001/*
002 * $Id$
003 */
004
005package edu.jas.ufd;
006
007
008import java.util.ArrayList;
009import java.util.List;
010import java.util.Map;
011import java.util.SortedMap;
012import java.util.TreeMap;
013
014import org.apache.logging.log4j.LogManager;
015import org.apache.logging.log4j.Logger;
016
017import edu.jas.arith.BigInteger;
018import edu.jas.arith.BigRational;
019import edu.jas.poly.GenPolynomial;
020import edu.jas.poly.GenPolynomialRing;
021import edu.jas.poly.PolyUtil;
022
023
024/**
025 * Rational number coefficients factorization algorithms. This class implements
026 * factorization methods for polynomials over rational numbers.
027 * @author Heinz Kredel
028 */
029
030public class FactorRational extends FactorAbsolute<BigRational> {
031
032
033    private static final Logger logger = LogManager.getLogger(FactorRational.class);
034
035
036    private static final boolean debug = logger.isInfoEnabled();
037
038
039    /**
040     * Factorization engine for integer base coefficients.
041     */
042    protected final FactorAbstract<BigInteger> iengine;
043
044
045    /**
046     * No argument constructor.
047     */
048    protected FactorRational() {
049        super(BigRational.ONE);
050        iengine = FactorFactory.getImplementation(BigInteger.ONE);
051    }
052
053
054    /**
055     * GenPolynomial base factorization of a squarefree polynomial.
056     * @param P squarefree GenPolynomial.
057     * @return [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i.
058     */
059    @Override
060    public List<GenPolynomial<BigRational>> baseFactorsSquarefree(GenPolynomial<BigRational> P) {
061        if (P == null) {
062            throw new IllegalArgumentException(this.getClass().getName() + " P == null");
063        }
064        List<GenPolynomial<BigRational>> factors = new ArrayList<GenPolynomial<BigRational>>();
065        if (P.isZERO()) {
066            return factors;
067        }
068        if (P.isONE()) {
069            factors.add(P);
070            return factors;
071        }
072        GenPolynomialRing<BigRational> pfac = P.ring;
073        if (pfac.nvar > 1) {
074            throw new IllegalArgumentException(
075                            this.getClass().getName() + " only for univariate polynomials");
076        }
077        GenPolynomial<BigRational> Pr = P;
078        BigRational ldcf = P.leadingBaseCoefficient();
079        if (!ldcf.isONE()) {
080            //System.out.println("ldcf = " + ldcf);
081            Pr = Pr.monic();
082        }
083        BigInteger bi = BigInteger.ONE;
084        GenPolynomialRing<BigInteger> ifac = new GenPolynomialRing<BigInteger>(bi, pfac);
085        GenPolynomial<BigInteger> Pi = PolyUtil.integerFromRationalCoefficients(ifac, Pr);
086        if (debug) {
087            logger.info("Pi = {}", Pi);
088        }
089        List<GenPolynomial<BigInteger>> ifacts = iengine.baseFactorsSquarefree(Pi);
090        logger.info("ifacts = {}", ifacts);
091        if (ifacts.size() <= 1) {
092            factors.add(P);
093            return factors;
094        }
095        List<GenPolynomial<BigRational>> rfacts = PolyUtil.fromIntegerCoefficients(pfac, ifacts);
096        //System.out.println("rfacts = " + rfacts);
097        rfacts = PolyUtil.monic(rfacts);
098        //System.out.println("rfacts = " + rfacts);
099        if (!ldcf.isONE()) {
100            GenPolynomial<BigRational> r = rfacts.get(0);
101            rfacts.remove(r);
102            r = r.multiply(ldcf);
103            rfacts.set(0, r);
104        }
105        logger.info("rfacts = {}", rfacts);
106        factors.addAll(rfacts);
107        return factors;
108    }
109
110
111    /**
112     * GenPolynomial factorization of a squarefree polynomial.
113     * @param P squarefree GenPolynomial.
114     * @return [p_1,...,p_k] with P = prod_{i=1, ..., k} p_i.
