001/*
002 * $Id$
003 */
004
005package edu.jas.gbufd;
006
007
008import java.util.ArrayList;
009import java.util.List;
010
011import org.apache.logging.log4j.Logger;
012import org.apache.logging.log4j.LogManager; 
013
014import edu.jas.gb.OrderedWordPairlist;
015import edu.jas.gb.WordGroebnerBaseAbstract;
016import edu.jas.gb.WordPair;
017import edu.jas.gb.WordPairList;
018import edu.jas.poly.GenWordPolynomial;
019import edu.jas.poly.GenWordPolynomialRing;
020import edu.jas.structure.GcdRingElem;
021import edu.jas.structure.RingFactory;
022
023
024/**
025 * Non-commutative word Groebner Base sequential algorithm. Implements Groebner
026 * bases and GB test. Coefficients can for example be integers or (commutative)
027 * univariate polynomials.
028 * @param <C> coefficient type
029 * @author Heinz Kredel
030 */
031
032public class WordGroebnerBasePseudoSeq<C extends GcdRingElem<C>> extends WordGroebnerBaseAbstract<C> {
033
034
035    private static final Logger logger = LogManager.getLogger(WordGroebnerBasePseudoSeq.class);
036
037
038    private static final boolean debug = logger.isDebugEnabled();
039
040
041    /**
042     * Coefficient ring factory.
043     */
044    protected final RingFactory<C> cofac;
045
046
047    /**
048     * Constructor.
049     * @param rf coefficient ring factory.
050     */
051    public WordGroebnerBasePseudoSeq(RingFactory<C> rf) {
052        this(rf, new WordPseudoReductionSeq<C>());
053    }
054
055
056    /**
057     * Constructor.
058     * @param rf coefficient ring factory.
059     * @param red Reduction engine
060     */
061    public WordGroebnerBasePseudoSeq(RingFactory<C> rf, WordPseudoReductionSeq<C> red) {
062        this(rf, red, new OrderedWordPairlist<C>());
063    }
064
065
066    /**
067     * Constructor.
068     * @param rf coefficient ring factory.
069     * @param red Reduction engine
070     * @param pl pair selection strategy
071     */
072    public WordGroebnerBasePseudoSeq(RingFactory<C> rf, WordPseudoReductionSeq<C> red, WordPairList<C> pl) {
073        super(red, pl);
074        cofac = rf;
075        if (!cofac.isCommutative()) {
076            logger.warn("reduction not correct for {}", cofac); //.toScript()
077        }
078        //engine = GCDFactory.<C> getImplementation(rf);
079        //not used: engine = (GreatestCommonDivisorAbstract<C>)GCDFactory.<C>getProxy( rf );
080    }
081
082
083    /**
084     * Word Groebner base using word pairlist class.
085     * @param F word polynomial list.
086     * @return GB(F) a finite non-commutative Groebner base of F, if it exists.
087     */
088    @Override
089    public List<GenWordPolynomial<C>> GB(List<GenWordPolynomial<C>> F) {
090        List<GenWordPolynomial<C>> G = normalizeZerosOnes(F);
091        //G = PolyUtil.<C> wordMonic(G);
092        G = basePrimitivePart(G);
093        if (G.size() <= 1) {
094            return G;
095        }
096        GenWordPolynomialRing<C> ring = G.get(0).ring;
097        if (!ring.coFac.isCommutative()) {
098            throw new IllegalArgumentException("coefficient ring not commutative");
099        }
100        //Collections.sort(G);
101        OrderedWordPairlist<C> pairlist = (OrderedWordPairlist<C>) strategy.create(ring);
102        pairlist.put(G);
103        logger.info("start {}", pairlist);
104
105        WordPair<C> pair;
106        GenWordPolynomial<C> pi;
107        GenWordPolynomial<C> pj;
108        List<GenWordPolynomial<C>> S;
109        GenWordPolynomial<C> H;
110        while (pairlist.hasNext()) {
111            pair = pairlist.removeNext();
112            //logger.debug("pair = {}", pair);
113            if (pair == null) {
114                continue;
115            }
116            pi = pair.pi;
117            pj = pair.pj;
118            if (debug) {
119                logger.info("pi = {}, pj = {}", pi, pj);
120            }
121
122            S = red.SPolynomials(pi, pj);
123            if (S.isEmpty()) {
124                continue;
125            }
126            for (GenWordPolynomial<C> s : S) {
127                if (s.isZERO()) {
128                    //pair.setZero();
129                    continue;
130                }
131                if (debug) {
