1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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2 | /* $Id$ */ |
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3 | |
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4 | //{{{ docu |
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5 | // |
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6 | // cf_map.cc - definition of class CFMap. |
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7 | // |
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8 | // Used by: cf_gcd.cc, fac_multivar.cc, sm_sparsemod.cc |
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9 | // |
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10 | //}}} |
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11 | |
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12 | #include "config.h" |
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13 | |
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14 | #include "canonicalform.h" |
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15 | #include "cf_map.h" |
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16 | #include "cf_iter.h" |
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17 | #include "templates/ftmpl_functions.h" |
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18 | |
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19 | //{{{ MapPair & MapPair::operator = ( const MapPair & p ) |
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20 | //{{{ docu |
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21 | // |
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22 | // MapPair::operator = - assignment operator. |
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23 | // |
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24 | //}}} |
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25 | MapPair & |
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26 | MapPair::operator = ( const MapPair & p ) |
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27 | { |
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28 | if ( this != &p ) { |
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29 | V = p.V; |
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30 | S = p.S; |
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31 | } |
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32 | return *this; |
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33 | } |
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34 | //}}} |
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35 | |
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36 | #ifndef NOSTREAMIO |
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37 | //{{{ OSTREAM & operator << ( OSTREAM & s, const MapPair & p ) |
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38 | //{{{ docu |
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39 | // |
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40 | // operator << - print a map pair ("V -> S"). |
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41 | // |
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42 | //}}} |
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43 | OSTREAM & |
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44 | operator << ( OSTREAM & s, const MapPair & p ) |
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45 | { |
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46 | s << p.var() << " -> " << p.subst(); |
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47 | return s; |
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48 | } |
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49 | //}}} |
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50 | |
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51 | void MapPair::print( OSTREAM&) const |
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52 | { |
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53 | } |
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54 | #endif /* NOSTREAMIO */ |
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55 | |
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56 | //{{{ CFMap::CFMap ( const CFList & L ) |
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57 | //{{{ docu |
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58 | // |
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59 | // CFMap::CFMap() - construct a CFMap from a CFList. |
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60 | // |
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61 | // Variable[i] will be mapped to CFList[i] under the resulting |
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62 | // map. |
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63 | // |
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64 | //}}} |
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65 | CFMap::CFMap ( const CFList & L ) |
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66 | { |
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67 | CFListIterator i; |
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68 | int j; |
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69 | for ( i = L, j = 1; i.hasItem(); i++, j++ ) |
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70 | P.insert( MapPair( Variable(j), i.getItem() ) ); |
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71 | } |
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72 | //}}} |
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73 | |
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74 | //{{{ CFMap & CFMap::operator = ( const CFMap & m ) |
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75 | //{{{ docu |
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76 | // |
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77 | // CFMap::operator = - assignment operator. |
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78 | // |
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79 | //}}} |
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80 | CFMap & |
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81 | CFMap::operator = ( const CFMap & m ) |
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82 | { |
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83 | if ( this != &m ) |
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84 | P = m.P; |
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85 | return *this; |
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86 | } |
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87 | //}}} |
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88 | |
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89 | //{{{ static int cmpfunc ( const MapPair & p1, const MapPair & p2 ) |
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90 | //{{{ docu |
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91 | // |
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92 | // cmpfunc() - compare two map pairs. |
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93 | // |
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94 | // Return -1 if p2's variable is less than p1's, 0 if they are |
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95 | // equal, 1 if p2's level is greater than p1's. |
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96 | // |
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97 | //}}} |
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98 | static int |
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99 | cmpfunc ( const MapPair & p1, const MapPair & p2 ) |
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100 | { |
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101 | if ( p1.var() > p2.var() ) return -1; |
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102 | else if ( p1.var() == p2.var() ) return 0; |
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103 | else return 1; |
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104 | } |
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105 | //}}} |
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106 | |
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107 | //{{{ static void insfunc ( MapPair & orgp, const MapPair & newp ) |
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108 | //{{{ docu |
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109 | // |
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110 | // insfunc() - assign newp to orgp. |
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111 | // |
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112 | // cmpfunc() and insfunc() are used as functions for inserting a |
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113 | // map pair into a map by CFMap::newpair(). |
