/**
* GenPolynomial squarefree factorization.
*
* @param P 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> squarefreeFactors(GenPolynomial<C> P) {
if (P == null) {
throw new IllegalArgumentException(this.getClass().getName() + " P != null");
}
GenPolynomialRing<C> pfac = P.ring;
if (pfac.nvar <= 1) {
return baseSquarefreeFactors(P);
}
SortedMap<GenPolynomial<C>, Long> sfactors = new TreeMap<GenPolynomial<C>, Long>();
if (P.isZERO()) {
return sfactors;
}
GenPolynomialRing<C> cfac = pfac.contract(1);
GenPolynomialRing<GenPolynomial<C>> rfac = new GenPolynomialRing<GenPolynomial<C>>(cfac, 1);
GenPolynomial<GenPolynomial<C>> Pr = PolyUtil.<C>recursive(rfac, P);
SortedMap<GenPolynomial<GenPolynomial<C>>, Long> PP = recursiveUnivariateSquarefreeFactors(Pr);
for (Map.Entry<GenPolynomial<GenPolynomial<C>>, Long> m : PP.entrySet()) {
Long i = m.getValue();
GenPolynomial<GenPolynomial<C>> Dr = m.getKey();
GenPolynomial<C> D = PolyUtil.<C>distribute(pfac, Dr);
sfactors.put(D, i);
}
return sfactors;
}
/**
* 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();
}
/** Test compare sequential with parallel GBase. */
public void testSequentialParallelGBase() {
List<GenPolynomial<BigRational>> Gs, Gp;
L = new ArrayList<GenPolynomial<BigRational>>();
a = fac.random(kl, ll, el, q);
b = fac.random(kl, ll, el, q);
c = fac.random(kl, ll, el, q);
d = fac.random(kl, ll, el, q);
e = d; // fac.random(kl, ll, el, q );
if (a.isZERO() || b.isZERO() || c.isZERO() || d.isZERO()) {
return;
}
L.add(a);
Gs = bbseq.GB(L);
Gp = bbpar.GB(L);
assertTrue("Gs.containsAll(Gp)", Gs.containsAll(Gp));
assertTrue("Gp.containsAll(Gs)", Gp.containsAll(Gs));
L = Gs;
L.add(b);
Gs = bbseq.GB(L);
Gp = bbpar.GB(L);
assertTrue("Gs.containsAll(Gp)", Gs.containsAll(Gp));
assertTrue("Gp.containsAll(Gs)", Gp.containsAll(Gs));
L = Gs;
L.add(c);
Gs = bbseq.GB(L);
Gp = bbpar.GB(L);
assertTrue("Gs.containsAll(Gp)", Gs.containsAll(Gp));
assertTrue("Gp.containsAll(Gs)", Gp.containsAll(Gs));
L = Gs;
L.add(d);
Gs = bbseq.GB(L);
Gp = bbpar.GB(L);
assertTrue("Gs.containsAll(Gp)", Gs.containsAll(Gp));
assertTrue("Gp.containsAll(Gs)", Gp.containsAll(Gs));
L = Gs;
L.add(e);
Gs = bbseq.GB(L);
Gp = bbpar.GB(L);
assertTrue("Gs.containsAll(Gp)", Gs.containsAll(Gp));
assertTrue("Gp.containsAll(Gs)", Gp.containsAll(Gs));
}
/** Test parallel GBase. */
public void testParallelGBase() {
L = new ArrayList<GenPolynomial<BigRational>>();
a = fac.random(kl, ll, el, q);
b = fac.random(kl, ll, el, q);
c = fac.random(kl, ll, el, q);
