Source code

001/*
002 * $Id: QuatGenSolvablePolynomialTest.java 5711 2017-01-22 22:28:05Z kredel $
003 */
004
005package edu.jas.poly;
006
007
008import java.util.List;
009
010import org.apache.log4j.BasicConfigurator;
011
012import edu.jas.arith.BigQuaternion;
013import edu.jas.arith.BigQuaternionRing;
014
015import junit.framework.Test;
016import junit.framework.TestCase;
017import junit.framework.TestSuite;
018
019
020/**
021 * BigQuaternion coefficients GenSolvablePolynomial tests with JUnit.
022 * @author Heinz Kredel
023 */
024
025public class QuatGenSolvablePolynomialTest extends TestCase {
026
027
028    /**
029     * main
030     */
031    public static void main(String[] args) {
032        BasicConfigurator.configure();
033        junit.textui.TestRunner.run(suite());
034    }
035
036
037    /**
038     * Constructs a <CODE>QuatGenSolvablePolynomialTest</CODE> object.
039     * @param name String.
040     */
041    public QuatGenSolvablePolynomialTest(String name) {
042        super(name);
043    }
044
045
046    /**
047     */
048    public static Test suite() {
049        TestSuite suite = new TestSuite(QuatGenSolvablePolynomialTest.class);
050        return suite;
051    }
052
053
054    BigQuaternionRing cfac;
055
056
057    GenSolvablePolynomialRing<BigQuaternion> fac;
058
059
060    GenSolvablePolynomial<BigQuaternion> a, b, c, d, e, f;
061
062
063    int rl = 6;
064
065
066    int kl = 3;
067
068
069    int ll = 7;
070
071
072    int el = 3;
073
074
075    float q = 0.33f;
076
077
078    @Override
079    protected void setUp() {
080        a = b = c = d = e = null;
081        cfac = new BigQuaternionRing();
082        fac = new GenSolvablePolynomialRing<BigQuaternion>(cfac, rl);
083        RelationGenerator<BigQuaternion> rel = new WeylRelations<BigQuaternion>();
084        rel.generate(fac);
085    }
086
087
088    @Override
089    protected void tearDown() {
090        a = b = c = d = e = null;
091        fac = null;
092        cfac = null;
093    }
094
095
096    /**
097     * Test constructor and toString.
098     */
099    public void testConstruction() {
100        c = fac.getONE();
101        assertTrue("length( c ) = 1", c.length() == 1);
102        assertTrue("isZERO( c )", !c.isZERO());
103        assertTrue("isONE( c )", c.isONE());
104
105        d = fac.getZERO();
106        assertTrue("length( d ) = 0", d.length() == 0);
107        assertTrue("isZERO( d )", d.isZERO());
108        assertTrue("isONE( d )", !d.isONE());
109    }
110
111
112    /**
113     * Test factory.
114     */
115    public void testFactory() {
116        assertFalse("!is comutative", fac.isCommutative());
117        assertFalse("!is field", fac.isField());
118        assertTrue("is associative", fac.isAssociative());
119
120        List<GenPolynomial<BigQuaternion>> gens = fac.generators();
121        //System.out.println("gens = " + gens);
122        assertTrue("#gens = 4+rl ", gens.size() == (4 + rl));
123    }
124
125
126    /**
127     * Test random polynomial.
128     */
129    public void testRandom() {
130        for (int i = 0; i < 3; i++) {
131            //a = fac.random(ll);
132            a = fac.random(kl, ll + i, el + (5 - i), q);
133            if (a.isZERO()) {
134                continue;
135            }
136            assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
137            assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
138            assertTrue(" not isONE( a" + i + " )", !a.isONE());
139        }
140    }
141
142
143    /**
144     * Test solvable addition.
145     */
146    public void testAddition() {
147        a = fac.random(kl, ll, el, q); // fac.random(ll);
148        b = fac.random(kl, ll, el, q); // fac.random(ll);
149
150        c = (GenSolvablePolynomial<BigQuaternion>) a.sum(b);
151        d = (GenSolvablePolynomial<BigQuaternion>) c.subtract(b);
152        assertEquals("a+b-b = a", a, d);
153
154        c = fac.random(kl, ll, el, q); //fac.random(ll);
155
156        ExpVector u = ExpVector.EVRAND(rl, el, q);
157        BigQuaternion x = cfac.random(kl);
158
159        b = new GenSolvablePolynomial<BigQuaternion>(fac, x, u);
160        c = (GenSolvablePolynomial<BigQuaternion>) a.sum(b);
161        d = (GenSolvablePolynomial<BigQuaternion>) a.sum(x, u);
162        assertEquals("a+p(x,u) = a+(x,u)", c, d);
163
164        c = (GenSolvablePolynomial<BigQuaternion>) a.subtract(b);
165        d = (GenSolvablePolynomial<BigQuaternion>) a.subtract(x, u);
166        assertEquals("a-p(x,u) = a-(x,u)", c, d);
167
168        a = new GenSolvablePolynomial<BigQuaternion>(fac);
169        assertTrue("a == 0", a.isZERO());
170    }
171
172
173    /**
174     * Test solvable multiplication.
