/**
* Real algebraic number sign.
*
* @param iv root isolating interval for f, with f(left) * f(right) < 0.
* @param f univariate polynomial, non-zero.
* @param g univariate polynomial, gcd(f,g) == 1.
* @return sign(g(v)), with v a new interval contained in iv such that g(v) != 0.
*/
public int realSign(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g) {
if (g == null || g.isZERO()) {
return 0;
}
if (f == null || f.isZERO() || f.isConstant()) {
return g.signum();
}
if (g.isConstant()) {
return g.signum();
}
Interval<C> v = invariantSignInterval(iv, f, g);
return realIntervalSign(v, f, g);
}
/**
* Real algebraic number sign.
*
* @param iv root isolating interval for f, with f(left) * f(right) < 0, with iv such that
* g(iv) != 0.
* @param f univariate polynomial, non-zero.
* @param g univariate polynomial, gcd(f,g) == 1.
* @return sign(g(iv)) .
*/
public int realIntervalSign(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g) {
if (g == null || g.isZERO()) {
return 0;
}
if (f == null || f.isZERO() || f.isConstant()) {
return g.signum();
}
if (g.isConstant()) {
return g.signum();
}
RingFactory<C> cfac = f.ring.coFac;
C c = iv.left.sum(iv.right);
c = c.divide(cfac.fromInteger(2));
C ev = PolyUtil.<C>evaluateMain(cfac, g, c);
// System.out.println("ev = " + ev);
return ev.signum();
}