1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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2 | /* $Id: canonicalform.cc,v 1.22 1997-10-22 15:51:36 schmidt Exp $ */ |
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3 | |
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4 | #include <config.h> |
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5 | |
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6 | #include "assert.h" |
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7 | |
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8 | #include "cf_defs.h" |
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9 | #include "cf_globals.h" |
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10 | #include "canonicalform.h" |
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11 | #include "cf_iter.h" |
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12 | #include "int_cf.h" |
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13 | #include "cf_factory.h" |
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14 | #include "imm.h" |
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15 | #include "gfops.h" |
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16 | #include "cf_binom.h" |
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17 | #if defined (USE_MEMUTIL) && ! defined (USE_OLD_MEMMAN) |
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18 | #include "memman.h" |
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19 | #endif |
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20 | |
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21 | #ifndef NOSTREAMIO |
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22 | CanonicalForm readCF( istream& ); |
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23 | #endif /* NOSTREAMIO */ |
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24 | |
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25 | //{{{ initialization |
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26 | int initializeGMP(); |
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27 | int initializeCharacteristic(); |
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28 | #ifdef SINGULAR |
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29 | int mmInit(void); |
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30 | #endif |
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31 | |
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32 | int |
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33 | initCanonicalForm( void ) |
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34 | { |
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35 | static bool initialized = false; |
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36 | if ( ! initialized ) { |
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37 | #if (defined (USE_MEMUTIL) && ! defined (USE_OLD_MEMMAN)) || defined (SINGULAR) |
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38 | (void)mmInit(); |
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39 | #endif |
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40 | |
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41 | (void)initializeCharacteristic(); |
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42 | (void)initializeGMP(); |
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43 | initPT(); |
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44 | initialized = true; |
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45 | } |
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46 | return 1; |
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47 | } |
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48 | //}}} |
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49 | |
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50 | //{{{ constructors, destructors, selectors |
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51 | CanonicalForm::CanonicalForm() : value( CFFactory::basic( (int)0 ) ) |
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52 | { |
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53 | } |
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54 | |
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55 | CanonicalForm::CanonicalForm( const int i ) : value( CFFactory::basic( i ) ) |
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56 | { |
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57 | } |
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58 | |
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59 | CanonicalForm::CanonicalForm( const CanonicalForm & cf ) : value( is_imm( cf.value ) ? cf.value : cf.value->copyObject() ) |
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60 | { |
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61 | } |
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62 | |
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63 | CanonicalForm::CanonicalForm( InternalCF * cf ) : value( cf ) |
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64 | { |
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65 | } |
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66 | |
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67 | CanonicalForm::CanonicalForm( const Variable & v ) : value( CFFactory::poly( v ) ) |
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68 | { |
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69 | } |
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70 | |
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71 | CanonicalForm::CanonicalForm( const Variable & v, int e ) : value( CFFactory::poly( v, e ) ) |
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72 | { |
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73 | } |
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74 | |
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75 | CanonicalForm::CanonicalForm( const char * str ) : value( CFFactory::basic( str ) ) |
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76 | { |
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77 | } |
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78 | |
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79 | CanonicalForm::~CanonicalForm() |
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80 | { |
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81 | if ( (! is_imm( value )) && value->deleteObject() ) |
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82 | delete value; |
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83 | } |
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84 | |
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85 | InternalCF* |
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86 | CanonicalForm::getval() const |
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87 | { |
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88 | if ( is_imm( value ) ) |
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89 | return value; |
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90 | else |
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91 | return value->copyObject(); |
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92 | } |
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93 | |
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94 | CanonicalForm |
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95 | CanonicalForm::deepCopy() const |
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96 | { |
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97 | if ( is_imm( value ) ) |
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98 | return *this; |
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99 | else |
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100 | return CanonicalForm( value->deepCopyObject() ); |
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101 | } |
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102 | //}}} |
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103 | |
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104 | //{{{ predicates |
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105 | bool |
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106 | CanonicalForm::isOne() const |
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107 | { |
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108 | if ( is_imm( value ) == FFMARK ) |
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109 | return imm_isone_p( value ); |
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110 | else if ( is_imm( value ) == GFMARK ) |
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111 | return imm_isone_gf( value ); |
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112 | else if ( is_imm( value ) ) |
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113 | return imm_isone( value ); |
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114 | else |
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115 | return value->isOne(); |
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116 | } |
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117 | |
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118 | bool |
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119 | CanonicalForm::isZero() const |
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120 | { |
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121 | if ( is_imm( value ) == FFMARK ) |
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122 | return imm_iszero_p( value ); |
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123 | else if ( is_imm( value ) == GFMARK ) |
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124 | return imm_iszero_gf( value ); |
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125 | else if ( is_imm( value ) ) |
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126 | return imm_iszero( value ); |
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127 | else |
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128 | return value->isZero(); |
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129 | } |
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130 | |
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131 | bool |
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132 | CanonicalForm::isImm() const |
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133 | { |
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134 | return is_imm( value ); |
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135 | } |