d = fac.random(kl, ll, el, q);
e = d; // fac.random(kl, ll, el, q );
if (a.isZERO() || b.isZERO() || c.isZERO() || d.isZERO()) {
return;
}
assertTrue("not isZERO( a )", !a.isZERO());
L.add(a);
L = bbpar.GB(L);
assertTrue("isGB( { a } )", bbpar.isGB(L));
assertTrue("not isZERO( b )", !b.isZERO());
L.add(b);
// System.out.println("L = " + L.size() );
L = bbpar.GB(L);
assertTrue("isGB( { a, b } )", bbpar.isGB(L));
assertTrue("not isZERO( c )", !c.isZERO());
L.add(c);
L = bbpar.GB(L);
assertTrue("isGB( { a, b, c } )", bbpar.isGB(L));
assertTrue("not isZERO( d )", !d.isZERO());
L.add(d);
L = bbpar.GB(L);
assertTrue("isGB( { a, b, c, d } )", bbpar.isGB(L));
assertTrue("not isZERO( e )", !e.isZERO());
L.add(e);
L = bbpar.GB(L);
assertTrue("isGB( { a, b, c, d, e } )", bbpar.isGB(L));
}
/**
* 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 modular evaluation gcd. */
public void testModEvalGcd() {
GreatestCommonDivisorAbstract<ModInteger> ufd_me = new GreatestCommonDivisorModEval();
for (int i = 0; i < 1; i++) {
a = dfac.random(kl * (i + 2), ll + 2 * i, el + 0 * i, q);
b = dfac.random(kl * (i + 2), ll + 2 * i, el + 0 * i, q);
c = dfac.random(kl * (i + 2), ll + 2 * i, el + 0 * i, q);
c = c.multiply(dfac.univariate(0));
// a = ufd.basePrimitivePart(a);
// b = ufd.basePrimitivePart(b);
if (a.isZERO() || b.isZERO() || c.isZERO()) {
// skip for this turn
continue;
}
assertTrue("length( c" + i + " ) <> 0", c.length() > 0);
// assertTrue(" not isZERO( c"+i+" )", !c.isZERO() );
// assertTrue(" not isONE( c"+i+" )", !c.isONE() );
a = a.multiply(c);
b = b.multiply(c);
// System.out.println("a = " + a);
// System.out.println("b = " + b);
d = ufd_me.gcd(a, b);
c = ufd.basePrimitivePart(c).abs();
e = PolyUtil.<ModInteger>basePseudoRemainder(d, c);
// System.out.println("c = " + c);
// System.out.println("d = " + d);
assertTrue("c | gcd(ac,bc) " + e, e.isZERO());
e = PolyUtil.<ModInteger>basePseudoRemainder(a, d);
// System.out.println("e = " + e);
assertTrue("gcd(a,b) | a" + e, e.isZERO());
e = PolyUtil.<ModInteger>basePseudoRemainder(b, d);
// System.out.println("e = " + e);
assertTrue("gcd(a,b) | b" + e, e.isZERO());
}
}
/**
* GenPolynomial absolute factorization of a irreducible polynomial.
*
* @param P irreducible! GenPolynomial.
* @return factors container: [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i in K(alpha)[x] for
* suitable alpha and p_i irreducible over L[x], where K \subset K(alpha) \subset L is an
* algebraically closed field over K. <b>Note:</b> K(alpha) not yet minimal.
