[493c477] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
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[b761b9] | 2 | /* $Id: int_poly.cc,v 1.5 1997-09-10 15:45:49 schmidt Exp $ */ |
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[2dd068] | 3 | |
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[9d7aaa] | 4 | #include <config.h> |
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| 5 | |
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[32e9cd7] | 6 | #ifndef NOSTREAMIO |
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[2dd068] | 7 | #include <string.h> |
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| 8 | #include <strstream.h> |
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[32e9cd7] | 9 | #endif /* NOSTREAMIO */ |
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[2dd068] | 10 | |
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| 11 | #include "assert.h" |
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[32e9cd7] | 12 | |
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[2dd068] | 13 | #include "cf_defs.h" |
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| 14 | #include "cf_factory.h" |
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| 15 | #include "int_cf.h" |
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| 16 | #include "int_poly.h" |
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| 17 | #include "canonicalform.h" |
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| 18 | #include "variable.h" |
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| 19 | #include "imm.h" |
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| 20 | |
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| 21 | |
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| 22 | InternalPoly::InternalPoly( termList first, termList last, const Variable & v ) |
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| 23 | { |
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| 24 | firstTerm = first; |
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| 25 | lastTerm = last; |
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| 26 | var = v; |
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| 27 | } |
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| 28 | |
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| 29 | InternalPoly::InternalPoly() |
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| 30 | { |
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| 31 | ASSERT( 0, "ups, why do you initialize an empty poly" ); |
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| 32 | } |
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| 33 | |
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| 34 | InternalPoly::InternalPoly( const Variable & v, const int e, const CanonicalForm& c ) |
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| 35 | { |
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| 36 | var = v; |
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| 37 | firstTerm = new term( 0, c, e ); |
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| 38 | lastTerm = firstTerm; |
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| 39 | } |
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| 40 | |
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| 41 | InternalPoly::InternalPoly( const InternalPoly& ) |
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| 42 | { |
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[32e9cd7] | 43 | ASSERT( 0, "ups there is something wrong in your code" ); |
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| 44 | }; |
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[2dd068] | 45 | |
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| 46 | InternalPoly::~InternalPoly() |
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| 47 | { |
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| 48 | freeTermList( firstTerm ); |
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| 49 | } |
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| 50 | |
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| 51 | InternalCF* |
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| 52 | InternalPoly::deepCopyObject() const |
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| 53 | { |
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| 54 | termList first, last; |
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| 55 | first = deepCopyTermList( firstTerm, last ); |
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| 56 | return new InternalPoly( first, last, var ); |
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| 57 | } |
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| 58 | |
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| 59 | InternalCF* |
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| 60 | InternalPoly::genZero() |
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| 61 | { |
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| 62 | return firstTerm->coeff.genZero().getval(); |
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| 63 | } |
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| 64 | |
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| 65 | InternalCF* |
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| 66 | InternalPoly::genOne() |
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| 67 | { |
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| 68 | return firstTerm->coeff.genOne().getval(); |
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| 69 | } |
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| 70 | |
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| 71 | bool |
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| 72 | InternalPoly::isUnivariate() const |
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| 73 | { |
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| 74 | termList cursor = firstTerm; |
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| 75 | while ( cursor ) { |
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| 76 | if ( ! cursor->coeff.inCoeffDomain() ) |
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| 77 | return false; |
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| 78 | cursor = cursor->next; |
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| 79 | } |
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| 80 | return true; |
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| 81 | } |
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| 82 | |
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| 83 | int |
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| 84 | InternalPoly::degree() |
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| 85 | { |
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| 86 | return firstTerm->exp; |
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| 87 | } |
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| 88 | |
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[b761b9] | 89 | //{{{ int InternalPoly::sign () const |
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| 90 | // docu: see CanonicalForm::sign() |
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[2dd068] | 91 | int |
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[b761b9] | 92 | InternalPoly::sign () const |
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[2dd068] | 93 | { |
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| 94 | return firstTerm->coeff.sign(); |
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| 95 | } |
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[b761b9] | 96 | //}}} |
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[2dd068] | 97 | |
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| 98 | CanonicalForm |
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| 99 | InternalPoly::lc() |
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| 100 | { |
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| 101 | return firstTerm->coeff.lc(); |
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| 102 | } |
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| 103 | |
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| 104 | CanonicalForm |
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| 105 | InternalPoly::LC() |
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| 106 | { |
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| 107 | return firstTerm->coeff; |
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| 108 | } |
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| 109 | |
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| 110 | int |
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| 111 | InternalPoly::taildegree() |
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| 112 | { |
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| 113 | return lastTerm->exp; |
