/*
 * $Id$
 */

package edu.jas.ufd;


import java.util.Map;
import java.util.SortedMap;
import java.util.TreeMap;

import org.apache.log4j.Logger;

import edu.jas.poly.ExpVector;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenPolynomialRing;
import edu.jas.poly.Monomial;
import edu.jas.poly.PolyUtil;
import edu.jas.structure.GcdRingElem;
import edu.jas.structure.Power;
import edu.jas.structure.RingFactory;


/**
 * Squarefree decomposition for infinite coefficient fields of characteristic p.
 * @author Heinz Kredel
 */

public class SquarefreeInfiniteFieldCharP> extends SquarefreeFieldCharP> {


    private static final Logger logger = Logger.getLogger(SquarefreeInfiniteFieldCharP.class);


    //private final boolean debug = logger.isDebugEnabled();


    /**
     * Squarefree engine for infinite ring of characteristic p base coefficients.
     */
    protected final SquarefreeAbstract qengine;


    /**
     * Constructor.
     */
    public SquarefreeInfiniteFieldCharP(RingFactory> fac) {
        super(fac);
        // isFinite() predicate now present
        if (fac.isFinite()) {
            throw new IllegalArgumentException("fac must be in-finite");
        }
        QuotientRing qfac = (QuotientRing) fac;
        GenPolynomialRing rfac = qfac.ring;
        qengine = (SquarefreeAbstract) SquarefreeFactory. getImplementation(rfac);
        //qengine = new SquarefreeFiniteFieldCharP(rfac.coFac);
        //qengine = new SquarefreeInfiniteRingCharP( rfac.coFac );
    }


    /* --------- quotient char-th roots --------------------- */


    /**
     * Squarefree factors of a Quotient.
     * @param P Quotient.
     * @return [p_1 -> e_1,...,p_k - > e_k] with P = prod_{i=1, ..., k}
     *         p_i**e_k.
     */
    @Override
    public SortedMap, Long> squarefreeFactors(Quotient P) {
        if (P == null) {
            throw new IllegalArgumentException(this.getClass().getName() + " P == null");
        }
        SortedMap, Long> factors = new TreeMap, Long>();
        if (P.isZERO()) {
            return factors;
        }
        if (P.isONE()) {
            factors.put(P, 1L);
            return factors;
        }
        GenPolynomial num = P.num;
        GenPolynomial den = P.den;
        QuotientRing pfac = P.ring;
        GenPolynomial one = pfac.ring.getONE();
        if (!num.isONE()) {
            SortedMap, Long> nfac = qengine.squarefreeFactors(num);
            //System.out.println("nfac = " + nfac);
            for (Map.Entry, Long> me : nfac.entrySet()) {
                GenPolynomial nfp = me.getKey();
                Quotient nf = new Quotient(pfac, nfp);
                factors.put(nf, me.getValue()); //nfac.get(nfp));
            }
        }
        if (den.isONE()) {
            if (factors.size() == 0) {
                factors.put(P, 1L);
            }
            return factors;
        }
        SortedMap, Long> dfac = qengine.squarefreeFactors(den);
        //System.out.println("dfac = " + dfac);
        for (Map.Entry, Long> me : dfac.entrySet()) {
            GenPolynomial dfp = me.getKey();
            Quotient df = new Quotient(pfac, one, dfp);
            factors.put(df, me.getValue()); //dfac.get(dfp));
        }
        if (factors.size() == 0) {
            factors.put(P, 1L);
        }
        return factors;
    }


    /**
     * Characteristics root of a Quotient.
     * @param P Quotient.
     * @return [p -> k] if exists k with e=charactristic(P)*k and P = p**e,
     *         else null.
     */
    public SortedMap, Long> rootCharacteristic(Quotient 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 (sf.size() == 0) {
            return null;
        }
        if (logger.isInfoEnabled()) {
            logger.info("sf,quot = " + sf);
        }
        // better: test if sf.size() == 2 // no, since num and den factors 
        Long k = null;
        Long cl = c.longValue();
        for (Map.Entry, Long> me : sf.entrySet()) {
            Quotient p = me.getKey();
            //System.out.println("p = " + p);
            if (p.isConstant()) { // todo: check for non-constants in coefficients
                continue;
            }
            Long e = me.getValue(); //sf.get(p);
            long E = e.longValue();
            long r = E % cl;
            if (r != 0) {
                //System.out.println("r = " + r);
                return null;
            }
            if (k == null) {
                k = e;
            } else if (k >= e) {
                k = e;
            }
        }
        if (k == null) {
            k = 1L; //return null;
        }
        // now c divides all exponents of non constant elements
        for (Map.Entry, Long> me : sf.entrySet()) {
            Quotient q = me.getKey();
            Long e = me.getValue(); //sf.get(q);
            //System.out.println("q = " + q + ", e = " + e);
            if (e >= k) {
                e = e / cl;
                //q = Power.> positivePower(q, e);
                root.put(q, e);
            } else { // constant case
                root.put(q, e);
            }
        }
        //System.out.println("root = " + root);
        return root;
    }


    /**
     * GenPolynomial char-th root main variable.
     * @param P univariate GenPolynomial with Quotient coefficients.
     * @return char-th_rootOf(P), or null, if P is no char-th root.
     */
    public GenPolynomial> rootCharacteristic(GenPolynomial> P) {
        if (P == null || P.isZERO()) {
            return P;
        }
        GenPolynomialRing> pfac = P.ring;
        if (pfac.nvar > 1) {
            // go to recursion
            GenPolynomialRing> cfac = pfac.contract(1);
            GenPolynomialRing>> rfac = new GenPolynomialRing>>(
                            cfac, 1);
            GenPolynomial>> Pr = PolyUtil.> recursive(rfac, P);
            GenPolynomial>> Prc = recursiveUnivariateRootCharacteristic(Pr);
            if (Prc == null) {
                return null;
            }
            GenPolynomial> D = PolyUtil.> distribute(pfac, Prc);
            return D;
        }
        RingFactory> rf = pfac.coFac;
        if (rf.characteristic().signum() != 1) {
            // basePthRoot not possible
            throw new IllegalArgumentException(P.getClass().getName() + " only for ModInteger polynomials "
                            + 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,root = " + sm);
            }
            Quotient r = rf.getONE();
            for (Map.Entry, Long> me : sm.entrySet()) {
                Quotient 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);
            d.doPutToMap(e, r);
        }
        logger.info("sm,root,d = " + d);
        return d;
    }


    /**
     * GenPolynomial char-th root univariate polynomial.
     * @param P GenPolynomial.
     * @return char-th_rootOf(P).
     */
    @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) {
            //System.out.println("m = " + m);
            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,base,root = " + sm);
            }
            Quotient r = rf.getONE();
            for (Map.Entry, Long> me : sm.entrySet()) {
                Quotient rp = me.getKey();
                //System.out.println("rp = " + rp);
                long gl = me.getValue(); //sm.get(rp);
                //System.out.println("gl = " + gl);
                Quotient re = rp;
                if (gl > 1) {
                    re = Power.> positivePower(rp, gl);
                }
                //System.out.println("re = " + re);
                r = r.multiply(re);
            }
            ExpVector e = ExpVector.create(1, 0, fl);
            d.doPutToMap(e, r);
        }
        if (logger.isInfoEnabled()) {
            logger.info("sm,base,d = " + d);
        }
        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 recursive 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;
            GenPolynomial> r = rootCharacteristic(m.c);
            if (r == null) {
                return null;
            }
            ExpVector e = ExpVector.create(1, 0, fl);
            d.doPutToMap(e, r);
        }
        return d;
    }

}