Source code

001/*
002 * $Id$
003 */
004
005package edu.jas.gbufd;
006
007
008import java.util.ArrayList;
009import java.util.Collections;
010import java.util.List;
011
012import org.apache.logging.log4j.Logger;
013import org.apache.logging.log4j.LogManager; 
014
015import edu.jas.gb.GroebnerBaseAbstract;
016import edu.jas.gb.Pair;
017import edu.jas.poly.ExpVector;
018import edu.jas.poly.GenPolynomial;
019import edu.jas.structure.RegularRingElem;
020
021
022/**
023 * Regular ring Groebner Base sequential algorithm. Implements R-Groebner bases
024 * and GB test.
025 * @param <C> coefficient type
026 * @author Heinz Kredel
027 */
028
029public class RGroebnerBaseSeq<C extends RegularRingElem<C>> extends GroebnerBaseAbstract<C> {
030
031
032    private static final Logger logger = LogManager.getLogger(RGroebnerBaseSeq.class);
033
034
035    private static final boolean debug = logger.isDebugEnabled();
036
037
038    /**
039     * Reduction engine.
040     */
041    protected RReduction<C> rred; // shadow super.red ??
042
043
044    /**
045     * Constructor.
046     */
047    public RGroebnerBaseSeq() {
048        this(new RReductionSeq<C>());
049    }
050
051
052    /**
053     * Constructor.
054     * @param rred R-Reduction engine
055     */
056    public RGroebnerBaseSeq(RReduction<C> rred) {
057        super(rred);
058        this.rred = rred;
059        assert super.red == this.rred;
060    }
061
062
063    /**
064     * R-Groebner base test.
065     * @param modv module variable number.
066     * @param F polynomial list.
067     * @return true, if F is a R-Groebner base, else false.
068     */
069    @Override
070    public boolean isGB(int modv, List<GenPolynomial<C>> F) {
071        if (F == null) {
072            return true;
073        }
074        if (!rred.isBooleanClosed(F)) {
075            if (debug) {
076                logger.debug("not boolean closed");
077            }
078            return false;
079        }
080        GenPolynomial<C> pi, pj, s;
081        for (int i = 0; i < F.size(); i++) {
082            pi = F.get(i);
083            for (int j = i + 1; j < F.size(); j++) {
084                pj = F.get(j);
085                if (!red.moduleCriterion(modv, pi, pj)) {
086                    continue;
087                }
088                // red.criterion4 not applicable
089                s = red.SPolynomial(pi, pj);
090                if (s.isZERO()) {
091                    continue;
092                }
093                s = red.normalform(F, s);
094                if (!s.isZERO()) {
095                    if (debug) {
096                        logger.debug("p{} = {}", i, pi);
097                        logger.debug("p{} = {}", j, pj);
098                        logger.debug("s-pol = {}", red.SPolynomial(pi, pj));
099                        logger.debug("s-pol({},{}) != 0: {}", i, j, s);
100                    }
101                    return false;
102                }
103            }
104        }
105        return true;
106    }
107
108
109    /**
110     * R-Groebner base using pairlist class.
111     * @param modv module variable number.
112     * @param F polynomial list.
113     * @return GB(F) a R-Groebner base of F.
