edu.jas.root
Interface ComplexRoots<C extends RingElem<C> & Rational>

Type Parameters:

C - coefficient type.

All Known Implementing Classes:

ComplexRootsAbstract, ComplexRootsSturm

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

Complex roots interface.

Author:

Heinz Kredel

Method Summary

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.
java.util.List<Rectangle<C>>	complexRoots(GenPolynomial<Complex<C>> a) List of complex roots of complex polynomial.
java.util.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 Detail

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

java.util.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

java.util.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