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/*
* $Id: SolvableReductionAbstract.java 4104 2012-08-18 10:00:59Z 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.GenSolvablePolynomial;
import edu.jas.structure.RingElem;
/**
* Solvable polynomial Reduction abstract class. Implements common left, right
* S-Polynomial, left normalform and left irreducible set.
* @param coefficient type
* @author Heinz Kredel
*/
public abstract class SolvableReductionAbstract> implements SolvableReduction {
private static final Logger logger = Logger.getLogger(SolvableReductionAbstract.class);
private final boolean debug = logger.isDebugEnabled();
/**
* Constructor.
*/
public SolvableReductionAbstract() {
}
/**
* Left S-Polynomial.
* @param Ap solvable polynomial.
* @param Bp solvable polynomial.
* @return left-spol(Ap,Bp) the left S-polynomial of Ap and Bp.
*/
public GenSolvablePolynomial leftSPolynomial(GenSolvablePolynomial Ap, GenSolvablePolynomial Bp) {
if (logger.isInfoEnabled()) {
if (Bp == null || Bp.isZERO()) {
if (Ap != null) {
return Ap.ring.getZERO();
}
return null;
}
if (Ap == null || Ap.isZERO()) {
return Bp.ring.getZERO();
}
if (!Ap.ring.equals(Bp.ring)) {
logger.error("rings not equal");
}
}
Map.Entry ma = Ap.leadingMonomial();
Map.Entry mb = Bp.leadingMonomial();
ExpVector e = ma.getKey();
ExpVector f = mb.getKey();
ExpVector g = e.lcm(f);
ExpVector e1 = g.subtract(e);
ExpVector f1 = g.subtract(f);
C a = ma.getValue();
C b = mb.getValue();
GenSolvablePolynomial App = Ap.multiplyLeft(b, e1);
GenSolvablePolynomial Bpp = Bp.multiplyLeft(a, f1);
GenSolvablePolynomial Cp = (GenSolvablePolynomial) App.subtract(Bpp);
return Cp;
}
/**
* S-Polynomial with recording.
* @param S recording matrix, is modified.
* @param i index of Ap in basis list.
* @param Ap a polynomial.
* @param j index of Bp in basis list.
* @param Bp a polynomial.
* @return leftSpol(Ap, Bp), the left S-Polynomial for Ap and Bp.
*/
public GenSolvablePolynomial leftSPolynomial(List> S, int i,
GenSolvablePolynomial Ap, int j, GenSolvablePolynomial Bp) {
if (debug /*logger.isInfoEnabled()*/) {
if (Bp == null || Bp.isZERO()) {
throw new ArithmeticException("Spol B is zero");
}
if (Ap == null || Ap.isZERO()) {
throw new ArithmeticException("Spol A is zero");
}
if (!Ap.ring.equals(Bp.ring)) {
logger.error("rings not equal");
}
}
Map.Entry ma = Ap.leadingMonomial();
Map.Entry mb = Bp.leadingMonomial();
ExpVector e = ma.getKey();
ExpVector f = mb.getKey();
ExpVector g = e.lcm(f);
ExpVector e1 = g.subtract(e);
ExpVector f1 = g.subtract(f);
C a = ma.getValue();
C b = mb.getValue();
GenSolvablePolynomial App = Ap.multiplyLeft(b, e1);
GenSolvablePolynomial Bpp = Bp.multiplyLeft(a, f1);
GenSolvablePolynomial Cp = (GenSolvablePolynomial) App.subtract(Bpp);
GenSolvablePolynomial zero = Ap.ring.getZERO();
GenSolvablePolynomial As = (GenSolvablePolynomial) zero.sum(b.negate(), e1);
GenSolvablePolynomial Bs = (GenSolvablePolynomial) zero.sum(a, f1);
S.set(i, As);
S.set(j, Bs);
return Cp;
}
/**
* Left Normalform Set.
* @param Ap solvable polynomial list.
* @param Pp solvable polynomial list.
* @return list of left-nf(a) with respect to Pp for all a in Ap.
*/
public List> leftNormalform(List> Pp,
List> Ap) {
if (Pp == null || Pp.isEmpty()) {
return Ap;
}
if (Ap == null || Ap.isEmpty()) {
return Ap;
}
ArrayList> red = new ArrayList>();
for (GenSolvablePolynomial A : Ap) {
A = leftNormalform(Pp, A);
red.add(A);
}
return red;
}
/**
* Left irreducible set.
