/**
* Real root bound. With f(M) * f(-M) != 0.
*
* @param f univariate polynomial.
* @return M such that -M < root(f) < M.
*/
public C realRootBound(GenPolynomial<C> f) {
if (f == null) {
return null;
}
RingFactory<C> cfac = f.ring.coFac;
C M = cfac.getONE();
if (f.isZERO() || f.isConstant()) {
return M;
}
C a = f.leadingBaseCoefficient().abs();
for (C c : f.getMap().values()) {
C d = c.abs().divide(a);
if (M.compareTo(d) < 0) {
M = d;
}
}
// 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) M instanceof RealAlgebraicNumber) {
RealAlgebraicNumber Mr = (RealAlgebraicNumber) M;
BigRational r = Mr.magnitude();
M = cfac.fromInteger(r.numerator()).divide(cfac.fromInteger(r.denominator()));
}
M = M.sum(f.ring.coFac.getONE());
// System.out.println("M = " + M);
return M;
}
/**
* Quotient summation.
*
* @param S Quotient.
* @return this+S.
*/
public Quotient<C> sum(Quotient<C> S) {
if (S == null || S.isZERO()) {
return this;
}
C n = num.multiply(S.den);
n = n.sum(den.multiply(S.num));
C d = den.multiply(S.den);
return new Quotient<C>(ring, n, d, false);
}
public static void main(String args[]) {
System.out.println("Inheritance Main");
A a = new A();
A b = new B();
A c = new C();
// B a1 = new A();
B b1 = new B();
B c1 = new C();
// C a2 = new A();
// C b2 = new B();
C c2 = new C();
System.out.println(a.hashCode());
a.sum();
a.sub();
System.out.println(b.hashCode());
b.sum();
b.sub();
System.out.println(c.hashCode());
c.sum();
c.sub();
System.out.println(b1.hashCode());
b1.sum();
b1.sub();
System.out.println(c1.hashCode());
c1.sum();
c1.sub();
System.out.println(c2.hashCode());
c2.sum();
c2.sub();
}
public C eval(C c1, C c2) {
return c1.sum(c2);
}