132                    logger.info("ht(S) = {}", s.leadingWord());
133                }
134                boolean t = pairlist.criterion3(pair.i, pair.j, s.leadingWord());
135                //System.out.println("criterion3(" + pair.i + "," + pair.j + ") = " + t);
136                //if ( !t ) {
137                //    continue;  
138                //}
139
140                H = red.normalform(G, s);
141                if (debug) {
142                    //logger.info("pair = {}", pair);
143                    //logger.info("ht(S) = {}", S.monic()); //.leadingWord() );
144                    logger.info("ht(H) = {}", H.monic()); //.leadingWord() );
145                }
146                if (H.isZERO()) {
147                    //pair.setZero();
148                    continue;
149                }
150                if (!t) {
151                    logger.info("criterion3({},{}) wrong: {} --> {}", pair.i, pair.j, s.leadingWord(), H.leadingWord());
152                }
153
154                //H = H.monic();
155                H = basePrimitivePart(H);
156                H = H.abs();
157                if (debug) {
158                    logger.info("ht(H) = {}", H.leadingWord());
159                }
160                if (H.isONE()) {
161                    G.clear();
162                    G.add(H);
163                    return G; // since no threads are activated
164                }
165                if (debug) {
166                    logger.info("H = {}", H);
167                }
168                if (H.length() > 0) {
169                    //l++;
170                    G.add(H);
171                    pairlist.put(H);
172                }
173            }
174        }
175        //logger.info("#sequential list = {}", G.size());
176        G = minimalGB(G);
177        logger.info("{}", pairlist);
178        //Collections.sort(G);
179        //Collections.reverse(G);
180        return G;
181    }
182
183
184    /**
185     * GenWordPolynomial base coefficient content.
186     * @param P GenWordPolynomial.
187     * @return cont(P).
188     */
189    public C baseContent(GenWordPolynomial<C> P) {
190        if (P == null) {
191            throw new IllegalArgumentException(this.getClass().getName() + " P != null");
192        }
193        if (P.isZERO()) {
194            return P.ring.getZEROCoefficient();
195        }
196        C d = null;
197        for (C c : P.getMap().values()) {
198            if (d == null) {
199                d = c;
200            } else {
201                d = d.gcd(c);
202            }
203            if (d.isONE()) {
204                return d;
205            }
206        }
207        if (d.signum() < 0) {
208            d = d.negate();
209        }
210        return d;
211    }
212
213
214    /**
215     * GenWordPolynomial base coefficient primitive part.
216     * @param P GenWordPolynomial.
217     * @return pp(P).
218     */
219    public GenWordPolynomial<C> basePrimitivePart(GenWordPolynomial<C> P) {
220        if (P == null) {
221            throw new IllegalArgumentException(this.getClass().getName() + " P != null");
222        }
223        if (P.isZERO()) {
224            return P;
225        }
226        C d = baseContent(P);
227        if (d.isONE()) {
228            return P;
229        }
230        GenWordPolynomial<C> pp = P.divide(d);
231        if (debug) {
232            GenWordPolynomial<C> p = pp.multiply(d);
233            if (!p.equals(P)) {
234                throw new ArithmeticException("pp(p)*cont(p) != p: ");
235            }
236        }
237        return pp;
238    }
239
240
241    /**
242     * List of GenWordPolynomial base coefficient primitive part.
243     * @param F list of GenWordPolynomials.
244     * @return pp(F).
245     */
246    public List<GenWordPolynomial<C>> basePrimitivePart(List<GenWordPolynomial<C>> F) {
247        if (F == null || F.isEmpty()) {
248            return F;
249        }
250        List<GenWordPolynomial<C>> Pp = new ArrayList<GenWordPolynomial<C>>(F.size());
251        for (GenWordPolynomial<C> f : F) {
252            GenWordPolynomial<C> p = basePrimitivePart(f);
253            Pp.add(p);
254        }
255        return Pp;
256    }
257
258}