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/*
* $Id: RPseudoReductionSeq.java 4061 2012-07-27 12:03:20Z kredel $
*/
package edu.jas.gbufd;
import java.util.List;
import java.util.Map;
import org.apache.log4j.Logger;
import edu.jas.poly.ExpVector;
import edu.jas.poly.GenPolynomial;
import edu.jas.structure.RegularRingElem;
/**
* Polynomial regular ring pseudo reduction sequential use algorithm. Implements
* fraction free normalform algorithm.
* @param coefficient type
* @author Heinz Kredel
*/
public class RPseudoReductionSeq> extends RReductionSeq implements
RPseudoReduction {
private static final Logger logger = Logger.getLogger(RPseudoReductionSeq.class);
private final boolean debug = logger.isDebugEnabled();
/**
* Constructor.
*/
public RPseudoReductionSeq() {
}
/**
* Normalform using r-reduction.
* @param Ap polynomial.
* @param Pp polynomial list.
* @return r-nf(Ap) with respect to Pp.
*/
@Override
@SuppressWarnings("unchecked")
public GenPolynomial normalform(List> Pp, GenPolynomial Ap) {
if (Pp == null || Pp.isEmpty()) {
return Ap;
}
if (Ap == null || Ap.isZERO()) {
return Ap;
}
int l;
GenPolynomial[] P;
synchronized (Pp) {
l = Pp.size();
P = (GenPolynomial[]) new GenPolynomial[l];
//P = Pp.toArray();
for (int i = 0; i < Pp.size(); i++) {
P[i] = Pp.get(i);
}
}
//System.out.println("l = " + l);
Map.Entry m;
ExpVector[] htl = new ExpVector[l];
C[] lbc = (C[]) new RegularRingElem[l]; // want
GenPolynomial[] p = (GenPolynomial[]) new GenPolynomial[l];
int i;
int j = 0;
for (i = 0; i < l; i++) {
if (P[i] == null) {
continue;
}
p[i] = P[i].abs();
m = p[i].leadingMonomial();
if (m != null) {
p[j] = p[i];
htl[j] = m.getKey();
lbc[j] = m.getValue();
j++;
}
}
l = j;
ExpVector e, f;
C a;
C r = null;
boolean mt = false;
GenPolynomial R = Ap.ring.getZERO();
GenPolynomial Q = null;
GenPolynomial S = Ap;
while (S.length() > 0) {
m = S.leadingMonomial();
e = m.getKey();
a = m.getValue();
//System.out.println("--a = " + a);
for (i = 0; i < l; i++) {
mt = e.multipleOf(htl[i]);
if (mt) {
C c = lbc[i];
//r = a.idempotent().multiply( c.idempotent() );
r = a.idempotentAnd(c);
mt = !r.isZERO(); // && mt
if (mt) {
f = e.subtract(htl[i]);
if (a.remainder(c).isZERO()) { //c.isUnit() ) {
a = a.divide(c);
if (a.isZERO()) {
throw new ArithmeticException("a.isZERO()");
}
} else {
c = c.fillOne();
S = S.multiply(c);
R = R.multiply(c);
}
Q = p[i].multiply(a, f);
S = S.subtract(Q);
f = S.leadingExpVector();
if (!e.equals(f)) {
a = Ap.ring.coFac.getZERO();
break;
}
a = S.leadingBaseCoefficient();
}
}
}
if (!a.isZERO()) { //! mt ) {
//logger.debug("irred");
R = R.sum(a, e);
S = S.reductum();
}
}
return R.abs(); // not monic if not boolean closed
}
/**
* Normalform using r-reduction.
* @param Pp polynomial list.
* @param Ap polynomial.
* @return ( nf(Ap), mf ) with respect to Pp and mf as multiplication factor
* for Ap.