* @param Pp solvable polynomial list.
* @return a list P of solvable polynomials which are in normalform wrt. P.
*/
public List> leftIrreducibleSet(List> Pp) {
ArrayList> P = new ArrayList>();
for (GenSolvablePolynomial a : Pp) {
if (a.length() != 0) {
a = (GenSolvablePolynomial) a.monic();
P.add(a);
}
}
int l = P.size();
if (l <= 1)
return P;
int irr = 0;
ExpVector e;
ExpVector f;
GenSolvablePolynomial a;
Iterator> it;
logger.debug("irr = ");
while (irr != l) {
it = P.listIterator();
a = it.next();
P.remove(0);
e = a.leadingExpVector();
a = leftNormalform(P, a);
logger.debug(String.valueOf(irr));
if (a.length() == 0) {
l--;
if (l <= 1) {
return P;
}
} else {
f = a.leadingExpVector();
if (f.signum() == 0) {
P = new ArrayList>();
P.add((GenSolvablePolynomial) a.monic());
return P;
}
if (e.equals(f)) {
irr++;
} else {
irr = 0;
a = (GenSolvablePolynomial) a.monic();
}
P.add(a);
}
}
//System.out.println();
return P;
}
/**
* Is reduction of normal form.
* @param row recording matrix.
* @param Pp a solvable polynomial list for reduction.
* @param Ap a solvable polynomial.
* @param Np nf(Pp,Ap), a left normal form of Ap wrt. Pp.
* @return true, if Np + sum( row[i]*Pp[i] ) == Ap, else false.
*/
@SuppressWarnings("unchecked")
public boolean isLeftReductionNF(List> row, List> Pp,
GenSolvablePolynomial Ap, GenSolvablePolynomial Np) {
if (row == null && Pp == null) {
if (Ap == null) {
return Np == null;
}
return Ap.equals(Np);
}
if (row == null || Pp == null) {
return false;
}
if (row.size() != Pp.size()) {
return false;
}
GenSolvablePolynomial t = Np;
GenSolvablePolynomial r;
GenSolvablePolynomial p;
for (int m = 0; m < Pp.size(); m++) {
r = row.get(m);
p = Pp.get(m);
if (r != null && p != null) {
if (t == null) {
t = r.multiply(p);
} else {
t = (GenSolvablePolynomial) t.sum(r.multiply(p));
}
}
//System.out.println("r = " + r );
//System.out.println("p = " + p );
}
if (debug) {
logger.info("t = " + t);
logger.info("a = " + Ap);
}
if (t == null) {
if (Ap == null) {
return true;
}
return Ap.isZERO();
}
t = (GenSolvablePolynomial) t.subtract(Ap);
return t.isZERO();
}
/**
* Right S-Polynomial.
* @param Ap solvable polynomial.
* @param Bp solvable polynomial.
* @return right-spol(Ap,Bp) the right S-polynomial of Ap and Bp.
*/
@SuppressWarnings("unchecked")
public GenSolvablePolynomial rightSPolynomial(GenSolvablePolynomial Ap, GenSolvablePolynomial Bp) {
if (logger.isInfoEnabled()) {
if (Bp == null || Bp.isZERO()) {
if (Ap != null) {
return Ap.ring.getZERO();
}
return null;
}
if (Ap == null || Ap.isZERO()) {
return Bp.ring.getZERO();
}
if (!Ap.ring.equals(Bp.ring)) {
logger.error("rings not equal");
}
}
ExpVector e = Ap.leadingExpVector();
ExpVector f = Bp.leadingExpVector();
ExpVector g = e.lcm(f);
ExpVector e1 = g.subtract(e);
ExpVector f1 = g.subtract(f);
GenSolvablePolynomial App = Ap.multiply(e1);
GenSolvablePolynomial Bpp = Bp.multiply(f1);
C a = App.leadingBaseCoefficient();
C b = Bpp.leadingBaseCoefficient();
App = App.multiply(b);
Bpp = Bpp.multiply(a);
GenSolvablePolynomial Cp = (GenSolvablePolynomial) App.subtract(Bpp);
return Cp;
}
}
