Source code

001/*
002 * $Id$
003 */
004
005package edu.jas.application;
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.poly.ExpVector;
016import edu.jas.poly.GenSolvablePolynomial;
017import edu.jas.poly.RecSolvablePolynomial;
018import edu.jas.poly.TableRelation;
019import edu.jas.structure.GcdRingElem;
020
021
022/**
023 * LocalSolvablePolynomial generic recursive solvable polynomials implementing
024 * RingElem. n-variate ordered solvable polynomials over solvable polynomial
025 * coefficients. Objects of this class are intended to be immutable. The
026 * implementation is based on TreeMap respectively SortedMap from exponents to
027 * coefficients by extension of GenPolynomial.
028 * Will be deprecated use QLRSolvablePolynomial.
029 * @param <C> coefficient type
030 * @author Heinz Kredel
031 */
032
033public class LocalSolvablePolynomial<C extends GcdRingElem<C>> extends
034                GenSolvablePolynomial<SolvableLocal<C>> {
035
036
037    /**
038     * The factory for the recursive solvable polynomial ring. Hides super.ring.
039     */
040    public final LocalSolvablePolynomialRing<C> ring;
041
042
043    private static final Logger logger = LogManager.getLogger(LocalSolvablePolynomial.class);
044
045
046    private static final boolean debug = logger.isDebugEnabled();
047
048
049    /**
050     * Constructor for zero LocalSolvablePolynomial.
051     * @param r solvable polynomial ring factory.
052     */
053    public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r) {
054        super(r);
055        ring = r;
056    }
057
058
059    /**
060     * Constructor for LocalSolvablePolynomial.
061     * @param r solvable polynomial ring factory.
062     * @param c coefficient polynomial.
063     * @param e exponent.
064     */
065    public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r, SolvableLocal<C> c, ExpVector e) {
066        this(r);
067        if (c != null && !c.isZERO()) {
068            val.put(e, c);
069        }
070    }
071
072
073    /**
074     * Constructor for LocalSolvablePolynomial.
075     * @param r solvable polynomial ring factory.
076     * @param c coefficient polynomial.
077     */
078    public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r, SolvableLocal<C> c) {
079        this(r, c, r.evzero);
080    }
081
082
083    /**
084     * Constructor for LocalSolvablePolynomial.
085     * @param r solvable polynomial ring factory.
086     * @param S solvable polynomial.
087     */
088    public LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r, GenSolvablePolynomial<SolvableLocal<C>> S) {
089        this(r, S.getMap());
090    }
091
092
093    /**
094     * Constructor for LocalSolvablePolynomial.
095     * @param r solvable polynomial ring factory.
096     * @param v the SortedMap of some other (solvable) polynomial.
097     */
098    protected LocalSolvablePolynomial(LocalSolvablePolynomialRing<C> r,
099                    SortedMap<ExpVector, SolvableLocal<C>> v) {
100        this(r);
101        val.putAll(v); // assume no zero coefficients
102    }
103
104
105    /**
106     * Get the corresponding element factory.
107     * @return factory for this Element.
108     * @see edu.jas.structure.Element#factory()
109     */
110    @Override
111    public LocalSolvablePolynomialRing<C> factory() {
112        return ring;
113    }
114
115
116    /**
117     * Clone this LocalSolvablePolynomial.
118     * @see java.lang.Object#clone()
119     */
120    @Override
121    public LocalSolvablePolynomial<C> copy() {
122        return new LocalSolvablePolynomial<C>(ring, this.val);
123    }
124
125
126    /**
127     * Comparison with any other object.
128     * @see java.lang.Object#equals(java.lang.Object)
129     */
130    @Override
131    public boolean equals(Object B) {
132        if (!(B instanceof LocalSolvablePolynomial)) {
133            return false;
134        }
135        return super.equals(B);
136    }
137
138
139    /**
140     * Hash code for this polynomial.
141     * @see java.lang.Object#hashCode()
142     */
143    @Override
144    public int hashCode() {
145        return super.hashCode();
146    }
147
148
149    /**
150     * LocalSolvablePolynomial multiplication.