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136 | |
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137 | bool |
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138 | CanonicalForm::inZ() const |
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139 | { |
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140 | if ( is_imm( value ) == INTMARK ) |
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141 | return true; |
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142 | else if ( is_imm( value ) ) |
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143 | return false; |
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144 | else |
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145 | return value->levelcoeff() == IntegerDomain; |
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146 | } |
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147 | |
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148 | bool |
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149 | CanonicalForm::inQ() const |
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150 | { |
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151 | if ( is_imm( value ) == INTMARK ) |
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152 | return true; |
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153 | else if ( is_imm( value ) ) |
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154 | return false; |
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155 | else |
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156 | return value->levelcoeff() == IntegerDomain || |
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157 | value->levelcoeff() == RationalDomain; |
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158 | } |
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159 | |
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160 | bool |
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161 | CanonicalForm::inFF() const |
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162 | { |
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163 | return is_imm( value ) == FFMARK; |
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164 | } |
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165 | |
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166 | bool |
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167 | CanonicalForm::inGF() const |
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168 | { |
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169 | return is_imm( value ) == GFMARK; |
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170 | } |
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171 | |
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172 | bool |
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173 | CanonicalForm::inPP() const |
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174 | { |
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175 | return ! is_imm( value ) && ( value->levelcoeff() == PrimePowerDomain ); |
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176 | } |
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177 | |
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178 | bool |
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179 | CanonicalForm::inBaseDomain() const |
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180 | { |
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181 | if ( is_imm( value ) ) |
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182 | return true; |
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183 | else |
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184 | return value->inBaseDomain(); |
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185 | } |
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186 | |
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187 | bool |
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188 | CanonicalForm::inExtension() const |
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189 | { |
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190 | if ( is_imm( value ) ) |
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191 | return false; |
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192 | else |
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193 | return value->inExtension(); |
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194 | } |
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195 | |
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196 | bool |
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197 | CanonicalForm::inCoeffDomain() const |
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198 | { |
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199 | if ( is_imm( value ) ) |
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200 | return true; |
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201 | else |
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202 | return value->inCoeffDomain(); |
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203 | } |
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204 | |
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205 | bool |
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206 | CanonicalForm::inPolyDomain() const |
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207 | { |
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208 | if ( is_imm( value ) ) |
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209 | return false; |
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210 | else |
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211 | return value->inPolyDomain(); |
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212 | } |
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213 | |
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214 | bool |
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215 | CanonicalForm::inQuotDomain() const |
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216 | { |
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217 | if ( is_imm( value ) ) |
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218 | return false; |
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219 | else |
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220 | return value->inQuotDomain(); |
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221 | } |
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222 | |
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223 | bool |
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224 | CanonicalForm::isFFinGF() const |
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225 | { |
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226 | return is_imm( value ) == GFMARK && gf_isff( imm2int( value ) ); |
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227 | } |
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228 | |
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229 | bool |
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230 | CanonicalForm::isUnivariate() const |
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231 | { |
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232 | if ( is_imm( value ) ) |
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233 | return false; |
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234 | else |
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235 | return value->isUnivariate(); |
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236 | } |
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237 | //}}} |
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238 | |
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239 | //{{{ conversion functions |
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240 | int |
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241 | CanonicalForm::intval() const |
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242 | { |
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243 | if ( is_imm( value ) ) |
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244 | return imm_intval( value ); |
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245 | else |
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246 | return value->intval(); |
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247 | } |
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248 | |
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249 | CanonicalForm |
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250 | CanonicalForm::mapinto () const |
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251 | { |
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252 | ASSERT( is_imm( value ) || ! value->inExtension(), "cannot map into different Extension" ); |
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253 | if ( is_imm( value ) ) |
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254 | if ( getCharacteristic() == 0 ) |
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255 | if ( is_imm( value ) == FFMARK ) |
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256 | return CanonicalForm( int2imm( ff_symmetric( imm2int( value ) ) ) ); |
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257 | else if ( is_imm( value ) == GFMARK ) |
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258 | return CanonicalForm( int2imm( ff_symmetric( gf_gf2ff( imm2int( value ) ) ) ) ); |
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259 | else |
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260 | return *this; |
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261 | else if ( CFFactory::gettype() == PrimePowerDomain ) |
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262 | return CanonicalForm( CFFactory::basic( imm2int( value ) ) ); |
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263 | else if ( getGFDegree() == 1 ) |
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264 | return CanonicalForm( int2imm_p( ff_norm( imm2int( value ) ) ) ); |
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265 | else |
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266 | return CanonicalForm( int2imm_gf( gf_int2gf( imm2int( value ) ) ) ); |
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267 | else if ( value->inBaseDomain() ) |
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268 | if ( getCharacteristic() == 0 ) |
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269 | if ( value->levelcoeff() == PrimePowerDomain ) |
