Source code

001
002/*
003 * $Id$
004 */
005
006package edu.jas.ufd;
007
008
009import java.io.IOException;
010import java.io.StringReader;
011import java.util.Arrays;
012import java.util.List;
013
014import edu.jas.arith.BigInteger;
015import edu.jas.kern.ComputerThreads;
016import edu.jas.kern.PrettyPrint;
017import edu.jas.poly.GenExteriorPolynomial;
018import edu.jas.poly.GenExteriorPolynomialRing;
019import edu.jas.poly.GenPolynomial;
020import edu.jas.poly.GenPolynomialRing;
021import edu.jas.poly.GenPolynomialTokenizer;
022import edu.jas.poly.IndexFactory;
023import edu.jas.poly.TermOrder;
024import edu.jas.structure.RingElem;
025
026import junit.framework.Test;
027import junit.framework.TestCase;
028import junit.framework.TestSuite;
029
030
031/**
032 * Quotient BigInteger coefficient GenPolynomial tests with JUnit.
033 * @author Heinz Kredel
034 */
035
036public class QuotIntPolynomialTest extends TestCase {
037
038
039    /**
040     * main.
041     */
042    public static void main(String[] args) {
043        junit.textui.TestRunner.run(suite());
044        ComputerThreads.terminate();
045    }
046
047
048    /**
049     * Constructs a <CODE>QoutIntPolynomialTest</CODE> object.
050     * @param name String.
051     */
052    public QuotIntPolynomialTest(String name) {
053        super(name);
054    }
055
056
057    /**
058     * suite.
059     */
060    public static Test suite() {
061        TestSuite suite = new TestSuite(QuotIntPolynomialTest.class);
062        return suite;
063    }
064
065
066    QuotientRing<BigInteger> eFac;
067
068
069    GenPolynomialRing<BigInteger> mfac;
070
071
072    GenPolynomialRing<Quotient<BigInteger>> qfac;
073
074
075    GenPolynomial<Quotient<BigInteger>> a, b, c, d, e;
076
077
078    int rl = 3;
079
080
081    int kl = 2; // degree of coefficient polynomials!!!
082
083
084    int ll = 4; //6;
085
086
087    int el = 3;
088
089
090    float q = 0.3f;
091
092
093    @Override
094    protected void setUp() {
095        a = b = c = d = e = null;
096        TermOrder to = new TermOrder(TermOrder.INVLEX);
097        String[] cv = new String[] { "a", "b", "c" };
098        BigInteger cfac = new BigInteger(1);
099        mfac = new GenPolynomialRing<BigInteger>(cfac, rl, to, cv);
100        eFac = new QuotientRing<BigInteger>(mfac);
101        String[] v = new String[] { "w", "x", "y", "z" };
102        qfac = new GenPolynomialRing<Quotient<BigInteger>>(eFac, rl + 1, v);
103    }
104
105
106    @Override
107    protected void tearDown() {
108        a = b = c = d = e = null;
109        //eFac.terminate();
110        eFac = null;
111        mfac = null;
112        qfac = null;
113        ComputerThreads.terminate();
114    }
115
116
117    /**
118     * Test constructor and toString.
119     */
120    public void testConstruction() {
121        c = qfac.getONE();
122        //System.out.println("c = " + c);
123        //System.out.println("c.val = " + c.val);
124        assertTrue("length( c ) = 1", c.length() == 1);
125        assertTrue("isZERO( c )", !c.isZERO());
126        assertTrue("isONE( c )", c.isONE());
127
128        d = qfac.getZERO();
129        //System.out.println("d = " + d);
130        //System.out.println("d.val = " + d.val);
131        assertTrue("length( d ) = 0", d.length() == 0);
132        assertTrue("isZERO( d )", d.isZERO());
133        assertTrue("isONE( d )", !d.isONE());
134    }
135
136
137    /**
138     * Test random polynomial.
