/** Test accessors. */
public void testAccessors() {
// rational numbers
BigRational rf = new BigRational();
// System.out.println("rf = " + rf);
// polynomials over rational numbers
GenPolynomialRing<BigRational> pf = new GenPolynomialRing<BigRational>(rf, rl);
// System.out.println("pf = " + pf);
// test 1
GenPolynomial<BigRational> p = pf.getONE();
// System.out.println("p = " + p);
ExpVector e = p.leadingExpVector();
BigRational c = p.leadingBaseCoefficient();
GenPolynomial<BigRational> f = new GenPolynomial<BigRational>(pf, c, e);
assertEquals("1 == 1 ", p, f);
GenPolynomial<BigRational> r = p.reductum();
assertTrue("red(1) == 0 ", r.isZERO());
// test 0
p = pf.getZERO();
// System.out.println("p = " + p);
e = p.leadingExpVector();
c = p.leadingBaseCoefficient();
f = new GenPolynomial<BigRational>(pf, c, e);
assertEquals("0 == 0 ", p, f);
r = p.reductum();
assertTrue("red(0) == 0 ", r.isZERO());
// test random
p = pf.random(kl, 2 * ll, el, q);
// System.out.println("p = " + p);
e = p.leadingExpVector();
c = p.leadingBaseCoefficient();
r = p.reductum();
f = new GenPolynomial<BigRational>(pf, c, e);
f = r.sum(f);
assertEquals("p == lm(f)+red(f) ", p, f);
// test iteration over random
GenPolynomial<BigRational> g;
g = p;
f = pf.getZERO();
while (!g.isZERO()) {
e = g.leadingExpVector();
c = g.leadingBaseCoefficient();
// System.out.println("c e = " + c + " " + e);
r = g.reductum();
f = f.sum(c, e);
g = r;
}
assertEquals("p == lm(f)+lm(red(f))+... ", p, f);
}
/** Test constructor and toString. */
public void testConstruction() {
c = fac.getONE();
assertTrue("length( c ) = 1", c.length() == 1);
assertTrue("isZERO( c )", !c.isZERO());
assertTrue("isONE( c )", c.isONE());
d = fac.getZERO();
assertTrue("length( d ) = 0", d.length() == 0);
assertTrue("isZERO( d )", d.isZERO());
assertTrue("isONE( d )", !d.isONE());
}
/** 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 coefficient map function. */
public void testMap() {
// integers
BigInteger rf = new BigInteger();
// System.out.println("rf = " + rf);
// polynomials over integral numbers
GenPolynomialRing<BigInteger> pf = new GenPolynomialRing<BigInteger>(rf, rl);
// System.out.println("pf = " + pf);
// random polynomial
GenPolynomial<BigInteger> p = pf.random(kl, 2 * ll, el, q);
// System.out.println("p = " + p);
// test times 1
GenPolynomial<BigInteger> q;
q = p.map(new Multiply<BigInteger>(rf.getONE()));
assertEquals("p == q ", p, q);
// test times 0
q = p.map(new Multiply<BigInteger>(rf.getZERO()));
assertTrue("q == 0 ", q.isZERO());
// test times -1
q = p.map(new Multiply<BigInteger>(rf.getONE().negate()));
assertEquals("p == q ", p.negate(), q);
}
/** Test random polynomial. */
public void testRandom() {
for (int i = 0; i < 7; i++) {
a = fac.random(ll);
// fac.random(rl+i, kl*(i+1), ll+2*i, el+i, q );
assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
assertTrue(" not isONE( a" + i + " )", !a.isONE());
}
}
/** Test constructors and factory. */
public void testConstructors() {
// rational numbers
BigRational rf = new BigRational();
// System.out.println("rf = " + rf);
// BigRational r = rf.fromInteger( 99 );
// System.out.println("r = " + r);
// r = rf.random( 9 ).sum(r);
// System.out.println("r = " + r);
// assertFalse("r.isZERO() = ", r.isZERO());
// RingElem<BigRational> re = new BigRational( 3 );
// System.out.println("re = " + re);
// rf = (BigRational) re;
// RingFactory<BigRational> ref = new BigRational( 3 );
// System.out.println("re = " + re);
// rf = (BigRational) ref;
// polynomials over rational numbers
GenPolynomialRing<BigRational> pf = new GenPolynomialRing<BigRational>(rf, 2);
// System.out.println("pf = " + pf);
GenPolynomial<BigRational> p = pf.getONE();
// System.out.println("p = " + p);
p = pf.random(9);
// System.out.println("p = " + p);
p = pf.getZERO();
// System.out.println("p = " + p);
RingElem<GenPolynomial<BigRational>> pe = new GenPolynomial<BigRational>(pf);
// System.out.println("pe = " + pe);
// System.out.println("p.equals(pe) = " + p.equals(pe) );
// System.out.println("p.equals(p) = " + p.equals(p) );
assertTrue("p.equals(pe) = ", p.equals(pe));
assertTrue("p.equals(p) = ", p.equals(p));
pe = pe.sum(p); // why not p = p.add(pe) ?