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| 114 | } |
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| 115 | |
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| 116 | CanonicalForm |
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| 117 | InternalPoly::tailcoeff() |
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| 118 | { |
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| 119 | return lastTerm->coeff; |
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| 120 | } |
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| 121 | |
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| 122 | CanonicalForm |
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| 123 | InternalPoly::coeff( int i ) |
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| 124 | { |
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| 125 | termList theCursor = firstTerm; |
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| 126 | while ( theCursor ) { |
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| 127 | if ( theCursor->exp == i ) |
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| 128 | return theCursor->coeff; |
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| 129 | else if ( theCursor->exp > i ) |
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| 130 | theCursor = theCursor->next; |
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| 131 | else |
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| 132 | theCursor = 0; |
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| 133 | } |
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| 134 | return 0; |
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| 135 | } |
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| 136 | |
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[32e9cd7] | 137 | #ifndef NOSTREAMIO |
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[2dd068] | 138 | void |
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| 139 | InternalPoly::print(ostream &aStream, char * aString ) |
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| 140 | { |
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[32e9cd7] | 141 | if ( ! firstTerm ) |
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[2dd068] | 142 | aStream << 0 << aString; |
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| 143 | else { |
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| 144 | char * theString; |
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| 145 | termList theCursor = firstTerm; |
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| 146 | while ( theCursor ) { |
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| 147 | ostrstream theStream; |
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| 148 | if ( theCursor->exp == 0 ) |
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| 149 | theCursor->coeff.print( aStream, aString ); |
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| 150 | else if ( theCursor->coeff.isOne() ) { |
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| 151 | aStream << var; |
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| 152 | if ( theCursor->exp != 1 ) |
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| 153 | aStream << '^' << theCursor->exp << aString; |
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| 154 | else |
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| 155 | aStream << aString; |
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| 156 | } |
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| 157 | else if ( theCursor->coeff.sign() < 0 && (-theCursor->coeff).isOne() ) { |
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| 158 | aStream << '-' << var; |
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| 159 | if ( theCursor->exp != 1 ) |
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| 160 | aStream << '^' << theCursor->exp << aString; |
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| 161 | else |
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| 162 | aStream << aString; |
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| 163 | } |
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| 164 | else { |
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| 165 | theStream << '*' << var; |
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| 166 | if ( theCursor->exp != 1 ) |
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| 167 | theStream << '^' << theCursor->exp << aString << ends; |
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| 168 | else |
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| 169 | theStream << aString << ends; // results from error in GNU strstream |
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| 170 | theString = theStream.str(); |
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| 171 | theCursor->coeff.print( aStream, theString ); |
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| 172 | delete [] theString; |
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| 173 | } |
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| 174 | theCursor = theCursor->next; |
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| 175 | if ( theCursor && ( theCursor->coeff.sign() >= 0 ) ) |
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| 176 | aStream << '+'; |
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| 177 | } |
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| 178 | } |
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| 179 | } |
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[32e9cd7] | 180 | #endif /* NOSTREAMIO */ |
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[2dd068] | 181 | |
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| 182 | InternalCF* |
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| 183 | InternalPoly::neg() |
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| 184 | { |
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| 185 | if ( getRefCount() == 1 ) { |
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| 186 | negateTermList( firstTerm ); |
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| 187 | return this; |
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| 188 | } |
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| 189 | else { |
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| 190 | decRefCount(); |
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| 191 | termList last, first = copyTermList( firstTerm, last, true ); |
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| 192 | return new InternalPoly( first, last, var ); |
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| 193 | } |
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| 194 | } |
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| 195 | |
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| 196 | InternalCF* |
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| 197 | InternalPoly::invert() |
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| 198 | { |
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| 199 | if ( inExtension() && getReduce( var ) ) { |
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| 200 | setReduce( var, false ); |
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| 201 | CanonicalForm a( this->copyObject() ); |
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| 202 | CanonicalForm b = getMipo( var ); |
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| 203 | CanonicalForm u, v; |
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| 204 | CanonicalForm g = extgcd( a, b, u, v ); |
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| 205 | setReduce( var, true ); |
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| 206 | return u.getval(); |
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| 207 | } |
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| 208 | else |
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| 209 | return CFFactory::basic( 0 ); |
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| 210 | } |
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| 211 | |
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| 212 | int |
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| 213 | InternalPoly::comparesame ( InternalCF* acoeff ) |
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| 214 | { |
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| 215 | InternalPoly* apoly = (InternalPoly*)acoeff; |
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| 216 | if ( this == apoly ) |
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| 217 | return 0; |
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| 218 | else { |
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| 219 | termList cur1 = firstTerm; |
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| 220 | termList cur2 = apoly->firstTerm; |
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| 221 | for ( ; cur1 && cur2; cur1 = cur1->next, cur2 = cur2->next ) |