151     * @param Bp LocalSolvablePolynomial.
152     * @return this*Bp, where * denotes solvable multiplication.
153     */
154    // not @Override
155    public LocalSolvablePolynomial<C> multiply(LocalSolvablePolynomial<C> Bp) {
156        if (Bp == null || Bp.isZERO()) {
157            return ring.getZERO();
158        }
159        if (this.isZERO()) {
160            return this;
161        }
162        if (Bp.isONE()) {
163            return this;
164        }
165        if (this.isONE()) {
166            return Bp;
167        }
168        assert (ring.nvar == Bp.ring.nvar);
169        if (debug) {
170            logger.debug("ring = " + ring);
171        }
172        //System.out.println("this = " + this + ", Bp = " + Bp);
173        ExpVector Z = ring.evzero;
174        LocalSolvablePolynomial<C> Dp = ring.getZERO().copy();
175        LocalSolvablePolynomial<C> zero = ring.getZERO().copy();
176        SolvableLocal<C> one = ring.getONECoefficient();
177
178        //LocalSolvablePolynomial<C> C1 = null;
179        //LocalSolvablePolynomial<C> C2 = null;
180        Map<ExpVector, SolvableLocal<C>> A = val;
181        Map<ExpVector, SolvableLocal<C>> B = Bp.val;
182        Set<Map.Entry<ExpVector, SolvableLocal<C>>> Bk = B.entrySet();
183        for (Map.Entry<ExpVector, SolvableLocal<C>> y : A.entrySet()) {
184            SolvableLocal<C> a = y.getValue();
185            ExpVector e = y.getKey();
186            if (debug)
187                logger.info("e = " + e + ", a = " + a);
188            //int[] ep = e.dependencyOnVariables();
189            //int el1 = ring.nvar + 1;
190            //if (ep.length > 0) {
191            //    el1 = ep[0];
192            //}
193            //int el1s = ring.nvar + 1 - el1;
194            for (Map.Entry<ExpVector, SolvableLocal<C>> x : Bk) {
195                SolvableLocal<C> b = x.getValue();
196                ExpVector f = x.getKey();
197                if (debug)
198                    logger.info("f = " + f + ", b = " + b);
199                int[] fp = f.dependencyOnVariables();
200                int fl1 = 0;
201                if (fp.length > 0) {
202                    fl1 = fp[fp.length - 1];
203                }
204                int fl1s = ring.nvar + 1 - fl1;
205                // polynomial with coefficient multiplication 
206                LocalSolvablePolynomial<C> Cps = ring.getZERO().copy();
207                //LocalSolvablePolynomial<C> Cs;
208                LocalSolvablePolynomial<C> qp;
209                if (ring.polCoeff.coeffTable.isEmpty() || b.isConstant() || e.isZERO()) { // symmetric
210                    Cps = new LocalSolvablePolynomial<C>(ring, b, e);
211                    if (debug)
212                        logger.info("symmetric coeff: b = " + b + ", e = " + e);
213                } else { // unsymmetric
214                    if (debug)
215                        logger.info("unsymmetric coeff: b = " + b + ", e = " + e);
216                    // compute e * b as ( e * 1/b.den ) * b.num
217                    if (b.den.isONE()) { // recursion base
218                        // for (Map.Entry<ExpVector, C> z : b.num.getMap().entrySet()) {
219                        //     C c = z.getValue();
220                        //     SolvableLocal<C> cc = b.ring.getONE().multiply(c);
221                        //     ExpVector g = z.getKey();
222                        //     if (debug)
223                        //         logger.info("g = " + g + ", c = " + c);
224                        //     int[] gp = g.dependencyOnVariables();
225                        //     int gl1 = 0;
226                        //     if (gp.length > 0) {
227                        //         gl1 = gp[gp.length - 1];
228                        //     }
229                        //     int gl1s = b.ring.ring.nvar + 1 - gl1;
230                        //     if (debug) {
231                        //         logger.info("gl1s = " + gl1s);
232                        //     }
233                        //     // split e = e1 * e2, g = g1 * g2
234                        //     ExpVector e1 = e;
235                        //     ExpVector e2 = Z;
