Source code

001/*
002 * $Id$
003 */
004
005package edu.jas.poly;
006
007
008import java.util.Map;
009import java.util.Set;
010import java.util.SortedMap;
011
012import org.apache.logging.log4j.Logger;
013import org.apache.logging.log4j.LogManager; 
014
015import edu.jas.structure.GcdRingElem;
016import edu.jas.structure.QuotPair;
017import edu.jas.structure.RingFactory;
018
019
020/**
021 * QLRSolvablePolynomial generic recursive solvable polynomials implementing
022 * RingElem. n-variate ordered solvable polynomials over solvable quotient,
023 * local and local-residue coefficients. Objects of this class are intended to
024 * be immutable. The implementation is based on TreeMap respectively SortedMap
025 * from exponents to coefficients by extension of GenPolynomial.
026 * @param <C> polynomial coefficient type
027 * @param <D> quotient coefficient type
028 * @author Heinz Kredel
029 */
030
031public class QLRSolvablePolynomial<C extends GcdRingElem<C> & QuotPair<GenPolynomial<D>>, D extends GcdRingElem<D>>
032                extends GenSolvablePolynomial<C> {
033
034
035    private static final Logger logger = LogManager.getLogger(QLRSolvablePolynomial.class);
036
037
038    private static final boolean debug = logger.isDebugEnabled();
039
040
041    /**
042     * The factory for the recursive solvable polynomial ring. Hides super.ring.
043     */
044    public final QLRSolvablePolynomialRing<C, D> ring;
045
046
047    /**
048     * Constructor for zero QLRSolvablePolynomial.
049     * @param r solvable polynomial ring factory.
050     */
051    public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C, D> r) {
052        super(r);
053        ring = r;
054    }
055
056
057    /**
058     * Constructor for QLRSolvablePolynomial.
059     * @param r solvable polynomial ring factory.
060     * @param c coefficient polynomial.
061     * @param e exponent.
062     */
063    public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C, D> r, C c, ExpVector e) {
064        this(r);
065        if (c != null && !c.isZERO()) {
066            val.put(e, c);
067        }
068    }
069
070
071    /**
072     * Constructor for QLRSolvablePolynomial.
073     * @param r solvable polynomial ring factory.
074     * @param c coefficient polynomial.
075     */
076    public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C, D> r, C c) {
077        this(r, c, r.evzero);
078    }
079
080
081    /**
082     * Constructor for QLRSolvablePolynomial.
083     * @param r solvable polynomial ring factory.
084     * @param S solvable polynomial.
085     */
086    public QLRSolvablePolynomial(QLRSolvablePolynomialRing<C, D> r, GenSolvablePolynomial<C> S) {
087        this(r, S.getMap());
088    }
089
090
091    /**
092     * Constructor for QLRSolvablePolynomial.
093     * @param r solvable polynomial ring factory.
094     * @param v the SortedMap of some other (solvable) polynomial.
095     */
096    protected QLRSolvablePolynomial(QLRSolvablePolynomialRing<C, D> r, SortedMap<ExpVector, C> v) {
097        this(r);
098        val.putAll(v); // assume no zero coefficients
099    }
100
101
102    /**
103     * Get the corresponding element factory.
104     * @return factory for this Element.
105     * @see edu.jas.structure.Element#factory()
106     */
107    @Override
108    public QLRSolvablePolynomialRing<C, D> factory() {
109        return ring;
110    }
111
112
113    /**
114     * Clone this QLRSolvablePolynomial.
115     * @see java.lang.Object#clone()
116     */
117    @Override
118    public QLRSolvablePolynomial<C, D> copy() {
119        return new QLRSolvablePolynomial<C, D>(ring, this.val);
120    }
121
122
123    /**
124     * Comparison with any other object.
125     * @see java.lang.Object#equals(java.lang.Object)
126     */
127    @Override
128    public boolean equals(Object B) {
129        if (!(B instanceof QLRSolvablePolynomial)) {
130            return false;
131        }
132        return super.equals(B);
133    }
134
135
136    /**
137     * Hash code for this polynomial.
