/**
* 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);
}
/** Test addition. */
public void testAddition() {
a = fac.random(ll);
b = fac.random(ll);
c = a.sum(b);
d = c.subtract(b);
assertEquals("a+b-b = a", a, d);
c = fac.random(ll);
ExpVector u = ExpVector.EVRAND(rl, el, q);
BigQuaternion x = BigQuaternion.QRAND(kl);
b = new GenPolynomial<BigQuaternion>(fac, x, u);
c = a.sum(b);
d = a.sum(x, u);
assertEquals("a+p(x,u) = a+(x,u)", c, d);
c = a.subtract(b);
d = a.subtract(x, u);
assertEquals("a-p(x,u) = a-(x,u)", c, d);
a = new GenPolynomial<BigQuaternion>(fac);
b = new GenPolynomial<BigQuaternion>(fac, x, u);
c = b.sum(a);
d = a.sum(x, u);
assertEquals("a+p(x,u) = a+(x,u)", c, d);
c = a.subtract(b);
d = a.subtract(x, u);
assertEquals("a-p(x,u) = a-(x,u)", c, d);
}
/**
* 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;
}
/** Test iterators. */
public void testIterators() {
// integers
BigInteger rf = new BigInteger();
// System.out.println("rf = " + rf);
// polynomials over integral numbers
GenPolynomialRing<BigInteger> pf = new GenPolynomialRing<BigInteger>(rf, rl);
// System.out.println("pf = " + pf);
// random polynomial
GenPolynomial<BigInteger> p = pf.random(kl, 2 * ll, el, q);
// System.out.println("p = " + p);
// test monomials
for (Monomial<BigInteger> m : p) {
// System.out.println("m = " + m);
assertFalse("m.c == 0 ", m.coefficient().isZERO());
assertFalse("m.e < (0) ", m.exponent().signum() < 0);
}
// test exponents
Iterator<ExpVector> et = p.exponentIterator();
while (et.hasNext()) {
ExpVector e = et.next();
// System.out.println("e = " + e);
assertFalse("e < (0) ", e.signum() < 0);
}
// test coefficents
Iterator<BigInteger> ct = p.coefficientIterator();
while (ct.hasNext()) {
BigInteger i = ct.next();
// System.out.println("i = " + i);
assertFalse("i == 0 ", i.isZERO());
}
}
/**
* Random solvable polynomial.
*
* @param k size of random coefficients.
* @param l number of terms.
* @param d maximal degree in each variable.
* @param q density of nozero exponents.
* @param rnd is a source for random bits.
* @return a random solvable polynomial.
*/
@Override
public GenSolvablePolynomial<C> random(int k, int l, int d, float q, Random rnd) {
GenSolvablePolynomial<C> r = getZERO(); // .clone();
// copy( ZERO );
// new GenPolynomial<C>( this, getZERO().val );
ExpVector e;
C a;
// add random coeffs and exponents
for (int i = 0; i < l; i++) {
e = ExpVector.EVRAND(nvar, d, q, rnd);
a = coFac.random(k, rnd);
r = (GenSolvablePolynomial<C>) r.sum(a, e);
// somewhat inefficient but clean
}
return r;
}
/**
* Reverse inverse graded lexicographical compare part. Compare entries between begin and end
* (-1).
*
* @param U
* @param V
* @param begin
* @param end
* @return 0 if U == V, -1 if U < V, 1 if U > V.
*/
public static int EVRIGLC(ExpVector U, ExpVector V, int begin, int end) {
return U.revInvGradCompareTo(V, begin, end);
}
/**
* Reverse inverse graded lexicographical compare.
*
* @param U
* @param V
* @return 0 if U == V, -1 if U < V, 1 if U > V.
*/
public static int EVRIGLC(ExpVector U, ExpVector V) {
return U.revInvGradCompareTo(V);
}
/**
* Reverse inverse lexicographical compare part. Compare entries between begin and end (-1).
*
* @param U
* @param V
* @param begin
* @param end
* @return 0 if U == V, -1 if U < V, 1 if U > V.
*/
public static int EVRILCP(ExpVector U, ExpVector V, int begin, int end) {
return U.revInvLexCompareTo(V, begin, end);
}
/**
* Reverse inverse lexicographical compare.
*
* @param U
* @param V
* @return 0 if U == V, -1 if U < V, 1 if U > V.
*/
public static int EVRILCP(ExpVector U, ExpVector V) {
return U.revInvLexCompareTo(V);
}
/**
* ExpVector divides test. Test if V is component wise greater or equal to this.
*
* @param V
* @return true if this divides V, else false.
*/
public boolean divides(ExpVector V) {
return V.multipleOf(this);
// return EVMT(V, this);
}
/**
* ExpVector summation.
*
* @param U
* @param V
* @return U+V.
*/
public static ExpVector EVSUM(ExpVector U, ExpVector V) {
return U.sum(V);
}
/**
* ExpVector substitution. Clone and set exponent to d at position i.
*
* @param U
* @param i position.
* @param d new exponent.
* @return substituted ExpVector.
*/
public static ExpVector EVSU(ExpVector U, int i, long d) {
return U.subst(i, d);
}
/**
* ExpVector least common multiple.
*
* @param U
* @param V
* @return component wise maximum of U and V.
*/
public static ExpVector EVLCM(ExpVector U, ExpVector V) {
return U.lcm(V);
}
/**
* ExpVector maximal degree.