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270 | return CFFactory::basic( getmpi( value, true ) ); |
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271 | else |
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272 | return *this; |
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273 | else if ( CFFactory::gettype() == PrimePowerDomain ) { |
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274 | ASSERT( value->levelcoeff() == PrimePowerDomain || value->levelcoeff() == IntegerDomain, "no proper map defined" ); |
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275 | if ( value->levelcoeff() == PrimePowerDomain ) |
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276 | return *this; |
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277 | else |
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278 | return CFFactory::basic( getmpi( value ) ); |
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279 | } |
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280 | else { |
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281 | int val; |
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282 | if ( value->levelcoeff() == IntegerDomain ) |
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283 | val = value->intmod( ff_prime ); |
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284 | else if ( value->levelcoeff() == RationalDomain ) |
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285 | return num().mapinto() / den().mapinto(); |
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286 | else { |
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287 | ASSERT( 0, "illegal domain" ); |
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288 | return 0; |
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289 | } |
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290 | if ( getGFDegree() > 1 ) |
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291 | return CanonicalForm( int2imm_gf( gf_int2gf( val ) ) ); |
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292 | else |
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293 | return CanonicalForm( int2imm_p( val ) ); |
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294 | } |
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295 | else { |
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296 | Variable x = value->variable(); |
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297 | CanonicalForm result; |
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298 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
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299 | result += power( x, i.exp() ) * i.coeff().mapinto(); |
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300 | return result; |
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301 | } |
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302 | } |
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303 | //}}} |
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304 | |
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305 | //{{{ CanonicalForm CanonicalForm::lc (), Lc (), LC (), LC ( v ) const |
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306 | //{{{ docu |
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307 | // |
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308 | // lc(), Lc(), LC() - leading coefficient functions. |
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309 | // |
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310 | // All methods return CO if CO is in a base domain. |
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311 | // |
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312 | // lc() returns the leading coefficient of CO with respect to |
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313 | // lexicographic ordering. Elements in an algebraic extension |
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314 | // are considered polynomials so lc() always returns a leading |
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315 | // coefficient in a base domain. This method is useful to get |
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316 | // the base domain over which CO is defined. |
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317 | // |
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318 | // Lc() returns the leading coefficient of CO with respect to |
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319 | // lexicographic ordering. In contrast to lc() elements in an |
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320 | // algebraic extension are considered coefficients so Lc() always |
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321 | // returns a leading coefficient in a coefficient domain. |
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322 | // |
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323 | // LC() returns the leading coefficient of CO where CO is |
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324 | // considered a univariate polynomial in its main variable. An |
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325 | // element of an algebraic extension is considered an univariate |
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326 | // polynomial, too. |
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327 | // |
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328 | // LC( v ) returns the leading coefficient of CO where CO is |
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329 | // considered an univariate polynomial in the polynomial variable |
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330 | // v. |
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331 | // Note: If v is less than the main variable of CO we have to |
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332 | // swap variables which may be quite expensive. |
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333 | // |
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334 | // Examples: |
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335 | // Let x < y be polynomial variables, a an algebraic variable. |
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336 | // |
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337 | // (3*a*x*y^2+y+x).lc() = 3 |
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338 | // (3*a*x*y^2+y+x).Lc() = 3*a |
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339 | // (3*a*x*y^2+y+x).LC() = 3*a*x |
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340 | // (3*a*x*y^2+y+x).LC( x ) = 3*a*y^2+1 |
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341 | // |
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342 | // (3*a^2+4*a).lc() = 3 |
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343 | // (3*a^2+4*a).Lc() = 3*a^2+4*a |
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344 | // (3*a^2+4*a).LC() = 3 |
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345 | // (3*a^2+4*a).LC( x ) = 3*a^2+4*a |
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346 | // |
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347 | // See also: InternalCF::lc(), InternalCF::Lc(), InternalCF::LC(), |
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348 | // InternalPoly::lc(), InternalPoly::Lc(), InternalPoly::LC(), |
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349 | // ::lc(), ::Lc(), ::LC(), ::LC( v ) |
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350 | // |
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351 | //}}} |
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352 | CanonicalForm |
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353 | CanonicalForm::lc () const |
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354 | { |
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355 | if ( is_imm( value ) ) |
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356 | return *this; |
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357 | else |
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358 | return value->lc(); |
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359 | } |
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360 | |
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361 | CanonicalForm |
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362 | CanonicalForm::Lc () const |
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363 | { |
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364 | if ( is_imm( value ) || value->inCoeffDomain() ) |
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365 | return *this; |
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366 | else |
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367 | return value->Lc(); |
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368 | } |
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369 | |
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370 | CanonicalForm |
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371 | CanonicalForm::LC () const |
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372 | { |
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373 | if ( is_imm( value ) ) |
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374 | return *this; |
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375 | else |
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376 | return value->LC(); |
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377 | } |
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378 | |
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379 | CanonicalForm |
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380 | CanonicalForm::LC ( const Variable & v ) const |
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381 | { |
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382 | if ( is_imm( value ) || value->inCoeffDomain() ) |
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383 | return *this; |
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384 | |
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385 | Variable x = value->variable(); |
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386 | if ( v > x ) |
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387 | return *this; |
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388 | else if ( v == x ) |
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389 | return value->LC(); |
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390 | else { |
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391 | CanonicalForm f = swapvar( *this, v, x ); |
