001/*
002 * $Id: ComplexRoots.java 5568 2016-08-03 19:14:39Z kredel $
003 */
004
005package edu.jas.root;
006
007
008import java.io.Serializable;
009import java.util.List;
010
011import edu.jas.arith.BigRational;
012import edu.jas.arith.Rational;
013import edu.jas.poly.Complex;
014import edu.jas.poly.GenPolynomial;
015import edu.jas.structure.RingElem;
016
017
018/**
019 * Complex roots interface.
020 * @param <C> coefficient type.
021 * @author Heinz Kredel
022 */
023public interface ComplexRoots<C extends RingElem<C> & Rational> extends Serializable {
024
025
026    /**
027     * Root bound. With f(-M + i M) * f(-M - i M) * f(M - i M) * f(M + i M) !=
028     * 0.
029     * @param f univariate polynomial.
030     * @return M such that root(f) is contained in the rectangle spanned by M.
031     */
032    public Complex<C> rootBound(GenPolynomial<Complex<C>> f);
033
034
035    /**
036     * Complex root count of complex polynomial on rectangle.
037     * @param rect rectangle.
038     * @param a univariate complex polynomial.
039     * @return root count of a in rectangle.
040     */
041    public long complexRootCount(Rectangle<C> rect, GenPolynomial<Complex<C>> a)
042                    throws InvalidBoundaryException;
043
044
045    /**
046     * List of complex roots of complex polynomial a on rectangle.
047     * @param rect rectangle.
048     * @param a univariate squarefree complex polynomial.
049     * @return list of complex roots.
050     */
051    public List<Rectangle<C>> complexRoots(Rectangle<C> rect, GenPolynomial<Complex<C>> a)
052                    throws InvalidBoundaryException;
053
054
055    /**
056     * List of complex roots of complex polynomial.
057     * @param a univariate complex polynomial.
058     * @return list of complex roots.
059     */
060    public List<Rectangle<C>> complexRoots(GenPolynomial<Complex<C>> a);
061
062
063    /**
064     * Complex root refinement of complex polynomial a on rectangle.
065     * @param rect rectangle containing exactly one complex root.
066     * @param a univariate squarefree complex polynomial.
067     * @param len rational length for refinement.
068     * @return refined complex root.
069     */
070    public Rectangle<C> complexRootRefinement(Rectangle<C> rect, GenPolynomial<Complex<C>> a, BigRational len)
071                    throws InvalidBoundaryException;
072
073}