1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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2 | |
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3 | #ifdef HAVE_CONFIG_H |
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4 | #include "config.h" |
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5 | #endif /* HAVE_CONFIG_H */ |
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6 | |
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7 | #ifndef NOSTREAMIO |
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8 | #include <string.h> |
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9 | #if defined(WINNT) && ! defined(__GNUC__) |
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10 | #include <strstrea.h> |
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11 | #else |
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12 | #if __GNUC__ < 3 |
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13 | #include <strstream.h> |
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14 | #else |
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15 | #include <strstream> |
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16 | using namespace std; |
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17 | #endif |
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18 | #endif |
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19 | #endif /* NOSTREAMIO */ |
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20 | |
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21 | #include "cf_assert.h" |
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22 | |
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23 | #include "cf_defs.h" |
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24 | #include "cf_factory.h" |
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25 | #include "int_cf.h" |
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26 | #include "int_int.h" |
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27 | #include "int_poly.h" |
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28 | #include "canonicalform.h" |
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29 | #include "variable.h" |
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30 | #include "imm.h" |
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31 | |
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32 | #ifdef HAVE_OMALLOC |
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33 | const omBin term::term_bin = omGetSpecBin(sizeof(term)); |
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34 | const omBin InternalPoly::InternalPoly_bin = omGetSpecBin(sizeof(InternalPoly)); |
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35 | #endif |
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36 | |
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37 | InternalPoly::InternalPoly( termList first, termList last, const Variable & v ) |
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38 | { |
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39 | firstTerm = first; |
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40 | lastTerm = last; |
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41 | var = v; |
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42 | } |
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43 | |
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44 | InternalPoly::InternalPoly() |
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45 | { |
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46 | ASSERT( 0, "ups, why do you initialize an empty poly" ); |
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47 | } |
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48 | |
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49 | InternalPoly::InternalPoly( const Variable & v, const int e, const CanonicalForm& c ) |
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50 | { |
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51 | var = v; |
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52 | firstTerm = new term( 0, c, e ); |
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53 | lastTerm = firstTerm; |
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54 | } |
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55 | |
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56 | InternalPoly::InternalPoly( const InternalPoly& ):InternalCF() |
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57 | { |
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58 | ASSERT( 0, "ups there is something wrong in your code" ); |
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59 | } |
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60 | |
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61 | InternalPoly::~InternalPoly() |
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62 | { |
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63 | freeTermList( firstTerm ); |
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64 | } |
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65 | |
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66 | InternalCF* |
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67 | InternalPoly::deepCopyObject() const |
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68 | { |
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69 | termList first, last; |
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70 | first = deepCopyTermList( firstTerm, last ); |
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71 | return new InternalPoly( first, last, var ); |
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72 | } |
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73 | |
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74 | InternalCF* |
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75 | InternalPoly::genZero() |
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76 | { |
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77 | return firstTerm->coeff.genZero().getval(); |
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78 | } |
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79 | |
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80 | InternalCF* |
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81 | InternalPoly::genOne() |
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82 | { |
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83 | return firstTerm->coeff.genOne().getval(); |
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84 | } |
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85 | |
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86 | bool |
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87 | InternalPoly::isUnivariate() const |
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88 | { |
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89 | termList cursor = firstTerm; |
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90 | while ( cursor ) |
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91 | { |
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92 | if ( ! cursor->coeff.inCoeffDomain() ) |
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93 | return false; |
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94 | cursor = cursor->next; |
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95 | } |
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96 | return true; |
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97 | } |
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98 | |
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99 | //{{{ int InternalPoly::degree () |
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100 | // docu: see CanonicalForm::sign () |
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101 | int |
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102 | InternalPoly::degree () |
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103 | { |
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104 | return firstTerm->exp; |
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105 | } |
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106 | //}}} |
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107 | |
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108 | //{{{ int InternalPoly::sign () const |
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109 | // docu: see CanonicalForm::sign() |
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110 | int |
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111 | InternalPoly::sign () const |
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112 | { |
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113 | return firstTerm->coeff.sign(); |
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114 | } |
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115 | //}}} |
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116 | |
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117 | //{{{ CanonicalForm InternalPoly::lc (), Lc (), LC () |
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118 | // docu: see CanonicalForm::lc(), Lc(), LC() |
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119 | CanonicalForm |
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120 | InternalPoly::lc () |
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121 | { |
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122 | return firstTerm->coeff.lc(); |
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123 | } |
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124 | |
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125 | CanonicalForm |
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126 | InternalPoly::Lc () |
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127 | { |
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128 | return firstTerm->coeff.Lc(); |
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129 | } |
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130 | |
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131 | CanonicalForm |
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132 | InternalPoly::LC () |
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133 | { |
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134 | return firstTerm->coeff; |
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135 | } |
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136 | //}}} |
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137 | |
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138 | //{{{ CanonicalForm InternalPoly::tailcoeff (), int InternalPoly::taildegree () |
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139 | // docu: see CanonicalForm::tailcoeff(), taildegree() |
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140 | CanonicalForm |
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141 | InternalPoly::tailcoeff () |
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142 | { |
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143 | return lastTerm->coeff; |
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144 | } |
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145 | |
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146 | int |
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147 | InternalPoly::taildegree () |
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148 | { |
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149 | return lastTerm->exp; |
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150 | } |
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151 | //}}} |
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152 | |
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153 | //{{{ CanonicalForm InternalPoly::coeff ( int i ) |
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154 | // docu: see CanonicalForm::operator []() |
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155 | CanonicalForm |
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156 | InternalPoly::coeff ( int i ) |
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157 | { |
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158 | termList theCursor = firstTerm; |
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159 | while ( theCursor ) |
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160 | { |
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161 | if ( theCursor->exp == i ) |
