1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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2 | |
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3 | //{{{ docu |
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4 | // |
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5 | // cf_ops.cc - simple structural algorithms. |
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6 | // |
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7 | // A 'structural' algorithm is an algorithm which gives |
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8 | // structural information on polynomials in contrast to a |
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9 | // 'mathematical' algorithm which calculates some mathematical |
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10 | // function. |
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11 | // |
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12 | // Compare these functions with the functions in cf_algorithm.cc, |
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13 | // which are mathematical algorithms. |
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14 | // |
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15 | // Used by: allmost everywhere |
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16 | // |
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17 | // Header file: canonicalform.h |
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18 | // |
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19 | //}}} |
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20 | |
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21 | #include "config.h" |
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22 | |
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23 | #include "cf_assert.h" |
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24 | |
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25 | #include "canonicalform.h" |
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26 | #include "variable.h" |
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27 | #include "cf_iter.h" |
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28 | |
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29 | //{{{ static Variable sv_x1, sv_x2; |
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30 | //{{{ docu |
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31 | // |
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32 | // sv_x1, sv_x2 - variables to swap by swapvar() and replacevar. |
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33 | // |
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34 | // These variables are initialized by swapvar() such that sv_x1 < |
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35 | // sv_x2. They are used by swapvar_between() and swapvar_rec() |
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36 | // to swap variables efficiently. |
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37 | // Furthermore, sv_x1 and sv_x2 are used by replacevar() and |
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38 | // replacevar_between(). |
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39 | // |
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40 | //}}} |
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41 | static Variable sv_x1, sv_x2; |
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42 | //}}} |
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43 | |
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44 | //{{{ static void swapvar_between ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term, int expx2 ) |
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45 | //{{{ docu |
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46 | // |
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47 | // swapvar_between() - replace occurences of sv_x1 in f with sv_x2. |
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48 | // |
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49 | // If Psi denotes the map which maps sv_x1 to sv_x2, this |
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50 | // function returns |
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51 | // |
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52 | // result + Psi(f) * term * sv_x1^expx2 |
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53 | // |
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54 | // Used by: swapvar() |
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55 | // |
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56 | //}}} |
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57 | static void |
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58 | swapvar_between ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term, int expx2 ) |
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59 | { |
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60 | if ( f.inCoeffDomain() || f.mvar() < sv_x1 ) |
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61 | // in this case, we do not have to replace anything |
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62 | result += term * power( sv_x1, expx2 ) * f; |
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63 | else if ( f.mvar() == sv_x1 ) |
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64 | // this is where the real work is done: this iterator |
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65 | // replaces sv_x1 with sv_x2 |
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66 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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67 | result += power( sv_x2, i.exp() ) * term * power( sv_x1, expx2 ) * i.coeff(); |
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68 | else |
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69 | // f's level is larger than sv_x1: descend down |
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70 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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71 | swapvar_between( i.coeff(), result, term * power( f.mvar(), i.exp() ), expx2 ); |
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72 | } |
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73 | static CanonicalForm |
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74 | swapvar_between1 ( const CanonicalForm & f ) |
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75 | { |
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76 | if ( f.inCoeffDomain() || f.mvar() < sv_x1 ) |
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77 | // in this case, we do not have to replace anything |
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78 | return f; |
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79 | else if ( f.mvar() == sv_x1 ) |
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80 | { |
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81 | // this is where the real work is done: this iterator |