*
* @param U
* @return maximal exponent.
*/
public static long EVMDEG(ExpVector U) {
return U.maxDeg();
}
/**
* ExpVector weighted degree.
*
* @param w weights.
* @param U
* @return weighted sum of all exponents.
*/
public static long EVWDEG(long[][] w, ExpVector U) {
return U.weightDeg(w);
}
/**
* ExpVector total degree.
*
* @param U
* @return sum of all exponents.
*/
public static long EVTDEG(ExpVector U) {
return U.totalDeg();
}
/**
* ExpVector sign.
*
* @param U
* @return 0 if U is zero, -1 if some entry is negative, 1 if no entry is negativ and at least one
* entry is positive.
*/
public static int EVSIGN(ExpVector U) {
return U.signum();
}
/**
* ExpVector substitution. Clone and set exponent to d at position i.
*
* @param i position.
* @param d new exponent.
* @return substituted ExpVector.
*/
public ExpVector subst(int i, long d) {
ExpVector V = (ExpVector) this.clone();
long e = V.setVal(i, d);
return V;
// return EVSU(this, i, d);
}
/**
* Inverse weighted lexicographical compare.
*
* @param w weight array.
* @param U
* @param V
* @return 0 if U == V, -1 if U < V, 1 if U > V.
*/
public static int EVIWLC(long[][] w, ExpVector U, ExpVector V) {
return U.invWeightCompareTo(w, V);
}
/**
* ExpVector absolute value.
*
* @param U
* @return abs(U).
*/
public static ExpVector EVABS(ExpVector U) {
return U.abs();
}
/**
* Inverse weighted lexicographical compare part. Compare entries between begin and end (-1).
*
* @param w weight array.
* @param U
* @param V
* @param begin
* @param end
* @return 0 if U == V, -1 if U < V, 1 if U > V.
*/
public static int EVIWLC(long[][] w, ExpVector U, ExpVector V, int begin, int end) {
return U.invWeightCompareTo(w, V, begin, end);
}
/**
* ExpVector difference. Result may have negative entries.
*
* @param U
* @param V
* @return U-V.
*/
public static ExpVector EVDIF(ExpVector U, ExpVector V) {
return U.subtract(V);
}
// 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;
}
/**
* ExpVector multiple test. Test if U is component wise greater or equal to V.
*
* @param U
* @param V
* @return true if U is a multiple of V, else false.
*/
public static boolean EVMT(ExpVector U, ExpVector V) {
return U.multipleOf(V);
}
/**
* ExpVector greatest common divisor.
*
* @param U
* @param V
* @return component wise minimum of U and V.
*/
public static ExpVector EVGCD(ExpVector U, ExpVector V) {
return U.gcd(V);
}
/**
* ExpVector negate.
*
* @param U
* @return -U.
*/
public static ExpVector EVNEG(ExpVector U) {
return U.negate();
}
/**
* ExpVector dependency on variables.
*
* @param U
* @return array of indices where U has positive exponents.
*/
public static int[] EVDOV(ExpVector U) {
return U.dependencyOnVariables();
}
/**
* Minimal ordered groebner basis.
*
* @param Fp a Groebner base.
* @return a reduced Groebner base of Fp.
*/
@SuppressWarnings("cast")
@Override
public List<GenPolynomial<C>> minimalGB(List<GenPolynomial<C>> Fp) {
GenPolynomial<C> a;
ArrayList<GenPolynomial<C>> G;
G = new ArrayList<GenPolynomial<C>>(Fp.size());
ListIterator<GenPolynomial<C>> it = Fp.listIterator();
while (it.hasNext()) {
a = it.next();
if (a.length() != 0) { // always true
// already monic a = a.monic();
G.add(a);
}
}
if (G.size() <= 1) {
return G;
}
ExpVector e;
ExpVector f;
GenPolynomial<C> p;
ArrayList<GenPolynomial<C>> F;
F = new ArrayList<GenPolynomial<C>>(G.size());
boolean mt;
while (G.size() > 0) {
a = G.remove(0);
e = a.leadingExpVector();
it = G.listIterator();
mt = false;
while (it.hasNext() && !mt) {
p = it.next();
f = p.leadingExpVector();
mt = e.multipleOf(f);
}
it = F.listIterator();
while (it.hasNext() && !mt) {
p = it.next();
f = p.leadingExpVector();
mt = e.multipleOf(f);
}
if (!mt) {
F.add(a);
} else {
// System.out.println("dropped " + a.length());
}
}
G = F;
if (G.size() <= 1) {
return G;
}
Collections.reverse(G); // important for lex GB
MiMPIReducerServer<C>[] mirs = (MiMPIReducerServer<C>[]) new MiMPIReducerServer[G.size()];
int i = 0;
F = new ArrayList<GenPolynomial<C>>(G.size());
while (G.size() > 0) {
a = G.remove(0);
// System.out.println("doing " + a.length());
List<GenPolynomial<C>> R = new ArrayList<GenPolynomial<C>>(G.size() + F.size());
R.addAll(G);
R.addAll(F);
mirs[i] = new MiMPIReducerServer<C>(R, a);
pool.addJob(mirs[i]);
i++;
F.add(a);
}
G = F;
F = new ArrayList<GenPolynomial<C>>(G.size());
for (i = 0; i < mirs.length; i++) {
a = mirs[i].getNF();
F.add(a);
}
return F;
}