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 | #include "config.h" |
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5 | |
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6 | #include "cf_assert.h" |
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7 | |
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8 | #include "cf_defs.h" |
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9 | #include "canonicalform.h" |
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10 | #include "cf_map.h" |
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11 | |
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12 | static int divexp = 1; |
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13 | |
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14 | static void divexpfunc ( CanonicalForm &, int & e ) |
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15 | { |
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16 | e /= divexp; |
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17 | } |
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18 | |
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19 | static int |
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20 | compareFactors( const CFFactor & f, const CFFactor & g ) |
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21 | { |
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22 | return f.exp() > g.exp(); |
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23 | } |
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24 | |
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25 | CFFList |
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26 | sortCFFList( CFFList & F ) |
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27 | { |
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28 | F.sort( compareFactors ); |
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29 | |
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30 | int exp; |
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31 | CanonicalForm f; |
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32 | CFFListIterator I = F; |
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33 | CFFList result; |
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34 | |
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35 | // join elements with the same degree |
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36 | while ( I.hasItem() ) { |
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37 | f = I.getItem().factor(); |
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38 | exp = I.getItem().exp(); |
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39 | I++; |
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40 | while ( I.hasItem() && I.getItem().exp() == exp ) { |
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41 | f *= I.getItem().factor(); |
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42 | I++; |
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43 | } |
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44 | result.append( CFFactor( f, exp ) ); |
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45 | } |
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46 | |
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47 | return result; |
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48 | } |
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49 | |
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50 | CFFList sqrFreeFp ( const CanonicalForm & f ) |
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51 | { |
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52 | CanonicalForm t0 = f, t, v, w, h; |
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53 | CanonicalForm leadcf = t0.lc(); |
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54 | Variable x = f.mvar(); |
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55 | CFFList F; |
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56 | int p = getCharacteristic(); |
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57 | int k, e = 1; |
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58 | |
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59 | if ( ! leadcf.isOne() ) |
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60 | t0 /= leadcf; |
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61 | |
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62 | divexp = p; |
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63 | while ( t0.degree(x) > 0 ) |
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64 | { |
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65 | t = gcd( t0, t0.deriv() ); |
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66 | v = t0 / t; |
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67 | k = 0; |
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68 | while ( v.degree(x) > 0 ) |
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69 | { |
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70 | k = k+1; |
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71 | if ( k % p == 0 ) |
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72 | { |
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73 | t /= v; |
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74 | k = k+1; |
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75 | } |
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76 | w = gcd( t, v ); |
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77 | h = v / w; |
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78 | v = w; |
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79 | t /= v; |
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80 | if ( h.degree(x) > 0 ) |
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81 | F.append( CFFactor( h/h.lc(), e*k ) ); |
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82 | } |
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83 | t0 = apply( t, divexpfunc ); |
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84 | e = p * e; |
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85 | } |
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86 | if ( ! leadcf.isOne() ) |
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87 | { |
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88 | if ( !F.isEmpty() && (F.getFirst().exp() == 1) ) |
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89 | { |
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90 | leadcf = F.getFirst().factor() * leadcf; |
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91 | F.removeFirst(); |
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92 | } |
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93 | F.insert( CFFactor( leadcf, 1 ) ); |
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94 | } |
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95 | return F; |
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96 | } |
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97 | |
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98 | bool isSqrFreeFp( const CanonicalForm & f ) |
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99 | { |
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100 | CFFList F = sqrFreeFp( f ); |
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101 | return ( F.length() == 1 && F.getFirst().exp() == 1 ); |
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102 | } |
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103 | |
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104 | bool isSqrFreeZ ( const CanonicalForm & f ) |
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105 | { |
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106 | return gcd( f, f.deriv() ).degree() == 0; |
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107 | } |
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108 | |
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109 | /* |
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110 | |
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111 | CFFList sqrFreeZ ( const CanonicalForm & a ) |
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112 | { |
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113 | CanonicalForm b = a.deriv(), c = gcd( a, b ); |
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114 | CanonicalForm y, z, w = a / c; |
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115 | int i = 1; |
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116 | CFFList F; |