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| 222 | if ( ( cur1->exp != cur2->exp ) || ( cur1->coeff != cur2->coeff ) ) |
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| 223 | if ( cur1->exp > cur2->exp ) |
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| 224 | return 1; |
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| 225 | else if ( cur1->exp < cur2->exp ) |
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| 226 | return -1; |
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| 227 | else if ( cur1->coeff > cur2->coeff ) |
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| 228 | return 1; |
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| 229 | else |
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| 230 | return -1; |
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| 231 | return cur1 != cur2; |
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| 232 | } |
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| 233 | } |
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| 234 | |
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| 235 | InternalCF* |
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| 236 | InternalPoly::addsame( InternalCF* aCoeff ) |
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| 237 | { |
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| 238 | InternalPoly * aPoly = (InternalPoly*)aCoeff; |
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| 239 | if ( getRefCount() == 1 ) { |
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| 240 | firstTerm = addTermList( firstTerm, aPoly->firstTerm, lastTerm, false ); |
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| 241 | if ( firstTerm && firstTerm->exp != 0 ) |
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| 242 | return this; |
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| 243 | else if ( firstTerm ) { |
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| 244 | InternalCF * res = firstTerm->coeff.getval(); |
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| 245 | delete this; |
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| 246 | return res; |
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| 247 | } |
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| 248 | else { |
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| 249 | delete this; |
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| 250 | return CFFactory::basic( 0 ); |
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| 251 | } |
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| 252 | } |
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| 253 | else { |
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| 254 | decRefCount(); |
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| 255 | termList last, first = copyTermList( firstTerm, last ); |
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| 256 | first = addTermList( first, aPoly->firstTerm, last, false ); |
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| 257 | if ( first && first->exp != 0 ) |
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| 258 | return new InternalPoly( first, last, var ); |
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| 259 | else if ( first ) { |
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| 260 | InternalCF * res = first->coeff.getval(); |
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| 261 | delete first; |
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| 262 | return res; |
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| 263 | } |
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| 264 | else |
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| 265 | return CFFactory::basic( 0 ); |
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| 266 | |
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| 267 | } |
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| 268 | } |
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| 269 | |
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| 270 | InternalCF* |
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| 271 | InternalPoly::subsame( InternalCF* aCoeff ) |
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| 272 | { |
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| 273 | InternalPoly * aPoly = (InternalPoly*)aCoeff; |
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| 274 | if ( getRefCount() == 1 ) { |
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| 275 | firstTerm = addTermList( firstTerm, aPoly->firstTerm, lastTerm, true ); |
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| 276 | if ( firstTerm && firstTerm->exp != 0 ) |
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| 277 | return this; |
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| 278 | else if ( firstTerm ) { |
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| 279 | InternalCF * res = firstTerm->coeff.getval(); |
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| 280 | delete this; |
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| 281 | return res; |
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| 282 | } |
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| 283 | else { |
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| 284 | delete this; |
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| 285 | return CFFactory::basic( 0 ); |
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| 286 | } |
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| 287 | } |
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| 288 | else { |
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| 289 | decRefCount(); |
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| 290 | termList last, first = copyTermList( firstTerm, last ); |
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| 291 | first = addTermList( first, aPoly->firstTerm, last, true ); |
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| 292 | if ( first && first->exp != 0 ) |
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| 293 | return new InternalPoly( first, last, var ); |
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| 294 | else if ( first ) { |
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| 295 | InternalCF * res = first->coeff.getval(); |
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| 296 | delete first; |
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| 297 | return res; |
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| 298 | } |
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| 299 | else |
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| 300 | return CFFactory::basic( 0 ); |
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| 301 | |
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| 302 | } |
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| 303 | } |
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| 304 | |
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| 305 | InternalCF* |
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| 306 | InternalPoly::mulsame( InternalCF* aCoeff ) |
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| 307 | { |
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| 308 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
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| 309 | termList resultFirst = 0, resultLast = 0; |
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| 310 | termList theCursor = firstTerm; |
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| 311 | |
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| 312 | while ( theCursor ) { |
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| 313 | resultFirst = mulAddTermList( resultFirst, aPoly->firstTerm, theCursor->coeff, theCursor->exp, resultLast, false ); |
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| 314 | theCursor = theCursor->next; |
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| 315 | } |
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| 316 | if ( inExtension() && getReduce( var ) ) { |
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| 317 | resultFirst = reduceTermList( resultFirst, (getInternalMipo( var ))->firstTerm, resultLast ); |
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| 318 | if ( resultFirst == 0 ) |
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| 319 | if ( getRefCount() == 1 ) { |
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| 320 | delete this; |
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| 321 | return CFFactory::basic(0); |
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| 322 | } |
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| 323 | else { |
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| 324 | decRefCount(); |
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| 325 | return CFFactory::basic(0); |
