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.LogManager;
013import org.apache.logging.log4j.Logger;
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(),
224                                            b.denominator());
225                        RingFactory<C> bfq = (RingFactory<C>) b.factory();
226                        Cps = new QLRSolvablePolynomial<C, D>(ring, bfq.getONE(), e);
227
228                        // coefficient multiplication with 1/den: 
229                        QLRSolvablePolynomial<C, D> qv = Cps;
230                        //C qden = new C(b.denominator().factory(), b.denominator()); // den/1
231                        C qden = ring.qpfac.create(b.denominator()); // den/1
232                        //System.out.println("qv = " + qv + ", den = " + den);
233                        // recursion with den==1:
234                        QLRSolvablePolynomial<C, D> v = qv.multiply(qden);
235                        QLRSolvablePolynomial<C, D> vl = qv.multiplyLeft(qden);
236                        //System.out.println("v = " + v + ", vl = " + vl + ", qden = " + qden);
237                        QLRSolvablePolynomial<C, D> vr = (QLRSolvablePolynomial<C, D>) v.subtract(vl);
238                        //C qdeni = new C(b.factory(), b.factory().getONE().numerator(), b.denominator());
239                        C qdeni = ring.qpfac.create(ring.qpfac.pairFactory().getONE(), b.denominator()); // 1/den
240                        //System.out.println("vr = " + vr + ", qdeni = " + qdeni);
241                        // recursion with smaller head term:
242                        if (qv.leadingExpVector().equals(vr.leadingExpVector())) {
243                            throw new IllegalArgumentException("qv !> vr: qv = " + qv + ", vr = " + vr);
244                        }
245                        QLRSolvablePolynomial<C, D> rq = vr.multiply(qdeni);
246                        qp = (QLRSolvablePolynomial<C, D>) qv.subtract(rq);
247                        qp = qp.multiplyLeft(qdeni);
248                        //System.out.println("qp_i = " + qp);
249                        Cps = qp;
250
251                        if (!b.numerator().isONE()) {
252                            //C qnum = new C(b.denominator().factory(), b.numerator()); // num/1
253                            C qnum = ring.qpfac.create(b.numerator()); // num/1
254                            // recursion with den == 1:
255                            Cps = Cps.multiply(qnum);
256                        }
257                    }
258                } // end coeff
259                if (debug)
260                    logger.info("coeff-den: Cps = {}", Cps);
261                // polynomial multiplication 
262                QLRSolvablePolynomial<C, D> Dps = ring.getZERO().copy();
263                QLRSolvablePolynomial<C, D> Ds = null;
264                QLRSolvablePolynomial<C, D> D1, D2;
265                if (ring.isCommutative() || Cps.isConstant() || f.isZERO()) { // symmetric
266                    if (debug)
267                        logger.info("symmetric poly: b = {}, e = {}", b, e);
268                    if (Cps.isConstant()) {
269                        ExpVector g = e.sum(f);
270                        Ds = new QLRSolvablePolynomial<C, D>(ring, Cps.leadingBaseCoefficient(), g); // symmetric!
271                    } else {
272                        Ds = Cps.shift(f); // symmetric
273                    }
274                } else { // eventually unsymmetric
275                    if (debug)
276                        logger.info("unsymmetric poly: Cps = {}, f = {}", Cps, f);
277                    for (Map.Entry<ExpVector, C> z : Cps.val.entrySet()) {
278                        // split g = g1 * g2, f = f1 * f2
279                        C c = z.getValue();
280                        ExpVector g = z.getKey();
281                        if (debug)
282                            logger.info("g = {}, c = {}", g, c);
283                        int[] gp = g.dependencyOnVariables();
284                        int gl1 = ring.nvar + 1;
285                        if (gp.length > 0) {
286                            gl1 = gp[0];
287                        }
288                        int gl1s = ring.nvar + 1 - gl1;
289                        if (gl1s <= fl1s) { // symmetric
290                            ExpVector h = g.sum(f);
291                            if (debug)
292                                logger.info("disjoint poly: g = {}, f = {}, h = {}", g, f, h);
