edu.jas.root

Class RootFactory

java.lang.Object

edu.jas.root.RootFactory

public class RootFactory
extends java.lang.Object

Roots factory.

Author:

Heinz Kredel

Constructor Summary

Constructors

Constructor and Description
RootFactory()

Method Summary

Modifier and Type	Method and Description
static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>	complexAlgebraicNumbers(GenPolynomial<C> f) Complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>	complexAlgebraicNumbers(GenPolynomial<C> f, BigRational eps) Complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>	complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f) Complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>	complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f, BigRational eps) Complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> boolean	isRoot(GenPolynomial<C> f, ComplexAlgebraicNumber<C> r) Is complex algebraic number a root of a polynomial.
static <C extends GcdRingElem<C> & Rational> boolean	isRoot(GenPolynomial<C> f, RealAlgebraicNumber<C> r) Is real algebraic number a root of a polynomial.
static <C extends GcdRingElem<C> & Rational> boolean	isRootComplex(GenPolynomial<Complex<C>> f, ComplexAlgebraicNumber<C> r) Is complex algebraic number a root of a complex polynomial.
static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>	realAlgebraicNumbers(GenPolynomial<C> f) Real algebraic numbers.
static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>	realAlgebraicNumbers(GenPolynomial<C> f, BigRational eps) Real algebraic numbers.
static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>	realAlgebraicNumbersField(GenPolynomial<C> f) Real algebraic numbers from a field.
static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>	realAlgebraicNumbersField(GenPolynomial<C> f, BigRational eps) Real algebraic numbers from a field.
static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>	realAlgebraicNumbersIrred(GenPolynomial<C> f) Real algebraic numbers from a irreducible polynomial.
static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>>	realAlgebraicNumbersIrred(GenPolynomial<C> f, BigRational eps) Real algebraic numbers from a irreducible polynomial.

Methods inherited from class java.lang.Object

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

Constructor Detail

RootFactory

public RootFactory()

Method Detail

isRoot

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

Is real algebraic number a root of a polynomial.

Parameters:

f - univariate polynomial.

r - real algebraic number.

Returns:

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

realAlgebraicNumbers

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

Real algebraic numbers.

Parameters:

f - univariate polynomial.

Returns:

a list of different real algebraic numbers.

realAlgebraicNumbers

public static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>> realAlgebraicNumbers(GenPolynomial<C> f,
                                                                                                                BigRational eps)

Real algebraic numbers.

Parameters:

f - univariate polynomial.

eps - rational precision.

Returns:

a list of different real algebraic numbers.

realAlgebraicNumbersField

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

Real algebraic numbers from a field.

Parameters:

f - univariate polynomial.

Returns:

a list of different real algebraic numbers from a field.

realAlgebraicNumbersField

public static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>> realAlgebraicNumbersField(GenPolynomial<C> f,
                                                                                                                     BigRational eps)

Real algebraic numbers from a field.

Parameters:

f - univariate polynomial.

eps - rational precision.

Returns:

a list of different real algebraic numbers from a field.

realAlgebraicNumbersIrred

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

Real algebraic numbers from a irreducible polynomial.

Parameters:

f - univariate irreducible polynomial.

Returns:

a list of different real algebraic numbers from a field.

realAlgebraicNumbersIrred

public static <C extends GcdRingElem<C> & Rational> java.util.List<RealAlgebraicNumber<C>> realAlgebraicNumbersIrred(GenPolynomial<C> f,
                                                                                                                     BigRational eps)

Real algebraic numbers from a irreducible polynomial.

Parameters:

f - univariate irreducible polynomial.

eps - rational precision.

Returns:

a list of different real algebraic numbers from a field.

isRoot

public static <C extends GcdRingElem<C> & Rational> boolean isRoot(GenPolynomial<C> f,
                                                                   ComplexAlgebraicNumber<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;

isRootComplex

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

Is complex algebraic number a root of a complex polynomial.

Parameters:

f - univariate complex polynomial.

r - complex algebraic number.

Returns:

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

complexAlgebraicNumbersComplex

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

Complex algebraic numbers.

Parameters:

f - univariate polynomial.

Returns:

a list of different complex algebraic numbers.

complexAlgebraicNumbersComplex

public static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>> complexAlgebraicNumbersComplex(GenPolynomial<Complex<C>> f,
                                                                                                                             BigRational eps)

Complex algebraic numbers.

Parameters:

f - univariate polynomial.

eps - rational precision.

Returns:

a list of different complex algebraic numbers.

complexAlgebraicNumbers

public static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>> complexAlgebraicNumbers(GenPolynomial<C> f)

Complex algebraic numbers.

Parameters:

f - univariate (rational) polynomial.

Returns:

a list of different complex algebraic numbers.

complexAlgebraicNumbers

public static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>> complexAlgebraicNumbers(GenPolynomial<C> f,
                                                                                                                      BigRational eps)

Complex algebraic numbers.

Parameters:

f - univariate (rational) polynomial.

eps - rational precision.

Returns:

a list of different complex algebraic numbers.