// JAVA6only: @Override
public int compareTo(Quotient<C> b) {
if (b == null || b.isZERO()) {
return this.signum();
}
C r = num.multiply(b.den);
C s = den.multiply(b.num);
C x = r.subtract(s);
return x.signum();
}
/**
* Quotient subtraction.
*
* @param S Quotient.
* @return this-S.
*/
public Quotient<C> subtract(Quotient<C> S) {
if (S == null || S.isZERO()) {
return this;
}
C n = num.multiply(S.den);
n = n.subtract(den.multiply(S.num));
C d = den.multiply(S.den);
return new Quotient<C>(ring, n, d, false);
}
/**
* Invariant interval for algebraic number magnitude.
*
* @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.
* @param eps length limit for interval length.
* @return v with v a new interval contained in iv such that |g(a) - g(b)| < eps for a, b in v
* in iv.
*/
public Interval<C> invariantMagnitudeInterval(
Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g, C eps) {
Interval<C> v = iv;
if (g == null || g.isZERO()) {
return v;
}
if (g.isConstant()) {
return v;
}
if (f == null || f.isZERO() || f.isConstant()) { // ?
return v;
}
GenPolynomial<C> gp = PolyUtil.<C>baseDeriviative(g);
// System.out.println("g = " + g);
// System.out.println("gp = " + gp);
C B = magnitudeBound(iv, gp);
// System.out.println("B = " + B);
RingFactory<C> cfac = f.ring.coFac;
C two = cfac.fromInteger(2);
while (B.multiply(v.length()).compareTo(eps) >= 0) {
C c = v.left.sum(v.right);
c = c.divide(two);
Interval<C> im = new Interval<C>(c, v.right);
if (signChange(im, f)) {
v = im;
} else {
v = new Interval<C>(v.left, c);
}
// System.out.println("v = " + v.toDecimal());
}
return v;
}
/**
* Quotient multiplication.
*
* @param S Quotient.
* @return this*S.
*/
public Quotient<C> multiply(Quotient<C> S) {
if (S == null || S.isZERO()) {
return S;
}
if (num.isZERO()) {
return this;
}
if (S.isONE()) {
return this;
}
if (this.isONE()) {
return S;
}
C n = num.multiply(S.num);
C d = den.multiply(S.den);
return new Quotient<C>(ring, n, d, false);
}
public C eval(C c) {
return c.multiply(x);
}
