static Polynomial[] linearize(Polynomial polynomial, Variable variable) {
List l = new ArrayList();
Generic x = variable.expressionValue();
Polynomial s = polynomial;
try {
Polynomial r = s.valueOf(x);
s = s.divide(r);
l.add(r);
while (true) s = s.divide(r);
} catch (NotDivisibleException e) {
}
IntegerDivisor d[] = new IntegerDivisor[2];
Generic p[] = new Generic[2];
Generic q[] = new Generic[2];
d[1] = IntegerDivisor.create(JsclInteger.valueOf(1));
loop:
while (d[1].hasNext()) {
p[1] = (Generic) d[1].next();
q[1] = d[1].integer(d[1].complementary());
d[0] = IntegerDivisor.create(s.tail().coef().integerValue());
while (d[0].hasNext()) {
p[0] = (Generic) d[0].next();
q[0] = d[0].integer(d[0].complementary());
if (ArrayComparator.comparator.compare(q, p) < 0) break loop;
for (int i = 0; i < 2; i++) {
Polynomial r =
s.valueOf(i == 0 ? p[1].multiply(x).subtract(p[0]) : p[1].multiply(x).add(p[0]));
for (boolean flag = true; true; flag = false) {
try {
s = s.divide(r);
} catch (NotDivisibleException e) {
break;
}
d[1].divide();
d[0].divide();
if (flag) l.add(r);
}
}
}
}
return (Polynomial[]) ArrayUtils.toArray(l, new Polynomial[l.size()]);
}
static Polynomial[] remainder(Polynomial s, Polynomial p, Generic t[]) {
Polynomial zero = s.valueOf(JsclInteger.valueOf(0));
Generic a[] = Basis.augment(t, s.remainderUpToCoefficient(p).elements());
Variable unk[] = Basis.augmentUnknown(new Variable[] {}, p.elements());
{
Variable u = unk[unk.length - 1];
System.arraycopy(unk, 0, unk, 1, unk.length - 1);
unk[0] = u;
}
Generic be[][] =
Linearization.compute(
Basis.compute(a, unk, Monomial.lexicographic, 0, Basis.DEGREE).elements(), unk);
for (int i = 0; i < be.length; i++) {
Polynomial r = substitute(p, be[i], unk);
try {
return new Polynomial[] {zero, r, s.divide(r)};
} catch (NotDivisibleException e) {
}
}
return new Polynomial[] {s, zero, zero};
}