Source code

001/*
002 * $Id: RatGenSolvablePolynomialTest.java 5905 2018-08-24 10:23:58Z kredel $
003 */
004
005package edu.jas.poly;
006
007
008import junit.framework.Test;
009import junit.framework.TestCase;
010import junit.framework.TestSuite;
011
012
013import edu.jas.arith.BigRational;
014
015
016/**
017 * BigRational coefficients GenSolvablePolynomial tests with JUnit.
018 * @author Heinz Kredel
019 */
020
021public class RatGenSolvablePolynomialTest extends TestCase {
022
023
024    /**
025     * main.
026     */
027    public static void main(String[] args) {
028        junit.textui.TestRunner.run(suite());
029    }
030
031
032    /**
033     * Constructs a <CODE>RatGenSolvablePolynomialTest</CODE> object.
034     * @param name String.
035     */
036    public RatGenSolvablePolynomialTest(String name) {
037        super(name);
038    }
039
040
041    /**
042     */
043    public static Test suite() {
044        TestSuite suite = new TestSuite(RatGenSolvablePolynomialTest.class);
045        return suite;
046    }
047
048
049    GenSolvablePolynomial<BigRational> a, b, c, d, e, f, x1, x2;
050
051
052    int rl = 5;
053
054
055    int kl = 10;
056
057
058    int ll = 5;
059
060
061    int el = 3;
062
063
064    float q = 0.5f;
065
066
067    RelationTable<BigRational> table;
068
069
070    GenSolvablePolynomialRing<BigRational> ring;
071
072
073    BigRational cfac;
074
075
076    @Override
077    protected void setUp() {
078        cfac = new BigRational(1);
079        ring = new GenSolvablePolynomialRing<BigRational>(cfac, rl);
080        table = ring.table;
081        a = b = c = d = e = null;
082    }
083
084
085    @Override
086    protected void tearDown() {
087        table = null;
088        ring = null;
089        a = b = c = d = e = null;
090    }
091
092
093    /**
094     * Test constructor and toString.
095     */
096    public void testConstructor() {
097        a = new GenSolvablePolynomial<BigRational>(ring);
098        assertTrue("length( a ) = 0", a.length() == 0);
099        assertTrue("isZERO( a )", a.isZERO());
100        assertTrue("isONE( a )", !a.isONE());
101
102        c = ring.getONE();
103        assertTrue("length( c ) = 1", c.length() == 1);
104        assertTrue("isZERO( c )", !c.isZERO());
105        assertTrue("isONE( c )", c.isONE());
106
107        d = ring.getZERO();
108        assertTrue("length( d ) = 0", d.length() == 0);
109        assertTrue("isZERO( d )", d.isZERO());
110        assertTrue("isONE( d )", !d.isONE());
111    }
112
113
114    /**
115     * Test random polynomial.
116     */
117    public void testRandom() {
118        assertTrue("isCommutative()", ring.isCommutative());
119
120        for (int i = 0; i < 2; i++) {
121            // a = ring.random(ll+2*i);
122            a = ring.random(kl * (i + 1), ll + 2 * i, el + i, q);
123            assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
124            assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
125            assertTrue(" not isONE( a" + i + " )", !a.isONE());
126        }
127    }
128
129
130    /**
131     * Test addition.