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82 | // replaces sv_x1 with sv_x2 |
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83 | CanonicalForm result; |
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84 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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85 | result += power( sv_x2, i.exp() ) * i.coeff(); |
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86 | return result; |
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87 | } |
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88 | else |
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89 | { |
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90 | // f's level is larger than sv_x1: descend down |
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91 | CanonicalForm result; |
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92 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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93 | result += swapvar_between1( i.coeff() ) * power( f.mvar(), i.exp() ); |
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94 | return result; |
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95 | } |
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96 | } |
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97 | //}}} |
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98 | |
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99 | //{{{ static void swapvar_rec ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term ) |
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100 | //{{{ docu |
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101 | // |
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102 | // swapvar_between() - swap occurences of sv_x1 and sv_x2 in f. |
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103 | // |
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104 | // If Psi denotes the map which swaps sv_x1 and sv_x2, this |
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105 | // function returns |
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106 | // |
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107 | // result + Psi(f) * term |
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108 | // |
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109 | // Used by: swapvar() |
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110 | // |
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111 | //}}} |
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112 | static void |
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113 | swapvar_rec ( const CanonicalForm & f, CanonicalForm & result, const CanonicalForm & term ) |
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114 | { |
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115 | if ( f.inCoeffDomain() || f.mvar() < sv_x1 ) |
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116 | // in this case, we do not have to swap anything |
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117 | result += term * f; |
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118 | else if ( f.mvar() == sv_x2 ) |
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119 | // this is where the real work is done: this iterator |
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120 | // replaces sv_x1 with sv_x2 in the coefficients of f and |
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121 | // remembers the exponents of sv_x2 in the last argument |
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122 | // of the call to swapvar_between() |
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123 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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124 | swapvar_between( i.coeff(), result, term, i.exp() ); |
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125 | else if ( f.mvar() < sv_x2 ) |
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126 | // sv_x2 does not occur in f, but sv_x1 does. Replace it. |
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127 | swapvar_between( f, result, term, 0 ); |
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128 | else |
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129 | // f's level is larger than sv_x2: descend down |
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130 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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131 | swapvar_rec( i.coeff(), result, term * power( f.mvar(), i.exp() ) ); |
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132 | } |
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133 | static CanonicalForm |
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134 | swapvar_rec1 ( const CanonicalForm & f ) |
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135 | { |
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136 | if ( f.inCoeffDomain() || f.mvar() < sv_x1 ) |
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137 | return f; |
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138 | else if ( f.mvar() == sv_x2 ) |
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139 | { |
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140 | CanonicalForm result; |
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141 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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142 | result += swapvar_between1( i.coeff() ) * power( sv_x1, i.exp() ); |
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143 | return result; |
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144 | } |
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145 | else if ( f.mvar() < sv_x2 ) |
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146 | return swapvar_between1( f ); |
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147 | else |
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148 | { |
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149 | CanonicalForm result; |
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150 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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151 | result += swapvar_rec1( i.coeff() ) * power( f.mvar(), i.exp() ); |
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152 | return result; |
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153 | } |
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154 | } |
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155 | //}}} |
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156 | |
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157 | //{{{ CanonicalForm swapvar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 ) |
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158 | //{{{ docu |
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159 | // |
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160 | // swapvar() - swap variables x1 and x2 in f. |
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161 | // |
