/**
* Univariate GenPolynomial algebraic partial fraction decomposition, Absolute factorization or
* Rothstein-Trager algorithm.
*
* @param A univariate GenPolynomial, deg(A) < deg(P).
* @param P univariate squarefree GenPolynomial, gcd(A,P) == 1.
* @return partial fraction container.
*/
public PartialFraction<C> baseAlgebraicPartialFraction(GenPolynomial<C> A, GenPolynomial<C> P) {
if (P == null || P.isZERO()) {
throw new RuntimeException(" P == null or P == 0");
}
if (A == null || A.isZERO()) {
throw new RuntimeException(" A == null or A == 0");
// PartialFraction(A,P,al,pl,empty,empty)
}
// System.out.println("\nP_base_algeb_part = " + P);
GenPolynomialRing<C> pfac = P.ring; // K[x]
if (pfac.nvar > 1) {
// System.out.println("facs_base_irred: univ");
throw new RuntimeException("only for univariate polynomials");
}
if (!pfac.coFac.isField()) {
// System.out.println("facs_base_irred: field");
throw new RuntimeException("only for field coefficients");
}
List<C> cfactors = new ArrayList<C>();
List<GenPolynomial<C>> cdenom = new ArrayList<GenPolynomial<C>>();
List<AlgebraicNumber<C>> afactors = new ArrayList<AlgebraicNumber<C>>();
List<GenPolynomial<AlgebraicNumber<C>>> adenom =
new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();
// P linear
if (P.degree(0) <= 1) {
cfactors.add(A.leadingBaseCoefficient());
cdenom.add(P);
return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
}
List<GenPolynomial<C>> Pfac = baseFactorsSquarefree(P);
// System.out.println("\nPfac = " + Pfac);
List<GenPolynomial<C>> Afac = engine.basePartialFraction(A, Pfac);
GenPolynomial<C> A0 = Afac.remove(0);
if (!A0.isZERO()) {
throw new RuntimeException(" A0 != 0: deg(A)>= deg(P)");
}
// algebraic and linear factors
int i = 0;
for (GenPolynomial<C> pi : Pfac) {
GenPolynomial<C> ai = Afac.get(i++);
if (pi.degree(0) <= 1) {
cfactors.add(ai.leadingBaseCoefficient());
cdenom.add(pi);
continue;
}
PartialFraction<C> pf = baseAlgebraicPartialFractionIrreducibleAbsolute(ai, pi);
// PartialFraction<C> pf = baseAlgebraicPartialFractionIrreducible(ai,pi);
cfactors.addAll(pf.cfactors);
cdenom.addAll(pf.cdenom);
afactors.addAll(pf.afactors);
adenom.addAll(pf.adenom);
}
return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
}
/** 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));
BigComplex x = a.leadingBaseCoefficient().inverse();
c = a.monic();
d = a.multiply(x);
assertEquals("a.monic() = a(1/ldcf(a))", c, d);
BigComplex y = b.leadingBaseCoefficient().inverse();
c = b.monic();
d = b.multiply(y);
assertEquals("b.monic() = b(1/ldcf(b))", c, d);
e = new GenPolynomial<BigComplex>(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);
}
/**
* Real algebraic number magnitude.
*
* @param iv root isolating interval for f, with f(left) * f(right) < 0.
* @param f univariate polynomial, non-zero.
* @param g univariate polynomial, gcd(f,g) == 1.
* @param eps length limit for interval length.
* @return g(iv) .
*/
public C realMagnitude(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g, C eps) {
if (g.isZERO() || g.isConstant()) {
return g.leadingBaseCoefficient();
}
Interval<C> v = invariantMagnitudeInterval(iv, f, g, eps);
return realIntervalMagnitude(v, f, g, eps);
}
/**
* Real root bound. With f(M) * f(-M) != 0.
*
* @param f univariate polynomial.
* @return M such that -M < root(f) < M.
