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 | #include "cf_factory.h" |
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8 | |
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9 | #include "cf_defs.h" |
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10 | #include "cf_globals.h" |
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11 | #include "canonicalform.h" |
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12 | #include "cf_iter.h" |
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13 | #include "int_cf.h" |
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14 | #include "cf_algorithm.h" |
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15 | #include "imm.h" |
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16 | #include "gfops.h" |
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17 | #include "cf_binom.h" |
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18 | |
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19 | #include "cf_gmp.h" |
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20 | |
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21 | |
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22 | #ifndef NOSTREAMIO |
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23 | CanonicalForm readCF( ISTREAM& ); |
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24 | #endif /* NOSTREAMIO */ |
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25 | |
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26 | //{{{ initialization |
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27 | int initializeGMP(); |
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28 | int initializeCharacteristic(); |
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29 | |
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30 | #ifdef SINGULAR |
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31 | extern int mmInit(void); |
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32 | #endif |
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33 | |
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34 | int |
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35 | initCanonicalForm( void ) |
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36 | { |
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37 | static bool initialized = false; |
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38 | if ( ! initialized ) { |
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39 | #if defined (SINGULAR) |
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40 | (void)mmInit(); |
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41 | #endif |
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42 | |
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43 | (void)initializeCharacteristic(); |
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44 | (void)initializeGMP(); |
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45 | initPT(); |
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46 | initialized = true; |
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47 | } |
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48 | return 1; |
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49 | } |
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50 | //}}} |
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51 | |
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52 | //{{{ constructors, destructors, selectors |
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53 | CanonicalForm::CanonicalForm( const char * str, const int base ) : value( CFFactory::basic( str, base ) ) |
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54 | { |
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55 | } |
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56 | |
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57 | InternalCF* |
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58 | CanonicalForm::getval() const |
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59 | { |
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60 | if ( is_imm( value ) ) |
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61 | return value; |
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62 | else |
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63 | return value->copyObject(); |
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64 | } |
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65 | |
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66 | CanonicalForm |
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67 | CanonicalForm::deepCopy() const |
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68 | { |
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69 | if ( is_imm( value ) ) |
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70 | return *this; |
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71 | else |
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72 | return CanonicalForm( value->deepCopyObject() ); |
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73 | } |
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74 | //}}} |
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75 | |
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76 | //{{{ predicates |
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77 | #if 0 |
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78 | bool |
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79 | CanonicalForm::isImm() const |
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80 | { |
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81 | return is_imm( value ); |
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82 | } |
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83 | #endif |
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84 | |
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85 | bool |
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86 | CanonicalForm::inZ() const |
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87 | { |
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88 | if ( is_imm( value ) == INTMARK ) |
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89 | return true; |
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90 | else if ( is_imm( value ) ) |
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91 | return false; |
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92 | else |
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93 | return value->levelcoeff() == IntegerDomain; |
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94 | } |
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95 | |
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96 | bool |
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97 | CanonicalForm::inQ() const |
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98 | { |
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99 | if ( is_imm( value ) == INTMARK ) |
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100 | return true; |
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101 | else if ( is_imm( value ) ) |
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102 | return false; |
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103 | else |
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104 | return value->levelcoeff() == IntegerDomain || |
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105 | value->levelcoeff() == RationalDomain; |
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106 | } |
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107 | |
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108 | bool |
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109 | CanonicalForm::inFF() const |
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110 | { |
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111 | return is_imm( value ) == FFMARK; |
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112 | } |
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113 | |
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114 | bool |
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115 | CanonicalForm::inGF() const |
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116 | { |
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117 | return is_imm( value ) == GFMARK; |
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118 | } |
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119 | |
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120 | bool |
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121 | CanonicalForm::inPP() const |
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122 | { |
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123 | return ! is_imm( value ) && ( value->levelcoeff() == PrimePowerDomain ); |
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124 | } |
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125 | |
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126 | bool |
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127 | CanonicalForm::inBaseDomain() const |
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128 | { |
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129 | if ( is_imm( value ) ) |
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130 | return true; |
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131 | else |
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132 | return value->inBaseDomain(); |
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133 | } |
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134 | |
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135 | bool |
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136 | CanonicalForm::inExtension() const |
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137 | { |
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138 | if ( is_imm( value ) ) |
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139 | return false; |
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140 | else |
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141 | return value->inExtension(); |
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142 | } |
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143 | |
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144 | bool |
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145 | CanonicalForm::inCoeffDomain() const |
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146 | { |
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147 | if ( is_imm( value ) ) |
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148 | return true; |
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149 | else |
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150 | return value->inCoeffDomain(); |
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151 | } |
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152 | |
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153 | bool |
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154 | CanonicalForm::inPolyDomain() const |
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155 | { |
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156 | if ( is_imm( value ) ) |
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157 | return false; |
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158 | else |
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159 | return value->inPolyDomain(); |
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160 | } |
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161 | |
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162 | bool |
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163 | CanonicalForm::inQuotDomain() const |
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164 | { |
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165 | if ( is_imm( value ) ) |
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166 | return false; |
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167 | else |
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168 | return value->inQuotDomain(); |
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169 | } |
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170 | |
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171 | bool |