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162 | // Returns the image of f under the map which maps x1 to x2 and |
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163 | // x2 to x1. This is done quite efficiently because it is used |
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164 | // really often. x1 and x2 should be polynomial variables. |
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165 | // |
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166 | //}}} |
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167 | CanonicalForm |
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168 | swapvar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 ) |
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169 | { |
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170 | ASSERT( x1.level() > 0 && x2.level() > 0, "cannot swap algebraic Variables" ); |
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171 | if ( f.inCoeffDomain() || x1 == x2 || ( x1 > f.mvar() && x2 > f.mvar() ) ) |
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172 | return f; |
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173 | else |
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174 | { |
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175 | CanonicalForm result = 0; |
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176 | if ( x1 > x2 ) |
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177 | { |
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178 | sv_x1 = x2; sv_x2 = x1; |
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179 | } |
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180 | else |
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181 | { |
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182 | sv_x1 = x1; sv_x2 = x2; |
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183 | } |
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184 | if ( f.mvar() < sv_x2 ) |
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185 | // we only have to replace sv_x1 by sv_x2 |
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186 | swapvar_between( f, result, 1, 0 ); |
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187 | else |
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188 | // we really have to swap variables |
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189 | swapvar_rec( f, result, 1 ); |
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190 | return result; |
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191 | } |
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192 | } |
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193 | CanonicalForm |
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194 | swapvar1 ( const CanonicalForm & f, const Variable & x1, const Variable & x2 ) |
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195 | { |
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196 | ASSERT( x1.level() > 0 && x2.level() > 0, "cannot swap algebraic variables" ); |
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197 | if ( f.inCoeffDomain() || x1 == x2 || ( x1 > f.mvar() && x2 > f.mvar() ) ) |
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198 | return f; |
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199 | else |
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200 | { |
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201 | CanonicalForm result = 0; |
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202 | if ( x1 > x2 ) { |
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203 | sv_x1 = x2; sv_x2 = x1; |
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204 | } |
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205 | else |
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206 | { |
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207 | sv_x1 = x1; sv_x2 = x2; |
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208 | } |
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209 | if ( f.mvar() < sv_x2 ) |
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210 | // we only have to replace sv_x1 by sv_x2 |
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211 | return swapvar_between1( f ); |
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212 | else |
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213 | // we really have to swap variables |
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214 | return swapvar_rec1( f ); |
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215 | } |
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216 | } |
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217 | //}}} |
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218 | |
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219 | //{{{ static CanonicalForm replacevar_between ( const CanonicalForm & f ) |
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220 | //{{{ docu |
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221 | // |
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222 | // replacevar_between() - replace occurences of sv_x1 in f with sv_x2. |
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223 | // |
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224 | // This is allmost the same as swapvar_between() except that |
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225 | // sv_x1 may be an algebraic variable, so we have to test on |
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226 | // 'f.inBaseDomain()' instead of 'f.inCoeffDomain()' in the |
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227 | // beginning. |
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228 | // |
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229 | // Used by: replacevar() |
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230 | // |
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231 | //}}} |
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232 | static CanonicalForm |
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233 | replacevar_between ( const CanonicalForm & f ) |
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234 | { |
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235 | if ( f.inBaseDomain() ) |
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236 | return f; |
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237 | |
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238 | Variable x = f.mvar(); |
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239 | |
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240 | if ( x < sv_x1 ) |
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241 | // in this case, we do not have to replace anything |
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242 | return f; |
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243 | else if ( x == sv_x1 ) |
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244 | { |
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245 | // this is where the real work is done: this iterator |