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117 | |
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118 | while ( ! c.degree() == 0 ) |
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119 | { |
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120 | y = gcd( w, c ); z = w / y; |
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121 | if ( degree( z ) > 0 ) |
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122 | if ( lc( z ).sign() < 0 ) |
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123 | F.append( CFFactor( -z, i ) ); |
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124 | else |
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125 | F.append( CFFactor( z, i ) ); |
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126 | i++; |
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127 | w = y; c = c / y; |
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128 | } |
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129 | if ( degree( w ) > 0 ) |
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130 | if ( lc( w ).sign() < 0 ) |
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131 | F.append( CFFactor( -w, i ) ); |
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132 | else |
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133 | F.append( CFFactor( w, i ) ); |
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134 | return F; |
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135 | } |
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136 | */ |
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137 | |
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138 | CFFList sqrFreeZ ( const CanonicalForm & a ) |
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139 | { |
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140 | if ( a.inCoeffDomain() ) |
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141 | return CFFactor( a, 1 ); |
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142 | CanonicalForm cont = content( a ); |
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143 | CanonicalForm aa = a / cont; |
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144 | CanonicalForm b = aa.deriv(), c = gcd( aa, b ); |
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145 | CanonicalForm y, z, w = aa / c; |
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146 | int i = 1; |
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147 | CFFList F; |
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148 | Variable v = aa.mvar(); |
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149 | while ( ! c.degree(v) == 0 ) |
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150 | { |
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151 | y = gcd( w, c ); z = w / y; |
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152 | if ( degree( z, v ) > 0 ) |
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153 | { |
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154 | if ( lc( z ).sign() < 0 ) |
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155 | F.append( CFFactor( -z, i ) ); |
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156 | else |
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157 | F.append( CFFactor( z, i ) ); |
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158 | } |
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159 | i++; |
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160 | w = y; c = c / y; |
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161 | } |
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162 | if ( degree( w,v ) > 0 ) |
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163 | { |
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164 | if ( lc( w ).sign() < 0 ) |
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165 | F.append( CFFactor( -w, i ) ); |
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166 | else |
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167 | F.append( CFFactor( w, i ) ); |
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168 | } |
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169 | if ( ! cont.isOne() ) |
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170 | F = Union( F, sqrFreeZ( cont ) ); |
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171 | if ( lc( a ).sign() < 0 ) |
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172 | { |
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173 | if ( F.getFirst().exp() == 1 ) |
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174 | { |
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175 | CanonicalForm f = F.getFirst().factor(); |
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176 | CFFListIterator(F).getItem() = CFFactor( -f, 1 ); |
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177 | } |
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178 | else |
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179 | F.insert( CFFactor( -1, 1 ) ); |
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180 | } |
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181 | return F; |
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182 | } |
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183 | |
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184 | CanonicalForm |
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185 | sqrfPart (const CanonicalForm& F) |
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186 | { |
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187 | if (F.inCoeffDomain()) |
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188 | return F; |
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189 | CFMap M; |
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190 | CanonicalForm A= compress (F, M); |
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191 | CanonicalForm w, v, b; |
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192 | CanonicalForm result; |
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193 | int i= 1; |
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194 | for (; i <= A.level(); i++) |
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195 | { |
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196 | if (!deriv (A, Variable (i)).isZero()) |
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197 | break; |
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198 | } |
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199 | |
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200 | w= gcd (A, deriv (A, Variable (i))); |
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201 | b= A/w; |
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202 | result= b; |
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203 | if (degree (w) < 1) |
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204 | return M (result); |
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205 | i++; |
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206 | for (; i <= A.level(); i++) |
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207 | { |
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208 | if (!deriv (w, Variable (i)).isZero()) |
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209 | { |
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210 | b= w; |
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211 | w= gcd (w, deriv (w, Variable (i))); |
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212 | b /= w; |
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213 | if (degree (b) < 1) |
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214 | break; |
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215 | CanonicalForm g= gcd (b, result); |
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216 | if (degree (g) > 0) |
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217 | result *= b/g; |
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218 | if (degree (g) <= 0) |
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219 | result *= b; |
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220 | } |
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221 | } |
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222 | result= M (result); |
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223 | return result; |
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224 | } |
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225 | |
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