*/
public C realRootBound(GenPolynomial<C> f) {
if (f == null) {
return null;
}
RingFactory<C> cfac = f.ring.coFac;
C M = cfac.getONE();
if (f.isZERO() || f.isConstant()) {
return M;
}
C a = f.leadingBaseCoefficient().abs();
for (C c : f.getMap().values()) {
C d = c.abs().divide(a);
if (M.compareTo(d) < 0) {
M = d;
}
}
// works also without this case, only for optimization
// to use rational number interval end points
// can fail if real root is in interval [r,r+1]
// for too low precision or too big r, since r is approximation
if ((Object) M instanceof RealAlgebraicNumber) {
RealAlgebraicNumber Mr = (RealAlgebraicNumber) M;
BigRational r = Mr.magnitude();
M = cfac.fromInteger(r.numerator()).divide(cfac.fromInteger(r.denominator()));
}
M = M.sum(f.ring.coFac.getONE());
// System.out.println("M = " + M);
return M;
}
/**
* Real algebraic number magnitude.
*
* @param iv root isolating interval for f, with f(left) * f(right) < 0, with iv such that
* |g(a) - g(b)| < eps for a, b in iv.
* @param f univariate polynomial, non-zero.
* @param g univariate polynomial, gcd(f,g) == 1.
* @param eps length limit for interval length.
* @return g(iv) .
*/
public C realIntervalMagnitude(Interval<C> iv, GenPolynomial<C> f, GenPolynomial<C> g, C eps) {
if (g.isZERO() || g.isConstant()) {
return g.leadingBaseCoefficient();
}
RingFactory<C> cfac = g.ring.coFac;
C c = iv.left.sum(iv.right);
c = c.divide(cfac.fromInteger(2));
C ev = PolyUtil.<C>evaluateMain(cfac, g, c);
// System.out.println("ev = " + ev);
return ev;
}
/**
* Magnitude bound.
*
* @param iv interval.
* @param f univariate polynomial.
* @return B such that |f(c)| < B for c in iv.
*/
public C magnitudeBound(Interval<C> iv, GenPolynomial<C> f) {
if (f == null) {
return null;
}
if (f.isZERO()) {
return f.ring.coFac.getONE();
}
if (f.isConstant()) {
return f.leadingBaseCoefficient().abs();
}
GenPolynomial<C> fa =
f.map(
new UnaryFunctor<C, C>() {
public C eval(C a) {
return a.abs();
}
});
// System.out.println("fa = " + fa);
C M = iv.left.abs();
if (M.compareTo(iv.right.abs()) < 0) {
M = iv.right.abs();
}
// System.out.println("M = " + M);
RingFactory<C> cfac = f.ring.coFac;
C B = PolyUtil.<C>evaluateMain(cfac, fa, M);
// works also without this case, only for optimization
// to use rational number interval end points
// can fail if real root is in interval [r,r+1]
// for too low precision or too big r, since r is approximation
if ((Object) B instanceof RealAlgebraicNumber) {
RealAlgebraicNumber Br = (RealAlgebraicNumber) B;
BigRational r = Br.magnitude();
B = cfac.fromInteger(r.numerator()).divide(cfac.fromInteger(r.denominator()));
}
// System.out.println("B = " + B);
return B;
}
/**
* Univariate GenPolynomial algebraic partial fraction decomposition, via absolute factorization
* to linear factors.
*
* @param A univariate GenPolynomial, deg(A) < deg(P).
* @param P univariate squarefree GenPolynomial, gcd(A,P) == 1.
* @return partial fraction container.
