Source code

001/*
002 * $Id$
003 */
004
005package edu.jas.application;
006
007
008import java.util.ArrayList;
009import java.util.List;
010import java.util.Map;
011
012import edu.jas.arith.BigRational;
013import edu.jas.kern.ComputerThreads;
014import edu.jas.poly.ExpVector;
015import edu.jas.poly.GenPolynomial;
016import edu.jas.poly.GenSolvablePolynomial;
017import edu.jas.poly.GenSolvablePolynomialRing;
018import edu.jas.poly.PolyUtil;
019import edu.jas.poly.QLRSolvablePolynomial;
020import edu.jas.poly.QLRSolvablePolynomialRing;
021import edu.jas.poly.RecSolvablePolynomial;
022import edu.jas.poly.RelationGenerator;
023import edu.jas.poly.TermOrder;
024import edu.jas.poly.WeylRelations;
025import edu.jas.poly.WeylRelationsIterated;
026
027import junit.framework.Test;
028import junit.framework.TestCase;
029import junit.framework.TestSuite;
030
031
032/**
033 * BigRational coefficients LocalSolvablePolynomial QLR representation tests
034 * with JUnit.
035 * @author Heinz Kredel
036 */
037
038public class LocalSolvablePolynomialQLRTest extends TestCase {
039
040
041    /**
042     * main.
043     */
044    public static void main(String[] args) {
045
046        junit.textui.TestRunner.run(suite());
047        ComputerThreads.terminate();
048    }
049
050
051    /**
052     * Constructs a <CODE>LocalSolvablePolynomialQLRTest</CODE> object.
053     * @param name String.
054     */
055    public LocalSolvablePolynomialQLRTest(String name) {
056        super(name);
057    }
058
059
060    /**
061     */
062    public static Test suite() {
063        TestSuite suite = new TestSuite(LocalSolvablePolynomialQLRTest.class);
064        return suite;
065    }
066
067
068    QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> a, b, c, d, e, f, x1, x2;
069
070
071    int rl = 4;
072
073
074    int kl = 1;
075
076
077    int ll = 4;
078
079
080    int el = 3;
081
082
083    float q = 0.2f;
084
085
086    String[] cvars = new String[] { "a", "b" };
087
088
089    String[] vars = new String[] { "w", "x", "y", "z" };
090
091
092    QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational> ring;
093
094
095    BigRational cfac;
096
097
098    //GenSolvablePolynomialRing<SolvableLocal<BigRational>> sring;
099
100
101    GenSolvablePolynomialRing<BigRational> cring;
102
103
104    SolvableLocalRing<BigRational> qcring;
105
106
107    SolvableIdeal<BigRational> sideal;
108
109
110    TermOrder tord = new TermOrder(TermOrder.INVLEX);
111
112
113    @Override
114    protected void setUp() {
115        cfac = new BigRational(1);
116        cring = new GenSolvablePolynomialRing<BigRational>(cfac, tord, cvars);
117        RelationGenerator<BigRational> wc = new WeylRelations<BigRational>();
118        cring.addRelations(wc); //wc.generate(cring);
119        List<GenSolvablePolynomial<BigRational>> il = new ArrayList<GenSolvablePolynomial<BigRational>>();
120        GenSolvablePolynomial<BigRational> p1 = cring.parse("b - a^2");
121        il.add(p1);
122        //p1 = cring.parse("a - b^5"); 
123        //il.add(p1);
124        sideal = new SolvableIdeal<BigRational>(cring, il);
125        qcring = new SolvableLocalRing<BigRational>(sideal);
126        ring = new QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational>(qcring, tord, vars);
127        RelationGenerator<SolvableLocal<BigRational>> wl = new WeylRelations<SolvableLocal<BigRational>>();
128        ring.addRelations(wl); //wl.generate(ring);
129        a = b = c = d = e = null;
130    }
131
132
133    @Override
134    protected void tearDown() {
135        ring = null;
136        a = b = c = d = e = null;
137    }
138
139
140    /**
141     * Test constructor, generators and properties.