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162 | return theCursor->coeff; |
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163 | else if ( theCursor->exp < i ) |
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164 | return CanonicalForm( 0 ); |
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165 | else |
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166 | theCursor = theCursor->next; |
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167 | } |
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168 | return CanonicalForm( 0 ); |
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169 | } |
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170 | //}}} |
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171 | |
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172 | #ifndef NOSTREAMIO |
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173 | void |
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174 | InternalPoly::print(OSTREAM &aStream, char * aString ) |
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175 | { |
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176 | if ( ! firstTerm ) |
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177 | aStream << 0 << aString; |
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178 | else |
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179 | { |
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180 | char * theString; |
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181 | termList theCursor = firstTerm; |
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182 | while ( theCursor ) |
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183 | { |
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184 | ostrstream theStream; |
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185 | if ( theCursor->exp == 0 ) |
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186 | theCursor->coeff.print( aStream, aString ); |
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187 | else if ( theCursor->coeff.isOne() ) |
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188 | { |
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189 | aStream << var; |
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190 | if ( theCursor->exp != 1 ) |
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191 | aStream << '^' << theCursor->exp << aString; |
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192 | else |
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193 | aStream << aString; |
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194 | } |
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195 | else if ( theCursor->coeff.sign() < 0 && (-theCursor->coeff).isOne() ) |
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196 | { |
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197 | aStream << '-' << var; |
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198 | if ( theCursor->exp != 1 ) |
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199 | aStream << '^' << theCursor->exp << aString; |
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200 | else |
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201 | aStream << aString; |
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202 | } |
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203 | else |
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204 | { |
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205 | theStream << '*' << var; |
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206 | if ( theCursor->exp != 1 ) |
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207 | theStream << '^' << theCursor->exp << aString << ends; |
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208 | else |
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209 | theStream << aString << ends; // results from error in GNU strstream |
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210 | theString = theStream.str(); |
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211 | theCursor->coeff.print( aStream, theString ); |
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212 | theStream.freeze(0);//delete [] theString; |
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213 | } |
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214 | theCursor = theCursor->next; |
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215 | if ( theCursor && ( theCursor->coeff.sign() >= 0 ) ) |
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216 | aStream << '+'; |
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217 | } |
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218 | } |
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219 | } |
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220 | #endif /* NOSTREAMIO */ |
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221 | |
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222 | //{{{ InternalCF * InternalPoly::neg () |
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223 | // docu: see CanonicalForm::operator -() |
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224 | InternalCF * |
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225 | InternalPoly::neg () |
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226 | { |
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227 | if ( getRefCount() <= 1 ) |
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228 | { |
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229 | negateTermList( firstTerm ); |
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230 | return this; |
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231 | } |
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232 | else |
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233 | { |
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234 | decRefCount(); |
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235 | termList last, first = copyTermList( firstTerm, last, true ); |
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236 | return new InternalPoly( first, last, var ); |
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237 | } |
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238 | } |
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239 | //}}} |
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240 | |
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241 | InternalCF* |
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242 | InternalPoly::invert() |
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243 | { |
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244 | if ( inExtension() && getReduce( var ) ) |
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245 | { |
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246 | setReduce( var, false ); |
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247 | CanonicalForm a( this->copyObject() ); |
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248 | CanonicalForm b = getMipo( var ); |
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249 | CanonicalForm u, v; |
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250 | CanonicalForm g = extgcd( a, b, u, v ); |
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251 | setReduce( var, true ); |
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252 | return u.getval(); |
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253 | } |
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254 | else |
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255 | return CFFactory::basic( 0L ); |
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256 | } |
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257 | |
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258 | InternalCF* |
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259 | InternalPoly::tryInvert ( const CanonicalForm& M, bool& fail) |
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260 | { |
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261 | if ( inExtension() && !getReduce ( var ) ) |
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262 | { |
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263 | CanonicalForm b, inverse; |
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264 | CanonicalForm F ( this ->copyObject() ); |
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265 | Variable a = M.mvar(); |
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266 | Variable x = Variable(1); |
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267 | F= mod (F, M); //reduce mod M |
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268 | CanonicalForm g= extgcd (replacevar( F, a, x ), replacevar( M, a, x ), inverse, b ); |
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269 | if(!g.isOne()) |
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270 | fail = true; |
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271 | else |
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272 | inverse = replacevar( inverse, x, a ); // change back to alg var |
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273 | CanonicalForm test= mod (inverse*F, M); |
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274 | return inverse.getval(); |
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275 | } |
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276 | else |
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277 | return CFFactory::basic( 0L ); |
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278 | } |
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279 | |
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280 | InternalCF* |
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281 | InternalPoly::addsame( InternalCF* aCoeff ) |
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282 | { |
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283 | InternalPoly * aPoly = (InternalPoly*)aCoeff; |
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284 | if ( getRefCount() <= 1 ) |
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285 | { |
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286 | firstTerm = addTermList( firstTerm, aPoly->firstTerm, lastTerm, false ); |
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287 | if ( firstTerm && firstTerm->exp != 0 ) |
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288 | return this; |
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289 | else if ( firstTerm ) |
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290 | { |
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291 | InternalCF * res = firstTerm->coeff.getval(); |
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292 | delete this; |
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293 | return res; |
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294 | } |
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295 | else |
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296 | { |
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297 | delete this; |
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298 | return CFFactory::basic( 0L ); |
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299 | } |
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300 | } |
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301 | else |
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302 | { |
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303 | decRefCount(); |
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304 | termList last, first = copyTermList( firstTerm, last ); |
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305 | first = addTermList( first, aPoly->firstTerm, last, false ); |
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306 | if ( first && first->exp != 0 ) |
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307 | return new InternalPoly( first, last, var ); |
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308 | else if ( first ) |
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309 | { |
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310 | InternalCF * res = first->coeff.getval(); |
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311 | delete first; |
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312 | return res; |
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313 | } |
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314 | else |