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172 | CanonicalForm::isFFinGF() const |
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173 | { |
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174 | return is_imm( value ) == GFMARK && gf_isff( imm2int( value ) ); |
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175 | } |
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176 | |
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177 | bool |
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178 | CanonicalForm::isUnivariate() const |
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179 | { |
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180 | if ( is_imm( value ) ) |
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181 | return false; |
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182 | else |
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183 | return value->isUnivariate(); |
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184 | } |
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185 | |
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186 | // is_homogeneous returns 1 iff f is homogeneous, 0 otherwise// |
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187 | bool |
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188 | CanonicalForm::isHomogeneous() const |
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189 | { |
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190 | if (this->isZero()) return true; |
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191 | else if (this->inCoeffDomain()) return true; |
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192 | else |
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193 | { |
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194 | #if 0 |
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195 | CFIterator i; |
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196 | int cdeg = -2, dummy; |
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197 | for ( i = *this; i.hasTerms(); i++ ) |
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198 | { |
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199 | if (!(i.coeff().isHomogeneous())) return false; |
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200 | if ( (dummy = totaldegree( i.coeff() ) + i.exp()) != cdeg ) |
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201 | { |
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202 | if (cdeg == -2) cdeg = dummy; |
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203 | else return false; |
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204 | } |
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205 | } |
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206 | return true; |
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207 | #else |
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208 | CFList termlist= get_Terms(*this); |
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209 | CFListIterator i; |
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210 | int deg= totaldegree(termlist.getFirst()); |
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211 | |
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212 | for ( i=termlist; i.hasItem(); i++ ) |
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213 | if ( totaldegree(i.getItem()) != deg ) return false; |
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214 | return true; |
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215 | #endif |
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216 | } |
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217 | } |
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218 | |
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219 | //}}} |
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220 | |
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221 | //{{{ conversion functions |
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222 | int |
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223 | CanonicalForm::intval() const |
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224 | { |
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225 | if ( is_imm( value ) ) |
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226 | return imm_intval( value ); |
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227 | else |
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228 | return value->intval(); |
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229 | } |
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230 | |
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231 | CanonicalForm |
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232 | CanonicalForm::mapinto () const |
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233 | { |
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234 | //ASSERT( is_imm( value ) || ! value->inExtension(), "cannot map into different Extension" ); |
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235 | if ( is_imm( value ) ) |
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236 | if ( getCharacteristic() == 0 ) |
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237 | if ( is_imm( value ) == FFMARK ) |
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238 | return CanonicalForm( int2imm( ff_symmetric( imm2int( value ) ) ) ); |
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239 | else if ( is_imm( value ) == GFMARK ) |
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240 | return CanonicalForm( int2imm( ff_symmetric( gf_gf2ff( imm2int( value ) ) ) ) ); |
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241 | else |
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242 | return *this; |
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243 | else if ( CFFactory::gettype() == PrimePowerDomain ) |
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244 | return CanonicalForm( CFFactory::basic( imm2int( value ) ) ); |
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245 | else if ( getGFDegree() == 1 ) |
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246 | return CanonicalForm( int2imm_p( ff_norm( imm2int( value ) ) ) ); |
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247 | else |
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248 | return CanonicalForm( int2imm_gf( gf_int2gf( imm2int( value ) ) ) ); |
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249 | else if ( value->inBaseDomain() ) |
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250 | if ( getCharacteristic() == 0 ) |
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251 | if ( value->levelcoeff() == PrimePowerDomain ) |
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252 | return CFFactory::basic( getmpi( value, true ) ); |
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253 | else |
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254 | return *this; |
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255 | else if ( CFFactory::gettype() == PrimePowerDomain ) |
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256 | { |
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257 | ASSERT( value->levelcoeff() == PrimePowerDomain || value->levelcoeff() == IntegerDomain, "no proper map defined" ); |
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258 | if ( value->levelcoeff() == PrimePowerDomain ) |
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259 | return *this; |
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260 | else |
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261 | return CFFactory::basic( getmpi( value ) ); |
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262 | } |
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263 | else |
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264 | { |
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265 | int val; |
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266 | if ( value->levelcoeff() == IntegerDomain ) |
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267 | val = value->intmod( ff_prime ); |
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268 | else if ( value->levelcoeff() == RationalDomain ) |
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269 | return num().mapinto() / den().mapinto(); |
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270 | else { |
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271 | ASSERT( 0, "illegal domain" ); |
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272 | return 0; |
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273 | } |
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274 | if ( getGFDegree() > 1 ) |
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275 | return CanonicalForm( int2imm_gf( gf_int2gf( val ) ) ); |
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276 | else |
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277 | return CanonicalForm( int2imm_p( val ) ); |
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278 | } |
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279 | else |
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280 | { |
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281 | Variable x = value->variable(); |
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282 | CanonicalForm result; |
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283 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
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284 | result += (power( x, i.exp() ) * i.coeff().mapinto()); |
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285 | return result; |
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286 | } |
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287 | } |
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288 | //}}} |
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289 | |
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290 | //{{{ CanonicalForm CanonicalForm::lc (), Lc (), LC (), LC ( v ) const |
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291 | //{{{ docu |
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292 | // |
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293 | // lc(), Lc(), LC() - leading coefficient functions. |
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294 | // |
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295 | // All methods return CO if CO is in a base domain. |
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296 | // |
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297 | // lc() returns the leading coefficient of CO with respect to |
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298 | // lexicographic ordering. Elements in an algebraic extension |
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299 | // are considered polynomials so lc() always returns a leading |
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300 | // coefficient in a base domain. This method is useful to get |
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301 | // the base domain over which CO is defined. |
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302 | // |
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303 | // Lc() returns the leading coefficient of CO with respect to |
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304 | // lexicographic ordering. In contrast to lc() elements in an |
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305 | // algebraic extension are considered coefficients so Lc() always |
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306 | // returns a leading coefficient in a coefficient domain. |
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307 | // |
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308 | // LC() returns the leading coefficient of CO where CO is |
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309 | // considered a univariate polynomial in its main variable. An |
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310 | // element of an algebraic extension is considered an univariate |
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311 | // polynomial, too. |
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312 | // |
