Source code

001/*
002 * $Id: ReductionTest.java 5863 2018-07-20 11:13:34Z kredel $
003 */
004
005package edu.jas.gbufd;
006
007import java.util.List;
008import java.util.ArrayList;
009import java.util.Map;
010
011import junit.framework.Test;
012import junit.framework.TestCase;
013import junit.framework.TestSuite;
014
015
016import edu.jas.structure.RingFactory;
017import edu.jas.arith.BigInteger;
018import edu.jas.arith.BigRational;
019import edu.jas.arith.BigComplex;
020import edu.jas.arith.Product;
021import edu.jas.arith.ProductRing;
022import edu.jas.poly.ExpVector;
023import edu.jas.poly.GenPolynomial;
024import edu.jas.poly.GenPolynomialRing;
025import edu.jas.poly.PolynomialList;
026
027
028/**
029 * Reduction tests with JUnit.
030 * @author Heinz Kredel
031 */
032
033public class ReductionTest extends TestCase {
034
035    /**
036     * main
037     */
038    public static void main (String[] args) {
039        junit.textui.TestRunner.run( suite() );
040    }
041
042    /**
043     * Constructs a <CODE>ReductionTest</CODE> object.
044     * @param name String
045     */
046    public ReductionTest(String name) {
047        super(name);
048    }
049
050    /**
051     * suite.
052     * @return a test suite.
053     */
054    public static Test suite() {
055        TestSuite suite= new TestSuite(ReductionTest.class);
056        return suite;
057    }
058
059
060    GenPolynomialRing<BigRational> fac;
061
062    GenPolynomial<BigRational> a, b, c, d, e;
063
064    List<GenPolynomial<BigRational>> L;
065    PolynomialList<BigRational> F, G;
066
067    //ReductionSeq<BigRational> red;
068    //Reduction<BigRational> redpar;
069
070    int rl = 4; 
071    int kl = 10;
072    int ll = 11;
073    int el = 5;
074    float q = 0.6f;
075
076    protected void setUp() {
077        a = b = c = d = e = null;
078        fac = new GenPolynomialRing<BigRational>( new BigRational(0), rl );
079        //red = new ReductionSeq<BigRational>();
080        //redpar = new ReductionPar<BigRational>();
081    }
082
083    protected void tearDown() {
084        a = b = c = d = e = null;
085        fac = null;
086        //red = null;
087        //redpar = null;
088    }
089
090
091    /**
092     * Test rational coefficient r-reduction.
093     */
094    public void testRationalRReduction() {
095        RingFactory<BigRational> bi = new BigRational(0);
096        ProductRing<BigRational> pr = new ProductRing<BigRational>(bi,3);
097
098        GenPolynomialRing<Product<BigRational>> fac 
099            = new GenPolynomialRing<Product<BigRational>>( pr, rl );
100
101        RReductionSeq<Product<BigRational>> rred 
102            = new RReductionSeq<Product<BigRational>>();
103
104        GenPolynomial<Product<BigRational>> a = fac.random(kl, ll, el, q );
105        GenPolynomial<Product<BigRational>> b = fac.random(kl, ll, el, q );
106        GenPolynomial<Product<BigRational>> d;
107
108        while ( a.isZERO() ) {
109            a = fac.random(kl, ll, el, q );
110        }
111        while ( b.isZERO() ) {
112            b = fac.random(kl, ll, el, q );
113        }
114
115        assertTrue("not isZERO( a )", !a.isZERO() );
116
117        List<GenPolynomial<Product<BigRational>>> L 
118            = new ArrayList<GenPolynomial<Product<BigRational>>>();
119        L.add(a);
120
121        GenPolynomial<Product<BigRational>> e 
122            = rred.normalform( L, a );
123        //System.out.println("a = " + a);
124        //System.out.println("e = " + e);
125        assertTrue("isNF( e )", rred.isNormalform(L,e) );
126
127        assertTrue("not isZERO( b )", !b.isZERO() );
128
129        L.add(b);
130        e = rred.normalform( L, a );
131        //System.out.println("b = " + b);
132        //System.out.println("e = " + e);
133        assertTrue("isNF( e )", rred.isNormalform(L,e) );
134
