Source code

001
002/*
003 * $Id: ComplexTest.java 5864 2018-07-20 14:28:52Z kredel $
004 */
005
006package edu.jas.poly;
007
008//import java.util.ArrayList;
009//import java.util.List;
010
011import junit.framework.Test;
012import junit.framework.TestCase;
013import junit.framework.TestSuite;
014
015
016import edu.jas.arith.BigRational;
017import edu.jas.arith.BigInteger;
018
019//import edu.jas.structure.RingElem;
020
021
022
023/**
024 * Complex test with JUnit. 
025 * @author Heinz Kredel
026 */
027
028public class ComplexTest extends TestCase {
029
030/**
031 * main.
032 */
033   public static void main (String[] args) {
034       junit.textui.TestRunner.run( suite() );
035   }
036
037/**
038 * Constructs a <CODE>ComplexTest</CODE> object.
039 * @param name String.
040 */
041   public ComplexTest(String name) {
042          super(name);
043   }
044
045/**
046 * suite.
047 */ 
048 public static Test suite() {
049     TestSuite suite= new TestSuite(ComplexTest.class);
050     return suite;
051   }
052
053   ComplexRing<BigInteger> fac;
054   GenPolynomialRing<BigRational> pfac;
055   ComplexRing< GenPolynomial<BigRational> > mfac;
056
057   Complex< BigInteger > a;
058   Complex< BigInteger > b;
059   Complex< BigInteger > c;
060   Complex< BigInteger > d;
061   Complex< BigInteger > e;
062
063   Complex< GenPolynomial<BigRational> > ap;
064   Complex< GenPolynomial<BigRational> > bp;
065   Complex< GenPolynomial<BigRational> > cp;
066   Complex< GenPolynomial<BigRational> > dp;
067   Complex< GenPolynomial<BigRational> > ep;
068
069
070   int rl = 1; 
071   int kl = 13;
072   int ll = 7;
073   int el = 3;
074   float q = 0.4f;
075   int il = 2; 
076   long p = 1152921504606846883L; // 2^60-93; 
077
078   @Override
079   protected void setUp() {
080       a = b = c = d = e = null;
081       ap = bp = cp = dp = ep = null;
082       BigInteger cfac = new BigInteger(1);
083       fac = new ComplexRing<BigInteger>( cfac );
084       pfac = new GenPolynomialRing<BigRational>( new BigRational(1), 1 );
085       GenPolynomial<BigRational> mo = pfac.random(kl,ll,el,q);
086       while ( mo.isConstant() ) {
087             mo = pfac.random(kl,ll,el,q);
088       }
089       mfac = new ComplexRing<GenPolynomial<BigRational>>( pfac );
090   }
091
092   @Override
093   protected void tearDown() {
094       a = b = c = d = e = null;
095       ap = bp = cp = dp = ep = null;
096       fac = null;
097       pfac = null;
098       mfac = null;
099   }
100
101
102/**
103 * Test constructor for integer.
104 * 
105 */
106 public void testIntConstruction() {
107     c = fac.getONE();
108     //System.out.println("c = " + c);
109     assertTrue("isZERO( c )", !c.isZERO() );
110     assertTrue("isONE( c )", c.isONE() );
111
112     d = fac.getZERO();
113     //System.out.println("d = " + d);
114     assertTrue("isZERO( d )", d.isZERO() );
115     assertTrue("isONE( d )", !d.isONE() );
116 }
117
118
119/**
120 * Test constructor for polynomial.
121 * 
122 */
123 public void testPolyConstruction() {
124     cp = mfac.getONE();
125     assertTrue("isZERO( cp )", !cp.isZERO() );
126     assertTrue("isONE( cp )", cp.isONE() );
127
128     dp = mfac.getZERO();
129     assertTrue("isZERO( dp )", dp.isZERO() );
130     assertTrue("isONE( dp )", !dp.isONE() );
131 }
132
133
134/**
135 * Test random integer.
136 * 
137 */
138 public void testIntRandom() {
139     for (int i = 0; i < 7; i++) {
140         a = fac.random(kl*(i+1));
141        if ( a.isZERO() ) {
142            continue;
143         }
144         //a = fac.random(kl*(i+1), ll+2*i, el+i, q );
145         //System.out.println("a = " + a);
146         assertTrue(" not isZERO( a"+i+" )", !a.isZERO() );
147         assertTrue(" not isONE( a"+i+" )", !a.isONE() );
148     }
149 }
150
151
152/**
153 * Test random polynomial.
154 * 
155 */
156 public void testPolyRandom() {
157     for (int i = 0; i < 7; i++) {
158         ap = mfac.random(kl+i);
159         if ( ap.isZERO() ) {
160            continue;
161         }
162         assertTrue(" not isZERO( ap"+i+" )", !ap.isZERO() );
163         assertTrue(" not isONE( ap"+i+" )", !ap.isONE() );
164     }
165 }
166
167
168/**
169 * Test integer addition.