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315 | return CFFactory::basic( 0L ); |
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316 | |
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317 | } |
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318 | } |
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319 | |
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320 | InternalCF* |
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321 | InternalPoly::subsame( InternalCF* aCoeff ) |
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322 | { |
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323 | InternalPoly * aPoly = (InternalPoly*)aCoeff; |
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324 | if ( getRefCount() <= 1 ) |
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325 | { |
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326 | firstTerm = addTermList( firstTerm, aPoly->firstTerm, lastTerm, true ); |
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327 | if ( firstTerm && firstTerm->exp != 0 ) |
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328 | return this; |
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329 | else if ( firstTerm ) |
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330 | { |
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331 | InternalCF * res = firstTerm->coeff.getval(); |
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332 | delete this; |
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333 | return res; |
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334 | } |
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335 | else |
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336 | { |
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337 | delete this; |
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338 | return CFFactory::basic( 0L ); |
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339 | } |
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340 | } |
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341 | else |
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342 | { |
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343 | decRefCount(); |
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344 | termList last, first = copyTermList( firstTerm, last ); |
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345 | first = addTermList( first, aPoly->firstTerm, last, true ); |
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346 | if ( first && first->exp != 0 ) |
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347 | return new InternalPoly( first, last, var ); |
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348 | else if ( first ) |
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349 | { |
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350 | InternalCF * res = first->coeff.getval(); |
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351 | delete first; |
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352 | return res; |
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353 | } |
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354 | else |
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355 | return CFFactory::basic( 0L ); |
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356 | |
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357 | } |
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358 | } |
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359 | |
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360 | InternalCF* |
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361 | InternalPoly::mulsame( InternalCF* aCoeff ) |
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362 | { |
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363 | if (is_imm(aCoeff)) return mulcoeff(aCoeff); |
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364 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
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365 | termList resultFirst = 0, resultLast = 0; |
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366 | termList theCursor = firstTerm; |
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367 | |
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368 | while ( theCursor ) |
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369 | { |
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370 | resultFirst = mulAddTermList( resultFirst, aPoly->firstTerm, |
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371 | theCursor->coeff, theCursor->exp, resultLast, false ); |
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372 | theCursor = theCursor->next; |
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373 | } |
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374 | if ( inExtension() && getReduce( var ) ) |
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375 | { |
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376 | resultFirst = reduceTermList( resultFirst, (getInternalMipo( var ))->firstTerm, resultLast ); |
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377 | if ( resultFirst == 0 ) |
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378 | { |
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379 | if ( getRefCount() <= 1 ) |
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380 | { |
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381 | delete this; |
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382 | return CFFactory::basic(0L); |
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383 | } |
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384 | else |
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385 | { |
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386 | decRefCount(); |
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387 | return CFFactory::basic(0L); |
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388 | } |
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389 | } |
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390 | else if ( resultFirst->exp == 0 ) |
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391 | { |
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392 | if ( getRefCount() <= 1 ) |
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393 | { |
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394 | InternalCF * res = resultFirst->coeff.getval(); |
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395 | delete resultFirst; |
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396 | delete this; |
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397 | return res; |
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398 | } |
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399 | else |
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400 | { |
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401 | decRefCount(); |
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402 | InternalCF * res = resultFirst->coeff.getval(); |
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403 | delete resultFirst; |
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404 | return res; |
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405 | } |
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406 | } |
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407 | } |
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408 | if ( getRefCount() <= 1 ) |
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409 | { |
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410 | freeTermList( firstTerm ); |
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411 | firstTerm = resultFirst; |
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412 | lastTerm = resultLast; |
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413 | return this; |
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414 | } |
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415 | else |
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416 | { |
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417 | decRefCount(); |
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418 | return new InternalPoly( resultFirst, resultLast, var ); |
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419 | } |
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420 | } |
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421 | |
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422 | InternalCF* |
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423 | InternalPoly::tryMulsame( InternalCF* aCoeff, const CanonicalForm& M) |
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424 | { |
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425 | if (is_imm(aCoeff)) |
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426 | return mulcoeff(aCoeff); |
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427 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
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428 | termList resultFirst = 0, resultLast = 0; |
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429 | termList theCursor = firstTerm; |
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430 | |
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431 | while ( theCursor ) |
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432 | { |
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433 | resultFirst = mulAddTermList( resultFirst, aPoly->firstTerm, |
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434 | theCursor->coeff, theCursor->exp, resultLast, false ); |
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435 | theCursor = theCursor->next; |
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436 | } |
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437 | if ( inExtension() && !getReduce( var ) ) |
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438 | { |
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439 | resultFirst= reduceTermList (resultFirst, ((InternalPoly*) M.getval())->firstTerm, resultLast); |
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440 | if ( resultFirst == 0 ) |
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441 | { |
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442 | if ( getRefCount() <= 1 ) |
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443 | { |
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444 | delete this; |
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445 | return CFFactory::basic(0L); |
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446 | } |
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447 | else |
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448 | { |
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449 | decRefCount(); |
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450 | return CFFactory::basic(0L); |
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451 | } |
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452 | } |
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453 | else if ( resultFirst->exp == 0 ) |
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454 | { |
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455 | if ( getRefCount() <= 1 ) |
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456 | { |
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457 | InternalCF * res = resultFirst->coeff.getval(); |
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458 | delete resultFirst; |
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459 | delete this; |
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460 | return res; |
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461 | } |
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462 | else |
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463 | { |
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464 | decRefCount(); |
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465 | InternalCF * res = resultFirst->coeff.getval(); |
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466 | delete resultFirst; |
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467 | return res; |
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468 | } |
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469 | } |
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470 | } |
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471 | if ( getRefCount() <= 1 ) |
