/**
* ResidueSolvableWordPolynomial left and right multiplication. Product with exponent vector.
*
* @param e exponent.
* @param f exponent.
* @return x<sup>e</sup> * this * x<sup>f</sup>, where * denotes solvable multiplication.
*/
@Override
public ResidueSolvableWordPolynomial<C> multiply(ExpVector e, ExpVector f) {
if (e == null || e.isZERO()) {
return this;
}
if (f == null || f.isZERO()) {
return this;
}
WordResidue<C> b = ring.getONECoefficient();
return multiply(b, e, b, f);
}
/**
* ResidueSolvableWordPolynomial multiplication. Left product with exponent vector.
*
* @param e exponent.
* @return x<sup>e</sup> * this, where * denotes solvable multiplication.
*/
@Override
public ResidueSolvableWordPolynomial<C> multiplyLeft(ExpVector e) {
if (e == null || e.isZERO()) {
return this;
}
ResidueSolvableWordPolynomial<C> Cp = ring.valueOf(e);
return Cp.multiply(this);
}
/**
* ResidueSolvableWordPolynomial multiplication. Commutative product with exponent vector.
*
* @param B solvable polynomial.
* @param f exponent vector.
* @return B*f, where * is commutative multiplication.
*/
protected ResidueSolvableWordPolynomial<C> shift(
ResidueSolvableWordPolynomial<C> B, ExpVector f) {
ResidueSolvableWordPolynomial<C> C = ring.getZERO().copy();
if (B == null || B.isZERO()) {
return C;
}
if (f == null || f.isZERO()) {
return B;
}
Map<ExpVector, WordResidue<C>> Cm = C.val;
Map<ExpVector, WordResidue<C>> Bm = B.val;
for (Map.Entry<ExpVector, WordResidue<C>> y : Bm.entrySet()) {
ExpVector e = y.getKey();
WordResidue<C> a = y.getValue();
ExpVector d = e.sum(f);
if (!a.isZERO()) {
Cm.put(d, a);
}
}
return C;
}
// cannot @Override, @NoOverride
public ResidueSolvableWordPolynomial<C> multiply(ResidueSolvableWordPolynomial<C> Bp) {
if (Bp == null || Bp.isZERO()) {
return ring.getZERO();
}
if (this.isZERO()) {
return this;
}
assert (ring.nvar == Bp.ring.nvar);
if (debug) {
logger.debug("ring = " + ring);
}
ExpVector Z = ring.evzero;
ResidueSolvableWordPolynomial<C> Dp = ring.getZERO().copy();
ResidueSolvableWordPolynomial<C> zero = ring.getZERO().copy();
WordResidue<C> one = ring.getONECoefficient();
Map<ExpVector, WordResidue<C>> A = val;
Map<ExpVector, WordResidue<C>> B = Bp.val;
Set<Map.Entry<ExpVector, WordResidue<C>>> Bk = B.entrySet();
for (Map.Entry<ExpVector, WordResidue<C>> y : A.entrySet()) {
WordResidue<C> a = y.getValue();
ExpVector e = y.getKey();
if (debug) logger.info("e = " + e + ", a = " + a);
for (Map.Entry<ExpVector, WordResidue<C>> x : Bk) {
WordResidue<C> b = x.getValue();
ExpVector f = x.getKey();
if (debug) logger.info("f = " + f + ", b = " + b);
int[] fp = f.dependencyOnVariables();
int fl1 = 0;
if (fp.length > 0) {
fl1 = fp[fp.length - 1];
}
int fl1s = ring.nvar + 1 - fl1;
// polynomial/residue coefficient multiplication
ResidueSolvableWordPolynomial<C> Cps = ring.getZERO().copy();
if (ring.polCoeff.coeffTable.isEmpty() || b.isConstant() || e.isZERO()) { // symmetric
Cps = new ResidueSolvableWordPolynomial<C>(ring, b, e);
if (debug) logger.info("symmetric coeff: b = " + b + ", e = " + e);
} else { // unsymmetric
if (debug) logger.info("unsymmetric coeff: b = " + b + ", e = " + e);
// recursive polynomial coefficient multiplication : e * b.val
RecSolvableWordPolynomial<C> rsp1 = new RecSolvableWordPolynomial<C>(ring.polCoeff, e);
RecSolvableWordPolynomial<C> rsp2 =
new RecSolvableWordPolynomial<C>(ring.polCoeff, b.val);
RecSolvableWordPolynomial<C> rsp3 = rsp1.multiply(rsp2);
Cps = ring.fromPolyCoefficients(rsp3);
}
if (debug) {
logger.info("coeff-poly: Cps = " + Cps);
}
// polynomial multiplication
ResidueSolvableWordPolynomial<C> Dps = ring.getZERO().copy();
ResidueSolvableWordPolynomial<C> Ds = null;
ResidueSolvableWordPolynomial<C> D1, D2;
if (ring.table.isEmpty() || Cps.isConstant() || f.isZERO()) { // symmetric
if (debug) logger.info("symmetric poly: b = " + b + ", e = " + e);
ExpVector g = e.sum(f);
if (Cps.isConstant()) {
Ds =
new ResidueSolvableWordPolynomial<C>(
ring, Cps.leadingBaseCoefficient(), g); // symmetric!