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114 | // |
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115 | //}}} |
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116 | static void |
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117 | insfunc ( MapPair & orgp, const MapPair & newp ) |
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118 | { |
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119 | orgp = newp; |
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120 | } |
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121 | //}}} |
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122 | |
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123 | //{{{ void CFMap::newpair ( const Variable & v, const CanonicalForm & s ) |
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124 | //{{{ docu |
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125 | // |
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126 | // CFMap::newpair() - insert a MapPair into a CFMap. |
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127 | // |
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128 | //}}} |
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129 | void |
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130 | CFMap::newpair ( const Variable & v, const CanonicalForm & s ) |
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131 | { |
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132 | P.insert( MapPair( v, s ), cmpfunc, insfunc ); |
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133 | } |
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134 | //}}} |
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135 | |
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136 | //{{{ static CanonicalForm subsrec ( const CanonicalForm & f, const MPListIterator & i ) |
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137 | //{{{ docu |
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138 | // |
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139 | // subsrec() - recursively apply the substitutions in i to f. |
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140 | // |
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141 | // Substitutes algebraic variables, too. The substituted |
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142 | // expression are not subject to further substitutions. |
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143 | // |
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144 | // Used by: CFMap::operator ()(). |
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145 | // |
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146 | //}}} |
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147 | static CanonicalForm |
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148 | subsrec ( const CanonicalForm & f, const MPListIterator & i ) |
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149 | { |
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150 | if ( f.inBaseDomain() ) return f; |
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151 | MPListIterator j = i; |
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152 | |
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153 | // skip MapPairs larger than the main variable of f |
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154 | while ( j.hasItem() && j.getItem().var() > f.mvar() ) j++; |
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155 | |
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156 | if ( j.hasItem() ) |
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157 | if ( j.getItem().var() != f.mvar() ) { |
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158 | // simply descend if the current MapPair variable is |
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159 | // not the main variable of f |
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160 | CanonicalForm result = 0; |
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161 | CFIterator I; |
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162 | for ( I = f; I.hasTerms(); I++ ) |
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163 | result += power( f.mvar(), I.exp() ) * subsrec( I.coeff(), j ); |
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164 | return result; |
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165 | } |
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166 | else { |
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167 | // replace the main variable of f with the image of |
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168 | // the current variable under MapPair |
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169 | CanonicalForm result = 0; |
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170 | CanonicalForm s = j.getItem().subst(); |
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171 | CFIterator I; |
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172 | // move on to the next MapPair |
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173 | j++; |
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174 | for ( I = f; I.hasTerms(); I++ ) |
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175 | result += subsrec( I.coeff(), j ) * power( s, I.exp() ); |
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176 | return result; |
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177 | } |
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178 | else |
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179 | return f; |
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180 | } |
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181 | //}}} |
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182 | |
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183 | //{{{ CanonicalForm CFMap::operator () ( const CanonicalForm & f ) const |
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184 | //{{{ docu |
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185 | // |
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186 | // CFMap::operator () - apply CO to f. |
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187 | // |
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188 | // See subsrec() for more detailed information. |
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189 | // |
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190 | //}}} |
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191 | CanonicalForm |
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192 | CFMap::operator () ( const CanonicalForm & f ) const |
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193 | { |
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194 | MPListIterator i = P; |
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195 | return subsrec( f, i ); |
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196 | } |
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197 | //}}} |
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198 | |
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199 | #ifndef NOSTREAMIO |
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200 | //{{{ OSTREAM & operator << ( OSTREAM & s, const CFMap & m ) |
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201 | //{{{ docu |
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202 | // |
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203 | // operator << - print a CFMap ("( V[1] -> S[1], ..., V[n] -> // S[n] )". |
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204 | // |
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205 | //}}} |
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206 | OSTREAM & |
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207 | operator << ( OSTREAM & s, const CFMap & m ) |
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208 | { |
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209 | m.P.print(s); |
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210 | return s; |
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211 | } |
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212 | //}}} |
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213 | #endif /* NOSTREAMIO */ |
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214 | |
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215 | //{{{ CanonicalForm compress ( const CanonicalForm & f, CFMap & m ) |
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216 | //{{{ docu |
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217 | // |
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218 | // compress() - compress the canonical form f. |
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219 | // |
