 | copy_new( l.N ); |
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94 | for( int i=l.N-1; i>=0; i-- ) |
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95 | { |
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96 | c[i] = l.c[i]; |
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97 | } |
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98 | N = l.N; |
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99 | } |
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100 | |
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101 | // ---------------------------------------------------------------------------- |
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102 | // Copy constructor |
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103 | // ---------------------------------------------------------------------------- |
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104 | |
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105 | linearForm::linearForm( const linearForm &l ) |
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106 | { |
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107 | copy_deep( l ); |
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108 | } |
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109 | |
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110 | // ---------------------------------------------------------------------------- |
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111 | // Destructor |
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112 | // ---------------------------------------------------------------------------- |
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113 | |
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114 | linearForm::~linearForm( ) |
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115 | { |
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116 | copy_delete( ); |
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117 | } |
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118 | |
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119 | // ---------------------------------------------------------------------------- |
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120 | // Define `=` to be a deep copy |
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121 | // ---------------------------------------------------------------------------- |
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122 | |
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123 | linearForm & linearForm::operator = ( const linearForm &l ) |
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124 | { |
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125 | copy_delete( ); |
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126 | copy_deep( l ); |
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127 | |
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128 | return *this; |
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129 | } |
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130 | |
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131 | // ---------------------------------------------------------------------------- |
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132 | // ostream for linear form |
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133 | // ---------------------------------------------------------------------------- |
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134 | |
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135 | #ifdef NPOLYGON_PRINT |
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136 | |
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137 | ostream & operator << ( ostream &s,const linearForm &l ) |
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138 | { |
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139 | for( int i=0; i<l.N; i++ ) |
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140 | { |
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141 | if( l.c[i] != (Rational)0 ) |
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142 | { |
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143 | if( i > 0 && l.c[i] >= (Rational)0 ) |
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144 | { |
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145 | #ifdef NPOLYGON_IOSTREAM |
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146 | s << "+"; |
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147 | #else |
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148 | fprintf( stdout,"+" ); |
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149 | #endif |
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150 | } |
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151 | |
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152 | s << l.c[i]; |
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153 | |
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154 | #ifdef NPOLYGON_IOSTREAM |
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155 | s << "*x" << i+1; |
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156 | #else |
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157 | fprintf( stdout,"*x%d",i+1 ); |
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158 | #endif |
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159 | } |
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160 | } |
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161 | return s; |
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162 | } |
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163 | |
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164 | #endif |
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165 | |
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166 | // ---------------------------------------------------------------------------- |
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167 | // Equality of linear forms |
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168 | // ---------------------------------------------------------------------------- |
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169 | |
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170 | int operator == ( const linearForm &l1,const linearForm &l2 ) |
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171 | { |
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172 | if( l1.N!=l2.N ) |
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173 | return FALSE; |
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174 | for( int i=l1.N-1; i >=0 ; i-- ) |
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175 | { |
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176 | if( l1.c[i]!=l2.c[i] ) |
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177 | return FALSE; |
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178 | } |
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179 | return TRUE; |
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180 | } |
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181 | |
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182 | |
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183 | // ---------------------------------------------------------------------------- |
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184 | // Newton weight of a monomial |
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185 | // ---------------------------------------------------------------------------- |
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186 | |
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187 | Rational linearForm::weight( poly m, const ring r ) const |
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188 | { |
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189 | Rational ret=(Rational)0; |
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190 | |
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191 | for( int i=0,j=1; i<N; i++,j++ ) |
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192 | { |
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193 | ret += c[i]*(Rational)p_GetExp( m,j,r ); |
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194 | } |
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195 | |
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196 | return ret; |
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197 | } |
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198 | |
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199 | // ---------------------------------------------------------------------------- |
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200 | // Newton weight of a polynomial |
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201 | // ---------------------------------------------------------------------------- |
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202 | |
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203 | Rational linearForm::pweight( poly m, const ring r ) const |
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204 | { |
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205 | if( m==(poly)NULL ) |
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206 | return (Rational)0; |
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207 | |
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208 | Rational ret = weight( m, r ); |
