/**
* GenPolynomial greatest squarefree divisor.
*
* @param P GenPolynomial.
* @return squarefree(pp(P)).
*/
@Override
public GenPolynomial<C> squarefreePart(GenPolynomial<C> P) {
if (P == null) {
throw new IllegalArgumentException(this.getClass().getName() + " P != null");
}
if (P.isZERO()) {
return P;
}
GenPolynomialRing<C> pfac = P.ring;
if (pfac.nvar <= 1) {
return baseSquarefreePart(P);
}
// just for the moment:
GenPolynomial<C> s = pfac.getONE();
SortedMap<GenPolynomial<C>, Long> factors = squarefreeFactors(P);
if (logger.isInfoEnabled()) {
logger.info("sqfPart,factors = " + factors);
}
for (GenPolynomial<C> sp : factors.keySet()) {
if (sp.isConstant()) {
continue;
}
s = s.multiply(sp);
}
return s.monic();
}
/**
* GenPolynomial polynomial greatest squarefree divisor.
*
* @param P GenPolynomial.
* @return squarefree(pp(P)).
*/
@Override
public GenPolynomial<C> baseSquarefreePart(GenPolynomial<C> P) {
if (P == null || P.isZERO()) {
return P;
}
GenPolynomialRing<C> pfac = P.ring;
if (pfac.nvar > 1) {
throw new IllegalArgumentException(
this.getClass().getName() + " only for univariate polynomials");
}
// just for the moment:
GenPolynomial<C> s = pfac.getONE();
SortedMap<GenPolynomial<C>, Long> factors = baseSquarefreeFactors(P);
logger.info("sqfPart,factors = " + factors);
for (GenPolynomial<C> sp : factors.keySet()) {
s = s.multiply(sp);
}
return s.monic();
}
/** 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);
}
/**
* GenPolynomial recursive univariate polynomial squarefree factorization.
*
* @param P recursive univariate GenPolynomial.
* @return [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i
* squarefree.
*/
@Override
public SortedMap<GenPolynomial<GenPolynomial<C>>, Long> recursiveUnivariateSquarefreeFactors(
GenPolynomial<GenPolynomial<C>> P) {
SortedMap<GenPolynomial<GenPolynomial<C>>, Long> sfactors =
new TreeMap<GenPolynomial<GenPolynomial<C>>, Long>();
if (P == null || P.isZERO()) {
return sfactors;
}
GenPolynomialRing<GenPolynomial<C>> pfac = P.ring;
if (pfac.nvar > 1) {
// recursiveContent not possible by return type
throw new IllegalArgumentException(
this.getClass().getName() + " only for univariate polynomials");
}
// if base coefficient ring is a field, make monic
GenPolynomialRing<C> cfac = (GenPolynomialRing<C>) pfac.coFac;
C ldbcf = P.leadingBaseCoefficient().leadingBaseCoefficient();
if (!ldbcf.isONE()) {
GenPolynomial<C> lc = cfac.getONE().multiply(ldbcf);
GenPolynomial<GenPolynomial<C>> pl = pfac.getONE().multiply(lc);
sfactors.put(pl, 1L);
C li = ldbcf.inverse();
// System.out.println("li = " + li);
P = P.multiply(cfac.getONE().multiply(li));
// System.out.println("P,monic = " + P);