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246 | // replaces sv_x1 with sv_x2 |
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247 | CanonicalForm result; |
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248 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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249 | result += power( sv_x2, i.exp() ) * i.coeff(); |
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250 | return result; |
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251 | } |
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252 | else |
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253 | { |
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254 | // f's level is larger than sv_x1: descend down |
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255 | CanonicalForm result; |
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256 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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257 | result += replacevar_between( i.coeff() ) * power( x, i.exp() ); |
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258 | return result; |
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259 | } |
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260 | } |
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261 | //}}} |
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262 | |
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263 | //{{{ CanonicalForm replacevar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 ) |
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264 | //{{{ docu |
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265 | // |
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266 | // replacevar() - replace all occurences of x1 in f by x2. |
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267 | // |
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268 | // In contrast to swapvar(), x1 may be an algebraic variable, but |
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269 | // x2 must be a polynomial variable. |
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270 | // |
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271 | //}}} |
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272 | CanonicalForm |
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273 | replacevar ( const CanonicalForm & f, const Variable & x1, const Variable & x2 ) |
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274 | { |
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275 | //ASSERT( x2.level() > 0, "cannot replace with algebraic variable" ); |
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276 | if ( f.inBaseDomain() || x1 == x2 || ( x1 > f.mvar() ) ) |
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277 | return f; |
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278 | else |
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279 | { |
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280 | sv_x1 = x1; |
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281 | sv_x2 = x2; |
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282 | return replacevar_between( f ); |
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283 | } |
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284 | } |
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285 | //}}} |
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286 | |
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287 | //{{{ static void fillVarsRec ( const CanonicalForm & f, int * vars ) |
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288 | //{{{ docu |
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289 | // |
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290 | // fillVarsRec - fill array describing occurences of variables in f. |
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291 | // |
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292 | // Only polynomial variables are looked up. The information is |
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293 | // stored in the arrary vars. vars should be large enough to |
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294 | // hold all information, i.e. larger than the level of f. |
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295 | // |
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296 | // Used by getVars() and getNumVars(). |
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297 | // |
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298 | //}}} |
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299 | static void |
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300 | fillVarsRec ( const CanonicalForm & f, int * vars ) |
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301 | { |
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302 | int n; |
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303 | if ( (n = f.level()) > 0 ) |
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304 | { |
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305 | vars[n] = 1; |
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306 | CFIterator i; |
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307 | for ( i = f; i.hasTerms(); ++i ) |
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308 | fillVarsRec( i.coeff(), vars ); |
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309 | } |
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310 | } |
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311 | //}}} |
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312 | |
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313 | //{{{ int getNumVars ( const CanonicalForm & f ) |
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314 | //{{{ docu |
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315 | // |
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316 | // getNumVars() - get number of polynomial variables in f. |
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317 | // |
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318 | //}}} |
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319 | int |
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320 | getNumVars ( const CanonicalForm & f ) |
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321 | { |
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322 | int n; |
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323 | if ( f.inCoeffDomain() ) |
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324 | return 0; |
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325 | else if ( (n = f.level()) == 1 ) |
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326 | return 1; |
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327 | else |
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328 | { |
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329 | int * vars = new int[ n+1 ]; |
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330 | int i; |