293                            Ds = (QLRSolvablePolynomial<C, D>) zero.sum(one, h); // symmetric!
294                        } else {
295                            ExpVector g1 = g.subst(gl1, 0);
296                            ExpVector g2 = Z.subst(gl1, g.getVal(gl1)); // bug el1, gl1
297                            ExpVector g4;
298                            ExpVector f1 = f.subst(fl1, 0);
299                            ExpVector f2 = Z.subst(fl1, f.getVal(fl1));
300                            if (debug) {
301                                logger.info("poly, g1 = {}, f1 = {}, Dps = {}", g1, f1, Dps);
302                                logger.info("poly, g2 = {}, f2 = {}", g2, f2);
303                            }
304                            TableRelation<C> rel = ring.table.lookup(g2, f2);
305                            if (debug)
306                                logger.info("poly, g  = {}, f = {}, rel = {}", g, f, rel);
307                            Ds = new QLRSolvablePolynomial<C, D>(ring, rel.p); //ring.copy(rel.p);
308                            if (rel.f != null) {
309                                D2 = new QLRSolvablePolynomial<C, D>(ring, one, rel.f);
310                                Ds = Ds.multiply(D2);
311                                if (rel.e == null) {
312                                    g4 = g2;
313                                } else {
314                                    g4 = g2.subtract(rel.e);
315                                }
316                                ring.table.update(g4, f2, Ds);
317                            }
318                            if (rel.e != null) {
319                                D1 = new QLRSolvablePolynomial<C, D>(ring, one, rel.e);
320                                Ds = D1.multiply(Ds);
321                                ring.table.update(g2, f2, Ds);
322                            }
323                            if (!f1.isZERO()) {
324                                D2 = new QLRSolvablePolynomial<C, D>(ring, one, f1);
325                                Ds = Ds.multiply(D2);
326                                //ring.table.update(?,f1,Ds)
327                            }
328                            if (!g1.isZERO()) {
329                                D1 = new QLRSolvablePolynomial<C, D>(ring, one, g1);
330                                Ds = D1.multiply(Ds);
331                                //ring.table.update(e1,?,Ds)
332                            }
333                        }
334                        Ds = Ds.multiplyLeft(c); // c * Ds
335                        //Dps = (QLRSolvablePolynomial<C, D>) Dps.sum(Ds);
336                        Dps.doAddTo(Ds);
337                    } // end Dps loop
338                    Ds = Dps;
339                }
340                Ds = Ds.multiplyLeft(a); // multiply(a,b); // non-symmetric 
341                if (debug)
342                    logger.debug("Ds = {}", Ds);
343                //Dp = (QLRSolvablePolynomial<C, D>) Dp.sum(Ds);
344                Dp.doAddTo(Ds);
345            } // end B loop
346        } // end A loop
347          //System.out.println("this * Bp = " + Dp);
348        return Dp;
349    }
350
351
352    /**
353     * QLRSolvablePolynomial left and right multiplication. Product with two
354     * polynomials.
355     * @param S QLRSolvablePolynomial.
356     * @param T QLRSolvablePolynomial.
357     * @return S*this*T.
358     */
359    // not @Override
360    public QLRSolvablePolynomial<C, D> multiply(QLRSolvablePolynomial<C, D> S,
361                    QLRSolvablePolynomial<C, D> T) {
362        if (S.isZERO() || T.isZERO() || this.isZERO()) {
363            return ring.getZERO();
364        }
365        if (S.isONE()) {
366            return multiply(T);
367        }
368        if (T.isONE()) {
369            return S.multiply(this);
370        }
371        return S.multiply(this).multiply(T);
372    }
373
374
375    /**
376     * QLRSolvablePolynomial multiplication. Product with coefficient ring
377     * element.
378     * @param b solvable coefficient.
379     * @return this*b, where * is coefficient multiplication.