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392 | if ( f.mvar() == x ) |
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393 | return swapvar( f.value->LC(), v, x ); |
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394 | else |
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395 | // v did not occur in f |
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396 | return *this; |
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397 | } |
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398 | } |
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399 | //}}} |
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400 | |
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401 | //{{{ int CanonicalForm::degree (), degree ( v ) const |
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402 | //{{{ docu |
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403 | // |
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404 | // degree() - degree methods. |
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405 | // |
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406 | // Both methods returns -1 for the zero polynomial and 0 if |
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407 | // CO is in a base domain. |
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408 | // |
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409 | // degree() returns the degree of CO in its main variable. |
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410 | // Elements in an algebraic extension are considered polynomials. |
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411 | // |
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412 | // degree( v ) returns the degree of CO with respect to v. |
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413 | // Elements in an algebraic extension are considered polynomials, |
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414 | // and v may be algebraic. |
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415 | // |
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416 | // See also: InternalCf::degree(), InternalPoly::degree(), |
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417 | // ::degree(), ::degree( v ) |
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418 | // |
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419 | //}}} |
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420 | int |
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421 | CanonicalForm::degree() const |
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422 | { |
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423 | int what = is_imm( value ); |
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424 | if ( what ) |
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425 | if ( what == GFMARK && imm_iszero_gf( value ) ) |
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426 | return -1; |
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427 | else if ( what == FFMARK && imm_iszero_gf( value ) ) |
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428 | return -1; |
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429 | else if ( what == INTMARK && imm_iszero( value ) ) |
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430 | return -1; |
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431 | else |
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432 | return 0; |
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433 | else |
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434 | return value->degree(); |
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435 | } |
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436 | |
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437 | int |
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438 | CanonicalForm::degree( const Variable & v ) const |
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439 | { |
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440 | int what = is_imm( value ); |
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441 | if ( what ) |
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442 | if ( what == GFMARK && imm_iszero_gf( value ) ) |
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443 | return -1; |
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444 | else if ( what == FFMARK && imm_iszero_gf( value ) ) |
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445 | return -1; |
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446 | else if ( what == INTMARK && imm_iszero( value ) ) |
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447 | return -1; |
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448 | else |
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449 | return 0; |
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450 | else if ( value->inBaseDomain() ) |
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451 | return value->degree(); |
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452 | |
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453 | Variable x = value->variable(); |
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454 | if ( v == x ) |
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455 | return value->degree(); |
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456 | else if ( v > x ) |
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457 | // relatively to v, f is in a coefficient ring |
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458 | return 0; |
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459 | else { |
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460 | int coeffdeg, result = 0; |
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461 | // search for maximum of coefficient degree |
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462 | for ( CFIterator i = *this; i.hasTerms(); i++ ) { |
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463 | coeffdeg = i.coeff().degree( v ); |
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464 | if ( coeffdeg > result ) |
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465 | result = coeffdeg; |
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466 | } |
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467 | return result; |
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468 | } |
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469 | } |
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470 | //}}} |
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471 | |
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472 | //{{{ CanonicalForm CanonicalForm::tailcoeff (), int CanonicalForm::taildegree () const |
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473 | //{{{ docu |
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474 | // |
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475 | // tailcoeff(), taildegree() - return least coefficient and |
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476 | // degree, resp. |
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477 | // |
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478 | // tailcoeff() returns the coefficient of the term with the least |
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479 | // degree in CO where CO is considered an univariate polynomial |
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480 | // in its main variable. Elements in an algebraic extension are |
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481 | // considered coefficients. |
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482 | // |
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483 | // taildegree() returns -1 for the zero polynomial, 0 if CO is in |
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484 | // a base domain, otherwise the least degree of CO where CO is |
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485 | // considered a univariate polynomial in its main variable. In |
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486 | // contrast to tailcoeff(), elements in an algebraic extension |
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487 | // are considered polynomials, not coefficients, and such may |
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488 | // have a taildegree larger than zero. |
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489 | // |
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490 | // See also: InternalCF::tailcoeff(), InternalCF::tailcoeff(), |
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491 | // InternalPoly::tailcoeff(), InternalPoly::taildegree, |
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492 | // ::tailcoeff(), ::taildegree() |
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493 | // |
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494 | //}}} |
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495 | CanonicalForm |
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496 | CanonicalForm::tailcoeff () const |
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497 | { |
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498 | if ( is_imm( value ) || value->inCoeffDomain() ) |
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499 | return *this; |
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500 | else |
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501 | return value->tailcoeff(); |
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502 | } |
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503 | |
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504 | int |
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505 | CanonicalForm::taildegree () const |
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506 | { |
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507 | int what = is_imm( value ); |
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508 | if ( what ) |
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509 | if ( what == GFMARK && imm_iszero_gf( value ) ) |
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510 | return -1; |
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511 | else if ( what == FFMARK && imm_iszero_gf( value ) ) |
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512 | return -1; |
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513 | else if ( what == INTMARK && imm_iszero( value ) ) |
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514 | return -1; |
