/**
* Magnitude bound.
*
* @param iv interval.
* @param f univariate polynomial.
* @return B such that |f(c)| < B for c in iv.
*/
public C magnitudeBound(Interval<C> iv, GenPolynomial<C> f) {
if (f == null) {
return null;
}
if (f.isZERO()) {
return f.ring.coFac.getONE();
}
if (f.isConstant()) {
return f.leadingBaseCoefficient().abs();
}
GenPolynomial<C> fa =
f.map(
new UnaryFunctor<C, C>() {
public C eval(C a) {
return a.abs();
}
});
// System.out.println("fa = " + fa);
C M = iv.left.abs();
if (M.compareTo(iv.right.abs()) < 0) {
M = iv.right.abs();
}
// System.out.println("M = " + M);
RingFactory<C> cfac = f.ring.coFac;
C B = PolyUtil.<C>evaluateMain(cfac, fa, M);
// works also without this case, only for optimization
// to use rational number interval end points
// can fail if real root is in interval [r,r+1]
// for too low precision or too big r, since r is approximation
if ((Object) B instanceof RealAlgebraicNumber) {
RealAlgebraicNumber Br = (RealAlgebraicNumber) B;
BigRational r = Br.magnitude();
B = cfac.fromInteger(r.numerator()).divide(cfac.fromInteger(r.denominator()));
}
// System.out.println("B = " + B);
return B;
}
