edu.jas.root.RootFactory Maven / Gradle / Ivy
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/*
* $Id: RootFactory.java 3974 2012-07-01 12:29:44Z kredel $
*/
package edu.jas.root;
import java.util.ArrayList;
import java.util.List;
import java.util.Set;
import java.util.Map;
import edu.jas.arith.Rational;
import edu.jas.arith.BigRational;
import edu.jas.poly.Complex;
import edu.jas.poly.ComplexRing;
import edu.jas.poly.PolyUtil;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenPolynomialRing;
import edu.jas.structure.GcdRingElem;
import edu.jas.ufd.FactorAbstract;
import edu.jas.ufd.FactorFactory;
import edu.jas.ufd.SquarefreeAbstract;
import edu.jas.ufd.SquarefreeFactory;
/**
* Roots factory.
* @author Heinz Kredel
*/
public class RootFactory {
/**
* Is real algebraic number a root of a polynomial.
* @param f univariate polynomial.
* @param r real algebraic number.
* @return true, if f(r) == 0, else false;
*/
public static & Rational>
boolean isRoot(GenPolynomial f, RealAlgebraicNumber r) {
RealAlgebraicRing rr = r.factory();
GenPolynomialRing> rfac
= new GenPolynomialRing>(rr,f.factory());
GenPolynomial> p;
p = PolyUtilRoot. convertToRealCoefficients(rfac,f);
RealAlgebraicNumber a = PolyUtil.> evaluateMain(rr,p,r);
return a.isZERO();
}
/**
* Real algebraic numbers.
* @param f univariate polynomial.
* @return a list of different real algebraic numbers.
*/
public static & Rational>
List> realAlgebraicNumbers(GenPolynomial f) {
RealRoots rr = new RealRootsSturm();
SquarefreeAbstract engine = SquarefreeFactory. getImplementation(f.ring.coFac);
Map,Long> SF = engine.squarefreeFactors(f);
Set> S = SF.keySet();
List> list = new ArrayList>();
for (GenPolynomial sp : S) {
List> iv = rr.realRoots(sp);
for (Interval I : iv) {
RealAlgebraicRing rar = new RealAlgebraicRing(sp, I);
RealAlgebraicNumber rn = rar.getGenerator();
long mult = SF.get(sp);
for ( int i = 0; i < mult; i++ ) {
list.add(rn);
}
}
}
return list;
}
/**
* Real algebraic numbers.
* @param f univariate polynomial.
* @param eps rational precision.
* @return a list of different real algebraic numbers.
*/
public static & Rational>
List> realAlgebraicNumbers(GenPolynomial f, BigRational eps) {
RealRoots rr = new RealRootsSturm();
SquarefreeAbstract engine = SquarefreeFactory. getImplementation(f.ring.coFac);
Map,Long> SF = engine.squarefreeFactors(f);
Set> S = SF.keySet();
List> list = new ArrayList>();
for (GenPolynomial sp : S) {
List> iv = rr.realRoots(sp,eps);
for (Interval I : iv) {
RealAlgebraicRing rar = new RealAlgebraicRing(sp, I);
rar.setEps(eps);
RealAlgebraicNumber rn = rar.getGenerator();
long mult = SF.get(sp);
for ( int i = 0; i < mult; i++ ) {
list.add(rn);
}
}
}
return list;
}
/**
* Real algebraic numbers from a field.
* @param f univariate polynomial.
* @return a list of different real algebraic numbers from a field.
*/
public static & Rational>
List> realAlgebraicNumbersField(GenPolynomial f) {
RealRoots rr = new RealRootsSturm();
FactorAbstract engine = FactorFactory. getImplementation(f.ring.coFac);
Map,Long> SF = engine.baseFactors(f);
Set> S = SF.keySet();
List> list = new ArrayList>();
for (GenPolynomial sp : S) {
List> iv = rr.realRoots(sp);
for (Interval I : iv) {
RealAlgebraicRing rar = new RealAlgebraicRing(sp, I, true);//field
RealAlgebraicNumber rn = rar.getGenerator();
long mult = SF.get(sp);
for ( int i = 0; i < mult; i++ ) {
list.add(rn);
}
}
}
return list;
}
/**
* Real algebraic numbers from a field.