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209 | Rational tmp; |
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210 | |
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211 | for( m=pNext(m); m!=(poly)NULL; pIter(m) ) |
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212 | { |
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213 | tmp = weight( m, r ); |
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214 | if( tmp<ret ) |
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215 | { |
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216 | ret = tmp; |
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217 | } |
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218 | } |
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219 | |
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220 | return ret; |
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221 | } |
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222 | |
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223 | // ---------------------------------------------------------------------------- |
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224 | // Newton weight of a monomial shifted by the product of the variables |
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225 | // ---------------------------------------------------------------------------- |
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226 | |
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227 | Rational linearForm::weight_shift( poly m, const ring r ) const |
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228 | { |
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229 | Rational ret=(Rational)0; |
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230 | |
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231 | for( int i=0,j=1; i<N; i++,j++ ) |
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232 | { |
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233 | ret += c[i]*(Rational)( p_GetExp( m,j,r ) + 1 ); |
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234 | } |
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235 | |
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236 | return ret; |
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237 | } |
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238 | |
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239 | // ---------------------------------------------------------------------------- |
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240 | // Newton weight of a monomial (forgetting the first variable) |
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241 | // ---------------------------------------------------------------------------- |
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242 | |
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243 | Rational linearForm::weight1( poly m, const ring r ) const |
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244 | { |
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245 | Rational ret=(Rational)0; |
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246 | |
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247 | for( int i=0,j=2; i<N; i++,j++ ) |
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248 | { |
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249 | ret += c[i]*(Rational)p_GetExp( m,j,r ); |
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250 | } |
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251 | |
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252 | return ret; |
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253 | } |
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254 | |
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255 | // ---------------------------------------------------------------------------- |
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256 | // Newton weight of a monomial shifted by the product of the variables |
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257 | // (forgetting the first variable) |
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258 | // ---------------------------------------------------------------------------- |
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259 | |
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260 | Rational linearForm::weight_shift1( poly m, const ring r ) const |
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261 | { |
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262 | Rational ret=(Rational)0; |
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263 | |
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264 | for( int i=0,j=2; i<N; i++,j++ ) |
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265 | { |
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266 | ret += c[i]*(Rational)( p_GetExp( m,j,r ) + 1 ); |
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267 | } |
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268 | |
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269 | return ret; |
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270 | } |
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271 | |
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272 | |
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273 | // ---------------------------------------------------------------------------- |
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274 | // Test if all coefficients of a linear form are positive |
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275 | // ---------------------------------------------------------------------------- |
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276 | |
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277 | int linearForm::positive( void ) |
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278 | { |
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279 | for( int i=0; i<N; i++ ) |
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280 | { |
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281 | if( c[i] <= (Rational)0 ) |
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282 | { |
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283 | return FALSE; |
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284 | } |
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285 | } |
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286 | return TRUE; |
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287 | } |
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288 | |
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289 | |
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290 | // ---------------------------------------------------------------------------- |
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291 | // Allocate memory for a newton polygon of k linear forms |
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292 | // ---------------------------------------------------------------------------- |
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293 | |
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294 | void newtonPolygon::copy_new( int k ) |
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295 | { |
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296 | if( k > 0 ) |
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297 | { |
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298 | l = new linearForm[k]; |
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299 | |
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300 | #ifndef NDEBUG |
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301 | if( l == (linearForm*)NULL ) |
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302 | { |
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303 | #ifdef NPOLYGON_PRINT |
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304 | #ifdef NPOLYGON_IOSTREAM |
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305 | cerr << |
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306 | "void newtonPolygon::copy_new( int k ): no memory left ...\n"; |
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307 | #else |
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308 | fprintf( stderr, |
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309 | "void newtonPolygon::copy_new( int k ): no memory left ...\n" ); |
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310 | #endif |
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311 | #endif |
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312 | |
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313 | HALT(); |
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314 | } |
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315 | #endif |
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316 | } |
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317 | else if( k == 0 ) |
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318 | { |
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319 | l = (linearForm*)NULL; |
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320 | } |
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321 | else if( k < 0 ) |
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322 | { |
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323 | #ifdef NPOLYGON_PRINT |
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324 | #ifdef NPOLYGON_IOSTREAM |