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313 | // LC( v ) returns the leading coefficient of CO where CO is |
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314 | // considered an univariate polynomial in the polynomial variable |
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315 | // v. |
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316 | // Note: If v is less than the main variable of CO we have to |
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317 | // swap variables which may be quite expensive. |
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318 | // |
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319 | // Examples: |
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320 | // Let x < y be polynomial variables, a an algebraic variable. |
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321 | // |
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322 | // (3*a*x*y^2+y+x).lc() = 3 |
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323 | // (3*a*x*y^2+y+x).Lc() = 3*a |
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324 | // (3*a*x*y^2+y+x).LC() = 3*a*x |
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325 | // (3*a*x*y^2+y+x).LC( x ) = 3*a*y^2+1 |
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326 | // |
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327 | // (3*a^2+4*a).lc() = 3 |
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328 | // (3*a^2+4*a).Lc() = 3*a^2+4*a |
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329 | // (3*a^2+4*a).LC() = 3 |
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330 | // (3*a^2+4*a).LC( x ) = 3*a^2+4*a |
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331 | // |
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332 | // See also: InternalCF::lc(), InternalCF::Lc(), InternalCF::LC(), |
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333 | // InternalPoly::lc(), InternalPoly::Lc(), InternalPoly::LC(), |
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334 | // ::lc(), ::Lc(), ::LC(), ::LC( v ) |
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335 | // |
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336 | //}}} |
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337 | CanonicalForm |
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338 | CanonicalForm::lc () const |
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339 | { |
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340 | if ( is_imm( value ) ) |
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341 | return *this; |
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342 | else |
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343 | return value->lc(); |
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344 | } |
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345 | |
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346 | CanonicalForm |
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347 | CanonicalForm::Lc () const |
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348 | { |
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349 | if ( is_imm( value ) || value->inCoeffDomain() ) |
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350 | return *this; |
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351 | else |
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352 | return value->Lc(); |
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353 | } |
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354 | |
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355 | CanonicalForm |
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356 | CanonicalForm::LC () const |
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357 | { |
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358 | if ( is_imm( value ) ) |
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359 | return *this; |
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360 | else |
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361 | return value->LC(); |
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362 | } |
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363 | |
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364 | CanonicalForm |
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365 | CanonicalForm::LC ( const Variable & v ) const |
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366 | { |
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367 | if ( is_imm( value ) || value->inCoeffDomain() ) |
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368 | return *this; |
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369 | |
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370 | Variable x = value->variable(); |
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371 | if ( v > x ) |
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372 | return *this; |
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373 | else if ( v == x ) |
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374 | return value->LC(); |
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375 | else { |
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376 | CanonicalForm f = swapvar( *this, v, x ); |
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377 | if ( f.mvar() == x ) |
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378 | return swapvar( f.value->LC(), v, x ); |
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379 | else |
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380 | // v did not occur in f |
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381 | return *this; |
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382 | } |
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383 | } |
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384 | //}}} |
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385 | |
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386 | //{{{ int CanonicalForm::degree (), degree ( v ) const |
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387 | //{{{ docu |
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388 | // |
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389 | // degree() - degree methods. |
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390 | // |
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391 | // Both methods returns -1 for the zero polynomial and 0 if |
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392 | // CO is in a base domain. |
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393 | // |
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394 | // degree() returns the degree of CO in its main variable. |
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395 | // Elements in an algebraic extension are considered polynomials. |
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396 | // |
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397 | // degree( v ) returns the degree of CO with respect to v. |
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398 | // Elements in an algebraic extension are considered polynomials, |
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399 | // and v may be algebraic. |
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400 | // |
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401 | // See also: InternalCf::degree(), InternalPoly::degree(), |
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402 | // ::degree(), ::degree( v ) |
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403 | // |
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404 | //}}} |
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405 | int |
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406 | CanonicalForm::degree() const |
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407 | { |
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408 | int what = is_imm( value ); |
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409 | if ( what ) |
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410 | if ( what == FFMARK ) |
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411 | return imm_iszero_p( value ) ? -1 : 0; |
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412 | else if ( what == INTMARK ) |
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413 | return imm_iszero( value ) ? -1 : 0; |
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414 | else |
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415 | return imm_iszero_gf( value ) ? -1 : 0; |
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416 | else |
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417 | return value->degree(); |
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418 | } |
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419 | |
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420 | int |
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421 | CanonicalForm::degree( const Variable & v ) const |
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422 | { |
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423 | int what = is_imm( value ); |
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424 | #if 0 |
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425 | if ( what ) |
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426 | if ( what == FFMARK ) |
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427 | return imm_iszero_p( value ) ? -1 : 0; |
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428 | else if ( what == INTMARK ) |
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429 | return imm_iszero( value ) ? -1 : 0; |
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430 | else |
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431 | return imm_iszero_gf( value ) ? -1 : 0; |
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432 | else if ( value->inBaseDomain() ) |
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433 | return value->degree(); |
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434 | #else |
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435 | switch(what) |
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436 | { |
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437 | case FFMARK: return imm_iszero_p( value ) ? -1 : 0; |
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438 | case INTMARK: return imm_iszero( value ) ? -1 : 0; |
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439 | case GFMARK: return imm_iszero_gf( value ) ? -1 : 0; |
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440 | case 0: if ( value->inBaseDomain() ) |
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441 | return value->degree(); |
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442 | break; |
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443 | } |
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444 | #endif |
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445 | |
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446 | Variable x = value->variable(); |
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447 | if ( v == x ) |
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448 | return value->degree(); |
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449 | else if ( v > x ) |
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450 | // relatively to v, f is in a coefficient ring |
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451 | return 0; |
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452 | else { |
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453 | int coeffdeg, result = 0; |
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454 | // search for maximum of coefficient degree |
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455 | for ( CFIterator i = *this; i.hasTerms(); i++ ) { |
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456 | coeffdeg = i.coeff().degree( v ); |
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457 | if ( coeffdeg > result ) |
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458 | result = coeffdeg; |
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459 | } |
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460 | return result; |
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461 | } |