138     * @see java.lang.Object#hashCode()
139     */
140    @Override
141    public int hashCode() {
142        return super.hashCode();
143    }
144
145
146    /**
147     * QLRSolvablePolynomial multiplication.
148     * @param Bp QLRSolvablePolynomial.
149     * @return this*Bp, where * denotes solvable multiplication.
150     */
151    // not @Override
152    @SuppressWarnings("unchecked")
153    public QLRSolvablePolynomial<C, D> multiply(QLRSolvablePolynomial<C, D> Bp) {
154        if (Bp == null || Bp.isZERO()) {
155            return ring.getZERO();
156        }
157        if (this.isZERO()) {
158            return this;
159        }
160        if (Bp.isONE()) {
161            return this;
162        }
163        if (this.isONE()) {
164            return Bp;
165        }
166        assert (ring.nvar == Bp.ring.nvar);
167        if (debug) {
168            logger.debug("ring = {}", ring);
169        }
170        //System.out.println("this = " + this + ", Bp = " + Bp);
171        ExpVector Z = ring.evzero;
172        QLRSolvablePolynomial<C, D> Dp = ring.getZERO().copy();
173        QLRSolvablePolynomial<C, D> zero = ring.getZERO().copy();
174        C one = ring.getONECoefficient();
175
176        Map<ExpVector, C> A = val;
177        Map<ExpVector, C> B = Bp.val;
178        Set<Map.Entry<ExpVector, C>> Bk = B.entrySet();
179        for (Map.Entry<ExpVector, C> y : A.entrySet()) {
180            C a = y.getValue();
181            ExpVector e = y.getKey();
182            if (debug)
183                logger.info("e = {}, a = {}", e, a);
184            //int[] ep = e.dependencyOnVariables();
185            //int el1 = ring.nvar + 1;
186            //if (ep.length > 0) {
187            //    el1 = ep[0];
188            //}
189            //int el1s = ring.nvar + 1 - el1;
190            for (Map.Entry<ExpVector, C> x : Bk) {
191                C b = x.getValue();
192                ExpVector f = x.getKey();
193                if (debug)
194                    logger.info("f = {}, b = {}", f, b);
195                int[] fp = f.dependencyOnVariables();
196                int fl1 = 0;
197                if (fp.length > 0) {
198                    fl1 = fp[fp.length - 1];
199                }
200                int fl1s = ring.nvar + 1 - fl1;
201                // polynomial with coefficient multiplication 
202                QLRSolvablePolynomial<C, D> Cps = ring.getZERO().copy();
203                //QLRSolvablePolynomial<C, D> Cs;
204                QLRSolvablePolynomial<C, D> qp;
205                if (ring.polCoeff.isCommutative() || b.isConstant() || e.isZERO()) { // symmetric
206                    Cps = new QLRSolvablePolynomial<C, D>(ring, b, e);
207                    if (debug)
208                        logger.info("symmetric coeff: b = {}, e = {}", b, e);
209                } else { // unsymmetric
210                    if (debug)
211                        logger.info("unsymmetric coeff: b = {}, e = {}", b, e);
212                    // compute e * b as ( e * 1/b.den ) * b.num
213                    if (b.denominator().isONE()) { // recursion base
214                        // recursive polynomial coefficient multiplication : e * b.num
215                        RecSolvablePolynomial<D> rsp1 = new RecSolvablePolynomial<D>(ring.polCoeff, e);
216                        RecSolvablePolynomial<D> rsp2 = new RecSolvablePolynomial<D>(ring.polCoeff,
217                                        b.numerator());
218                        RecSolvablePolynomial<D> rsp3 = rsp1.multiply(rsp2);
219                        QLRSolvablePolynomial<C, D> rsp = ring.fromPolyCoefficients(rsp3);
220                        Cps = rsp;
221                    } else { // b.denominator() != 1
222                        if (debug)
223                            logger.info("coeff-num: Cps = {}, num = {}, den = {}", Cps, b.numerator(), b.denominator());
224                        RingFactory<C> bfq = (RingFactory<C>) b.factory();
225                        Cps = new QLRSolvablePolynomial<C, D>(ring, bfq.getONE(), e);
226