139     */
140    public void testRandom() {
141        for (int i = 0; i < 3; i++) {
142            //a = qfac.random(ll+i);
143            a = qfac.random(kl, ll + i, el, q);
144            //System.out.println("a["+i+"] = " + a);
145            if (a.isZERO() || a.isONE()) {
146                continue;
147            }
148            assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
149            assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
150            assertTrue(" not isONE( a" + i + " )", !a.isONE());
151
152            b = a.monic();
153            Quotient<BigInteger> ldbcf = b.leadingBaseCoefficient();
154            //System.out.println("b["+i+"] = " + b);
155            assertTrue("ldbcf( b" + i + " ) == 1 " + b + ", a = " + a, ldbcf.isONE());
156        }
157    }
158
159
160    /**
161     * Test addition.
162     */
163    public void testAddition() {
164        a = qfac.random(kl, ll, el, q);
165        b = qfac.random(kl, ll, el, q);
166        //System.out.println("a = " + a);
167        //System.out.println("b = " + b);
168        //System.out.println("a = " + a.toString( qfac.getVars() ));
169        //System.out.println("b = " + b.toString( qfac.getVars() ));
170
171        c = a.sum(b);
172        d = c.subtract(b);
173        assertEquals("a+b-b = a", a, d);
174
175        c = a.sum(b);
176        d = b.sum(a);
177        //System.out.println("c = " + c.toString( qfac.getVars() ));
178        //System.out.println("c = " + c);
179        //System.out.println("d = " + d);
180
181        assertEquals("a+b = b+a", c, d);
182
183        c = qfac.random(kl, ll, el, q);
184        d = c.sum(a.sum(b));
185        e = c.sum(a).sum(b);
186        assertEquals("c+(a+b) = (c+a)+b", d, e);
187
188        c = a.sum(qfac.getZERO());
189        d = a.subtract(qfac.getZERO());
190        assertEquals("a+0 = a-0", c, d);
191
192        c = qfac.getZERO().sum(a);
193        d = qfac.getZERO().subtract(a.negate());
194        assertEquals("0+a = 0+(-a)", c, d);
195    }
196
197
198    /**
199     * Test object multiplication.
200     */
201    public void testMultiplication() {
202        a = qfac.random(kl, ll, el, q);
203        //assertTrue("not isZERO( a )", !a.isZERO() );
204
205        b = qfac.random(kl, ll, el, q);
206        //assertTrue("not isZERO( b )", !b.isZERO() );
207
208        c = b.multiply(a);
209        d = a.multiply(b);
210        if (!a.isZERO() && !b.isZERO()) {
211            assertTrue("not isZERO( c )", !c.isZERO());
212            assertTrue("not isZERO( d )", !d.isZERO());
213        }
214
215        //System.out.println("a = " + a);
216        //System.out.println("b = " + b);
217        e = d.subtract(c);
218        assertTrue("isZERO( a*b-b*a ) " + e, e.isZERO());
219
220        assertTrue("a*b = b*a", c.equals(d));
221        assertEquals("a*b = b*a", c, d);
222
223        c = qfac.random(kl, ll, el, q);
224        //System.out.println("c = " + c);
225        d = a.multiply(b.multiply(c));
226        e = (a.multiply(b)).multiply(c);
227
228        //System.out.println("d = " + d);
229        //System.out.println("e = " + e);
230
231        //System.out.println("d-e = " + d.subtract(c) );
232
233        assertEquals("a(bc) = (ab)c", d, e);
234        assertTrue("a(bc) = (ab)c", d.equals(e));
235
236        c = a.multiply(qfac.getONE());
237        d = qfac.getONE().multiply(a);
238        assertEquals("a*1 = 1*a", c, d);
239
240        if (a.isUnit()) {
241            c = a.inverse();
242            d = c.multiply(a);
243            //System.out.println("a = " + a);
244            //System.out.println("c = " + c);
245            //System.out.println("d = " + d);
246            assertTrue("a*1/a = 1", d.isONE());
247        }
248    }
249
250
251    /**
252     * Test parse().