* @param f univariate polynomial.
* @param eps rational precision.
* @return a list of different real algebraic numbers from a field.
*/
public static & Rational>
List> realAlgebraicNumbersField(GenPolynomial f, BigRational eps) {
RealRoots rr = new RealRootsSturm();
FactorAbstract engine = FactorFactory. getImplementation(f.ring.coFac);
Map,Long> SF = engine.baseFactors(f);
Set> S = SF.keySet();
List> list = new ArrayList>();
for (GenPolynomial sp : S) {
List> iv = rr.realRoots(sp,eps);
for (Interval I : iv) {
RealAlgebraicRing rar = new RealAlgebraicRing(sp, I, true);//field
rar.setEps(eps);
RealAlgebraicNumber rn = rar.getGenerator();
long mult = SF.get(sp);
for ( int i = 0; i < mult; i++ ) {
list.add(rn);
}
}
}
return list;
}
/**
* Real algebraic numbers from a irreducible polynomial.
* @param f univariate irreducible polynomial.
* @return a list of different real algebraic numbers from a field.
*/
public static & Rational>
List> realAlgebraicNumbersIrred(GenPolynomial f) {
RealRoots rr = new RealRootsSturm();
List> list = new ArrayList>();
List> iv = rr.realRoots(f);
for (Interval I : iv) {
RealAlgebraicRing rar = new RealAlgebraicRing(f, I, true);//field
RealAlgebraicNumber rn = rar.getGenerator();
list.add(rn);
}
return list;
}
/**
* Real algebraic numbers from a irreducible polynomial.
* @param f univariate irreducible polynomial.
* @param eps rational precision.
* @return a list of different real algebraic numbers from a field.
*/
public static & Rational>
List> realAlgebraicNumbersIrred(GenPolynomial f, BigRational eps) {
RealRoots rr = new RealRootsSturm();
List> list = new ArrayList>();
List> iv = rr.realRoots(f,eps);
for (Interval I : iv) {
RealAlgebraicRing rar = new RealAlgebraicRing(f, I, true);//field
rar.setEps(eps);
RealAlgebraicNumber rn = rar.getGenerator();
list.add(rn);
}
return list;
}
/**
* Is complex algebraic number a root of a polynomial.
* @param f univariate polynomial.
* @param r complex algebraic number.
* @return true, if f(r) == 0, else false;
*/
public static & Rational>
boolean isRoot(GenPolynomial f, ComplexAlgebraicNumber r) {
ComplexAlgebraicRing cr = r.factory();
GenPolynomialRing> cfac
= new GenPolynomialRing>(cr,f.factory());
GenPolynomial> p;
p = PolyUtilRoot. convertToComplexCoefficients(cfac,f);
ComplexAlgebraicNumber a = PolyUtil.> evaluateMain(cr,p,r);
return a.isZERO();
}
/**
* Is complex algebraic number a root of a complex polynomial.
* @param f univariate complex polynomial.
* @param r complex algebraic number.
* @return true, if f(r) == 0, else false;
*/
public static & Rational>
boolean isRootComplex(GenPolynomial> f, ComplexAlgebraicNumber r) {
ComplexAlgebraicRing cr = r.factory();
GenPolynomialRing> cfac
= new GenPolynomialRing>(cr,f.factory());
GenPolynomial> p;
p = PolyUtilRoot. convertToComplexCoefficientsFromComplex(cfac,f);
ComplexAlgebraicNumber a = PolyUtil.> evaluateMain(cr,p,r);
return a.isZERO();
}
/**
* Complex algebraic numbers.