227                        // coefficient multiplication with 1/den: 
228                        QLRSolvablePolynomial<C, D> qv = Cps;
229                        //C qden = new C(b.denominator().factory(), b.denominator()); // den/1
230                        C qden = ring.qpfac.create(b.denominator()); // den/1
231                        //System.out.println("qv = " + qv + ", den = " + den);
232                        // recursion with den==1:
233                        QLRSolvablePolynomial<C, D> v = qv.multiply(qden);
234                        QLRSolvablePolynomial<C, D> vl = qv.multiplyLeft(qden);
235                        //System.out.println("v = " + v + ", vl = " + vl + ", qden = " + qden);
236                        QLRSolvablePolynomial<C, D> vr = (QLRSolvablePolynomial<C, D>) v.subtract(vl);
237                        //C qdeni = new C(b.factory(), b.factory().getONE().numerator(), b.denominator());
238                        C qdeni = ring.qpfac.create(ring.qpfac.pairFactory().getONE(), b.denominator()); // 1/den
239                        //System.out.println("vr = " + vr + ", qdeni = " + qdeni);
240                        // recursion with smaller head term:
241                        if (qv.leadingExpVector().equals(vr.leadingExpVector())) {
242                            throw new IllegalArgumentException("qr !> vr: qv = " + qv + ", vr = " + vr);
243                        }
244                        QLRSolvablePolynomial<C, D> rq = vr.multiply(qdeni);
245                        qp = (QLRSolvablePolynomial<C, D>) qv.subtract(rq);
246                        qp = qp.multiplyLeft(qdeni);
247                        //System.out.println("qp_i = " + qp);
248                        Cps = qp;
249
250                        if (!b.numerator().isONE()) {
251                            //C qnum = new C(b.denominator().factory(), b.numerator()); // num/1
252                            C qnum = ring.qpfac.create(b.numerator()); // num/1
253                            // recursion with den == 1:
254                            Cps = Cps.multiply(qnum);
255                        }
256                    }
257                } // end coeff
258                if (debug)
259                    logger.info("coeff-den: Cps = {}", Cps);
260                // polynomial multiplication 
261                QLRSolvablePolynomial<C, D> Dps = ring.getZERO().copy();
262                QLRSolvablePolynomial<C, D> Ds = null;
263                QLRSolvablePolynomial<C, D> D1, D2;
264                if (ring.isCommutative() || Cps.isConstant() || f.isZERO()) { // symmetric
265                    if (debug)
266                        logger.info("symmetric poly: b = {}, e = {}", b, e);
267                    if (Cps.isConstant()) {
268                        ExpVector g = e.sum(f);
269                        Ds = new QLRSolvablePolynomial<C, D>(ring, Cps.leadingBaseCoefficient(), g); // symmetric!
270                    } else {
271                        Ds = Cps.shift(f); // symmetric
272                    }
273                } else { // eventually unsymmetric
274                    if (debug)
275                        logger.info("unsymmetric poly: Cps = {}, f = {}", Cps, f);
276                    for (Map.Entry<ExpVector, C> z : Cps.val.entrySet()) {
277                        // split g = g1 * g2, f = f1 * f2
278                        C c = z.getValue();
279                        ExpVector g = z.getKey();
280                        if (debug)
281                            logger.info("g = {}, c = {}", g, c);
282                        int[] gp = g.dependencyOnVariables();
283                        int gl1 = ring.nvar + 1;
284                        if (gp.length > 0) {
285                            gl1 = gp[0];
286                        }
287                        int gl1s = ring.nvar + 1 - gl1;
288                        if (gl1s <= fl1s) { // symmetric
289                            ExpVector h = g.sum(f);
290                            if (debug)
291                                logger.info("disjoint poly: g = {}, f = {}, h = {}", g, f, h);