253     */
254    public void testParse() {
255        a = qfac.random(kl, ll * 2, el * 2, q * 2);
256        //assertTrue("not isZERO( a )", !a.isZERO() );
257
258        //PrettyPrint.setInternal();
259        //System.out.println("a = " + a);
260        PrettyPrint.setPretty();
261        //System.out.println("a = " + a);
262        String p = a.toString(qfac.getVars());
263        //System.out.println("p = " + p);
264        b = qfac.parse(p);
265        //System.out.println("b = " + b.toString( qfac.getVars() ) );
266
267        //c = a.subtract(b);
268        //System.out.println("c = " + c);
269        assertEquals("parse(a.toSting()) = a", a, b);
270    }
271
272
273    /**
274     * Test exterior derivation.
275     */
276    @SuppressWarnings("unchecked")
277    public void testDerivation() {
278        // integers
279        BigInteger rf = new BigInteger();
280        //System.out.println("rf = " + rf.toScriptFactory());
281
282        // 3/6 commuting vars
283        String[] vars = new String[] { "x1", "x2", "x3" };
284        //System.out.println("vars = " + Arrays.toString(vars));
285
286        // polynomials over integers
287        GenPolynomialRing<BigInteger> pf = new GenPolynomialRing<BigInteger>(rf, vars);
288        //System.out.println("pf = " + pf.toScript());
289
290        QuotientRing<BigInteger> qf = new QuotientRing<BigInteger>(pf);
291        //System.out.println("qf = " + qf.toScript());
292
293        assertTrue("commutative", qf.isCommutative());
294        assertTrue("associative", qf.isAssociative());
295        assertTrue("not field", qf.isField());
296        assertEquals("qf == qf: ", qf, qf);
297
298        String s = qf.toScript();
299        //System.out.println("qf.toScript: " + s + ", " + s.length());
300        assertEquals("#s == 42: " + s, s.length(), 42);
301
302        s = qf.toString();
303        //System.out.println("qf.toString: " + s + ", " + s.length());
304        assertEquals("#s == 41: " + s, s.length(), 41);
305
306        Quotient<BigInteger> p = qf.getONE();
307        //System.out.println("p = " + p);
308        assertTrue("p == 1", p.isONE());
309        p = qf.getZERO();
310        assertTrue("p == 0", p.isZERO());
311        //System.out.println("p = " + p);
312
313        List<Quotient<BigInteger>> gens = qf.generators();
314        //System.out.println("gens = " + gens);
315        assertTrue("#gens == 4", gens.size() == 4);
316
317        RingElem<Quotient<BigInteger>> qe = new Quotient<BigInteger>(qf);
318        //System.out.println("qe = " + qe);
319        assertTrue("p.equals(qe) = ", p.equals(qe));
320        assertTrue("p.equals(p) = ", p.equals(p));
321
322        qe = qe.sum(p);
323        //System.out.println("qe = " + qe);
324        assertTrue("qe.isZERO() = ", qe.isZERO());
325        //p = pf.random(9);
326        p = qf.random(kl, ll, el, q);
327        p = p.subtract(p);
328        //System.out.println("p = " + p);
329        //System.out.println("p.isZERO() = " + p.isZERO());
330        assertTrue("p.isZERO() = ", p.isZERO());
331
332
333        // exterior polynomials over (polynomials over integers)
334        // 3 non-commuting vars
335        IndexFactory wf2 = new IndexFactory(3);
336        //System.out.println("wf2 = " + wf2);
337
338        GenExteriorPolynomialRing<Quotient<BigInteger>> ppf;
339        ppf = new GenExteriorPolynomialRing<Quotient<BigInteger>>(qf, wf2);
340        //System.out.println("ppf = " + ppf.toScript());
