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/*
* $Id: SquarefreeFiniteFieldCharP.java 4125 2012-08-19 19:05:22Z kredel $
*/
package edu.jas.ufd;
import java.util.Map;
import java.util.SortedMap;
import java.util.TreeMap;
import org.apache.log4j.Logger;
import edu.jas.arith.BigInteger;
import edu.jas.poly.ExpVector;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenPolynomialRing;
import edu.jas.poly.Monomial;
import edu.jas.structure.GcdRingElem;
import edu.jas.structure.Power;
import edu.jas.structure.RingFactory;
/**
* Squarefree decomposition for finite coefficient fields of characteristic p.
* @author Heinz Kredel
*/
public class SquarefreeFiniteFieldCharP> extends SquarefreeFieldCharP {
private static final Logger logger = Logger.getLogger(SquarefreeFiniteFieldCharP.class);
//private final boolean debug = logger.isDebugEnabled();
/**
* Constructor.
*/
public SquarefreeFiniteFieldCharP(RingFactory fac) {
super(fac);
// isFinite() predicate now present
if (!fac.isFinite()) {
throw new IllegalArgumentException("fac must be finite");
}
}
/* --------- char-th roots --------------------- */
/**
* Characteristics root of a coefficient. Note: not needed at the
* moment.
* @param p coefficient.
* @return [p -> k] if exists k with e=k*charactristic(c) and c = p**e,
* else null.
*/
public SortedMap rootCharacteristic(C p) {
if (p == null) {
throw new IllegalArgumentException(this.getClass().getName() + " p == null");
}
// already checked in constructor:
//java.math.BigInteger c = p.factory().characteristic();
//if ( c.signum() == 0 ) {
// return null;
//}
SortedMap root = new TreeMap();
if (p.isZERO()) {
return root;
}
// true for finite fields:
root.put(p, 1L);
return root;
}
/**
* Characteristics root of a coefficient.
* @param c coefficient.
* @return r with r**p == c, if such an r exists, else null.
*/
public C coeffRootCharacteristic(C c) {
if (c == null || c.isZERO()) {
return c;
}
C r = c;
if (aCoFac == null && qCoFac == null) {
// case ModInteger: c**p == c
return r;
}
if (aCoFac != null) {
// case AlgebraicNumber: r = c**(p**(d-1)), r**p == c
long d = aCoFac.totalExtensionDegree();
//System.out.println("d = " + d);
if (d <= 1) {
return r;
}
BigInteger p = new BigInteger(aCoFac.characteristic());
BigInteger q = Power. positivePower(p, d - 1);
//System.out.println("p**(d-1) = " + q);
r = Power. positivePower(r, q.getVal());
//System.out.println("r**q = " + r);
return r;
}
if (qCoFac != null) {
throw new UnsupportedOperationException("case QuotientRing not yet implemented");
}
return r;
}
/**
* Characteristics root of a polynomial. Note: call only in
* recursion.
* @param P polynomial.
* @return [p -> k] if exists k with e=k*charactristic(P) and P = p**e,
* else null.