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331 | for ( i = 0; i < n; i++ ) vars[i] = 0; |
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332 | |
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333 | // look for variables |
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334 | for ( CFIterator I = f; I.hasTerms(); ++I ) |
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335 | fillVarsRec( I.coeff(), vars ); |
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336 | |
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337 | // count them |
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338 | int m = 0; |
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339 | for ( i = 1; i < n; i++ ) |
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340 | if ( vars[i] != 0 ) m++; |
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341 | |
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342 | delete [] vars; |
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343 | // do not forget to count our own variable |
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344 | return m+1; |
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345 | } |
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346 | } |
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347 | //}}} |
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348 | |
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349 | //{{{ CanonicalForm getVars ( const CanonicalForm & f ) |
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350 | //{{{ docu |
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351 | // |
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352 | // getVars() - get polynomial variables of f. |
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353 | // |
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354 | // Return the product of all of them, 1 if there are not any. |
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355 | // |
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356 | //}}} |
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357 | CanonicalForm |
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358 | getVars ( const CanonicalForm & f ) |
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359 | { |
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360 | int n; |
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361 | if ( f.inCoeffDomain() ) |
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362 | return 1; |
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363 | else if ( (n = f.level()) == 1 ) |
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364 | return Variable( 1 ); |
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365 | else |
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366 | { |
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367 | int * vars = new int[ n+1 ]; |
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368 | int i; |
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369 | for ( i = 0; i <= n; i++ ) vars[i] = 0; |
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370 | |
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371 | // look for variables |
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372 | for ( CFIterator I = f; I.hasTerms(); ++I ) |
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373 | fillVarsRec( I.coeff(), vars ); |
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374 | |
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375 | // multiply them all |
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376 | CanonicalForm result = 1; |
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377 | for ( i = n; i > 0; i-- ) |
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378 | if ( vars[i] != 0 ) result *= Variable( i ); |
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379 | |
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380 | delete [] vars; |
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381 | // do not forget our own variable |
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382 | return f.mvar() * result; |
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383 | } |
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384 | } |
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385 | //}}} |
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386 | |
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387 | //{{{ CanonicalForm apply ( const CanonicalForm & f, void (*mf)( CanonicalForm &, int & ) ) |
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388 | //{{{ docu |
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389 | // |
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390 | // apply() - apply mf to terms of f. |
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391 | // |
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392 | // Calls mf( f[i], i ) for each term f[i]*x^i of f and builds a |
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393 | // new term from the result. If f is in a coefficient domain, |
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394 | // mf( f, i ) should result in an i == 0, since otherwise it is |
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395 | // not clear which variable to use for the resulting term. |
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396 | // |
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397 | // An example: |
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398 | // |
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399 | // void |
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400 | // diff( CanonicalForm & f, int & i ) |
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401 | // { |
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402 | // f = f * i; |
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403 | // if ( i > 0 ) i--; |
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404 | // } |
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405 | // |
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406 | // Then apply( f, diff ) is differentation of f with respect to the |
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407 | // main variable of f. |
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408 | // |
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409 | //}}} |
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410 | CanonicalForm |
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411 | apply ( const CanonicalForm & f, void (*mf)( CanonicalForm &, int & ) ) |
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412 | { |
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413 | if ( f.inCoeffDomain() ) |
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414 | { |
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415 | int exp = 0; |
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416 | CanonicalForm result = f; |
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417 | mf( result, exp ); |
