/** Test object multiplication. */
public void testMultiplication() {
a = fac.random(ll);
assertTrue("not isZERO( a )", !a.isZERO());
b = fac.random(ll);
assertTrue("not isZERO( b )", !b.isZERO());
c = b.multiply(a);
d = a.multiply(b);
assertTrue("not isZERO( c )", !c.isZERO());
assertTrue("not isZERO( d )", !d.isZERO());
// System.out.println("a = " + a);
// System.out.println("b = " + b);
e = d.subtract(c);
assertTrue("!isZERO( a*b-b*a ) " + e, !e.isZERO());
assertTrue("a*b = b*a", !c.equals(d));
// assertEquals("a*b = b*a",c,d);
c = fac.random(ll);
// System.out.println("c = " + c);
d = a.multiply(b.multiply(c));
e = (a.multiply(b)).multiply(c);
// System.out.println("d = " + d);
// System.out.println("e = " + e);
// System.out.println("d-e = " + d.subtract(c) );
assertEquals("a(bc) = (ab)c", d, e);
assertTrue("a(bc) = (ab)c", d.equals(e));
BigQuaternion x = a.leadingBaseCoefficient().inverse();
c = a.monic();
d = a.multiply(x);
assertEquals("a.monic() = a(1/ldcf(a))", c, d);
BigQuaternion y = b.leadingBaseCoefficient().inverse();
c = b.monic();
d = b.multiply(y);
assertEquals("b.monic() = b(1/ldcf(b))", c, d);
e = new GenPolynomial<BigQuaternion>(fac, y);
d = b.multiply(e);
assertEquals("b.monic() = b(1/ldcf(b))", c, d);
// d = e.multiply(b);
// assertEquals("b.monic() = (1/ldcf(b) (0))*b",c,d);
}
/** Test weight homogeneous. */
public void testWeightHomogeneous() {
// rational numbers
BigRational rf = new BigRational();
// System.out.println("rf = " + rf);
// weight term order
long[] weight = new long[] {2, 3, 4, 5};
TermOrder to = TermOrderByName.weightOrder(weight);
// System.out.println("to = " + to);
// polynomials over rational numbers
GenPolynomialRing<BigRational> pf = new GenPolynomialRing<BigRational>(rf, 4, to);
// System.out.println("pf = " + pf.toScript());
// test 1
GenPolynomial<BigRational> p = pf.getONE();
// System.out.println("p = " + p);
assertTrue("1 is weight homogeneous " + p, p.isWeightHomogeneous());
// test 0
p = pf.getZERO();
// System.out.println("p = " + p);
assertTrue("0 is weight homogeneous " + p, p.isWeightHomogeneous());
// test random
p = pf.random(kl, 3 * ll, el, q);
// System.out.println("p = " + p);
assertFalse("rnd is weight homogeneous " + p, p.isWeightHomogeneous());
GenPolynomial<BigRational> pl = p.leadingWeightPolynomial();
// System.out.println("pl = " + pl);
assertTrue("lw(rnd) is weight homogeneous " + pl, pl.isWeightHomogeneous());
GenPolynomial<BigRational> r = pf.random(kl, 3 * ll, el, q);
// System.out.println("r = " + r);
assertFalse("rnd is weight homogeneous " + r, r.isWeightHomogeneous());
GenPolynomial<BigRational> rl = r.leadingWeightPolynomial();
// System.out.println("rl = " + rl);
assertTrue("lw(rnd) is weight homogeneous " + rl, rl.isWeightHomogeneous());
GenPolynomial<BigRational> t = pl.multiply(rl);
// System.out.println("t = " + t);
assertTrue("lw(rnd)*lw(rnd) is weight homogeneous " + t, t.isWeightHomogeneous());
}
/** Test homogeneous. */
public void testHomogeneous() {
// rational numbers
BigRational rf = new BigRational();
// System.out.println("rf = " + rf);
// polynomials over rational numbers
GenPolynomialRing<BigRational> pf = new GenPolynomialRing<BigRational>(rf, 2); // rl);
// System.out.println("pf = " + pf);
// test 1
GenPolynomial<BigRational> p = pf.getONE();
// System.out.println("p = " + p);
assertTrue("1 is homogeneous " + p, p.isHomogeneous());
// test 0
p = pf.getZERO();
// System.out.println("p = " + p);
assertTrue("0 is homogeneous " + p, p.isHomogeneous());
// test random
p = pf.random(kl, 2 * ll, el, q);
// p = pf.random(kl,ll,el,q);
// System.out.println("p = " + p);
assertFalse("rnd is homogeneous " + p, p.isHomogeneous());
// make homogeneous
GenPolynomialRing<BigRational> pfh = pf.extend(1);
// System.out.println("pfh = " + pfh);
// remove block order
TermOrder to = new TermOrder(TermOrder.IGRLEX);
pfh = new GenPolynomialRing<BigRational>(pfh, to);
// System.out.println("pfh = " + pfh);
GenPolynomial<BigRational> ph = p.homogenize(pfh);
// System.out.println("ph = " + ph);
assertTrue("ph is homogeneous " + ph, ph.isHomogeneous());
GenPolynomial<BigRational> ps = ph.deHomogenize(pf);
// System.out.println("ps = " + ps);
assertEquals("phs == p ", ps, p); // findbugs
// System.out.println("p is homogeneous = " + p.isHomogeneous());
// System.out.println("ph is homogeneous = " + ph.isHomogeneous());
GenPolynomial<BigRational> s = pf.random(kl, ll, el, q);
// System.out.println("s = " + s);
assertFalse("rnd is homogeneous " + s, s.isHomogeneous());
GenPolynomial<BigRational> sh = s.homogenize(pfh);
// System.out.println("sh = " + sh);
assertTrue("sh is homogeneous " + sh, sh.isHomogeneous());
GenPolynomial<BigRational> ss = sh.deHomogenize(pf);
// System.out.println("ss = " + ss);
assertEquals("ss = s ", ss, s);
GenPolynomial<BigRational> th = ph.multiply(sh);
// System.out.println("th = " + th);
assertTrue("th is homogeneous " + th, th.isHomogeneous());
GenPolynomial<BigRational> t = p.multiply(s);
// System.out.println("t = " + t);
GenPolynomial<BigRational> ts = th.deHomogenize(pf);
// System.out.println("ts = " + ts);
assertEquals("ts = t ", ts, t);
}