135        GenPolynomial<Product<BigRational>> c = fac.getONE();
136        a = a.sum(c);
137        e = rred.normalform( L, a );
138        //System.out.println("a = " + a);
139        //System.out.println("e = " + e);
140        assertTrue("isNF( e )", rred.isNormalform(L,e) ); 
141
142        L = new ArrayList<GenPolynomial<Product<BigRational>>>();
143        L.add( a );
144        assertTrue("isTopRed( a )", rred.isTopReducible(L,a) ); 
145        assertTrue("isRed( a )", rred.isReducible(L,a) ); 
146        //b = fac.random(kl, ll, el, q );
147        L.add( b );
148        assertTrue("isTopRed( b )", rred.isTopReducible(L,b) ); 
149        assertTrue("isRed( b )", rred.isReducible(L,b) ); 
150        c = fac.random(kl, ll, el, q );
151        e = rred.normalform( L, c );
152        assertTrue("isNF( e )", rred.isNormalform(L,e) ); 
153
154        c = rred.booleanClosure(a);
155        //System.out.println("a = " + a);
156        //System.out.println("c = " + c);
157        assertTrue("isBC( c )", rred.isBooleanClosed(c) ); 
158
159        b = a.subtract(c);
160        //System.out.println("b = " + b);
161        d = rred.booleanRemainder(a);
162        //System.out.println("d = " + d);
163        assertEquals("a-BC(a)=BR(a)", b, d ); 
164
165        e = c.sum(d);
166        //System.out.println("e = " + e);
167        assertEquals("a==BC(a)+BR(a)", a, e ); 
168
169        List<GenPolynomial<Product<BigRational>>> B;
170        List<GenPolynomial<Product<BigRational>>> Br;
171        L = new ArrayList<GenPolynomial<Product<BigRational>>>();
172        L.add( a );
173        B  = rred.booleanClosure(L);
174        Br = rred.reducedBooleanClosure(L);
175        //System.out.println("L  = " + L);
176        //System.out.println("B = " + B);
177        //System.out.println("Br = " + Br);
178        assertTrue("isBC( B )", rred.isBooleanClosed(B) ); 
179        assertTrue("isBC( Br )", rred.isReducedBooleanClosed(Br) ); 
180        assertTrue("isBC( Br )", rred.isBooleanClosed(Br) ); 
181        //not always: assertEquals("B == Br", B, Br ); 
182
183        L.add( b );
184        B  = rred.booleanClosure(L);
185        Br = rred.reducedBooleanClosure(L);
186        //System.out.println("L = " + L);
187        //System.out.println("B = " + B);
188        //System.out.println("Br = " + Br);
189        assertTrue("isBC( B )", rred.isBooleanClosed(B) ); 
190        assertTrue("isBC( Br )", rred.isReducedBooleanClosed(Br) ); 
191        assertTrue("isBC( Br )", rred.isBooleanClosed(Br) ); 
192        //not always: assertEquals("B == Br", B, Br ); 
193
194        while ( c.isZERO() ) {
195            c = fac.random(kl, ll, el, q );
196        }
197        L.add( c );
198        B  = rred.booleanClosure(L);
199        Br = rred.reducedBooleanClosure(L);
200        //System.out.println("L = " + L);
201        //System.out.println("B = " + B);
202        //System.out.println("Br = " + Br);
203        assertTrue("isBC( B )", rred.isBooleanClosed(B) ); 
204        assertTrue("isBC( Br )", rred.isReducedBooleanClosed(Br) ); 
205        assertTrue("isBC( Br )", rred.isBooleanClosed(Br) ); 
206        //not always: assertEquals("B == Br", B, Br ); 
207
208        while ( d.isZERO() ) {
209            d = fac.random(kl, ll, el, q );
210        }
211        L.add( d );
212        B  = rred.booleanClosure(L);
213        Br = rred.reducedBooleanClosure(L);
214        //System.out.println("L = " + L);
215        //System.out.println("B = " + B);
216        //System.out.println("Br = " + Br);
217        assertTrue("isBC( B )", rred.isBooleanClosed(B) ); 
218        assertTrue("isBC( Br )", rred.isReducedBooleanClosed(Br) ); 
219        assertTrue("isBC( Br )", rred.isBooleanClosed(Br) ); 
220        //not always: assertEquals("B == Br", B, Br ); 
221    }
222
223
224    /**
225     * Test rational coefficient r-reduction with recording.
