/**
* GenPolynomial is absolute factorization.
*
* @param facs factors map container.
* @return true if P = prod_{i=1,...,k} p_i**e_i , else false.
*/
public boolean isAbsoluteFactorization(FactorsMap<C> facs) {
if (facs == null) {
throw new IllegalArgumentException("facs may not be null");
}
GenPolynomial<C> P = facs.poly;
GenPolynomial<C> t = P.ring.getONE();
for (GenPolynomial<C> f : facs.factors.keySet()) {
long e = facs.factors.get(f);
GenPolynomial<C> g = Power.<GenPolynomial<C>>positivePower(f, e);
t = t.multiply(g);
}
if (P.equals(t) || P.equals(t.negate())) {
return true;
}
if (facs.afactors == null) {
return false;
}
for (Factors<C> fs : facs.afactors.keySet()) {
if (!isAbsoluteFactorization(fs)) {
return false;
}
long e = facs.afactors.get(fs);
GenPolynomial<C> g = Power.<GenPolynomial<C>>positivePower(fs.poly, e);
t = t.multiply(g);
}
boolean b = P.equals(t) || P.equals(t.negate());
if (!b) {
System.out.println("\nFactorsMap: " + facs);
System.out.println("P = " + P);
System.out.println("t = " + t);
}
return b;
}
/**
* GenPolynomial is absolute factorization.
*
* @param facs factors list container.
* @return true if P = prod_{i=1,...,r} p_i, else false.
*/
public boolean isAbsoluteFactorization(FactorsList<C> facs) {
if (facs == null) {
throw new IllegalArgumentException("facs may not be null");
}
GenPolynomial<C> P = facs.poly;
GenPolynomial<C> t = P.ring.getONE();
for (GenPolynomial<C> f : facs.factors) {
t = t.multiply(f);
}
if (P.equals(t) || P.equals(t.negate())) {
return true;
}
if (facs.afactors == null) {
return false;
}
for (Factors<C> fs : facs.afactors) {
if (!isAbsoluteFactorization(fs)) {
return false;
}
t = t.multiply(facs.poly);
}
// return P.equals(t) || P.equals(t.negate());
boolean b = P.equals(t) || P.equals(t.negate());
if (!b) {
System.out.println("\nFactorsList: " + facs);
System.out.println("P = " + P);
System.out.println("t = " + t);
}
return b;
}
/**
* Polynomial is char-th root.
*
* @param P polynomial.
* @param F = [p_1 -> e_1, ..., p_k -> e_k].
* @return true if P = prod_{i=1,...,k} p_i**(e_i*p), else false.
*/
public boolean isCharRoot(GenPolynomial<C> P, SortedMap<GenPolynomial<C>, Long> F) {
if (P == null || F == null) {
throw new IllegalArgumentException("P and F may not be null");
}
if (P.isZERO() && F.size() == 0) {
return true;
}
GenPolynomial<C> t = P.ring.getONE();
long p = P.ring.characteristic().longValue();
for (Map.Entry<GenPolynomial<C>, Long> me : F.entrySet()) {
GenPolynomial<C> f = me.getKey();
Long E = me.getValue(); // F.get(f);
long e = E.longValue();
GenPolynomial<C> g = Power.<GenPolynomial<C>>positivePower(f, e);
if (!f.isConstant()) {
g = Power.<GenPolynomial<C>>positivePower(g, p);
}
t = t.multiply(g);
}
boolean f = P.equals(t) || P.equals(t.negate());
if (!f) {
System.out.println("\nfactorization(map): " + f);
System.out.println("P = " + P);
System.out.println("t = " + t);
P = P.monic();
t = t.monic();
f = P.equals(t) || P.equals(t.negate());
if (f) {
return f;
}
System.out.println("\nfactorization(map): " + f);
System.out.println("P = " + P);
System.out.println("t = " + t);
}
return f;
}
/** Test scalar multiplication. */
public void testPolynomialMultiplication() {
BigRational cfac = new BigRational(1);
GenPolynomialRing<BigRational> pfac = new GenPolynomialRing<BigRational>(cfac, rl);
GenVectorModul<GenPolynomial<BigRational>> mfac =
new GenVectorModul<GenPolynomial<BigRational>>(pfac, ll);
GenPolynomial<BigRational> r, s, t;
GenVector<GenPolynomial<BigRational>> a, b, c, d, e;
r = pfac.random(kl);
// System.out.println("r = " + r);
s = r.negate();
// System.out.println("s = " + s);
a = mfac.random(kl, q);
// System.out.println("a = " + a);
c = a.scalarMultiply(r);
d = a.scalarMultiply(s);
e = c.sum(d);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
// System.out.println("e = " + e);
assertEquals("a*b + a*(-b) = 0", e, mfac.getZERO());
b = mfac.random(kl, q);
// System.out.println("b = " + b);
t = pfac.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 = a", a, d);
t = pfac.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);
}