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472 | { |
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473 | freeTermList( firstTerm ); |
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474 | firstTerm = resultFirst; |
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475 | lastTerm = resultLast; |
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476 | return this; |
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477 | } |
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478 | else |
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479 | { |
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480 | decRefCount(); |
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481 | return new InternalPoly( resultFirst, resultLast, var ); |
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482 | } |
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483 | } |
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484 | |
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485 | InternalCF* |
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486 | InternalPoly::dividesame( InternalCF* aCoeff ) |
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487 | { |
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488 | return divsame( aCoeff ); |
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489 | } |
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490 | |
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491 | |
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492 | InternalCF* |
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493 | InternalPoly::divsame( InternalCF* aCoeff ) |
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494 | { |
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495 | if ( inExtension() && getReduce( var ) ) |
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496 | { |
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497 | InternalCF * dummy = aCoeff->invert(); |
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498 | if (is_imm(dummy)) dummy=this->mulsame(dummy); |
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499 | else dummy = dummy->mulsame( this ); |
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500 | if ( getRefCount() <= 1 ) |
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501 | { |
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502 | delete this; |
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503 | return dummy; |
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504 | } |
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505 | else |
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506 | { |
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507 | decRefCount(); |
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508 | return dummy; |
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509 | } |
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510 | } |
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511 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
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512 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
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513 | CanonicalForm coeff, newcoeff; |
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514 | int exp, newexp; |
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515 | bool singleObject; |
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516 | |
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517 | if ( getRefCount() <= 1 ) |
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518 | { |
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519 | first = firstTerm; last = lastTerm; singleObject = true; |
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520 | } |
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521 | else |
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522 | { |
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523 | first = copyTermList( firstTerm, last ); singleObject = false; |
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524 | decRefCount(); |
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525 | } |
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526 | coeff = aPoly->firstTerm->coeff; |
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527 | exp = aPoly->firstTerm->exp; |
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528 | while (first && ( first->exp >= exp ) ) |
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529 | { |
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530 | newcoeff = first->coeff / coeff; |
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531 | newexp = first->exp - exp; |
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532 | dummy = first; |
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533 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
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534 | delete dummy; |
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535 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
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536 | } |
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537 | freeTermList( first ); |
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538 | if ( singleObject ) |
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539 | { |
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540 | if ( resultfirst && resultfirst->exp != 0 ) |
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541 | { |
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542 | firstTerm = resultfirst; |
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543 | lastTerm = resultlast; |
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544 | return this; |
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545 | } |
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546 | else if ( resultfirst ) |
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547 | { |
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548 | InternalCF * res = resultfirst->coeff.getval(); |
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549 | delete resultfirst; |
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550 | firstTerm = 0; |
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551 | delete this; |
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552 | return res; |
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553 | } |
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554 | else |
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555 | { |
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556 | // this should not happen (evtl use assertion) |
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557 | ASSERT( 0, "FATAL ERROR, PLEASE INFORM THE AUTHOR" ); |
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558 | firstTerm = 0; |
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559 | delete this; |
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560 | return CFFactory::basic( 0L ); |
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561 | } |
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562 | } |
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563 | else |
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564 | { |
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565 | if ( resultfirst && resultfirst->exp != 0 ) |
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566 | return new InternalPoly( resultfirst, resultlast, var ); |
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567 | else if ( resultfirst ) |
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568 | { |
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569 | InternalCF * res = resultfirst->coeff.getval(); |
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570 | delete resultfirst; |
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571 | return res; |
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572 | } |
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573 | else |
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574 | return CFFactory::basic( 0L ); |
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575 | } |
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576 | } |
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577 | |
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578 | InternalCF* |
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579 | InternalPoly::tryDivsame( InternalCF* aCoeff, const CanonicalForm& M, bool& fail ) |
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580 | { |
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581 | if ( inExtension() && !getReduce( var ) ) |
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582 | { |
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583 | InternalCF * dummy = aCoeff->tryInvert(M, fail); |
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584 | if (fail) |
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585 | return CFFactory::basic( 0L ); |
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586 | if (is_imm(dummy)) dummy=this->tryMulsame(dummy, M); |
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587 | else dummy = dummy->tryMulsame( this, M); |
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588 | if (fail) |
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589 | { |
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590 | if (getRefCount() <= 1) |
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591 | delete this; |
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592 | else |
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593 | decRefCount(); |
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594 | return dummy; |
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595 | } |
---|
596 | if ( getRefCount() <= 1 ) |
---|
597 | { |
---|
598 | delete this; |
---|
599 | return dummy; |
---|
600 | } |
---|
601 | else |
---|
602 | { |
---|
603 | decRefCount(); |
---|
604 | return dummy; |
---|
605 | } |
---|
606 | } |
---|
607 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
---|
608 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
---|
609 | CanonicalForm coeff, newcoeff; |
---|
610 | int exp, newexp; |
---|
611 | bool singleObject; |
---|
612 | |
---|
613 | if ( getRefCount() <= 1 ) |
---|
614 | { |
---|
615 | first = firstTerm; last = lastTerm; singleObject = true; |
---|
616 | } |
---|
617 | else |
---|
618 | { |
---|
619 | first = copyTermList( firstTerm, last ); singleObject = false; |
---|
620 | decRefCount(); |
---|
621 | } |
---|
622 | coeff = aPoly->firstTerm->coeff; |
---|
623 | exp = aPoly->firstTerm->exp; |
---|
624 | while (first && ( first->exp >= exp ) ) |
---|
625 | { |
---|
626 | newcoeff= first->coeff.tryDiv (coeff, M, fail); |
---|
627 | if (fail) |
---|
628 | { |
---|
629 | freeTermList (first); |
---|
630 | return CFFactory::basic (0L); |
---|
631 | } |
---|
632 | newcoeff= reduce (newcoeff, M); |
---|
633 | newexp = first->exp - exp; |
---|
634 | dummy = first; |
---|
635 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
---|
636 | delete dummy; |
---|
637 | if (!newcoeff.isZero()) |
---|
638 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
---|
639 | } |
---|
640 | freeTermList( first ); |
---|
641 | if ( singleObject ) |
---|
642 | { |
---|
643 | if ( resultfirst && resultfirst->exp != 0 ) |
---|
644 | { |
---|
645 | firstTerm = resultfirst; |
---|
646 | lastTerm = resultlast; |
---|
647 | return this; |
---|
648 | } |
---|
649 | else if ( resultfirst ) |
---|
650 | { |
---|
651 | InternalCF * res = resultfirst->coeff.getval(); |
---|
652 | delete resultfirst; |
---|
653 | firstTerm = 0; |
---|
654 | delete this; |
---|
655 | return res; |
---|
656 | } |
---|
657 | else |
---|
658 | { |
---|
659 | // this should not happen (evtl use assertion) |
---|
660 | ASSERT( 0, "FATAL ERROR, PLEASE INFORM THE AUTHOR" ); |
---|
661 | firstTerm = 0; |
---|
662 | delete this; |
---|
663 | return CFFactory::basic( 0L ); |
---|
664 | } |
---|
665 | } |
---|
666 | else |
---|
667 | { |
---|
668 | if ( resultfirst && resultfirst->exp != 0 ) |
---|
669 | return new InternalPoly( resultfirst, resultlast, var ); |
---|
670 | else if ( resultfirst ) |
---|
671 | { |
---|
672 | InternalCF * res = resultfirst->coeff.getval(); |
---|
673 | delete resultfirst; |
---|
674 | return res; |
---|
675 | } |
---|
676 | else |
---|
677 | return CFFactory::basic( 0L ); |