115     */
116    @Override
117    public List<GenPolynomial<BigRational>> factorsSquarefree(GenPolynomial<BigRational> P) {
118        if (P == null) {
119            throw new IllegalArgumentException(this.getClass().getName() + " P == null");
120        }
121        List<GenPolynomial<BigRational>> factors = new ArrayList<GenPolynomial<BigRational>>();
122        if (P.isZERO()) {
123            return factors;
124        }
125        if (P.isONE()) {
126            factors.add(P);
127            return factors;
128        }
129        GenPolynomialRing<BigRational> pfac = P.ring;
130        if (pfac.nvar == 1) {
131            return baseFactorsSquarefree(P);
132        }
133        GenPolynomial<BigRational> Pr = P;
134        BigRational ldcf = P.leadingBaseCoefficient();
135        if (!ldcf.isONE()) {
136            //System.out.println("ldcf = " + ldcf);
137            Pr = Pr.monic();
138        }
139        BigInteger bi = BigInteger.ONE;
140        GenPolynomialRing<BigInteger> ifac = new GenPolynomialRing<BigInteger>(bi, pfac);
141        GenPolynomial<BigInteger> Pi = PolyUtil.integerFromRationalCoefficients(ifac, Pr);
142        if (debug) {
143            logger.info("Pi = {}", Pi);
144        }
145        List<GenPolynomial<BigInteger>> ifacts = iengine.factorsSquarefree(Pi);
146        logger.info("ifacts = {}", ifacts);
147        if (ifacts.size() <= 1) {
148            factors.add(P);
149            return factors;
150        }
151        List<GenPolynomial<BigRational>> rfacts = PolyUtil.fromIntegerCoefficients(pfac, ifacts);
152        //System.out.println("rfacts = " + rfacts);
153        rfacts = PolyUtil.monic(rfacts);
154        //System.out.println("rfacts = " + rfacts);
155        if (!ldcf.isONE()) {
156            GenPolynomial<BigRational> r = rfacts.get(0);
157            rfacts.remove(r);
158            r = r.multiply(ldcf);
159            rfacts.set(0, r);
160        }
161        logger.info("rfacts = {}", rfacts);
162        factors.addAll(rfacts);
163        return factors;
164    }
165
166
167    /**
168     * GenPolynomial factorization of a polynomial.
169     * @param P GenPolynomial.
170     * @return [p_1 -&gt; e_1, ..., p_k -&gt; e_k] with P = prod_{i=1,...,k}
171     *         p_i**e_i and p_i irreducible.
172     */
173    @Override
174    public SortedMap<GenPolynomial<BigRational>, Long> factors(GenPolynomial<BigRational> P) {
175        if (P == null) {
176            throw new IllegalArgumentException(this.getClass().getName() + " P == null");
177        }
178        GenPolynomialRing<BigRational> pfac = P.ring;
179        SortedMap<GenPolynomial<BigRational>, Long> factors = new TreeMap<GenPolynomial<BigRational>, Long>(
180                        pfac.getComparator());
181        if (P.isZERO()) {
182            return factors;
183        }
184        if (P.isONE()) {
185            factors.put(P, 1L);
186            return factors;
187        }
188        if (pfac.nvar == 1) {
189            return baseFactors(P);
190        }
191        GenPolynomial<BigRational> Pr = P;
192        BigInteger bi = BigInteger.ONE;
193        GenPolynomialRing<BigInteger> ifac = new GenPolynomialRing<BigInteger>(bi, pfac);
194        GenPolynomial<BigInteger> Pi = PolyUtil.integerFromRationalCoefficients(ifac, Pr);
195        if (debug) {
196            logger.info("Pi = {}", Pi);
197        }
198        SortedMap<GenPolynomial<BigInteger>, Long> ifacts = iengine.factors(Pi);
199        logger.info("ifacts = {}", ifacts);
200        for (Map.Entry<GenPolynomial<BigInteger>, Long> me : ifacts.entrySet()) {
201            GenPolynomial<BigInteger> g = me.getKey();
202            if (g.isONE()) { // skip 1
203                continue;
204            }
205            Long d = me.getValue(); // facs.get(g);
206            GenPolynomial<BigRational> rp = PolyUtil.fromIntegerCoefficients(pfac, g);
207            factors.put(rp, d);
208        }
209        return factors;
210    }
211
212}