236                        //     if (!e.isZERO()) {
237                        //         e1 = e.subst(el1, 0);
238                        //         e2 = Z.subst(el1, e.getVal(el1));
239                        //     }
240                        //     ExpVector e4;
241                        //     ExpVector g1 = g;
242                        //     ExpVector g2 = Zc;
243                        //     if (!g.isZERO()) {
244                        //         g1 = g.subst(gl1, 0);
245                        //         g2 = Zc.subst(gl1, g.getVal(gl1));
246                        //     }
247                        //     if (debug)
248                        //         logger.info("coeff, e1 = " + e1 + ", e2 = " + e2);
249                        //     if (debug)
250                        //         logger.info("coeff, g1 = " + g1 + ", g2 = " + g2);
251                        //     TableRelation<GenPolynomial<C>> crel = ring.coeffTable.lookup(e2, g2);
252                        //     if (debug)
253                        //         logger.info("coeff, crel = " + crel.p);
254                        //     if (debug)
255                        //         logger.info("coeff, e  = " + e + " g, = " + g + ", crel = " + crel);
256                        //     Cs = ring.fromPolyCoefficients(crel.p); //LocalSolvablePolynomial<C>(ring, crel.p);
257                        //     // rest of multiplication and update relations
258                        //     if (crel.f != null) {
259                        //         SolvableLocal<C> c2 = b.ring.getONE().multiply(crel.f);
260                        //         C2 = new LocalSolvablePolynomial<C>(ring, c2, Z);
261                        //         Cs = Cs.multiply(C2);
262                        //         if (crel.e == null) {
263                        //             e4 = e2;
264                        //         } else {
265                        //             e4 = e2.subtract(crel.e);
266                        //         }
267                        //         ring.coeffTable.update(e4, g2, ring.toPolyCoefficients(Cs));
268                        //     }
269                        //     if (crel.e != null) { // process left part
270                        //         C1 = new LocalSolvablePolynomial<C>(ring, one, crel.e);
271                        //         Cs = C1.multiply(Cs);
272                        //         ring.coeffTable.update(e2, g2, ring.toPolyCoefficients(Cs));
273                        //     }
274                        //     if (!g1.isZERO()) { // process right part
275                        //         SolvableLocal<C> c2 = b.ring.getONE().multiply(g1);
276                        //         C2 = new LocalSolvablePolynomial<C>(ring, c2, Z);
277                        //         Cs = Cs.multiply(C2);
278                        //     }
279                        //     if (!e1.isZERO()) { // process left part
280                        //         C1 = new LocalSolvablePolynomial<C>(ring, one, e1);
281                        //         Cs = C1.multiply(Cs);
282                        //     }
283                        //     //System.out.println("e1*Cs*g1 = " + Cs);
284                        //     Cs = Cs.multiplyLeft(cc); // cc * Cs
285                        //     Cps = (LocalSolvablePolynomial<C>) Cps.sum(Cs);
286                        // } // end b.num loop 
287                        // recursive polynomial coefficient multiplication : e * b.num
288                        RecSolvablePolynomial<C> rsp1 = new RecSolvablePolynomial<C>(ring.polCoeff, e);
289                        RecSolvablePolynomial<C> rsp2 = new RecSolvablePolynomial<C>(ring.polCoeff, b.num);
290                        RecSolvablePolynomial<C> rsp3 = rsp1.multiply(rsp2);
291                        LocalSolvablePolynomial<C> rsp = ring.fromPolyCoefficients(rsp3);
292                        Cps = rsp;
293                        // if (rsp.compareTo(Cps) != 0) {
294                        //     logger.info("coeff-poly: Cps = " + Cps);
295                        //     logger.info("coeff-poly: rsp = " + rsp);
