/**
* Sign changes on interval bounds.
*
* @param iv root isolating interval with f(left) * f(right) != 0.
* @param f univariate polynomial.
* @return true if f(left) * f(right) < 0, else false
*/
public boolean signChange(Interval<C> iv, GenPolynomial<C> f) {
if (f == null) {
return false;
}
RingFactory<C> cfac = f.ring.coFac;
C l = PolyUtil.<C>evaluateMain(cfac, f, iv.left);
C r = PolyUtil.<C>evaluateMain(cfac, f, iv.right);
return l.signum() * r.signum() < 0;
}
// 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();
}
/**
* Count changes in sign.
*
* @param <C> coefficient type.
* @param L list of coefficients.
* @return number of sign changes in L.
*/
public static <C extends RingElem<C>> long signVar(List<C> L) {
long v = 0;
if (L == null || L.isEmpty()) {
return v;
}
C A = L.get(0);
for (int i = 1; i < L.size(); i++) {
C B = L.get(i);
while (B == null || B.signum() == 0) {
i++;
if (i >= L.size()) {
return v;
}
B = L.get(i);
}
if (A.signum() * B.signum() < 0) {
v++;
}
A = B;
}
return v;
}
/**
* 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();
}
/**
* The constructor creates a Quotient object from a ring factory and a numerator and denominator
* element.
*
* @param r ring factory.
* @param n numerator.
* @param d denominator.
* @param isred true if gcd(n,d) == 1, else false.
*/
@SuppressWarnings("unchecked")
protected Quotient(QuotientRing<C> r, C n, C d, boolean isred) {
if (d == null || d.isZERO()) {
throw new IllegalArgumentException("denominator may not be zero");
}
ring = r;
if (d.signum() < 0) {
n = n.negate();
d = d.negate();
}
if (isred) {
num = n;
den = d;
return;
}
// must reduce to lowest terms
if (n instanceof GcdRingElem && d instanceof GcdRingElem) {
GcdRingElem ng = (GcdRingElem) n;
GcdRingElem dg = (GcdRingElem) d;
C gcd = (C) ng.gcd(dg);
if (debug) {
logger.info("gcd = " + gcd);
}
// RingElem<C> gcd = ring.ring.getONE();
if (gcd.isONE()) {
num = n;
den = d;
} else {
num = n.divide(gcd);
den = d.divide(gcd);
}
// } else { // univariate polynomial?
} else {
logger.warn("gcd = ????");
num = n;
den = d;
}
}
/**
* Quotient signum.
*
* @see edu.jas.structure.RingElem#signum()
* @return signum(this).
*/
public int signum() {
return num.signum();
}