ldbcf = P.leadingBaseCoefficient().leadingBaseCoefficient();
if (debug) {
logger.debug("new ldbcf: " + ldbcf);
}
}
// factors of content
GenPolynomial<C> Pc = engine.recursiveContent(P);
if (logger.isInfoEnabled()) {
logger.info("Pc = " + Pc);
}
Pc = Pc.monic();
if (!Pc.isONE()) {
P = PolyUtil.<C>coefficientPseudoDivide(P, Pc);
}
SortedMap<GenPolynomial<C>, Long> rsf = squarefreeFactors(Pc);
if (logger.isInfoEnabled()) {
logger.info("rsf = " + rsf);
}
// add factors of content
for (Map.Entry<GenPolynomial<C>, Long> me : rsf.entrySet()) {
GenPolynomial<C> c = me.getKey();
if (!c.isONE()) {
GenPolynomial<GenPolynomial<C>> cr = pfac.getONE().multiply(c);
Long rk = me.getValue(); // rsf.get(c);
sfactors.put(cr, rk);
}
}
// factors of recursive polynomial
GenPolynomial<GenPolynomial<C>> T0 = P;
long e = 1L;
GenPolynomial<GenPolynomial<C>> Tp;
GenPolynomial<GenPolynomial<C>> T = null;
GenPolynomial<GenPolynomial<C>> V = null;
long k = 0L;
long mp = 0L;
boolean init = true;
while (true) {
if (init) {
if (T0.isConstant() || T0.isZERO()) {
break;
}
Tp = PolyUtil.<C>recursiveDeriviative(T0);
T = engine.recursiveUnivariateGcd(T0, Tp);
T = PolyUtil.<C>monic(T);
V = PolyUtil.<C>recursivePseudoDivide(T0, T);
// System.out.println("iT0 = " + T0);
// System.out.println("iTp = " + Tp);
// System.out.println("iT = " + T);
// System.out.println("iV = " + V);
k = 0L;
mp = 0L;
init = false;
}
if (V.isConstant()) {
mp = pfac.characteristic().longValue(); // assert != 0
// T0 = PolyUtil.<C> recursiveModRoot(T,mp);
T0 = recursiveUnivariateRootCharacteristic(T);
logger.info("char root: T0r = " + T0 + ", Tr = " + T);
if (T0 == null) {
// break;
T0 = pfac.getZERO();
}
e = e * mp;
init = true;
// continue;
}
k++;
if (mp != 0L && k % mp == 0L) {
T = PolyUtil.<C>recursivePseudoDivide(T, V);
System.out.println("k = " + k);
// System.out.println("T = " + T);
k++;
}
GenPolynomial<GenPolynomial<C>> W = engine.recursiveUnivariateGcd(T, V);
W = PolyUtil.<C>monic(W);
GenPolynomial<GenPolynomial<C>> z = PolyUtil.<C>recursivePseudoDivide(V, W);
// System.out.println("W = " + W);
// System.out.println("z = " + z);
V = W;
T = PolyUtil.<C>recursivePseudoDivide(T, V);
// System.out.println("V = " + V);
// System.out.println("T = " + T);
// was: if ( z.degree(0) > 0 ) {
if (!z.isONE() && !z.isZERO()) {
z = PolyUtil.<C>monic(z);
logger.info("z,put = " + z);
sfactors.put(z, (e * k));
}
}
logger.info("exit char root: T0 = " + T0 + ", T = " + T);
if (sfactors.size() == 0) {
sfactors.put(pfac.getONE(), 1L);
}
return sfactors;
}
/**
* GenPolynomial polynomial squarefree factorization.
*
* @param A GenPolynomial.
* @return [p_1 -> e_1, ..., p_k -> e_k] with P = prod_{i=1,...,k} p_i^{e_i} and p_i
* squarefree.