132     */
133    public void testAddition() {
134        a = ring.random(kl, ll, el, q);
135
136        c = (GenSolvablePolynomial<BigRational>) a.subtract(a);
137        assertTrue("a-a = 0", c.isZERO());
138
139        b = (GenSolvablePolynomial<BigRational>) a.sum(a);
140        c = (GenSolvablePolynomial<BigRational>) b.subtract(a);
141
142        assertEquals("a+a-a = a", c, a);
143        assertTrue("a+a-a = a", c.equals(a));
144
145        b = ring.random(kl, ll, el, q);
146        c = (GenSolvablePolynomial<BigRational>) b.sum(a);
147        d = (GenSolvablePolynomial<BigRational>) a.sum(b);
148
149        assertEquals("a+b = b+a", c, d);
150        assertTrue("a+b = b+a", c.equals(d));
151
152        c = ring.random(kl, ll, el, q);
153        d = (GenSolvablePolynomial<BigRational>) a.sum(b.sum(c));
154        e = (GenSolvablePolynomial<BigRational>) a.sum(b).sum(c);
155
156        assertEquals("a+(b+c) = (a+b)+c", d, e);
157        assertTrue("a+(b+c) = (a+b)+c", d.equals(e));
158
159        ExpVector u = ExpVector.random(rl, el, q);
160        BigRational x = cfac.random(kl);
161
162        b = ring.getONE().multiply(x, u);
163        c = (GenSolvablePolynomial<BigRational>) a.sum(b);
164        d = (GenSolvablePolynomial<BigRational>) a.sum(x, u);
165        assertEquals("a+p(x,u) = a+(x,u)", c, d);
166
167        c = (GenSolvablePolynomial<BigRational>) a.subtract(b);
168        d = (GenSolvablePolynomial<BigRational>) a.subtract(x, u);
169        assertEquals("a-p(x,u) = a-(x,u)", c, d);
170
171        a = ring.getZERO();
172        b = ring.getONE().multiply(x, u);
173        c = (GenSolvablePolynomial<BigRational>) b.sum(a);
174        d = (GenSolvablePolynomial<BigRational>) a.sum(x, u);
175        assertEquals("a+p(x,u) = a+(x,u)", c, d);
176
177        c = (GenSolvablePolynomial<BigRational>) a.subtract(b);
178        d = (GenSolvablePolynomial<BigRational>) a.subtract(x, u);
179        assertEquals("a-p(x,u) = a-(x,u)", c, d);
180    }
181
182
183    /**
184     * Test object multiplication.
185     */
186    @SuppressWarnings("cast")
187    public void testMultiplication() {
188        a = ring.random(kl, ll, el, q);
189        assertTrue("not isZERO( a )", !a.isZERO());
190        //a = RatGenSolvablePolynomial.DIRRAS(1, kl, 4, el, q );
191
192        b = ring.random(kl, ll, el, q);
193        assertTrue("not isZERO( b )", !b.isZERO());
194
195        c = b.multiply(a);
196        d = a.multiply(b);
197        assertTrue("not isZERO( c )", !c.isZERO());
198        assertTrue("not isZERO( d )", !d.isZERO());
199
200        e = (GenSolvablePolynomial<BigRational>) d.subtract(c);
201        assertTrue("isZERO( a*b-b*a ) " + e, e.isZERO());
202
203        assertEquals("a*b = b*a", c, d);
204        assertTrue("a*b = b*a", c.equals(d));
205
206        c = ring.random(kl, ll, el, q);
207        d = a.multiply(b.multiply(c));
208        e = (a.multiply(b)).multiply(c);
209
210        assertEquals("a(bc) = (ab)c", d, e);
211        assertTrue("a(bc) = (ab)c", d.equals(e));
212
213        BigRational x = a.leadingBaseCoefficient().inverse();
214        c = (GenSolvablePolynomial<BigRational>) a.monic();
215        d = a.multiply(x);
216        assertEquals("a.monic() = a(1/ldcf(a))", c, d);
217
218        ExpVector u = ring.evzero;
219        BigRational y = b.leadingBaseCoefficient().inverse();
220        c = (GenSolvablePolynomial<BigRational>) b.monic();
221        d = b.multiply(y, u);
222        assertEquals("b.monic() = b(1/ldcf(b))", c, d);
223
224        e = ring.getONE().multiply(y, u);
225        d = b.multiply(e);
226        assertEquals("b.monic() = b(1/ldcf(b))", c, d);
227
228        d = e.multiply(b);
229        assertEquals("b.monic() = (1/ldcf(b) (0))*b", c, d);
230
231        d = a.monic();
232        assertTrue("a.monic(): ", d.leadingBaseCoefficient().isONE());
233    }
234
235
236    /**
237     * Test Weyl polynomials.