175     */
176    @SuppressWarnings("cast")
177    public void testMultiplication() {
178        do {
179            a = fac.random(kl, ll, el, q); //fac.random(ll);
180        } while (a.isZERO());
181
182        do {
183            b = fac.random(kl, ll, el, q); //fac.random(ll);
184        } while (b.isZERO());
185
186        c = (GenSolvablePolynomial<BigQuaternion>) b.multiply(a);
187        d = (GenSolvablePolynomial<BigQuaternion>) a.multiply(b);
188        assertTrue("not isZERO( c )", !c.isZERO());
189        assertTrue("not isZERO( d )", !d.isZERO());
190        //System.out.println("a = " + a);
191        //System.out.println("b = " + b);
192        //System.out.println("c = " + c);
193        //System.out.println("d = " + d);
194        e = (GenSolvablePolynomial<BigQuaternion>) d.subtract(c);
195        assertTrue("!isZERO( a*b-b*a ) " + e, !e.isZERO());
196        //assertTrue("a*b = b*a", !c.equals(d));
197        //assertEquals("a*b = b*a",c,d);
198
199        c = fac.random(kl, ll, el, q);
200        //System.out.println("c = " + c);
201        d = (GenSolvablePolynomial<BigQuaternion>) a.multiply(b.multiply(c));
202        e = (GenSolvablePolynomial<BigQuaternion>) (a.multiply(b)).multiply(c);
203        //System.out.println("d = " + d);
204        //System.out.println("e = " + e);
205        //System.out.println("d-e = " + d.subtract(c) );
206
207        assertEquals("a(bc) = (ab)c", d, e);
208        //assertTrue("a(bc) = (ab)c", d.equals(e));
209
210        BigQuaternion x = a.leadingBaseCoefficient().inverse();
211        c = (GenSolvablePolynomial<BigQuaternion>) a.monic();
212        d = (GenSolvablePolynomial<BigQuaternion>) a.multiplyLeft(x);
213        assertEquals("a.monic() = a(1/ldcf(a))", c, d);
214
215        BigQuaternion y = b.leadingBaseCoefficient().inverse();
216        c = (GenSolvablePolynomial<BigQuaternion>) b.monic();
217        d = (GenSolvablePolynomial<BigQuaternion>) b.multiplyLeft(y);
218        assertEquals("b.monic() = b(1/ldcf(b))", c, d);
219
220        e = new GenSolvablePolynomial<BigQuaternion>(fac, y);
221        d = (GenSolvablePolynomial<BigQuaternion>) e.multiply(b);
222        assertEquals("b.monic() = b(1/ldcf(b))", c, d);
223    }
224
225
226    /**
227     * Test solvable left and right multiplication.
228     */
229    public void testDoubleMultiplication() {
230        a = fac.random(kl, 3, el, q); //fac.random(ll);
231        b = fac.random(kl, 2, el, q); //fac.random(ll);
232        c = fac.random(kl, 3, el, q); //fac.random(ll);
233
234        d = a.multiply(b).multiply(c);
235        e = b.multiply(a, c);
236        assertEquals("a b c = b.multiply(a,c)", d, e);
237
238        BigQuaternion qa, qb, qc, qd;
239
240        // search non commuting qa, qb
241        do {
242            qa = cfac.random(kl);
243            qb = cfac.random(kl);
244            qc = qa.multiply(qb);
245            qd = qb.multiply(qa);
246        } while (qc.equals(qd));
247        //System.out.println("qa = " + qa);
248        //System.out.println("qb = " + qb);
249        //System.out.println("qc = " + qc);
250        //System.out.println("qd = " + qd);
251
252        a = fac.univariate(0);
253        d = a.multiply(qa, qb);
254        e = a.multiply(qb, qa);
255        //System.out.println("a = " + a);
256        //System.out.println("d = " + d);
257        //System.out.println("e = " + e);
258        assertTrue("a.multiply(qa,qb) != a.multiply(qb,qq)",
259                        !d.equals(e) || d.leadingExpVector().equals(e.leadingExpVector()));
260
261        // commuting variables
262        ExpVector ea = fac.univariate(1).leadingExpVector();
263        ExpVector eb = fac.univariate(2).leadingExpVector();
264        //System.out.println("ea = " + ea);
265        //System.out.println("eb = " + eb);
266
267        d = a.multiply(ea, eb);
268        e = a.multiply(eb, ea);
269        //System.out.println("d = " + d);
270        //System.out.println("e = " + e);
271        assertTrue("a.multiply(ea,eb) == a.multiply(eb,eq)", d.equals(e));
272
273        d = a.multiply(qa, ea, qb, eb);
274        e = a.multiply(qb, eb, qa, ea);
275        //System.out.println("d = " + d);
276        //System.out.println("e = " + e);
277        assertTrue("a.multiply(qa,ea,qb,eb) != a.multiply(qb,eb,qa,ea)",
278                        d.equals(e) || d.leadingExpVector().equals(e.leadingExpVector()));
279    }
280
281
282    /**
283     * Test division of polynomials.