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| 326 | } |
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| 327 | else if ( resultFirst->exp == 0 ) |
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| 328 | if ( getRefCount() == 1 ) { |
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| 329 | InternalCF * res = resultFirst->coeff.getval(); |
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| 330 | delete resultFirst; |
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| 331 | delete this; |
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| 332 | return res; |
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| 333 | } |
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| 334 | else { |
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| 335 | decRefCount(); |
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| 336 | InternalCF * res = resultFirst->coeff.getval(); |
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| 337 | delete resultFirst; |
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| 338 | return res; |
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| 339 | } |
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| 340 | } |
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| 341 | if ( getRefCount() == 1 ) { |
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| 342 | freeTermList( firstTerm ); |
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| 343 | firstTerm = resultFirst; |
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| 344 | lastTerm = resultLast; |
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| 345 | return this; |
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| 346 | } |
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| 347 | else { |
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| 348 | decRefCount(); |
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| 349 | return new InternalPoly( resultFirst, resultLast, var ); |
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| 350 | } |
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| 351 | } |
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| 352 | |
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| 353 | InternalCF* |
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| 354 | InternalPoly::dividesame( InternalCF* aCoeff ) |
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| 355 | { |
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| 356 | return divsame( aCoeff ); |
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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::divsame( InternalCF* aCoeff ) |
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| 362 | { |
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| 363 | if ( inExtension() && getReduce( var ) ) { |
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| 364 | InternalCF * dummy = aCoeff->invert(); |
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| 365 | dummy = dummy->mulsame( this ); |
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| 366 | if ( getRefCount() == 1 ) { |
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| 367 | delete this; |
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| 368 | return dummy; |
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| 369 | } |
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| 370 | else { |
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| 371 | decRefCount(); |
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| 372 | return dummy; |
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| 373 | } |
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| 374 | } |
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| 375 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
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| 376 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
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| 377 | CanonicalForm coeff, newcoeff; |
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| 378 | int exp, newexp; |
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| 379 | bool singleObject; |
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| 380 | |
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| 381 | if ( getRefCount() == 1 ) { |
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| 382 | first = firstTerm; last = lastTerm; singleObject = true; |
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| 383 | } |
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| 384 | else { |
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| 385 | first = copyTermList( firstTerm, last ); singleObject = false; |
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| 386 | decRefCount(); |
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| 387 | } |
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| 388 | coeff = aPoly->firstTerm->coeff; |
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| 389 | exp = aPoly->firstTerm->exp; |
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| 390 | while (first && ( first->exp >= exp ) ) { |
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| 391 | newcoeff = first->coeff / coeff; |
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| 392 | newexp = first->exp - exp; |
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| 393 | dummy = first; |
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| 394 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
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| 395 | delete dummy; |
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| 396 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
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| 397 | } |
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| 398 | freeTermList( first ); |
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| 399 | if ( singleObject ) { |
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| 400 | if ( resultfirst && resultfirst->exp != 0 ) { |
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| 401 | firstTerm = resultfirst; |
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| 402 | lastTerm = resultlast; |
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| 403 | return this; |
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| 404 | } |
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| 405 | else if ( resultfirst ) { |
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| 406 | InternalCF * res = resultfirst->coeff.getval(); |
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| 407 | delete resultfirst; |
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| 408 | firstTerm = 0; |
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| 409 | delete this; |
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| 410 | return res; |
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| 411 | } |
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| 412 | else { |
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| 413 | // this should not happen (evtl use assertion) |
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| 414 | ASSERT( 0, "FATAL ERROR, PLEASE INFORM THE AUTHOR" ); |
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| 415 | firstTerm = 0; |
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| 416 | delete this; |
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| 417 | return CFFactory::basic( 0 ); |
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| 418 | } |
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| 419 | } |
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| 420 | else { |
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| 421 | if ( resultfirst && resultfirst->exp != 0 ) |
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| 422 | return new InternalPoly( resultfirst, resultlast, var ); |
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| 423 | else if ( resultfirst ) { |
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| 424 | InternalCF * res = resultfirst->coeff.getval(); |
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| 425 | delete resultfirst; |
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| 426 | return res; |
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| 427 | } |
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| 428 | else |
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| 429 | return CFFactory::basic( 0 ); |
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| 430 | } |
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| 431 | } |
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| 432 | |
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| 433 | InternalCF* |
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| 434 | InternalPoly::modulosame( InternalCF* aCoeff ) |
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| 435 | { |