*/
public Factors<C> factorsAbsoluteIrreducible(GenPolynomial<C> P) {
if (P == null) {
throw new RuntimeException(this.getClass().getName() + " P == null");
}
if (P.isZERO()) {
return new Factors<C>(P);
}
GenPolynomialRing<C> pfac = P.ring; // K[x]
if (pfac.nvar <= 1) {
return baseFactorsAbsoluteIrreducible(P);
}
if (!pfac.coFac.isField()) {
throw new RuntimeException("only for field coefficients");
}
List<GenPolynomial<C>> factors = new ArrayList<GenPolynomial<C>>();
if (P.degree() <= 1) {
return new Factors<C>(P);
}
// find field extension K(alpha)
GenPolynomial<C> up = P;
RingFactory<C> cf = pfac.coFac;
long cr = cf.characteristic().longValue(); // char might be larger
if (cr == 0L) {
cr = Long.MAX_VALUE;
}
long rp = 0L;
for (int i = 0; i < (pfac.nvar - 1); i++) {
rp = 0L;
GenPolynomialRing<C> nfac = pfac.contract(1);
String[] vn = new String[] {pfac.getVars()[pfac.nvar - 1]};
GenPolynomialRing<GenPolynomial<C>> rfac =
new GenPolynomialRing<GenPolynomial<C>>(nfac, 1, pfac.tord, vn);
GenPolynomial<GenPolynomial<C>> upr = PolyUtil.<C>recursive(rfac, up);
// System.out.println("upr = " + upr);
GenPolynomial<C> ep;
do {
if (rp >= cr) {
throw new RuntimeException("elements of prime field exhausted: " + cr);
}
C r = cf.fromInteger(rp); // cf.random(rp);
// System.out.println("r = " + r);
ep = PolyUtil.<C>evaluateMain(nfac, upr, r);
// System.out.println("ep = " + ep);
rp++;
} while (!isSquarefree(ep) /*todo: || ep.degree() <= 1*/); // max deg
up = ep;
pfac = nfac;
}
up = up.monic();
if (debug) {
logger.info("P(" + rp + ") = " + up);
// System.out.println("up = " + up);
}
if (debug && !isSquarefree(up)) {
throw new RuntimeException("not irreducible up = " + up);
}
if (up.degree(0) <= 1) {
return new Factors<C>(P);
}
// find irreducible factor of up
List<GenPolynomial<C>> UF = baseFactorsSquarefree(up);
// System.out.println("UF = " + UF);
FactorsList<C> aUF = baseFactorsAbsoluteSquarefree(up);
// System.out.println("aUF = " + aUF);
AlgebraicNumberRing<C> arfac = aUF.findExtensionField();
// System.out.println("arfac = " + arfac);
long e = up.degree(0);
// search factor polynomial with smallest degree
for (int i = 0; i < UF.size(); i++) {
GenPolynomial<C> upi = UF.get(i);
long d = upi.degree(0);
if (1 <= d && d <= e) {
up = upi;
e = up.degree(0);
}
}
if (up.degree(0) <= 1) {
return new Factors<C>(P);
}
if (debug) {
logger.info("field extension by " + up);
}
List<GenPolynomial<AlgebraicNumber<C>>> afactors =
new ArrayList<GenPolynomial<AlgebraicNumber<C>>>();
// setup field extension K(alpha)
// String[] vars = new String[] { "z_" + Math.abs(up.hashCode() % 1000) };
String[] vars = pfac.newVars("z_");
pfac = pfac.clone();
String[] ovars = pfac.setVars(vars); // side effects!
GenPolynomial<C> aup = pfac.copy(up); // hack to exchange the variables
// AlgebraicNumberRing<C> afac = new AlgebraicNumberRing<C>(aup,true); // since irreducible
AlgebraicNumberRing<C> afac = arfac;
int depth = afac.depth();
// System.out.println("afac = " + afac);
GenPolynomialRing<AlgebraicNumber<C>> pafac =
new GenPolynomialRing<AlgebraicNumber<C>>(afac, P.ring.nvar, P.ring.tord, P.ring.getVars());
// System.out.println("pafac = " + pafac);
// convert to K(alpha)
GenPolynomial<AlgebraicNumber<C>> Pa =
PolyUtil.<C>convertToRecAlgebraicCoefficients(depth, pafac, P);
// System.out.println("Pa = " + Pa);
// factor over K(alpha)
FactorAbstract<AlgebraicNumber<C>> engine = FactorFactory.<C>getImplementation(afac);
afactors = engine.factorsSquarefree(Pa);
if (debug) {
logger.info("K(alpha) factors multi = " + afactors);
// System.out.println("K(alpha) factors = " + afactors);
}
if (afactors.size() <= 1) {
return new Factors<C>(P);
}
// normalize first factor to monic
GenPolynomial<AlgebraicNumber<C>> p1 = afactors.get(0);
AlgebraicNumber<C> p1c = p1.leadingBaseCoefficient();
if (!p1c.isONE()) {
GenPolynomial<AlgebraicNumber<C>> p2 = afactors.get(1);
afactors.remove(p1);
afactors.remove(p2);
p1 = p1.divide(p1c);
p2 = p2.multiply(p1c);
afactors.add(p1);
afactors.add(p2);
}
// recursion for splitting field
// find minimal field extension K(beta) \subset K(alpha)
return new Factors<C>(P, afac, Pa, afactors);
}
/**
* 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 base absolute factorization of a irreducible polynomial.