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418 | ASSERT( exp == 0, "illegal result, do not know what variable to use" ); |
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419 | return result; |
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420 | } |
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421 | else |
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422 | { |
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423 | CanonicalForm result, coeff; |
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424 | CFIterator i; |
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425 | int exp; |
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426 | Variable x = f.mvar(); |
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427 | for ( i = f; i.hasTerms(); i++ ) |
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428 | { |
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429 | coeff = i.coeff(); |
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430 | exp = i.exp(); |
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431 | mf( coeff, exp ); |
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432 | if ( ! coeff.isZero() ) |
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433 | result += power( x, exp ) * coeff; |
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434 | } |
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435 | return result; |
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436 | } |
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437 | } |
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438 | //}}} |
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439 | |
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440 | //{{{ CanonicalForm mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) ) |
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441 | //{{{ docu |
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442 | // |
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443 | // mapdomain() - map all coefficients of f through mf. |
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444 | // |
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445 | // Recursively descends down through f to the coefficients which |
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446 | // are in a coefficient domain mapping each such coefficient |
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447 | // through mf and returns the result. |
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448 | // |
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449 | //}}} |
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450 | CanonicalForm |
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451 | mapdomain ( const CanonicalForm & f, CanonicalForm (*mf)( const CanonicalForm & ) ) |
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452 | { |
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453 | if ( f.inBaseDomain() ) |
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454 | return mf( f ); |
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455 | else |
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456 | { |
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457 | CanonicalForm result = 0; |
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458 | CFIterator i; |
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459 | Variable x = f.mvar(); |
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460 | for ( i = f; i.hasTerms(); i++ ) |
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461 | result += power( x, i.exp() ) * mapdomain( i.coeff(), mf ); |
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462 | return result; |
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463 | } |
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464 | } |
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465 | //}}} |
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466 | |
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467 | //{{{ static void degreesRec ( const CanonicalForm & f, int * degs ) |
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468 | //{{{ docu |
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469 | // |
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470 | // degreesRec() - recursively get degrees of f. |
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471 | // |
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472 | // Used by degrees(). |
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473 | // |
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474 | //}}} |
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475 | static void |
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476 | degreesRec ( const CanonicalForm & f, int * degs ) |
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477 | { |
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478 | if ( ! f.inCoeffDomain() ) |
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479 | { |
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480 | int level = f.level(); |
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481 | int deg = f.degree(); |
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482 | // calculate the maximum degree of all coefficients which |
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483 | // are in the same level |
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484 | if ( degs[level] < deg ) |
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485 | degs[level] = f.degree(); |
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486 | for ( CFIterator i = f; i.hasTerms(); i++ ) |
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487 | degreesRec( i.coeff(), degs ); |
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488 | } |
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489 | } |
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490 | //}}} |
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491 | |
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492 | //{{{ int * degrees ( const CanonicalForm & f, int * degs ) |
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493 | //{{{ docu |
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494 | // |
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495 | // degress() - return the degrees of all polynomial variables in f. |
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496 | // |
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497 | // Returns 0 if f is in a coefficient domain, the degrees of f in |
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498 | // all its polynomial variables in an array of int otherwise: |
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499 | // |
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500 | // degrees( f, 0 )[i] = degree( f, Variable(i) ) |
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501 | // |
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502 | // If degs is not the zero pointer the degrees are stored in this |