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462 | } |
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463 | //}}} |
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464 | |
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465 | //{{{ CanonicalForm CanonicalForm::tailcoeff (), int CanonicalForm::taildegree () const |
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466 | //{{{ docu |
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467 | // |
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468 | // tailcoeff(), taildegree() - return least coefficient and |
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469 | // degree, resp. |
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470 | // |
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471 | // tailcoeff() returns the coefficient of the term with the least |
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472 | // degree in CO where CO is considered an univariate polynomial |
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473 | // in its main variable. Elements in an algebraic extension are |
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474 | // considered coefficients. |
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475 | // |
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476 | // taildegree() returns -1 for the zero polynomial, 0 if CO is in |
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477 | // a base domain, otherwise the least degree of CO where CO is |
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478 | // considered a univariate polynomial in its main variable. In |
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479 | // contrast to tailcoeff(), elements in an algebraic extension |
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480 | // are considered polynomials, not coefficients, and such may |
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481 | // have a taildegree larger than zero. |
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482 | // |
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483 | // See also: InternalCF::tailcoeff(), InternalCF::tailcoeff(), |
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484 | // InternalPoly::tailcoeff(), InternalPoly::taildegree, |
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485 | // ::tailcoeff(), ::taildegree() |
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486 | // |
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487 | //}}} |
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488 | CanonicalForm |
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489 | CanonicalForm::tailcoeff () const |
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490 | { |
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491 | if ( is_imm( value ) || value->inCoeffDomain() ) |
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492 | return *this; |
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493 | else |
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494 | return value->tailcoeff(); |
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495 | } |
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496 | |
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497 | int |
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498 | CanonicalForm::taildegree () const |
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499 | { |
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500 | int what = is_imm( value ); |
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501 | if ( what ) |
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502 | if ( what == FFMARK ) |
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503 | return imm_iszero_p( value ) ? -1 : 0; |
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504 | else if ( what == INTMARK ) |
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505 | return imm_iszero( value ) ? -1 : 0; |
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506 | else |
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507 | return imm_iszero_gf( value ) ? -1 : 0; |
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508 | else |
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509 | return value->taildegree(); |
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510 | } |
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511 | //}}} |
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512 | |
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513 | //{{{ int CanonicalForm::level (), Variable CanonicalForm::mvar () const |
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514 | //{{{ docu |
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515 | // |
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516 | // level(), mvar() - return level and main variable of CO. |
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517 | // |
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518 | // level() returns the level of CO. For a list of the levels and |
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519 | // their meanings, see cf_defs.h. |
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520 | // |
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521 | // mvar() returns the main variable of CO or Variable() if CO is |
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522 | // in a base domain. |
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523 | // |
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524 | // See also: InternalCF::level(), InternalCF::variable(), |
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525 | // InternalPoly::level(), InternalPoly::variable(), ::level(), |
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526 | // ::mvar() |
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527 | // |
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528 | //}}} |
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529 | int |
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530 | CanonicalForm::level () const |
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531 | { |
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532 | if ( is_imm( value ) ) |
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533 | return LEVELBASE; |
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534 | else |
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535 | return value->level(); |
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536 | } |
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537 | |
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538 | Variable |
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539 | CanonicalForm::mvar () const |
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540 | { |
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541 | if ( is_imm( value ) ) |
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542 | return Variable(); |
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543 | else |
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544 | return value->variable(); |
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545 | } |
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546 | //}}} |
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547 | |
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548 | //{{{ CanonicalForm CanonicalForm::num (), den () const |
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549 | //{{{ docu |
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550 | // |
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551 | // num(), den() - return numinator and denominator of CO. |
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552 | // |
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553 | // num() returns the numinator of CO if CO is a rational number, |
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554 | // CO itself otherwise. |
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555 | // |
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556 | // den() returns the denominator of CO if CO is a rational |
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557 | // number, 1 (from the current domain!) otherwise. |
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558 | // |
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559 | // See also: InternalCF::num(), InternalCF::den(), |
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560 | // InternalRational::num(), InternalRational::den(), ::num(), |
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561 | // ::den() |
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562 | // |
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563 | //}}} |
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564 | CanonicalForm |
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565 | CanonicalForm::num () const |
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566 | { |
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567 | if ( is_imm( value ) ) |
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568 | return *this; |
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569 | else |
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570 | return CanonicalForm( value->num() ); |
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571 | } |
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572 | |
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573 | CanonicalForm |
---|
574 | CanonicalForm::den () const |
---|
575 | { |
---|
576 | if ( is_imm( value ) ) |
---|
577 | return CanonicalForm( 1 ); |
---|
578 | else |
---|
579 | return CanonicalForm( value->den() ); |
---|
580 | } |
---|
581 | //}}} |
---|
582 | |
---|
583 | //{{{ assignment operators |
---|
584 | CanonicalForm & |
---|
585 | CanonicalForm::operator += ( const CanonicalForm & cf ) |
---|
586 | { |
---|
587 | int what = is_imm( value ); |
---|
588 | if ( what ) { |
---|
589 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
590 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
591 | value = imm_add_p( value, cf.value ); |
---|
592 | else if ( what == GFMARK ) |
---|
593 | value = imm_add_gf( value, cf.value ); |
---|
594 | else if ( what ) |
---|
595 | value = imm_add( value, cf.value ); |
---|
596 | else { |
---|
597 | InternalCF * dummy = cf.value->copyObject(); |
---|
598 | value = dummy->addcoeff( value ); |
---|
599 | } |
---|
600 | } |
---|
601 | else if ( is_imm( cf.value ) ) |
---|
602 | value = value->addcoeff( cf.value ); |
---|
603 | else if ( value->level() == cf.value->level() ) { |
---|
604 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
605 | value = value->addsame( cf.value ); |
---|
606 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
607 | value = value->addcoeff( cf.value ); |
---|
608 | else { |
---|
609 | InternalCF * dummy = cf.value->copyObject(); |
---|
610 | dummy = dummy->addcoeff( value ); |
---|
611 | if ( value->deleteObject() ) delete value; |
---|
612 | value = dummy; |
---|
613 | } |
---|
614 | } |
---|
615 | else if ( level() > cf.level() ) |
---|
616 | value = value->addcoeff( cf.value ); |
---|
617 | else { |
---|
618 | InternalCF * dummy = cf.value->copyObject(); |
---|
619 | dummy = dummy->addcoeff( value ); |
---|
620 | if ( value->deleteObject() ) delete value; |
---|
621 | value = dummy; |
---|
622 | } |
---|
623 | return *this; |
---|
624 | } |
---|
625 | |
---|
626 | CanonicalForm & |
---|
627 | CanonicalForm::operator -= ( const CanonicalForm & cf ) |
---|
628 | { |
---|
629 | int what = is_imm( value ); |
---|
630 | if ( what ) { |
---|
631 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
632 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
633 | value = imm_sub_p( value, cf.value ); |
---|
634 | else if ( what == GFMARK ) |
---|
635 | value = imm_sub_gf( value, cf.value ); |
---|
636 | else if ( what ) |
---|
637 | value = imm_sub( value, cf.value ); |
---|
638 | else { |
---|
639 | InternalCF * dummy = cf.value->copyObject(); |
---|
640 | value = dummy->subcoeff( value, true ); |
---|
641 | } |
---|
642 | } |
---|
643 | else if ( is_imm( cf.value ) ) |
---|
644 | value = value->subcoeff( cf.value, false ); |
---|
645 | else if ( value->level() == cf.value->level() ) { |
---|
646 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
647 | value = value->subsame( cf.value ); |
