Package edu.jas.root

Class RootFactory

java.lang.Object

edu.jas.root.RootFactory

public class RootFactory
extends java.lang.Object

Roots factory. Generate real and complex algebraic numbers from root intervals or rectangles.

Author:

Heinz Kredel

Constructor Summary

Constructors

Constructor	Description
RootFactory()

Method Summary

Modifier and Type	Method	Description
static <C extends GcdRingElem<C> & Rational> AlgebraicRoots<C>	algebraicRoots(GenPolynomial<C> f)	Roots as real and complex algebraic numbers.
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> DecimalRoots<C>	decimalRoots(GenPolynomial<C> f, BigRational eps)	Roots as real and complex decimal numbers.
static <C extends GcdRingElem<C> & Rational> DecimalRoots<C>	decimalRoots(AlgebraicRoots<C> ar, BigRational eps)	Roots as real and complex decimal numbers.
static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<BigDecimal>>	filterOutRealRoots(GenPolynomial<C> f, java.util.List<Complex<BigDecimal>> c, java.util.List<BigDecimal> r, BigRational eps)	Filter real roots from complex roots.
static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>>	filterOutRealRoots(GenPolynomial<C> f, java.util.List<ComplexAlgebraicNumber<C>> c, java.util.List<RealAlgebraicNumber<C>> r)	Filter real roots from complex roots.
static <C extends GcdRingElem<C> & Rational> boolean	isRealRoot(GenPolynomial<C> f, Complex<BigDecimal> c, BigDecimal r, BigRational eps)	Is complex decimal number a real root of a polynomial.
static <C extends GcdRingElem<C> & Rational> boolean	isRealRoot(GenPolynomial<C> f, ComplexAlgebraicNumber<C> c, RealAlgebraicNumber<C> r)	Is complex algebraic number a real root of a polynomial.
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.
static <C extends GcdRingElem<C> & Rational> void	rootRefine(AlgebraicRoots<C> a, BigRational eps)	Root refinement of real and complex algebraic numbers.
static <C extends GcdRingElem<C> & Rational> AlgebraicRoots<C>	rootsOfUnity(AlgebraicRoots<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

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;

isRealRoot

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

Is complex algebraic number a real root of a polynomial.

Parameters:

f - univariate polynomial.

c - complex algebraic number.

r - real algebraic number.

Returns:

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

isRealRoot

public static <C extends GcdRingElem<C> & Rational> boolean isRealRoot(GenPolynomial<C> f,
                                                                       Complex<BigDecimal> c,
                                                                       BigDecimal r,
                                                                       BigRational eps)

Is complex decimal number a real root of a polynomial.

Parameters:

f - univariate polynomial.

c - complex decimal number.

r - real decimal number.

eps - desired precision.

Returns:

true, if f(c) == 0 and c == r, 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.

filterOutRealRoots

public static <C extends GcdRingElem<C> & Rational> java.util.List<ComplexAlgebraicNumber<C>> filterOutRealRoots(GenPolynomial<C> f,
                                                                                                                 java.util.List<ComplexAlgebraicNumber<C>> c,
                                                                                                                 java.util.List<RealAlgebraicNumber<C>> r)

Filter real roots from complex roots.

Parameters:

f - univariate polynomial.

c - list of complex algebraic numbers.

r - list of real algebraic numbers.

Returns:

c minus the real roots from r

filterOutRealRoots

public static <C extends GcdRingElem<C> & Rational> java.util.List<Complex<BigDecimal>> filterOutRealRoots(GenPolynomial<C> f,
                                                                                                           java.util.List<Complex<BigDecimal>> c,
                                                                                                           java.util.List<BigDecimal> r,
                                                                                                           BigRational eps)

Filter real roots from complex roots.

Parameters:

f - univariate polynomial.

c - list of complex decimal numbers.

r - list of real decimal numbers.

eps - desired precision.

Returns:

c minus the real roots from r

algebraicRoots

public static <C extends GcdRingElem<C> & Rational> AlgebraicRoots<C> algebraicRoots(GenPolynomial<C> f)

Roots as real and complex algebraic numbers.

Parameters:

f - univariate polynomial.

Returns:

container of real and complex algebraic numbers.

rootsOfUnity

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

Roots of unity of real and complex algebraic numbers.

Parameters:

ar - container of real and complex algebraic numbers.

Returns:

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

rootRefine

public static <C extends GcdRingElem<C> & Rational> void rootRefine(AlgebraicRoots<C> a,
                                                                    BigRational eps)

Root refinement of real and complex algebraic numbers.

Parameters:

a - container of real and complex algebraic numbers.

eps - desired precision for root intervals and rectangles.

decimalRoots

public static <C extends GcdRingElem<C> & Rational> DecimalRoots<C> decimalRoots(GenPolynomial<C> f,
                                                                                 BigRational eps)

Roots as real and complex decimal numbers.

Parameters:

f - univariate polynomial.

eps - desired precision.

Returns:

container of real and complex decimal numbers.

decimalRoots

public static <C extends GcdRingElem<C> & Rational> DecimalRoots<C> decimalRoots(AlgebraicRoots<C> ar,
                                                                                 BigRational eps)

Roots as real and complex decimal numbers.

Parameters:

ar - container for real and complex algebraic roots.

eps - desired precision.

Returns:

container of real and complex decimal numbers.