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| 436 | return modsame( aCoeff ); |
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| 437 | } |
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| 438 | |
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| 439 | InternalCF* |
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| 440 | InternalPoly::modsame( InternalCF* aCoeff ) |
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| 441 | { |
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| 442 | if ( inExtension() && getReduce( var ) ) { |
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| 443 | if ( deleteObject() ) delete this; |
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| 444 | return CFFactory::basic( 0 ); |
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| 445 | } |
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| 446 | InternalPoly *aPoly = (InternalPoly*)aCoeff; |
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| 447 | termList dummy, first, last; |
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| 448 | CanonicalForm coeff, newcoeff; |
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| 449 | int exp, newexp; |
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| 450 | bool singleObject; |
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| 451 | |
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| 452 | if ( getRefCount() == 1 ) { |
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| 453 | first = firstTerm; last = lastTerm; singleObject = true; |
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| 454 | } |
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| 455 | else { |
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| 456 | first = copyTermList( firstTerm, last ); singleObject = false; |
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| 457 | decRefCount(); |
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| 458 | } |
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| 459 | coeff = aPoly->firstTerm->coeff; |
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| 460 | exp = aPoly->firstTerm->exp; |
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| 461 | while (first && ( first->exp >= exp ) ) { |
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| 462 | newcoeff = first->coeff / coeff; |
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| 463 | newexp = first->exp - exp; |
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| 464 | dummy = first; |
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| 465 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
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| 466 | delete dummy; |
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| 467 | } |
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| 468 | if ( singleObject ) { |
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| 469 | if ( first && first->exp != 0 ) { |
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| 470 | firstTerm = first; |
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| 471 | lastTerm = last; |
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| 472 | return this; |
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| 473 | } |
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| 474 | else if ( first ) { |
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| 475 | InternalCF * res = first->coeff.getval(); |
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| 476 | delete first; |
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| 477 | firstTerm = 0; |
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| 478 | delete this; |
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| 479 | return res; |
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| 480 | } |
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| 481 | else { |
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| 482 | firstTerm = 0; |
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| 483 | delete this; |
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| 484 | return CFFactory::basic( 0 ); |
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| 485 | } |
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| 486 | } |
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| 487 | else { |
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| 488 | if ( first && first->exp != 0 ) |
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| 489 | return new InternalPoly( first, last, var ); |
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| 490 | else if ( first ) { |
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| 491 | InternalCF * res = first->coeff.getval(); |
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| 492 | delete first; |
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| 493 | return res; |
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| 494 | } |
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| 495 | else |
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| 496 | return CFFactory::basic( 0 ); |
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| 497 | } |
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| 498 | } |
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| 499 | |
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| 500 | |
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| 501 | void |
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| 502 | InternalPoly::divremsame( InternalCF* acoeff, InternalCF*& quot, InternalCF*& rem ) |
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| 503 | { |
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| 504 | if ( inExtension() && getReduce( var ) ) { |
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| 505 | InternalCF * dummy = acoeff->invert(); |
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| 506 | quot = dummy->mulsame( this ); |
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| 507 | rem = CFFactory::basic( 0 ); |
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| 508 | } |
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| 509 | else { |
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| 510 | InternalPoly *aPoly = (InternalPoly*)acoeff; |
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| 511 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
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| 512 | CanonicalForm coeff, newcoeff; |
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| 513 | int exp, newexp; |
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| 514 | |
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| 515 | first = copyTermList( firstTerm, last ); |
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| 516 | |
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| 517 | coeff = aPoly->firstTerm->coeff; |
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| 518 | exp = aPoly->firstTerm->exp; |
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| 519 | while (first && ( first->exp >= exp ) ) { |
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| 520 | newcoeff = first->coeff / coeff; |
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| 521 | newexp = first->exp - exp; |
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| 522 | dummy = first; |
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| 523 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
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| 524 | delete dummy; |
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| 525 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
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| 526 | } |
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| 527 | if ( resultfirst ) |
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| 528 | if ( resultfirst->exp == 0 ) { |
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| 529 | quot = resultfirst->coeff.getval(); |
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| 530 | delete resultfirst; |
---|
| 531 | } |
---|
| 532 | else |
---|
| 533 | quot = new InternalPoly( resultfirst, resultlast, var ); |
---|
| 534 | else |
---|
| 535 | quot = CFFactory::basic( 0 ); |
---|
| 536 | if ( first ) |
---|
| 537 | if ( first->exp == 0 ) { |
---|
| 538 | rem = first->coeff.getval(); |
---|
| 539 | delete first; |
---|
| 540 | } |
---|
| 541 | else |
---|
| 542 | rem = new InternalPoly( first, last, var ); |
---|
| 543 | else |
---|
| 544 | rem = CFFactory::basic( 0 ); |
---|
| 545 | } |
---|
| 546 | } |
---|
| 547 | |
---|
| 548 | |
---|
| 549 | bool |
---|
| 550 | InternalPoly::divremsamet( InternalCF* acoeff, InternalCF*& quot, InternalCF*& rem ) |
---|
| 551 | { |
---|
| 552 | if ( inExtension() && getReduce( var ) ) { |
---|
| 553 | divremsame( acoeff, quot, rem ); |
---|
| 554 | return true; |
---|
| 555 | } |
---|
| 556 | InternalPoly *aPoly = (InternalPoly*)acoeff; |
---|
| 557 | termList dummy, first, last, resultfirst = 0, resultlast = 0; |