142     */
143    public void testConstructor() {
144        assertFalse("not commutative", ring.isCommutative());
145        assertTrue("associative", ring.isAssociative());
146
147        a = new QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>(ring);
148        assertTrue("length( a ) = 0", a.length() == 0);
149        assertTrue("isZERO( a )", a.isZERO());
150        assertTrue("isONE( a )", !a.isONE());
151
152        c = ring.getONE();
153        assertTrue("length( c ) = 1", c.length() == 1);
154        assertTrue("isZERO( c )", !c.isZERO());
155        assertTrue("isONE( c )", c.isONE());
156
157        d = ring.getZERO();
158        assertTrue("length( d ) = 0", d.length() == 0);
159        assertTrue("isZERO( d )", d.isZERO());
160        assertTrue("isONE( d )", !d.isONE());
161        //System.out.println("d = " + d);
162
163        //System.out.println("");
164        for (GenPolynomial<SolvableLocal<BigRational>> g : ring.generators()) {
165            //System.out.println("g = " + g + ", ");
166            assertFalse("not isZERO( g )", g.isZERO());
167        }
168        //System.out.println("");
169        assertTrue("isAssociative: ", ring.isAssociative());
170    }
171
172
173    /**
174     * Test random polynomial.
175     */
176    public void testRandom() {
177        for (int i = 0; i < 5; i++) {
178            // a = ring.random(ll+2*i);
179            a = ring.random(kl, ll + 2 * i, el + i, q);
180            //System.out.println("a = " + a);
181            assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
182            assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
183            assertTrue(" not isONE( a" + i + " )", !a.isONE());
184        }
185    }
186
187
188    /**
189     * Test addition.
190     */
191    @SuppressWarnings("unchecked")
192    public void testAddition() {
193        a = ring.random(kl + 1, ll, el, q);
194        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.subtract(a);
195        assertTrue("a-a = 0", c.isZERO());
196
197        b = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(a);
198        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) b.subtract(a);
199        assertEquals("a+a-a = a", c, a);
200
201        b = ring.random(kl, ll, el, q);
202        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) b.sum(a);
203        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(b);
204        assertEquals("a+b = b+a", c, d);
205
206        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(b);
207        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) c.subtract(b);
208        //System.out.println("a = " + a);
209        //System.out.println("d = " + d);
210        assertEquals("a+b-b = a", a, d);
211
212        c = ring.random(kl, ll, el, q);
213        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(b.sum(c));
214        e = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(b).sum(c);
215        assertEquals("a+(b+c) = (a+b)+c", d, e);
216        //System.out.println("a = " + a);
217        //System.out.println("b = " + b);
218        //System.out.println("c = " + c);
219        //System.out.println("d = " + d);
220        //System.out.println("e = " + e);
221
222        ExpVector u = ExpVector.random(rl, el, q);
223        SolvableLocal<BigRational> x = qcring.random(kl);
224        //System.out.println("x = " + x);
225        //System.out.println("u = " + u);
226
227        b = ring.getONE().multiply(x, u);
228        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(b);
229        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(x, u);
230        //System.out.println("a = " + a);
231        //System.out.println("b = " + b);
232        //System.out.println("c = " + c);
233        //System.out.println("d = " + d);
234        assertEquals("a+p(x,u) = a+(x,u)", c, d);
235
236        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.subtract(b);
237        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.subtract(x, u);
238        assertEquals("a-p(x,u) = a-(x,u)", c, d);
239
240        a = ring.getZERO();
241        b = ring.getONE().multiply(x, u);
242        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) b.sum(a);
243        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.sum(x, u);
244        assertEquals("a+p(x,u) = a+(x,u)", c, d);
245
246        c = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.subtract(b);
247        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.subtract(x, u);
248        assertEquals("a-p(x,u) = a-(x,u)", c, d);
249    }
250
251
252    /**
253     * Test multiplication.