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220 | // Compress the polynomial f such that the levels of its |
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221 | // polynomial variables are ordered without any gaps starting |
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222 | // from level 1. Return the compressed polynomial and a map m to |
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223 | // undo the compression. That is, if f' = compress(f, m), than f |
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224 | // = m(f'). |
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225 | // |
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226 | //}}} |
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227 | CanonicalForm |
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228 | compress ( const CanonicalForm & f, CFMap & m ) |
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229 | { |
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230 | CanonicalForm result = f; |
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231 | int i, n; |
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232 | int * degs = degrees( f ); |
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233 | |
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234 | m = CFMap(); |
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235 | n = i = 1; |
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236 | while ( i <= level( f ) ) { |
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237 | while( degs[i] == 0 ) i++; |
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238 | if ( i != n ) { |
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239 | // swap variables and remember the swap in the map |
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240 | m.newpair( Variable( n ), Variable( i ) ); |
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241 | result = swapvar( result, Variable( i ), Variable( n ) ); |
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242 | } |
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243 | n++; i++; |
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244 | } |
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245 | delete [] degs; |
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246 | return result; |
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247 | } |
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248 | //}}} |
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249 | |
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250 | //{{{ void compress ( const CFArray & a, CFMap & M, CFMap & N ) |
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251 | //{{{ docu |
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252 | // |
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253 | // compress() - compress the variables occuring in an a. |
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254 | // |
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255 | // Compress the polynomial variables occuring in a so that their |
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256 | // levels are ordered without any gaps starting from level 1. |
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257 | // Return the CFMap M to realize the compression and its inverse, |
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258 | // the CFMap N. Note that if you compress a member of a using M |
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259 | // the result of the compression is not necessarily compressed, |
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260 | // since the map is constructed using all variables occuring in |
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261 | // a. |
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262 | // |
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263 | //}}} |
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264 | void |
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265 | compress ( const CFArray & a, CFMap & M, CFMap & N ) |
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266 | { |
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267 | M = N = CFMap(); |
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268 | if ( a.size() == 0 ) |
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269 | return; |
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270 | int maxlevel = level( a[a.min()] ); |
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271 | int i, j; |
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272 | |
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273 | // get the maximum of levels in a |
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274 | for ( i = a.min() + 1; i <= a.max(); i++ ) |
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275 | if ( level( a[i] ) > maxlevel ) |
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276 | maxlevel = level( a[i] ); |
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277 | if ( maxlevel <= 0 ) |
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278 | return; |
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279 | |
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280 | int * degs = new int[maxlevel+1]; |
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281 | int * tmp = new int[maxlevel+1]; |
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282 | for ( i = 1; i <= maxlevel; i++ ) |
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283 | degs[i] = 0; |
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284 | |
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285 | // calculate the union of all levels occuring in a |
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286 | for ( i = a.min(); i <= a.max(); i++ ) { |
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287 | tmp = degrees( a[i], tmp ); |
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288 | for ( j = 1; j <= level( a[i] ); j++ ) |
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289 | if ( tmp[j] != 0 ) |
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290 | degs[j] = 1; |
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291 | } |
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292 | |
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293 | // create the maps |
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294 | i = 1; j = 1; |
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295 | while ( i <= maxlevel ) { |
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296 | if ( degs[i] != 0 ) { |
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297 | M.newpair( Variable(i), Variable(j) ); |
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298 | N.newpair( Variable(j), Variable(i) ); |
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299 | j++; |
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300 | } |
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301 | i++; |
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302 | } |
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303 | delete [] tmp; |
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304 | delete [] degs; |
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305 | } |
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306 | //}}} |
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307 | |
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308 | /* |
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309 | * compute positions p1 and pe of optimal variables: |
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310 | * pe is used in "ezgcd" and |
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311 | * p1 in "gcd_poly1" |
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312 | */ |
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313 | static |
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314 | void optvalues ( const int * df, const int * dg, const int n, int & p1, int &pe ) |
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315 | { |
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316 | int i, o1, oe; |
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317 | i = p1 = pe = 0; |
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318 | do |
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319 | { |
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320 | i++; |
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321 | if ( i > n ) return; |
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322 | } while ( ( df[i] == 0 ) || ( dg[i] == 0 ) ); |
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323 | p1 = pe = i; |
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324 | if ( df[i] > dg[i] ) |