---|
| 558 | CanonicalForm coeff, newcoeff, dummycoeff; |
---|
| 559 | int exp, newexp; |
---|
| 560 | bool divideok = true; |
---|
| 561 | |
---|
| 562 | // if ( ! ::divremt( lastTerm->coeff, aPoly->lastTerm->coeff, newcoeff, dummycoeff ) ) |
---|
| 563 | // return false; |
---|
| 564 | |
---|
| 565 | first = copyTermList( firstTerm, last ); |
---|
| 566 | |
---|
| 567 | coeff = aPoly->firstTerm->coeff; |
---|
| 568 | exp = aPoly->firstTerm->exp; |
---|
| 569 | while (first && ( first->exp >= exp ) && divideok ) { |
---|
| 570 | divideok = ::divremt( first->coeff, coeff, newcoeff, dummycoeff ); |
---|
| 571 | if ( divideok && dummycoeff.isZero() ) { |
---|
| 572 | newexp = first->exp - exp; |
---|
| 573 | dummy = first; |
---|
| 574 | first = mulAddTermList( first->next, aPoly->firstTerm->next, newcoeff, newexp, last, true ); |
---|
| 575 | delete dummy; |
---|
| 576 | appendTermList( resultfirst, resultlast, newcoeff, newexp ); |
---|
| 577 | } |
---|
| 578 | else |
---|
| 579 | divideok = false; |
---|
| 580 | } |
---|
| 581 | if ( divideok ) { |
---|
| 582 | if ( resultfirst ) |
---|
| 583 | if ( resultfirst->exp == 0 ) { |
---|
| 584 | quot = resultfirst->coeff.getval(); |
---|
| 585 | delete resultfirst; |
---|
| 586 | } |
---|
| 587 | else |
---|
| 588 | quot = new InternalPoly( resultfirst, resultlast, var ); |
---|
| 589 | else |
---|
| 590 | quot = CFFactory::basic( 0 ); |
---|
| 591 | if ( first ) |
---|
| 592 | if ( first->exp == 0 ) { |
---|
| 593 | rem = first->coeff.getval(); |
---|
| 594 | delete first; |
---|
| 595 | } |
---|
| 596 | else |
---|
| 597 | rem = new InternalPoly( first, last, var ); |
---|
| 598 | else |
---|
| 599 | rem = CFFactory::basic( 0 ); |
---|
| 600 | } |
---|
| 601 | else { |
---|
| 602 | freeTermList( resultfirst ); |
---|
| 603 | freeTermList( first ); |
---|
| 604 | } |
---|
| 605 | return divideok; |
---|
| 606 | } |
---|
| 607 | |
---|
| 608 | int |
---|
| 609 | InternalPoly::comparecoeff ( InternalCF* acoeff ) |
---|
| 610 | { |
---|
| 611 | return 1; |
---|
| 612 | } |
---|
| 613 | |
---|
| 614 | InternalCF* |
---|
| 615 | InternalPoly::addcoeff( InternalCF* cc ) |
---|
| 616 | { |
---|
| 617 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
| 618 | if ( c.isZero() ) |
---|
| 619 | return this; |
---|
| 620 | else { |
---|
| 621 | if ( getRefCount() == 1 ) { |
---|
| 622 | if ( lastTerm->exp == 0 ) { |
---|
| 623 | lastTerm->coeff += c; |
---|
| 624 | if ( lastTerm->coeff.isZero() ) { |
---|
| 625 | termList cursor = firstTerm; |
---|
| 626 | while ( cursor->next != lastTerm ) |
---|
| 627 | cursor = cursor->next; |
---|
| 628 | delete lastTerm; |
---|
| 629 | cursor->next = 0; |
---|
| 630 | lastTerm = cursor; |
---|
| 631 | } |
---|
| 632 | } |
---|
| 633 | else { |
---|
| 634 | lastTerm->next = new term( 0, c, 0 ); |
---|
| 635 | lastTerm = lastTerm->next; |
---|
| 636 | } |
---|
| 637 | return this; |
---|
| 638 | } |
---|
| 639 | else { |
---|
| 640 | decRefCount(); |
---|
| 641 | termList last, first = copyTermList( firstTerm, last, false ); |
---|
| 642 | if ( last->exp == 0 ) { |
---|
| 643 | last->coeff += c; |
---|
| 644 | if ( last->coeff.isZero() ) { |
---|
| 645 | termList cursor = first; |
---|
| 646 | while ( cursor->next != last ) |
---|
| 647 | cursor = cursor->next; |
---|
| 648 | delete last; |
---|
| 649 | cursor->next = 0; |
---|
| 650 | last = cursor; |
---|
| 651 | } |
---|
| 652 | } |
---|
| 653 | else { |
---|
| 654 | last->next = new term( 0, c, 0 ); |
---|
| 655 | last = last->next; |
---|
| 656 | } |
---|
| 657 | return new InternalPoly( first, last, var ); |
---|
| 658 | } |
---|
| 659 | } |
---|
| 660 | } |
---|
| 661 | |
---|
| 662 | InternalCF* |
---|
| 663 | InternalPoly::subcoeff( InternalCF* cc, bool negate ) |
---|
| 664 | { |
---|
| 665 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
| 666 | if ( c.isZero() ) |
---|
| 667 | if ( getRefCount() > 1 ) { |
---|
| 668 | decRefCount(); |
---|
| 669 | termList last, first = copyTermList( firstTerm, last, negate ); |
---|
| 670 | return new InternalPoly( first, last, var ); |
---|
| 671 | } |
---|
| 672 | else { |
---|
| 673 | if ( negate ) |
---|
| 674 | negateTermList( firstTerm ); |
---|
| 675 | return this; |
---|
| 676 | } |
---|
| 677 | else { |
---|
| 678 | if ( getRefCount() == 1 ) { |
---|
| 679 | if ( lastTerm->exp == 0 ) { |
---|
| 680 | if ( negate ) { |
---|
| 681 | negateTermList( firstTerm ); |
---|
| 682 | lastTerm->coeff += c; |
---|
| 683 | } |
---|
| 684 | else |
---|
| 685 | lastTerm->coeff -= c; |
---|
| 686 | if ( lastTerm->coeff.isZero() ) { |
---|
| 687 | termList cursor = firstTerm; |
---|
| 688 | while ( cursor->next != lastTerm ) |
---|
| 689 | cursor = cursor->next; |
---|
| 690 | delete lastTerm; |
---|
| 691 | cursor->next = 0; |
---|
| 692 | lastTerm = cursor; |
---|
| 693 | } |
---|
| 694 | } |
---|
| 695 | else { |
---|
| 696 | if ( negate ) { |
---|
| 697 | negateTermList( firstTerm ); |
---|
| 698 | lastTerm->next = new term( 0, c, 0 ); |
---|
| 699 | } |
---|
| 700 | else |
---|
| 701 | lastTerm->next = new term( 0, -c, 0 ); |
---|
| 702 | lastTerm = lastTerm->next; |
---|
| 703 | } |
---|
| 704 | return this; |
---|
| 705 | } |
---|
| 706 | else { |
---|
| 707 | decRefCount(); |
---|
| 708 | termList last, first = copyTermList( firstTerm, last, negate ); |
---|
| 709 | if ( last->exp == 0 ) { |
---|
| 710 | if ( negate ) |
---|
| 711 | last->coeff += c; |
---|
| 712 | else |
---|
| 713 | last->coeff -= c; |
---|
| 714 | if ( last->coeff.isZero() ) { |
---|
| 715 | termList cursor = first; |
---|
| 716 | while ( cursor->next != last ) |
---|
| 717 | cursor = cursor->next; |
---|
| 718 | delete last; |
---|
| 719 | cursor->next = 0; |
---|
| 720 | last = cursor; |
---|
| 721 | } |
---|
| 722 | } |
---|
| 723 | else { |
---|
| 724 | if ( negate ) |
---|
| 725 | last->next = new term( 0, c, 0 ); |
---|
| 726 | else |
---|
| 727 | last->next = new term( 0, -c, 0 ); |
---|
| 728 | last = last->next; |
---|
| 729 | } |
---|
| 730 | return new InternalPoly( first, last, var ); |
---|
| 731 | } |
---|
| 732 | } |
---|
| 733 | } |
---|
| 734 | |
---|
| 735 | InternalCF* |
---|
| 736 | InternalPoly::mulcoeff( InternalCF* cc ) |
---|
| 737 | { |
---|
| 738 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
| 739 | if ( c.isZero() ) { |
---|
| 740 | if ( getRefCount() == 1 ) { |
---|
| 741 | delete this; |
---|
| 742 | return CFFactory::basic( 0 ); |
---|
| 743 | } |
---|
| 744 | else { |
---|
| 745 | decRefCount(); |
---|
| 746 | return CFFactory::basic( 0 ); |
---|
| 747 | } |
---|
| 748 | } |
---|
| 749 | else if ( c.isOne() ) |
---|
| 750 | return this; |
---|
| 751 | else { |
---|
| 752 | if ( getRefCount() == 1 ) { |
---|
| 753 | mulTermList( firstTerm, c, 0 ); |
---|
| 754 | return this; |
---|
| 755 | } |
---|
| 756 | else { |
---|
| 757 | decRefCount(); |
---|
| 758 | termList last, first = copyTermList( firstTerm, last ); |
---|
| 759 | mulTermList( first, c, 0 ); |
---|
| 760 | return new InternalPoly( first, last, var ); |
---|
| 761 | } |
---|
| 762 | } |
---|
| 763 | } |
---|
| 764 | |
---|
| 765 | InternalCF* |
---|
| 766 | InternalPoly::dividecoeff( InternalCF* c, bool invert ) |
---|
| 767 | { |
---|
| 768 | return divcoeff( c, invert ); |
---|
| 769 | } |
---|
| 770 | |
---|
| 771 | InternalCF* |
---|
| 772 | InternalPoly::divcoeff( InternalCF* cc, bool invert ) |
---|
| 773 | { |
---|
| 774 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
| 775 | if ( inExtension() && getReduce( var ) && invert ) { |
---|
| 776 | InternalCF * dummy; |
---|
| 777 | dummy = this->invert(); |
---|
| 778 | dummy = dummy->mulcoeff( cc ); |
---|
| 779 | if ( getRefCount() == 1 ) { |
---|
| 780 | delete this; |
---|
| 781 | return dummy; |
---|
| 782 | } |
---|
| 783 | else { |
---|
| 784 | decRefCount(); |
---|
| 785 | return dummy; |
---|
| 786 | } |
---|
| 787 | } |
---|
| 788 | if ( invert ) |
---|
| 789 | if ( getRefCount() == 1 ) { |
---|
| 790 | delete this; |
---|
| 791 | return CFFactory::basic( 0 ); |
---|
| 792 | } |
---|
| 793 | else { |
---|
| 794 | decRefCount(); |
---|
| 795 | return CFFactory::basic( 0 ); |
---|
| 796 | } |
---|
| 797 | if ( c.isOne() ) |
---|
| 798 | return this; |
---|
| 799 | else { |
---|
| 800 | if ( getRefCount() == 1 ) { |
---|
| 801 | firstTerm = divTermList( firstTerm, c, lastTerm ); |
---|
| 802 | if ( firstTerm && firstTerm->exp != 0 ) |
---|
| 803 | return this; |
---|
| 804 | else if ( firstTerm ) { |
---|
| 805 | InternalCF * res = firstTerm->coeff.getval(); |
---|
| 806 | delete this; |
---|
| 807 | return res; |
---|
| 808 | } |
---|
| 809 | else { |
---|
| 810 | delete this; |
---|
| 811 | return CFFactory::basic( 0 ); |
---|
| 812 | } |
---|
| 813 | } |
---|
| 814 | else { |
---|
| 815 | decRefCount(); |
---|
| 816 | termList last, first = copyTermList( firstTerm, last ); |
---|
| 817 | first = divTermList( first, c, last ); |
---|
| 818 | if ( first && first->exp != 0 ) |
---|
