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/*
* $Id: EReductionSeq.java 4115 2012-08-19 13:18:59Z kredel $
*/
package edu.jas.gb;
import java.util.ArrayList;
import java.util.Iterator;
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.RingElem;
/**
* Polynomial E-Reduction sequential use algorithm. Implements normalform.
* @param coefficient type
* @author Heinz Kredel
*/
public class EReductionSeq> extends DReductionSeq implements EReduction {
private static final Logger logger = Logger.getLogger(DReductionSeq.class);
/**
* Constructor.
*/
public EReductionSeq() {
}
/**
* Is top reducible.
* @param A polynomial.
* @param P polynomial list.
* @return true if A is top reducible with respect to P.
*/
//SuppressWarnings("unchecked") // not jet working
@Override
public boolean isTopReducible(List> P, GenPolynomial A) {
if (P == null || P.isEmpty()) {
return false;
}
if (A == null || A.isZERO()) {
return false;
}
boolean mt = false;
ExpVector e = A.leadingExpVector();
C a = A.leadingBaseCoefficient();
for (GenPolynomial p : P) {
mt = e.multipleOf(p.leadingExpVector());
if (mt) {
C b = p.leadingBaseCoefficient();
C r = a.remainder(b);
mt = !r.equals(a);
if (mt) {
return true;
}
}
}
return false;
}
/**
* Is in Normalform.
* @param Ap polynomial.
* @param Pp polynomial list.
* @return true if Ap is in normalform with respect to Pp.
*/
@SuppressWarnings("unchecked")
@Override
public boolean isNormalform(List> Pp, GenPolynomial Ap) {
if (Pp == null || Pp.isEmpty()) {
return true;
}
if (Ap == null || Ap.isZERO()) {
return true;
}
int l;
GenPolynomial[] P;
synchronized (Pp) {
l = Pp.size();
P = new GenPolynomial[l];
//P = Pp.toArray();
for (int i = 0; i < Pp.size(); i++) {
P[i] = Pp.get(i);
}
}
ExpVector[] htl = new ExpVector[l];
C[] lbc = (C[]) new RingElem[l]; // want
GenPolynomial[] p = new GenPolynomial[l];
Map.Entry m;
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;
boolean mt = false;
Map Am = Ap.getMap();
for (Map.Entry me : Am.entrySet()) {
ExpVector e = me.getKey();
C a = me.getValue(); //Am.get(e);
for (i = 0; i < l; i++) {
mt = e.multipleOf(htl[i]);
if (mt) {
C r = a.remainder(lbc[i]);
mt = !r.equals(a);
if (mt) {
return false;
}
}
}
}
return true;
}
/**
* Normalform using e-reduction.
* @param Ap polynomial.
* @param Pp polynomial list.
* @return e-nf(Ap) with respect to Pp.
*/
@SuppressWarnings("unchecked")
@Override
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).abs();
}
}
Map.Entry m;
ExpVector[] htl = new ExpVector[l];
C[] lbc = (C[]) new RingElem[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 = null;
ExpVector f = null;
C a = null;
C b = null;
C r = null;
GenPolynomial R = Ap.ring.getZERO();
GenPolynomial T = Ap.ring.getZERO();
GenPolynomial Q = null;
GenPolynomial S = Ap;
//try { // required to avoid a compiler error in the while loop
while (S.length() > 0) {
boolean mt = false;
m = S.leadingMonomial();
e = m.getKey();
a = m.getValue();
for (i = 0; i < l; i++) {
mt = e.multipleOf(htl[i]);
if (mt) {
f = e.subtract(htl[i]);
//logger.info("red div = " + f);
r = a.remainder(lbc[i]);
b = a.divide(lbc[i]);
if (f == null) { // compiler produced this case
System.out.println("f = null: " + e + ", " + htl[i]);
Q = p[i].multiply(b);
} else {
Q = p[i].multiply(b, f);
}
S = S.subtract(Q); // ok also with reductum
//System.out.println(" r = " + r);
a = r;
if (r.isZERO()) {
break;
}
}
}
if (!a.isZERO()) { //! mt ) {
//logger.debug("irred");
R = R.sum(a, e);
//S = S.subtract( a, e );
S = S.reductum();
}
//System.out.println(" R = " + R);
//System.out.println(" S = " + S);
}
//} catch (Exception ex) {
// System.out.println("R = " + R);
// System.out.println("S = " + S);
// System.out.println("f = " + f + ", " + e + ", " + htl[i]);
// System.out.println("a = " + a + ", " + b + ", " + r + ", " + lbc[i]);
// //throw ex;
// return T;
//}
return R.abs();
}
/**
* Normalform with recording.
* @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")
// not jet working
public GenPolynomial normalform(List> row, List> Pp,
GenPolynomial Ap) {
if (Pp == null || Pp.isEmpty()) {
return Ap;
}
if (Ap == null || Ap.isZERO()) {
return Ap;
}
throw new UnsupportedOperationException("not jet implemented");
/*
int l = Pp.size();
GenPolynomial[] P = new GenPolynomial[l];
synchronized (Pp) {
//P = Pp.toArray();
for ( int i = 0; i < Pp.size(); i++ ) {
P[i] = Pp.get(i);
}
}
ExpVector[] htl = new ExpVector[ l ];
Object[] lbc = new Object[ l ]; // want
GenPolynomial[] p = new GenPolynomial[ l ];
Map.Entry m;
int j = 0;
int i;
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;
C a;
boolean mt = false;
GenPolynomial zero = Ap.ring.getZERO();
GenPolynomial R = Ap.ring.getZERO();
GenPolynomial fac = null;
// GenPolynomial T = null;
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 ) break;
}
if ( ! mt ) {
//logger.debug("irred");
R = R.sum( a, e );
S = S.subtract( a, e );
// System.out.println(" S = " + S);
//throw new RuntimeException("Syzygy no GB");
} else {
e = e.subtract( htl[i] );
//logger.info("red div = " + e);
C c = (C)lbc[i];
a = a.divide( c );
Q = p[i].multiply( a, e );
S = S.subtract( Q );
fac = row.get(i);
if ( fac == null ) {
fac = zero.sum( a, e );
} else {
fac = fac.sum( a, e );
}
row.set(i,fac);
}
}
return R;
*/
}
/**
* Irreducible set.
* @param Pp polynomial list.
* @return a list P of polynomials which are in normalform wrt. P.
*/
@Override
public List> irreducibleSet(List> Pp) {
ArrayList> P = new ArrayList>();
if (Pp == null) {
return null;
}
for (GenPolynomial a : Pp) {
if (!a.isZERO()) {
P.add(a);
}
}
int l = P.size();
if (l <= 1)
return P;
int irr = 0;
ExpVector e;
ExpVector f;
C c;
C d;
GenPolynomial a;
Iterator> it;
logger.debug("irr = ");
while (irr != l) {
//it = P.listIterator();
//a = P.get(0); //it.next();
a = P.remove(0);
e = a.leadingExpVector();
c = a.leadingBaseCoefficient();
a = normalform(P, a);
logger.debug(String.valueOf(irr));
if (a.isZERO()) {
l--;
if (l <= 1) {
return P;
}
} else {
f = a.leadingExpVector();
d = a.leadingBaseCoefficient();
if (e.equals(f) && c.equals(d)) {
irr++;
} else {
irr = 0;
}
P.add(a);
}
}
//System.out.println();
return P;
}
}
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