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503 | // array. In this case degs should be larger than the level of |
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504 | // f. If degs is the zero pointer, an array of sufficient size |
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505 | // is allocated automatically. |
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506 | // |
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507 | //}}} |
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508 | int * degrees ( const CanonicalForm & f, int * degs ) |
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509 | { |
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510 | if ( f.inCoeffDomain() ) |
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511 | return 0; |
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512 | else |
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513 | { |
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514 | int level = f.level(); |
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515 | if ( degs == 0 ) |
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516 | degs = new int[level+1]; |
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517 | for ( int i = 0; i <= level; i++ ) |
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518 | degs[i] = 0; |
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519 | degreesRec( f, degs ); |
---|
520 | return degs; |
---|
521 | } |
---|
522 | } |
---|
523 | //}}} |
---|
524 | |
---|
525 | //{{{ int totaldegree ( const CanonicalForm & f ) |
---|
526 | //{{{ docu |
---|
527 | // |
---|
528 | // totaldegree() - return the total degree of f. |
---|
529 | // |
---|
530 | // If f is zero, return -1. If f is in a coefficient domain, |
---|
531 | // return 0. Otherwise return the total degree of f in all |
---|
532 | // polynomial variables. |
---|
533 | // |
---|
534 | //}}} |
---|
535 | int totaldegree ( const CanonicalForm & f ) |
---|
536 | { |
---|
537 | if ( f.isZero() ) |
---|
538 | return -1; |
---|
539 | else if ( f.inCoeffDomain() ) |
---|
540 | return 0; |
---|
541 | else |
---|
542 | { |
---|
543 | CFIterator i; |
---|
544 | int cdeg = 0, dummy; |
---|
545 | // calculate maximum over all coefficients of f, taking |
---|
546 | // in account our own exponent |
---|
547 | for ( i = f; i.hasTerms(); i++ ) |
---|
548 | if ( (dummy = totaldegree( i.coeff() ) + i.exp()) > cdeg ) |
---|
549 | cdeg = dummy; |
---|
550 | return cdeg; |
---|
551 | } |
---|
552 | } |
---|
553 | //}}} |
---|
554 | |
---|
555 | //{{{ int totaldegree ( const CanonicalForm & f, const Variable & v1, const Variable & v2 ) |
---|
556 | //{{{ docu |
---|
557 | // |
---|
558 | // totaldegree() - return the total degree of f as a polynomial |
---|
559 | // in the polynomial variables between v1 and v2 (inclusively). |
---|
560 | // |
---|
561 | // If f is zero, return -1. If f is in a coefficient domain, |
---|
562 | // return 0. Also, return 0 if v1 > v2. Otherwise, take f to be |
---|
563 | // a polynomial in the polynomial variables between v1 and v2 and |
---|
564 | // return its total degree. |
---|
565 | // |
---|
566 | //}}} |
---|
567 | int |
---|
568 | totaldegree ( const CanonicalForm & f, const Variable & v1, const Variable & v2 ) |
---|
569 | { |
---|
570 | if ( f.isZero() ) |
---|
571 | return -1; |
---|
572 | else if ( v1 > v2 ) |
---|
573 | return 0; |
---|
574 | else if ( f.inCoeffDomain() ) |
---|
575 | return 0; |
---|
576 | else if ( f.mvar() < v1 ) |
---|
577 | return 0; |
---|
578 | else if ( f.mvar() == v1 ) |
---|
579 | return f.degree(); |
---|
580 | else if ( f.mvar() > v2 ) |
---|
581 | { |
---|
582 | // v2's level is larger than f's level, descend down |
---|
583 | CFIterator i; |
---|
584 | int cdeg = 0, dummy; |
---|
585 | // calculate maximum over all coefficients of f |
---|
586 | for ( i = f; i.hasTerms(); i++ ) |
---|
587 | if ( (dummy = totaldegree( i.coeff(), v1, v2 )) > cdeg ) |
---|
588 | cdeg = dummy; |
---|
589 | return cdeg; |
---|
590 | } |
---|
591 | else |
---|
592 | { |
---|
593 | // v1 < f.mvar() <= v2 |
---|
594 | CFIterator i; |
---|
595 | int cdeg = 0, dummy; |
---|
596 | // calculate maximum over all coefficients of f, taking |
---|
597 | // in account our own exponent |
---|
598 | for ( i = f; i.hasTerms(); i++ ) |
---|
599 | if ( (dummy = totaldegree( i.coeff(), v1, v2 ) + i.exp()) > cdeg ) |
---|
600 | cdeg = dummy; |
---|
601 | return cdeg; |
---|
602 | } |
---|
603 | } |
---|
604 | //}}} |
---|
605 | |
---|
606 | //{{{ int size ( const CanonicalForm & f, const Variable & v ) |
---|
607 | //{{{ docu |
---|
608 | // |
---|
609 | // size() - count number of monomials of f with level higher |
---|
610 | // or equal than level of v. |
---|
611 | // |
---|
612 | // Returns one if f is in an base domain. |
---|
613 | // |
---|
614 | //}}} |
---|
615 | int |
---|
616 | size ( const CanonicalForm & f, const Variable & v ) |
---|
617 | { |
---|
618 | if ( f.inBaseDomain() ) |
---|
619 | return 1; |
---|
620 | |
---|
621 | if ( f.mvar() < v ) |
---|
622 | // polynomials with level < v1 are counted as coefficients |
---|
623 | return 1; |
---|
624 | else |
---|
625 | { |
---|
626 | CFIterator i; |
---|
627 | int result = 0; |
---|
628 | // polynomials with level > v2 are not counted al all |
---|
629 | for ( i = f; i.hasTerms(); i++ ) |
---|
630 | result += size( i.coeff(), v ); |
---|
631 | return result; |
---|
632 | } |
---|
633 | } |
---|
634 | //}}} |
---|
635 | |
---|
636 | //{{{ int size ( const CanonicalForm & f ) |
---|
637 | //{{{ docu |
---|
638 | // |
---|
639 | // size() - return number of monomials in f which are in an |
---|
640 | // coefficient domain. |
---|
641 | // |
---|
642 | // Returns one if f is in an coefficient domain. |
---|
643 | // |
---|
644 | //}}} |
---|
645 | int |
---|
646 | size ( const CanonicalForm & f ) |
---|
647 | { |
---|
648 | if ( f.inCoeffDomain() ) |
---|
649 | return 1; |
---|
650 | else |
---|
651 | { |
---|
652 | int result = 0; |
---|
653 | CFIterator i; |
---|
654 | for ( i = f; i.hasTerms(); i++ ) |
---|
655 | result += size( i.coeff() ); |
---|
656 | return result; |
---|
657 | } |
---|
658 | } |
---|
659 | //}}} |
---|
660 | |
---|
661 | CanonicalForm reduce(const CanonicalForm & f, const CanonicalForm & M) |
---|
662 | { // polynomials in M.mvar() are considered coefficients |
---|
663 | // M univariate monic polynomial |
---|
664 | // the coefficients of f are reduced modulo M |
---|
665 | if(f.inBaseDomain() || f.level() < M.level()) |
---|
666 | return f; |
---|
667 | if(f.level() == M.level()) |
---|
668 | { |
---|
669 | if(f.degree() < M.degree()) |
---|
670 | return f; |
---|
671 | CanonicalForm tmp = mod (f, M); |
---|
672 | return tmp; |
---|
673 | } |
---|
674 | // here: f.level() > M.level() |
---|
675 | CanonicalForm result = 0; |
---|
676 | for(CFIterator i=f; i.hasTerms(); i++) |
---|
677 | result += reduce(i.coeff(),M) * power(f.mvar(),i.exp()); |
---|
678 | return result; |
---|
679 | } |
---|