| 819 | return new InternalPoly( first, last, var ); |
---|
| 820 | else if ( first ) { |
---|
| 821 | InternalCF * res = first->coeff.getval(); |
---|
| 822 | delete first; |
---|
| 823 | return res; |
---|
| 824 | } |
---|
| 825 | else { |
---|
| 826 | delete first; |
---|
| 827 | return CFFactory::basic( 0 ); |
---|
| 828 | } |
---|
| 829 | } |
---|
| 830 | } |
---|
| 831 | } |
---|
| 832 | |
---|
| 833 | InternalCF* |
---|
| 834 | InternalPoly::modulocoeff( InternalCF* cc, bool invert ) |
---|
| 835 | { |
---|
| 836 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
[76470b9] | 837 | if ( invert ) { |
---|
[2dd068] | 838 | if ( deleteObject() ) delete this; |
---|
| 839 | return c.getval(); |
---|
| 840 | } |
---|
| 841 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
| 842 | if ( deleteObject() ) delete this; |
---|
| 843 | return CFFactory::basic( 0 ); |
---|
| 844 | } |
---|
| 845 | |
---|
| 846 | InternalCF* |
---|
| 847 | InternalPoly::modcoeff( InternalCF* cc, bool invert ) |
---|
| 848 | { |
---|
| 849 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
| 850 | if ( invert ) { |
---|
| 851 | if ( deleteObject() ) delete this; |
---|
| 852 | return c.getval(); |
---|
| 853 | } |
---|
| 854 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
| 855 | if ( c.isOne() ) { |
---|
| 856 | if ( getRefCount() == 1 ) { |
---|
| 857 | delete this; |
---|
| 858 | return CFFactory::basic( 0 ); |
---|
| 859 | } |
---|
| 860 | else { |
---|
| 861 | decRefCount(); |
---|
| 862 | return CFFactory::basic( 0 ); |
---|
| 863 | } |
---|
| 864 | } |
---|
| 865 | else { |
---|
| 866 | if ( getRefCount() == 1 ) { |
---|
| 867 | firstTerm = modTermList( firstTerm, c, lastTerm ); |
---|
| 868 | if ( firstTerm && firstTerm->exp != 0 ) |
---|
| 869 | return this; |
---|
| 870 | else if ( firstTerm ) { |
---|
| 871 | InternalCF * res = firstTerm->coeff.getval(); |
---|
| 872 | delete this; |
---|
| 873 | return res; |
---|
| 874 | } |
---|
| 875 | else { |
---|
| 876 | delete this; |
---|
| 877 | return CFFactory::basic( 0 ); |
---|
| 878 | } |
---|
| 879 | } |
---|
| 880 | else { |
---|
| 881 | decRefCount(); |
---|
| 882 | termList last, first = copyTermList( firstTerm, last ); |
---|
| 883 | first = modTermList( first, c, last ); |
---|
| 884 | if ( first && first->exp != 0 ) |
---|
| 885 | return new InternalPoly( first, last, var ); |
---|
| 886 | else if ( first ) { |
---|
| 887 | InternalCF * res = first->coeff.getval(); |
---|
| 888 | delete first; |
---|
| 889 | return res; |
---|
| 890 | } |
---|
| 891 | else { |
---|
| 892 | delete first; |
---|
| 893 | return CFFactory::basic( 0 ); |
---|
| 894 | } |
---|
| 895 | } |
---|
| 896 | } |
---|
| 897 | } |
---|
| 898 | |
---|
| 899 | void |
---|
| 900 | InternalPoly::divremcoeff( InternalCF* cc, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
| 901 | { |
---|
| 902 | if ( inExtension() && getReduce( var ) ) { |
---|
| 903 | quot = copyObject(); |
---|
| 904 | quot = quot->dividecoeff( cc, invert ); |
---|
| 905 | rem = CFFactory::basic( 0 ); |
---|
| 906 | } |
---|
| 907 | else if ( invert ) { |
---|
| 908 | if ( is_imm( cc ) ) |
---|
| 909 | rem = cc; |
---|
| 910 | else |
---|
| 911 | rem = cc->copyObject(); |
---|
| 912 | quot = CFFactory::basic( 0 ); |
---|
| 913 | } |
---|
| 914 | else { |
---|
| 915 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
| 916 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
| 917 | termList quotlast, quotfirst = copyTermList( firstTerm, quotlast ); |
---|
| 918 | quotfirst = divTermList( quotfirst, c, quotlast ); |
---|
| 919 | if ( quotfirst ) |
---|
| 920 | if ( quotfirst->exp == 0 ) { |
---|
| 921 | quot = quotfirst->coeff.getval(); |
---|
| 922 | delete quotfirst; |
---|
| 923 | } |
---|
| 924 | else |
---|
| 925 | quot = new InternalPoly( quotfirst, quotlast, var ); |
---|
| 926 | else |
---|
| 927 | quot = CFFactory::basic( 0 ); |
---|
| 928 | rem = CFFactory::basic( 0 ); |
---|
| 929 | } |
---|
| 930 | } |
---|
| 931 | |
---|
| 932 | bool |
---|
| 933 | InternalPoly::divremcoefft( InternalCF* cc, InternalCF*& quot, InternalCF*& rem, bool invert ) |
---|
| 934 | { |
---|
| 935 | if ( inExtension() && getReduce( var ) ) { |
---|
| 936 | quot = copyObject(); |
---|
| 937 | quot = quot->dividecoeff( cc, invert ); |
---|
| 938 | rem = CFFactory::basic( 0 ); |
---|
| 939 | return true; |
---|
| 940 | } |
---|
| 941 | else if ( invert ) { |
---|
| 942 | if ( is_imm( cc ) ) |
---|
| 943 | rem = cc; |
---|
| 944 | else |
---|
| 945 | rem = cc->copyObject(); |
---|
| 946 | quot = CFFactory::basic( 0 ); |
---|
| 947 | return true; |
---|
| 948 | } |
---|
| 949 | CanonicalForm c( is_imm(cc) ? cc : cc->copyObject() ); |
---|
| 950 | ASSERT( ! c.isZero(), "divide by zero!" ); |
---|
| 951 | termList quotfirst, quotcursor; |
---|
| 952 | termList cursor; |
---|
| 953 | CanonicalForm cquot, crem; |
---|
| 954 | bool divideok = true; |
---|
| 955 | |
---|
| 956 | cursor = firstTerm; |
---|
| 957 | quotcursor = quotfirst = new term; |
---|
| 958 | |
---|
| 959 | while ( cursor && divideok ) { |
---|
| 960 | divideok = ::divremt( cursor->coeff, c, cquot, crem ); |
---|
| 961 | divideok = divideok && crem.isZero(); |
---|
| 962 | if ( divideok ) { |
---|
| 963 | if ( ! cquot.isZero() ) { |
---|
| 964 | quotcursor->next = new term( 0, cquot, cursor->exp ); |
---|
| 965 | quotcursor = quotcursor->next; |
---|
| 966 | } |
---|
| 967 | cursor = cursor->next; |
---|
| 968 | } |
---|
| 969 | } |
---|
| 970 | quotcursor->next = 0; |
---|
| 971 | if ( divideok ) { |
---|
| 972 | cursor = quotfirst; quotfirst = quotfirst->next; delete cursor; |
---|
| 973 | if ( quotfirst ) |
---|
| 974 | if ( quotfirst->exp == 0 ) { |
---|
| 975 | quot = quotfirst->coeff.getval(); |
---|
| 976 | delete quotfirst; |
---|
| 977 | } |
---|
| 978 | else |
---|
| 979 | quot = new InternalPoly( quotfirst, quotcursor, var ); |
---|
| 980 | else |
---|
| 981 | quot = CFFactory::basic( 0 ); |
---|
| 982 | rem = CFFactory::basic( 0 ); |
---|
| 983 | } |
---|
| 984 | else { |
---|
| 985 | freeTermList( quotfirst ); |
---|
| 986 | } |
---|
| 987 | return divideok; |
---|
| 988 | } |
---|
| 989 | |
---|
| 990 | // static functions |
---|
| 991 | |
---|
| 992 | termList |
---|
| 993 | InternalPoly::copyTermList ( termList aTermList, termList& theLastTerm, bool negate ) |
---|
| 994 | { |
---|
[32e9cd7] | 995 | if ( aTermList == 0 ) |
---|
[2dd068] | 996 | return 0; |
---|
| 997 | else if ( negate ) { |
---|
| 998 | termList sourceCursor = aTermList; |
---|
| 999 | termList dummy = new term; |
---|
| 1000 | termList targetCursor = dummy; |
---|
| 1001 | |
---|
| 1002 | while ( sourceCursor ) { |
---|
| 1003 | targetCursor->next = new term( 0, -sourceCursor->coeff, sourceCursor->exp ); |
---|
| 1004 | targetCursor = targetCursor->next; |
---|
| 1005 | sourceCursor = sourceCursor->next; |
---|
| 1006 | } |
---|
| 1007 | targetCursor->next = 0; |
---|
| 1008 | theLastTerm = targetCursor; |
---|
| 1009 | targetCursor = dummy->next; |
---|
| 1010 | delete dummy; |
---|
| 1011 | return targetCursor; |
---|
| 1012 | } |
---|
| 1013 | else { |
---|
| 1014 | termList sourceCursor = aTermList; |
---|
| 1015 | termList dummy = new term; |
---|
| 1016 | termList targetCursor = dummy; |
---|
| 1017 | |
---|
| 1018 | while ( sourceCursor ) { |
---|
| 1019 | targetCursor->next = new term( 0, sourceCursor->coeff, sourceCursor->exp ); |
---|
| 1020 | targetCursor = targetCursor->next; |
---|
| 1021 | sourceCursor = sourceCursor->next; |
---|
| 1022 | } |
---|
| 1023 | targetCursor->next = 0; |
---|
| 1024 | theLastTerm = targetCursor; |
---|
| 1025 | targetCursor = dummy->next; |
---|
| 1026 | delete dummy; |
---|
| 1027 | return targetCursor; |
---|
| 1028 | } |
---|
| 1029 | } |
---|
| 1030 | |
---|
| 1031 | termList |
---|
| 1032 | InternalPoly::deepCopyTermList ( termList aTermList, termList& theLastTerm ) |
---|
| 1033 | { |
---|
[32e9cd7] | 1034 | if ( aTermList == 0 ) |
---|
[2dd068] | 1035 | return 0; |
---|
| 1036 | else { |
---|
| 1037 | termList sourceCursor = aTermList; |
---|
| 1038 | termList dummy = new term; |
---|
| 1039 | termList targetCursor = dummy; |
---|
| 1040 | |
---|
| 1041 | while ( sourceCursor ) { |
---|
| 1042 | targetCursor->next = new term( 0, sourceCursor->coeff.deepCopy(), sourceCursor->exp ); |
---|
| 1043 | targetCursor = targetCursor->next; |
---|
| 1044 | sourceCursor = sourceCursor->next; |
---|
| 1045 | } |
---|
| 1046 | targetCursor->next = 0; |
---|
| 1047 | theLastTerm = targetCursor; |
---|
| 1048 | targetCursor = dummy->next; |
---|
| 1049 | delete dummy; |
---|
| 1050 | return targetCursor; |
---|
| 1051 | } |
---|
| 1052 | } |
---|
| 1053 | |
---|
| 1054 | void |
---|
| 1055 | InternalPoly::freeTermList ( termList aTermList ) |
---|
| 1056 | { |
---|
| 1057 | termList cursor = aTermList; |
---|
| 1058 | |
---|
| 1059 | while ( cursor ) { |
---|
| 1060 | cursor = cursor->next; |
---|
| 1061 | delete aTermList; |
---|
| 1062 | aTermList = cursor; |