226     */
227    public void testRatRReductionRecording() {
228        RingFactory<BigRational> bi = new BigRational(0);
229        ProductRing<BigRational> pr = new ProductRing<BigRational>(bi,3);
230
231        GenPolynomialRing<Product<BigRational>> fac 
232            = new GenPolynomialRing<Product<BigRational>>( pr, rl );
233
234        RReductionSeq<Product<BigRational>> rred 
235            = new RReductionSeq<Product<BigRational>>();
236
237        GenPolynomial<Product<BigRational>> a = fac.random(kl, ll, el, q );
238        GenPolynomial<Product<BigRational>> b = fac.random(kl, ll, el, q );
239        GenPolynomial<Product<BigRational>> c, d, e;
240
241        while ( a.isZERO() ) {
242            a = fac.random(kl, ll, el, q );
243        }
244        while ( b.isZERO() ) {
245            b = fac.random(kl, ll, el, q );
246        }
247        c = fac.random(kl, ll, el, q );
248        d = fac.random(kl, ll, el, q );
249
250        List<GenPolynomial<Product<BigRational>>> row = null;
251        List<GenPolynomial<Product<BigRational>>> L;
252
253        assertTrue("not isZERO( a )", !a.isZERO() );
254        assertTrue("not isZERO( b )", !b.isZERO() );
255
256        L = new ArrayList<GenPolynomial<Product<BigRational>>>();
257
258        L.add(a);
259        row = new ArrayList<GenPolynomial<Product<BigRational>>>( L.size() );
260        for ( int m = 0; m < L.size(); m++ ) {
261            row.add(null);
262        }
263        e = rred.normalform( row, L, a );
264        //not for regular rings: assertTrue("isZERO( e )", e.isZERO() );
265
266        //System.out.println("row = " + row);
267        //System.out.println("L   = " + L);
268        //System.out.println("a   = " + a);
269        //System.out.println("e   = " + e);
270
271        assertTrue("is Reduction ", rred.isReductionNF(row,L,a,e) );
272
273        L.add(b);
274        row = new ArrayList<GenPolynomial<Product<BigRational>>>( L.size() );
275        for ( int m = 0; m < L.size(); m++ ) {
276            row.add(null);
277        }
278        e = rred.normalform( row, L, b );
279        assertTrue("is Reduction ", rred.isReductionNF(row,L,b,e) );
280
281        L.add(c);
282        row = new ArrayList<GenPolynomial<Product<BigRational>>>( L.size() );
283        for ( int m = 0; m < L.size(); m++ ) {
284            row.add(null);
285        }
286        e = rred.normalform( row, L, c );
287        assertTrue("is Reduction ", rred.isReductionNF(row,L,c,e) );
288
289        L.add(d);
290        row = new ArrayList<GenPolynomial<Product<BigRational>>>( L.size() );
291        for ( int m = 0; m < L.size(); m++ ) {
292            row.add(null);
293        }
294        e = rred.normalform( row, L, d );
295        assertTrue("is Reduction ", rred.isReductionNF(row,L,d,e) );
296    }
297
298
299    /**
300     * Test integer coefficient pseudo-reduction.