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515 | else |
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516 | return 0; |
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517 | else |
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518 | return value->taildegree(); |
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519 | } |
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520 | //}}} |
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521 | |
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522 | //{{{ int CanonicalForm::level (), Variable CanonicalForm::mvar () const |
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523 | //{{{ docu |
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524 | // |
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525 | // level(), mvar() - return level and main variable of CO. |
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526 | // |
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527 | // level() returns the level of CO. For a list of the levels and |
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528 | // their meanings, see cf_defs.h. |
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529 | // |
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530 | // mvar() returns the main variable of CO or Variable() if CO is |
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531 | // in a base domain. |
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532 | // |
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533 | // See also: InternalCF::level(), InternalCF::variable(), |
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534 | // InternalPoly::level(), InternalPoly::variable(), ::level(), |
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535 | // ::mvar() |
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536 | // |
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537 | //}}} |
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538 | int |
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539 | CanonicalForm::level () const |
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540 | { |
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541 | if ( is_imm( value ) ) |
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542 | return LEVELBASE; |
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543 | else |
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544 | return value->level(); |
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545 | } |
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546 | |
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547 | Variable |
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548 | CanonicalForm::mvar () const |
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549 | { |
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550 | if ( is_imm( value ) ) |
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551 | return Variable(); |
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552 | else |
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553 | return value->variable(); |
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554 | } |
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555 | //}}} |
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556 | |
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557 | //{{{ CanonicalForm CanonicalForm::num (), den () const |
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558 | //{{{ docu |
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559 | // |
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560 | // num(), den() - return numinator and denominator of CO. |
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561 | // |
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562 | // num() returns the numinator of CO if CO is a rational number, |
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563 | // CO itself otherwise. |
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564 | // |
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565 | // den() returns the denominator of CO if CO is a rational |
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566 | // number, 1 (from the current domain!) otherwise. |
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567 | // |
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568 | // See also: InternalCF::num(), InternalCF::den(), |
---|
569 | // InternalRational::num(), InternalRational::den(), ::num(), |
---|
570 | // ::den() |
---|
571 | // |
---|
572 | //}}} |
---|
573 | CanonicalForm |
---|
574 | CanonicalForm::num () const |
---|
575 | { |
---|
576 | if ( is_imm( value ) ) |
---|
577 | return *this; |
---|
578 | else |
---|
579 | return CanonicalForm( value->num() ); |
---|
580 | } |
---|
581 | |
---|
582 | CanonicalForm |
---|
583 | CanonicalForm::den () const |
---|
584 | { |
---|
585 | if ( is_imm( value ) ) |
---|
586 | return CanonicalForm( 1 ); |
---|
587 | else |
---|
588 | return CanonicalForm( value->den() ); |
---|
589 | } |
---|
590 | //}}} |
---|
591 | |
---|
592 | //{{{ assignment operators |
---|
593 | CanonicalForm & |
---|
594 | CanonicalForm::operator = ( const CanonicalForm & cf ) |
---|
595 | { |
---|
596 | if ( this != &cf ) { |
---|
597 | if ( (! is_imm( value )) && value->deleteObject() ) |
---|
598 | delete value; |
---|
599 | value = (is_imm( cf.value )) ? cf.value : cf.value->copyObject(); |
---|
600 | } |
---|
601 | return *this; |
---|
602 | } |
---|
603 | |
---|
604 | CanonicalForm & |
---|
605 | CanonicalForm::operator = ( const int cf ) |
---|
606 | { |
---|
607 | if ( (! is_imm( value )) && value->deleteObject() ) |
---|
608 | delete value; |
---|
609 | value = CFFactory::basic( cf ); |
---|
610 | return *this; |
---|
611 | } |
---|
612 | |
---|
613 | CanonicalForm & |
---|
614 | CanonicalForm::operator += ( const CanonicalForm & cf ) |
---|
615 | { |
---|
616 | int what = is_imm( value ); |
---|
617 | if ( what ) { |
---|
618 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
619 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
620 | value = imm_add_p( value, cf.value ); |
---|
621 | else if ( what == GFMARK ) |
---|
622 | value = imm_add_gf( value, cf.value ); |
---|
623 | else if ( what ) |
---|
624 | value = imm_add( value, cf.value ); |
---|
625 | else { |
---|
626 | InternalCF * dummy = cf.value->copyObject(); |
---|
627 | value = dummy->addcoeff( value ); |
---|
628 | } |
---|
629 | } |
---|
630 | else if ( is_imm( cf.value ) ) |
---|
631 | value = value->addcoeff( cf.value ); |
---|
632 | else if ( value->level() == cf.value->level() ) { |
---|
633 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
634 | value = value->addsame( cf.value ); |
---|
635 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
636 | value = value->addcoeff( cf.value ); |
---|
637 | else { |
---|
638 | InternalCF * dummy = cf.value->copyObject(); |
---|
639 | dummy = dummy->addcoeff( value ); |
---|
640 | if ( value->deleteObject() ) delete value; |
---|
641 | value = dummy; |
---|
642 | } |
---|
643 | } |
---|
644 | else if ( level() > cf.level() ) |
---|
645 | value = value->addcoeff( cf.value ); |
---|
646 | else { |
---|
647 | InternalCF * dummy = cf.value->copyObject(); |
---|
648 | dummy = dummy->addcoeff( value ); |
---|
649 | if ( value->deleteObject() ) delete value; |
---|
650 | value = dummy; |
---|
651 | } |
---|
652 | return *this; |
---|
653 | } |
---|
654 | |
---|
655 | CanonicalForm & |
---|
656 | CanonicalForm::operator -= ( const CanonicalForm & cf ) |
---|
657 | { |
---|
658 | int what = is_imm( value ); |
---|
659 | if ( what ) { |
---|
660 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
661 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
662 | value = imm_sub_p( value, cf.value ); |
---|
663 | else if ( what == GFMARK ) |
---|
664 | value = imm_sub_gf( value, cf.value ); |
---|
665 | else if ( what ) |
---|
666 | value = imm_sub( value, cf.value ); |
---|
667 | else { |
---|
668 | InternalCF * dummy = cf.value->copyObject(); |
---|
669 | value = dummy->subcoeff( value, true ); |
---|
670 | } |
---|
671 | } |
---|
672 | else if ( is_imm( cf.value ) ) |
---|
673 | value = value->subcoeff( cf.value, false ); |
---|
674 | else if ( value->level() == cf.value->level() ) { |
---|
675 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
676 | value = value->subsame( cf.value ); |
---|
677 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
678 | value = value->subcoeff( cf.value, false ); |
---|
679 | else { |
---|
680 | InternalCF * dummy = cf.value->copyObject(); |
---|
681 | dummy = dummy->subcoeff( value, true ); |
---|
682 | if ( value->deleteObject() ) delete value; |
---|
683 | value = dummy; |
---|
684 | } |
---|
685 | } |
---|
686 | else if ( level() > cf.level() ) |
---|
687 | value = value->subcoeff( cf.value, false ); |
---|
688 | else { |
---|
689 | InternalCF * dummy = cf.value->copyObject(); |
---|
690 | dummy = dummy->subcoeff( value, true ); |
---|
691 | if ( value->deleteObject() ) delete value; |
---|
692 | value = dummy; |
---|
693 | } |
---|
694 | return *this; |
---|
695 | } |
---|
696 | |
---|
697 | CanonicalForm & |
---|
698 | CanonicalForm::operator *= ( const CanonicalForm & cf ) |
---|
699 | { |
---|
700 | int what = is_imm( value ); |
---|
701 | if ( what ) { |
---|
702 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
703 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
704 | value = imm_mul_p( value, cf.value ); |
---|
705 | else if ( what == GFMARK ) |
---|
706 | value = imm_mul_gf( value, cf.value ); |
---|
707 | else if ( what ) |
---|
708 | value = imm_mul( value, cf.value ); |
---|
709 | else { |
---|
710 | InternalCF * dummy = cf.value->copyObject(); |
---|
711 | value = dummy->mulcoeff( value ); |
---|
712 | } |
---|
713 | } |
---|
714 | else if ( is_imm( cf.value ) ) |
---|
715 | value = value->mulcoeff( cf.value ); |
---|
716 | else if ( value->level() == cf.value->level() ) { |
---|
717 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
718 | value = value->mulsame( cf.value ); |
---|
719 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
720 | value = value->mulcoeff( cf.value ); |
---|
721 | else { |
---|
722 | InternalCF * dummy = cf.value->copyObject(); |
---|
723 | dummy = dummy->mulcoeff( value ); |
---|
724 | if ( value->deleteObject() ) delete value; |
---|
725 | value = dummy; |
---|
726 | } |
---|
727 | } |
---|
728 | else if ( level() > cf.level() ) |
---|
729 | value = value->mulcoeff( cf.value ); |
---|
730 | else { |
---|
731 | InternalCF * dummy = cf.value->copyObject(); |