---|
648 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
649 | value = value->subcoeff( cf.value, false ); |
---|
650 | else { |
---|
651 | InternalCF * dummy = cf.value->copyObject(); |
---|
652 | dummy = dummy->subcoeff( value, true ); |
---|
653 | if ( value->deleteObject() ) delete value; |
---|
654 | value = dummy; |
---|
655 | } |
---|
656 | } |
---|
657 | else if ( level() > cf.level() ) |
---|
658 | value = value->subcoeff( cf.value, false ); |
---|
659 | else { |
---|
660 | InternalCF * dummy = cf.value->copyObject(); |
---|
661 | dummy = dummy->subcoeff( value, true ); |
---|
662 | if ( value->deleteObject() ) delete value; |
---|
663 | value = dummy; |
---|
664 | } |
---|
665 | return *this; |
---|
666 | } |
---|
667 | |
---|
668 | CanonicalForm & |
---|
669 | CanonicalForm::operator *= ( const CanonicalForm & cf ) |
---|
670 | { |
---|
671 | int what = is_imm( value ); |
---|
672 | if ( what ) { |
---|
673 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
674 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
675 | value = imm_mul_p( value, cf.value ); |
---|
676 | else if ( what == GFMARK ) |
---|
677 | value = imm_mul_gf( value, cf.value ); |
---|
678 | else if ( what ) |
---|
679 | value = imm_mul( value, cf.value ); |
---|
680 | else { |
---|
681 | InternalCF * dummy = cf.value->copyObject(); |
---|
682 | value = dummy->mulcoeff( value ); |
---|
683 | } |
---|
684 | } |
---|
685 | else if ( is_imm( cf.value ) ) |
---|
686 | value = value->mulcoeff( cf.value ); |
---|
687 | else if ( value->level() == cf.value->level() ) { |
---|
688 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
689 | value = value->mulsame( cf.value ); |
---|
690 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
691 | value = value->mulcoeff( cf.value ); |
---|
692 | else { |
---|
693 | InternalCF * dummy = cf.value->copyObject(); |
---|
694 | dummy = dummy->mulcoeff( value ); |
---|
695 | if ( value->deleteObject() ) delete value; |
---|
696 | value = dummy; |
---|
697 | } |
---|
698 | } |
---|
699 | else if ( level() > cf.level() ) |
---|
700 | value = value->mulcoeff( cf.value ); |
---|
701 | else { |
---|
702 | InternalCF * dummy = cf.value->copyObject(); |
---|
703 | dummy = dummy->mulcoeff( value ); |
---|
704 | if ( value->deleteObject() ) delete value; |
---|
705 | value = dummy; |
---|
706 | } |
---|
707 | return *this; |
---|
708 | } |
---|
709 | |
---|
710 | CanonicalForm & |
---|
711 | CanonicalForm::operator /= ( const CanonicalForm & cf ) |
---|
712 | { |
---|
713 | int what = is_imm( value ); |
---|
714 | if ( what ) { |
---|
715 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
716 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
717 | value = imm_div_p( value, cf.value ); |
---|
718 | else if ( what == GFMARK ) |
---|
719 | value = imm_div_gf( value, cf.value ); |
---|
720 | else if ( what ) |
---|
721 | value = imm_divrat( value, cf.value ); |
---|
722 | else { |
---|
723 | InternalCF * dummy = cf.value->copyObject(); |
---|
724 | value = dummy->dividecoeff( value, true ); |
---|
725 | } |
---|
726 | } |
---|
727 | else if ( is_imm( cf.value ) ) |
---|
728 | value = value->dividecoeff( cf.value, false ); |
---|
729 | else if ( value->level() == cf.value->level() ) { |
---|
730 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
731 | value = value->dividesame( cf.value ); |
---|
732 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
733 | value = value->dividecoeff( cf.value, false ); |
---|
734 | else { |
---|
735 | InternalCF * dummy = cf.value->copyObject(); |
---|
736 | dummy = dummy->dividecoeff( value, true ); |
---|
737 | if ( value->deleteObject() ) delete value; |
---|
738 | value = dummy; |
---|
739 | } |
---|
740 | } |
---|
741 | else if ( level() > cf.level() ) |
---|
742 | value = value->dividecoeff( cf.value, false ); |
---|
743 | else { |
---|
744 | InternalCF * dummy = cf.value->copyObject(); |
---|
745 | dummy = dummy->dividecoeff( value, true ); |
---|
746 | if ( value->deleteObject() ) delete value; |
---|
747 | value = dummy; |
---|
748 | } |
---|
749 | return *this; |
---|
750 | } |
---|
751 | |
---|
752 | CanonicalForm & |
---|
753 | CanonicalForm::div ( const CanonicalForm & cf ) |
---|
754 | { |
---|
755 | int what = is_imm( value ); |
---|
756 | if ( what ) { |
---|
757 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
758 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
759 | value = imm_div_p( value, cf.value ); |
---|
760 | else if ( what == GFMARK ) |
---|
761 | value = imm_div_gf( value, cf.value ); |
---|
762 | else if ( what ) |
---|
763 | value = imm_div( value, cf.value ); |
---|
764 | else { |
---|
765 | InternalCF * dummy = cf.value->copyObject(); |
---|
766 | value = dummy->divcoeff( value, true ); |
---|
767 | } |
---|
768 | } |
---|
769 | else if ( is_imm( cf.value ) ) |
---|
770 | value = value->divcoeff( cf.value, false ); |
---|
771 | else if ( value->level() == cf.value->level() ) { |
---|
772 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
773 | value = value->divsame( cf.value ); |
---|
774 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
775 | value = value->divcoeff( cf.value, false ); |
---|
776 | else { |
---|
777 | InternalCF * dummy = cf.value->copyObject(); |
---|
778 | dummy = dummy->divcoeff( value, true ); |
---|
779 | if ( value->deleteObject() ) delete value; |
---|
780 | value = dummy; |
---|
781 | } |
---|
782 | } |
---|
783 | else if ( level() > cf.level() ) |
---|
784 | value = value->divcoeff( cf.value, false ); |
---|
785 | else { |
---|
786 | InternalCF * dummy = cf.value->copyObject(); |
---|
787 | dummy = dummy->divcoeff( value, true ); |
---|
788 | if ( value->deleteObject() ) delete value; |
---|
789 | value = dummy; |
---|
790 | } |
---|
791 | return *this; |
---|
792 | } |
---|
793 | |
---|
794 | //same as divremt but handles zero divisors in case we are in Z_p[x]/(f) where f is not irreducible |
---|
795 | CanonicalForm & |
---|
796 | CanonicalForm::tryDiv ( const CanonicalForm & cf, const CanonicalForm& M, bool& fail ) |
---|
797 | { |
---|
798 | ASSERT (getCharacteristic() > 0, "expected positive characteristic"); |
---|
799 | ASSERT (!getReduce (M.mvar()), "do not reduce modulo M"); |
---|
800 | fail= false; |
---|
801 | int what = is_imm( value ); |
---|
802 | if ( what ) { |
---|
803 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
804 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
805 | value = imm_div_p( value, cf.value ); |
---|
806 | else if ( what == GFMARK ) |
---|
807 | value = imm_div_gf( value, cf.value ); |
---|
808 | else { |
---|
809 | InternalCF * dummy = cf.value->copyObject(); |
---|
810 | value = dummy->divcoeff( value, true ); |
---|
811 | } |
---|
812 | } |
---|
813 | else if ( is_imm( cf.value ) ) |
---|
814 | value = value->tryDivcoeff (cf.value, false, M, fail); |
---|
815 | else if ( value->level() == cf.value->level() ) { |
---|
816 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
817 | value = value->tryDivsame( cf.value, M, fail ); |
---|
818 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
819 | value = value->tryDivcoeff( cf.value, false, M, fail ); |
---|
820 | else { |
---|
821 | InternalCF * dummy = cf.value->copyObject(); |
---|
822 | dummy = dummy->tryDivcoeff( value, true, M, fail ); |
---|
823 | if ( value->deleteObject() ) delete value; |
---|
824 | value = dummy; |
---|
825 | } |
---|
826 | } |
---|
827 | else if ( level() > cf.level() ) |
---|
828 | value = value->tryDivcoeff( cf.value, false, M, fail ); |
---|
829 | else { |
---|
830 | InternalCF * dummy = cf.value->copyObject(); |
---|
831 | dummy = dummy->tryDivcoeff( value, true, M, fail ); |
---|
832 | if ( value->deleteObject() ) delete value; |
---|
833 | value = dummy; |
---|
834 | } |
---|
835 | return *this; |
---|
836 | } |
---|
837 | |
---|
838 | CanonicalForm & |
---|
839 | CanonicalForm::operator %= ( const CanonicalForm & cf ) |
---|
840 | { |
---|
841 | int what = is_imm( value ); |
---|
842 | if ( what ) { |
---|
843 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
844 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
845 | value = imm_mod_p( value, cf.value ); |
---|
846 | else if ( what == GFMARK ) |
---|
847 | value = imm_mod_gf( value, cf.value ); |
---|
848 | else if ( what ) |
---|
849 | value = imm_mod( value, cf.value ); |
---|
850 | else { |
---|
851 | InternalCF * dummy = cf.value->copyObject(); |
---|
852 | value = dummy->modulocoeff( value, true ); |
---|
853 | } |
---|
854 | } |
---|
855 | else if ( is_imm( cf.value ) ) |
---|
856 | value = value->modulocoeff( cf.value, false ); |
---|
857 | else if ( value->level() == cf.value->level() ) { |
---|
858 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
859 | value = value->modulosame( cf.value ); |
---|
860 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
861 | value = value->modulocoeff( cf.value, false ); |
---|
862 | else { |
---|
863 | InternalCF * dummy = cf.value->copyObject(); |
---|
864 | dummy = dummy->modulocoeff( value, true ); |
---|
865 | if ( value->deleteObject() ) delete value; |
---|
866 | value = dummy; |
---|
867 | } |
---|
868 | } |
---|
869 | else if ( level() > cf.level() ) |
---|
870 | value = value->modulocoeff( cf.value, false ); |
---|
871 | else { |
---|
872 | InternalCF * dummy = cf.value->copyObject(); |
---|
873 | dummy = dummy->modulocoeff( value, true ); |
---|
874 | if ( value->deleteObject() ) delete value; |
---|
875 | value = dummy; |
---|
876 | } |
---|
877 | return *this; |
---|
878 | } |
---|
879 | |
---|
880 | CanonicalForm & |
---|
881 | CanonicalForm::mod ( const CanonicalForm & cf ) |
---|
882 | { |
---|
883 | int what = is_imm( value ); |
---|
884 | if ( what ) { |
---|
885 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
886 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
887 | value = imm_mod_p( value, cf.value ); |
---|
888 | else if ( what == GFMARK ) |
---|
889 | value = imm_mod_gf( value, cf.value ); |
---|
890 | else if ( what ) |
---|
891 | value = imm_mod( value, cf.value ); |
---|
892 | else { |
---|
893 | InternalCF * dummy = cf.value->copyObject(); |
---|
894 | value = dummy->modcoeff( value, true ); |
---|
895 | } |
---|
896 | } |
---|
897 | else if ( is_imm( cf.value ) ) |
---|
898 | value = value->modcoeff( cf.value, false ); |
---|
899 | else if ( value->level() == cf.value->level() ) { |
---|
900 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
901 | value = value->modsame( cf.value ); |
---|
902 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
903 | value = value->modcoeff( cf.value, false ); |
---|
904 | else { |
---|
905 | InternalCF * dummy = cf.value->copyObject(); |
---|
906 | dummy = dummy->modcoeff( value, true ); |
---|
907 | if ( value->deleteObject() ) delete value; |
---|
908 | value = dummy; |
---|
909 | } |
---|
910 | } |
---|
911 | else if ( level() > cf.level() ) |
---|
912 | value = value->modcoeff( cf.value, false ); |
---|
913 | else { |
---|
914 | InternalCF * dummy = cf.value->copyObject(); |
---|
915 | dummy = dummy->modcoeff( value, true ); |
---|
916 | if ( value->deleteObject() ) delete value; |
---|
917 | value = dummy; |
---|
918 | } |
---|
919 | return *this; |
---|
920 | } |
---|
921 | |
---|
922 | void |
---|
923 | divrem ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r ) |
---|
924 | { |
---|
925 | InternalCF * qq = 0, * rr = 0; |
---|
926 | int what = is_imm( f.value ); |
---|
927 | if ( what ) |
---|
928 | if ( is_imm( g.value ) ) { |
---|
929 | if ( what == FFMARK ) |
---|
930 | imm_divrem_p( f.value, g.value, qq, rr ); |
---|
931 | else if ( what == GFMARK ) |
---|
932 | imm_divrem_gf( f.value, g.value, qq, rr ); |
---|
933 | else |
---|
934 | imm_divrem( f.value, g.value, qq, rr ); |
---|
935 | } |
---|
936 | else |
---|
937 | g.value->divremcoeff( f.value, qq, rr, true ); |
---|
938 | else if ( (what=is_imm( g.value )) ) |
---|
939 | f.value->divremcoeff( g.value, qq, rr, false ); |
---|
940 | else if ( f.value->level() == g.value->level() ) |
---|
941 | if ( f.value->levelcoeff() == g.value->levelcoeff() ) |
---|
942 | f.value->divremsame( g.value, qq, rr ); |
---|
943 | else if ( f.value->levelcoeff() > g.value->levelcoeff() ) |
---|
944 | f.value->divremcoeff( g.value, qq, rr, false ); |
---|
945 | else |
---|
946 | g.value->divremcoeff( f.value, qq, rr, true ); |