*
* @param P irreducible! univariate GenPolynomial.
* @return factors container: [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i in K(alpha)[x] for
* suitable alpha and p_i irreducible over L[x], where K \subset K(alpha) \subset L is an
* algebraically closed field over K. <b>Note:</b> K(alpha) not yet minimal.
*/
public Factors<C> baseFactorsAbsoluteIrreducible(GenPolynomial<C> P) {
if (P == null) {
throw new RuntimeException(this.getClass().getName() + " P == null");
}
if (P.isZERO()) {
return new Factors<C>(P);
}
// System.out.println("\nP_base_irred = " + 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");
}
if (P.degree(0) <= 1) {
return new Factors<C>(P);
}
// setup field extension K(alpha) where alpha = z_xx
// String[] vars = new String[] { "z_" + Math.abs(P.hashCode() % 1000) };
String[] vars = pfac.newVars("z_");
pfac = pfac.clone();
vars = pfac.setVars(vars);
GenPolynomial<C> aP = pfac.copy(P); // hack to exchange the variables
AlgebraicNumberRing<C> afac = new AlgebraicNumberRing<C>(aP, true); // since irreducible
if (logger.isInfoEnabled()) {
logger.info("K(alpha) = " + afac);
logger.info("K(alpha) = " + afac.toScript());
// System.out.println("K(alpha) = " + afac);
}
GenPolynomialRing<AlgebraicNumber<C>> pafac =
new GenPolynomialRing<AlgebraicNumber<C>>(afac, aP.ring.nvar, aP.ring.tord, /*old*/ vars);
// convert to K(alpha)
GenPolynomial<AlgebraicNumber<C>> Pa = PolyUtil.<C>convertToAlgebraicCoefficients(pafac, P);
if (logger.isInfoEnabled()) {
logger.info("P over K(alpha) = " + Pa);
// logger.info("P over K(alpha) = " + Pa.toScript());
// System.out.println("P in K(alpha) = " + Pa);
}
// factor over K(alpha)
FactorAbstract<AlgebraicNumber<C>> engine = FactorFactory.<C>getImplementation(afac);
// System.out.println("K(alpha) engine = " + engine);
List<GenPolynomial<AlgebraicNumber<C>>> factors = engine.baseFactorsSquarefree(Pa);
// System.out.println("factors = " + factors);
if (logger.isInfoEnabled()) {
logger.info("factors over K(alpha) = " + factors);
// System.out.println("factors over K(alpha) = " + factors);
}
List<GenPolynomial<AlgebraicNumber<C>>> faca =
new ArrayList<GenPolynomial<AlgebraicNumber<C>>>(factors.size());
;
List<Factors<AlgebraicNumber<C>>> facar = new ArrayList<Factors<AlgebraicNumber<C>>>();
for (GenPolynomial<AlgebraicNumber<C>> fi : factors) {
if (fi.degree(0) <= 1) {
faca.add(fi);
} else {
// System.out.println("fi.deg > 1 = " + fi);
FactorAbsolute<AlgebraicNumber<C>> aengine =
(FactorAbsolute<AlgebraicNumber<C>>) FactorFactory.<C>getImplementation(afac);
Factors<AlgebraicNumber<C>> fif = aengine.baseFactorsAbsoluteIrreducible(fi);
// System.out.println("fif = " + fif);
facar.add(fif);
}
}
if (facar.size() == 0) {
facar = null;
}
// find minimal field extension K(beta) \subset K(alpha)
return new Factors<C>(P, afac, Pa, faca, facar);
}
/** 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;
}