292                            Ds = (QLRSolvablePolynomial<C, D>) zero.sum(one, h); // symmetric!
293                        } else {
294                            ExpVector g1 = g.subst(gl1, 0);
295                            ExpVector g2 = Z.subst(gl1, g.getVal(gl1)); // bug el1, gl1
296                            ExpVector g4;
297                            ExpVector f1 = f.subst(fl1, 0);
298                            ExpVector f2 = Z.subst(fl1, f.getVal(fl1));
299                            if (debug) {
300                                logger.info("poly, g1 = {}, f1 = {}, Dps = {}", g1, f1, Dps);
301                                logger.info("poly, g2 = {}, f2 = {}", g2, f2);
302                            }
303                            TableRelation<C> rel = ring.table.lookup(g2, f2);
304                            if (debug)
305                                logger.info("poly, g  = {}, f = {}, rel = {}", g, f, rel);
306                            Ds = new QLRSolvablePolynomial<C, D>(ring, rel.p); //ring.copy(rel.p);
307                            if (rel.f != null) {
308                                D2 = new QLRSolvablePolynomial<C, D>(ring, one, rel.f);
309                                Ds = Ds.multiply(D2);
310                                if (rel.e == null) {
311                                    g4 = g2;
312                                } else {
313                                    g4 = g2.subtract(rel.e);
314                                }
315                                ring.table.update(g4, f2, Ds);
316                            }
317                            if (rel.e != null) {
318                                D1 = new QLRSolvablePolynomial<C, D>(ring, one, rel.e);
319                                Ds = D1.multiply(Ds);
320                                ring.table.update(g2, f2, Ds);
321                            }
322                            if (!f1.isZERO()) {
323                                D2 = new QLRSolvablePolynomial<C, D>(ring, one, f1);
324                                Ds = Ds.multiply(D2);
325                                //ring.table.update(?,f1,Ds)
326                            }
327                            if (!g1.isZERO()) {
328                                D1 = new QLRSolvablePolynomial<C, D>(ring, one, g1);
329                                Ds = D1.multiply(Ds);
330                                //ring.table.update(e1,?,Ds)
331                            }
332                        }
333                        Ds = Ds.multiplyLeft(c); // c * Ds
334                        //Dps = (QLRSolvablePolynomial<C, D>) Dps.sum(Ds);
335                        Dps.doAddTo(Ds);
336                    } // end Dps loop
337                    Ds = Dps;
338                }
339                Ds = Ds.multiplyLeft(a); // multiply(a,b); // non-symmetric 
340                if (debug)
341                    logger.debug("Ds = {}", Ds);
342                //Dp = (QLRSolvablePolynomial<C, D>) Dp.sum(Ds);
343                Dp.doAddTo(Ds);
344            } // end B loop
345        } // end A loop
346          //System.out.println("this * Bp = " + Dp);
347        return Dp;
348    }
349
350
351    /**
352     * QLRSolvablePolynomial left and right multiplication. Product with two
353     * polynomials.
354     * @param S QLRSolvablePolynomial.
355     * @param T QLRSolvablePolynomial.
356     * @return S*this*T.
357     */
358    // not @Override
359    public QLRSolvablePolynomial<C, D> multiply(QLRSolvablePolynomial<C, D> S, QLRSolvablePolynomial<C, D> T) {
360        if (S.isZERO() || T.isZERO() || this.isZERO()) {
361            return ring.getZERO();
362        }
363        if (S.isONE()) {
364            return multiply(T);
365        }
366        if (T.isONE()) {
367            return S.multiply(this);
368        }
369        return S.multiply(this).multiply(T);
370    }
371
372
373    /**
374     * QLRSolvablePolynomial multiplication. Product with coefficient ring
375     * element.
376     * @param b solvable coefficient.
377     * @return this*b, where * is coefficient multiplication.