---|
732 | dummy = dummy->mulcoeff( value ); |
---|
733 | if ( value->deleteObject() ) delete value; |
---|
734 | value = dummy; |
---|
735 | } |
---|
736 | return *this; |
---|
737 | } |
---|
738 | |
---|
739 | CanonicalForm & |
---|
740 | CanonicalForm::operator /= ( const CanonicalForm & cf ) |
---|
741 | { |
---|
742 | int what = is_imm( value ); |
---|
743 | if ( what ) { |
---|
744 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
745 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
746 | value = imm_div_p( value, cf.value ); |
---|
747 | else if ( what == GFMARK ) |
---|
748 | value = imm_div_gf( value, cf.value ); |
---|
749 | else if ( what ) |
---|
750 | value = imm_divrat( value, cf.value ); |
---|
751 | else { |
---|
752 | InternalCF * dummy = cf.value->copyObject(); |
---|
753 | value = dummy->dividecoeff( value, true ); |
---|
754 | } |
---|
755 | } |
---|
756 | else if ( is_imm( cf.value ) ) |
---|
757 | value = value->dividecoeff( cf.value, false ); |
---|
758 | else if ( value->level() == cf.value->level() ) { |
---|
759 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
760 | value = value->dividesame( cf.value ); |
---|
761 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
762 | value = value->dividecoeff( cf.value, false ); |
---|
763 | else { |
---|
764 | InternalCF * dummy = cf.value->copyObject(); |
---|
765 | dummy = dummy->dividecoeff( value, true ); |
---|
766 | if ( value->deleteObject() ) delete value; |
---|
767 | value = dummy; |
---|
768 | } |
---|
769 | } |
---|
770 | else if ( level() > cf.level() ) |
---|
771 | value = value->dividecoeff( cf.value, false ); |
---|
772 | else { |
---|
773 | InternalCF * dummy = cf.value->copyObject(); |
---|
774 | dummy = dummy->dividecoeff( value, true ); |
---|
775 | if ( value->deleteObject() ) delete value; |
---|
776 | value = dummy; |
---|
777 | } |
---|
778 | return *this; |
---|
779 | } |
---|
780 | |
---|
781 | CanonicalForm & |
---|
782 | CanonicalForm::div ( const CanonicalForm & cf ) |
---|
783 | { |
---|
784 | int what = is_imm( value ); |
---|
785 | if ( what ) { |
---|
786 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
787 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
788 | value = imm_div_p( value, cf.value ); |
---|
789 | else if ( what == GFMARK ) |
---|
790 | value = imm_div_gf( value, cf.value ); |
---|
791 | else if ( what ) |
---|
792 | value = imm_div( value, cf.value ); |
---|
793 | else { |
---|
794 | InternalCF * dummy = cf.value->copyObject(); |
---|
795 | value = dummy->divcoeff( value, true ); |
---|
796 | } |
---|
797 | } |
---|
798 | else if ( is_imm( cf.value ) ) |
---|
799 | value = value->divcoeff( cf.value, false ); |
---|
800 | else if ( value->level() == cf.value->level() ) { |
---|
801 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
802 | value = value->divsame( cf.value ); |
---|
803 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
804 | value = value->divcoeff( cf.value, false ); |
---|
805 | else { |
---|
806 | InternalCF * dummy = cf.value->copyObject(); |
---|
807 | dummy = dummy->divcoeff( value, true ); |
---|
808 | if ( value->deleteObject() ) delete value; |
---|
809 | value = dummy; |
---|
810 | } |
---|
811 | } |
---|
812 | else if ( level() > cf.level() ) |
---|
813 | value = value->divcoeff( cf.value, false ); |
---|
814 | else { |
---|
815 | InternalCF * dummy = cf.value->copyObject(); |
---|
816 | dummy = dummy->divcoeff( value, true ); |
---|
817 | if ( value->deleteObject() ) delete value; |
---|
818 | value = dummy; |
---|
819 | } |
---|
820 | return *this; |
---|
821 | } |
---|
822 | |
---|
823 | CanonicalForm & |
---|
824 | CanonicalForm::operator %= ( const CanonicalForm & cf ) |
---|
825 | { |
---|
826 | int what = is_imm( value ); |
---|
827 | if ( what ) { |
---|
828 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
829 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
830 | value = imm_mod_p( value, cf.value ); |
---|
831 | else if ( what == GFMARK ) |
---|
832 | value = imm_mod_gf( value, cf.value ); |
---|
833 | else if ( what ) |
---|
834 | value = imm_mod( value, cf.value ); |
---|
835 | else { |
---|
836 | InternalCF * dummy = cf.value->copyObject(); |
---|
837 | value = dummy->modulocoeff( value, true ); |
---|
838 | } |
---|
839 | } |
---|
840 | else if ( is_imm( cf.value ) ) |
---|
841 | value = value->modulocoeff( cf.value, false ); |
---|
842 | else if ( value->level() == cf.value->level() ) { |
---|
843 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
844 | value = value->modulosame( cf.value ); |
---|
845 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
846 | value = value->modulocoeff( cf.value, false ); |
---|
847 | else { |
---|
848 | InternalCF * dummy = cf.value->copyObject(); |
---|
849 | dummy = dummy->modulocoeff( value, true ); |
---|
850 | if ( value->deleteObject() ) delete value; |
---|
851 | value = dummy; |
---|
852 | } |
---|
853 | } |
---|
854 | else if ( level() > cf.level() ) |
---|
855 | value = value->modulocoeff( cf.value, false ); |
---|
856 | else { |
---|
857 | InternalCF * dummy = cf.value->copyObject(); |
---|
858 | dummy = dummy->modulocoeff( value, true ); |
---|
859 | if ( value->deleteObject() ) delete value; |
---|
860 | value = dummy; |
---|
861 | } |
---|
862 | return *this; |
---|
863 | } |
---|
864 | |
---|
865 | CanonicalForm & |
---|
866 | CanonicalForm::mod ( const CanonicalForm & cf ) |
---|
867 | { |
---|
868 | int what = is_imm( value ); |
---|
869 | if ( what ) { |
---|
870 | ASSERT ( ! is_imm( cf.value ) || (what==is_imm( cf.value )), "illegal base coefficients" ); |
---|
871 | if ( (what = is_imm( cf.value )) == FFMARK ) |
---|
872 | value = imm_mod_p( value, cf.value ); |
---|
873 | else if ( what == GFMARK ) |
---|
874 | value = imm_mod_gf( value, cf.value ); |
---|
875 | else if ( what ) |
---|
876 | value = imm_mod( value, cf.value ); |
---|
877 | else { |
---|
878 | InternalCF * dummy = cf.value->copyObject(); |
---|
879 | value = dummy->modcoeff( value, true ); |
---|
880 | } |
---|
881 | } |
---|
882 | else if ( is_imm( cf.value ) ) |
---|
883 | value = value->modcoeff( cf.value, false ); |
---|
884 | else if ( value->level() == cf.value->level() ) { |
---|
885 | if ( value->levelcoeff() == cf.value->levelcoeff() ) |
---|
886 | value = value->modsame( cf.value ); |
---|
887 | else if ( value->levelcoeff() > cf.value->levelcoeff() ) |
---|
888 | value = value->modcoeff( cf.value, false ); |
---|
889 | else { |
---|
890 | InternalCF * dummy = cf.value->copyObject(); |
---|
891 | dummy = dummy->modcoeff( value, true ); |
---|
892 | if ( value->deleteObject() ) delete value; |
---|
893 | value = dummy; |
---|
894 | } |
---|
895 | } |
---|
896 | else if ( level() > cf.level() ) |
---|
897 | value = value->modcoeff( cf.value, false ); |
---|
898 | else { |
---|
899 | InternalCF * dummy = cf.value->copyObject(); |
---|
900 | dummy = dummy->modcoeff( value, true ); |
---|
901 | if ( value->deleteObject() ) delete value; |
---|
902 | value = dummy; |
---|
903 | } |
---|
904 | return *this; |
---|
905 | } |
---|
906 | |
---|
907 | void |
---|
908 | divrem ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r ) |
---|
909 | { |
---|
910 | InternalCF * qq = 0, * rr = 0; |
---|
911 | int what = is_imm( f.value ); |
---|
912 | if ( what ) |
---|
913 | if ( is_imm( g.value ) ) { |
---|
914 | if ( what == FFMARK ) |
---|
915 | imm_divrem_p( f.value, g.value, qq, rr ); |
---|
916 | else if ( what == GFMARK ) |
---|
917 | imm_divrem_gf( f.value, g.value, qq, rr ); |
---|
918 | else |
---|
919 | imm_divrem( f.value, g.value, qq, rr ); |
---|
920 | } |
---|
921 | else |
---|
922 | g.value->divremcoeff( f.value, qq, rr, true ); |
---|
923 | else if ( (what=is_imm( g.value )) ) |
---|
924 | f.value->divremcoeff( g.value, qq, rr, false ); |
---|
925 | else if ( f.value->level() == g.value->level() ) |
---|
926 | if ( f.value->levelcoeff() == g.value->levelcoeff() ) |
---|
927 | f.value->divremsame( g.value, qq, rr ); |
---|
928 | else if ( f.value->levelcoeff() > g.value->levelcoeff() ) |
---|
929 | f.value->divremcoeff( g.value, qq, rr, false ); |
---|
930 | else |
---|
931 | g.value->divremcoeff( f.value, qq, rr, true ); |
---|
932 | else if ( f.value->level() > g.value->level() ) |
---|
933 | f.value->divremcoeff( g.value, qq, rr, false ); |
---|
934 | else |
---|
935 | g.value->divremcoeff( f.value, qq, rr, true ); |
---|
936 | ASSERT( qq != 0 && rr != 0, "error in divrem" ); |
---|
937 | q = CanonicalForm( qq ); |
---|
938 | r = CanonicalForm( rr ); |
---|
939 | } |
---|
940 | |
---|
941 | bool |
---|
942 | divremt ( const CanonicalForm & f, const CanonicalForm & g, CanonicalForm & q, CanonicalForm & r ) |
---|
943 | { |
---|
944 | InternalCF * qq = 0, * rr = 0; |
---|
945 | int what = is_imm( f.value ); |
---|
946 | bool result = true; |
---|
947 | if ( what ) |
---|
948 | if ( is_imm( g.value ) ) { |
---|
949 | if ( what == FFMARK ) |
---|
950 | imm_divrem_p( f.value, g.value, qq, rr ); |
---|
951 | else if ( what == GFMARK ) |
---|
952 | imm_divrem_gf( f.value, g.value, qq, rr ); |
---|
953 | else |
---|
954 | imm_divrem( f.value, g.value, qq, rr ); |
---|
955 | } |
---|
956 | else |
---|
957 | result = g.value->divremcoefft( f.value, qq, rr, true ); |
---|
958 | else if ( (what=is_imm( g.value )) ) |
---|
959 | result = f.value->divremcoefft( g.value, qq, rr, false ); |
---|
960 | else if ( f.value->level() == g.value->level() ) |
---|
961 | if ( f.value->levelcoeff() == g.value->levelcoeff() ) |
---|
962 | result = f.value->divremsamet( g.value, qq, rr ); |
---|
963 | else if ( f.value->levelcoeff() > g.value->levelcoeff() ) |
---|
964 | result = f.value->divremcoefft( g.value, qq, rr, false ); |
---|
965 | else |
---|
966 | result = g.value->divremcoefft( f.value, qq, rr, true ); |
---|
967 | else if ( f.value->level() > g.value->level() ) |
---|
968 | result = f.value->divremcoefft( g.value, qq, rr, false ); |
---|
969 | else |
---|
970 | result = g.value->divremcoefft( f.value, qq, rr, true ); |
---|
971 | if ( result ) { |
---|
972 | ASSERT( qq != 0 && rr != 0, "error in divrem" ); |
---|
973 | q = CanonicalForm( qq ); |
---|
974 | r = CanonicalForm( rr ); |
---|
975 | } |
---|
976 | else { |
---|
977 | q = 0; r = 0; |
---|
978 | } |
---|
979 | return result; |
---|
980 | } |
---|
981 | //}}} |
---|
982 | |
---|
983 | //{{{ CanonicalForm CanonicalForm::operator () ( f ), operator () ( f, v ) const |
---|
984 | //{{{ docu |
---|
985 | // |
---|
986 | // operator ()() - evaluation operator. |
---|
987 | // |
---|
988 | // Both operators return CO if CO is in a base domain. |