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325 | { |
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326 | o1 = df[i]; oe = dg[i]; |
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327 | } |
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328 | else |
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329 | { |
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330 | o1 = dg[i]; oe = df[i]; |
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331 | } |
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332 | while ( i < n ) |
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333 | { |
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334 | i++; |
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335 | if ( ( df[i] != 0 ) && ( dg[i] != 0 ) ) |
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336 | { |
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337 | if ( df[i] > dg[i] ) |
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338 | { |
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339 | if ( o1 >= df[i]) { o1 = df[i]; p1 = i; } |
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340 | if ( oe < dg[i]) { oe = dg[i]; pe = i; } |
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341 | } |
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342 | else |
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343 | { |
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344 | if ( o1 >= dg[i]) { o1 = dg[i]; p1 = i; } |
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345 | if ( oe < df[i]) { oe = df[i]; pe = i; } |
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346 | } |
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347 | } |
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348 | } |
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349 | } |
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350 | |
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351 | |
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352 | //{{{ void compress ( const CanonicalForm & f, const CanonicalForm & g, CFMap & M, CFMap & N ) |
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353 | //{{{ docu |
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354 | // |
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355 | // compress() - compress the variables occurring in f and g with respect |
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356 | // to optimal variables |
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357 | // |
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358 | // Compress the polynomial variables occurring in f and g so that |
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359 | // the levels of variables common to f and g are ordered without |
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360 | // any gaps starting from level 1, whereas the variables occuring |
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361 | // in only one of f or g are moved to levels higher than the |
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362 | // levels of the common variables. Return the CFMap M to realize |
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363 | // the compression and its inverse, the CFMap N. |
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364 | // N needs only variables common to f and g. |
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365 | // |
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366 | //}}} |
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367 | void |
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368 | compress ( const CanonicalForm & f, const CanonicalForm & g, CFMap & M, CFMap & N ) |
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369 | { |
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370 | int n = tmax( f.level(), g.level() ); |
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371 | int i, k, p1, pe; |
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372 | int * degsf = new int[n+1]; |
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373 | int * degsg = new int[n+1]; |
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374 | |
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375 | for ( i = 0; i <= n; i++ ) |
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376 | { |
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377 | degsf[i] = degsg[i] = 0; |
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378 | } |
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379 | |
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380 | degsf = degrees( f, degsf ); |
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381 | degsg = degrees( g, degsg ); |
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382 | optvalues( degsf, degsg, n, p1, pe ); |
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383 | |
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384 | i = 1; k = 1; |
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385 | if ( pe > 1 ) |
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386 | { |
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387 | M.newpair( Variable(pe), Variable(k) ); |
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388 | N.newpair( Variable(k), Variable(pe) ); |
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389 | k++; |
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390 | } |
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391 | while ( i <= n ) |
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392 | { |
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393 | if ( degsf[i] > 0 && degsg[i] > 0 ) |
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394 | { |
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395 | if ( ( i != k ) && ( i != pe ) && ( i != p1 ) ) |
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396 | { |
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397 | M.newpair( Variable(i), Variable(k) ); |
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398 | N.newpair( Variable(k), Variable(i) ); |
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399 | } |
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400 | k++; |
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401 | } |
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402 | i++; |
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403 | } |
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404 | if ( p1 != pe ) |
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405 | { |
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406 | M.newpair( Variable(p1), Variable(k) ); |
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407 | N.newpair( Variable(k), Variable(p1) ); |
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408 | k++; |
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409 | } |
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410 | i = 1; |
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411 | while ( i <= n ) |
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412 | { |
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413 | if ( degsf[i] > 0 && degsg[i] == 0 ) { |
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414 | if ( i != k ) |
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415 | { |
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416 | M.newpair( Variable(i), Variable(k) ); |
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417 | k++; |
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418 | } |
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419 | } |
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420 | else if ( degsf[i] == 0 && degsg[i] > 0 ) |
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421 | { |
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422 | if ( i != k ) |
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423 | { |
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424 | M.newpair( Variable(i), Variable(k) ); |
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425 | k++; |
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426 | } |
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427 | } |
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428 | i++; |
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429 | } |
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430 | |
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431 | delete [] degsf; |
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432 | delete [] degsg; |
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433 | } |
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434 | //}}} |
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