301     */
302    public void testIntegerPseudoReduction() {
303        BigInteger bi = new BigInteger(0);
304        GenPolynomialRing<BigInteger> fac 
305            = new GenPolynomialRing<BigInteger>( bi, rl );
306
307        PseudoReductionSeq<BigInteger> pred = new PseudoReductionSeq<BigInteger>();
308
309        GenPolynomial<BigInteger> a = fac.random(kl, ll, el, q );
310        GenPolynomial<BigInteger> b = fac.random(kl, ll, el, q );
311
312        if ( a.isZERO() || b.isZERO() ) {
313            return;
314        }
315
316        assertTrue("not isZERO( a )", !a.isZERO() );
317
318        List<GenPolynomial<BigInteger>> L 
319            = new ArrayList<GenPolynomial<BigInteger>>();
320        L.add(a);
321
322        GenPolynomial<BigInteger> e;
323        e = pred.normalform( L, a );
324        //System.out.println("a = " + a);
325        //System.out.println("e = " + e);
326        assertTrue("isZERO( e )", e.isZERO() );
327
328        assertTrue("not isZERO( b )", !b.isZERO() );
329
330        L.add(b);
331        e = pred.normalform( L, a );
332        //System.out.println("b = " + b);
333        //System.out.println("e = " + e);
334        assertTrue("isZERO( e ) some times", e.isZERO() ); 
335
336
337        GenPolynomial<BigInteger> c = fac.getONE();
338        a = a.sum(c);
339        e = pred.normalform( L, a );
340        //System.out.println("b = " + b);
341        //System.out.println("e = " + e);
342        assertTrue("isConstant( e ) some times", e.isConstant() ); 
343
344        L = new ArrayList<GenPolynomial<BigInteger>>();
345        a = c.multiply( bi.fromInteger(4) );
346        b = c.multiply( bi.fromInteger(5) );
347        L.add( a );
348        e = pred.normalform( L, b );
349        //System.out.println("a = " + a);
350        //System.out.println("b = " + b);
351        //System.out.println("e = " + e);
352        assertTrue("isZERO( e )", e.isZERO() ); 
353
354        a = fac.random(kl, ll, el, q ); //.abs();
355        b = fac.random(kl, ll, el, q ); //.abs();
356        //System.out.println("a = " + a);
357        //System.out.println("b = " + b);
358 
359        L = new ArrayList<GenPolynomial<BigInteger>>();
360        L.add( a );
361        assertTrue("isTopRed( a )", pred.isTopReducible(L,a) ); 
362        assertTrue("isRed( a )", pred.isReducible(L,a) ); 
363        b = fac.random(kl, ll, el, q );
364        L.add( b );
365        assertTrue("isTopRed( b )", pred.isTopReducible(L,b) ); 
366        assertTrue("isRed( b )", pred.isReducible(L,b) ); 
367        c = fac.random(kl, ll, el, q );
368        e = pred.normalform( L, c );
369        assertTrue("isNF( e )", pred.isNormalform(L,e) ); 
370    }
371
372
373    /**
374     * Test integer pseudo coefficient reduction with recording.
375     */
376    public void testIntReductionRecording() {
377        BigInteger bi = new BigInteger(0);
378        GenPolynomialRing<BigInteger> fac 
379            = new GenPolynomialRing<BigInteger>( bi, rl );
380
381        PseudoReductionSeq<BigInteger> pred = new PseudoReductionSeq<BigInteger>();
382
383        GenPolynomial<BigInteger> a = fac.random(kl, ll, el, q );
384        GenPolynomial<BigInteger> b = fac.random(kl, ll, el, q );
385        GenPolynomial<BigInteger> c, d, e, f;
386
387        if ( a.isZERO() || b.isZERO() ) {
388            return;
389        }
390        c = fac.random(kl, ll, el+1, q );
391        d = fac.random(kl, ll, el+2, q );
392
393        // ------------
394        //a = fac.parse(" 1803 x0 * x1^4 - 299 x0^3 * x1^2 - 464 x1^4 + 648 x1^3 + 383 x0^3 + 1633 ");
395        //b = fac.parse(" 593 x0^4 * x1^4 - 673 x0^3 * x1^4 + 36 x0^4 + 627 x1^2 + 617 x1 + 668 x0 + 168 ");