380     */
381    @Override
382    public QLRSolvablePolynomial<C, D> multiply(C b) {
383        QLRSolvablePolynomial<C, D> Cp = ring.getZERO().copy();
384        if (b == null || b.isZERO()) {
385            return Cp;
386        }
387        if (b.isONE()) {
388            return this;
389        }
390        Cp = new QLRSolvablePolynomial<C, D>(ring, b, ring.evzero);
391        return multiply(Cp);
392    }
393
394
395    /**
396     * QLRSolvablePolynomial left and right multiplication. Product with
397     * coefficient ring element.
398     * @param b coefficient polynomial.
399     * @param c coefficient polynomial.
400     * @return b*this*c, where * is coefficient multiplication.
401     */
402    @Override
403    public QLRSolvablePolynomial<C, D> multiply(C b, C c) {
404        QLRSolvablePolynomial<C, D> Cp = ring.getZERO().copy();
405        if (b == null || b.isZERO()) {
406            return Cp;
407        }
408        if (c == null || c.isZERO()) {
409            return Cp;
410        }
411        if (b.isONE() && c.isONE()) {
412            return this;
413        }
414        Cp = new QLRSolvablePolynomial<C, D>(ring, b, ring.evzero);
415        QLRSolvablePolynomial<C, D> Dp = new QLRSolvablePolynomial<C, D>(ring, c, ring.evzero);
416        return multiply(Cp, Dp);
417    }
418
419
420    /**
421     * QLRSolvablePolynomial multiplication. Product with exponent vector.
422     * @param e exponent.
423     * @return this * x<sup>e</sup>, where * denotes solvable multiplication.
424     */
425    @Override
426    public QLRSolvablePolynomial<C, D> multiply(ExpVector e) {
427        if (e == null || e.isZERO()) {
428            return this;
429        }
430        C b = ring.getONECoefficient();
431        return multiply(b, e);
432    }
433
434
435    /**
436     * QLRSolvablePolynomial left and right multiplication. Product with
437     * exponent vector.
438     * @param e exponent.
439     * @param f exponent.
440     * @return x<sup>e</sup> * this * x<sup>f</sup>, where * denotes solvable
441     *         multiplication.
442     */
443    @Override
444    public QLRSolvablePolynomial<C, D> multiply(ExpVector e, ExpVector f) {
445        if (e == null || e.isZERO()) {
446            return this;
447        }
448        if (f == null || f.isZERO()) {
449            return this;
450        }
451        C b = ring.getONECoefficient();
452        return multiply(b, e, b, f);
453    }
454
455
456    /**
457     * QLRSolvablePolynomial multiplication. Product with ring element and
458     * exponent vector.
459     * @param b coefficient polynomial.
460     * @param e exponent.
461     * @return this * b x<sup>e</sup>, where * denotes solvable multiplication.
462     */
463    @Override
464    public QLRSolvablePolynomial<C, D> multiply(C b, ExpVector e) {
465        if (b == null || b.isZERO()) {
466            return ring.getZERO();
467        }
468        if (b.isONE() && e.isZERO()) {
469            return this;
470        }
471        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
472        return multiply(Cp);
473    }
474
475
476    /**
477     * QLRSolvablePolynomial left and right multiplication. Product with ring
478     * element and exponent vector.
479     * @param b coefficient polynomial.
480     * @param e exponent.
481     * @param c coefficient polynomial.
482     * @param f exponent.
483     * @return b x<sup>e</sup> * this * c x<sup>f</sup>, where * denotes
484     *         solvable multiplication.
485     */
486    @Override
487    public QLRSolvablePolynomial<C, D> multiply(C b, ExpVector e, C c, ExpVector f) {
488        if (b == null || b.isZERO()) {
489            return ring.getZERO();
490        }
491        if (c == null || c.isZERO()) {
492            return ring.getZERO();
493        }
494        if (b.isONE() && e.isZERO() && c.isONE() && f.isZERO()) {
495            return this;
496        }
497        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
498        QLRSolvablePolynomial<C, D> Dp = new QLRSolvablePolynomial<C, D>(ring, c, f);
499        return multiply(Cp, Dp);
500    }
501
502
503    /**
504     * QLRSolvablePolynomial multiplication. Left product with ring element and
505     * exponent vector.