* @param f univariate polynomial.
* @return a list of different complex algebraic numbers.
*/
public static & Rational>
List> complexAlgebraicNumbersComplex(GenPolynomial> f) {
ComplexRoots cr = new ComplexRootsSturm(f.ring.coFac);
SquarefreeAbstract> engine = SquarefreeFactory
.> getImplementation(f.ring.coFac);
Map>,Long> SF = engine.squarefreeFactors(f);
Set>> S = SF.keySet();
List> list = new ArrayList>();
for (GenPolynomial> sp : S) {
List> iv = cr.complexRoots(sp);
for (Rectangle I : iv) {
ComplexAlgebraicRing car = new ComplexAlgebraicRing(sp, I);
ComplexAlgebraicNumber cn = car.getGenerator();
long mult = SF.get(sp);
for ( int i = 0; i < mult; i++ ) {
list.add(cn);
}
}
}
return list;
}
/**
* Complex algebraic numbers.
* @param f univariate polynomial.
* @param eps rational precision.
* @return a list of different complex algebraic numbers.
*/
public static & Rational>
List> complexAlgebraicNumbersComplex(GenPolynomial> f, BigRational eps) {
ComplexRoots cr = new ComplexRootsSturm(f.ring.coFac);
SquarefreeAbstract> engine = SquarefreeFactory
.> getImplementation(f.ring.coFac);
Map>,Long> SF = engine.squarefreeFactors(f);
Set>> S = SF.keySet();
List> list = new ArrayList>();
for (GenPolynomial> sp : S) {
List> iv = cr.complexRoots(sp);
for (Rectangle I : iv) {
Rectangle Iv = I;
try {
Iv = cr.complexRootRefinement(I,sp,eps);
} catch (InvalidBoundaryException e) {
e.printStackTrace();
}
ComplexAlgebraicRing car = new ComplexAlgebraicRing(sp, Iv);
car.setEps(eps);
ComplexAlgebraicNumber cn = car.getGenerator();
long mult = SF.get(sp);
for ( int i = 0; i < mult; i++ ) {
list.add(cn);
}
}
}
return list;
}
/**
* Complex algebraic numbers.
* @param f univariate (rational) polynomial.
* @return a list of different complex algebraic numbers.
*/
public static & Rational>
List> complexAlgebraicNumbers(GenPolynomial f) {
if ( f.ring.coFac instanceof Complex ) {
throw new IllegalArgumentException("f already has Complex coefficients " + f.ring);
}
if ( f.ring.coFac instanceof ComplexAlgebraicRing ) {
throw new UnsupportedOperationException("unsupported ComplexAlgebraicRing coefficients " + f.ring);
}
ComplexRing cr = new ComplexRing( f.ring.coFac );
GenPolynomialRing> fac = new GenPolynomialRing>(cr,f.ring);
GenPolynomial> fc = PolyUtil.complexFromAny(fac,f);
return complexAlgebraicNumbersComplex(fc);
}
/**
* Complex algebraic numbers.
* @param f univariate (rational) polynomial.
* @param eps rational precision.
* @return a list of different complex algebraic numbers.
*/
public static & Rational>
List> complexAlgebraicNumbers(GenPolynomial f, BigRational eps) {
if ( f.ring.coFac instanceof Complex ) {
throw new IllegalArgumentException("f already has Complex coefficients " + f.ring);
}
if ( f.ring.coFac instanceof ComplexAlgebraicRing ) {
throw new UnsupportedOperationException("unsupported ComplexAlgebraicRing coefficients " + f.ring);
}
ComplexRing cr = new ComplexRing( f.ring.coFac );
GenPolynomialRing> fac = new GenPolynomialRing>(cr,f.ring);
GenPolynomial> fc = PolyUtil.complexFromAny(fac,f);
return complexAlgebraicNumbersComplex(fc,eps);
}
}
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