*/
@Override
public SortedMap<GenPolynomial<C>, Long> baseSquarefreeFactors(GenPolynomial<C> A) {
SortedMap<GenPolynomial<C>, Long> sfactors = new TreeMap<GenPolynomial<C>, Long>();
if (A == null || A.isZERO()) {
return sfactors;
}
GenPolynomialRing<C> pfac = A.ring;
if (A.isConstant()) {
C coeff = A.leadingBaseCoefficient();
// System.out.println("coeff = " + coeff + " @ " + coeff.factory());
SortedMap<C, Long> rfactors = squarefreeFactors(coeff);
// System.out.println("rfactors,const = " + rfactors);
if (rfactors != null && rfactors.size() > 0) {
for (Map.Entry<C, Long> me : rfactors.entrySet()) {
C c = me.getKey();
if (!c.isONE()) {
GenPolynomial<C> cr = pfac.getONE().multiply(c);
Long rk = me.getValue(); // rfactors.get(c);
sfactors.put(cr, rk);
}
}
} else {
sfactors.put(A, 1L);
}
return sfactors;
}
if (pfac.nvar > 1) {
throw new IllegalArgumentException(
this.getClass().getName() + " only for univariate polynomials");
}
C ldbcf = A.leadingBaseCoefficient();
if (!ldbcf.isONE()) {
A = A.divide(ldbcf);
SortedMap<C, Long> rfactors = squarefreeFactors(ldbcf);
// System.out.println("rfactors,ldbcf = " + rfactors);
if (rfactors != null && rfactors.size() > 0) {
for (Map.Entry<C, Long> me : rfactors.entrySet()) {
C c = me.getKey();
if (!c.isONE()) {
GenPolynomial<C> cr = pfac.getONE().multiply(c);
Long rk = me.getValue(); // rfactors.get(c);
sfactors.put(cr, rk);
}
}
} else {
GenPolynomial<C> f1 = pfac.getONE().multiply(ldbcf);
// System.out.println("gcda sqf f1 = " + f1);
sfactors.put(f1, 1L);
}
ldbcf = pfac.coFac.getONE();
}
GenPolynomial<C> T0 = A;
long e = 1L;
GenPolynomial<C> Tp;
GenPolynomial<C> T = null;
GenPolynomial<C> V = null;
long k = 0L;
long mp = 0L;
boolean init = true;
while (true) {
// System.out.println("T0 = " + T0);
if (init) {
if (T0.isConstant() || T0.isZERO()) {
break;
}
Tp = PolyUtil.<C>baseDeriviative(T0);
T = engine.baseGcd(T0, Tp);
T = T.monic();
V = PolyUtil.<C>basePseudoDivide(T0, T);
// System.out.println("iT0 = " + T0);
// System.out.println("iTp = " + Tp);
// System.out.println("iT = " + T);
// System.out.println("iV = " + V);
// System.out.println("const(iV) = " + V.isConstant());
k = 0L;
mp = 0L;
init = false;
}
if (V.isConstant()) {
mp = pfac.characteristic().longValue(); // assert != 0
// T0 = PolyUtil.<C> baseModRoot(T,mp);
T0 = baseRootCharacteristic(T);
logger.info("char root: T0 = " + T0 + ", T = " + T);
if (T0 == null) {
// break;
T0 = pfac.getZERO();
}
e = e * mp;
init = true;
continue;
}
k++;
if (mp != 0L && k % mp == 0L) {
T = PolyUtil.<C>basePseudoDivide(T, V);
System.out.println("k = " + k);
// System.out.println("T = " + T);
k++;
}
GenPolynomial<C> W = engine.baseGcd(T, V);
W = W.monic();
GenPolynomial<C> z = PolyUtil.<C>basePseudoDivide(V, W);
// System.out.println("W = " + W);
// System.out.println("z = " + z);
V = W;
T = PolyUtil.<C>basePseudoDivide(T, V);
// System.out.println("V = " + V);
// System.out.println("T = " + T);
if (z.degree(0) > 0) {
if (ldbcf.isONE() && !z.leadingBaseCoefficient().isONE()) {
z = z.monic();
logger.info("z,monic = " + z);
}
sfactors.put(z, (e * k));
}
}
// look, a stupid error:
// if ( !ldbcf.isONE() ) {
// GenPolynomial<C> f1 = sfactors.firstKey();
// long e1 = sfactors.remove(f1);
// System.out.println("gcda sqf c = " + c);
// f1 = f1.multiply(c);
// //System.out.println("gcda sqf f1e = " + f1);
// sfactors.put(f1,e1);
// }
logger.info("exit char root: T0 = " + T0 + ", T = " + T);
return sfactors;
}