Package edu.jas.application

Class RootFactoryApp

java.lang.Object

edu.jas.application.RootFactoryApp

public class RootFactoryApp
extends java.lang.Object

Roots factory.

Author:

Heinz Kredel

Constructor Summary

Constructors

Constructor	Description
RootFactoryApp()

Method Summary

Modifier and Type	Method	Description
static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<RealAlgebraicNumber<C>>>	complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f)	Complex algebraic number roots.
static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<RealAlgebraicNumber<C>>>	complexAlgebraicNumbersSquarefree(GenPolynomial<Complex<C>> f)	Complex algebraic number roots.
static <C extends GcdRingElem<C> & Rational> boolean	isRoot(GenPolynomial<Complex<C>> f, Complex<RealAlgebraicNumber<C>> r)	Is complex algebraic number a root of a polynomial.
static <C extends GcdRingElem<C> & Rational> boolean	isRoot(GenPolynomial<Complex<C>> f, java.util.List<Complex<RealAlgebraicNumber<C>>> R)	Is complex algebraic number a root of a polynomial.
static <C extends GcdRingElem<C> & Rational> boolean	isRootRealCoeff(GenPolynomial<C> f, Complex<RealAlgebraicNumber<C>> r)	Is complex algebraic number a root of a polynomial.
static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>	rootReduce(AlgebraicNumberRing<C> a, AlgebraicNumberRing<C> b)	Root reduce of real and complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>	rootReduce(GenPolynomial<C> a, GenPolynomial<C> b)	Root reduce of real and complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>	rootReduce(AlgebraicRoots<C> a, AlgebraicRoots<C> b)	Root reduce of real and complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C>	rootsOfUnity(AlgebraicRootsPrimElem<C> ar)	Roots of unity of real and complex algebraic numbers.

Methods inherited from class java.lang.Object

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

Constructor Detail

RootFactoryApp

public RootFactoryApp()

Method Detail

isRootRealCoeff

public static <C extends GcdRingElem<C> & Rational> boolean isRootRealCoeff(GenPolynomial<C> f,
                                                                            Complex<RealAlgebraicNumber<C>> r)

Is complex algebraic number a root of a polynomial.

Parameters:

f - univariate polynomial.

r - complex algebraic number.

Returns:

true, if f(r) == 0, else false;

isRoot

public static <C extends GcdRingElem<C> & Rational> boolean isRoot(GenPolynomial<Complex<C>> f,
                                                                   Complex<RealAlgebraicNumber<C>> r)

Is complex algebraic number a root of a polynomial.

Parameters:

f - univariate polynomial.

r - complex algebraic number.

Returns:

true, if f(r) == 0, else false;

isRoot

public static <C extends GcdRingElem<C> & Rational> boolean isRoot(GenPolynomial<Complex<C>> f,
                                                                   java.util.List<Complex<RealAlgebraicNumber<C>>> R)

Is complex algebraic number a root of a polynomial.

Parameters:

f - univariate polynomial.

R - list of complex algebraic numbers.

Returns:

true, if f(r) == 0 for all r in R, else false;

complexAlgebraicNumbersComplex

public static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<RealAlgebraicNumber<C>>> complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f)

Complex algebraic number roots.

Parameters:

f - univariate polynomial.

Returns:

a list of different complex algebraic numbers, with f(c) == 0 for c in roots.

complexAlgebraicNumbersSquarefree

public static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<RealAlgebraicNumber<C>>> complexAlgebraicNumbersSquarefree(GenPolynomial<Complex<C>> f)

Complex algebraic number roots.

Parameters:

f - univariate squarefree polynomial.

Returns:

a list of different complex algebraic numbers, with f(c) == 0 for c in roots.

rootReduce

public static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C> rootReduce(AlgebraicRoots<C> a,
                                                                                         AlgebraicRoots<C> b)

Root reduce of real and complex algebraic numbers.

Parameters:

a - container of real and complex algebraic numbers.

b - container of real and complex algebraic numbers.

Returns:

container of real and complex algebraic numbers of the primitive element of a and b.

rootReduce

public static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C> rootReduce(GenPolynomial<C> a,
                                                                                         GenPolynomial<C> b)

Root reduce of real and complex algebraic numbers.

Parameters:

a - polynomial.

b - polynomial.

Returns:

container of real and complex algebraic numbers of the primitive element of a and b.

rootReduce

public static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C> rootReduce(AlgebraicNumberRing<C> a,
                                                                                         AlgebraicNumberRing<C> b)

Root reduce of real and complex algebraic numbers.

Parameters:

a - algebraic number ring.

b - algebraic number ring.

Returns:

container of real and complex algebraic numbers of the primitive element of a and b.

rootsOfUnity

public static <C extends GcdRingElem<C> & Rational> AlgebraicRootsPrimElem<C> rootsOfUnity(AlgebraicRootsPrimElem<C> ar)

Roots of unity of real and complex algebraic numbers.

Parameters:

ar - container of real and complex algebraic numbers with primitive element.

Returns:

container of real and complex algebraic numbers which are roots of unity.