341
342        GenExteriorPolynomial<Quotient<BigInteger>> pp = ppf.getONE();
343        //System.out.println("pp = " + pp);
344        assertTrue("pp == 1", pp.isONE());
345        //pp = ppf.random(2);
346        pp = ppf.random(kl, ll, el);
347        //System.out.println("pp = " + pp);
348        pp = ppf.getZERO();
349        //System.out.println("pp = " + pp);
350        assertTrue("pp == 0", pp.isZERO());
351
352        List<GenExteriorPolynomial<Quotient<BigInteger>>> pgens = ppf.generators();
353        //System.out.println("pgens = " + pgens);
354        assertTrue("#pgens == 4+3", pgens.size() == 4 + 3);
355
356
357        //pp = ppf.random(2);
358        pp = ppf.random(kl, ll, el);
359        //System.out.println("\npp = " + pp);
360        assertFalse("pp.isZERO() = ", pp.isZERO());
361        long deg = pp.degree();
362        //System.out.println("deg = " + deg);
363
364        GenExteriorPolynomial<Quotient<BigInteger>> der;
365        der = PolyUfdUtil.<BigInteger> exteriorDerivativeQuot(pp);
366        //System.out.println("der = " + der);
367        //System.out.println("deg = " + deg + ", deg(der) = " + der.degree());
368        assertTrue("deg >= 0: ", deg >= 0 && der.degree() >= 0);
369        deg = der.degree();
370        der = PolyUfdUtil.<BigInteger> exteriorDerivativeQuot(der);
371        //System.out.println("der(der) = " + der);
372        //System.out.println("deg = " + deg + ", deg(der) = " + der.degree());
373        assertTrue("deg >= 0: ", deg >= 0 && der.degree() >= 0);
374
375
376        StringReader sr = new StringReader("{x1 x2 | x3 } E(1) E(2)");
377        //System.out.println("sr = " + sr);
378        GenPolynomialTokenizer tok = new GenPolynomialTokenizer(sr);
379        //System.out.println("ppf = " + ppf.toScript());
380
381        // parse with tokenizer
382        try {
383            pp = (GenExteriorPolynomial<Quotient<BigInteger>>) tok.nextExteriorPolynomial(ppf);
384        } catch (IOException e) {
385            e.printStackTrace();
386            return;
387        }
388        //System.out.println("\npp = " + pp);
389        deg = pp.degree();
390        der = PolyUfdUtil.<BigInteger> exteriorDerivativeQuot(pp);
391        //System.out.println("der = " + der);
392        assertTrue("deg >= 0: ", deg >= 0 && der.degree() >= 0);
393
394
395        sr = new StringReader("{x3 | x2} E(1) + x3 E(2)");
396        //sr = new StringReader("x1 E(1) + x2 E(2)");
397        //sr = new StringReader("x2 E(1) + x1 E(2)");
398        //System.out.println("sr = " + sr);
399        tok = new GenPolynomialTokenizer(sr);
400        //System.out.println("ppf = " + ppf.toScript());
401
402        // parse with tokenizer
403        try {
404            pp = (GenExteriorPolynomial<Quotient<BigInteger>>) tok.nextExteriorPolynomial(ppf);
405        } catch (IOException e) {
406            e.printStackTrace();
407            return;
408        }
409        //System.out.println("\npp = " + pp);
410        deg = pp.degree();
411        der = PolyUfdUtil.<BigInteger> exteriorDerivativeQuot(pp);
412        //System.out.println("der = " + der);
413        assertTrue("deg >= 0: ", deg >= 0 && der.degree() >= 0);
414        deg = der.degree();
415        der = PolyUfdUtil.<BigInteger> exteriorDerivativeQuot(der);
416        //System.out.println("der(der) = " + der);
417        assertTrue("deg >= 0: ", deg >= 0 && der.degree() >= 0);
418    }
419
420}