254     */
255    @SuppressWarnings("unchecked")
256    public void testMultiplication() {
257        //System.out.println("ring = " + ring);
258        a = ring.random(kl, ll - 1, el - 1, q);
259        //a = ring.parse(" b y z + a w z ");  
260        b = ring.random(kl, ll - 1, el - 1, q);
261        //b = ring.parse(" w x - b x "); 
262
263        c = b.multiply(a);
264        d = a.multiply(b);
265        //System.out.println("a = " + a);
266        //System.out.println("b = " + b);
267        //System.out.println("c = " + c);
268        //System.out.println("d = " + d);
269        assertTrue("a*b != b*a", c.equals(d) || c.leadingExpVector().equals(d.leadingExpVector()));
270
271        c = ring.random(kl, ll - 1, el - 1, q);
272        d = a.multiply(b.multiply(c));
273        e = a.multiply(b).multiply(c);
274        assertEquals("a(bc) = (ab)c", d, e);
275        //System.out.println("a = " + a);
276        //System.out.println("b = " + b);
277        //System.out.println("c = " + c);
278        //System.out.println("d = " + d);
279        //System.out.println("e = " + e);
280
281        SolvableLocal<BigRational> xp = a.leadingBaseCoefficient().inverse();
282        d = a.multiply(xp);
283        assertTrue("monic(a) = a*(1/ldcf(ldcf(a)))", d.leadingBaseCoefficient().isONE());
284        //System.out.println("a = " + a);
285        //System.out.println("d = " + d);
286
287        d = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.monic();
288        assertTrue("a.monic(): ", d.leadingBaseCoefficient().isONE());
289    }
290
291
292    /**
293     * Test commutative ring.
294     */
295    @SuppressWarnings("unchecked")
296    public void testCommutative() {
297        //System.out.println("table = " + ring.table.toString(vars));
298        //System.out.println("table = " + ring.table.toScript());
299        //System.out.println("ring = " + ring);
300        //System.out.println("ring.table = " + ring.table.toScript());
301        //assertEquals("table == ring.table: ", table, ring.table); // ?
302        assertTrue("# relations == 2", ring.table.size() == 2);
303
304        cring = new GenSolvablePolynomialRing<BigRational>(cfac, tord, cvars);
305        List<GenSolvablePolynomial<BigRational>> il = new ArrayList<GenSolvablePolynomial<BigRational>>();
306        GenSolvablePolynomial<BigRational> p1 = cring.parse("b - a^2");
307        il.add(p1);
308        sideal = new SolvableIdeal<BigRational>(cring, il);
309        qcring = new SolvableLocalRing<BigRational>(sideal);
310        ring = new QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational>(qcring, ring);
311        //table = ring.table;
312        //System.out.println("table = " + table.toString(vars));
313        //System.out.println("ring = " + ring);
314
315        assertTrue("isCommutative()", ring.isCommutative());
316        assertTrue("isAssociative()", ring.isAssociative());
317
318        a = ring.random(kl, ll, el, q);
319        //a = ring.parse(" b x y z + a w z ");
320        //System.out.println("a = " + a);
321        b = ring.random(kl, ll, el, q);
322        //b = ring.parse(" w y z - b x ");
323        //System.out.println("b = " + b);
324
325        // commutative
326        c = b.multiply(a);
327        //System.out.println("c = " + c);
328        d = a.multiply(b);
329        //d = ring.getONE(); 
330        //System.out.println("d = " + d);
331        assertEquals("b*a == a*b: ", c, d);
332    }
333
334
335    /**
336     * Test distributive law.
337     */
338    @SuppressWarnings("unchecked")
339    public void testDistributive() {
340        a = ring.random(kl, ll, el, q);
341        b = ring.random(kl, ll, el, q);
342        c = ring.random(kl, ll, el, q);
343
344        d = a.multiply((QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) b.sum(c));
345        e = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a.multiply(b).sum(a.multiply(c));
346        assertEquals("a*(b+c) = a*b+a*c", d, e);
347    }
348
349
350    /**
351     * Test solvable coefficient ring.