---|
678 | } |
---|
679 | } |
---|
680 | |
---|
681 | InternalCF* |
---|
682 | InternalPoly::modulosame( InternalCF* aCoeff ) |
---|
683 | { |
---|
684 | return modsame( aCoeff ); |
---|
685 | } |
---|
686 | |
---|
687 | InternalCF* |
---|
688 | InternalPoly::modsame( InternalCF* aCoeff ) |
---|
689 | { |
---|
690 | if ( inExtension() && getReduce( var ) ) |
---|
691 | { |
---|
692 | if ( deleteObject() ) delete this; |
---|
693 | return CFFactory::basic( 0L ); |
---|
694 | } |
---|
695 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
---|
696 | termList dummy, first, last; |
---|
697 | CanonicalForm coeff, newcoeff; |
---|
698 | int exp, newexp; |
---|
699 | bool singleObject; |
---|
700 | |
---|
701 | if ( getRefCount() <= 1 ) |
---|
702 | { |
---|
703 | first = firstTerm; last = lastTerm; singleObject = true; |
---|
704 | } |
---|
705 | else |
---|
706 | { |
---|
707 | first = copyTermList( firstTerm, last ); singleObject = false; |
---|
708 | decRefCount(); |
---|
709 | } |
---|
710 | coeff = aPoly->firstTerm->coeff; |
---|
711 | exp = aPoly->firstTerm->exp; |
---|
712 | while (first && ( first->exp >= exp ) ) |
---|
713 | { |
---|
714 | newcoeff = first->coeff / coeff; |
---|
715 | newexp = first->exp - exp; |
---|
716 | dummy = first; |
---|
717 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
---|
718 | delete dummy; |
---|
719 | } |
---|
720 | if ( singleObject ) |
---|
721 | { |
---|
722 | if ( first && first->exp != 0 ) |
---|
723 | { |
---|
724 | firstTerm = first; |
---|
725 | lastTerm = last; |
---|
726 | return this; |
---|
727 | } |
---|
728 | else if ( first ) |
---|
729 | { |
---|
730 | InternalCF * res = first->coeff.getval(); |
---|
731 | delete first; |
---|
732 | firstTerm = 0; |
---|
733 | delete this; |
---|
734 | return res; |
---|
735 | } |
---|
736 | else |
---|
737 | { |
---|
738 | firstTerm = 0; |
---|
739 | delete this; |
---|
740 | return CFFactory::basic( 0L ); |
---|
741 | } |
---|
742 | } |
---|
743 | else |
---|
744 | { |
---|
745 | if ( first && first->exp != 0 ) |
---|
746 | return new InternalPoly( first, last, var ); |
---|
747 | else if ( first ) |
---|
748 | { |
---|
749 | InternalCF * res = first->coeff.getval(); |
---|
750 | delete first; |
---|
751 | return res; |
---|
752 | } |
---|
753 | else |
---|
754 | return CFFactory::basic( 0L ); |
---|
755 | } |
---|
756 | } |
---|
757 | |
---|
758 | |
---|
759 | void |
---|
760 | InternalPoly::divremsame( InternalCF* acoeff, InternalCF*& quot, InternalCF*& rem ) |
---|
761 | { |
---|
762 | if ( inExtension() && getReduce( var ) ) |
---|
763 | { |
---|
764 | InternalCF * dummy = acoeff->invert(); |
---|
765 | quot = dummy->mulsame( this ); |
---|
766 | rem = CFFactory::basic( 0L ); |
---|
767 | } |
---|
768 | else |
---|
769 | { |
---|
770 | InternalPoly *aPoly = (InternalPoly*)acoeff; |
---|
771 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
---|
772 | CanonicalForm coeff, newcoeff; |
---|
773 | int exp, newexp; |
---|
774 | |
---|
775 | first = copyTermList( firstTerm, last ); |
---|
776 | |
---|
777 | coeff = aPoly->firstTerm->coeff; |
---|
778 | exp = aPoly->firstTerm->exp; |
---|
779 | while (first && ( first->exp >= exp ) ) |
---|
780 | { |
---|
781 | newcoeff = first->coeff / coeff; |
---|
782 | newexp = first->exp - exp; |
---|
783 | dummy = first; |
---|
784 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
---|
785 | delete dummy; |
---|
786 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
---|
787 | } |
---|
788 | if ( resultfirst ) |
---|
789 | if ( resultfirst->exp == 0 ) |
---|
790 | { |
---|
791 | quot = resultfirst->coeff.getval(); |
---|
792 | delete resultfirst; |
---|
793 | } |
---|
794 | else |
---|
795 | quot = new InternalPoly( resultfirst, resultlast, var ); |
---|
796 | else |
---|
797 | quot = CFFactory::basic( 0L ); |
---|
798 | if ( first ) |
---|
799 | if ( first->exp == 0 ) |
---|
800 | { |
---|
801 | rem = first->coeff.getval(); |
---|
802 | delete first; |
---|
803 | } |
---|
804 | else |
---|
805 | rem = new InternalPoly( first, last, var ); |
---|
806 | else |
---|
807 | rem = CFFactory::basic( 0L ); |
---|
808 | } |
---|
809 | } |
---|
810 | |
---|
811 | bool |
---|
812 | InternalPoly::divremsamet( InternalCF* acoeff, InternalCF*& quot, InternalCF*& rem ) |
---|
813 | { |
---|
814 | if ( inExtension() && getReduce( var ) ) |
---|
815 | { |
---|
816 | divremsame( acoeff, quot, rem ); |
---|
817 | return true; |
---|
818 | } |
---|
819 | InternalPoly *aPoly = (InternalPoly*)acoeff; |
---|
820 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
---|
821 | CanonicalForm coeff, newcoeff, dummycoeff; |
---|
822 | int exp, newexp; |
---|
823 | bool divideok = true; |
---|
824 | |
---|
825 | // if ( ! ::divremt( lastTerm->coeff, aPoly->lastTerm->coeff, newcoeff, dummycoeff ) ) |
---|
826 | // return false; |
---|
827 | |
---|
828 | first = copyTermList( firstTerm, last ); |
---|
829 | |
---|
830 | coeff = aPoly->firstTerm->coeff; |
---|
831 | exp = aPoly->firstTerm->exp; |
---|
832 | while (first && ( first->exp >= exp ) && divideok ) |
---|
833 | { |
---|
834 | divideok = divremt( first->coeff, coeff, newcoeff, dummycoeff ); |
---|
835 | if ( divideok && dummycoeff.isZero() ) |
---|
836 | { |
---|
837 | newexp = first->exp - exp; |
---|
838 | dummy = first; |
---|
839 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
---|
840 | delete dummy; |
---|
841 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
---|
842 | } |
---|
843 | else |
---|
844 | divideok = false; |
---|
845 | } |
---|
846 | if ( divideok ) |
---|
847 | { |
---|
848 | if ( resultfirst ) |
---|
849 | if ( resultfirst->exp == 0 ) |
---|
850 | { |
---|
851 | quot = resultfirst->coeff.getval(); |
---|
852 | delete resultfirst; |
---|
853 | } |
---|
854 | else |
---|
855 | quot = new InternalPoly( resultfirst, resultlast, var ); |
---|
856 | else |
---|
857 | quot = CFFactory::basic( 0L ); |
---|
858 | if ( first ) |
---|
859 | if ( first->exp == 0 ) |
---|
860 | { |
---|
861 | rem = first->coeff.getval(); |
---|
862 | delete first; |
---|
863 | } |
---|
864 | else |
---|
865 | rem = new InternalPoly( first, last, var ); |
---|
866 | else |
---|
867 | rem = CFFactory::basic( 0L ); |
---|
868 | } |
---|
869 | else |
---|
870 | { |
---|
871 | freeTermList( resultfirst ); |
---|
872 | freeTermList( first ); |
---|
873 | } |
---|
874 | return divideok; |
---|
875 | } |
---|
876 | |
---|
877 | bool |
---|
878 | InternalPoly::tryDivremsamet( InternalCF* acoeff, InternalCF*& quot, InternalCF*& rem, const CanonicalForm& M, bool& fail) |
---|
879 | { |
---|
880 | if (inExtension() && !getReduce (var)) |
---|
881 | { |
---|
882 | InternalCF * dummy = acoeff->tryInvert(M, fail); |
---|
883 | if (fail) |
---|
884 | return false; |
---|
885 | quot = dummy->tryMulsame( this, M); |
---|
886 | rem = CFFactory::basic( 0L ); |
---|
887 | if (fail) |
---|
888 | return false; |
---|
889 | return true; |
---|
890 | } |
---|
891 | InternalPoly *aPoly = (InternalPoly*)acoeff; |
---|
892 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
---|
893 | CanonicalForm coeff, newcoeff, dummycoeff; |
---|
894 | int exp, newexp; |
---|
895 | bool divideok = true; |
---|
896 | |
---|
897 | first = copyTermList( firstTerm, last ); |
---|
898 | |
---|
899 | coeff = aPoly->firstTerm->coeff; |
---|
900 | exp = aPoly->firstTerm->exp; |
---|
901 | while (first && ( first->exp >= exp ) && divideok ) |
---|
902 | { |
---|
903 | divideok = tryDivremt( first->coeff, coeff, newcoeff, dummycoeff, M, fail ); |
---|
904 | if (fail) |
---|
905 | { |
---|
906 | freeTermList (first); |
---|
907 | return false; |
---|
908 | } |
---|
909 | if ( divideok && dummycoeff.isZero() ) |
---|
910 | { |
---|
911 | newexp = first->exp - exp; |
---|
912 | dummy = first; |
---|
913 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
---|
914 | delete dummy; |
---|
915 | if (!newcoeff.isZero()) |
---|
916 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
---|
917 | } |
---|
918 | else |
---|
919 | divideok = false; |
---|
920 | } |
---|
921 | if ( divideok ) |
---|
922 | { |
---|
923 | if ( resultfirst ) |
---|
924 | if ( resultfirst->exp == 0 ) |
---|
925 | { |
---|
926 | quot = resultfirst->coeff.getval(); |
---|
927 | delete resultfirst; |
---|
928 | } |
---|
929 | else |
---|
930 | quot = new InternalPoly( resultfirst, resultlast, var ); |
---|
931 | else |
---|
932 | quot = CFFactory::basic( 0L ); |
---|
933 | if ( first ) |
---|
934 | if ( first->exp == 0 ) |
---|
935 | { |
---|
936 | rem = first->coeff.getval(); |
---|
937 | delete first; |
---|
938 | } |
---|
939 | else |
---|
940 | { |
---|
941 | if (first->coeff.isZero()) |
---|
942 | { |
---|
943 | rem= CFFactory::basic (0L); |
---|
944 | delete first; |
---|
945 | } |
---|
946 | else |
---|
947 | rem = new InternalPoly( first, last, var ); |
---|
948 | } |
---|
949 | else |
---|
950 | rem = CFFactory::basic( 0L ); |
---|
951 | } |
---|
952 | else |
---|
953 | { |
---|
954 | freeTermList( resultfirst ); |
---|
955 | freeTermList( first ); |
---|
956 | } |
---|
957 | return divideok; |
---|
958 | } |
---|
959 | |
---|
960 | //{{{ int InternalPoly::comparesame, comparecoeff ( InternalCF * acoeff ) |
---|
961 | //{{{ docu |
---|
962 | // |
---|
963 | // comparesame(), comparecoeff() - compare with an |
---|
964 | // InternalPoly. |
---|
965 | // |
---|
966 | // comparecoeff() always returns 1 since CO is defined to be |
---|
967 | // larger than anything which is a coefficient w.r.t. CO. |
---|
968 | // |
---|
969 | // comparesame() compares the coefficient vectors of f=CO and |
---|
970 | // g=acoeff w.r.t to a lexicographic order in the following way: |
---|
971 | // f < g iff there exists an 0 <= i <= max(deg(f),deg(g)) s.t. |
---|
972 | // i) f[j] = g[j] for all i < j <= max(deg(f),deg(g)) and |
---|
973 | // ii) g[i] occurs in g (i.e. is not equal to zero) and |
---|
974 | // f[i] does not occur in f or f[i] < g[i] if f[i] occurs |
---|
975 | // where f[i] denotes the coefficient to the power x^i of f. |
---|
976 | // |
---|
977 | // As usual, comparesame() returns 1 if CO is larger than c, 0 if |
---|
978 | // CO equals c, and -1 if CO is less than c. However, this |
---|
979 | // function is optimized to test on equality since this is its |
---|
980 | // most important and frequent usage. |
---|
981 | // |
---|
982 | // See the respective `CanonicalForm'-methods for an explanation |
---|
983 | // why we define such a strange (but total) ordering on |
---|
984 | // polynomials. |
---|
985 | // |
---|
986 | // See also: CanonicalForm::operator <(), CanonicalForm::operator ==() |
---|
987 | // |
---|
988 | //}}} |
---|
989 | int |
---|
990 | InternalPoly::comparesame ( InternalCF * acoeff ) |
---|
991 | { |
---|
992 | ASSERT( ! ::is_imm( acoeff ) && acoeff->level() > LEVELBASE, "incompatible base coefficients" ); |
---|
993 | InternalPoly* apoly = (InternalPoly*)acoeff; |
---|
994 | // check on triviality |
---|
995 | if ( this == apoly ) |
---|
996 | return 0; |
---|
997 | else |
---|
998 | { |
---|
999 | termList cursor1 = firstTerm; |
---|
1000 | termList cursor2 = apoly->firstTerm; |
---|
1001 | for ( ; cursor1 && cursor2; cursor1 = cursor1->next, cursor2 = cursor2->next ) |
---|
1002 | // we test on inequality of coefficients at this |
---|
1003 | // point instead of testing on "less than" at the |
---|
1004 | // last `else' in the enclosed `if' statement since a |
---|
1005 | // test on inequaltiy in general is cheaper |
---|
1006 | if ( (cursor1->exp != cursor2->exp) || (cursor1->coeff != cursor2->coeff) ) |
---|
1007 | { |
---|
1008 | if ( cursor1->exp > cursor2->exp ) |
---|
1009 | return 1; |
---|
1010 | else if ( cursor1->exp < cursor2->exp ) |
---|
1011 | return -1; |
---|
1012 | else if ( cursor1->coeff > cursor2->coeff ) |
---|
1013 | return 1; |
---|
1014 | else |
---|
1015 | return -1; |
---|
1016 | } |
---|
1017 | // check trailing terms |
---|
1018 | if ( cursor1 == cursor2 ) |
---|
1019 | return 0; |
---|
1020 | else if ( cursor1 != 0 ) |
---|
1021 | return 1; |
---|
1022 | else |
---|
1023 | return -1; |
---|
1024 | } |
---|
1025 | } |
---|
1026 | |
---|
1027 | int |
---|
1028 | InternalPoly::comparecoeff ( InternalCF * ) |
---|
1029 | { |
---|
1030 | return 1; |
---|
1031 | } |
---|
1032 | //}}} |
---|
1033 | |
---|
1034 | InternalCF* |
---|
1035 | InternalPoly::addcoeff( InternalCF* cc ) |
---|
1036 | { |
---|
1037 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1038 | if ( c.isZero() ) |
---|
1039 | return this; |
---|
1040 | else |