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325 | cerr << "void newtonPolygon::copy_new( int k ): k < 0 ...\n"; |
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326 | #else |
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327 | fprintf( stderr, |
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328 | "void newtonPolygon::copy_new( int k ): k < 0 ...\n" ); |
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329 | #endif |
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330 | #endif |
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331 | |
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332 | HALT(); |
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333 | } |
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334 | } |
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335 | |
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336 | // ---------------------------------------------------------------------------- |
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337 | // Delete the memory of a Newton polygon |
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338 | // ---------------------------------------------------------------------------- |
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339 | |
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340 | void newtonPolygon::copy_delete( void ) |
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341 | { |
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342 | if( l != (linearForm*)NULL && N > 0 ) |
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343 | delete [] l; |
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344 | copy_zero( ); |
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345 | } |
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346 | |
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347 | // ---------------------------------------------------------------------------- |
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348 | // Initialize deep from another Newton polygon |
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349 | // ---------------------------------------------------------------------------- |
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350 | |
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351 | void newtonPolygon::copy_deep( const newtonPolygon &np ) |
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352 | { |
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353 | copy_new( np.N ); |
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354 | for( int i=0; i<np.N; i++ ) |
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355 | { |
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356 | l[i] = np.l[i]; |
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357 | } |
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358 | N = np.N; |
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359 | } |
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360 | |
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361 | // ---------------------------------------------------------------------------- |
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362 | // Copy constructor |
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363 | // ---------------------------------------------------------------------------- |
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364 | |
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365 | newtonPolygon::newtonPolygon( const newtonPolygon &np ) |
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366 | { |
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367 | copy_deep( np ); |
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368 | } |
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369 | |
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370 | // ---------------------------------------------------------------------------- |
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371 | // Destructor |
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372 | // ---------------------------------------------------------------------------- |
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373 | |
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374 | newtonPolygon::~newtonPolygon( ) |
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375 | { |
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376 | copy_delete( ); |
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377 | } |
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378 | |
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379 | // ---------------------------------------------------------------------------- |
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380 | // We define `=` to be a deep copy |
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381 | // ---------------------------------------------------------------------------- |
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382 | |
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383 | newtonPolygon & newtonPolygon::operator = ( const newtonPolygon &np ) |
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384 | { |
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385 | copy_delete( ); |
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386 | copy_deep( np ); |
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387 | |
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388 | return *this; |
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389 | } |
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390 | |
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391 | // ---------------------------------------------------------------------------- |
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392 | // Initialize a Newton polygon from a polynomial |
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393 | // ---------------------------------------------------------------------------- |
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394 | |
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395 | newtonPolygon::newtonPolygon( poly f, const ring s ) |
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396 | { |
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397 | copy_zero( ); |
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398 | |
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399 | int *r=new int[s->N]; |
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400 | poly *m=new poly[s->N]; |
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401 | |
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402 | |
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403 | KMatrix<Rational> mat(s->N,s->N+1 ); |
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404 | |
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405 | int i,j,stop=FALSE; |
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406 | linearForm sol; |
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407 | |
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408 | // --------------- |
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409 | // init counters |
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410 | // --------------- |
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411 | |
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412 | for( i=0; i<s->N; i++ ) |
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413 | { |
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414 | r[i] = i; |
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415 | } |
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416 | |
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417 | m[0] = f; |
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418 | |
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419 | for( i=1; i<s->N; i++ ) |
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420 | { |
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421 | m[i] = pNext(m[i-1]); |
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422 | } |
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423 | |
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424 | // ----------------------------- |
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425 | // find faces (= linear forms) |
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426 | // ----------------------------- |
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427 | |
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428 | do |
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429 | { |
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430 | // --------------------------------------------------- |
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431 | // test if monomials p.m[r[0]]m,...,p.m[r[p.vars-1]] |
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432 | // are linearely independent |
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433 | // --------------------------------------------------- |
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434 | |
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435 | for( i=0; i<s->N; i++ ) |
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436 | { |
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437 | for( j=0; j<s->N; j++ ) |
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438 | { |
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439 | // mat.set( i,j,pGetExp( m[r[i]],j+1 ) ); |