352     */
353    @SuppressWarnings("unchecked")
354    public void testSolvableCoeffs() {
355        GenSolvablePolynomialRing<BigRational> csring = new GenSolvablePolynomialRing<BigRational>(cfac, tord,
356                        cvars);
357        //RelationGenerator<BigRational> wc = new WeylRelations<BigRational>();
358        //no: csring.addRelations(wc); //wc.generate(csring);
359        //assertTrue("# relations == 1", csring.table.size() == 1);
360        assertTrue("isCommutative()", csring.isCommutative());
361        assertTrue("isAssociative()", csring.isAssociative());
362
363        List<GenSolvablePolynomial<BigRational>> il = new ArrayList<GenSolvablePolynomial<BigRational>>();
364        GenSolvablePolynomial<BigRational> p1 = csring.parse("b - a^2");
365        il.add(p1);
366        //p1 = csring.parse("a - b^5");
367        //il.add(p1);
368        sideal = new SolvableIdeal<BigRational>(csring, il);
369        SolvableLocalRing<BigRational> qcsring = new SolvableLocalRing<BigRational>(sideal);
370        assertTrue("isCommutative()", qcsring.isCommutative());
371        assertTrue("isAssociative()", qcsring.isAssociative());
372
373        ring = new QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational>(qcsring, ring);
374        RelationGenerator<SolvableLocal<BigRational>> wl = new WeylRelations<SolvableLocal<BigRational>>();
375        ring.addRelations(wl); //wl.generate(ring);
376        assertTrue("# relations == 2", ring.table.size() == 2);
377        assertFalse("isCommutative()", ring.isCommutative());
378        assertTrue("isAssociative()", ring.isAssociative());
379        //System.out.println("ring = " + ring);
380
381        RecSolvablePolynomial<BigRational> r1 = ring.polCoeff.parse("x");
382        GenSolvablePolynomial<BigRational> r2 = csring.parse("b");
383        RecSolvablePolynomial<BigRational> rp = ring.polCoeff.parse("b x + a"); // + a
384        //System.out.println("r1 = " + r1);
385        //System.out.println("r2 = " + r2);
386        //System.out.println("rp = " + rp);
387        ring.polCoeff.coeffTable.update(r1.leadingExpVector(), r2.leadingExpVector(), rp);
388        //System.out.println("ring = " + ring.toScript());
389        //System.out.println("ring.polCoeff = " + ring.polCoeff);
390        assertFalse("isCommutative()", ring.isCommutative());
391        assertTrue("isAssociative()", ring.isAssociative());
392
393        List<GenPolynomial<SolvableLocal<BigRational>>> gens = ring.generators();
394        for (GenPolynomial<SolvableLocal<BigRational>> x : gens) {
395            GenSolvablePolynomial<SolvableLocal<BigRational>> xx = (GenSolvablePolynomial<SolvableLocal<BigRational>>) x;
396            a = new QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>(ring, xx);
397            //System.out.println("a = " + a);
398            for (GenPolynomial<SolvableLocal<BigRational>> y : gens) {
399                GenSolvablePolynomial<SolvableLocal<BigRational>> yy = (GenSolvablePolynomial<SolvableLocal<BigRational>>) y;
400                b = new QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>(ring, yy);
401                //System.out.println("b = " + b);
402                c = a.multiply(b);
403                //System.out.println("gens: " + a + " * " + b + " = " + c);
404                ExpVector ev = a.leadingExpVector().sum(b.leadingExpVector());
405                assertTrue("LT(a)*LT(b) == LT(c)", c.leadingExpVector().equals(ev));
406            }
407        }
408        //System.out.println("=============");
409        //a = ring.random(kl, ll, el, q);
410        //a = ring.getONE();
411        a = ring.parse("x^2 + a b");
412        //System.out.println("a = " + a.toScript());
413        //b = ring.random(kl, ll, el, q);
414        //b = ring.getONE();
415        b = ring.parse("a b + a"); // a b^2 + a 
416        b = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) b.inverse();
417        //System.out.println("b = " + b.toScript());
418
419        // non-commutative
420        c = b.multiply(a);
421        d = a.multiply(b);
422        //System.out.println("a = " + a.toScript());
423        //System.out.println("b = " + b.toScript());
424        //System.out.println("c = " + c.toScript());
425        //System.out.println("d = " + d.toScript());
426        assertTrue("a*b != b*a", c.equals(d) || c.leadingExpVector().equals(d.leadingExpVector()));
427
428        e = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) b.inverse();
429        //System.out.println("e = " + e.toScript());
430        assertTrue("b*b^-1 == 1", e.multiply(b).isONE());
431
432        c = e.multiply(c);
433        d = d.multiply(e);
434        //System.out.println("a = " + a.toScript());
435        //System.out.println("b = " + b.toScript());
436        //System.out.println("c = " + c.toScript());
437        //System.out.println("d = " + d.toScript());
438        assertTrue("a == b * 1/b * a", a.equals(c));
439        assertTrue("a == a * 1/b * b", a.equals(d));
440    }
441
442
443    /**
444     * Test extension and contraction for Weyl relations.