506     * @param b coefficient polynomial.
507     * @param e exponent.
508     * @return b x<sup>e</sup> * this, where * denotes solvable multiplication.
509     */
510    @Override
511    public QLRSolvablePolynomial<C, D> multiplyLeft(C b, ExpVector e) {
512        if (b == null || b.isZERO()) {
513            return ring.getZERO();
514        }
515        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
516        return Cp.multiply(this);
517    }
518
519
520    /**
521     * QLRSolvablePolynomial multiplication. Left product with exponent vector.
522     * @param e exponent.
523     * @return x<sup>e</sup> * this, where * denotes solvable multiplication.
524     */
525    @Override
526    public QLRSolvablePolynomial<C, D> multiplyLeft(ExpVector e) {
527        if (e == null || e.isZERO()) {
528            return this;
529        }
530        C b = ring.getONECoefficient();
531        QLRSolvablePolynomial<C, D> Cp = new QLRSolvablePolynomial<C, D>(ring, b, e);
532        return Cp.multiply(this);
533    }
534
535
536    /**
537     * QLRSolvablePolynomial multiplication. Left product with coefficient ring
538     * element.
539     * @param b coefficient polynomial.
540     * @return b*this, where * is coefficient multiplication.
541     */
542    @Override
543    public QLRSolvablePolynomial<C, D> multiplyLeft(C b) {
544        QLRSolvablePolynomial<C, D> Cp = ring.getZERO().copy();
545        if (b == null || b.isZERO()) {
546            return Cp;
547        }
548        Map<ExpVector, C> Cm = Cp.val; //getMap();
549        Map<ExpVector, C> Am = val;
550        C c;
551        for (Map.Entry<ExpVector, C> y : Am.entrySet()) {
552            ExpVector e = y.getKey();
553            C a = y.getValue();
554            c = b.multiply(a);
555            if (!c.isZERO()) {
556                Cm.put(e, c);
557            }
558        }
559        return Cp;
560    }
561
562
563    /**
564     * QLRSolvablePolynomial multiplication. Left product with 'monomial'.
565     * @param m 'monomial'.
566     * @return m * this, where * denotes solvable multiplication.
567     */
568    @Override
569    public QLRSolvablePolynomial<C, D> multiplyLeft(Map.Entry<ExpVector, C> m) {
570        if (m == null) {
571            return ring.getZERO();
572        }
573        return multiplyLeft(m.getValue(), m.getKey());
574    }
575
576
577    /**
578     * QLRSolvablePolynomial multiplication. Product with 'monomial'.
579     * @param m 'monomial'.
580     * @return this * m, where * denotes solvable multiplication.
581     */
582    @Override
583    public QLRSolvablePolynomial<C, D> multiply(Map.Entry<ExpVector, C> m) {
584        if (m == null) {
585            return ring.getZERO();
586        }
587        return multiply(m.getValue(), m.getKey());
588    }
589
590
591    /**
592     * QLRSolvablePolynomial multiplication with exponent vector.
593     * @param f exponent vector.
594     * @return B*f, where * is commutative multiplication.
595     */
596    protected QLRSolvablePolynomial<C, D> shift(ExpVector f) {
597        QLRSolvablePolynomial<C, D> C = ring.getZERO().copy();
598        if (this.isZERO()) {
599            return C;
600        }
601        if (f == null || f.isZERO()) {
602            return this;
603        }
604        Map<ExpVector, C> Cm = C.val;
605        Map<ExpVector, C> Bm = this.val;
606        for (Map.Entry<ExpVector, C> y : Bm.entrySet()) {
607            ExpVector e = y.getKey();
608            C a = y.getValue();
609            ExpVector d = e.sum(f);
610            if (!a.isZERO()) {
611                Cm.put(d, a);
612            }
613        }
614        return C;
615    }
616
617}