Package edu.jas.root
Interface ComplexRoots<C extends RingElem<C> & Rational>
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- Type Parameters:
C
- coefficient type.
- All Superinterfaces:
java.io.Serializable
- All Known Implementing Classes:
ComplexRootsAbstract
,ComplexRootsSturm
public interface ComplexRoots<C extends RingElem<C> & Rational> extends java.io.Serializable
Complex roots interface.- Author:
- Heinz Kredel
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Method Summary
All Methods Instance Methods Abstract Methods 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.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.
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Method Detail
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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.
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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
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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
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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.
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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
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