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440 | mat.set( i,j,p_GetExp( m[i],j+1,s ) ); |
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441 | } |
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442 | mat.set( i,j,1 ); |
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443 | } |
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444 | |
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445 | if( mat.solve( &(sol.c),&(sol.N) ) == s->N ) |
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446 | { |
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447 | // --------------------------------- |
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448 | // check if linearForm is positive |
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449 | // check if linearForm is extremal |
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450 | // --------------------------------- |
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451 | |
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452 | if( sol.positive( ) && sol.pweight( f,s ) >= (Rational)1 ) |
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453 | { |
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454 | // ---------------------------------- |
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455 | // this is a face or the polyhedron |
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456 | // ---------------------------------- |
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457 | |
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458 | add_linearForm( sol ); |
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459 | sol.c = (Rational*)NULL; |
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460 | sol.N = 0; |
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461 | } |
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462 | } |
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463 | |
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464 | // -------------------- |
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465 | // increment counters |
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466 | // -------------------- |
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467 | |
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468 | for( i=1; r[i-1] + 1 == r[i] && i < s->N; i++ ); |
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469 | |
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470 | for( j=0; j<i-1; j++ ) |
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471 | { |
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472 | r[j]=j; |
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473 | } |
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474 | |
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475 | if( i>1 ) |
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476 | { |
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477 | m[0]=f; |
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478 | for( j=1; j<i-1; j++ ) |
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479 | { |
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480 | m[j]=pNext(m[j-1]); |
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481 | } |
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482 | } |
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483 | r[i-1]++; |
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484 | m[i-1]=pNext(m[i-1]); |
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485 | |
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486 | if( m[s->N-1] == (poly)NULL ) |
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487 | { |
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488 | stop = TRUE; |
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489 | } |
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490 | } while( stop == FALSE ); |
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491 | } |
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492 | |
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493 | #ifdef NPOLYGON_PRINT |
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494 | |
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495 | ostream & operator << ( ostream &s,const newtonPolygon &a ) |
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496 | { |
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497 | #ifdef NPOLYGON_IOSTREAM |
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498 | s << "Newton polygon:" << endl; |
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499 | #else |
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500 | fprintf( stdout,"Newton polygon:\n" ); |
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501 | #endif |
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502 | |
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503 | for( int i=0; i<a.N; i++ ) |
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504 | { |
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505 | s << a.l[i]; |
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506 | |
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507 | #ifdef NPOLYGON_IOSTREAM |
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508 | s << endl; |
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509 | #else |
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510 | fprintf( stdout,"\n" ); |
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511 | #endif |
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512 | } |
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513 | |
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514 | return s; |
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515 | } |
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516 | |
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517 | #endif |
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518 | |
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519 | // ---------------------------------------------------------------------------- |
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520 | // Add a face to the newton polygon |
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521 | // ---------------------------------------------------------------------------- |
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522 | |
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523 | void newtonPolygon::add_linearForm( const linearForm &l0 ) |
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524 | { |
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525 | int i; |
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526 | newtonPolygon np; |
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527 | |
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528 | // ------------------------------------- |
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529 | // test if linear form is already here |
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530 | // ------------------------------------- |
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531 | |
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532 | for( i=0; i<N; i++ ) |
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533 | { |
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534 | if( l0==l[i] ) |
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535 | { |
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536 | return; |
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537 | } |
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538 | } |
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539 | |
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540 | np.copy_new( N+1 ); |
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541 | np.N = N+1; |
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542 | |
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543 | for( i=0; i<N; i++ ) |
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544 | { |
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545 | np.l[i].copy_shallow( l[i] ); |
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546 | l[i].copy_zero( ); |
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547 | } |
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548 | |
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549 | np.l[N] = l0; |
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550 | |
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551 | copy_delete( ); |
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552 | copy_shallow( np ); |
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553 | np.copy_zero( ); |
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554 | |
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555 | return; |
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556 | } |
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557 | |
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558 | // ---------------------------------------------------------------------------- |
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559 | // Newton weight of a monomial |
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560 | // ---------------------------------------------------------------------------- |
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561 | |
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562 | Rational newtonPolygon::weight( poly m, const ring r ) const |