296                        //     //System.out.println("rsp.compareTo(Cps) != 0");
297                        //     //} else {
298                        //     //System.out.println("rsp.compareTo(Cps) == 0");
299                        // }
300                    } else { // b.den != 1
301                        if (debug)
302                            logger.info("coeff-num: Cps = " + Cps + ", num = " + b.num + ", den = " + b.den);
303                        Cps = new LocalSolvablePolynomial<C>(ring, b.ring.getONE(), e);
304
305                        // coefficient multiplication with 1/den: 
306                        LocalSolvablePolynomial<C> qv = Cps;
307                        SolvableLocal<C> qden = new SolvableLocal<C>(b.ring, b.den); // den/1
308                        //System.out.println("qv = " + qv + ", den = " + den);
309                        // recursion with den==1:
310                        LocalSolvablePolynomial<C> v = qv.multiply(qden);
311                        LocalSolvablePolynomial<C> vl = qv.multiplyLeft(qden);
312                        //System.out.println("v = " + v + ", vl = " + vl + ", qden = " + qden);
313                        LocalSolvablePolynomial<C> vr = (LocalSolvablePolynomial<C>) v.subtract(vl);
314                        SolvableLocal<C> qdeni = new SolvableLocal<C>(b.ring, b.ring.ring.getONE(), b.den);
315                        //System.out.println("vr = " + vr + ", qdeni = " + qdeni);
316                        // recursion with smaller head term:
317                        LocalSolvablePolynomial<C> rq = vr.multiply(qdeni);
318                        qp = (LocalSolvablePolynomial<C>) qv.subtract(rq);
319                        qp = qp.multiplyLeft(qdeni);
320                        //System.out.println("qp_i = " + qp);
321                        Cps = qp;
322
323                        if (!b.num.isONE()) {
324                            SolvableLocal<C> qnum = new SolvableLocal<C>(b.ring, b.num); // num/1
325                            // recursion with den == 1:
326                            Cps = Cps.multiply(qnum);
327                        }
328                    }
329                } // end coeff
330                if (debug)
331                    logger.info("coeff-den: Cps = " + Cps);
332                // polynomial multiplication 
333                LocalSolvablePolynomial<C> Dps = ring.getZERO().copy();
334                LocalSolvablePolynomial<C> Ds = null;
335                LocalSolvablePolynomial<C> D1, D2;
336                if (ring.table.isEmpty() || Cps.isConstant() || f.isZERO()) { // symmetric
337                    if (debug)
338                        logger.info("symmetric poly: b = " + b + ", e = " + e);
339                    ExpVector g = e.sum(f);
340                    if (Cps.isConstant()) {
341                        Ds = new LocalSolvablePolynomial<C>(ring, Cps.leadingBaseCoefficient(), g); // symmetric!
342                    } else {
343                        Ds = Cps.shift(f); // symmetric
344                    }
345                } else { // eventually unsymmetric
346                    if (debug)
347                        logger.info("unsymmetric poly: Cps = " + Cps + ", f = " + f);
348                    for (Map.Entry<ExpVector, SolvableLocal<C>> z : Cps.val.entrySet()) {
349                        // split g = g1 * g2, f = f1 * f2
350                        SolvableLocal<C> c = z.getValue();
351                        ExpVector g = z.getKey();
352                        if (debug)
353                            logger.info("g = " + g + ", c = " + c);
354                        int[] gp = g.dependencyOnVariables();
355                        int gl1 = ring.nvar + 1;
356                        if (gp.length > 0) {
357                            gl1 = gp[0];
358                        }
359                        int gl1s = ring.nvar + 1 - gl1;
360                        if (gl1s <= fl1s) { // symmetric
361                            ExpVector h = g.sum(f);
362                            if (debug)
363                                logger.info("disjoint poly: g = " + g + ", f = " + f + ", h = " + h);
