CGAL 5.0 - Polynomial
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Computes the polynomial subresultant of two polynomials \( p\) and \( q\) of degree \( n\) and \( m\), respectively, as defined in the documentation of PolynomialTraits_d::PolynomialSubresultants
. Moreover, for \( \mathrm{Sres}_i(p,q)\), polynomials \( u_i\) and \( v_i\) with \( \deg u_i\leq m-i-1\) and \( \deg v_i\leq n-i-1\) are computed such that \( \mathrm{Sres}_i(p,q)=u_i p + v_i q\). \( u_i\) and \( v_i\) are called the cofactors of \( \mathrm{Sres}_i(p,q)\).
The result is written in three output ranges, each of length \( \min\{n,m\}+1\), starting with the \( 0\)-th subresultant and the corresponding cofactors.
Operations | |
template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 > | |
OutputIterator1 | operator() (Polynomial_d p, Polynomial_d q, OutputIterator1 sres, OutputIterator2 co_p, OutputIterator3 co_q) |
computes the subresultants of \( p\) and \( q\), and the cofactors, with respect to the outermost variable. More... | |
template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 > | |
OutputIterator1 | operator() (Polynomial_d p, Polynomial_d q, OutputIterator1 sres, OutputIterator2 co_p, OutputIterator3 co_q, int i) |
computes the subresultants of \( p\) and \( q\), and the cofactors, with respect to \( x_i\). More... | |
OutputIterator1 PolynomialTraits_d::PolynomialSubresultantsWithCofactors::operator() | ( | Polynomial_d | p, |
Polynomial_d | q, | ||
OutputIterator1 | sres, | ||
OutputIterator2 | co_p, | ||
OutputIterator3 | co_q | ||
) |
computes the subresultants of \( p\) and \( q\), and the cofactors, with respect to the outermost variable.
Each element is of type PolynomialTraits_d::Polynomial_d
.
OutputIterator1 PolynomialTraits_d::PolynomialSubresultantsWithCofactors::operator() | ( | Polynomial_d | p, |
Polynomial_d | q, | ||
OutputIterator1 | sres, | ||
OutputIterator2 | co_p, | ||
OutputIterator3 | co_q, | ||
int | i | ||
) |
computes the subresultants of \( p\) and \( q\), and the cofactors, with respect to \( x_i\).
Each element is of type PolynomialTraits_d::Polynomial_d
.