---|
947 | else if ( f.value->level() > g.value->level() ) |
---|
948 | f.value->divremcoeff( g.value, qq, rr, false ); |
---|
949 | else |
---|
950 | g.value->divremcoeff( f.value, qq, rr, true ); |
---|
951 | ASSERT( qq != 0 && rr != 0, "error in divrem" ); |
---|
952 | q = CanonicalForm( qq ); |
---|
953 | r = CanonicalForm( rr ); |
---|
954 | } |
---|
955 | |
---|
956 | bool |
---|
957 | divremt ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r ) |
---|
958 | { |
---|
959 | InternalCF * qq = 0, * rr = 0; |
---|
960 | int what = is_imm( f.value ); |
---|
961 | bool result = true; |
---|
962 | if ( what ) |
---|
963 | if ( is_imm( g.value ) ) { |
---|
964 | if ( what == FFMARK ) |
---|
965 | imm_divrem_p( f.value, g.value, qq, rr ); |
---|
966 | else if ( what == GFMARK ) |
---|
967 | imm_divrem_gf( f.value, g.value, qq, rr ); |
---|
968 | else |
---|
969 | imm_divrem( f.value, g.value, qq, rr ); |
---|
970 | } |
---|
971 | else |
---|
972 | result = g.value->divremcoefft( f.value, qq, rr, true ); |
---|
973 | else if ( (what=is_imm( g.value )) ) |
---|
974 | result = f.value->divremcoefft( g.value, qq, rr, false ); |
---|
975 | else if ( f.value->level() == g.value->level() ) |
---|
976 | if ( f.value->levelcoeff() == g.value->levelcoeff() ) |
---|
977 | result = f.value->divremsamet( g.value, qq, rr ); |
---|
978 | else if ( f.value->levelcoeff() > g.value->levelcoeff() ) |
---|
979 | result = f.value->divremcoefft( g.value, qq, rr, false ); |
---|
980 | else |
---|
981 | result = g.value->divremcoefft( f.value, qq, rr, true ); |
---|
982 | else if ( f.value->level() > g.value->level() ) |
---|
983 | result = f.value->divremcoefft( g.value, qq, rr, false ); |
---|
984 | else |
---|
985 | result = g.value->divremcoefft( f.value, qq, rr, true ); |
---|
986 | if ( result ) { |
---|
987 | ASSERT( qq != 0 && rr != 0, "error in divrem" ); |
---|
988 | q = CanonicalForm( qq ); |
---|
989 | r = CanonicalForm( rr ); |
---|
990 | } |
---|
991 | else { |
---|
992 | q = 0; r = 0; |
---|
993 | } |
---|
994 | return result; |
---|
995 | } |
---|
996 | |
---|
997 | //same as divremt but handles zero divisors in case we are in Z_p[x]/(f) where f is not irreducible |
---|
998 | bool |
---|
999 | tryDivremt ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r, const CanonicalForm& M, bool& fail ) |
---|
1000 | { |
---|
1001 | ASSERT (getCharacteristic() > 0, "expected positive characteristic"); |
---|
1002 | ASSERT (!getReduce (M.mvar()), "do not reduce modulo M"); |
---|
1003 | fail= false; |
---|
1004 | InternalCF * qq = 0, * rr = 0; |
---|
1005 | int what = is_imm( f.value ); |
---|
1006 | bool result = true; |
---|
1007 | if ( what ) |
---|
1008 | if ( is_imm( g.value ) ) { |
---|
1009 | if ( what == FFMARK ) |
---|
1010 | imm_divrem_p( f.value, g.value, qq, rr ); |
---|
1011 | else if ( what == GFMARK ) |
---|
1012 | imm_divrem_gf( f.value, g.value, qq, rr ); |
---|
1013 | } |
---|
1014 | else |
---|
1015 | result = g.value->tryDivremcoefft( f.value, qq, rr, true, M, fail ); |
---|
1016 | else if ( (what=is_imm( g.value )) ) |
---|
1017 | result = f.value->tryDivremcoefft( g.value, qq, rr, false, M, fail ); |
---|
1018 | else if ( f.value->level() == g.value->level() ) |
---|
1019 | if ( f.value->levelcoeff() == g.value->levelcoeff() ) |
---|
1020 | result = f.value->tryDivremsamet( g.value, qq, rr, M, fail ); |
---|
1021 | else if ( f.value->levelcoeff() > g.value->levelcoeff() ) |
---|
1022 | result = f.value->tryDivremcoefft( g.value, qq, rr, false, M, fail ); |
---|
1023 | else |
---|
1024 | result = g.value->tryDivremcoefft( f.value, qq, rr, true, M, fail ); |
---|
1025 | else if ( f.value->level() > g.value->level() ) |
---|
1026 | result = f.value->tryDivremcoefft( g.value, qq, rr, false, M, fail ); |
---|
1027 | else |
---|
1028 | result = g.value->tryDivremcoefft( f.value, qq, rr, true, M, fail ); |
---|
1029 | if (fail) |
---|
1030 | { |
---|
1031 | q= 0; |
---|
1032 | r= 0; |
---|
1033 | return false; |
---|
1034 | } |
---|
1035 | if ( result ) { |
---|
1036 | ASSERT( qq != 0 && rr != 0, "error in divrem" ); |
---|
1037 | q = CanonicalForm( qq ); |
---|
1038 | r = CanonicalForm( rr ); |
---|
1039 | q= reduce (q, M); |
---|
1040 | r= reduce (r, M); |
---|
1041 | } |
---|
1042 | else { |
---|
1043 | q = 0; r = 0; |
---|
1044 | } |
---|
1045 | return result; |
---|
1046 | } |
---|
1047 | |
---|
1048 | //}}} |
---|
1049 | |
---|
1050 | //{{{ CanonicalForm CanonicalForm::operator () ( f ), operator () ( f, v ) const |
---|
1051 | //{{{ docu |
---|
1052 | // |
---|
1053 | // operator ()() - evaluation operator. |
---|
1054 | // |
---|
1055 | // Both operators return CO if CO is in a base domain. |
---|
1056 | // |
---|
1057 | // operator () ( f ) returns CO with f inserted for the main |
---|
1058 | // variable. Elements in an algebraic extension are considered |
---|
1059 | // polynomials. |
---|
1060 | // |
---|
1061 | // operator () ( f, v ) returns CO with f inserted for v. |
---|
1062 | // Elements in an algebraic extension are considered polynomials |
---|
1063 | // and v may be an algebraic variable. |
---|
1064 | // |
---|
1065 | //}}} |
---|
1066 | CanonicalForm |
---|
1067 | CanonicalForm::operator () ( const CanonicalForm & f ) const |
---|
1068 | { |
---|
1069 | if ( is_imm( value ) || value->inBaseDomain() ) |
---|
1070 | return *this; |
---|
1071 | else { |
---|
1072 | #if 0 |
---|
1073 | CFIterator i = *this; |
---|
1074 | int lastExp = i.exp(); |
---|
1075 | CanonicalForm result = i.coeff(); |
---|
1076 | i++; |
---|
1077 | while ( i.hasTerms() ) { |
---|
1078 | if ( (lastExp - i.exp()) == 1 ) |
---|
1079 | result *= f; |
---|
1080 | else |
---|
1081 | result *= power( f, lastExp - i.exp() ); |
---|
1082 | result += i.coeff(); |
---|
1083 | lastExp = i.exp(); |
---|
1084 | i++; |
---|
1085 | } |
---|
1086 | if ( lastExp != 0 ) |
---|
1087 | result *= power( f, lastExp ); |
---|
1088 | #else |
---|
1089 | CFIterator i = *this; |
---|
1090 | int lastExp = i.exp(); |
---|
1091 | CanonicalForm result = i.coeff(); |
---|
1092 | i++; |
---|
1093 | while ( i.hasTerms() ) |
---|
1094 | { |
---|
1095 | int i_exp=i.exp(); |
---|
1096 | if ( (lastExp - i_exp /* i.exp()*/) == 1 ) |
---|
1097 | result *= f; |
---|
1098 | else |
---|
1099 | result *= power( f, lastExp - i_exp /*i.exp()*/ ); |
---|
1100 | result += i.coeff(); |
---|
1101 | lastExp = i_exp /*i.exp()*/; |
---|
1102 | i++; |
---|
1103 | } |
---|
1104 | if ( lastExp != 0 ) |
---|
1105 | result *= power( f, lastExp ); |
---|
1106 | #endif |
---|
1107 | return result; |
---|
1108 | } |
---|
1109 | } |
---|
1110 | |
---|
1111 | CanonicalForm |
---|
1112 | CanonicalForm::operator () ( const CanonicalForm & f, const Variable & v ) const |
---|
1113 | { |
---|
1114 | if ( is_imm( value ) || value->inBaseDomain() ) |
---|
1115 | return *this; |
---|
1116 | |
---|
1117 | Variable x = value->variable(); |
---|
1118 | if ( v > x ) |
---|
1119 | return *this; |
---|
1120 | else if ( v == x ) |
---|
1121 | return (*this)( f ); |
---|
1122 | else { |
---|
1123 | // v is less than main variable of f |
---|
1124 | CanonicalForm result = 0; |
---|
1125 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
---|
1126 | result += i.coeff()( f, v ) * power( x, i.exp() ); |
---|
1127 | return result; |
---|
1128 | } |
---|
1129 | } |
---|
1130 | //}}} |
---|
1131 | |
---|
1132 | //{{{ CanonicalForm CanonicalForm::operator [] ( int i ) const |
---|
1133 | //{{{ docu |
---|
1134 | // |
---|
1135 | // operator []() - return i'th coefficient from CO. |
---|
1136 | // |
---|
1137 | // Returns CO if CO is in a base domain and i equals zero. |
---|
1138 | // Returns zero (from the current domain) if CO is in a base |
---|
1139 | // domain and i is larger than zero. Otherwise, returns the |
---|
1140 | // coefficient to x^i in CO (if x denotes the main variable of |
---|
1141 | // CO) or zero if CO does not contain x^i. Elements in an |
---|
1142 | // algebraic extension are considered polynomials. i should be |
---|
1143 | // larger or equal zero. |
---|
1144 | // |
---|
1145 | // Note: Never use a loop like |
---|
1146 | // |
---|
1147 | // for ( int i = degree( f ); i >= 0; i-- ) |
---|
1148 | // foo( i, f[ i ] ); |
---|
1149 | // |
---|
1150 | // which is much slower than |
---|
1151 | // |
---|
1152 | // for ( int i = degree( f ), CFIterator I = f; I.hasTerms(); I++ ) { |
---|
1153 | // // fill gap with zeroes |
---|
1154 | // for ( ; i > I.exp(); i-- ) |
---|
1155 | // foo( i, 0 ); |
---|
1156 | // // at this point, i == I.exp() |
---|
1157 | // foo( i, i.coeff() ); |
---|
1158 | // i--; |
---|
1159 | // } |
---|
1160 | // // work through trailing zeroes |
---|
1161 | // for ( ; i >= 0; i-- ) |
---|
1162 | // foo( i, 0 ); |
---|
1163 | // |
---|
1164 | //}}} |
---|
1165 | CanonicalForm |
---|
1166 | CanonicalForm::operator [] ( int i ) const |
---|
1167 | { |
---|
1168 | ASSERT( i >= 0, "index to operator [] less than zero" ); |
---|
1169 | if ( is_imm( value ) ) |
---|
1170 | if ( i == 0 ) |
---|
1171 | return *this; |
---|
1172 | else |
---|
1173 | return CanonicalForm( 0 ); |
---|
1174 | else |
---|
1175 | return value->coeff( i ); |
---|
1176 | } |
---|
1177 | //}}} |
---|
1178 | |
---|
1179 | //{{{ CanonicalForm CanonicalForm::deriv (), deriv ( x ) |
---|
1180 | //{{{ docu |
---|
1181 | // |
---|
1182 | // deriv() - return the formal derivation of CO. |
---|
1183 | // |
---|
1184 | // deriv() derives CO with respect to its main variable. Returns |
---|
1185 | // zero from the current domain if f is in a coefficient domain. |
---|
1186 | // |
---|
1187 | // deriv( x ) derives CO with respect to x. x should be a |
---|
1188 | // polynomial variable. Returns zero from the current domain if |
---|
1189 | // f is in a coefficient domain. |
---|
1190 | // |
---|
1191 | // See also: ::deriv() |
---|
1192 | // |
---|
1193 | //}}} |
---|
1194 | CanonicalForm |
---|
1195 | CanonicalForm::deriv () const |
---|
1196 | { |
---|
1197 | if ( is_imm( value ) || value->inCoeffDomain() ) |
---|
1198 | return CanonicalForm( 0 ); |
---|
1199 | else { |
---|
1200 | CanonicalForm result = 0; |
---|
1201 | Variable x = value->variable(); |
---|
1202 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
---|
1203 | if ( i.exp() > 0 ) |
---|
1204 | result += power( x, i.exp()-1 ) * i.coeff() * i.exp(); |
---|
1205 | return result; |
---|
1206 | } |
---|
1207 | } |
---|
1208 | |
---|
1209 | CanonicalForm |
---|
1210 | CanonicalForm::deriv ( const Variable & x ) const |
---|
1211 | { |
---|
1212 | ASSERT( x.level() > 0, "cannot derive with respect to algebraic variables" ); |
---|
1213 | if ( is_imm( value ) || value->inCoeffDomain() ) |
---|
1214 | return CanonicalForm( 0 ); |
---|
1215 | |
---|
1216 | Variable y = value->variable(); |
---|
1217 | if ( x > y ) |
---|
1218 | return CanonicalForm( 0 ); |
---|
1219 | else if ( x == y ) |
---|
1220 | return deriv(); |
---|
1221 | else { |
---|
1222 | CanonicalForm result = 0; |
---|
1223 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
---|
1224 | result += i.coeff().deriv( x ) * power( y, i.exp() ); |
---|
1225 | return result; |
---|
1226 | } |
---|
1227 | } |
---|
1228 | //}}} |
---|
1229 | |
---|
1230 | //{{{ int CanonicalForm::sign () const |
---|
1231 | //{{{ docu |
---|
1232 | // |
---|
1233 | // sign() - return sign of CO. |
---|
1234 | // |
---|
1235 | // If CO is an integer or a rational number, the sign is defined |
---|
1236 | // as usual. If CO is an element of a prime power domain or of |
---|
1237 | // FF(p) and SW_SYMMETRIC_FF is on, the sign of CO is the sign of |
---|
1238 | // the symmetric representation of CO. If CO is in GF(q) or in |
---|
1239 | // FF(p) and SW_SYMMETRIC_FF is off, the sign of CO is zero iff |
---|
1240 | // CO is zero, otherwise the sign is one. |
---|
1241 | // |
---|
1242 | // If CO is a polynomial or in an extension of one of the base |
---|
1243 | // domains, the sign of CO is the sign of its leading |
---|
1244 | // coefficient. |
---|
1245 | // |
---|
1246 | // See also: InternalCF::sign(), InternalInteger::sign(), |
---|
1247 | // InternalPrimePower::sign(), InternalRational::sign(), |
---|
1248 | // InternalPoly::sign(), imm_sign(), gf_sign() |
---|
1249 | // |
---|
1250 | //}}} |
---|
1251 | int |
---|
1252 | CanonicalForm::sign () const |
---|
1253 | { |
---|
1254 | if ( is_imm( value ) ) |
---|