364                            Ds = (LocalSolvablePolynomial<C>) zero.sum(one, h); // symmetric!
365                        } else {
366                            ExpVector g1 = g.subst(gl1, 0);
367                            ExpVector g2 = Z.subst(gl1, g.getVal(gl1)); // bug el1, gl1
368                            ExpVector g4;
369                            ExpVector f1 = f.subst(fl1, 0);
370                            ExpVector f2 = Z.subst(fl1, f.getVal(fl1));
371                            if (debug) {
372                                logger.info("poly, g1 = " + g1 + ", f1 = " + f1 + ", Dps = " + Dps);
373                                logger.info("poly, g2 = " + g2 + ", f2 = " + f2);
374                            }
375                            TableRelation<SolvableLocal<C>> rel = ring.table.lookup(g2, f2);
376                            if (debug)
377                                logger.info("poly, g  = " + g + ", f  = " + f + ", rel = " + rel);
378                            Ds = new LocalSolvablePolynomial<C>(ring, rel.p); //ring.copy(rel.p);
379                            if (rel.f != null) {
380                                D2 = new LocalSolvablePolynomial<C>(ring, one, rel.f);
381                                Ds = Ds.multiply(D2);
382                                if (rel.e == null) {
383                                    g4 = g2;
384                                } else {
385                                    g4 = g2.subtract(rel.e);
386                                }
387                                ring.table.update(g4, f2, Ds);
388                            }
389                            if (rel.e != null) {
390                                D1 = new LocalSolvablePolynomial<C>(ring, one, rel.e);
391                                Ds = D1.multiply(Ds);
392                                ring.table.update(g2, f2, Ds);
393                            }
394                            if (!f1.isZERO()) {
395                                D2 = new LocalSolvablePolynomial<C>(ring, one, f1);
396                                Ds = Ds.multiply(D2);
397                                //ring.table.update(?,f1,Ds)
398                            }
399                            if (!g1.isZERO()) {
400                                D1 = new LocalSolvablePolynomial<C>(ring, one, g1);
401                                Ds = D1.multiply(Ds);
402                                //ring.table.update(e1,?,Ds)
403                            }
404                        }
405                        Ds = Ds.multiplyLeft(c); // c * Ds
406                        Dps = (LocalSolvablePolynomial<C>) Dps.sum(Ds);
407                    } // end Dps loop
408                    Ds = Dps;
409                }
410                Ds = Ds.multiplyLeft(a); // multiply(a,b); // non-symmetric 
411                if (debug)
412                    logger.debug("Ds = " + Ds);
413                Dp = (LocalSolvablePolynomial<C>) Dp.sum(Ds);
414            } // end B loop
415        } // end A loop
416          //System.out.println("this * Bp = " + Dp);
417        return Dp;
418    }
419
420
421    /**
422     * LocalSolvablePolynomial left and right multiplication. Product with two
423     * polynomials.
424     * @param S LocalSolvablePolynomial.
425     * @param T LocalSolvablePolynomial.
426     * @return S*this*T.
427     */
428    // not @Override
429    public LocalSolvablePolynomial<C> multiply(LocalSolvablePolynomial<C> S, LocalSolvablePolynomial<C> T) {
430        if (S.isZERO() || T.isZERO() || this.isZERO()) {
431            return ring.getZERO();
432        }
433        if (S.isONE()) {
434            return multiply(T);
435        }
436        if (T.isONE()) {
437            return S.multiply(this);
438        }
439        return S.multiply(this).multiply(T);
440    }
441
442
443    /**
444     * LocalSolvablePolynomial multiplication. Product with coefficient ring
445     * element.
446     * @param b solvable coefficient.
447     * @return this*b, where * is coefficient multiplication.
448     */
449    @Override
450    public LocalSolvablePolynomial<C> multiply(SolvableLocal<C> b) {
451        LocalSolvablePolynomial<C> Cp = ring.getZERO().copy();
452        if (b == null || b.isZERO()) {
453            return Cp;
454        }
455        if (b.isONE()) {
456            return this;
457        }
458        Cp = new LocalSolvablePolynomial<C>(ring, b, ring.evzero);
459        return multiply(Cp);
460    }
461
462
463    /**
464     * LocalSolvablePolynomial left and right multiplication. Product with
465     * coefficient ring element.
466     * @param b coefficient polynomial.
467     * @param c coefficient polynomial.
468     * @return b*this*c, where * is coefficient multiplication.