445     */
446    @SuppressWarnings("unchecked")
447    public void testExtendContractWeyl() {
448        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> r1 = ring.parse("x");
449        GenSolvablePolynomial<BigRational> r2 = cring.parse("a");
450        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> rp = ring.parse("a x + b");
451        ring.polCoeff.coeffTable.update(r1.leadingExpVector(), r2.leadingExpVector(),
452                        ring.toPolyCoefficients(rp));
453
454        int k = rl;
455        QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational> pfe = ring.extend(k);
456        //System.out.println("pfe = " + pfe);
457        QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational> pfec = pfe.contract(k);
458        //System.out.println("pfec = " + pfec);
459        assertEquals("ring == pfec", ring, pfec);
460
461        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> a = ring.random(kl, ll, el, q);
462        //System.out.println("a = " + a);
463
464        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> ae = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a
465                        .extend(pfe, 0, 0);
466        //System.out.println("ae = " + ae);
467
468        Map<ExpVector, GenPolynomial<SolvableLocal<BigRational>>> m = ae.contract(pfec);
469        List<GenPolynomial<SolvableLocal<BigRational>>> ml = new ArrayList<GenPolynomial<SolvableLocal<BigRational>>>(
470                        m.values());
471        GenPolynomial<SolvableLocal<BigRational>> aec = ml.get(0);
472        //System.out.println("ae  = " + ae);
473        //System.out.println("aec = " + aec);
474        assertEquals("a == aec", a, aec);
475    }
476
477
478    /**
479     * Test reversion for Weyl relations.
480     */
481    @SuppressWarnings("unchecked")
482    public void testReverseWeyl() {
483        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> r1 = ring.parse("x");
484        GenSolvablePolynomial<BigRational> r2 = cring.parse("a");
485        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> rp = ring.parse("a x + b");
486        ring.polCoeff.coeffTable.update(r1.leadingExpVector(), r2.leadingExpVector(),
487                        ring.toPolyCoefficients(rp));
488
489        QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational> pfr = ring.reverse();
490        QLRSolvablePolynomialRing<SolvableLocal<BigRational>, BigRational> pfrr = pfr.reverse();
491        assertEquals("pf == pfrr", ring, pfrr);
492        //System.out.println("ring = " + ring);
493        //System.out.println("pfr = " + pfr);
494
495        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> a = ring.random(kl, ll, el, q);
496        //System.out.println("a = " + a);
497
498        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> ar = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) a
499                        .reverse(pfr);
500        QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational> arr = (QLRSolvablePolynomial<SolvableLocal<BigRational>, BigRational>) ar
501                        .reverse(pfrr);
502        assertEquals("a == arr", a, arr);
503        //System.out.println("ar = " + ar);
504        //System.out.println("arr = " + arr);
505    }
506
507
508    /**
509     * Test recursive for Weyl relations.