170 * 
171 */
172 public void testIntAddition() {
173
174     a = fac.random(kl);
175     b = fac.random(kl);
176
177     c = a.sum(b);
178     d = c.subtract(b);
179     assertEquals("a+b-b = a",a,d);
180
181     c = a.sum(b);
182     d = b.sum(a);
183     assertEquals("a+b = b+a",c,d);
184
185     c = fac.random(kl);
186     d = c.sum( a.sum(b) );
187     e = c.sum( a ).sum(b);
188     assertEquals("c+(a+b) = (c+a)+b",d,e);
189
190
191     c = a.sum( fac.getZERO() );
192     d = a.subtract( fac.getZERO() );
193     assertEquals("a+0 = a-0",c,d);
194
195     c = fac.getZERO().sum( a );
196     d = fac.getZERO().subtract( a.negate() );
197     assertEquals("0+a = 0+(-a)",c,d);
198 }
199
200
201/**
202 * Test polynomial addition.
203 * 
204 */
205 public void testPolyAddition() {
206
207     ap = mfac.random(kl);
208     bp = mfac.random(kl);
209     //System.out.println("a = " + a);
210     //System.out.println("b = " + b);
211
212     cp = ap.sum(bp);
213     dp = cp.subtract(bp);
214     assertEquals("a+b-b = a",ap,dp);
215
216     cp = ap.sum(bp);
217     dp = bp.sum(ap);
218     //System.out.println("c = " + c);
219     //System.out.println("d = " + d);
220
221     assertEquals("a+b = b+a",cp,dp);
222
223     cp = mfac.random(kl);
224     dp = cp.sum( ap.sum(bp) );
225     ep = cp.sum( ap ).sum(bp);
226     assertEquals("c+(a+b) = (c+a)+b",dp,ep);
227
228
229     cp = ap.sum( mfac.getZERO() );
230     dp = ap.subtract( mfac.getZERO() );
231     assertEquals("a+0 = a-0",cp,dp);
232
233     cp = mfac.getZERO().sum( ap );
234     dp = mfac.getZERO().subtract( ap.negate() );
235     assertEquals("0+a = 0+(-a)",cp,dp);
236}
237
238
239/**
240 * Test integer multiplication.
241 * 
242 */
243 public void testIntMultiplication() {
244
245     a = fac.random(kl);
246     if ( a.isZERO() ) {
247        return;
248     }
249     assertTrue("not isZERO( a )", !a.isZERO() );
250
251     b = fac.random(kl);
252     if ( b.isZERO() ) {
253        return;
254     }
255     assertTrue("not isZERO( b )", !b.isZERO() );
256
257     c = b.multiply(a);
258     d = a.multiply(b);
259     assertTrue("not isZERO( c )", !c.isZERO() );
260     assertTrue("not isZERO( d )", !d.isZERO() );
261
262     //System.out.println("a = " + a);
263     //System.out.println("b = " + b);
264     e = d.subtract(c);
265     assertTrue("isZERO( a*b-b*a ) " + e, e.isZERO() );
266
267     assertTrue("a*b = b*a", c.equals(d) );
268     assertEquals("a*b = b*a",c,d);
269
270     c = fac.random(kl);
271     //System.out.println("c = " + c);
272     d = a.multiply( b.multiply(c) );
273     e = (a.multiply(b)).multiply(c);
274
275     //System.out.println("d = " + d);
276     //System.out.println("e = " + e);
277
278     //System.out.println("d-e = " + d.subtract(c) );
279
280     assertEquals("a(bc) = (ab)c",d,e);
281     assertTrue("a(bc) = (ab)c", d.equals(e) );
282
283     c = a.multiply( fac.getONE() );
284     d = fac.getONE().multiply( a );
285     assertEquals("a*1 = 1*a",c,d);
286
287     if ( a.isUnit() ) {
288        c = a.inverse();
289        d = c.multiply(a);
290        //System.out.println("a = " + a);
291        //System.out.println("c = " + c);
292        //System.out.println("d = " + d);
293        assertTrue("a*1/a = 1",d.isONE()); 
294     }
295 }
296
297
298/**
299 * Test polynomial multiplication.
