/** Test scalar multiplication. */
public void testMultiplication() {
BigRational cfac = new BigRational(1);
GenVectorModul<BigRational> mfac = new GenVectorModul<BigRational>(cfac, ll);
BigRational r, s, t;
GenVector<BigRational> a, b, c, d, e;
r = cfac.random(kl);
// System.out.println("r = " + r);
s = r.inverse();
// System.out.println("s = " + s);
a = mfac.random(kl, q);
// System.out.println("a = " + a);
c = a.scalarMultiply(r);
d = c.scalarMultiply(s);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
assertEquals("a*b*(1/b) = a", a, d);
b = mfac.random(kl, q);
// System.out.println("b = " + b);
t = cfac.getONE();
// System.out.println("t = " + t);
c = a.linearCombination(b, t);
d = b.linearCombination(a, t);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
assertEquals("a+1*b = b+1*a", c, d);
c = a.linearCombination(b, t);
d = a.sum(b);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
assertEquals("a+1*b = b+1*a", c, d);
s = t.negate();
// System.out.println("s = " + s);
c = a.linearCombination(b, t);
d = c.linearCombination(b, s);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
assertEquals("a+1*b+(-1)*b = a", a, d);
c = a.linearCombination(t, b, t);
d = c.linearCombination(t, b, s);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
assertEquals("a*1+b*1+b*(-1) = a", a, d);
t = cfac.getZERO();
// System.out.println("t = " + t);
c = a.linearCombination(b, t);
// System.out.println("c = " + c);
assertEquals("a+0*b = a", a, c);
d = a.linearCombination(t, b, t);
// System.out.println("d = " + d);
assertEquals("0*a+0*b = 0", mfac.getZERO(), d);
r = a.scalarProduct(b);
s = b.scalarProduct(a);
// System.out.println("r = " + r);
// System.out.println("s = " + s);
assertEquals("a.b = b.a", r, s);
}
/** Test rational coefficient reduction with recording. */
public void testRatReductionRecording() {
List<GenWordPolynomial<BigRational>> lrow, rrow = null;
do {
a = fac.random(kl, ll, el);
} while (a.isZERO());
do {
b = fac.random(kl, ll, el);
} while (b.isZERO());
c = fac.random(kl, ll, el);
d = fac.random(kl, ll, el);
// System.out.println("a = " + a);
// System.out.println("b = " + b);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
L = new ArrayList<GenWordPolynomial<BigRational>>();
L.add(a);
lrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
rrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
e = fac.getZERO();
for (int m = 0; m < L.size(); m++) {
lrow.add(e);
rrow.add(e);
}
e = red.normalform(lrow, rrow, L, a);
// System.out.println("e = " + e);
// System.out.println("lrow = " + lrow);
// System.out.println("rrow = " + rrow);
assertTrue("isZERO( e )", e.isZERO());
assertTrue("is Reduction ", red.isReductionNF(lrow, rrow, L, a, e));
L.add(b);
lrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
rrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
e = fac.getZERO();
for (int m = 0; m < L.size(); m++) {
lrow.add(e);
rrow.add(e);
}
e = red.normalform(lrow, rrow, L, b);
// System.out.println("e = " + e);
// System.out.println("lrow = " + lrow);
// System.out.println("rrow = " + rrow);
assertTrue("is Reduction ", red.isReductionNF(lrow, rrow, L, b, e));
L.add(c);
lrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
rrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
e = fac.getZERO();
for (int m = 0; m < L.size(); m++) {
lrow.add(e);
rrow.add(e);
}
e = red.normalform(lrow, rrow, L, c);
// System.out.println("e = " + e);
// System.out.println("lrow = " + lrow);
// System.out.println("rrow = " + rrow);
assertTrue("is Reduction ", red.isReductionNF(lrow, rrow, L, c, e));
L.add(d);
lrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
rrow = new ArrayList<GenWordPolynomial<BigRational>>(L.size());
e = fac.getZERO();
for (int m = 0; m < L.size(); m++) {
lrow.add(e);
rrow.add(e);
}
Word u = new Word(wfac, "f");
Word v = new Word(wfac, "abc");
d = a.multiply(cfac.random(3), u, v);
// System.out.println("d = " + d);
e = red.normalform(lrow, rrow, L, d);
// System.out.println("e = " + e);
// System.out.println("lrow = " + lrow);
// System.out.println("rrow = " + rrow);
assertTrue("is Reduction ", red.isReductionNF(lrow, rrow, L, d, e));
}