---|
1041 | { |
---|
1042 | if ( getRefCount() <= 1 ) |
---|
1043 | { |
---|
1044 | if ( lastTerm->exp == 0 ) |
---|
1045 | { |
---|
1046 | lastTerm->coeff += c; |
---|
1047 | if ( lastTerm->coeff.isZero() ) |
---|
1048 | { |
---|
1049 | termList cursor = firstTerm; |
---|
1050 | while ( cursor->next != lastTerm ) |
---|
1051 | cursor = cursor->next; |
---|
1052 | delete lastTerm; |
---|
1053 | cursor->next = 0; |
---|
1054 | lastTerm = cursor; |
---|
1055 | } |
---|
1056 | } |
---|
1057 | else |
---|
1058 | { |
---|
1059 | lastTerm->next = new term( 0, c, 0 ); |
---|
1060 | lastTerm = lastTerm->next; |
---|
1061 | } |
---|
1062 | return this; |
---|
1063 | } |
---|
1064 | else |
---|
1065 | { |
---|
1066 | decRefCount(); |
---|
1067 | termList last, first = copyTermList( firstTerm, last, false ); |
---|
1068 | if ( last->exp == 0 ) |
---|
1069 | { |
---|
1070 | last->coeff += c; |
---|
1071 | if ( last->coeff.isZero() ) |
---|
1072 | { |
---|
1073 | termList cursor = first; |
---|
1074 | while ( cursor->next != last ) |
---|
1075 | cursor = cursor->next; |
---|
1076 | delete last; |
---|
1077 | cursor->next = 0; |
---|
1078 | last = cursor; |
---|
1079 | } |
---|
1080 | } |
---|
1081 | else |
---|
1082 | { |
---|
1083 | last->next = new term( 0, c, 0L ); |
---|
1084 | last = last->next; |
---|
1085 | } |
---|
1086 | return new InternalPoly( first, last, var ); |
---|
1087 | } |
---|
1088 | } |
---|
1089 | } |
---|
1090 | |
---|
1091 | InternalCF* |
---|
1092 | InternalPoly::subcoeff( InternalCF* cc, bool negate ) |
---|
1093 | { |
---|
1094 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1095 | if ( c.isZero() ) |
---|
1096 | if ( getRefCount() > 1 ) |
---|
1097 | { |
---|
1098 | decRefCount(); |
---|
1099 | termList last, first = copyTermList( firstTerm, last, negate ); |
---|
1100 | return new InternalPoly( first, last, var ); |
---|
1101 | } |
---|
1102 | else |
---|
1103 | { |
---|
1104 | if ( negate ) |
---|
1105 | negateTermList( firstTerm ); |
---|
1106 | return this; |
---|
1107 | } |
---|
1108 | else |
---|
1109 | { |
---|
1110 | if ( getRefCount() <= 1 ) |
---|
1111 | { |
---|
1112 | if ( lastTerm->exp == 0 ) |
---|
1113 | { |
---|
1114 | if ( negate ) |
---|
1115 | { |
---|
1116 | negateTermList( firstTerm ); |
---|
1117 | lastTerm->coeff += c; |
---|
1118 | } |
---|
1119 | else |
---|
1120 | lastTerm->coeff -= c; |
---|
1121 | if ( lastTerm->coeff.isZero() ) |
---|
1122 | { |
---|
1123 | termList cursor = firstTerm; |
---|
1124 | while ( cursor->next != lastTerm ) |
---|
1125 | cursor = cursor->next; |
---|
1126 | delete lastTerm; |
---|
1127 | cursor->next = 0; |
---|
1128 | lastTerm = cursor; |
---|
1129 | } |
---|
1130 | } |
---|
1131 | else |
---|
1132 | { |
---|
1133 | if ( negate ) |
---|
1134 | { |
---|
1135 | negateTermList( firstTerm ); |
---|
1136 | lastTerm->next = new term( 0, c, 0 ); |
---|
1137 | } |
---|
1138 | else |
---|
1139 | lastTerm->next = new term( 0, -c, 0 ); |
---|
1140 | lastTerm = lastTerm->next; |
---|
1141 | } |
---|
1142 | return this; |
---|
1143 | } |
---|
1144 | else |
---|
1145 | { |
---|
1146 | decRefCount(); |
---|
1147 | termList last, first = copyTermList( firstTerm, last, negate ); |
---|
1148 | if ( last->exp == 0 ) |
---|
1149 | { |
---|
1150 | if ( negate ) |
---|
1151 | last->coeff += c; |
---|
1152 | else |
---|
1153 | last->coeff -= c; |
---|
1154 | if ( last->coeff.isZero() ) |
---|
1155 | { |
---|
1156 | termList cursor = first; |
---|
1157 | while ( cursor->next != last ) |
---|
1158 | cursor = cursor->next; |
---|
1159 | delete last; |
---|
1160 | cursor->next = 0; |
---|
1161 | last = cursor; |
---|
1162 | } |
---|
1163 | } |
---|
1164 | else |
---|
1165 | { |
---|
1166 | if ( negate ) |
---|
1167 | last->next = new term( 0, c, 0 ); |
---|
1168 | else |
---|
1169 | last->next = new term( 0, -c, 0 ); |
---|
1170 | last = last->next; |
---|
1171 | } |
---|
1172 | return new InternalPoly( first, last, var ); |
---|
1173 | } |
---|
1174 | } |
---|
1175 | } |
---|
1176 | |
---|
1177 | InternalCF* |
---|
1178 | InternalPoly::mulcoeff( InternalCF* cc ) |
---|
1179 | { |
---|
1180 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1181 | if ( c.isZero() ) |
---|
1182 | { |
---|
1183 | if ( getRefCount() <= 1 ) |
---|
1184 | { |
---|
1185 | delete this; |
---|
1186 | return CFFactory::basic( 0L ); |
---|
1187 | } |
---|
1188 | else |
---|
1189 | { |
---|
1190 | decRefCount(); |
---|
1191 | return CFFactory::basic( 0L ); |
---|
1192 | } |
---|
1193 | } |
---|
1194 | else if ( c.isOne() ) |
---|
1195 | return this; |
---|
1196 | else |
---|
1197 | { |
---|
1198 | if ( getRefCount() <= 1 ) |
---|
1199 | { |
---|
1200 | mulTermList( firstTerm, c, 0L ); |
---|
1201 | return this; |
---|
1202 | } |
---|
1203 | else |
---|
1204 | { |
---|
1205 | decRefCount(); |
---|
1206 | termList last, first = copyTermList( firstTerm, last ); |
---|
1207 | mulTermList( first, c, 0 ); |
---|
1208 | return new InternalPoly( first, last, var ); |
---|
1209 | } |
---|
1210 | } |
---|
1211 | } |
---|
1212 | |
---|
1213 | InternalCF* |
---|
1214 | InternalPoly::dividecoeff( InternalCF* cc, bool invert ) |
---|
1215 | { |
---|
1216 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1217 | if ( inExtension() && getReduce( var ) && invert ) |
---|
1218 | { |
---|
1219 | InternalCF * dummy; |
---|
1220 | dummy = this->invert(); |
---|
1221 | if (is_imm(dummy)) |
---|
1222 | { |
---|
1223 | if (is_imm(cc)) |
---|
1224 | { |
---|
1225 | InternalInteger *d=new InternalInteger(imm2int(dummy)*imm2int(cc)); |
---|
1226 | dummy=d; |
---|
1227 | } |
---|
1228 | else |
---|
1229 | dummy=cc->mulcoeff(dummy); |
---|
1230 | } |
---|
1231 | else dummy = dummy->mulcoeff( cc ); |
---|
1232 | if ( getRefCount() <= 1 ) |
---|
1233 | { |
---|
1234 | delete this; |
---|
1235 | return dummy; |
---|
1236 | } |
---|
1237 | else |
---|
1238 | { |
---|
1239 | decRefCount(); |
---|
1240 | return dummy; |
---|
1241 | } |
---|
1242 | } |
---|
1243 | if ( invert ) |
---|
1244 | { |
---|
1245 | if ( getRefCount() <= 1 ) |
---|
1246 | { |
---|
1247 | delete this; |
---|
1248 | return CFFactory::basic( 0L ); |
---|
1249 | } |
---|
1250 | else |
---|
1251 | { |
---|
1252 | decRefCount(); |
---|
1253 | return CFFactory::basic( 0L ); |
---|
1254 | } |
---|
1255 | } |
---|
1256 | if ( c.isOne() ) |
---|
1257 | return this; |
---|
1258 | else |
---|
1259 | { |
---|
1260 | if ( getRefCount() <= 1 ) |
---|
1261 | { |
---|
1262 | firstTerm = divideTermList( firstTerm, c, lastTerm ); |
---|
1263 | if ( firstTerm && firstTerm->exp != 0 ) |
---|
1264 | return this; |
---|
1265 | else if ( firstTerm ) |
---|
1266 | { |
---|
1267 | InternalCF * res = firstTerm->coeff.getval(); |
---|
1268 | delete this; |
---|
1269 | return res; |
---|
1270 | } |
---|
1271 | else |
---|
1272 | { |
---|
1273 | delete this; |
---|
1274 | return CFFactory::basic( 0L ); |
---|
1275 | } |
---|
1276 | } |
---|
1277 | else |
---|
1278 | { |
---|
1279 | decRefCount(); |
---|
1280 | termList last, first = copyTermList( firstTerm, last ); |
---|
1281 | first = divideTermList( first, c, last ); |
---|
1282 | if ( first && first->exp != 0 ) |
---|
1283 | return new InternalPoly( first, last, var ); |
---|
1284 | else if ( first ) |
---|
1285 | { |
---|
1286 | InternalCF * res = first->coeff.getval(); |
---|
1287 | delete first; |
---|
1288 | return res; |
---|
1289 | } |
---|
1290 | else |
---|
1291 | { |
---|
1292 | delete first; |
---|
1293 | return CFFactory::basic( 0L ); |
---|
1294 | } |
---|
1295 | } |
---|
1296 | } |
---|
1297 | } |
---|
1298 | |
---|
1299 | InternalCF* |
---|
1300 | InternalPoly::tryDividecoeff( InternalCF* cc, bool invert, const CanonicalForm& M, bool& fail ) |
---|
1301 | { |
---|
1302 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1303 | if ( inExtension() && !getReduce( var ) && invert ) |
---|
1304 | { |
---|
1305 | InternalCF * dummy; |
---|
1306 | dummy = this->tryInvert(M, fail); |
---|
1307 | if (fail) |
---|
1308 | { |
---|
1309 | if (getRefCount() <= 1) |
---|
1310 | delete this; |
---|
1311 | else |
---|
1312 | decRefCount(); |
---|
1313 | return dummy; //is equal to CFFactory::basic ( 0L ) in this case |
---|
1314 | } |
---|
1315 | if (is_imm(dummy)) |
---|
1316 | { |
---|
1317 | if (is_imm(cc)) |
---|
1318 | { |
---|
1319 | InternalInteger *d=new InternalInteger(imm2int(dummy)*imm2int(cc)); |
---|
1320 | dummy=d; |
---|
1321 | } |
---|
1322 | else |
---|
1323 | dummy=cc->mulcoeff(dummy); |
---|
1324 | } |
---|
1325 | else dummy = dummy->mulcoeff( cc ); |
---|
1326 | if ( getRefCount() <= 1 ) |
---|
1327 | { |
---|
1328 | delete this; |
---|
1329 | return dummy; |
---|
1330 | } |
---|
1331 | else |
---|
1332 | { |
---|
1333 | decRefCount(); |
---|
1334 | return dummy; |
---|
1335 | } |
---|
1336 | } |
---|
1337 | if ( invert ) |
---|
1338 | { |
---|
1339 | if ( getRefCount() <= 1 ) |
---|
1340 | { |
---|
1341 | delete this; |
---|
1342 | return CFFactory::basic( 0L ); |
---|
1343 | } |
---|
1344 | else |
---|
1345 | { |
---|
1346 | decRefCount(); |
---|
1347 | return CFFactory::basic( 0L ); |
---|
1348 | } |
---|
1349 | } |
---|
1350 | if ( c.isOne() ) |
---|
1351 | return this; |
---|
1352 | //one should never get here |
---|
1353 | else |
---|
1354 | { |
---|
1355 | if ( getRefCount() <= 1 ) |
---|
1356 | { |
---|
1357 | firstTerm = divideTermList( firstTerm, c, lastTerm ); |
---|
1358 | if ( firstTerm && firstTerm->exp != 0 ) |
---|
1359 | return this; |
---|
1360 | else if ( firstTerm ) |
---|
1361 | { |
---|
1362 | InternalCF * res = firstTerm->coeff.getval(); |
---|
1363 | delete this; |
---|
1364 | return res; |
---|
1365 | } |
---|
1366 | else |
---|
1367 | { |
---|
1368 | delete this; |
---|
1369 | return CFFactory::basic( 0L ); |
---|
1370 | } |
---|
1371 | } |
---|
1372 | else |
---|
1373 | { |
---|
1374 | decRefCount(); |
---|
1375 | termList last, first = copyTermList( firstTerm, last ); |
---|
1376 | first = divideTermList( first, c, last ); |
---|
1377 | if ( first && first->exp != 0 ) |
---|
1378 | return new InternalPoly( first, last, var ); |
---|
1379 | else if ( first ) |
---|
1380 | { |
---|
1381 | InternalCF * res = first->coeff.getval(); |
---|
1382 | delete first; |
---|
1383 | return res; |
---|
1384 | } |
---|
1385 | else |
---|
1386 | { |
---|
1387 | delete first; |
---|
1388 | return CFFactory::basic( 0L ); |
---|
1389 | } |
---|
1390 | } |
---|
1391 | } |
---|
1392 | } |
---|
1393 | |
---|
1394 | |
---|
1395 | InternalCF* |
---|
1396 | InternalPoly::divcoeff( InternalCF* cc, bool invert ) |
---|
1397 | { |
---|
1398 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1399 | if ( inExtension() && getReduce( var ) && invert ) |
---|
1400 | { |
---|
1401 | InternalCF * dummy; |
---|
1402 | dummy = this->invert(); |
---|
1403 | dummy = dummy->mulcoeff( cc ); |
---|
1404 | if ( getRefCount() <= 1 ) |
---|
1405 | { |
---|
1406 | delete this; |
---|
1407 | return dummy; |
---|
1408 | } |
---|
1409 | else |
---|
1410 | { |
---|
1411 | decRefCount(); |
---|
1412 | return dummy; |
---|
1413 | } |
---|
1414 | } |
---|
1415 | if ( invert ) |
---|
1416 | { |
---|
1417 | if ( getRefCount() <= 1 ) |
---|
1418 | { |
---|
1419 | delete this; |
---|
1420 | return CFFactory::basic( 0L ); |
---|
1421 | } |
---|
1422 | else |
---|
1423 | { |
---|
1424 | decRefCount(); |
---|
1425 | return CFFactory::basic( 0L ); |
---|
1426 | } |
---|
1427 | } |
---|
1428 | if ( c.isOne() ) |
---|
1429 | return this; |
---|
1430 | else |
---|
1431 | { |
---|
1432 | if ( getRefCount() <= 1 ) |
---|
1433 | { |
---|
1434 | firstTerm = divTermList( firstTerm, c, lastTerm ); |
---|
1435 | if ( firstTerm && firstTerm->exp != 0 ) |
---|
1436 | return this; |
---|
1437 | else if ( firstTerm ) |
---|
1438 | { |
---|
1439 | InternalCF * res = firstTerm->coeff.getval(); |
---|
1440 | delete this; |
---|
1441 | return res; |
---|
1442 | } |
---|
1443 | else |
---|
1444 | { |
---|
1445 | delete this; |
---|
1446 | return CFFactory::basic( 0L ); |
---|
1447 | } |
---|
1448 | } |
---|
1449 | else |
---|
1450 | { |
---|
1451 | decRefCount(); |
---|
1452 | termList last, first = copyTermList( firstTerm, last ); |
---|
1453 | first = divTermList( first, c, last ); |
---|
1454 | if ( first && first->exp != 0 ) |
---|
1455 | return new InternalPoly( first, last, var ); |
---|
1456 | else if ( first ) |
---|
1457 | { |
---|
1458 | InternalCF * res = first->coeff.getval(); |
---|
1459 | delete first; |
---|
1460 | return res; |
---|
1461 | } |
---|
1462 | else |
---|
1463 | { |
---|
1464 | delete first; |