284     */
285    public void testDivide() {
286        assertFalse("isCommutative()", fac.isCommutative());
287        assertTrue("isAssociative()", fac.isAssociative());
288
289        do {
290            a = fac.random(kl, ll, el, q);
291        } while (a.isZERO());
292        //System.out.println("a = " + a);
293
294        do {
295            b = fac.random(kl, ll, el, q);
296        } while (b.isZERO());
297        //System.out.println("b = " + b);
298
299        // non commutative
300        c = b.multiply(a);
301        d = a.multiply(b);
302        //System.out.println("c = " + c);
303        //System.out.println("d = " + d);
304        assertTrue("not isZERO( c )", !c.isZERO());
305        assertTrue("not isZERO( d )", !d.isZERO());
306
307        e = (GenSolvablePolynomial<BigQuaternion>) d.subtract(c);
308        assertTrue("a*b != b*a", !c.equals(d) || c.leadingExpVector().equals(d.leadingExpVector()));
309
310        // divide 
311        e = c.divide(a);
312        //System.out.println("e = " + e);
313        f = c.rightDivide(b);
314        //System.out.println("f = " + f);
315        assertEquals("b == b*a/a: " + e, e, b);
316        assertEquals("a == b*a/b: " + e, f, a);
317
318        e = d.rightDivide(a);
319        //System.out.println("e = " + e);
320        f = d.divide(b);
321        //System.out.println("f = " + f);
322        assertEquals("b == a*b/a: " + e, e, b);
323        assertEquals("a == a*b/b: " + e, f, a);
324    }
325
326
327    /**
328     * Test distributive law.
329     */
330    public void testDistributive() {
331        a = fac.random(kl, ll, el, q);
332        b = fac.random(kl, ll, el, q);
333        c = fac.random(kl, ll, el, q);
334
335        d = a.multiply((GenSolvablePolynomial<BigQuaternion>) b.sum(c));
336        e = (GenSolvablePolynomial<BigQuaternion>) a.multiply(b).sum(a.multiply(c));
337
338        assertEquals("a(b+c) = ab+ac", d, e);
339    }
340
341
342    /**
343     * Test coefficient multiplication.
344     */
345    public void testCoeffMultiplication() {
346        a = fac.random(kl, ll, el, q);
347        //System.out.println("a = " + a);
348
349        c = a.monic();
350        //System.out.println("c = " + c);
351
352        BigQuaternion qa = cfac.random(5);
353        //System.out.println("qa = " + qa);
354        BigQuaternion qb = qa.inverse();
355        //System.out.println("qb = " + qb);
356        BigQuaternion qc = qa.multiply(qb);
357        //System.out.println("qc = " + qc);
358        BigQuaternion qd = qb.multiply(qa);
359        //System.out.println("qc = " + qc);
360        assertEquals("qa*(1/qa) == (1/qa)*qa ", qc, qd);
361
362        b = c.multiply(qa).multiply(qb);
363        //System.out.println("b = " + b);
364
365        d = c.multiplyLeft(qa).multiplyLeft(qb);
366        //System.out.println("d = " + d);
367        assertEquals("c*qa*qb = qb*qa*c", b, d);
368        //e = (GenSolvablePolynomial<BigQuaternion>)b.subtract(d);
369        //System.out.println("e = " + e);
370
371        b = c.multiply(qa).multiplyLeft(qb);
372        //System.out.println("b = " + b);
373
374        d = c.multiplyLeft(qb).multiply(qa);
375        //System.out.println("d = " + d);
376        //e = (GenSolvablePolynomial<BigQuaternion>)b.subtract(d);
377        //System.out.println("e = " + e);
378        assertEquals("qb*(c*qa) == (qb*c)*qa", b, d);
379    }
380
381}