CGAL 4.12.1 - Polynomial
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Note: This functor is optional!
Computes the Sturm-Habicht polynomials of a polynomial \( f\) of degree \( n\), as defined in the documentation of PolynomialTraits_d::SturmHabichtSequence
. Moreover, for \( \mathrm{Stha}_i(f)\), polynomials \( u_i\) and \( v_i\) with \( \deg u_i\leq n-i-2\) and \( \deg v_i\leq n-i-1\) are computed such that \( \mathrm{Sres}_i(p,q)=u_i f + v_i f'\). \( u_i\) and \( v_i\) are called the cofactors of \( \mathrm{Stha}_i(f)\).
The result is written in three output ranges, each of length \( \min\{n,m\}+1\), starting with the \( 0\)-th Sturm-Habicht polynomial \( \mathrm{Stha_0(f)}\) and the corresponding cofactors.
Operations | |
template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 > | |
OutputIterator1 | operator() (Polynomial_d f, OutputIterator1 stha, OutputIterator2 co_f, OutputIterator3 co_fx) |
computes the Sturm-Habicht sequence of \( f\), and the cofactors, with respect to the outermost variable. More... | |
template<typename OutputIterator1 , typename OutputIterator2 , typename OutputIterator3 > | |
OutputIterator1 | operator() (Polynomial_d f, OutputIterator1 stha, OutputIterator2 co_f, OutputIterator3 co_fx, int i) |
computes the Sturm-Habicht sequence of \( f\), and the cofactors, with respect to \( x_i\). More... | |
OutputIterator1 PolynomialTraits_d::SturmHabichtSequenceWithCofactors::operator() | ( | Polynomial_d | f, |
OutputIterator1 | stha, | ||
OutputIterator2 | co_f, | ||
OutputIterator3 | co_fx | ||
) |
computes the Sturm-Habicht sequence of \( f\), and the cofactors, with respect to the outermost variable.
Each element is of type PolynomialTraits_d::Polynomial_d
.
OutputIterator1 PolynomialTraits_d::SturmHabichtSequenceWithCofactors::operator() | ( | Polynomial_d | f, |
OutputIterator1 | stha, | ||
OutputIterator2 | co_f, | ||
OutputIterator3 | co_fx, | ||
int | i | ||
) |
computes the Sturm-Habicht sequence of \( f\), and the cofactors, with respect to \( x_i\).
Each element is of type PolynomialTraits_d::Polynomial_d
.