---|
1465 | return CFFactory::basic( 0L ); |
---|
1466 | } |
---|
1467 | } |
---|
1468 | } |
---|
1469 | } |
---|
1470 | |
---|
1471 | InternalCF* |
---|
1472 | InternalPoly::tryDivcoeff( InternalCF* cc, bool invert, const CanonicalForm& M, bool& fail ) |
---|
1473 | { |
---|
1474 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1475 | if ( inExtension() && !getReduce( var ) && invert ) |
---|
1476 | { |
---|
1477 | InternalCF * dummy; |
---|
1478 | dummy = this->tryInvert(M, fail); |
---|
1479 | if (fail) |
---|
1480 | { |
---|
1481 | if (getRefCount() <= 1) |
---|
1482 | delete this; |
---|
1483 | else |
---|
1484 | decRefCount(); |
---|
1485 | return dummy; |
---|
1486 | } |
---|
1487 | dummy = dummy->mulcoeff( cc ); |
---|
1488 | if ( getRefCount() <= 1 ) |
---|
1489 | { |
---|
1490 | delete this; |
---|
1491 | return dummy; |
---|
1492 | } |
---|
1493 | else |
---|
1494 | { |
---|
1495 | decRefCount(); |
---|
1496 | return dummy; |
---|
1497 | } |
---|
1498 | } |
---|
1499 | if ( invert ) |
---|
1500 | { |
---|
1501 | if ( getRefCount() <= 1 ) |
---|
1502 | { |
---|
1503 | delete this; |
---|
1504 | return CFFactory::basic( 0L ); |
---|
1505 | } |
---|
1506 | else |
---|
1507 | { |
---|
1508 | decRefCount(); |
---|
1509 | return CFFactory::basic( 0L ); |
---|
1510 | } |
---|
1511 | } |
---|
1512 | if ( c.isOne() ) |
---|
1513 | return this; |
---|
1514 | else |
---|
1515 | { |
---|
1516 | if ( getRefCount() <= 1 ) |
---|
1517 | { |
---|
1518 | firstTerm = tryDivTermList( firstTerm, c, lastTerm, M, fail ); |
---|
1519 | if (fail) |
---|
1520 | { |
---|
1521 | delete this; |
---|
1522 | return CFFactory::basic (0L); |
---|
1523 | } |
---|
1524 | if ( firstTerm && firstTerm->exp != 0 ) |
---|
1525 | return this; |
---|
1526 | else if ( firstTerm ) |
---|
1527 | { |
---|
1528 | InternalCF * res = firstTerm->coeff.getval(); |
---|
1529 | delete this; |
---|
1530 | return res; |
---|
1531 | } |
---|
1532 | else |
---|
1533 | { |
---|
1534 | delete this; |
---|
1535 | return CFFactory::basic( 0L ); |
---|
1536 | } |
---|
1537 | } |
---|
1538 | else |
---|
1539 | { |
---|
1540 | decRefCount(); |
---|
1541 | termList last, first = copyTermList( firstTerm, last ); |
---|
1542 | first = tryDivTermList( first, c, last, M, fail ); |
---|
1543 | if (fail) |
---|
1544 | { |
---|
1545 | delete this; |
---|
1546 | return CFFactory::basic (0L); |
---|
1547 | } |
---|
1548 | if (fail) |
---|
1549 | { |
---|
1550 | delete first; |
---|
1551 | return CFFactory::basic (0L); |
---|
1552 | } |
---|
1553 | if ( first && first->exp != 0 ) |
---|
1554 | return new InternalPoly( first, last, var ); |
---|
1555 | else if ( first ) |
---|
1556 | { |
---|
1557 | InternalCF * res = first->coeff.getval(); |
---|
1558 | delete first; |
---|
1559 | return res; |
---|
1560 | } |
---|
1561 | else |
---|
1562 | { |
---|
1563 | delete first; |
---|
1564 | return CFFactory::basic( 0L ); |
---|
1565 | } |
---|
1566 | } |
---|
1567 | } |
---|
1568 | } |
---|
1569 | |
---|
1570 | InternalCF* |
---|
1571 | InternalPoly::modulocoeff( InternalCF* cc, bool invert ) |
---|
1572 | { |
---|
1573 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1574 | if ( invert ) |
---|
1575 | { |
---|
1576 | if ( deleteObject() ) delete this; |
---|
1577 | return c.getval(); |
---|
1578 | } |
---|
1579 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
1580 | if ( deleteObject() ) delete this; |
---|
1581 | return CFFactory::basic( 0L ); |
---|
1582 | } |
---|
1583 | |
---|
1584 | InternalCF* |
---|
1585 | InternalPoly::modcoeff( InternalCF* cc, bool invert ) |
---|
1586 | { |
---|
1587 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1588 | if ( invert ) |
---|
1589 | { |
---|
1590 | if ( deleteObject() ) delete this; |
---|
1591 | return c.getval(); |
---|
1592 | } |
---|
1593 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
1594 | if ( c.isOne() ) |
---|
1595 | { |
---|
1596 | if ( getRefCount() <= 1 ) |
---|
1597 | { |
---|
1598 | delete this; |
---|
1599 | return CFFactory::basic( 0L ); |
---|
1600 | } |
---|
1601 | else |
---|
1602 | { |
---|
1603 | decRefCount(); |
---|
1604 | return CFFactory::basic( 0L ); |
---|
1605 | } |
---|
1606 | } |
---|
1607 | else |
---|
1608 | { |
---|
1609 | if ( getRefCount() <= 1 ) |
---|
1610 | { |
---|
1611 | firstTerm = modTermList( firstTerm, c, lastTerm ); |
---|
1612 | if ( firstTerm && firstTerm->exp != 0 ) |
---|
1613 | return this; |
---|
1614 | else if ( firstTerm ) |
---|
1615 | { |
---|
1616 | InternalCF * res = firstTerm->coeff.getval(); |
---|
1617 | delete this; |
---|
1618 | return res; |
---|
1619 | } |
---|
1620 | else |
---|
1621 | { |
---|
1622 | delete this; |
---|
1623 | return CFFactory::basic( 0L ); |
---|
1624 | } |
---|
1625 | } |
---|
1626 | else |
---|
1627 | { |
---|
1628 | decRefCount(); |
---|
1629 | termList last, first = copyTermList( firstTerm, last ); |
---|
1630 | first = modTermList( first, c, last ); |
---|
1631 | if ( first && first->exp != 0 ) |
---|
1632 | return new InternalPoly( first, last, var ); |
---|
1633 | else if ( first ) |
---|
1634 | { |
---|
1635 | InternalCF * res = first->coeff.getval(); |
---|
1636 | delete first; |
---|
1637 | return res; |
---|
1638 | } |
---|
1639 | else |
---|
1640 | { |
---|
1641 | delete first; |
---|
1642 | return CFFactory::basic( 0L ); |
---|
1643 | } |
---|
1644 | } |
---|
1645 | } |
---|
1646 | } |
---|
1647 | |
---|
1648 | void |
---|
1649 | InternalPoly::divremcoeff( InternalCF* cc, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
1650 | { |
---|
1651 | if ( inExtension() && getReduce( var ) ) |
---|
1652 | { |
---|
1653 | quot = copyObject(); |
---|
1654 | quot = quot->dividecoeff( cc, invert ); |
---|
1655 | rem = CFFactory::basic( 0L ); |
---|
1656 | } |
---|
1657 | else if ( invert ) |
---|
1658 | { |
---|
1659 | if ( is_imm( cc ) ) |
---|
1660 | rem = cc; |
---|
1661 | else |
---|
1662 | rem = cc->copyObject(); |
---|
1663 | quot = CFFactory::basic( 0L ); |
---|
1664 | } |
---|
1665 | else |
---|
1666 | { |
---|
1667 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1668 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
1669 | termList quotlast, quotfirst = copyTermList( firstTerm, quotlast ); |
---|
1670 | quotfirst = divideTermList( quotfirst, c, quotlast ); |
---|
1671 | if ( quotfirst ) |
---|
1672 | if ( quotfirst->exp == 0 ) |
---|
1673 | { |
---|
1674 | quot = quotfirst->coeff.getval(); |
---|
1675 | delete quotfirst; |
---|
1676 | } |
---|
1677 | else |
---|
1678 | quot = new InternalPoly( quotfirst, quotlast, var ); |
---|
1679 | else |
---|
1680 | quot = CFFactory::basic( 0L ); |
---|
1681 | rem = CFFactory::basic( 0L ); |
---|
1682 | } |
---|
1683 | } |
---|
1684 | |
---|
1685 | bool |
---|
1686 | InternalPoly::divremcoefft( InternalCF* cc, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
1687 | { |
---|
1688 | if ( inExtension() && getReduce( var ) ) |
---|
1689 | { |
---|
1690 | quot = copyObject(); |
---|
1691 | quot = quot->dividecoeff( cc, invert ); |
---|
1692 | rem = CFFactory::basic( 0L ); |
---|
1693 | return true; |
---|
1694 | } |
---|
1695 | else if ( invert ) |
---|
1696 | { |
---|
1697 | if ( is_imm( cc ) ) |
---|
1698 | rem = cc; |
---|
1699 | else |
---|
1700 | rem = cc->copyObject(); |
---|
1701 | quot = CFFactory::basic( 0L ); |
---|
1702 | return true; |
---|
1703 | } |
---|
1704 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1705 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
1706 | termList quotfirst, quotcursor; |
---|
1707 | termList cursor; |
---|
1708 | CanonicalForm cquot, crem; |
---|
1709 | bool divideok = true; |
---|
1710 | |
---|
1711 | cursor = firstTerm; |
---|
1712 | quotcursor = quotfirst = new term; |
---|
1713 | |
---|
1714 | while ( cursor && divideok ) |
---|
1715 | { |
---|
1716 | divideok = divremt( cursor->coeff, c, cquot, crem ); |
---|
1717 | divideok = divideok && crem.isZero(); |
---|
1718 | if ( divideok ) |
---|
1719 | { |
---|
1720 | if ( ! cquot.isZero() ) |
---|
1721 | { |
---|
1722 | quotcursor->next = new term( 0, cquot, cursor->exp ); |
---|
1723 | quotcursor = quotcursor->next; |
---|
1724 | } |
---|
1725 | cursor = cursor->next; |
---|
1726 | } |
---|
1727 | } |
---|
1728 | quotcursor->next = 0; |
---|
1729 | if ( divideok ) |
---|
1730 | { |
---|
1731 | cursor = quotfirst; quotfirst = quotfirst->next; delete cursor; |
---|
1732 | if ( quotfirst ) |
---|
1733 | if ( quotfirst->exp == 0 ) |
---|
1734 | { |
---|
1735 | quot = quotfirst->coeff.getval(); |
---|
1736 | delete quotfirst; |
---|
1737 | } |
---|
1738 | else |
---|
1739 | quot = new InternalPoly( quotfirst, quotcursor, var ); |
---|
1740 | else |
---|
1741 | quot = CFFactory::basic( 0L ); |
---|
1742 | rem = CFFactory::basic( 0L ); |
---|
1743 | } |
---|
1744 | else |
---|
1745 | { |
---|
1746 | freeTermList( quotfirst ); |
---|
1747 | } |
---|
1748 | return divideok; |
---|
1749 | } |
---|
1750 | |
---|
1751 | bool |
---|
1752 | InternalPoly::tryDivremcoefft( InternalCF* cc, InternalCF*& quot, InternalCF*& rem, bool invert, const CanonicalForm& M, bool& fail ) |
---|
1753 | { |
---|
1754 | if ( inExtension() && !getReduce( var ) ) |
---|
1755 | { |
---|
1756 | quot = copyObject(); |
---|
1757 | quot = quot->tryDividecoeff( cc, invert, M, fail ); |
---|
1758 | if (fail) |
---|
1759 | return false; |
---|
1760 | rem = CFFactory::basic( 0L ); |
---|
1761 | return true; |
---|
1762 | } |
---|
1763 | else if ( invert ) |
---|
1764 | { |
---|
1765 | if ( is_imm( cc ) ) |
---|
1766 | rem = cc; |
---|
1767 | else |
---|
1768 | rem = cc->copyObject(); |
---|
1769 | quot = CFFactory::basic( 0L ); |
---|
1770 | return true; |
---|
1771 | } |
---|
1772 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
1773 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
1774 | termList quotfirst, quotcursor; |
---|
1775 | termList cursor; |
---|
1776 | CanonicalForm cquot, crem; |
---|
1777 | bool divideok = true; |
---|
1778 | |
---|
1779 | cursor = firstTerm; |
---|
1780 | quotcursor = quotfirst = new term; |
---|
1781 | |
---|
1782 | while ( cursor && divideok ) |
---|
1783 | { |
---|
1784 | divideok = tryDivremt( cursor->coeff, c, cquot, crem, M, fail ); |
---|
1785 | if (fail) |
---|
1786 | { |
---|
1787 | freeTermList (quotfirst); |
---|
1788 | return false; |
---|
1789 | } |
---|
1790 | divideok = divideok && crem.isZero(); |
---|
1791 | if ( divideok ) |
---|
1792 | { |
---|
1793 | if ( ! cquot.isZero() ) |
---|
1794 | { |
---|
1795 | quotcursor->next = new term( 0, cquot, cursor->exp ); |
---|
1796 | quotcursor = quotcursor->next; |
---|
1797 | } |
---|
1798 | cursor = cursor->next; |
---|
1799 | } |
---|
1800 | } |
---|
1801 | quotcursor->next = 0; |
---|
1802 | if ( divideok ) |
---|
1803 | { |
---|
1804 | cursor = quotfirst; quotfirst = quotfirst->next; delete cursor; |
---|
1805 | if ( quotfirst ) |
---|
1806 | if ( quotfirst->exp == 0 ) |
---|
1807 | { |
---|
1808 | quot = quotfirst->coeff.getval(); |
---|
1809 | delete quotfirst; |
---|
1810 | } |
---|
1811 | else |
---|
1812 | quot = new InternalPoly( quotfirst, quotcursor, var ); |
---|
1813 | else |
---|
1814 | quot = CFFactory::basic( 0L ); |
---|
1815 | rem = CFFactory::basic( 0L ); |
---|
1816 | } |
---|
1817 | else |
---|
1818 | { |
---|
1819 | freeTermList( quotfirst ); |
---|
1820 | } |
---|
1821 | return divideok; |
---|
1822 | } |
---|
1823 | |
---|
1824 | // static functions |
---|
1825 | |
---|
1826 | termList |
---|
1827 | InternalPoly::copyTermList ( termList aTermList, termList& theLastTerm, bool negate ) |
---|
1828 | { |
---|
1829 | if ( aTermList == 0 ) |
---|
1830 | return 0; |
---|
1831 | else if ( negate ) |
---|
1832 | { |
---|
1833 | termList sourceCursor = aTermList; |
---|
1834 | termList dummy = new term; |
---|
1835 | termList targetCursor = dummy; |
---|
1836 | |
---|
1837 | while ( sourceCursor ) |
---|
1838 | { |
---|
1839 | targetCursor->next = new term( 0, -sourceCursor->coeff, sourceCursor->exp ); |
---|
1840 | targetCursor = targetCursor->next; |
---|
1841 | sourceCursor = sourceCursor->next; |
---|
1842 | } |
---|
1843 | targetCursor->next = 0; |
---|
1844 | theLastTerm = targetCursor; |
---|
1845 | targetCursor = dummy->next; |
---|
1846 | delete dummy; |
---|
1847 | return targetCursor; |
---|
1848 | } |
---|
1849 | else |
---|
1850 | { |
---|
1851 | termList sourceCursor = aTermList; |
---|
1852 | termList dummy = new term; |
---|
1853 | termList targetCursor = dummy; |
---|
1854 | |
---|
1855 | while ( sourceCursor ) |
---|
1856 | { |
---|