---|
989 | // |
---|
990 | // operator () ( f ) returns CO with f inserted for the main |
---|
991 | // variable. Elements in an algebraic extension are considered |
---|
992 | // polynomials. |
---|
993 | // |
---|
994 | // operator () ( f, v ) returns CO with f inserted for v. |
---|
995 | // Elements in an algebraic extension are considered polynomials |
---|
996 | // and v may be an algebraic variable. |
---|
997 | // |
---|
998 | //}}} |
---|
999 | CanonicalForm |
---|
1000 | CanonicalForm::operator () ( const CanonicalForm & f ) const |
---|
1001 | { |
---|
1002 | if ( is_imm( value ) || value->inBaseDomain() ) |
---|
1003 | return *this; |
---|
1004 | else { |
---|
1005 | CFIterator i = *this; |
---|
1006 | int lastExp = i.exp(); |
---|
1007 | CanonicalForm result = i.coeff(); |
---|
1008 | i++; |
---|
1009 | while ( i.hasTerms() ) { |
---|
1010 | if ( (lastExp - i.exp()) == 1 ) |
---|
1011 | result *= f; |
---|
1012 | else |
---|
1013 | result *= power( f, lastExp - i.exp() ); |
---|
1014 | result += i.coeff(); |
---|
1015 | lastExp = i.exp(); |
---|
1016 | i++; |
---|
1017 | } |
---|
1018 | if ( lastExp != 0 ) |
---|
1019 | result *= power( f, lastExp ); |
---|
1020 | return result; |
---|
1021 | } |
---|
1022 | } |
---|
1023 | |
---|
1024 | CanonicalForm |
---|
1025 | CanonicalForm::operator () ( const CanonicalForm & f, const Variable & v ) const |
---|
1026 | { |
---|
1027 | if ( is_imm( value ) || value->inBaseDomain() ) |
---|
1028 | return *this; |
---|
1029 | |
---|
1030 | Variable x = value->variable(); |
---|
1031 | if ( v > x ) |
---|
1032 | return *this; |
---|
1033 | else if ( v == x ) |
---|
1034 | return (*this)( f ); |
---|
1035 | else { |
---|
1036 | // v is less than main variable of f |
---|
1037 | CanonicalForm result = 0; |
---|
1038 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
---|
1039 | result += i.coeff()( f, v ) * power( x, i.exp() ); |
---|
1040 | return result; |
---|
1041 | } |
---|
1042 | } |
---|
1043 | //}}} |
---|
1044 | |
---|
1045 | //{{{ CanonicalForm CanonicalForm::operator [] ( int i ) const |
---|
1046 | //{{{ docu |
---|
1047 | // |
---|
1048 | // operator []() - return i'th coefficient from CO. |
---|
1049 | // |
---|
1050 | // Returns CO if CO is in a base domain and i equals zero. |
---|
1051 | // Returns zero (from the current domain) if CO is in a base |
---|
1052 | // domain and i is larger than zero. Otherwise, returns the |
---|
1053 | // coefficient to x^i in CO (if x denotes the main variable of |
---|
1054 | // CO) or zero if CO does not contain x^i. Elements in an |
---|
1055 | // algebraic extension are considered polynomials. i should be |
---|
1056 | // larger or equal zero. |
---|
1057 | // |
---|
1058 | // Note: Never use a loop like |
---|
1059 | // |
---|
1060 | // for ( int i = degree( f ); i >= 0; i-- ) |
---|
1061 | // foo( i, f[ i ] ); |
---|
1062 | // |
---|
1063 | // This is much slower than |
---|
1064 | // |
---|
1065 | // for ( int i = degree( f ), CFIterator I = f; I.hasTerms(); I++ ) { |
---|
1066 | // // fill gap with zeroes |
---|
1067 | // for ( ; i > I.exp(); i-- ) |
---|
1068 | // foo( i, 0 ); |
---|
1069 | // // at this point, i == I.exp() |
---|
1070 | // foo( i, i.coeff() ); |
---|
1071 | // i--; |
---|
1072 | // } |
---|
1073 | // // work through trailing zeroes |
---|
1074 | // for ( ; i >= 0; i-- ) |
---|
1075 | // foo( i, 0 ); |
---|
1076 | // |
---|
1077 | //}}} |
---|
1078 | CanonicalForm |
---|
1079 | CanonicalForm::operator [] ( int i ) const |
---|
1080 | { |
---|
1081 | ASSERT( i >= 0, "index to operator [] less than zero" ); |
---|
1082 | if ( is_imm( value ) ) |
---|
1083 | if ( i == 0 ) |
---|
1084 | return *this; |
---|
1085 | else |
---|
1086 | return CanonicalForm( 0 ); |
---|
1087 | else |
---|
1088 | return value->coeff( i ); |
---|
1089 | } |
---|
1090 | //}}} |
---|
1091 | |
---|
1092 | //{{{ CanonicalForm CanonicalForm::deriv (), deriv ( x ) |
---|
1093 | //{{{ docu |
---|
1094 | // |
---|
1095 | // deriv() - return the formal derivation of CO. |
---|
1096 | // |
---|
1097 | // deriv() derives CO with respect to its main variable. Returns |
---|
1098 | // zero if f is in a coefficient domain. |
---|
1099 | // |
---|
1100 | // deriv( x ) derives CO with respect to x. x should be a |
---|
1101 | // polynomial variable. Returns zero if f is in a coefficient |
---|
1102 | // domain. |
---|
1103 | // |
---|
1104 | // See also: ::deriv() |
---|
1105 | // |
---|
1106 | //}}} |
---|
1107 | CanonicalForm |
---|
1108 | CanonicalForm::deriv () const |
---|
1109 | { |
---|
1110 | if ( is_imm( value ) || value->inCoeffDomain() ) |
---|
1111 | return CanonicalForm( 0 ); |
---|
1112 | else { |
---|
1113 | CanonicalForm result = 0; |
---|
1114 | Variable x = value->variable(); |
---|
1115 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
---|
1116 | if ( i.exp() > 0 ) |
---|
1117 | result += power( x, i.exp()-1 ) * i.coeff() * i.exp(); |
---|
1118 | return result; |
---|
1119 | } |
---|
1120 | } |
---|
1121 | |
---|
1122 | CanonicalForm |
---|
1123 | CanonicalForm::deriv ( const Variable & x ) const |
---|
1124 | { |
---|
1125 | ASSERT( x.level() > 0, "cannot derive with respect to algebraic variables" ); |
---|
1126 | if ( is_imm( value ) || value->inCoeffDomain() ) |
---|
1127 | return CanonicalForm( 0 ); |
---|
1128 | |
---|
1129 | Variable y = value->variable(); |
---|
1130 | if ( x > y ) |
---|
1131 | return CanonicalForm( 0 ); |
---|
1132 | else if ( x == y ) |
---|
1133 | return deriv(); |
---|
1134 | else { |
---|
1135 | CanonicalForm result = 0; |
---|
1136 | for ( CFIterator i = *this; i.hasTerms(); i++ ) |
---|
1137 | result += i.coeff().deriv( x ) * power( y, i.exp() ); |
---|
1138 | return result; |
---|
1139 | } |
---|
1140 | } |
---|
1141 | //}}} |
---|
1142 | |
---|
1143 | //{{{ int CanonicalForm::sign () const |
---|
1144 | //{{{ docu |
---|
1145 | // |
---|
1146 | // sign() - return sign of CO. |
---|
1147 | // |
---|
1148 | // If CO is an integer or a rational number, the sign is defined |
---|
1149 | // as usual. If CO is an element of a prime power domain or in a |
---|
1150 | // finite field and SW_SYMMETRIC_FF is on the sign of CO is the |
---|
1151 | // sign of the symmetric representation of CO. If CO is in GF(q) |
---|
1152 | // or in a finite field and SW_SYMMETRIC_FF is off, the sign of |
---|
1153 | // CO is zero iff CO is zero, otherwise the sign is one. |
---|
1154 | // |
---|
1155 | // If CO is a polynomial or in an extension of one of the base |
---|
1156 | // domains, the sign of CO is the sign of its leading |
---|
1157 | // coefficient. |
---|
1158 | // |
---|
1159 | // See also: InternalCF::sign(), InternalInteger::sign(), |
---|
1160 | // InternalPrimePower::sign(), InternalRational::sign(), |
---|
1161 | // InternalPoly::sign(), imm_sign(), gf_sign() |
---|
1162 | // |
---|
1163 | //}}} |
---|
1164 | int |
---|
1165 | CanonicalForm::sign () const |
---|
1166 | { |
---|
1167 | if ( is_imm( value ) ) |
---|
1168 | return imm_sign( value ); |
---|
1169 | else |
---|
1170 | return value->sign(); |
---|
1171 | } |
---|
1172 | //}}} |
---|
1173 | |
---|
1174 | //{{{ CanonicalForm CanonicalForm::sqrt () const |
---|
1175 | //{{{ docu |
---|
1176 | // |
---|
1177 | // sqrt() - calculate integer square root. |
---|
1178 | // |
---|
1179 | // CO has to be an integer greater or equal zero. Returns the |
---|
1180 | // largest integer less or equal sqrt(CO). |
---|
1181 | // |
---|
1182 | // In the immediate case, we use the newton method to find the |
---|
1183 | // root. The algorithm is from H. Cohen - 'A Course in |
---|
1184 | // Computational Algebraic Number Theory', ch. 1.7.1. |
---|
1185 | // |
---|
1186 | // See also: InternalCF::sqrt(), InternalInteger::sqrt(), ::sqrt() |
---|
1187 | // |
---|
1188 | //}}} |
---|
1189 | CanonicalForm |
---|
1190 | CanonicalForm::sqrt () const |
---|
1191 | { |
---|
1192 | if ( is_imm( value ) ) { |
---|
1193 | ASSERT( is_imm( value ) == INTMARK, "sqrt() not implemented" ); |
---|
1194 | int n = imm2int( value ); |
---|
1195 | ASSERT( n >= 0, "arg to sqrt() less than zero" ); |
---|
1196 | if ( n == 0 || n == 1 ) |
---|
1197 | return CanonicalForm( n ); |
---|
1198 | else { |
---|
1199 | int x, y = n; |
---|
1200 | do { |
---|
1201 | x = y; |
---|
1202 | // the intermediate result may not fit into an |
---|
1203 | // integer, but the result does |
---|
1204 | y = (unsigned int)(x + n/x)/2; |
---|
1205 | } while ( y < x ); |
---|
1206 | return CanonicalForm( x ); |
---|
1207 | } |
---|
1208 | } |
---|
1209 | else |
---|
1210 | return CanonicalForm( value->sqrt() ); |
---|
1211 | } |
---|
1212 | //}}} |
---|
1213 | |
---|
1214 | //{{{ int CanonicalForm::ilog2 () const |
---|
1215 | //{{{ docu |
---|
1216 | // |
---|
1217 | // ilog2() - integer logarithm to base 2. |
---|
1218 | // |
---|
1219 | // Returns the largest integer less or equal logarithm of CO to |
---|
1220 | // base 2. CO should be a positive integer. |
---|
1221 | // |
---|
1222 | // See also: InternalCF::ilog2(), InternalInteger::ilog2(), ::ilog2() |
---|
1223 | // |
---|
1224 | //}}} |
---|
1225 | int |
---|
1226 | CanonicalForm::ilog2 () const |
---|
1227 | { |
---|
1228 | if ( is_imm( value ) ) { |
---|
1229 | ASSERT( is_imm( value ) == INTMARK, "ilog2() not implemented" ); |
---|
1230 | int a = imm2int( value ); |
---|
1231 | ASSERT( a > 0, "arg to ilog2() less or equal zero" ); |
---|
1232 | int n = -1; |
---|
1233 | while ( a != 0 ) { |
---|
1234 | n++; |
---|
1235 | a /= 2; |
---|
1236 | } |
---|
1237 | return n; |
---|
1238 | } |
---|
1239 | else |
---|
1240 | return value->ilog2(); |
---|
1241 | } |
---|
1242 | //}}} |
---|
1243 | |
---|
1244 | //{{{ CanonicalForm CanonicalForm::gcd( const CanonicalForm & ) const |
---|
1245 | CanonicalForm |
---|
1246 | CanonicalForm::gcd( const CanonicalForm & ) const |
---|
1247 | { |
---|
1248 | // return ::gcd( *this, f ); |
---|
1249 | return 1; |
---|
1250 | } |
---|
1251 | //}}} |
---|
1252 | |
---|
1253 | //{{{ comparison operators |
---|
1254 | bool |
---|
1255 | operator == ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1256 | { |
---|
1257 | int what = is_imm( lhs.value ); |
---|
1258 | if ( what ) |
---|
1259 | if ( what == is_imm( rhs.value ) ) |
---|
1260 | return lhs.value == rhs.value; |
---|
1261 | else |
---|
1262 | return false; |
---|
1263 | else if ( is_imm( rhs.value ) ) |
---|
1264 | return false; |
---|
1265 | else if ( lhs.level() == rhs.level() ) |
---|
1266 | if ( lhs.value->levelcoeff() >= rhs.value->levelcoeff() ) |
---|
1267 | return lhs.value->comparesame( rhs.value ) == 0; |
---|
1268 | else |