} else {
Ds = shift(Cps, f); // symmetric
}
} else { // eventually unsymmetric
if (debug) logger.info("unsymmetric poly: Cps = " + Cps + ", f = " + f);
for (Map.Entry<ExpVector, WordResidue<C>> z : Cps.val.entrySet()) {
// split g = g1 * g2, f = f1 * f2
WordResidue<C> c = z.getValue();
ExpVector g = z.getKey();
if (debug) logger.info("g = " + g + ", c = " + c);
int[] gp = g.dependencyOnVariables();
int gl1 = ring.nvar + 1;
if (gp.length > 0) {
gl1 = gp[0];
}
int gl1s = ring.nvar + 1 - gl1;
if (gl1s <= fl1s) { // symmetric
ExpVector h = g.sum(f);
if (debug) logger.info("disjoint poly: g = " + g + ", f = " + f + ", h = " + h);
Ds = (ResidueSolvableWordPolynomial<C>) zero.sum(one, h); // symmetric!
} else {
ExpVector g1 = g.subst(gl1, 0);
ExpVector g2 = Z.subst(gl1, g.getVal(gl1)); // bug el1, gl1
ExpVector g4;
ExpVector f1 = f.subst(fl1, 0);
ExpVector f2 = Z.subst(fl1, f.getVal(fl1));
if (debug) logger.info("poly, g1 = " + g1 + ", f1 = " + f1 + ", Dps = " + Dps);
if (debug) logger.info("poly, g2 = " + g2 + ", f2 = " + f2);
TableRelation<WordResidue<C>> rel = ring.table.lookup(g2, f2);
if (debug) logger.info("poly, g = " + g + ", f = " + f + ", rel = " + rel);
Ds = new ResidueSolvableWordPolynomial<C>(ring, rel.p); // ring.copy(rel.p);
if (rel.f != null) {
D2 = new ResidueSolvableWordPolynomial<C>(ring, one, rel.f);
Ds = Ds.multiply(D2);
if (rel.e == null) {
g4 = g2;
} else {
g4 = g2.subtract(rel.e);
}
ring.table.update(g4, f2, Ds);
}
if (rel.e != null) {
D1 = new ResidueSolvableWordPolynomial<C>(ring, one, rel.e);
Ds = D1.multiply(Ds);
ring.table.update(g2, f2, Ds);
}
if (!f1.isZERO()) {
D2 = new ResidueSolvableWordPolynomial<C>(ring, one, f1);
Ds = Ds.multiply(D2);
// ring.table.update(?,f1,Ds)
}
if (!g1.isZERO()) {
D1 = new ResidueSolvableWordPolynomial<C>(ring, one, g1);
Ds = D1.multiply(Ds);
// ring.table.update(e1,?,Ds)
}
}
Ds = Ds.multiplyLeft(c); // assume c commutes with Cs
Dps = (ResidueSolvableWordPolynomial<C>) Dps.sum(Ds);
} // end Dps loop
Ds = Dps;
}
Ds = Ds.multiplyLeft(a); // multiply(a,b); // non-symmetric
if (debug) logger.debug("Ds = " + Ds);
Dp = (ResidueSolvableWordPolynomial<C>) Dp.sum(Ds);
} // end B loop
} // end A loop
return Dp;
}