*/
public SortedMap, Long> rootCharacteristic(GenPolynomial P) {
if (P == null) {
throw new IllegalArgumentException(this.getClass().getName() + " P == null");
}
java.math.BigInteger c = P.ring.characteristic();
if (c.signum() == 0) {
return null;
}
SortedMap, Long> root = new TreeMap, Long>();
if (P.isZERO()) {
return root;
}
if (P.isONE()) {
root.put(P, 1L);
return root;
}
SortedMap, Long> sf = squarefreeFactors(P);
if (logger.isInfoEnabled()) {
logger.info("sf = " + sf);
}
// better: test if sf.size() == 1 // not ok
Long k = null;
for (Map.Entry, Long> me : sf.entrySet()) {
GenPolynomial p = me.getKey();
if (p.isConstant()) {
//System.out.println("p,const = " + p);
continue;
}
Long e = me.getValue(); //sf.get(p);
java.math.BigInteger E = new java.math.BigInteger(e.toString());
java.math.BigInteger r = E.remainder(c);
if (!r.equals(java.math.BigInteger.ZERO)) {
//System.out.println("r = " + r);
return null;
}
if (k == null) {
k = e;
} else if (k.compareTo(e) >= 0) {
k = e;
}
}
// now c divides all exponents
Long cl = c.longValue();
GenPolynomial rp = P.ring.getONE();
for (Map.Entry, Long> me : sf.entrySet()) {
GenPolynomial q = me.getKey();
Long e = me.getValue(); // sf.get(q);
if (q.isConstant()) { // ensure p-th root
C qc = q.leadingBaseCoefficient();
//System.out.println("qc,const = " + qc + ", e = " + e);
if (e > 1L) {
qc = Power. positivePower(qc, e);
//e = 1L;
}
C qr = coeffRootCharacteristic(qc);
//System.out.println("qr,const = " + qr);
q = P.ring.getONE().multiply(qr);
root.put(q, 1L);
continue;
}
if (e > k) {
long ep = e / cl;
q = Power.> positivePower(q, ep);
}
rp = rp.multiply(q);
}
if (k != null) {
k = k / cl;
root.put(rp, k);
}
//System.out.println("sf,root = " + root);
return root;
}
/**
* GenPolynomial char-th root univariate polynomial. Base coefficient type
* must be finite field, that is ModInteger or
* AlgebraicNumber<ModInteger> etc.
* @param P GenPolynomial.
* @return char-th_rootOf(P), or null if no char-th root.
*/
@Override
public GenPolynomial baseRootCharacteristic(GenPolynomial P) {
if (P == null || P.isZERO()) {
return P;
}
GenPolynomialRing pfac = P.ring;
if (pfac.nvar > 1) {
// basePthRoot not possible by return type
throw new IllegalArgumentException(P.getClass().getName() + " only for univariate polynomials");
}
RingFactory rf = pfac.coFac;
if (rf.characteristic().signum() != 1) {
// basePthRoot not possible
throw new IllegalArgumentException(P.getClass().getName() + " only for char p > 0 " + rf);
}
long mp = rf.characteristic().longValue();
GenPolynomial d = pfac.getZERO().copy();
for (Monomial m : P) {
ExpVector f = m.e;
long fl = f.getVal(0);
if (fl % mp != 0) {
return null;
}
fl = fl / mp;
ExpVector e = ExpVector.create(1, 0, fl);
// for m.c exists a char-th root, since finite field
C r = coeffRootCharacteristic(m.c);
d.doPutToMap(e, r);
}
return d;
}
/**
* GenPolynomial char-th root univariate polynomial with polynomial
* coefficients.
* @param P recursive univariate GenPolynomial.
* @return char-th_rootOf(P), or null if P is no char-th root.
*/
@Override
public GenPolynomial> recursiveUnivariateRootCharacteristic(
GenPolynomial> P) {
if (P == null || P.isZERO()) {
return P;
}
GenPolynomialRing> pfac = P.ring;
if (pfac.nvar > 1) {
// basePthRoot not possible by return type
throw new IllegalArgumentException(P.getClass().getName() + " only for univariate polynomials");
}
RingFactory> rf = pfac.coFac;
if (rf.characteristic().signum() != 1) {
// basePthRoot not possible
throw new IllegalArgumentException(P.getClass().getName() + " only for char p > 0 " + rf);
}
long mp = rf.characteristic().longValue();
GenPolynomial> d = pfac.getZERO().copy();
for (Monomial> m : P) {
ExpVector f = m.e;
long fl = f.getVal(0);
if (fl % mp != 0) {
return null;
}
fl = fl / mp;
SortedMap, Long> sm = rootCharacteristic(m.c);
if (sm == null) {
return null;
}
if (logger.isInfoEnabled()) {
logger.info("sm,rec = " + sm);
}
GenPolynomial r = rf.getONE();
for (Map.Entry, Long> me : sm.entrySet()) {
GenPolynomial rp = me.getKey();
long gl = me.getValue(); //sm.get(rp);
if (gl > 1) {
rp = Power.> positivePower(rp, gl);
}
r = r.multiply(rp);
}
ExpVector e = ExpVector.create(1, 0, fl);
//System.out.println("put-root r = " + r + ", e = " + e);
d.doPutToMap(e, r);
}
return d;
}
}
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