---|
| 1063 | } |
---|
| 1064 | } |
---|
| 1065 | |
---|
| 1066 | void |
---|
| 1067 | InternalPoly::negateTermList ( termList terms ) |
---|
| 1068 | { |
---|
| 1069 | termList cursor = terms; |
---|
| 1070 | while ( cursor ) { |
---|
| 1071 | cursor->coeff = -cursor->coeff; |
---|
| 1072 | cursor = cursor->next; |
---|
| 1073 | } |
---|
| 1074 | } |
---|
| 1075 | |
---|
| 1076 | termList |
---|
| 1077 | InternalPoly::addTermList ( termList theList, termList aList, termList& lastTerm, bool negate ) |
---|
| 1078 | { |
---|
| 1079 | termList theCursor = theList; |
---|
| 1080 | termList aCursor = aList; |
---|
| 1081 | termList predCursor = 0; |
---|
| 1082 | |
---|
| 1083 | while ( theCursor && aCursor ) { |
---|
| 1084 | if ( theCursor->exp == aCursor->exp ) { |
---|
| 1085 | if ( negate ) |
---|
| 1086 | theCursor->coeff -= aCursor->coeff; |
---|
| 1087 | else |
---|
| 1088 | theCursor->coeff += aCursor->coeff; |
---|
| 1089 | if ( theCursor->coeff.isZero() ) { |
---|
| 1090 | if ( predCursor ) { |
---|
| 1091 | predCursor->next = theCursor->next; |
---|
| 1092 | delete theCursor; |
---|
| 1093 | theCursor = predCursor->next; |
---|
| 1094 | } |
---|
| 1095 | else { |
---|
| 1096 | theList = theList->next; |
---|
| 1097 | delete theCursor; |
---|
| 1098 | theCursor = theList; |
---|
| 1099 | } |
---|
| 1100 | } |
---|
| 1101 | else { |
---|
| 1102 | predCursor = theCursor; |
---|
| 1103 | theCursor = theCursor->next; |
---|
| 1104 | } |
---|
| 1105 | aCursor = aCursor->next; |
---|
| 1106 | } |
---|
| 1107 | else if ( theCursor->exp < aCursor->exp ) { |
---|
| 1108 | if ( negate ) |
---|
| 1109 | if ( predCursor ) { |
---|
| 1110 | predCursor->next = new term( theCursor, -aCursor->coeff, aCursor->exp ); |
---|
| 1111 | predCursor = predCursor->next; |
---|
| 1112 | } |
---|
| 1113 | else { |
---|
| 1114 | theList = new term( theCursor, -aCursor->coeff, aCursor->exp ); |
---|
| 1115 | predCursor = theList; |
---|
| 1116 | } |
---|
[32e9cd7] | 1117 | else |
---|
[2dd068] | 1118 | if ( predCursor ) { |
---|
| 1119 | predCursor->next = new term( theCursor, aCursor->coeff, aCursor->exp ); |
---|
| 1120 | predCursor = predCursor->next; |
---|
| 1121 | } |
---|
| 1122 | else { |
---|
| 1123 | theList = new term( theCursor, aCursor->coeff, aCursor->exp ); |
---|
| 1124 | predCursor = theList; |
---|
| 1125 | } |
---|
| 1126 | aCursor = aCursor->next; |
---|
[32e9cd7] | 1127 | } |
---|
[2dd068] | 1128 | else { |
---|
| 1129 | predCursor = theCursor; |
---|
| 1130 | theCursor = theCursor->next; |
---|
| 1131 | } |
---|
| 1132 | } |
---|
| 1133 | if ( aCursor ) { |
---|
| 1134 | if ( predCursor ) |
---|
| 1135 | predCursor->next = copyTermList( aCursor, lastTerm, negate ); |
---|
| 1136 | else |
---|
| 1137 | theList = copyTermList( aCursor, lastTerm, negate ); |
---|
| 1138 | } |
---|
| 1139 | else if ( ! theCursor ) |
---|
| 1140 | lastTerm = predCursor; |
---|
| 1141 | |
---|
| 1142 | return theList; |
---|
| 1143 | } |
---|
| 1144 | |
---|
| 1145 | void |
---|
| 1146 | InternalPoly::mulTermList ( termList theCursor, const CanonicalForm& coeff, const int exp ) |
---|
| 1147 | { |
---|
| 1148 | while ( theCursor ) { |
---|
| 1149 | theCursor->coeff *= coeff; |
---|
| 1150 | theCursor->exp += exp; |
---|
| 1151 | theCursor = theCursor->next; |
---|
| 1152 | } |
---|
| 1153 | } |
---|
| 1154 | |
---|
| 1155 | termList |
---|
| 1156 | InternalPoly::divTermList ( termList firstTerm, const CanonicalForm& coeff, termList& lastTerm ) |
---|
| 1157 | { |
---|
| 1158 | termList theCursor = firstTerm; |
---|
| 1159 | lastTerm = 0; |
---|
| 1160 | termList dummy; |
---|
| 1161 | |
---|
| 1162 | while ( theCursor ) { |
---|
| 1163 | theCursor->coeff /= coeff; |
---|
| 1164 | if ( theCursor->coeff.isZero() ) { |
---|
| 1165 | if ( theCursor == firstTerm ) |
---|
| 1166 | firstTerm = theCursor->next; |
---|
| 1167 | else |
---|
| 1168 | lastTerm->next = theCursor->next; |
---|
| 1169 | dummy = theCursor; |
---|
| 1170 | theCursor = theCursor->next; |
---|
| 1171 | delete dummy; |
---|
| 1172 | } |
---|
| 1173 | else { |
---|
| 1174 | lastTerm = theCursor; |
---|
| 1175 | theCursor = theCursor->next; |
---|
| 1176 | } |
---|
| 1177 | } |
---|
| 1178 | return firstTerm; |
---|
| 1179 | } |
---|
| 1180 | |
---|
| 1181 | termList |
---|
| 1182 | InternalPoly::modTermList ( termList firstTerm, const CanonicalForm& coeff, termList& lastTerm ) |
---|
| 1183 | { |
---|
| 1184 | termList theCursor = firstTerm; |
---|
| 1185 | lastTerm = 0; |
---|
| 1186 | termList dummy; |
---|
| 1187 | |
---|
| 1188 | while ( theCursor ) { |
---|
| 1189 | theCursor->coeff.mod( coeff ); |
---|
| 1190 | if ( theCursor->coeff.isZero() ) { |
---|
| 1191 | if ( theCursor == firstTerm ) |
---|
| 1192 | firstTerm = theCursor->next; |
---|
| 1193 | else |
---|
| 1194 | lastTerm->next = theCursor->next; |
---|
| 1195 | dummy = theCursor; |
---|
| 1196 | theCursor = theCursor-> next; |
---|
| 1197 | delete dummy; |
---|
| 1198 | } |
---|
| 1199 | else { |
---|
| 1200 | lastTerm = theCursor; |
---|
| 1201 | theCursor = theCursor->next; |
---|
| 1202 | } |
---|
| 1203 | } |
---|
| 1204 | return firstTerm; |
---|
| 1205 | } |
---|
| 1206 | |
---|
| 1207 | void |
---|
| 1208 | InternalPoly::appendTermList ( termList& first, termList& last, const CanonicalForm& coeff, const int exp ) |
---|
| 1209 | { |
---|
| 1210 | if ( last ) { |
---|
| 1211 | last->next = new term( 0, coeff, exp ); |
---|
| 1212 | last = last->next; |
---|
| 1213 | } |
---|
| 1214 | else { |
---|
| 1215 | first = new term( 0, coeff, exp ); |
---|
| 1216 | last = first; |
---|
| 1217 | } |
---|
| 1218 | } |
---|
| 1219 | |
---|
| 1220 | termList |
---|
| 1221 | InternalPoly::mulAddTermList ( termList theList, termList aList, const CanonicalForm & c, const int exp, termList & lastTerm, bool negate ) |
---|
| 1222 | { |
---|
| 1223 | termList theCursor = theList; |
---|
| 1224 | termList aCursor = aList; |
---|
| 1225 | termList predCursor = 0; |
---|
| 1226 | CanonicalForm coeff; |
---|
| 1227 | |
---|
| 1228 | if ( negate ) |
---|
| 1229 | coeff = -c; |
---|
| 1230 | else |
---|
| 1231 | coeff = c; |
---|
| 1232 | |
---|
| 1233 | while ( theCursor && aCursor ) { |
---|
| 1234 | if ( theCursor->exp == aCursor->exp + exp ) { |
---|
| 1235 | theCursor->coeff += aCursor->coeff * coeff; |
---|
| 1236 | if ( theCursor->coeff.isZero() ) { |
---|
| 1237 | if ( predCursor ) { |
---|
| 1238 | predCursor->next = theCursor->next; |
---|
| 1239 | delete theCursor; |
---|
| 1240 | theCursor = predCursor->next; |
---|
| 1241 | } |
---|
| 1242 | else { |
---|
| 1243 | theList = theList->next; |
---|
| 1244 | delete theCursor; |
---|
| 1245 | theCursor = theList; |
---|
| 1246 | } |
---|
| 1247 | } |
---|
| 1248 | else { |
---|
| 1249 | predCursor = theCursor; |
---|
| 1250 | theCursor = theCursor->next; |
---|
| 1251 | } |
---|
| 1252 | aCursor = aCursor->next; |
---|
| 1253 | } |
---|
| 1254 | else if ( theCursor->exp < aCursor->exp + exp ) { |
---|
| 1255 | if ( predCursor ) { |
---|
| 1256 | predCursor->next = new term( theCursor, aCursor->coeff * coeff, aCursor->exp + exp ); |
---|
| 1257 | predCursor = predCursor->next; |
---|
| 1258 | } |
---|
| 1259 | else { |
---|
| 1260 | theList = new term( theCursor, aCursor->coeff * coeff, aCursor->exp + exp ); |
---|
| 1261 | predCursor = theList; |
---|
| 1262 | } |
---|
| 1263 | aCursor = aCursor->next; |
---|
| 1264 | } |
---|
| 1265 | else { |
---|
| 1266 | predCursor = theCursor; |
---|
| 1267 | theCursor = theCursor->next; |
---|
| 1268 | } |
---|
| 1269 | } |
---|
| 1270 | if ( aCursor ) { |
---|
| 1271 | if ( predCursor ) { |
---|
| 1272 | predCursor->next = copyTermList( aCursor, lastTerm ); |
---|
| 1273 | predCursor = predCursor->next; |
---|
| 1274 | } |
---|
| 1275 | else { |
---|
| 1276 | theList = copyTermList( aCursor, lastTerm ); |
---|
| 1277 | predCursor = theList; |
---|
| 1278 | } |
---|
| 1279 | while ( predCursor ) { |
---|
| 1280 | predCursor->exp += exp; |
---|
| 1281 | predCursor->coeff *= coeff; |
---|
| 1282 | predCursor = predCursor->next; |
---|
| 1283 | } |
---|
| 1284 | } |
---|
| 1285 | else if ( ! theCursor ) |
---|
| 1286 | lastTerm = predCursor; |
---|
| 1287 | return theList; |
---|
| 1288 | } |
---|
| 1289 | |
---|
| 1290 | termList |
---|
| 1291 | InternalPoly::reduceTermList ( termList first, termList redterms, termList & last ) |
---|
| 1292 | { |
---|
| 1293 | CanonicalForm coeff = redterms->coeff; |
---|
| 1294 | CanonicalForm newcoeff; |
---|
| 1295 | int newexp; |
---|
| 1296 | int exp = redterms->exp; |
---|
| 1297 | termList dummy; |
---|
| 1298 | while ( first && ( first->exp >= exp ) ) { |
---|
| 1299 | newcoeff = first->coeff / coeff; |
---|
| 1300 | newexp = first->exp - exp; |
---|
| 1301 | dummy = first; |
---|
| 1302 | first = mulAddTermList( first->next, redterms->next, newcoeff, newexp, last, true ); |
---|
| 1303 | delete dummy; |
---|
| 1304 | } |
---|
| 1305 | return first; |
---|
| 1306 | } |
---|