Interface ComplexRoots<C extends RingElem<C> & Rational>

Type Parameters:

C - coefficient type.

All Superinterfaces:

Serializable

All Known Implementing Classes:

ComplexRootsAbstract, ComplexRootsSturm

public interface ComplexRoots<C extends RingElem<C> & Rational>
extends Serializable

Complex roots interface.

Method Summary

Modifier and Type	Method	Description
long	complexRootCount(Rectangle<C> rect, GenPolynomial<Complex<C>> a)	Complex root count of complex polynomial on rectangle.
Rectangle<C>	complexRootRefinement(Rectangle<C> rect, GenPolynomial<Complex<C>> a, BigRational len)	Complex root refinement of complex polynomial a on rectangle.
List<Rectangle<C>>	complexRoots(GenPolynomial<Complex<C>> a)	List of complex roots of complex polynomial.
List<Rectangle<C>>	complexRoots(Rectangle<C> rect, GenPolynomial<Complex<C>> a)	List of complex roots of complex polynomial a on rectangle.
Complex<C>	rootBound(GenPolynomial<Complex<C>> f)	Root bound.

Method Details

rootBound

Complex<C> rootBound(GenPolynomial<Complex<C>> f)

Root bound. With f(-M + i M) * f(-M - i M) * f(M - i M) * f(M + i M) != 0.

Parameters:

f - univariate polynomial.

Returns:

M such that root(f) is contained in the rectangle spanned by M.

complexRootCount

long complexRootCount(Rectangle<C> rect,
 GenPolynomial<Complex<C>> a)
               throws InvalidBoundaryException

Complex root count of complex polynomial on rectangle.

Parameters:

rect - rectangle.

a - univariate complex polynomial.

Returns:

root count of a in rectangle.

Throws:

InvalidBoundaryException

complexRoots

List<Rectangle<C>> complexRoots(Rectangle<C> rect,
 GenPolynomial<Complex<C>> a)
                         throws InvalidBoundaryException

List of complex roots of complex polynomial a on rectangle.

Parameters:

rect - rectangle.

a - univariate squarefree complex polynomial.

Returns:

list of complex roots.

Throws:

InvalidBoundaryException

complexRoots

List<Rectangle<C>> complexRoots(GenPolynomial<Complex<C>> a)

List of complex roots of complex polynomial.

Parameters:

a - univariate complex polynomial.

Returns:

list of complex roots.

complexRootRefinement

Rectangle<C> complexRootRefinement(Rectangle<C> rect,
 GenPolynomial<Complex<C>> a,
 BigRational len)
                            throws InvalidBoundaryException

Complex root refinement of complex polynomial a on rectangle.

Parameters:

rect - rectangle containing exactly one complex root.

a - univariate squarefree complex polynomial.

len - rational length for refinement.

Returns:

refined complex root.

Throws:

InvalidBoundaryException