396        //b = b.multiply( fac.parse(" 10567759154481 " ) );
397        //c = a.multiply( fac.parse(" 593 x0^3 - 938267 x0^2 - 435355888 x0 - 202005132032 ") );
398
399        //d = a.multiply( fac.parse(" 3475696715811 x0^3 - 3050126808003 x0^2 - 784946666064 x0 - 202005132032 ") );
400
401        //-------------
402
403        List<GenPolynomial<BigInteger>> row = null;
404        List<GenPolynomial<BigInteger>> L;
405
406        PseudoReductionEntry<BigInteger> mf;
407
408        assertTrue("not isZERO( a )", !a.isZERO() );
409        assertTrue("not isZERO( b )", !b.isZERO() );
410
411        L = new ArrayList<GenPolynomial<BigInteger>>();
412
413        L.add(a);
414        row = new ArrayList<GenPolynomial<BigInteger>>( L.size() );
415        for ( int m = 0; m < L.size(); m++ ) {
416            row.add(null);
417        }
418        mf = pred.normalformFactor( L, a );
419        e = mf.pol;
420        f = a.multiply( mf.multiplicator );
421        e = pred.normalform( row, L, f );
422        assertTrue("isZERO( e )", e.isZERO() );
423        assertTrue("is Reduction ", pred.isNormalform(L,e) );
424        assertTrue("is ReductionNF ", pred.isReductionNF(row,L,f,e) );
425
426        L.add(b);
427        row = new ArrayList<GenPolynomial<BigInteger>>( L.size() );
428        for ( int m = 0; m < L.size(); m++ ) {
429            row.add(null);
430        }
431        mf = pred.normalformFactor( L, a );
432        e = mf.pol;
433        f = a.multiply( mf.multiplicator );
434        e = pred.normalform( row, L, f );
435        assertTrue("is Reduction ", pred.isNormalform(L,e) );
436        assertTrue("is ReductionNF ", pred.isReductionNF(row,L,f,e) );
437
438        L.add(c);
439        row = new ArrayList<GenPolynomial<BigInteger>>( L.size() );
440        for ( int m = 0; m < L.size(); m++ ) {
441            row.add(null);
442        }
443        mf = pred.normalformFactor( L, a );
444        e = mf.pol;
445        f = a.multiply( mf.multiplicator );
446        e = pred.normalform( row, L, f );
447        assertTrue("is Reduction ", pred.isNormalform(L,e) );
448        assertTrue("is ReductionNF ", pred.isReductionNF(row,L,f,e) );
449
450        L.add(d);
451        row = new ArrayList<GenPolynomial<BigInteger>>( L.size() );
452        for ( int m = 0; m < L.size(); m++ ) {
453            row.add(null);
454        }
455        mf = pred.normalformFactor( L, a );
456        e = mf.pol;
457        f = a.multiply( mf.multiplicator );
458        e = pred.normalform( row, L, f );
459        assertTrue("is Reduction ", pred.isNormalform(L,e) );
460        assertTrue("is ReductionNF ", pred.isReductionNF(row,L,f,e) );
461    }
462
463
464    /**
465     * Test integer coefficient pseudo r-reduction.
466     */
467    public void testIntegerRReduction() {
468        RingFactory<BigInteger> bi = new BigInteger(0);
469        ProductRing<BigInteger> pr = new ProductRing<BigInteger>(bi,3);
470
471        GenPolynomialRing<Product<BigInteger>> fac 
472            = new GenPolynomialRing<Product<BigInteger>>( pr, rl );
473
474        RReductionSeq<Product<BigInteger>> rpred 
475            = new RPseudoReductionSeq<Product<BigInteger>>();
476
477        GenPolynomial<Product<BigInteger>> a = fac.random(kl, ll, el, q );
478        GenPolynomial<Product<BigInteger>> b = fac.random(kl, ll, el, q );
479        GenPolynomial<Product<BigInteger>> c, d, e;
480
481        while ( a.isZERO() ) {
482            a = fac.random(kl, ll, el, q );
483        }
484        while ( b.isZERO() ) {
485            b = fac.random(kl, ll, el, q );
486        }
487
488        assertTrue("not isZERO( a )", !a.isZERO() );
489
490        List<GenPolynomial<Product<BigInteger>>> L 
