edu.jas.root

Interface RealRoots<C extends RingElem<C> & Rational>

Type Parameters:

C - coefficient type.

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

RealRootsAbstract, RealRootsSturm

public interface RealRoots<C extends RingElem<C> & Rational>
extends java.io.Serializable

Real roots interface.

Author:

Heinz Kredel

Method Summary

Methods

Modifier and Type	Method and Description
C	realMagnitude(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g, C eps) Real algebraic number magnitude.
C	realRootBound(GenPolynomial<C> f) Real root bound.
long	realRootCount(Interval<C> iv, GenPolynomial<C> f) Number of real roots in interval.
java.util.List<Interval<C>>	realRoots(GenPolynomial<C> f) Isolating intervals for the real roots.
java.util.List<Interval<C>>	realRoots(GenPolynomial<C> f, BigRational eps) Isolating intervals for the real roots.
java.util.List<Interval<C>>	realRoots(GenPolynomial<C> f, C eps) Isolating intervals for the real roots.
int	realSign(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g) Real algebraic number sign.
Interval<C>	refineInterval(Interval<C> iv, GenPolynomial<C> f, C eps) Refine interval.
java.util.List<Interval<C>>	refineIntervals(java.util.List<Interval<C>> V, GenPolynomial<C> f, C eps) Refine intervals.
boolean	signChange(Interval<C> iv, GenPolynomial<C> f) Sign changes on interval bounds.

Method Detail

realRootBound

C realRootBound(GenPolynomial<C> f)

Real root bound. With f(M) * f(-M) != 0.

Parameters:

f - univariate polynomial.

Returns:

M such that -M < root(f) > M.

realRoots

java.util.List<Interval<C>> realRoots(GenPolynomial<C> f)

Isolating intervals for the real roots.

Parameters:

f - univariate polynomial.

Returns:

a list of isolating intervalls for the real roots of f.

realRoots

java.util.List<Interval<C>> realRoots(GenPolynomial<C> f,
                                    C eps)

Isolating intervals for the real roots.

Parameters:

f - univariate polynomial.

eps - requested intervals length.

Returns:

a list of isolating intervals v such that |v| < eps.

realRoots

java.util.List<Interval<C>> realRoots(GenPolynomial<C> f,
                                    BigRational eps)

Isolating intervals for the real roots.

Parameters:

f - univariate polynomial.

eps - requested intervals length.

Returns:

a list of isolating intervals v such that |v| < eps.

signChange

boolean signChange(Interval<C> iv,
                 GenPolynomial<C> f)

Sign changes on interval bounds.

Parameters:

iv - root isolating interval with f(left) * f(right) != 0.

f - univariate polynomial.

Returns:

true if f(left) * f(right) < 0, else false

realRootCount

long realRootCount(Interval<C> iv,
                 GenPolynomial<C> f)

Number of real roots in interval.

Parameters:

iv - interval with f(left) * f(right) != 0.

f - univariate polynomial.

Returns:

number of real roots of f in I.

refineInterval

Interval<C> refineInterval(Interval<C> iv,
                         GenPolynomial<C> f,
                         C eps)

Refine interval.

Parameters:

iv - root isolating interval with f(left) * f(right) < 0.

f - univariate polynomial, non-zero.

eps - requested interval length.

Returns:

a new interval v such that |v| < eps.

refineIntervals

java.util.List<Interval<C>> refineIntervals(java.util.List<Interval<C>> V,
                                          GenPolynomial<C> f,
                                          C eps)

Refine intervals.

Parameters:

V - list of isolating intervals with f(left) * f(right) < 0.

f - univariate polynomial, non-zero.

eps - requested intervals length.

Returns:

a list of new intervals v such that |v| < eps.

realSign

int realSign(Interval<C> iv,
           GenPolynomial<C> f,
           GenPolynomial<C> g)

Real algebraic number sign.

Parameters:

iv - root isolating interval for f, with f(left) * f(right) < 0.

f - univariate polynomial, non-zero.

g - univariate polynomial, gcd(f,g) == 1.

Returns:

sign(g(v)), with v a new interval contained in iv such that g(v) != 0.

realMagnitude

C realMagnitude(Interval<C> iv,
              GenPolynomial<C> f,
              GenPolynomial<C> g,
              C eps)

Real algebraic number magnitude.

Parameters:

iv - root isolating interval for f, with f(left) * f(right) < 0.

f - univariate polynomial, non-zero.

g - univariate polynomial, gcd(f,g) == 1.

eps - length limit for interval length.

Returns:

g(iv).