---|
1269 | return rhs.value->comparesame( lhs.value ) == 0; |
---|
1270 | else |
---|
1271 | return false; |
---|
1272 | } |
---|
1273 | |
---|
1274 | bool |
---|
1275 | operator != ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1276 | { |
---|
1277 | int what = is_imm( lhs.value ); |
---|
1278 | if ( what ) |
---|
1279 | if ( what == is_imm( rhs.value ) ) |
---|
1280 | return lhs.value != rhs.value; |
---|
1281 | else |
---|
1282 | return true; |
---|
1283 | else if ( is_imm( rhs.value ) ) |
---|
1284 | return true; |
---|
1285 | else if ( lhs.level() == rhs.level() ) |
---|
1286 | if ( lhs.value->levelcoeff() >= rhs.value->levelcoeff() ) |
---|
1287 | return lhs.value->comparesame( rhs.value ) != 0; |
---|
1288 | else |
---|
1289 | return rhs.value->comparesame( lhs.value ) != 0; |
---|
1290 | else |
---|
1291 | return true; |
---|
1292 | } |
---|
1293 | |
---|
1294 | bool |
---|
1295 | operator > ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1296 | { |
---|
1297 | int what = is_imm( lhs.value ); |
---|
1298 | if ( what ) { |
---|
1299 | ASSERT ( ! is_imm( rhs.value ) || (what==is_imm( rhs.value )), "illegal base coefficients" ); |
---|
1300 | if ( what == INTMARK ) { |
---|
1301 | if ( what == is_imm( rhs.value ) ) |
---|
1302 | return imm_cmp( lhs.value, rhs.value ) > 0; |
---|
1303 | else |
---|
1304 | return rhs.value->comparecoeff( lhs.value ) < 0; |
---|
1305 | } |
---|
1306 | else if ( what == FFMARK ) { |
---|
1307 | if ( what == is_imm( rhs.value ) ) |
---|
1308 | return imm_cmp_p( lhs.value, rhs.value ) > 0; |
---|
1309 | else |
---|
1310 | return rhs.value->comparecoeff( lhs.value ) < 0; |
---|
1311 | } |
---|
1312 | else { |
---|
1313 | if ( what == is_imm( rhs.value ) ) |
---|
1314 | return imm_cmp_gf( lhs.value, rhs.value ) > 0; |
---|
1315 | else |
---|
1316 | return rhs.value->comparecoeff( lhs.value ) < 0; |
---|
1317 | } |
---|
1318 | } |
---|
1319 | else if ( is_imm( rhs.value ) ) |
---|
1320 | return lhs.value->comparecoeff( rhs.value ) > 0; |
---|
1321 | else if ( lhs.level() == rhs.level() ) |
---|
1322 | if ( lhs.value->levelcoeff() == rhs.value->levelcoeff() ) |
---|
1323 | return lhs.value->comparesame( rhs.value ) > 0; |
---|
1324 | else if ( lhs.value->levelcoeff() > rhs.value->levelcoeff() ) |
---|
1325 | return lhs.value->comparecoeff( lhs.value ) > 0; |
---|
1326 | else |
---|
1327 | return rhs.value->comparecoeff( lhs.value ) < 0; |
---|
1328 | else |
---|
1329 | return lhs.value->level() > rhs.value->level(); |
---|
1330 | } |
---|
1331 | |
---|
1332 | bool |
---|
1333 | operator < ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
1334 | { |
---|
1335 | int what = is_imm( lhs.value ); |
---|
1336 | if ( what ) { |
---|
1337 | ASSERT ( ! is_imm( rhs.value ) || (what==is_imm( rhs.value )), "illegal base coefficients" ); |
---|
1338 | if ( what == INTMARK ) { |
---|
1339 | if ( what == is_imm( rhs.value ) ) |
---|
1340 | return imm_cmp( lhs.value, rhs.value ) < 0; |
---|
1341 | else |
---|
1342 | return rhs.value->comparecoeff( lhs.value ) > 0; |
---|
1343 | } |
---|
1344 | else if ( what == FFMARK ) { |
---|
1345 | if ( what == is_imm( rhs.value ) ) |
---|
1346 | return imm_cmp( lhs.value, rhs.value ) < 0; |
---|
1347 | else |
---|
1348 | return rhs.value->comparecoeff( lhs.value ) > 0; |
---|
1349 | } |
---|
1350 | else { |
---|
1351 | if ( what == is_imm( rhs.value ) ) |
---|
1352 | return imm_cmp( lhs.value, rhs.value ) < 0; |
---|
1353 | else |
---|
1354 | return rhs.value->comparecoeff( lhs.value ) > 0; |
---|
1355 | } |
---|
1356 | } |
---|
1357 | else if ( is_imm( rhs.value ) ) |
---|
1358 | return lhs.value->comparecoeff( rhs.value ) < 0; |
---|
1359 | else if ( lhs.level() == rhs.level() ) |
---|
1360 | if ( lhs.value->levelcoeff() == rhs.value->levelcoeff() ) |
---|
1361 | return lhs.value->comparesame( rhs.value ) < 0; |
---|
1362 | else if ( lhs.value->levelcoeff() > rhs.value->levelcoeff() ) |
---|
1363 | return lhs.value->comparecoeff( lhs.value ) < 0; |
---|
1364 | else |
---|
1365 | return rhs.value->comparecoeff( lhs.value ) > 0; |
---|
1366 | else |
---|
1367 | return lhs.value->level() < rhs.value->level(); |
---|
1368 | } |
---|
1369 | //}}} |
---|
1370 | |
---|
1371 | //{{{ arithmetic operators |
---|
1372 | CanonicalForm |
---|
1373 | operator - ( const CanonicalForm & cf ) |
---|
1374 | { |
---|
1375 | CanonicalForm result( cf ); |
---|
1376 | int what = is_imm( result.value ); |
---|
1377 | if ( what == FFMARK ) |
---|
1378 | result.value = imm_neg_p( result.value ); |
---|
1379 | else if ( what == GFMARK ) |
---|
1380 | result.value = imm_neg_gf( result.value ); |
---|
1381 | else if ( what ) |
---|
1382 | result.value = imm_neg( result.value ); |
---|
1383 | else |
---|
1384 | result.value = result.value->neg(); |
---|
1385 | return result; |
---|
1386 | } |
---|
1387 | |
---|
1388 | CanonicalForm |
---|
1389 | operator + ( const CanonicalForm &c1, const CanonicalForm &c2 ) |
---|
1390 | { |
---|
1391 | CanonicalForm result( c1 ); |
---|
1392 | result += c2; |
---|
1393 | return result; |
---|
1394 | } |
---|
1395 | |
---|
1396 | CanonicalForm |
---|
1397 | operator - ( const CanonicalForm &c1, const CanonicalForm &c2 ) |
---|
1398 | { |
---|
1399 | CanonicalForm result( c1 ); |
---|
1400 | result -= c2; |
---|
1401 | return result; |
---|
1402 | } |
---|
1403 | |
---|
1404 | CanonicalForm |
---|
1405 | operator * ( const CanonicalForm &c1, const CanonicalForm &c2 ) |
---|
1406 | { |
---|
1407 | CanonicalForm result( c1 ); |
---|
1408 | result *= c2; |
---|
1409 | return result; |
---|
1410 | } |
---|
1411 | |
---|
1412 | CanonicalForm |
---|
1413 | operator / ( const CanonicalForm &c1, const CanonicalForm &c2 ) |
---|
1414 | { |
---|
1415 | CanonicalForm result( c1 ); |
---|
1416 | result /= c2; |
---|
1417 | return result; |
---|
1418 | } |
---|
1419 | |
---|
1420 | CanonicalForm |
---|
1421 | div ( const CanonicalForm &c1, const CanonicalForm &c2 ) |
---|
1422 | { |
---|
1423 | CanonicalForm result( c1 ); |
---|
1424 | result.div( c2 ); |
---|
1425 | return result; |
---|
1426 | } |
---|
1427 | |
---|
1428 | CanonicalForm |
---|
1429 | mod ( const CanonicalForm &c1, const CanonicalForm &c2 ) |
---|
1430 | { |
---|
1431 | CanonicalForm result( c1 ); |
---|
1432 | result.mod( c2 ); |
---|
1433 | return result; |
---|
1434 | } |
---|
1435 | |
---|
1436 | CanonicalForm |
---|
1437 | operator % ( const CanonicalForm &c1, const CanonicalForm &c2 ) |
---|
1438 | { |
---|
1439 | CanonicalForm result( c1 ); |
---|
1440 | result %= c2; |
---|
1441 | return result; |
---|
1442 | } |
---|
1443 | //}}} |
---|
1444 | |
---|
1445 | //{{{ input/output |
---|
1446 | #ifndef NOSTREAMIO |
---|
1447 | void |
---|
1448 | CanonicalForm::print( ostream & os, char * str ) const |
---|
1449 | { |
---|
1450 | if ( is_imm( value ) ) |
---|
1451 | imm_print( os, value, str ); |
---|
1452 | else |
---|
1453 | value->print( os, str ); |
---|
1454 | } |
---|
1455 | |
---|
1456 | ostream& |
---|
1457 | operator << ( ostream & os, const CanonicalForm & cf ) |
---|
1458 | { |
---|
1459 | cf.print( os, "" ); |
---|
1460 | return os; |
---|
1461 | } |
---|
1462 | |
---|
1463 | istream& |
---|
1464 | operator >> ( istream & is, CanonicalForm & cf ) |
---|
1465 | { |
---|
1466 | #ifndef SINGULAR |
---|
1467 | cf = readCF( is ); |
---|
1468 | return is; |
---|
1469 | #else /* SINGULAR */ |
---|
1470 | return 0; |
---|
1471 | #endif /* SINGULAR */ |
---|
1472 | } |
---|
1473 | #endif /* NOSTREAMIO */ |
---|
1474 | //}}} |
---|
1475 | |
---|
1476 | //{{{ genCoeff(), genOne(), genZero() |
---|
1477 | CanonicalForm |
---|
1478 | CanonicalForm::genCoeff( int type, int i ) |
---|
1479 | { |
---|
1480 | return CanonicalForm( CFFactory::basic( type, i ) ); |
---|
1481 | } |
---|
1482 | |
---|
1483 | CanonicalForm |
---|
1484 | CanonicalForm::genZero() const |
---|
1485 | { |
---|
1486 | int what = is_imm( value ); |
---|
1487 | if ( what == FFMARK ) |
---|
1488 | return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 0 ) ); |
---|
1489 | else if ( what == GFMARK ) |
---|
1490 | return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 0 ) ); |
---|
1491 | else if ( what ) |
---|
1492 | return CanonicalForm( CFFactory::basic( IntegerDomain, 0 ) ); |
---|
1493 | else |
---|
1494 | return CanonicalForm( value->genZero() ); |
---|
1495 | } |
---|
1496 | |
---|
1497 | CanonicalForm |
---|
1498 | CanonicalForm::genOne() const |
---|
1499 | { |
---|
1500 | int what = is_imm( value ); |
---|
1501 | if ( what == FFMARK ) |
---|
1502 | return CanonicalForm( CFFactory::basic( FiniteFieldDomain, 1 ) ); |
---|
1503 | else if ( what == GFMARK ) |
---|
1504 | return CanonicalForm( CFFactory::basic( GaloisFieldDomain, 1 ) ); |
---|
1505 | else if ( what ) |
---|
1506 | return CanonicalForm( CFFactory::basic( IntegerDomain, 1 ) ); |
---|
1507 | else |
---|
1508 | return CanonicalForm( value->genOne() ); |
---|
1509 | } |
---|
1510 | //}}} |
---|
1511 | |
---|
1512 | //{{{ exponentiation |
---|
1513 | CanonicalForm |
---|
1514 | power ( const CanonicalForm & f, int n ) |
---|
1515 | { |
---|
1516 | ASSERT( n >= 0, "illegal exponent" ); |
---|
1517 | if ( f == 0 ) |
---|
1518 | return 0; |
---|
1519 | else if ( f == 1 ) |
---|
1520 | return f; |
---|
1521 | else if ( f == -1 ) { |
---|
1522 | if ( n % 2 == 0 ) |
---|
1523 | return 1; |
---|
1524 | else |
---|
1525 | return -1; |
---|
1526 | } |
---|
1527 | else if ( n == 0 ) |
---|
1528 | return 1; |
---|
1529 | else { |
---|
1530 | CanonicalForm result = f; |
---|
1531 | for ( int i = 1; i < n; i++ ) |
---|
1532 | result *= f; |
---|
1533 | return result; |
---|
1534 | } |
---|
1535 | } |
---|
1536 | |
---|
1537 | CanonicalForm |
---|
1538 | power ( const Variable & v, int n ) |
---|
1539 | { |
---|
1540 | ASSERT( n >= 0, "illegal exponent" ); |
---|
1541 | if ( n == 0 ) |
---|
1542 | return 1; |
---|
1543 | else if ( n == 1 ) |
---|
1544 | return v; |
---|
1545 | else if ( v.level() < 0 ) { |
---|
1546 | CanonicalForm result( v, n-1 ); |
---|
1547 | return result * v; |
---|
1548 | } |
---|
1549 | else |
---|
1550 | return CanonicalForm( v, n ); |
---|
1551 | } |
---|
1552 | //}}} |
---|
1553 | |
---|
1554 | //{{{ switches |
---|
1555 | void |
---|
1556 | On( int sw ) |
---|
1557 | { |
---|
1558 | cf_glob_switches.On( sw ); |
---|
1559 | } |
---|
1560 | |
---|
1561 | void |
---|
1562 | Off( int sw ) |
---|
1563 | { |
---|
1564 | cf_glob_switches.Off( sw ); |
---|
1565 | } |
---|
1566 | |
---|
1567 | bool |
---|
1568 | isOn( int sw ) |
---|
1569 | { |
---|
1570 | return cf_glob_switches.isOn( sw ); |
---|
1571 | } |
---|
1572 | //}}} |
---|