// System.out.println("pe = " + pe);
assertTrue("pe.isZERO() = ", pe.isZERO());
p = pf.random(9);
p = p.subtract(p);
// System.out.println("p = " + p);
// System.out.println("p.isZERO() = " + p.isZERO());
assertTrue("p.isZERO() = ", p.isZERO());
// polynomials over (polynomials over rational numbers)
GenPolynomialRing<GenPolynomial<BigRational>> ppf =
new GenPolynomialRing<GenPolynomial<BigRational>>(pf, 3);
// System.out.println("ppf = " + ppf);
GenPolynomial<GenPolynomial<BigRational>> pp = ppf.getONE();
// System.out.println("pp = " + pp);
pp = ppf.random(2);
// System.out.println("pp = " + pp);
pp = ppf.getZERO();
// System.out.println("pp = " + pp);
RingElem<GenPolynomial<GenPolynomial<BigRational>>> ppe =
new GenPolynomial<GenPolynomial<BigRational>>(ppf);
// System.out.println("ppe = " + ppe);
// System.out.println("pp.equals(ppe) = " + pp.equals(ppe) );
// System.out.println("pp.equals(pp) = " + pp.equals(pp) );
assertTrue("pp.equals(ppe) = ", pp.equals(ppe));
assertTrue("pp.equals(pp) = ", pp.equals(pp));
ppe = ppe.sum(pp); // why not pp = pp.add(ppe) ?
// System.out.println("ppe = " + ppe);
assertTrue("ppe.isZERO() = ", ppe.isZERO());
pp = ppf.random(2);
pp = pp.subtract(pp);
// System.out.println("pp = " + pp);
// System.out.println("pp.isZERO() = " + pp.isZERO());
assertTrue("pp.isZERO() = ", pp.isZERO());
// polynomials over (polynomials over (polynomials over rational numbers))
GenPolynomialRing<GenPolynomial<GenPolynomial<BigRational>>> pppf =
new GenPolynomialRing<GenPolynomial<GenPolynomial<BigRational>>>(ppf, 4);
// System.out.println("pppf = " + pppf);
GenPolynomial<GenPolynomial<GenPolynomial<BigRational>>> ppp = pppf.getONE();
// System.out.println("ppp = " + ppp);
ppp = pppf.random(2);
// System.out.println("ppp = " + ppp);
ppp = pppf.getZERO();
// System.out.println("ppp = " + ppp);
RingElem<GenPolynomial<GenPolynomial<GenPolynomial<BigRational>>>> pppe =
new GenPolynomial<GenPolynomial<GenPolynomial<BigRational>>>(pppf);
// System.out.println("pppe = " + pppe);
// System.out.println("ppp.equals(pppe) = " + ppp.equals(pppe) );
// System.out.println("ppp.equals(ppp) = " + ppp.equals(ppp) );
assertTrue("ppp.equals(pppe) = ", ppp.equals(pppe));
assertTrue("ppp.equals(ppp) = ", ppp.equals(ppp));
pppe = pppe.sum(ppp); // why not ppp = ppp.add(pppe) ?
// System.out.println("pppe = " + pppe);
assertTrue("pppe.isZERO() = ", pppe.isZERO());
ppp = pppf.random(2);
ppp = ppp.subtract(ppp);
// System.out.println("ppp = " + ppp);
// System.out.println("ppp.isZERO() = " + ppp.isZERO());
assertTrue("ppp.isZERO() = ", ppp.isZERO());
// some tests
// GenPolynomial<BigRational> pfx = new GenPolynomial<BigRational>();
// System.out.println("pfx = " + pfx);
}