114     */
115    public List<GenPolynomial<C>> GB(int modv, List<GenPolynomial<C>> F) {
116        /* boolean closure */
117        List<GenPolynomial<C>> bcF = rred.reducedBooleanClosure(F);
118        logger.info("#bcF-#F = {}", (bcF.size() - F.size()));
119        F = bcF;
120        /* normalize input */
121        List<GenPolynomial<C>> G = new ArrayList<GenPolynomial<C>>();
122        OrderedRPairlist<C> pairlist = null;
123        for (GenPolynomial<C> p : F) {
124            if (!p.isZERO()) {
125                p = p.monic(); //p.abs(); // not monic, monic if boolean closed
126                if (p.isONE()) {
127                    G.clear();
128                    G.add(p);
129                    return G; // since boolean closed and no threads are activated
130                }
131                G.add(p); //G.add( 0, p ); //reverse list
132                if (pairlist == null) {
133                    pairlist = new OrderedRPairlist<C>(modv, p.ring);
134                }
135                // putOne not required
136                pairlist.put(p);
137            }
138        }
139        if (G.size() <= 1) {
140            return G; // since boolean closed and no threads are activated
141        }
142        /* loop on critical pairs */
143        Pair<C> pair;
144        GenPolynomial<C> pi;
145        GenPolynomial<C> pj;
146        GenPolynomial<C> S;
147        //GenPolynomial<C> D;
148        GenPolynomial<C> H;
149        List<GenPolynomial<C>> bcH;
150        //int len = G.size();
151        //System.out.println("len = " + len);
152        while (pairlist.hasNext()) {
153            pair = pairlist.removeNext();
154            //System.out.println("pair = " + pair);
155            if (pair == null)
156                continue;
157
158            pi = pair.pi;
159            pj = pair.pj;
160            if (logger.isDebugEnabled()) {
161                logger.debug("pi    = {}", pi);
162                logger.debug("pj    = {}", pj);
163            }
164            if (!red.moduleCriterion(modv, pi, pj)) {
165                continue;
166            }
167
168            // S-polynomial -----------------------
169            // Criterion3() Criterion4() not applicable
170            S = red.SPolynomial(pi, pj);
171            if (S.isZERO()) {
172                pair.setZero();
173                continue;
174            }
175            logger.debug("ht(S) = {}", S.leadingExpVector());
176
177            H = red.normalform(G, S);
178            if (H.isZERO()) {
179                pair.setZero();
180                continue;
181            }
182            //H = H.monic(); // only for boolean closed H
183            logger.debug("ht(H) = {}", H.leadingExpVector());
184
185            if (H.isONE()) { // mostly useless
186                G.clear();
187                G.add(H);
188                return G; // not boolean closed ok, since no threads are activated
189            }
190            logger.debug("H = {}", H);
191            if (!H.isZERO()) {
192                logger.info("Sred = {}", H);
193                //len = G.size();
194                bcH = rred.reducedBooleanClosure(G, H);
195                logger.info("#bcH = {}", bcH.size());
196                for (GenPolynomial<C> h : bcH) {
197                    h = h.monic(); // monic() ok, since boolean closed
198                    G.add(h);
199                    pairlist.put(h);
200                }
201                if (debug) {
202                    if (!pair.getUseCriterion3() || !pair.getUseCriterion4()) {
203                        logger.info("H != 0 but: {}", pair);
204                    }
205                }
206            }
207        }
208        logger.debug("#sequential list = {}", G.size());
209        G = minimalGB(G);
210        //G = red.irreducibleSet(G);
211        logger.info("{}", pairlist);
212        return G;
213    }
214
215
216    /**
217     * Minimal ordered Groebner basis.
218     * @param Gp a Groebner base.
219     * @return a reduced Groebner base of Gp.