1255 | return imm_sign( value ); |
---|
1256 | else |
---|
1257 | return value->sign(); |
---|
1258 | } |
---|
1259 | //}}} |
---|
1260 | |
---|
1261 | //{{{ CanonicalForm CanonicalForm::sqrt () const |
---|
1262 | //{{{ docu |
---|
1263 | // |
---|
1264 | // sqrt() - calculate integer square root. |
---|
1265 | // |
---|
1266 | // CO has to be an integer greater or equal zero. Returns the |
---|
1267 | // largest integer less or equal sqrt(CO). |
---|
1268 | // |
---|
1269 | // In the immediate case, we use the newton method to find the |
---|
1270 | // root. The algorithm is from H. Cohen - 'A Course in |
---|
1271 | // Computational Algebraic Number Theory', ch. 1.7.1. |
---|
1272 | // |
---|
1273 | // See also: InternalCF::sqrt(), InternalInteger::sqrt(), ::sqrt() |
---|
1274 | // |
---|
1275 | //}}} |
---|
1276 | CanonicalForm |
---|
1277 | CanonicalForm::sqrt () const |
---|
1278 | { |
---|
1279 | if ( is_imm( value ) ) { |
---|
1280 | ASSERT( is_imm( value ) == INTMARK, "sqrt() not implemented" ); |
---|
1281 | int n = imm2int( value ); |
---|
1282 | ASSERT( n >= 0, "arg to sqrt() less than zero" ); |
---|
1283 | if ( n == 0 || n == 1 ) |
---|
1284 | return CanonicalForm( n ); |
---|
1285 | else { |
---|
1286 | int x, y = n; |
---|
1287 | do { |
---|
1288 | x = y; |
---|
1289 | // the intermediate result may not fit into an |
---|
1290 | // integer, but the result does |
---|
1291 | y = (unsigned int)(x + n/x)/2; |
---|
1292 | } while ( y < x ); |
---|
1293 | return CanonicalForm( x ); |
---|
1294 | } |
---|
1295 | } |
---|
1296 | else |
---|
1297 | return CanonicalForm( value->sqrt() ); |
---|
1298 | } |
---|
1299 | //}}} |
---|
1300 | |
---|
1301 | //{{{ int CanonicalForm::ilog2 () const |
---|
1302 | //{{{ docu |
---|
1303 | // |
---|
1304 | // ilog2() - integer logarithm to base 2. |
---|
1305 | // |
---|
1306 | // Returns the largest integer less or equal logarithm of CO to |
---|
1307 | // base 2. CO should be a positive integer. |
---|
1308 | // |
---|
1309 | // See also: InternalCF::ilog2(), InternalInteger::ilog2(), ::ilog2() |
---|
1310 | // |
---|
1311 | //}}} |
---|
1312 | int |
---|
1313 | CanonicalForm::ilog2 () const |
---|
1314 | { |
---|
1315 | if ( is_imm( value ) ) |
---|
1316 | { |
---|
1317 | ASSERT( is_imm( value ) == INTMARK, "ilog2() not implemented" ); |
---|
1318 | int a = imm2int( value ); |
---|
1319 | ASSERT( a > 0, "arg to ilog2() less or equal zero" ); |
---|
1320 | return ::ilog2(a); |
---|
1321 | } |
---|
1322 | else |
---|
1323 | return value->ilog2(); |
---|
1324 | } |
---|
1325 | //}}} |
---|
1326 | |
---|
1327 | //{{{ bool operator ==, operator != ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1328 | //{{{ docu |
---|
1329 | // |
---|
1330 | // operator ==(), operator !=() - compare canonical forms on |
---|
1331 | // (in)equality. |
---|
1332 | // |
---|
1333 | // operator ==() returns true iff lhs equals rhs. |
---|
1334 | // operator !=() returns true iff lhs does not equal rhs. |
---|
1335 | // |
---|
1336 | // This is the point in factory where we essentially use that |
---|
1337 | // CanonicalForms in fact are canonical. There must not be two |
---|
1338 | // different representations of the same mathematical object, |
---|
1339 | // otherwise, such (in)equality will not be recognized by these |
---|
1340 | // operators. In other word, we rely on the fact that structural |
---|
1341 | // different factory objects in any case represent different |
---|
1342 | // mathematical objects. |
---|
1343 | // |
---|
1344 | // So we use the following procedure to test on equality (and |
---|
1345 | // analogously on inequality). First, we check whether lhs.value |
---|
1346 | // equals rhs.value. If so we are ready and return true. |
---|
1347 | // Second, if one of the operands is immediate, but the other one |
---|
1348 | // not, we return false. Third, if the operand's levels differ |
---|
1349 | // we return false. Fourth, if the operand's levelcoeffs differ |
---|
1350 | // we return false. At last, we call the corresponding internal |
---|
1351 | // method to compare both operands. |
---|
1352 | // |
---|
1353 | // Both operands should have coefficients from the same base domain. |
---|
1354 | // |
---|
1355 | // Note: To compare with the zero or the unit of the current domain, |
---|
1356 | // you better use the methods `CanonicalForm::isZero()' or |
---|
1357 | // `CanonicalForm::isOne()', resp., than something like `f == 0', |
---|
1358 | // since the latter is quite a lot slower. |
---|
1359 | // |
---|
1360 | // See also: InternalCF::comparesame(), |
---|
1361 | // InternalInteger::comparesame(), InternalRational::comparesame(), |
---|
1362 | // InternalPrimePower::comparesame(), InternalPoly::comparesame() |
---|
1363 | // |
---|
1364 | //}}} |
---|
1365 | bool |
---|
1366 | operator == ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1367 | { |
---|
1368 | if ( lhs.value == rhs.value ) |
---|
1369 | return true; |
---|
1370 | else if ( is_imm( rhs.value ) || is_imm( lhs.value ) ) { |
---|
1371 | ASSERT( ! is_imm( rhs.value ) || |
---|
1372 | ! is_imm( lhs.value ) || |
---|
1373 | is_imm( rhs.value ) == is_imm( lhs.value ), |
---|
1374 | "incompatible operands" ); |
---|
1375 | return false; |
---|
1376 | } |
---|
1377 | else if ( lhs.value->level() != rhs.value->level() ) |
---|
1378 | return false; |
---|
1379 | else if ( lhs.value->levelcoeff() != rhs.value->levelcoeff() ) |
---|
1380 | return false; |
---|
1381 | else |
---|
1382 | return rhs.value->comparesame( lhs.value ) == 0; |
---|
1383 | } |
---|
1384 | |
---|
1385 | bool |
---|
1386 | operator != ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1387 | { |
---|
1388 | if ( lhs.value == rhs.value ) |
---|
1389 | return false; |
---|
1390 | else if ( is_imm( rhs.value ) || is_imm( lhs.value ) ) { |
---|
1391 | ASSERT( ! is_imm( rhs.value ) || |
---|
1392 | ! is_imm( lhs.value ) || |
---|
1393 | is_imm( rhs.value ) == is_imm( lhs.value ), |
---|
1394 | "incompatible operands" ); |
---|
1395 | return true; |
---|
1396 | } |
---|
1397 | else if ( lhs.value->level() != rhs.value->level() ) |
---|
1398 | return true; |
---|
1399 | else if ( lhs.value->levelcoeff() != rhs.value->levelcoeff() ) |
---|
1400 | return true; |
---|
1401 | else return rhs.value->comparesame( lhs.value ) != 0; |
---|
1402 | } |
---|
1403 | //}}} |
---|
1404 | |
---|
1405 | //{{{ bool operator >, operator < ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1406 | //{{{ docu |
---|
1407 | // |
---|
1408 | // operator >(), operator <() - compare canonical forms. on size or |
---|
1409 | // level. |
---|
1410 | // |
---|
1411 | // The most common and most useful application of these operators |
---|
1412 | // is to compare two integers or rationals, of course. However, |
---|
1413 | // these operators are defined on all other base domains and on |
---|
1414 | // polynomials, too. From a mathematical point of view this may |
---|
1415 | // seem meaningless, since there is no ordering on finite fields |
---|
1416 | // or on polynomials respecting the algebraic structure. |
---|
1417 | // Nevertheless, from a programmer's point of view it may be |
---|
1418 | // sensible to order these objects, e.g. to sort them. |
---|
1419 | // |
---|
1420 | // Therefore, the ordering defined by these operators in any case |
---|
1421 | // is a total ordering which fulfills the law of trichotomy. |
---|
1422 | // |
---|
1423 | // It is clear how this is done in the case of the integers and |
---|
1424 | // the rationals. For finite fields, all you can say is that |
---|
1425 | // zero is the minimal element w.r.t. the ordering, the other |
---|
1426 | // elements are ordered in an arbitrary (but total!) way. For |
---|
1427 | // polynomials, you have an ordering derived from the |
---|
1428 | // lexicographical ordering of monomials. E.g. if lm(f) < lm(g) |
---|
1429 | // w.r.t. lexicographic ordering, then f < g. For more details, |
---|
1430 | // refer to the documentation of `InternalPoly::operator <()'. |
---|
1431 | // |
---|
1432 | // Both operands should have coefficients from the same base domain. |
---|
1433 | // |
---|
1434 | // The scheme how both operators are implemented is allmost the |
---|
1435 | // same as for the assignment operators (check for immediates, |
---|
1436 | // then check levels, then check levelcoeffs, then call the |
---|
1437 | // appropriate internal comparesame()/comparecoeff() method). |
---|
1438 | // For more information, confer to the overview for the |
---|
1439 | // arithmetic operators. |
---|
1440 | // |
---|
1441 | // See also: InternalCF::comparesame(), |
---|
1442 | // InternalInteger::comparesame(), InternalRational::comparesame(), |
---|
1443 | // InternalPrimePower::comparesame(), InternalPoly::comparesame(), |
---|
1444 | // InternalCF::comparecoeff(), InternalInteger::comparecoeff(), |
---|
1445 | // InternalRational::comparecoeff(), |
---|
1446 | // InternalPrimePower::comparecoeff(), InternalPoly::comparecoeff(), |
---|
1447 | // imm_cmp(), imm_cmp_p(), imm_cmp_gf() |
---|
1448 | // |
---|
1449 | //}}} |
---|
1450 | bool |
---|
1451 | operator > ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1452 | { |
---|
1453 | int what = is_imm( rhs.value ); |
---|
1454 | if ( is_imm( lhs.value ) ) { |
---|
1455 | ASSERT( ! what || (what == is_imm( lhs.value )), "incompatible operands" ); |
---|
1456 | if ( what == 0 ) |
---|
1457 | return rhs.value->comparecoeff( lhs.value ) < 0; |
---|
1458 | else if ( what == INTMARK ) |
---|
1459 | return imm_cmp( lhs.value, rhs.value ) > 0; |
---|
1460 | else if ( what == FFMARK ) |
---|
1461 | return imm_cmp_p( lhs.value, rhs.value ) > 0; |
---|
1462 | else |
---|
1463 | return imm_cmp_gf( lhs.value, rhs.value ) > 0; |
---|
1464 | } |
---|
1465 | else if ( what ) |
---|
1466 | return lhs.value->comparecoeff( rhs.value ) > 0; |
---|
1467 | else if ( lhs.value->level() == rhs.value->level() ) |
---|
1468 | if ( lhs.value->levelcoeff() == rhs.value->levelcoeff() ) |
---|
1469 | return lhs.value->comparesame( rhs.value ) > 0; |
---|
1470 | else if ( lhs.value->levelcoeff() > rhs.value->levelcoeff() ) |
---|
1471 | return lhs.value->comparecoeff( rhs.value ) > 0; |
---|
1472 | else |
---|
1473 | return rhs.value->comparecoeff( lhs.value ) < 0; |
---|
1474 | else |
---|
1475 | return lhs.value->level() > rhs.value->level(); |
---|
1476 | } |
---|
1477 | |
---|
1478 | bool |
---|
1479 | operator < ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1480 | { |
---|
1481 | int what = is_imm( rhs.value ); |
---|
1482 | if ( is_imm( lhs.value ) ) { |
---|
1483 | ASSERT( ! what || (what == is_imm( lhs.value )), "incompatible operands" ); |
---|
1484 | if ( what == 0 ) |
---|
1485 | return rhs.value->comparecoeff( lhs.value ) > 0; |
---|
1486 | else if ( what == INTMARK ) |
---|
1487 | return imm_cmp( lhs.value, rhs.value ) < 0; |
---|
1488 | else if ( what == FFMARK ) |
---|
1489 | return imm_cmp_p( lhs.value, rhs.value ) < 0; |
---|
1490 | else |
---|
1491 | return imm_cmp_gf( lhs.value, rhs.value ) < 0; |
---|
1492 | } |
---|
1493 | else if ( what ) |
---|
1494 | return lhs.value->comparecoeff( rhs.value ) < 0; |
---|
1495 | else if ( lhs.value->level() == rhs.value->level() ) |
---|
1496 | if ( lhs.value->levelcoeff() == rhs.value->levelcoeff() ) |
---|
1497 | return lhs.value->comparesame( rhs.value ) < 0; |
---|
1498 | else if ( lhs.value->levelcoeff() > rhs.value->levelcoeff() ) |
---|
1499 | return lhs.value->comparecoeff( rhs.value ) < 0; |
---|
1500 | else |
---|
1501 | return rhs.value->comparecoeff( lhs.value ) > 0; |
---|
1502 | else |
---|
1503 | return lhs.value->level() < rhs.value->level(); |
---|
1504 | } |
---|
1505 | //}}} |
---|
1506 | |
---|
1507 | //{{{ CanonicalForm bgcd ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
1508 | //{{{ docu |
---|
1509 | // |
---|
1510 | // bgcd() - return base coefficient gcd. |
---|
1511 | // |
---|
1512 | // If both f and g are integers and `SW_RATIONAL' is off the |
---|
1513 | // positive greatest common divisor of f and g is returned. |
---|
1514 | // Otherwise, if `SW_RATIONAL' is on or one of f and g is not an |
---|
1515 | // integer, the greatest common divisor is trivial: either zero |
---|
1516 | // if f and g equal zero or one (both from the current domain). |
---|
1517 | // |
---|
1518 | // f and g should come from one base domain which should be not |