491            = new ArrayList<GenPolynomial<Product<BigInteger>>>();
492        L.add(a);
493
494        e = rpred.normalform( L, a );
495        //System.out.println("a = " + a);
496        //System.out.println("e = " + e);
497        assertTrue("isNF( e )", rpred.isNormalform(L,e) );
498
499        assertTrue("not isZERO( b )", !b.isZERO() );
500
501        L.add(b);
502        e = rpred.normalform( L, a );
503        assertTrue("isNF( e )", rpred.isNormalform(L,e) );
504
505        c = fac.getONE();
506        a = a.sum(c);
507        e = rpred.normalform( L, a );
508        assertTrue("isNF( e )", rpred.isNormalform(L,e) ); 
509
510        L = new ArrayList<GenPolynomial<Product<BigInteger>>>();
511        L.add( a );
512        assertTrue("isTopRed( a )", rpred.isTopReducible(L,a) ); 
513        assertTrue("isRed( a )", rpred.isReducible(L,a) ); 
514        //b = fac.random(kl, ll, el, q );
515        L.add( b );
516        assertTrue("isTopRed( b )", rpred.isTopReducible(L,b) ); 
517        assertTrue("isRed( b )", rpred.isReducible(L,b) ); 
518        c = fac.random(kl, ll, el, q );
519        e = rpred.normalform( L, c );
520        assertTrue("isNF( e )", rpred.isNormalform(L,e) ); 
521
522        c = rpred.booleanClosure(a);
523        //System.out.println("\nboolean closure");
524        //System.out.println("a = " + a);
525        //System.out.println("c = " + c);
526        assertTrue("isBC( c )", rpred.isBooleanClosed(c) ); 
527
528        b = a.subtract(c);
529        //System.out.println("b = " + b);
530        d = rpred.booleanRemainder(a);
531        //System.out.println("d = " + d);
532        assertEquals("a-BC(a)=BR(a)", b, d ); 
533
534        e = c.sum(d);
535        //System.out.println("e = " + e);
536        assertEquals("a==BC(a)+BR(a)", a, e ); 
537
538        List<GenPolynomial<Product<BigInteger>>> B;
539        List<GenPolynomial<Product<BigInteger>>> Br;
540        L = new ArrayList<GenPolynomial<Product<BigInteger>>>();
541        L.add( a );
542        B  = rpred.booleanClosure(L);
543        Br = rpred.reducedBooleanClosure(L);
544        assertTrue("isBC( B )", rpred.isBooleanClosed(B) ); 
545        assertTrue("isBC( Br )", rpred.isReducedBooleanClosed(Br) ); 
546        assertTrue("isBC( Br )", rpred.isBooleanClosed(Br) ); 
547        //not always: assertEquals("B == Br", B, Br ); 
548
549        L.add( b );
550        B  = rpred.booleanClosure(L);
551        Br = rpred.reducedBooleanClosure(L);
552        assertTrue("isBC( B )", rpred.isBooleanClosed(B) ); 
553        assertTrue("isBC( Br )", rpred.isReducedBooleanClosed(Br) ); 
554        assertTrue("isBC( Br )", rpred.isBooleanClosed(Br) ); 
555        //not always: assertEquals("B == Br", B, Br ); 
556
557        L.add( c );
558        B  = rpred.booleanClosure(L);
559        Br = rpred.reducedBooleanClosure(L);
560        assertTrue("isBC( B )", rpred.isBooleanClosed(B) ); 
561        assertTrue("isBC( Br )", rpred.isReducedBooleanClosed(Br) ); 
562        assertTrue("isBC( Br )", rpred.isBooleanClosed(Br) ); 
563        //not always: assertEquals("B == Br", B, Br ); 
564
565        while ( d.isZERO() ) {
566            d = fac.random(kl, ll, el, q );
567        }
568        L.add( d );
569        B  = rpred.booleanClosure(L);
570        Br = rpred.reducedBooleanClosure(L);
571        assertTrue("isBC( B )", rpred.isBooleanClosed(B) ); 
572        assertTrue("isBC( Br )", rpred.isReducedBooleanClosed(Br) ); 
573        assertTrue("isBC( Br )", rpred.isBooleanClosed(Br) ); 
574        //not always: assertEquals("B == Br", B, Br ); 
575    }
576
577
578    /**
579     * Test integer pseudo coefficient r-reduction with recording.