510     */
511    @SuppressWarnings("unchecked")
512    public void testRecursiveWeyl() {
513        GenSolvablePolynomialRing<GenPolynomial<SolvableLocal<BigRational>>> rsring = ring.recursive(2); // 1,2,3
514        //System.out.println("rsring = " + rsring.toScript());
515
516        GenSolvablePolynomial<SolvableLocal<BigRational>> ad, bd, cd, dd;
517        RecSolvablePolynomial<SolvableLocal<BigRational>> ar, br, cr, dr;
518        ad = ring.random(kl, ll, el, q);
519        bd = ring.random(kl, ll, el, q);
520        //ad = sring.parse("7/2 y^2 * z"); // - 15/2 w^2 + 262/225");
521        //bd = sring.parse("-10/13 x "); //+ 413/150");
522        //ad = (GenSolvablePolynomial<BigRational>) ad.monic();
523        //bd = (GenSolvablePolynomial<BigRational>) bd.monic();
524
525        //System.out.println("ad = " + ad);
526        //System.out.println("bd = " + bd);
527
528        cd = ad.multiply(bd);
529        //System.out.println("cd = " + cd);
530
531        ar = (RecSolvablePolynomial<SolvableLocal<BigRational>>) PolyUtil
532                        .<SolvableLocal<BigRational>> recursive(rsring, ad);
533        br = (RecSolvablePolynomial<SolvableLocal<BigRational>>) PolyUtil
534                        .<SolvableLocal<BigRational>> recursive(rsring, bd);
535        //System.out.println("ar = " + ar);
536        //System.out.println("br = " + br);
537
538        cr = ar.multiply(br);
539        //System.out.println("cr = " + cr);
540        //System.out.println("cr.ring = " + cr.ring.toScript());
541
542        dr = (RecSolvablePolynomial<SolvableLocal<BigRational>>) PolyUtil
543                        .<SolvableLocal<BigRational>> recursive(rsring, cd);
544        //System.out.println("dr = " + dr);
545
546        assertEquals("dr.ring == cr.ring", dr.ring, cr.ring);
547        assertEquals("dr == cr", dr, cr);
548
549        dd = (GenSolvablePolynomial<SolvableLocal<BigRational>>) PolyUtil
550                        .<SolvableLocal<BigRational>> distribute(ring, cr);
551        // //System.out.println("dd = " + dd);
552        assertEquals("dd == cd", dd, cd);
553    }
554
555
556    /*
557     * Test recursive for iterated Weyl relations.
558     */
559    public void testRecursiveIteratedWeyl() {
560        String[] svars = new String[] { "w", "x", "y", "z" };
561        GenSolvablePolynomialRing<BigRational> sring = new GenSolvablePolynomialRing<BigRational>(cfac, tord,
562                        svars);
563        RelationGenerator<BigRational> wlc = new WeylRelationsIterated<BigRational>();
564        wlc.generate(sring);
565        assertFalse("isCommutative()", sring.isCommutative());
566        assertTrue("isAssociative()", sring.isAssociative());
567        //System.out.println("sring = " + sring.toScript());
568
569        GenSolvablePolynomialRing<GenPolynomial<BigRational>> rsring = sring.recursive(2); // 1,2,3
570        //System.out.println("rsring = " + rsring); //.toScript());
571        //System.out.println("rsring = " + rsring.toScript());
572
573        GenSolvablePolynomial<BigRational> ad, bd, cd, dd;
574        RecSolvablePolynomial<BigRational> ar, br, cr, dr;
575        ad = sring.random(kl, ll, el, q);
576        bd = sring.random(kl, ll, el, q);
577        //ad = (GenSolvablePolynomial<BigRational>) ad.monic();
578        //bd = (GenSolvablePolynomial<BigRational>) bd.monic();
579
580        //System.out.println("ad = " + ad);
581        //System.out.println("bd = " + bd);
582
583        cd = ad.multiply(bd);
584        //System.out.println("cd = " + cd);
585
586        ar = (RecSolvablePolynomial<BigRational>) PolyUtil.<BigRational> recursive(rsring, ad);
587        br = (RecSolvablePolynomial<BigRational>) PolyUtil.<BigRational> recursive(rsring, bd);
588        //System.out.println("ar = " + ar);
589        //System.out.println("br = " + br);
590
591        cr = ar.multiply(br);
592        //System.out.println("cr = " + cr);
593
594        dr = (RecSolvablePolynomial<BigRational>) PolyUtil.<BigRational> recursive(rsring, cd);
595        //System.out.println("dr = " + dr);
596
597        assertEquals("dr.ring == cr.ring", dr.ring, cr.ring);
598        assertEquals("dr == cr", dr, cr);
599
600        dd = (GenSolvablePolynomial<BigRational>) PolyUtil.<BigRational> distribute(sring, cr);
601        //System.out.println("dd = " + dd);
602        assertEquals("dd == cd", dd, cd);
603    }
604
605}