*/
@SuppressWarnings("unchecked")
public PseudoReductionEntry normalformFactor(List> Pp, GenPolynomial Ap) {
if (Ap == null) {
return null;
}
C mfac = Ap.ring.getONECoefficient();
PseudoReductionEntry pf = new PseudoReductionEntry(Ap, mfac);
if (Pp == null || Pp.isEmpty()) {
return pf;
}
if (Ap.isZERO()) {
return pf;
}
int l;
GenPolynomial[] P;
synchronized (Pp) {
l = Pp.size();
P = (GenPolynomial[]) new GenPolynomial[l];
//P = Pp.toArray();
for (int i = 0; i < Pp.size(); i++) {
P[i] = Pp.get(i);
}
}
//System.out.println("l = " + l);
Map.Entry m;
ExpVector[] htl = new ExpVector[l];
C[] lbc = (C[]) new RegularRingElem[l]; // want
GenPolynomial[] p = (GenPolynomial[]) new GenPolynomial[l];
int i;
int j = 0;
for (i = 0; i < l; i++) {
if (P[i] == null) {
continue;
}
p[i] = P[i].abs();
m = p[i].leadingMonomial();
if (m != null) {
p[j] = p[i];
htl[j] = m.getKey();
lbc[j] = m.getValue();
j++;
}
}
l = j;
ExpVector e, f;
C a;
C r = null;
boolean mt = false;
GenPolynomial R = Ap.ring.getZERO();
GenPolynomial Q = null;
GenPolynomial S = Ap;
while (S.length() > 0) {
m = S.leadingMonomial();
e = m.getKey();
a = m.getValue();
//System.out.println("--a = " + a);
for (i = 0; i < l; i++) {
mt = e.multipleOf(htl[i]);
if (mt) {
C c = lbc[i];
//r = a.idempotent().multiply( c.idempotent() );
r = a.idempotentAnd(c);
mt = !r.isZERO(); // && mt
if (mt) {
f = e.subtract(htl[i]);
if (a.remainder(c).isZERO()) { //c.isUnit() ) {
a = a.divide(c);
if (a.isZERO()) {
throw new ArithmeticException("a.isZERO()");
}
} else {
c = c.fillOne();
S = S.multiply(c);
R = R.multiply(c);
mfac = mfac.multiply(c);
}
Q = p[i].multiply(a, f);
S = S.subtract(Q);
f = S.leadingExpVector();
if (!e.equals(f)) {
a = Ap.ring.coFac.getZERO();
break;
}
a = S.leadingBaseCoefficient();
}
}
}
if (!a.isZERO()) { //! mt ) {
//logger.debug("irred");
R = R.sum(a, e);
S = S.reductum();
}
}
pf = new PseudoReductionEntry(R, mfac); //.abs(); // not monic if not boolean closed
return pf;
}
/**
* Normalform with recording. Note: Only meaningfull if all divisions
* are exact. Compute first the multiplication factor m with
* normalform(Pp,Ap,m), then call this method with
* normalform(row,Pp,m*Ap).
* @param row recording matrix, is modified.
* @param Pp a polynomial list for reduction.
* @param Ap a polynomial.
* @return nf(Pp,Ap), the normal form of Ap wrt. Pp.
*/
@Override
@SuppressWarnings("unchecked")
public GenPolynomial normalform(List> row, List> Pp,
GenPolynomial Ap) {
if (Pp == null || Pp.isEmpty()) {
return Ap;
}
if (Ap == null || Ap.isZERO()) {
return Ap;
}
int l;
GenPolynomial[] P;
synchronized (Pp) {
l = Pp.size();
P = (GenPolynomial[]) new GenPolynomial[l];
//P = Pp.toArray();
for (int i = 0; i < Pp.size(); i++) {
P[i] = Pp.get(i);
}
}
//System.out.println("l = " + l);
Map.Entry m;
ExpVector[] htl = new ExpVector[l];
C[] lbc = (C[]) new RegularRingElem[l]; // want
GenPolynomial[] p = (GenPolynomial[]) new GenPolynomial[l];
int i;
int j = 0;
for (i = 0; i < l; i++) {
p[i] = P[i];
m = p[i].leadingMonomial();
if (m != null) {
p[j] = p[i];
htl[j] = m.getKey();
lbc[j] = m.getValue();
j++;
}
}
l = j;
ExpVector e, f;
C a, b;
C r = null;
boolean mt = false;
GenPolynomial fac = null;
GenPolynomial zero = Ap.ring.getZERO();
GenPolynomial R = Ap.ring.getZERO();
GenPolynomial Q = null;
GenPolynomial S = Ap;
while (S.length() > 0) {
m = S.leadingMonomial();
e = m.getKey();
a = m.getValue();
for (i = 0; i < l; i++) {
mt = e.multipleOf(htl[i]);
if (mt) {
C c = lbc[i];
//r = a.idempotent().multiply( c.idempotent() );
r = a.idempotentAnd(c);
//System.out.println("r = " + r);
mt = !r.isZERO(); // && mt
if (mt) {
b = a.remainder(c);
if (b.isZERO()) {
a = a.divide(c);
if (a.isZERO()) {
throw new ArithmeticException("a.isZERO()");
}
} else {
c = c.fillOne();
S = S.multiply(c);
R = R.multiply(c);
}
f = e.subtract(htl[i]);
if (debug) {
logger.info("red div = " + f);
}
Q = p[i].multiply(a, f);
S = S.subtract(Q); // not ok with reductum
fac = row.get(i);
if (fac == null) {
fac = zero.sum(a, f);
} else {
fac = fac.sum(a, f);
}
row.set(i, fac);
f = S.leadingExpVector();
if (!e.equals(f)) {
a = Ap.ring.coFac.getZERO();
break;
}
a = S.leadingBaseCoefficient();
}
}
}
if (!a.isZERO()) { //! mt ) {
//logger.debug("irred");
R = R.sum(a, e);
S = S.reductum();
}
}
return R; //.abs(); // not monic if not boolean closed
}
/*
* -------- boolean closure stuff -----------------------------------------
* -------- is all in superclass
*/
}
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