469     */
470    @Override
471    public LocalSolvablePolynomial<C> multiply(SolvableLocal<C> b, SolvableLocal<C> c) {
472        LocalSolvablePolynomial<C> Cp = ring.getZERO().copy();
473        if (b == null || b.isZERO()) {
474            return Cp;
475        }
476        if (c == null || c.isZERO()) {
477            return Cp;
478        }
479        if (b.isONE() && c.isONE()) {
480            return this;
481        }
482        Cp = new LocalSolvablePolynomial<C>(ring, b, ring.evzero);
483        LocalSolvablePolynomial<C> Dp = new LocalSolvablePolynomial<C>(ring, c, ring.evzero);
484        return multiply(Cp, Dp);
485    }
486
487
488    /**
489     * LocalSolvablePolynomial multiplication. Product with exponent vector.
490     * @param e exponent.
491     * @return this * x<sup>e</sup>, where * denotes solvable multiplication.
492     */
493    @Override
494    public LocalSolvablePolynomial<C> multiply(ExpVector e) {
495        if (e == null || e.isZERO()) {
496            return this;
497        }
498        SolvableLocal<C> b = ring.getONECoefficient();
499        return multiply(b, e);
500    }
501
502
503    /**
504     * LocalSolvablePolynomial left and right multiplication. Product with
505     * exponent vector.
506     * @param e exponent.
507     * @param f exponent.
508     * @return x<sup>e</sup> * this * x<sup>f</sup>, where * denotes solvable
509     *         multiplication.
510     */
511    @Override
512    public LocalSolvablePolynomial<C> multiply(ExpVector e, ExpVector f) {
513        if (e == null || e.isZERO()) {
514            return this;
515        }
516        if (f == null || f.isZERO()) {
517            return this;
518        }
519        SolvableLocal<C> b = ring.getONECoefficient();
520        return multiply(b, e, b, f);
521    }
522
523
524    /**
525     * LocalSolvablePolynomial multiplication. Product with ring element and
526     * exponent vector.
527     * @param b coefficient polynomial.
528     * @param e exponent.
529     * @return this * b x<sup>e</sup>, where * denotes solvable multiplication.
530     */
531    @Override
532    public LocalSolvablePolynomial<C> multiply(SolvableLocal<C> b, ExpVector e) {
533        if (b == null || b.isZERO()) {
534            return ring.getZERO();
535        }
536        if (b.isONE() && e.isZERO()) {
537            return this;
538        }
539        LocalSolvablePolynomial<C> Cp = new LocalSolvablePolynomial<C>(ring, b, e);
540        return multiply(Cp);
541    }
542
543
544    /**
545     * LocalSolvablePolynomial left and right multiplication. Product with ring
546     * element and exponent vector.
547     * @param b coefficient polynomial.
548     * @param e exponent.
549     * @param c coefficient polynomial.
550     * @param f exponent.
551     * @return b x<sup>e</sup> * this * c x<sup>f</sup>, where * denotes
552     *         solvable multiplication.
553     */
554    @Override
555    public LocalSolvablePolynomial<C> multiply(SolvableLocal<C> b, ExpVector e, SolvableLocal<C> c,
556                    ExpVector f) {
557        if (b == null || b.isZERO()) {
558            return ring.getZERO();
559        }
560        if (c == null || c.isZERO()) {
561            return ring.getZERO();
562        }
563        if (b.isONE() && e.isZERO() && c.isONE() && f.isZERO()) {
564            return this;
565        }
566        LocalSolvablePolynomial<C> Cp = new LocalSolvablePolynomial<C>(ring, b, e);
567        LocalSolvablePolynomial<C> Dp = new LocalSolvablePolynomial<C>(ring, c, f);
568        return multiply(Cp, Dp);
569    }
570
571
572    /**
573     * LocalSolvablePolynomial multiplication. Left product with ring element
574     * and exponent vector.
575     * @param b coefficient polynomial.
576     * @param e exponent.
577     * @return b x<sup>e</sup> * this, where * denotes solvable multiplication.