---|
1519 | // the prime power domain. |
---|
1520 | // |
---|
1521 | // Implementation: |
---|
1522 | // |
---|
1523 | // CanonicalForm::bgcd() handles the immediate case with a |
---|
1524 | // standard euclidean algorithm. For the non-immediate cases |
---|
1525 | // `InternalCF::bgcdsame()' or `InternalCF::bgcdcoeff()', resp. are |
---|
1526 | // called following the usual level/levelcoeff approach. |
---|
1527 | // |
---|
1528 | // InternalCF::bgcdsame() and |
---|
1529 | // InternalCF::bgcdcoeff() throw an assertion ("not implemented") |
---|
1530 | // |
---|
1531 | // InternalInteger::bgcdsame() is a wrapper around `mpz_gcd()' |
---|
1532 | // which takes some care about immediate results and the sign |
---|
1533 | // of the result |
---|
1534 | // InternalInteger::bgcdcoeff() is a wrapper around |
---|
1535 | // `mpz_gcd_ui()' which takes some care about the sign |
---|
1536 | // of the result |
---|
1537 | // |
---|
1538 | // InternalRational::bgcdsame() and |
---|
1539 | // InternalRational::bgcdcoeff() always return one |
---|
1540 | // |
---|
1541 | //}}} |
---|
1542 | CanonicalForm |
---|
1543 | bgcd ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
1544 | { |
---|
1545 | // check immediate cases |
---|
1546 | int what = is_imm( g.value ); |
---|
1547 | if ( is_imm( f.value ) ) |
---|
1548 | { |
---|
1549 | ASSERT( ! what || (what == is_imm( f.value )), "incompatible operands" ); |
---|
1550 | if ( what == 0 ) |
---|
1551 | return g.value->bgcdcoeff( f.value ); |
---|
1552 | else if ( what == INTMARK && ! cf_glob_switches.isOn( SW_RATIONAL ) ) |
---|
1553 | { |
---|
1554 | // calculate gcd using standard integer |
---|
1555 | // arithmetic |
---|
1556 | int fInt = imm2int( f.value ); |
---|
1557 | int gInt = imm2int( g.value ); |
---|
1558 | |
---|
1559 | if ( fInt < 0 ) fInt = -fInt; |
---|
1560 | if ( gInt < 0 ) gInt = -gInt; |
---|
1561 | // swap fInt and gInt |
---|
1562 | if ( gInt > fInt ) |
---|
1563 | { |
---|
1564 | int swap = gInt; |
---|
1565 | gInt = fInt; |
---|
1566 | fInt = swap; |
---|
1567 | } |
---|
1568 | |
---|
1569 | // now, 0 <= gInt <= fInt. Start the loop. |
---|
1570 | while ( gInt ) |
---|
1571 | { |
---|
1572 | // calculate (fInt, gInt) = (gInt, fInt%gInt) |
---|
1573 | int r = fInt % gInt; |
---|
1574 | fInt = gInt; |
---|
1575 | gInt = r; |
---|
1576 | } |
---|
1577 | |
---|
1578 | return CanonicalForm( fInt ); |
---|
1579 | } |
---|
1580 | else |
---|
1581 | // we do not go for maximal speed for these stupid |
---|
1582 | // special cases |
---|
1583 | return CanonicalForm( f.isZero() && g.isZero() ? 0 : 1 ); |
---|
1584 | } |
---|
1585 | else if ( what ) |
---|
1586 | return f.value->bgcdcoeff( g.value ); |
---|
1587 | |
---|
1588 | int fLevel = f.value->level(); |
---|
1589 | int gLevel = g.value->level(); |
---|
1590 | |
---|
1591 | // check levels |
---|
1592 | if ( fLevel == gLevel ) |
---|
1593 | { |
---|
1594 | fLevel = f.value->levelcoeff(); |
---|
1595 | gLevel = g.value->levelcoeff(); |
---|
1596 | |
---|
1597 | // check levelcoeffs |
---|
1598 | if ( fLevel == gLevel ) |
---|
1599 | return f.value->bgcdsame( g.value ); |
---|
1600 | else if ( fLevel < gLevel ) |
---|
1601 | return g.value->bgcdcoeff( f.value ); |
---|
1602 | else |
---|
1603 | return f.value->bgcdcoeff( g.value ); |
---|
1604 | } |
---|
1605 | else if ( fLevel < gLevel ) |
---|
1606 | return g.value->bgcdcoeff( f.value ); |
---|
1607 | else |
---|
1608 | return f.value->bgcdcoeff( g.value ); |
---|
1609 | } |
---|
1610 | //}}} |
---|
1611 | |
---|
1612 | //{{{ CanonicalForm bextgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
---|
1613 | //{{{ docu |
---|
1614 | // |
---|
1615 | // bextgcd() - return base coefficient extended gcd. |
---|
1616 | // |
---|
1617 | //}}} |
---|
1618 | CanonicalForm |
---|
1619 | bextgcd ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & a, CanonicalForm & b ) |
---|
1620 | { |
---|
1621 | // check immediate cases |
---|
1622 | int what = is_imm( g.value ); |
---|
1623 | if ( is_imm( f.value ) ) { |
---|
1624 | ASSERT( ! what || (what == is_imm( f.value )), "incompatible operands" ); |
---|
1625 | if ( what == 0 ) |
---|
1626 | return g.value->bextgcdcoeff( f.value, b, a ); |
---|
1627 | else if ( what == INTMARK && ! cf_glob_switches.isOn( SW_RATIONAL ) ) { |
---|
1628 | // calculate extended gcd using standard integer |
---|
1629 | // arithmetic |
---|
1630 | int fInt = imm2int( f.value ); |
---|
1631 | int gInt = imm2int( g.value ); |
---|
1632 | |
---|
1633 | // to avoid any system dpendencies with `%', we work |
---|
1634 | // with positive numbers only. To a pity, we have to |
---|
1635 | // redo all the checks when assigning to a and b. |
---|
1636 | if ( fInt < 0 ) fInt = -fInt; |
---|
1637 | if ( gInt < 0 ) gInt = -gInt; |
---|
1638 | // swap fInt and gInt |
---|
1639 | if ( gInt > fInt ) { |
---|
1640 | int swap = gInt; |
---|
1641 | gInt = fInt; |
---|
1642 | fInt = swap; |
---|
1643 | } |
---|
1644 | |
---|
1645 | int u = 1; int v = 0; |
---|
1646 | int uNext = 0; int vNext = 1; |
---|
1647 | |
---|
1648 | // at any step, we have: |
---|
1649 | // fInt_0 * u + gInt_0 * v = fInt |
---|
1650 | // fInt_0 * uNext + gInt_0 * vNext = gInt |
---|
1651 | // where fInt_0 and gInt_0 denote the values of fint |
---|
1652 | // and gInt, resp., at the beginning |
---|
1653 | while ( gInt ) { |
---|
1654 | int r = fInt % gInt; |
---|
1655 | int q = fInt / gInt; |
---|
1656 | int uSwap = u - q * uNext; |
---|
1657 | int vSwap = v - q * vNext; |
---|
1658 | |
---|
1659 | // update variables |
---|
1660 | fInt = gInt; |
---|
1661 | gInt = r; |
---|
1662 | u = uNext; v = vNext; |
---|
1663 | uNext = uSwap; vNext = vSwap; |
---|
1664 | } |
---|
1665 | |
---|
1666 | // now, assign to a and b |
---|
1667 | int fTest = imm2int( f.value ); |
---|
1668 | int gTest = imm2int( g.value ); |
---|
1669 | if ( gTest > fTest ) { |
---|
1670 | a = v; b = u; |
---|
1671 | } else { |
---|
1672 | a = u; b = v; |
---|
1673 | } |
---|
1674 | if ( fTest < 0 ) a = -a; |
---|
1675 | if ( gTest < 0 ) b = -b; |
---|
1676 | return CanonicalForm( fInt ); |
---|
1677 | } else |
---|
1678 | // stupid special cases |
---|
1679 | if ( ! f.isZero() ) { |
---|
1680 | a = 1/f; b = 0; return CanonicalForm( 1 ); |
---|
1681 | } else if ( ! g.isZero() ) { |
---|
1682 | a = 0; b = 1/g; return CanonicalForm( 1 ); |
---|
1683 | } else { |
---|
1684 | a = 0; b = 0; return CanonicalForm( 0 ); |
---|
1685 | } |
---|
1686 | } |
---|
1687 | else if ( what ) |
---|
1688 | return f.value->bextgcdcoeff( g.value, a, b ); |
---|
1689 | |
---|
1690 | int fLevel = f.value->level(); |
---|
1691 | int gLevel = g.value->level(); |
---|
1692 | |
---|
1693 | // check levels |
---|
1694 | if ( fLevel == gLevel ) { |
---|
1695 | fLevel = f.value->levelcoeff(); |
---|
1696 | gLevel = g.value->levelcoeff(); |
---|
1697 | |
---|
1698 | // check levelcoeffs |
---|
1699 | if ( fLevel == gLevel ) |
---|
1700 | return f.value->bextgcdsame( g.value, a, b ); |
---|
1701 | else if ( fLevel < gLevel ) |
---|
1702 | return g.value->bextgcdcoeff( f.value, b, a ); |
---|
1703 | else |
---|
1704 | return f.value->bextgcdcoeff( g.value, a, b ); |
---|
1705 | } |
---|
1706 | else if ( fLevel < gLevel ) |
---|
1707 | return g.value->bextgcdcoeff( f.value, b, a ); |
---|
1708 | else |
---|
1709 | return f.value->bextgcdcoeff( g.value, a, b ); |
---|
1710 | } |
---|
1711 | //}}} |
---|
1712 | |
---|
1713 | CanonicalForm |
---|
1714 | blcm ( const CanonicalForm & f, const CanonicalForm & g ) |
---|
1715 | { |
---|
1716 | if ( f.isZero() || g.isZero() ) |
---|
1717 | return CanonicalForm( 0 ); |
---|
1718 | /* |
---|
1719 | else if (f.isOne()) |
---|
1720 | return g; |
---|
1721 | else if (g.isOne()) |
---|
1722 | return f; |
---|
1723 | */ |
---|
1724 | else |
---|
1725 | return (f / bgcd( f, g )) * g; |
---|
1726 | } |
---|
1727 | |
---|
1728 | //{{{ input/output |
---|
1729 | #ifndef NOSTREAMIO |
---|
1730 | void |
---|
1731 | CanonicalForm::print( OSTREAM & os, char * str ) const |
---|
1732 | { |
---|
1733 | if ( is_imm( value ) ) |
---|
1734 | imm_print( os, value, str ); |
---|
1735 | else |
---|
1736 | value->print( os, str ); |
---|
1737 | } |
---|
1738 | |
---|
1739 | void |
---|
1740 | CanonicalForm::print( OSTREAM & os ) const |
---|
1741 | { |
---|
1742 | if ( is_imm( value ) ) |
---|
1743 | imm_print( os, value, "" ); |
---|
1744 | else |
---|
1745 | value->print( os, "" ); |
---|
1746 | } |
---|
1747 | |
---|
1748 | OSTREAM& |
---|
1749 | operator << ( OSTREAM & os, const CanonicalForm & cf ) |
---|
1750 | { |
---|
1751 | cf.print( os, "" ); |
---|
1752 | return os; |
---|
1753 | } |
---|
1754 | |
---|
1755 | ISTREAM& |
---|
1756 | operator >> ( ISTREAM & is, CanonicalForm & cf ) |
---|
1757 | { |
---|
1758 | cf = readCF( is ); |
---|
1759 | return is; |
---|
1760 | } |
---|
1761 | #endif /* NOSTREAMIO */ |
---|
1762 | //}}} |
---|
1763 | |
---|
1764 | //{{{ genCoeff(), genOne(), genZero() |
---|
1765 | CanonicalForm |
---|
1766 | CanonicalForm::genCoeff( int type, int i ) |
---|
1767 | { |
---|
1768 | return CanonicalForm( CFFactory::basic( type, i ) ); |
---|
1769 | } |
---|
1770 | |
---|
1771 | CanonicalForm |
---|
1772 | CanonicalForm::genZero() const |
---|
1773 | { |
---|
1774 | int what = is_imm( value ); |
---|
1775 | if ( what == FFMARK ) |
---|
1776 | return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 0 ) ); |
---|
1777 | else if ( what == GFMARK ) |
---|
1778 | return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 0 ) ); |
---|
1779 | else if ( what ) |
---|
1780 | return CanonicalForm( CFFactory::basic( IntegerDomain, 0 ) ); |
---|
1781 | else |
---|
1782 | return CanonicalForm( value->genZero() ); |
---|
1783 | } |
---|
1784 | |
---|
1785 | CanonicalForm |
---|
1786 | CanonicalForm::genOne() const |
---|
1787 | { |
---|
1788 | int what = is_imm( value ); |
---|
1789 | if ( what == FFMARK ) |
---|
1790 | return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 1 ) ); |
---|
1791 | else if ( what == GFMARK ) |
---|
1792 | return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 1 ) ); |
---|
1793 | else if ( what ) |
---|
1794 | return CanonicalForm( CFFactory::basic( IntegerDomain, 1 ) ); |
---|
1795 | else |
---|
1796 | return CanonicalForm( value->genOne() ); |
---|
1797 | } |
---|
1798 | //}}} |
---|
1799 | |
---|
1800 | //{{{ exponentiation |
---|
1801 | CanonicalForm |
---|
1802 | power ( const CanonicalForm & f, int n ) |
---|
1803 | { |
---|
1804 | ASSERT( n >= 0, "illegal exponent" ); |
---|
1805 | if ( f.isZero() ) |
---|
1806 | return 0; |
---|
1807 | else if ( f.isOne() ) |
---|
1808 | return f; |
---|
1809 | else if ( f == -1 ) |
---|
1810 | { |
---|
1811 | if ( n % 2 == 0 ) |
---|
1812 | return 1; |
---|
1813 | else |
---|
1814 | return -1; |
---|
1815 | } |
---|
1816 | else if ( n == 0 ) |
---|
1817 | return 1; |
---|
1818 | |
---|
1819 | //else if (f.inGF()) |
---|
1820 | //{ |
---|
1821 | //} |
---|
1822 | else |
---|
1823 | { |
---|
1824 | CanonicalForm g,h; |
---|
1825 | h=f; |
---|
1826 | while(n%2==0) |
---|
1827 | { |
---|
1828 | h*=h; |
---|
1829 | n/=2; |
---|
1830 | } |
---|
1831 | g=h; |
---|
1832 | while(1) |
---|
1833 | { |
---|
1834 | n/=2; |
---|
1835 | if(n==0) |
---|
1836 | return g; |
---|
1837 | h*=h; |
---|
1838 | if(n%2!=0) g*=h; |
---|
1839 | } |
---|
1840 | } |
---|
1841 | } |
---|
1842 | |
---|
1843 | CanonicalForm |
---|
1844 | power ( const Variable & v, int n ) |
---|
1845 | { |
---|
1846 | ASSERT( n >= 0, "illegal exponent" ); |
---|
1847 | if ( n == 0 ) |
---|
1848 | return 1; |
---|
1849 | else if ( n == 1 ) |
---|
1850 | return v; |
---|
1851 | else if (( v.level() < 0 ) && (hasMipo(v))) |
---|
1852 | { |
---|
1853 | CanonicalForm result( v, n-1 ); |
---|
1854 | return result * v; |
---|
1855 | } |
---|
1856 | else |
---|
1857 | return CanonicalForm( v, n ); |
---|
1858 | } |
---|
1859 | //}}} |
---|
1860 | |
---|
1861 | //{{{ switches |
---|
1862 | void |
---|
1863 | On( int sw ) |
---|
1864 | { |
---|
1865 | cf_glob_switches.On( sw ); |
---|
1866 | } |
---|
1867 | |
---|
1868 | void |
---|
1869 | Off( int sw ) |
---|
1870 | { |
---|
1871 | cf_glob_switches.Off( sw ); |
---|
1872 | } |
---|
1873 | |
---|
1874 | bool |
---|
1875 | isOn( int sw ) |
---|
1876 | { |
---|
1877 | return cf_glob_switches.isOn( sw ); |
---|
1878 | } |
---|
1879 | //}}} |
---|