580     */
581    public void testIntRReductionRecording() {
582        RingFactory<BigInteger> bi = new BigInteger(0);
583        ProductRing<BigInteger> pr = new ProductRing<BigInteger>(bi,3);
584
585        GenPolynomialRing<Product<BigInteger>> fac 
586            = new GenPolynomialRing<Product<BigInteger>>( pr, rl );
587
588        RPseudoReductionSeq<Product<BigInteger>> rpred 
589            = new RPseudoReductionSeq<Product<BigInteger>>();
590
591        GenPolynomial<Product<BigInteger>> a = fac.random(kl, ll, el, q );
592        GenPolynomial<Product<BigInteger>> b = fac.random(kl, ll, el, q );
593        GenPolynomial<Product<BigInteger>> c, d, e, f;
594
595        while ( a.isZERO() ) {
596            a = fac.random(kl, ll, el, q );
597        }
598        while ( b.isZERO() ) {
599            b = fac.random(kl, ll, el, q );
600        }
601        assertTrue("not isZERO( a )", !a.isZERO() );
602        assertTrue("not isZERO( b )", !b.isZERO() );
603
604        c = fac.random(kl, ll, el, q );
605        d = fac.random(kl, ll, el, q );
606
607        List<GenPolynomial<Product<BigInteger>>> row = null;
608        List<GenPolynomial<Product<BigInteger>>> L;
609
610        PseudoReductionEntry<Product<BigInteger>> mf;
611
612        L = new ArrayList<GenPolynomial<Product<BigInteger>>>();
613
614        L.add(a);
615        row = new ArrayList<GenPolynomial<Product<BigInteger>>>( L.size() );
616        for ( int m = 0; m < L.size(); m++ ) {
617            row.add(null);
618        }
619        mf = rpred.normalformFactor( L, a );
620        e = mf.pol;
621        f = a.multiply( mf.multiplicator );
622        e = rpred.normalform( row, L, f );
623        //not for regular rings: assertTrue("isZERO( e )", e.isZERO() );
624        assertTrue("is Reduction ", rpred.isNormalform(L,e) );
625        assertTrue("is ReductionNF ", rpred.isReductionNF(row,L,f,e) );
626
627        L.add(b);
628        row = new ArrayList<GenPolynomial<Product<BigInteger>>>( L.size() );
629        for ( int m = 0; m < L.size(); m++ ) {
630            row.add(null);
631        }
632        mf = rpred.normalformFactor( L, a );
633        e = mf.pol;
634        f = a.multiply( mf.multiplicator );
635        e = rpred.normalform( row, L, f );
636        assertTrue("is Reduction ", rpred.isNormalform(L,e) );
637        assertTrue("is ReductionNF ", rpred.isReductionNF(row,L,f,e) );
638
639        L.add(c);
640        row = new ArrayList<GenPolynomial<Product<BigInteger>>>( L.size() );
641        for ( int m = 0; m < L.size(); m++ ) {
642            row.add(null);
643        }
644        mf = rpred.normalformFactor( L, a );
645        e = mf.pol;
646        f = a.multiply( mf.multiplicator );
647        e = rpred.normalform( row, L, f );
648        assertTrue("is Reduction ", rpred.isNormalform(L,e) );
649        assertTrue("is ReductionNF ", rpred.isReductionNF(row,L,f,e) );
650
651        L.add(d);
652        row = new ArrayList<GenPolynomial<Product<BigInteger>>>( L.size() );
653        for ( int m = 0; m < L.size(); m++ ) {
654            row.add(null);
655        }
656        mf = rpred.normalformFactor( L, a );
657        e = mf.pol;
658        f = a.multiply( mf.multiplicator );
659        e = rpred.normalform( row, L, f );
660        assertTrue("is Reduction ", rpred.isNormalform(L,e) );
661        assertTrue("is ReductionNF ", rpred.isReductionNF(row,L,f,e) );
662    }
663
664}