1857 | targetCursor->next = new term( 0, sourceCursor->coeff, sourceCursor->exp ); |
---|
1858 | targetCursor = targetCursor->next; |
---|
1859 | sourceCursor = sourceCursor->next; |
---|
1860 | } |
---|
1861 | targetCursor->next = 0; |
---|
1862 | theLastTerm = targetCursor; |
---|
1863 | targetCursor = dummy->next; |
---|
1864 | delete dummy; |
---|
1865 | return targetCursor; |
---|
1866 | } |
---|
1867 | } |
---|
1868 | |
---|
1869 | termList |
---|
1870 | InternalPoly::deepCopyTermList ( termList aTermList, termList& theLastTerm ) |
---|
1871 | { |
---|
1872 | if ( aTermList == 0 ) |
---|
1873 | return 0; |
---|
1874 | else |
---|
1875 | { |
---|
1876 | termList sourceCursor = aTermList; |
---|
1877 | termList dummy = new term; |
---|
1878 | termList targetCursor = dummy; |
---|
1879 | |
---|
1880 | while ( sourceCursor ) |
---|
1881 | { |
---|
1882 | targetCursor->next = new term( 0, sourceCursor->coeff.deepCopy(), sourceCursor->exp ); |
---|
1883 | targetCursor = targetCursor->next; |
---|
1884 | sourceCursor = sourceCursor->next; |
---|
1885 | } |
---|
1886 | targetCursor->next = 0; |
---|
1887 | theLastTerm = targetCursor; |
---|
1888 | targetCursor = dummy->next; |
---|
1889 | delete dummy; |
---|
1890 | return targetCursor; |
---|
1891 | } |
---|
1892 | } |
---|
1893 | |
---|
1894 | void |
---|
1895 | InternalPoly::freeTermList ( termList aTermList ) |
---|
1896 | { |
---|
1897 | termList cursor = aTermList; |
---|
1898 | |
---|
1899 | while ( cursor ) |
---|
1900 | { |
---|
1901 | cursor = cursor->next; |
---|
1902 | delete aTermList; |
---|
1903 | aTermList = cursor; |
---|
1904 | } |
---|
1905 | } |
---|
1906 | |
---|
1907 | void |
---|
1908 | InternalPoly::negateTermList ( termList terms ) |
---|
1909 | { |
---|
1910 | termList cursor = terms; |
---|
1911 | while ( cursor ) |
---|
1912 | { |
---|
1913 | cursor->coeff = -cursor->coeff; |
---|
1914 | cursor = cursor->next; |
---|
1915 | } |
---|
1916 | } |
---|
1917 | |
---|
1918 | termList |
---|
1919 | InternalPoly::addTermList ( termList theList, termList aList, termList& lastTerm, bool negate ) |
---|
1920 | { |
---|
1921 | termList theCursor = theList; |
---|
1922 | termList aCursor = aList; |
---|
1923 | termList predCursor = 0; |
---|
1924 | |
---|
1925 | while ( theCursor && aCursor ) |
---|
1926 | { |
---|
1927 | if ( theCursor->exp == aCursor->exp ) |
---|
1928 | { |
---|
1929 | if ( negate ) |
---|
1930 | theCursor->coeff -= aCursor->coeff; |
---|
1931 | else |
---|
1932 | theCursor->coeff += aCursor->coeff; |
---|
1933 | if ( theCursor->coeff.isZero() ) |
---|
1934 | { |
---|
1935 | if ( predCursor ) |
---|
1936 | { |
---|
1937 | predCursor->next = theCursor->next; |
---|
1938 | delete theCursor; |
---|
1939 | theCursor = predCursor->next; |
---|
1940 | } |
---|
1941 | else |
---|
1942 | { |
---|
1943 | theList = theList->next; |
---|
1944 | delete theCursor; |
---|
1945 | theCursor = theList; |
---|
1946 | } |
---|
1947 | } |
---|
1948 | else |
---|
1949 | { |
---|
1950 | predCursor = theCursor; |
---|
1951 | theCursor = theCursor->next; |
---|
1952 | } |
---|
1953 | aCursor = aCursor->next; |
---|
1954 | } |
---|
1955 | else if ( theCursor->exp < aCursor->exp ) |
---|
1956 | { |
---|
1957 | if ( negate ) |
---|
1958 | if ( predCursor ) |
---|
1959 | { |
---|
1960 | predCursor->next = new term( theCursor, -aCursor->coeff, aCursor->exp ); |
---|
1961 | predCursor = predCursor->next; |
---|
1962 | } |
---|
1963 | else |
---|
1964 | { |
---|
1965 | theList = new term( theCursor, -aCursor->coeff, aCursor->exp ); |
---|
1966 | predCursor = theList; |
---|
1967 | } |
---|
1968 | else |
---|
1969 | if ( predCursor ) |
---|
1970 | { |
---|
1971 | predCursor->next = new term( theCursor, aCursor->coeff, aCursor->exp ); |
---|
1972 | predCursor = predCursor->next; |
---|
1973 | } |
---|
1974 | else |
---|
1975 | { |
---|
1976 | theList = new term( theCursor, aCursor->coeff, aCursor->exp ); |
---|
1977 | predCursor = theList; |
---|
1978 | } |
---|
1979 | aCursor = aCursor->next; |
---|
1980 | } |
---|
1981 | else |
---|
1982 | { |
---|
1983 | predCursor = theCursor; |
---|
1984 | theCursor = theCursor->next; |
---|
1985 | } |
---|
1986 | } |
---|
1987 | if ( aCursor ) |
---|
1988 | { |
---|
1989 | if ( predCursor ) |
---|
1990 | predCursor->next = copyTermList( aCursor, lastTerm, negate ); |
---|
1991 | else |
---|
1992 | theList = copyTermList( aCursor, lastTerm, negate ); |
---|
1993 | } |
---|
1994 | else if ( ! theCursor ) |
---|
1995 | lastTerm = predCursor; |
---|
1996 | |
---|
1997 | return theList; |
---|
1998 | } |
---|
1999 | |
---|
2000 | void |
---|
2001 | InternalPoly::mulTermList ( termList theCursor, const CanonicalForm& coeff, const int exp ) |
---|
2002 | { |
---|
2003 | while ( theCursor ) |
---|
2004 | { |
---|
2005 | theCursor->coeff *= coeff; |
---|
2006 | theCursor->exp += exp; |
---|
2007 | theCursor = theCursor->next; |
---|
2008 | } |
---|
2009 | } |
---|
2010 | |
---|
2011 | termList |
---|
2012 | InternalPoly::divideTermList ( termList firstTerm, const CanonicalForm& coeff, termList& lastTerm ) |
---|
2013 | { |
---|
2014 | termList theCursor = firstTerm; |
---|
2015 | lastTerm = 0; |
---|
2016 | termList dummy; |
---|
2017 | |
---|
2018 | while ( theCursor ) |
---|
2019 | { |
---|
2020 | theCursor->coeff /= coeff; |
---|
2021 | if ( theCursor->coeff.isZero() ) |
---|
2022 | { |
---|
2023 | if ( theCursor == firstTerm ) |
---|
2024 | firstTerm = theCursor->next; |
---|
2025 | else |
---|
2026 | lastTerm->next = theCursor->next; |
---|
2027 | dummy = theCursor; |
---|
2028 | theCursor = theCursor->next; |
---|
2029 | delete dummy; |
---|
2030 | } |
---|
2031 | else |
---|
2032 | { |
---|
2033 | lastTerm = theCursor; |
---|
2034 | theCursor = theCursor->next; |
---|
2035 | } |
---|
2036 | } |
---|
2037 | return firstTerm; |
---|
2038 | } |
---|
2039 | |
---|
2040 | termList |
---|
2041 | InternalPoly::divTermList ( termList firstTerm, const CanonicalForm& coeff, termList& lastTerm ) |
---|
2042 | { |
---|
2043 | termList theCursor = firstTerm; |
---|
2044 | lastTerm = 0; |
---|
2045 | termList dummy; |
---|
2046 | |
---|
2047 | while ( theCursor ) |
---|
2048 | { |
---|
2049 | theCursor->coeff.div( coeff ); |
---|
2050 | if ( theCursor->coeff.isZero() ) |
---|
2051 | { |
---|
2052 | if ( theCursor == firstTerm ) |
---|
2053 | firstTerm = theCursor->next; |
---|
2054 | else |
---|
2055 | lastTerm->next = theCursor->next; |
---|
2056 | dummy = theCursor; |
---|
2057 | theCursor = theCursor->next; |
---|
2058 | delete dummy; |
---|
2059 | } |
---|
2060 | else |
---|
2061 | { |
---|
2062 | lastTerm = theCursor; |
---|
2063 | theCursor = theCursor->next; |
---|
2064 | } |
---|
2065 | } |
---|
2066 | return firstTerm; |
---|
2067 | } |
---|
2068 | |
---|
2069 | termList |
---|
2070 | InternalPoly::tryDivTermList ( termList firstTerm, const CanonicalForm& coeff, termList& lastTerm, const CanonicalForm& M, bool& fail ) |
---|
2071 | { |
---|
2072 | termList theCursor = firstTerm; |
---|
2073 | lastTerm = 0; |
---|
2074 | termList dummy; |
---|
2075 | |
---|
2076 | while ( theCursor ) |
---|
2077 | { |
---|
2078 | theCursor->coeff.tryDiv( coeff, M, fail ); |
---|
2079 | if (fail) |
---|
2080 | return 0; |
---|
2081 | if ( theCursor->coeff.isZero() ) |
---|
2082 | { |
---|
2083 | if ( theCursor == firstTerm ) |
---|
2084 | firstTerm = theCursor->next; |
---|
2085 | else |
---|
2086 | lastTerm->next = theCursor->next; |
---|
2087 | dummy = theCursor; |
---|
2088 | theCursor = theCursor->next; |
---|
2089 | delete dummy; |
---|
2090 | } |
---|
2091 | else |
---|
2092 | { |
---|
2093 | lastTerm = theCursor; |
---|
2094 | theCursor = theCursor->next; |
---|
2095 | } |
---|
2096 | } |
---|
2097 | return firstTerm; |
---|
2098 | } |
---|
2099 | |
---|
2100 | termList |
---|
2101 | InternalPoly::modTermList ( termList firstTerm, const CanonicalForm& coeff, termList& lastTerm ) |
---|
2102 | { |
---|
2103 | termList theCursor = firstTerm; |
---|
2104 | lastTerm = 0; |
---|
2105 | termList dummy; |
---|
2106 | |
---|
2107 | while ( theCursor ) |
---|
2108 | { |
---|
2109 | theCursor->coeff.mod( coeff ); |
---|
2110 | if ( theCursor->coeff.isZero() ) |
---|
2111 | { |
---|
2112 | if ( theCursor == firstTerm ) |
---|
2113 | firstTerm = theCursor->next; |
---|
2114 | else |
---|
2115 | lastTerm->next = theCursor->next; |
---|
2116 | dummy = theCursor; |
---|
2117 | theCursor = theCursor-> next; |
---|
2118 | delete dummy; |
---|
2119 | } |
---|
2120 | else |
---|
2121 | { |
---|
2122 | lastTerm = theCursor; |
---|
2123 | theCursor = theCursor->next; |
---|
2124 | } |
---|
2125 | } |
---|
2126 | return firstTerm; |
---|
2127 | } |
---|
2128 | |
---|
2129 | void |
---|
2130 | InternalPoly::appendTermList ( termList& first, termList& last, const CanonicalForm& coeff, const int exp ) |
---|
2131 | { |
---|
2132 | if ( last ) |
---|
2133 | { |
---|
2134 | last->next = new term( 0, coeff, exp ); |
---|
2135 | last = last->next; |
---|
2136 | } |
---|
2137 | else |
---|
2138 | { |
---|
2139 | first = new term( 0, coeff, exp ); |
---|
2140 | last = first; |
---|
2141 | } |
---|
2142 | } |
---|
2143 | |
---|
2144 | termList |
---|
2145 | InternalPoly::mulAddTermList ( termList theList, termList aList, const CanonicalForm & c, const int exp, termList & lastTerm, bool negate ) |
---|
2146 | { |
---|
2147 | termList theCursor = theList; |
---|
2148 | termList aCursor = aList; |
---|
2149 | termList predCursor = 0; |
---|
2150 | CanonicalForm coeff; |
---|
2151 | |
---|
2152 | if ( negate ) |
---|
2153 | coeff = -c; |
---|
2154 | else |
---|
2155 | coeff = c; |
---|
2156 | |
---|
2157 | while ( theCursor && aCursor ) |
---|
2158 | { |
---|
2159 | if ( theCursor->exp == aCursor->exp + exp ) |
---|
2160 | { |
---|
2161 | theCursor->coeff += aCursor->coeff * coeff; |
---|
2162 | if ( theCursor->coeff.isZero() ) |
---|
2163 | { |
---|
2164 | if ( predCursor ) |
---|
2165 | { |
---|
2166 | predCursor->next = theCursor->next; |
---|
2167 | delete theCursor; |
---|
2168 | theCursor = predCursor->next; |
---|
2169 | } |
---|
2170 | else |
---|
2171 | { |
---|
2172 | theList = theList->next; |
---|
2173 | delete theCursor; |
---|
2174 | theCursor = theList; |
---|
2175 | } |
---|
2176 | } |
---|
2177 | else |
---|
2178 | { |
---|
2179 | predCursor = theCursor; |
---|
2180 | theCursor = theCursor->next; |
---|
2181 | } |
---|
2182 | aCursor = aCursor->next; |
---|
2183 | } |
---|
2184 | else if ( theCursor->exp < aCursor->exp + exp ) |
---|
2185 | { |
---|
2186 | if ( predCursor ) |
---|
2187 | { |
---|
2188 | predCursor->next = new term( theCursor, aCursor->coeff * coeff, aCursor->exp + exp ); |
---|
2189 | predCursor = predCursor->next; |
---|
2190 | } |
---|
2191 | else |
---|
2192 | { |
---|
2193 | theList = new term( theCursor, aCursor->coeff * coeff, aCursor->exp + exp ); |
---|
2194 | predCursor = theList; |
---|
2195 | } |
---|
2196 | aCursor = aCursor->next; |
---|
2197 | } |
---|
2198 | else |
---|
2199 | { |
---|
2200 | predCursor = theCursor; |
---|
2201 | theCursor = theCursor->next; |
---|
2202 | } |
---|
2203 | } |
---|
2204 | if ( aCursor ) |
---|
2205 | { |
---|
2206 | if ( predCursor ) |
---|
2207 | { |
---|
2208 | predCursor->next = copyTermList( aCursor, lastTerm ); |
---|
2209 | predCursor = predCursor->next; |
---|
2210 | } |
---|
2211 | else |
---|
2212 | { |
---|
2213 | theList = copyTermList( aCursor, lastTerm ); |
---|
2214 | predCursor = theList; |
---|
2215 | } |
---|
2216 | while ( predCursor ) |
---|
2217 | { |
---|
2218 | predCursor->exp += exp; |
---|
2219 | predCursor->coeff *= coeff; |
---|
2220 | predCursor = predCursor->next; |
---|
2221 | } |
---|
2222 | } |
---|
2223 | else if ( ! theCursor ) |
---|
2224 | lastTerm = predCursor; |
---|
2225 | return theList; |
---|
2226 | } |
---|
2227 | |
---|
2228 | termList |
---|
2229 | InternalPoly::reduceTermList ( termList first, termList redterms, termList & last ) |
---|
2230 | { |
---|
2231 | CanonicalForm coeff = CanonicalForm (1)/redterms->coeff; |
---|
2232 | CanonicalForm newcoeff; |
---|
2233 | int newexp; |
---|
2234 | int exp = redterms->exp; |
---|
2235 | termList dummy; |
---|
2236 | while ( first && ( first->exp >= exp ) ) |
---|
2237 | { |
---|
2238 | newcoeff = first->coeff * coeff; |
---|
2239 | newexp = first->exp - exp; |
---|
2240 | dummy = first; |
---|
2241 | first = mulAddTermList( first->next, redterms->next, newcoeff, newexp, last, true ); |
---|
2242 | delete dummy; |
---|
2243 | } |
---|
2244 | return first; |
---|
2245 | } |
---|
2246 | |
---|