Package edu.jas.root

Class PolyUtilRoot

java.lang.Object

edu.jas.root.PolyUtilRoot

public class PolyUtilRoot
extends java.lang.Object

Polynomial utilities related to real and complex roots.

Author:

Heinz Kredel

Constructor Summary

Constructors

Constructor	Description
PolyUtilRoot()

Method Summary

Modifier and Type	Method	Description
static <C extends GcdRingElem<C> & Rational> GenPolynomial<AlgebraicNumber<C>>	algebraicFromRealCoefficients(GenPolynomialRing<AlgebraicNumber<C>> afac, GenPolynomial<RealAlgebraicNumber<C>> A)	Convert to AlgebraicNumber coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<Complex<C>>	complexFromAny(GenPolynomial<C> f)	Convert to Complex coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>	convertRecursiveToAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<GenPolynomial<C>> A)	Convert to RealAlgebraicNumber coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>	convertToAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<C> A)	Convert to RealAlgebraicNumber coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<ComplexAlgebraicNumber<C>>	convertToComplexCoefficients(GenPolynomialRing<ComplexAlgebraicNumber<C>> pfac, GenPolynomial<C> A)	Convert to ComplexAlgebraicNumber coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<ComplexAlgebraicNumber<C>>	convertToComplexCoefficientsFromComplex(GenPolynomialRing<ComplexAlgebraicNumber<C>> pfac, GenPolynomial<Complex<C>> A)	Convert to ComplexAlgebraicNumber coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>	convertToRealCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<C> A)	Convert to RealAlgebraicNumber coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>	convertToRecAlgebraicCoefficients(int depth, GenPolynomialRing<RealAlgebraicNumber<C>> pfac, GenPolynomial<C> A)	Convert to recursive RealAlgebraicNumber coefficients.
static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>>	realFromAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> rfac, GenPolynomial<AlgebraicNumber<C>> A)	Convert to RealAlgebraicNumber coefficients.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

PolyUtilRoot

public PolyUtilRoot()

Method Detail

convertToAlgebraicCoefficients

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>> convertToAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac,
                                                                                                                         GenPolynomial<C> A)

Convert to RealAlgebraicNumber coefficients. Represent as polynomial with RealAlgebraicNumber coefficients, C is e.g. ModInteger or BigRational.

Parameters:

pfac - result polynomial factory.

A - polynomial with C coefficients to be converted.

Returns:

polynomial with RealAlgebraicNumber<C> coefficients.

convertToRecAlgebraicCoefficients

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>> convertToRecAlgebraicCoefficients(int depth,
                                                                                                                            GenPolynomialRing<RealAlgebraicNumber<C>> pfac,
                                                                                                                            GenPolynomial<C> A)

Convert to recursive RealAlgebraicNumber coefficients. Represent as polynomial with recursive RealAlgebraicNumber coefficients, C is e.g. ModInteger or BigRational.

Parameters:

depth - recursion depth of RealAlgebraicNumber coefficients.

pfac - result polynomial factory.

A - polynomial with C coefficients to be converted.

Returns:

polynomial with RealAlgebraicNumber<C> coefficients.

convertRecursiveToAlgebraicCoefficients

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>> convertRecursiveToAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac,
                                                                                                                                  GenPolynomial<GenPolynomial<C>> A)

Convert to RealAlgebraicNumber coefficients. Represent as polynomial with RealAlgebraicNumber coefficients, C is e.g. ModInteger or BigRational.

Parameters:

pfac - result polynomial factory.

A - recursive polynomial with GenPolynomial<BigInteger> coefficients to be converted.

Returns:

polynomial with RealAlgebraicNumber<C> coefficients.

algebraicFromRealCoefficients

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<AlgebraicNumber<C>> algebraicFromRealCoefficients(GenPolynomialRing<AlgebraicNumber<C>> afac,
                                                                                                                    GenPolynomial<RealAlgebraicNumber<C>> A)

Convert to AlgebraicNumber coefficients. Represent as polynomial with AlgebraicNumber coefficients.

Parameters:

afac - result polynomial factory.

A - polynomial with RealAlgebraicNumber<C> coefficients to be converted.

Returns:

polynomial with AlgebraicNumber<C> coefficients.

realFromAlgebraicCoefficients

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>> realFromAlgebraicCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> rfac,
                                                                                                                        GenPolynomial<AlgebraicNumber<C>> A)

Convert to RealAlgebraicNumber coefficients. Represent as polynomial with RealAlgebraicNumber coefficients.

Parameters:

rfac - result polynomial factory.

A - polynomial with AlgebraicNumber<C> coefficients to be converted.

Returns:

polynomial with RealAlgebraicNumber<C> coefficients.

convertToRealCoefficients

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<RealAlgebraicNumber<C>> convertToRealCoefficients(GenPolynomialRing<RealAlgebraicNumber<C>> pfac,
                                                                                                                    GenPolynomial<C> A)

Convert to RealAlgebraicNumber coefficients. Represent as polynomial with RealAlgebraicNumber coefficients, C is e.g. BigRational.

Parameters:

pfac - result polynomial factory.

A - polynomial with C coefficients to be converted.

Returns:

polynomial with RealAlgebraicNumber<C> coefficients.

convertToComplexCoefficients

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<ComplexAlgebraicNumber<C>> convertToComplexCoefficients(GenPolynomialRing<ComplexAlgebraicNumber<C>> pfac,
                                                                                                                          GenPolynomial<C> A)

Convert to ComplexAlgebraicNumber coefficients. Represent as polynomial with ComplexAlgebraicNumber coefficients, C is e.g. BigRational.

Parameters:

pfac - result polynomial factory.

A - polynomial with C coefficients to be converted.

Returns:

polynomial with ComplexAlgebraicNumber<C> coefficients.

convertToComplexCoefficientsFromComplex

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<ComplexAlgebraicNumber<C>> convertToComplexCoefficientsFromComplex(GenPolynomialRing<ComplexAlgebraicNumber<C>> pfac,
                                                                                                                                     GenPolynomial<Complex<C>> A)

Convert to ComplexAlgebraicNumber coefficients. Represent as polynomial with ComplexAlgebraicNumber coefficients, C is e.g. BigRational.

Parameters:

pfac - result polynomial factory.

A - polynomial with C coefficients to be converted.

Returns:

polynomial with ComplexAlgebraicNumber<C> coefficients.

complexFromAny

public static <C extends GcdRingElem<C> & Rational> GenPolynomial<Complex<C>> complexFromAny(GenPolynomial<C> f)

Convert to Complex coefficients. Represent as polynomial with Complex<C> coefficients.

Parameters:

f - univariate polynomial.

Returns:

f with complex coefficients