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563 | { |
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564 | Rational ret = l[0].weight( m,r ); |
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565 | Rational tmp; |
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566 | |
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567 | for( int i=1; i<N; i++ ) |
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568 | { |
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569 | tmp = l[i].weight( m,r ); |
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570 | |
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571 | if( tmp < ret ) |
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572 | { |
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573 | ret = tmp; |
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574 | } |
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575 | } |
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576 | return ret; |
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577 | } |
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578 | |
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579 | // ---------------------------------------------------------------------------- |
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580 | // Newton weight of a monomial shifted by the product of the variables |
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581 | // ---------------------------------------------------------------------------- |
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582 | |
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583 | Rational newtonPolygon::weight_shift( poly m, const ring r ) const |
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584 | { |
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585 | Rational ret = l[0].weight_shift( m, r ); |
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586 | Rational tmp; |
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587 | |
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588 | for( int i=1; i<N; i++ ) |
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589 | { |
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590 | tmp = l[i].weight_shift( m, r ); |
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591 | |
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592 | if( tmp < ret ) |
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593 | { |
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594 | ret = tmp; |
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595 | } |
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596 | } |
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597 | return ret; |
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598 | } |
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599 | |
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600 | // ---------------------------------------------------------------------------- |
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601 | // Newton weight of a monomial (forgetting the first variable) |
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602 | // ---------------------------------------------------------------------------- |
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603 | |
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604 | Rational newtonPolygon::weight1( poly m, const ring r ) const |
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605 | { |
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606 | Rational ret = l[0].weight1( m, r ); |
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607 | Rational tmp; |
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608 | |
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609 | for( int i=1; i<N; i++ ) |
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610 | { |
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611 | tmp = l[i].weight1( m, r ); |
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612 | |
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613 | if( tmp < ret ) |
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614 | { |
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615 | ret = tmp; |
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616 | } |
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617 | } |
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618 | return ret; |
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619 | } |
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620 | |
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621 | // ---------------------------------------------------------------------------- |
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622 | // Newton weight of a monomial shifted by the product of the variables |
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623 | // (forgetting the first variable) |
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624 | // ---------------------------------------------------------------------------- |
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625 | |
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626 | Rational newtonPolygon::weight_shift1( poly m, const ring r ) const |
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627 | { |
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628 | Rational ret = l[0].weight_shift1( m, r ); |
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629 | Rational tmp; |
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630 | |
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631 | for( int i=1; i<N; i++ ) |
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632 | { |
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633 | tmp = l[i].weight_shift1( m, r ); |
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634 | |
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635 | if( tmp < ret ) |
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636 | { |
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637 | ret = tmp; |
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638 | } |
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639 | } |
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640 | return ret; |
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641 | } |
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642 | |
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643 | /* |
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644 | // ---------------------------------------------------------------------------- |
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645 | // Chcek if the polynomial belonging to the Newton polygon |
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646 | // is semiquasihomogeneous (sqh) |
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647 | // ---------------------------------------------------------------------------- |
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648 | |
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649 | int newtonPolygon::is_sqh( void ) const |
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650 | { |
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651 | return ( N==1 ? TRUE : FALSE ); |
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652 | } |
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653 | |
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654 | // ---------------------------------------------------------------------------- |
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655 | // If the polynomial belonging to the Newton polygon is sqh, |
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656 | // return its weights vector |
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657 | // ---------------------------------------------------------------------------- |
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658 | |
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659 | Rational* newtonPolygon::sqh_weights( void ) const |
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660 | { |
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661 | return ( N==1 ? l[0].c : (Rational*)NULL ); |
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662 | } |
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663 | |
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664 | int newtonPolygon::sqh_N( void ) const |
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665 | { |
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666 | return ( N==1 ? l[0].N : 0 ); |
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667 | } |
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668 | */ |
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669 | |
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670 | #endif /* HAVE_SPECTRUM */ |
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671 | // ---------------------------------------------------------------------------- |
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672 | // npolygon.cc |
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673 | // end of file |
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674 | // ---------------------------------------------------------------------------- |
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675 | |
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