378     */
379    @Override
380    public QLRSolvablePolynomial<C, D> multiply(C b) {
381        QLRSolvablePolynomial<C, D> Cp = ring.getZERO().copy();
382        if (b == null || b.isZERO()) {
383            return Cp;
384        }
385        if (b.isONE()) {
386            return this;
387        }
388        Cp = new QLRSolvablePolynomial<C, D>(ring, b, ring.evzero);
389        return multiply(Cp);
390    }
391
392
393    /**
394     * QLRSolvablePolynomial left and right multiplication. Product with
395     * coefficient ring element.
396     * @param b coefficient polynomial.
397     * @param c coefficient polynomial.
398     * @return b*this*c, where * is coefficient multiplication.
399     */
400    @Override
401    public QLRSolvablePolynomial<C, D> multiply(C b, C c) {
402        QLRSolvablePolynomial<C, D> Cp = ring.getZERO().copy();
403        if (b == null || b.isZERO()) {
404            return Cp;
405        }
406        if (c == null || c.isZERO()) {
407            return Cp;
408        }
409        if (b.isONE() && c.isONE()) {
410            return this;
411        }
412        Cp = new QLRSolvablePolynomial<C, D>(ring, b, ring.evzero);
413        QLRSolvablePolynomial<C, D> Dp = new QLRSolvablePolynomial<C, D>(ring, c, ring.evzero);
414        return multiply(Cp, Dp);
415    }
416
417
418    /**
419     * QLRSolvablePolynomial multiplication. Product with exponent vector.
420     * @param e exponent.
421     * @return this * x<sup>e</sup>, where * denotes solvable multiplication.
422     */
423    @Override
424    public QLRSolvablePolynomial<C, D> multiply(ExpVector e) {
425        if (e == null || e.isZERO()) {
426            return this;
427        }
428        C b = ring.getONECoefficient();
429        return multiply(b, e);
430    }
431
432
433    /**
434     * QLRSolvablePolynomial left and right multiplication. Product with
435     * exponent vector.
436     * @param e exponent.
437     * @param f exponent.
438     * @return x<sup>e</sup> * this * x<sup>f</sup>, where * denotes solvable
439     *         multiplication.
440     */
441    @Override
442    public QLRSolvablePolynomial<C, D> multiply(ExpVector e, ExpVector f) {
443        if (e == null || e.isZERO()) {
444            return this;
445        }
446        if (f == null || f.isZERO()) {
447            return this;
448        }
449        C b = ring.getONECoefficient();
450        return multiply(b, e, b, f);
451    }
452
453
454    /**
455     * QLRSolvablePolynomial multiplication. Product with ring element and
456     * exponent vector.
457     * @param b coefficient polynomial.
458     * @param e exponent.
459     * @return this * b x<sup>e</sup>, where * denotes solvable multiplication.
460     */
461    @Override
462    public QLRSolvablePolynomial<C, D> multiply(C b, ExpVector e) {
463        if (b == null || b.isZERO()) {
464            return ring.getZERO();
465        }
466        if (b.isONE() && e.isZERO()) {
467            return this;
468        }
469        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
470        return multiply(Cp);
471    }
472
473
474    /**
475     * QLRSolvablePolynomial left and right multiplication. Product with ring
476     * element and exponent vector.
477     * @param b coefficient polynomial.
478     * @param e exponent.
479     * @param c coefficient polynomial.
480     * @param f exponent.
481     * @return b x<sup>e</sup> * this * c x<sup>f</sup>, where * denotes
482     *         solvable multiplication.
483     */
484    @Override
485    public QLRSolvablePolynomial<C, D> multiply(C b, ExpVector e, C c, ExpVector f) {
486        if (b == null || b.isZERO()) {
487            return ring.getZERO();
488        }
489        if (c == null || c.isZERO()) {
490            return ring.getZERO();
491        }
492        if (b.isONE() && e.isZERO() && c.isONE() && f.isZERO()) {
493            return this;
494        }
495        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
496        QLRSolvablePolynomial<C, D> Dp = new QLRSolvablePolynomial<C, D>(ring, c, f);
497        return multiply(Cp, Dp);
498    }
499
500
501    /**
502     * QLRSolvablePolynomial multiplication. Left product with ring element and
503     * exponent vector.