*/
public PartialFraction<C> baseAlgebraicPartialFractionIrreducibleAbsolute(
GenPolynomial<C> A, GenPolynomial<C> P) {
if (P == null || P.isZERO()) {
throw new RuntimeException(" P == null or P == 0");
}
// System.out.println("\nP_base_algeb_part = " + P);
GenPolynomialRing<C> pfac = P.ring; // K[x]
if (pfac.nvar > 1) {
// System.out.println("facs_base_irred: univ");
throw new RuntimeException("only for univariate polynomials");
}
if (!pfac.coFac.isField()) {
// System.out.println("facs_base_irred: field");
throw new RuntimeException("only for field coefficients");
}
List<C> cfactors = new ArrayList<C>();
List<GenPolynomial<C>> cdenom = new ArrayList<GenPolynomial<C>>();
List<AlgebraicNumber<C>> afactors = new ArrayList<AlgebraicNumber<C>>();
List<GenPolynomial<AlgebraicNumber<C>>> adenom =
new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();
// P linear
if (P.degree(0) <= 1) {
cfactors.add(A.leadingBaseCoefficient());
cdenom.add(P);
return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
}
// non linear case
Factors<C> afacs = factorsAbsoluteIrreducible(P);
// System.out.println("linear algebraic factors = " + afacs);
// System.out.println("afactors = " + afacs.afactors);
// System.out.println("arfactors = " + afacs.arfactors);
// System.out.println("arfactors pol = " + afacs.arfactors.get(0).poly);
// System.out.println("arfactors2 = " + afacs.arfactors.get(0).afactors);
List<GenPolynomial<AlgebraicNumber<C>>> fact = afacs.getFactors();
// System.out.println("factors = " + fact);
GenPolynomial<AlgebraicNumber<C>> Pa = afacs.apoly;
GenPolynomial<AlgebraicNumber<C>> Aa =
PolyUtil.<C>convertToRecAlgebraicCoefficients(1, Pa.ring, A);
GreatestCommonDivisorAbstract<AlgebraicNumber<C>> aengine = GCDFactory.getProxy(afacs.afac);
// System.out.println("denom = " + Pa);
// System.out.println("numer = " + Aa);
List<GenPolynomial<AlgebraicNumber<C>>> numers = aengine.basePartialFraction(Aa, fact);
// System.out.println("part frac = " + numers);
GenPolynomial<AlgebraicNumber<C>> A0 = numers.remove(0);
if (!A0.isZERO()) {
throw new RuntimeException(" A0 != 0: deg(A)>= deg(P)");
}
int i = 0;
for (GenPolynomial<AlgebraicNumber<C>> fa : fact) {
GenPolynomial<AlgebraicNumber<C>> an = numers.get(i++);
if (fa.degree(0) <= 1) {
afactors.add(an.leadingBaseCoefficient());
adenom.add(fa);
continue;
}
System.out.println("fa = " + fa);
Factors<AlgebraicNumber<C>> faf = afacs.getFactor(fa);
System.out.println("faf = " + faf);
List<GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>>> fafact = faf.getFactors();
GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> Aaa =
PolyUtil.<AlgebraicNumber<C>>convertToRecAlgebraicCoefficients(1, faf.apoly.ring, an);
GreatestCommonDivisorAbstract<AlgebraicNumber<AlgebraicNumber<C>>> aaengine =
GCDFactory.getImplementation(faf.afac);
List<GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>>> anumers =
aaengine.basePartialFraction(Aaa, fafact);
System.out.println("algeb part frac = " + anumers);
GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> A0a = anumers.remove(0);
if (!A0a.isZERO()) {
throw new RuntimeException(" A0 != 0: deg(A)>= deg(P)");
}
int k = 0;
for (GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> faa : fafact) {
GenPolynomial<AlgebraicNumber<AlgebraicNumber<C>>> ana = anumers.get(k++);
System.out.println("faa = " + faa);
System.out.println("ana = " + ana);
if (faa.degree(0) > 1) {
throw new RuntimeException(" faa not linear");
}
GenPolynomial<AlgebraicNumber<C>> ana1 =
(GenPolynomial<AlgebraicNumber<C>>) (GenPolynomial) ana;
GenPolynomial<AlgebraicNumber<C>> faa1 =
(GenPolynomial<AlgebraicNumber<C>>) (GenPolynomial) faa;
afactors.add(ana1.leadingBaseCoefficient());
adenom.add(faa1);
}
}
return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
}
/**
* Univariate GenPolynomial algebraic partial fraction decomposition, Rothstein-Trager algorithm.