300 * 
301 */
302 public void testPolyMultiplication() {
303
304     ap = mfac.random(kl);
305     if ( ap.isZERO() ) {
306        return;
307     }
308     assertTrue("not isZERO( a )", !ap.isZERO() );
309
310     bp = mfac.random(kl);
311     if ( bp.isZERO() ) {
312        return;
313     }
314     assertTrue("not isZERO( b )", !bp.isZERO() );
315
316     cp = bp.multiply(ap);
317     dp = ap.multiply(bp);
318     assertTrue("not isZERO( c )", !cp.isZERO() );
319     assertTrue("not isZERO( d )", !dp.isZERO() );
320
321     //System.out.println("a = " + a);
322     //System.out.println("b = " + b);
323     ep = dp.subtract(cp);
324     assertTrue("isZERO( a*b-b*a ) " + ep, ep.isZERO() );
325
326     assertTrue("a*b = b*a", cp.equals(dp) );
327     assertEquals("a*b = b*a",cp,dp);
328
329     cp = mfac.random(kl);
330     //System.out.println("c = " + c);
331     dp = ap.multiply( bp.multiply(cp) );
332     ep = (ap.multiply(bp)).multiply(cp);
333
334     //System.out.println("d = " + d);
335     //System.out.println("e = " + e);
336
337     //System.out.println("d-e = " + d.subtract(c) );
338
339     assertEquals("a(bc) = (ab)c",dp,ep);
340     assertTrue("a(bc) = (ab)c", dp.equals(ep) );
341
342     cp = ap.multiply( mfac.getONE() );
343     dp = mfac.getONE().multiply( ap );
344     assertEquals("a*1 = 1*a",cp,dp);
345
346     if ( ap.isUnit() ) {
347        cp = ap.inverse();
348        dp = cp.multiply(ap);
349        //System.out.println("a = " + a);
350        //System.out.println("c = " + c);
351        //System.out.println("d = " + d);
352        assertTrue("a*1/a = 1",dp.isONE()); 
353     }
354 }
355
356
357/**
358 * Test integer division.
359 * 
360 */
361 public void testIntDivision() {
362
363     a = fac.random(kl*2);
364     if ( a.isZERO() ) {
365        return;
366     }
367     assertTrue("not isZERO( a )", !a.isZERO() );
368
369     b = fac.random(kl);
370     if ( b.isZERO() ) {
371        return;
372     }
373     assertTrue("not isZERO( b )", !b.isZERO() );
374     //System.out.println("a = " + a);
375     //System.out.println("b = " + b);
376
377     c = a.divide(b);
378     //System.out.println("c = " + c);
379     d = a.remainder(b);
380     //System.out.println("d = " + d);
381
382     e = b.multiply(c).sum(d);
383     //System.out.println("e = " + e);
384     assertEquals("a = b (a/b) + a%b ", a, e );
385
386     c = a.gcd(b);
387     d = a.divide(c);
388     e = b.divide(c);
389     //System.out.println("c = " + c);
390     //System.out.println("d = " + d);
391     //System.out.println("e = " + e);
392
393     d = c.multiply(d);
394     e = c.multiply(e);
395     //System.out.println("d = " + d);
396     //System.out.println("e = " + e);
397
398     assertEquals("a/gcd(a,b)*gcd(a,b) = a ", a, d );
399     assertEquals("b/gcd(a,b)*gcd(a,b) = b ", b, e );
400
401     Complex<BigInteger>[] gf = a.egcd(b);
402     c = gf[0];
403     d = gf[1];
404     e = gf[2];
405     //System.out.println("c = " + c);
406     //System.out.println("d = " + d);
407     //System.out.println("e = " + e);
408     d = d.multiply(a);
409     e = e.multiply(b);
410     d = d.sum( e );
411     //System.out.println("d = " + d);
412     assertEquals("d*a + e*b = c = gcd(a,b)", c, d );
413 }
414
415
416/**
417 * Test polynomial division.
418 * 
419 */
420 public void testPolyDivision() {
421
422     ap = mfac.random(kl);
423     if ( ap.isZERO() ) {
424        return;
425     }
426     assertTrue("not isZERO( ap )", !ap.isZERO() );
427
428     bp = mfac.random(kl/2);
429     if ( bp.isZERO() ) {
430        return;
431     }
432     assertTrue("not isZERO( bp )", !bp.isZERO() );
433     //System.out.println("ap = " + ap);
434     //System.out.println("bp = " + bp);
435
436     cp = ap.divide(bp);
437     //System.out.println("cp = " + cp);
438     dp = ap.remainder(bp);
439     //System.out.println("dp = " + dp);
440
441     ep = bp.multiply(cp).sum(dp);
442     //System.out.println("ep = " + ep);
443     assertEquals("ap = bp (ap/bp) + ap%bp ", ap, ep );
444
445     // not applicable:
446//      cp = ap.gcd(bp);
447//      dp = ap.divide(cp);
448//      ep = bp.divide(cp);
449//      System.out.println("cp = " + cp);
450//      System.out.println("dp = " + dp);
451//      System.out.println("ep = " + ep);
452
453//      dp = cp.multiply(dp);
454//      ep = cp.multiply(ep);
455//      System.out.println("dp = " + dp);
456//      System.out.println("ep = " + ep);
457
458//      assertEquals("ap/gcd(ap,bp)*gcd(ap,bp) = ap ", ap, dp );
459//      assertEquals("bp/gcd(ap,bp)*gcd(ap,bp) = bp ", bp, ep );
460 }
461
462}