504     * @param b coefficient polynomial.
505     * @param e exponent.
506     * @return b x<sup>e</sup> * this, where * denotes solvable multiplication.
507     */
508    @Override
509    public QLRSolvablePolynomial<C, D> multiplyLeft(C b, ExpVector e) {
510        if (b == null || b.isZERO()) {
511            return ring.getZERO();
512        }
513        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
514        return Cp.multiply(this);
515    }
516
517
518    /**
519     * QLRSolvablePolynomial multiplication. Left product with exponent vector.
520     * @param e exponent.
521     * @return x<sup>e</sup> * this, where * denotes solvable multiplication.
522     */
523    @Override
524    public QLRSolvablePolynomial<C, D> multiplyLeft(ExpVector e) {
525        if (e == null || e.isZERO()) {
526            return this;
527        }
528        C b = ring.getONECoefficient();
529        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
530        return Cp.multiply(this);
531    }
532
533
534    /**
535     * QLRSolvablePolynomial multiplication. Left product with coefficient ring
536     * element.
537     * @param b coefficient polynomial.
538     * @return b*this, where * is coefficient multiplication.
539     */
540    @Override
541    public QLRSolvablePolynomial<C, D> multiplyLeft(C b) {
542        QLRSolvablePolynomial<C, D> Cp = ring.getZERO().copy();
543        if (b == null || b.isZERO()) {
544            return Cp;
545        }
546        Map<ExpVector, C> Cm = Cp.val; //getMap();
547        Map<ExpVector, C> Am = val;
548        C c;
549        for (Map.Entry<ExpVector, C> y : Am.entrySet()) {
550            ExpVector e = y.getKey();
551            C a = y.getValue();
552            c = b.multiply(a);
553            if (!c.isZERO()) {
554                Cm.put(e, c);
555            }
556        }
557        return Cp;
558    }
559
560
561    /**
562     * QLRSolvablePolynomial multiplication. Left product with 'monomial'.
563     * @param m 'monomial'.
564     * @return m * this, where * denotes solvable multiplication.
565     */
566    @Override
567    public QLRSolvablePolynomial<C, D> multiplyLeft(Map.Entry<ExpVector, C> m) {
568        if (m == null) {
569            return ring.getZERO();
570        }
571        return multiplyLeft(m.getValue(), m.getKey());
572    }
573
574
575    /**
576     * QLRSolvablePolynomial multiplication. Product with 'monomial'.
577     * @param m 'monomial'.
578     * @return this * m, where * denotes solvable multiplication.
579     */
580    @Override
581    public QLRSolvablePolynomial<C, D> multiply(Map.Entry<ExpVector, C> m) {
582        if (m == null) {
583            return ring.getZERO();
584        }
585        return multiply(m.getValue(), m.getKey());
586    }
587
588
589    /**
590     * QLRSolvablePolynomial multiplication with exponent vector. 
591     * @param f exponent vector.
592     * @return B*f, where * is commutative multiplication.
593     */
594    protected QLRSolvablePolynomial<C, D> shift(ExpVector f) {
595        QLRSolvablePolynomial<C, D> C = ring.getZERO().copy();
596        if (this.isZERO()) {
597            return C;
598        }
599        if (f == null || f.isZERO()) {
600            return this;
601        }
602        Map<ExpVector, C> Cm = C.val;
603        Map<ExpVector, C> Bm = this.val;
604        for (Map.Entry<ExpVector, C> y : Bm.entrySet()) {
605            ExpVector e = y.getKey();
606            C a = y.getValue();
607            ExpVector d = e.sum(f);
608            if (!a.isZERO()) {
609                Cm.put(d, a);
610            }
611        }
612        return C;
613    }
614
615}