*
* @param A univariate GenPolynomial, deg(A) < deg(P).
* @param P univariate squarefree GenPolynomial, gcd(A,P) == 1.
* @return partial fraction container.
*/
@Deprecated
public PartialFraction<C> baseAlgebraicPartialFractionIrreducible(
GenPolynomial<C> A, GenPolynomial<C> P) {
if (P == null || P.isZERO()) {
throw new RuntimeException(" P == null or P == 0");
}
// System.out.println("\nP_base_algeb_part = " + P);
GenPolynomialRing<C> pfac = P.ring; // K[x]
if (pfac.nvar > 1) {
// System.out.println("facs_base_irred: univ");
throw new RuntimeException("only for univariate polynomials");
}
if (!pfac.coFac.isField()) {
// System.out.println("facs_base_irred: field");
throw new RuntimeException("only for field coefficients");
}
List<C> cfactors = new ArrayList<C>();
List<GenPolynomial<C>> cdenom = new ArrayList<GenPolynomial<C>>();
List<AlgebraicNumber<C>> afactors = new ArrayList<AlgebraicNumber<C>>();
List<GenPolynomial<AlgebraicNumber<C>>> adenom =
new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();
// P linear
if (P.degree(0) <= 1) {
cfactors.add(A.leadingBaseCoefficient());
cdenom.add(P);
return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
}
// deriviative
GenPolynomial<C> Pp = PolyUtil.<C>baseDeriviative(P);
// no: Pp = Pp.monic();
// System.out.println("\nP = " + P);
// System.out.println("Pp = " + Pp);
// Q[t]
String[] vars = new String[] {"t"};
GenPolynomialRing<C> cfac = new GenPolynomialRing<C>(pfac.coFac, 1, pfac.tord, vars);
GenPolynomial<C> t = cfac.univariate(0);
// System.out.println("t = " + t);
// Q[x][t]
GenPolynomialRing<GenPolynomial<C>> rfac =
new GenPolynomialRing<GenPolynomial<C>>(pfac, cfac); // sic
// System.out.println("rfac = " + rfac.toScript());
// transform polynomials to bi-variate polynomial
GenPolynomial<GenPolynomial<C>> Ac = PolyUfdUtil.<C>introduceLowerVariable(rfac, A);
// System.out.println("Ac = " + Ac);
GenPolynomial<GenPolynomial<C>> Pc = PolyUfdUtil.<C>introduceLowerVariable(rfac, P);
// System.out.println("Pc = " + Pc);
GenPolynomial<GenPolynomial<C>> Pcp = PolyUfdUtil.<C>introduceLowerVariable(rfac, Pp);
// System.out.println("Pcp = " + Pcp);
// Q[t][x]
GenPolynomialRing<GenPolynomial<C>> rfac1 = Pc.ring;
// System.out.println("rfac1 = " + rfac1.toScript());
// A - t P'
GenPolynomial<GenPolynomial<C>> tc = rfac1.getONE().multiply(t);
// System.out.println("tc = " + tc);
GenPolynomial<GenPolynomial<C>> At = Ac.subtract(tc.multiply(Pcp));
// System.out.println("At = " + At);
GreatestCommonDivisorSubres<C> engine = new GreatestCommonDivisorSubres<C>();
// = GCDFactory.<C>getImplementation( cfac.coFac );
GreatestCommonDivisorAbstract<AlgebraicNumber<C>> aengine = null;
GenPolynomial<GenPolynomial<C>> Rc = engine.recursiveResultant(Pc, At);
// System.out.println("Rc = " + Rc);
GenPolynomial<C> res = Rc.leadingBaseCoefficient();
// no: res = res.monic();