238     */
239    public void testWeyl() {
240        int rloc = 4;
241        ring = new GenSolvablePolynomialRing<BigRational>(cfac, rloc);
242
243        RelationGenerator<BigRational> wl = new WeylRelations<BigRational>();
244        wl.generate(ring);
245        table = ring.table;
246        //System.out.println("table = " + table);
247        //System.out.println("ring = " + ring);
248
249        assertFalse("isCommutative()", ring.isCommutative());
250        assertTrue("isAssociative()", ring.isAssociative());
251
252        a = ring.random(kl, ll, el, q);
253        assertTrue("not isZERO( a )", !a.isZERO());
254        //System.out.println("a = " + a);
255
256        b = ring.random(kl, ll, el, q);
257        assertTrue("not isZERO( b )", !b.isZERO());
258        //System.out.println("b = " + b);
259
260
261        // non commutative
262        c = b.multiply(a);
263        d = a.multiply(b);
264        //System.out.println("c = " + c);
265        //System.out.println("d = " + d);
266        assertTrue("not isZERO( c )", !c.isZERO());
267        assertTrue("not isZERO( d )", !d.isZERO());
268
269        e = (GenSolvablePolynomial<BigRational>) d.subtract(c);
270        assertTrue("!isZERO( a*b-b*a ) " + e, !e.isZERO());
271        assertTrue("a*b != b*a", c.equals(d) || c.leadingExpVector().equals(d.leadingExpVector()));
272
273        c = ring.random(kl, ll, el, q);
274        //System.out.println("\na = " + a);
275        //System.out.println("\nb = " + b);
276        //System.out.println("\nc = " + c);
277
278        // associative
279        //x1 = b.multiply(c);
280        //System.out.println("\nx1 = " + x1);
281        d = a.multiply(b.multiply(c));
282
283        //x2 = a.multiply(b);
284        //System.out.println("\nx2 = " + x2);
285        e = a.multiply(b).multiply(c);
286
287        //System.out.println("\nd = " + d);
288        //System.out.println("\ne = " + e);
289
290        //f = (GenSolvablePolynomial<BigRational>)d.subtract(e);
291        //System.out.println("\nf = " + f);
292
293        assertEquals("a(bc) = (ab)c", d, e);
294        assertTrue("a(bc) = (ab)c", d.equals(e));
295    }
296
297
298    /**
299     * Test division of polynomials.
300     */
301    public void testDivide() {
302        int rloc = 4;
303        ring = new GenSolvablePolynomialRing<BigRational>(cfac, rloc);
304
305        RelationGenerator<BigRational> wl = new WeylRelations<BigRational>();
306        wl.generate(ring);
307        //System.out.println("ring = " + ring.toScript());
308
309        assertFalse("isCommutative()", ring.isCommutative());
310        assertTrue("isAssociative()", ring.isAssociative());
311
312        do {
313            a = ring.random(kl, ll, el, q);
314        } while(a.isZERO());
315        //System.out.println("a = " + a);
316
317        do {
318            b = ring.random(kl, ll, el, q);
319        } while(b.isZERO());
320        //System.out.println("b = " + b);
321
322        // non commutative
323        c = b.multiply(a);
324        d = a.multiply(b);
325        //System.out.println("c = " + c);
326        //System.out.println("d = " + d);
327        assertTrue("not isZERO( c )", !c.isZERO());
328        assertTrue("not isZERO( d )", !d.isZERO());
329
330        e = (GenSolvablePolynomial<BigRational>) d.subtract(c);
331        assertTrue("a*b != b*a", !c.equals(d) || c.leadingExpVector().equals(d.leadingExpVector()));
332
333        // divide 
334        e = c.divide(a);
335        //System.out.println("e = " + e);
336        f = c.rightDivide(b);
337        //System.out.println("f = " + f);
338        assertEquals("b == b*a/a: " + e, e, b);
339        assertEquals("a == b*a/b: " + e, f, a);
340
341        e = d.rightDivide(a);
342        //System.out.println("e = " + e);
343        f = d.divide(b);
344        //System.out.println("f = " + f);
345        assertEquals("b == a*b/a: " + e, e, b);
346        assertEquals("a == a*b/b: " + e, f, a);
347    }
348
349
350    /**
351     * Test distributive law.
352     */
353    public void testDistributive() {
354        int rloc = 4;
355        ring = new GenSolvablePolynomialRing<BigRational>(cfac, rloc);
356
357        RelationGenerator<BigRational> wl = new WeylRelations<BigRational>();
358        wl.generate(ring);
359        //table = ring.table;
360        //System.out.println("table = " + table);
361        //System.out.println("ring = " + ring);
362
363        a = ring.random(kl, ll, el, q);
364        b = ring.random(kl, ll, el, q);
365        c = ring.random(kl, ll, el, q);
366
367        d = a.multiply((GenSolvablePolynomial<BigRational>) b.sum(c));
368        e = (GenSolvablePolynomial<BigRational>) a.multiply(b).sum(a.multiply(c));
369
370        assertEquals("a(b+c) = ab+ac", d, e);
371    }
372}