578     */
579    @Override
580    public LocalSolvablePolynomial<C> multiplyLeft(SolvableLocal<C> b, ExpVector e) {
581        if (b == null || b.isZERO()) {
582            return ring.getZERO();
583        }
584        LocalSolvablePolynomial<C> Cp = new LocalSolvablePolynomial<C>(ring, b, e);
585        return Cp.multiply(this);
586    }
587
588
589    /**
590     * LocalSolvablePolynomial multiplication. Left product with exponent
591     * vector.
592     * @param e exponent.
593     * @return x<sup>e</sup> * this, where * denotes solvable multiplication.
594     */
595    @Override
596    public LocalSolvablePolynomial<C> multiplyLeft(ExpVector e) {
597        if (e == null || e.isZERO()) {
598            return this;
599        }
600        SolvableLocal<C> b = ring.getONECoefficient();
601        LocalSolvablePolynomial<C> Cp = new LocalSolvablePolynomial<C>(ring, b, e);
602        return Cp.multiply(this);
603    }
604
605
606    /**
607     * LocalSolvablePolynomial multiplication. Left product with coefficient
608     * ring element.
609     * @param b coefficient polynomial.
610     * @return b*this, where * is coefficient multiplication.
611     */
612    @Override
613    public LocalSolvablePolynomial<C> multiplyLeft(SolvableLocal<C> b) {
614        LocalSolvablePolynomial<C> Cp = ring.getZERO().copy();
615        if (b == null || b.isZERO()) {
616            return Cp;
617        }
618        Map<ExpVector, SolvableLocal<C>> Cm = Cp.val; //getMap();
619        Map<ExpVector, SolvableLocal<C>> Am = val;
620        SolvableLocal<C> c;
621        for (Map.Entry<ExpVector, SolvableLocal<C>> y : Am.entrySet()) {
622            ExpVector e = y.getKey();
623            SolvableLocal<C> a = y.getValue();
624            c = b.multiply(a);
625            if (!c.isZERO()) {
626                Cm.put(e, c);
627            }
628        }
629        return Cp;
630    }
631
632
633    /**
634     * LocalSolvablePolynomial multiplication. Left product with 'monomial'.
635     * @param m 'monomial'.
636     * @return m * this, where * denotes solvable multiplication.
637     */
638    @Override
639    public LocalSolvablePolynomial<C> multiplyLeft(Map.Entry<ExpVector, SolvableLocal<C>> m) {
640        if (m == null) {
641            return ring.getZERO();
642        }
643        return multiplyLeft(m.getValue(), m.getKey());
644    }
645
646
647    /**
648     * LocalSolvablePolynomial multiplication. Product with 'monomial'.
649     * @param m 'monomial'.
650     * @return this * m, where * denotes solvable multiplication.
651     */
652    @Override
653    public LocalSolvablePolynomial<C> multiply(Map.Entry<ExpVector, SolvableLocal<C>> m) {
654        if (m == null) {
655            return ring.getZERO();
656        }
657        return multiply(m.getValue(), m.getKey());
658    }
659
660
661    /**
662     * LocalSolvablePolynomial multiplication. Left product with coefficient
663     * ring element.
664     * @param f exponent vector.
665     * @return B*f, where * is commutative multiplication.
666     */
667    protected LocalSolvablePolynomial<C> shift(ExpVector f) {
668        LocalSolvablePolynomial<C> C = ring.getZERO().copy();
669        if (this.isZERO()) {
670            return C;
671        }
672        if (f == null || f.isZERO()) {
673            return this;
674        }
675        Map<ExpVector, SolvableLocal<C>> Cm = C.val;
676        Map<ExpVector, SolvableLocal<C>> Bm = this.val;
677        for (Map.Entry<ExpVector, SolvableLocal<C>> y : Bm.entrySet()) {
678            ExpVector e = y.getKey();
679            SolvableLocal<C> a = y.getValue();
680            ExpVector d = e.sum(f);
681            if (!a.isZERO()) {
682                Cm.put(d, a);
683            }
684        }
685        return C;
686    }
687
688}