// System.out.println("\nres = " + res);
SortedMap<GenPolynomial<C>, Long> resfac = baseFactors(res);
// System.out.println("resfac = " + resfac + "\n");
for (GenPolynomial<C> r : resfac.keySet()) {
// System.out.println("\nr(t) = " + r);
if (r.isConstant()) {
continue;
}
// if ( r.degree(0) <= 1L ) {
// System.out.println("warning linear factor in resultant ignored");
// continue;
// //throw new RuntimeException("input not irreducible");
// }
// vars = new String[] { "z_" + Math.abs(r.hashCode() % 1000) };
vars = pfac.newVars("z_");
pfac = pfac.clone();
vars = pfac.setVars(vars);
r = pfac.copy(r); // hack to exchange the variables
// System.out.println("r(z_) = " + r);
AlgebraicNumberRing<C> afac = new AlgebraicNumberRing<C>(r, true); // since irreducible
logger.debug("afac = " + afac.toScript());
AlgebraicNumber<C> a = afac.getGenerator();
// no: a = a.negate();
// System.out.println("a = " + a);
// K(alpha)[x]
GenPolynomialRing<AlgebraicNumber<C>> pafac =
new GenPolynomialRing<AlgebraicNumber<C>>(afac, Pc.ring);
// System.out.println("pafac = " + pafac.toScript());
// convert to K(alpha)[x]
GenPolynomial<AlgebraicNumber<C>> Pa = PolyUtil.<C>convertToAlgebraicCoefficients(pafac, P);
// System.out.println("Pa = " + Pa);
GenPolynomial<AlgebraicNumber<C>> Pap = PolyUtil.<C>convertToAlgebraicCoefficients(pafac, Pp);
// System.out.println("Pap = " + Pap);
GenPolynomial<AlgebraicNumber<C>> Aa = PolyUtil.<C>convertToAlgebraicCoefficients(pafac, A);
// System.out.println("Aa = " + Aa);
// A - a P'
GenPolynomial<AlgebraicNumber<C>> Ap = Aa.subtract(Pap.multiply(a));
// System.out.println("Ap = " + Ap);
if (aengine == null) {
aengine = GCDFactory.<AlgebraicNumber<C>>getImplementation(afac);
// System.out.println("aengine = " + aengine);
}
GenPolynomial<AlgebraicNumber<C>> Ga = aengine.baseGcd(Pa, Ap);
// System.out.println("Ga = " + Ga);
if (Ga.isConstant()) {
// System.out.println("warning constant gcd ignored");
continue;
}
afactors.add(a);
adenom.add(Ga);
// quadratic case
if (P.degree(0) == 2 && Ga.degree(0) == 1) {
GenPolynomial<AlgebraicNumber<C>>[] qra =
PolyUtil.<AlgebraicNumber<C>>basePseudoQuotientRemainder(Pa, Ga);
GenPolynomial<AlgebraicNumber<C>> Qa = qra[0];
if (!qra[1].isZERO()) {
throw new RuntimeException("remainder not zero");
}
// System.out.println("Qa = " + Qa);
afactors.add(a.negate());
adenom.add(Qa);
}
if (false && P.degree(0) == 3 && Ga.degree(0) == 1) {
GenPolynomial<AlgebraicNumber<C>>[] qra =
PolyUtil.<AlgebraicNumber<C>>basePseudoQuotientRemainder(Pa, Ga);
GenPolynomial<AlgebraicNumber<C>> Qa = qra[0];
if (!qra[1].isZERO()) {
throw new RuntimeException("remainder not zero");
}
System.out.println("Qa3 = " + Qa);
// afactors.add( a.negate() );
// adenom.add( Qa );
}
}
return new PartialFraction<C>(A, P, cfactors, cdenom, afactors, adenom);
}
/**
* 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;
}