220     */
221    @Override
222    public List<GenPolynomial<C>> minimalGB(List<GenPolynomial<C>> Gp) {
223        if (Gp == null || Gp.size() <= 1) {
224            return Gp;
225        }
226        // remove zero polynomials
227        List<GenPolynomial<C>> G = new ArrayList<GenPolynomial<C>>(Gp.size());
228        for (GenPolynomial<C> a : Gp) {
229            if (a != null && !a.isZERO()) { // always true in GB()
230                // already positive a = a.abs();
231                G.add(a);
232            }
233        }
234        //if (G.size() <= 1) {
235            //wg monic do not return G;
236        //}
237        // remove top reducible polynomials
238        GenPolynomial<C> a, b;
239        List<GenPolynomial<C>> F;
240        List<GenPolynomial<C>> bcH;
241        F = new ArrayList<GenPolynomial<C>>(G.size());
242        while (G.size() > 0) {
243            a = G.remove(0);
244            b = a;
245            if (red.isTopReducible(G, a) || red.isTopReducible(F, a)) {
246                // drop polynomial 
247                if (logger.isInfoEnabled()) {
248                    List<GenPolynomial<C>> ff;
249                    ff = new ArrayList<GenPolynomial<C>>(G);
250                    ff.addAll(F);
251                    a = red.normalform(ff, a);
252                    if (!a.isZERO()) { // happens
253                        logger.info("minGB not zero {}", a);
254                        bcH = rred.reducedBooleanClosure(G, a);
255                        if (bcH.size() > 1) { // never happened so far
256                            System.out.println("minGB not bc: bcH size = " + bcH.size());
257                            F.add(b); // do not replace, stay with b
258                        } else {
259                            //System.out.println("minGB add bc(a): a = " + a + ", bc(a) = " + bcH.get(0));
260                            F.addAll(bcH);
261                        }
262                    } else {
263                        //System.out.println("minGB dropped " + b);
264                    }
265                }
266            } else {
267                F.add(a);
268            }
269        }
270        G = F;
271        //if (G.size() <= 1) {
272            // wg monic return G;
273        //}
274        Collections.reverse(G); // important for lex GB
275        // reduce remaining polynomials
276        int len = G.size();
277        int el = 0;
278        while (el < len) {
279            a = G.remove(0);
280            b = a;
281            //System.out.println("doing " + a.length());
282            a = red.normalform(G, a);
283            bcH = rred.reducedBooleanClosure(G, a);
284            if (bcH.size() > 1) {
285                System.out.println("minGB not bc: bcH size = " + bcH.size());
286                G.add(b); // do not reduce
287            } else {
288                G.addAll(bcH);
289            }
290            el++;
291        }
292        // make monic if possible
293        F = new ArrayList<GenPolynomial<C>>(G.size());
294        for (GenPolynomial<C> p : G) {
295            a = p.monic().abs();
296            if (p.length() != a.length()) {
297                System.out.println("minGB not bc: #p != #a: a = " + a + ", p = " + p);
298                a = p; // dont make monic for now
299            }
300            F.add(a);
301        }
302        G = F;
303
304        /* stratify: collect polynomials with equal leading terms */
305        ExpVector e, f;
306        F = new ArrayList<GenPolynomial<C>>(G.size());
307        for (int i = 0; i < G.size(); i++) {
308            a = G.get(i);
309            if (a == null || a.isZERO()) {
310                continue;
311            }
312            e = a.leadingExpVector();
313            for (int j = i + 1; j < G.size(); j++) {
314                b = G.get(j);
315                if (b == null || b.isZERO()) {
316                    continue;
317                }
318                f = b.leadingExpVector();
319                if (e.equals(f)) {
320                    //System.out.println("minGB e == f: " + a + ", " + b);
321                    a = a.sum(b);
322                    G.set(j, null);
323                }
324            }
325            F.add(a);
326        }
327        G = F;
328
329        /* info on boolean algebra element blocks 
330        Map<C,List<GenPolynomial<C>>> bd = new TreeMap<C,List<GenPolynomial<C>>>();
331        for ( GenPolynomial<C> p : G ) { 
332            C cf = p.leadingBaseCoefficient();
333            cf = cf.idempotent();
334            List<GenPolynomial<C>> block = bd.get( cf );
335            if ( block == null ) {
336               block = new ArrayList<GenPolynomial<C>>();
337            }
338            block.add( p ); 
339            bd.put( cf, block );
340        }
341        System.out.println("\nminGB bd:");
342        for( C k: bd.keySet() ) {
343           System.out.println("\nkey = " + k + ":");
344           System.out.println("val = " + bd.get(k));
345        }
346        System.out.println();
347        */
348        return G;
349    }
350
351}