CGAL 5.4  Polynomial

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 \( \deg u_i\leq mi1\) and \( \deg v_i\leq ni1\) 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
.