Source code

001/*
002 * $Id: ANumGenPolynomialTest.java 4071 2012-07-27 19:59:38Z kredel $
003 */
004
005package edu.jas.poly;
006
007
008import junit.framework.Test;
009import junit.framework.TestCase;
010import junit.framework.TestSuite;
011
012import edu.jas.arith.BigRational;
013
014
015/**
016 * AlgebraicNumber coefficients GenPolynomial tests with JUnit.
017 * @author Heinz Kredel.
018 */
019
020public class ANumGenPolynomialTest extends TestCase {
021
022
023    /**
024     * main
025     */
026    public static void main(String[] args) {
027        junit.textui.TestRunner.run(suite());
028    }
029
030
031    /**
032     * Constructs a <CODE>ANumGenPolynomialTest</CODE> object.
033     * @param name String.
034     */
035    public ANumGenPolynomialTest(String name) {
036        super(name);
037    }
038
039
040    /**
041     * suite.
042     */
043    public static Test suite() {
044        TestSuite suite = new TestSuite(ANumGenPolynomialTest.class);
045        return suite;
046    }
047
048
049    //private final static int bitlen = 100;
050
051    GenPolynomialRing<AlgebraicNumber<BigRational>> fac;
052
053
054    AlgebraicNumberRing<BigRational> cfac;
055
056
057    GenPolynomial<AlgebraicNumber<BigRational>> a;
058
059
060    GenPolynomial<AlgebraicNumber<BigRational>> b;
061
062
063    GenPolynomial<AlgebraicNumber<BigRational>> c;
064
065
066    GenPolynomial<AlgebraicNumber<BigRational>> d;
067
068
069    GenPolynomial<AlgebraicNumber<BigRational>> e;
070
071
072    int rl = 3;
073
074
075    int kl = 10;
076
077
078    int ll = 5;
079
080
081    int el = 5;
082
083
084    float q = 0.5f;
085
086
087    @Override
088    protected void setUp() {
089        a = b = c = d = e = null;
090        BigRational r = new BigRational(1);
091        // univariate minimal polynomial
092        GenPolynomialRing<BigRational> mfac = new GenPolynomialRing<BigRational>(r, 1);
093        GenPolynomial<BigRational> modul = mfac.random(3);
094        while (modul.isZERO() || modul.isUnit() || modul.isConstant()) {
095            modul = mfac.random(3);
096        }
097        modul = modul.sum(mfac.fromInteger(3L));
098
099        cfac = new AlgebraicNumberRing<BigRational>(modul.monic());
100        fac = new GenPolynomialRing<AlgebraicNumber<BigRational>>(cfac, rl);
101    }
102
103
104    @Override
105    protected void tearDown() {
106        a = b = c = d = e = null;
107        fac = null;
108    }
109
110
111    /**
112     * Test constructor //and toString
113     * 
114     */
115    public void testConstruction() {
116        c = fac.getONE();
117        //System.out.println("c = " + c);
118        assertTrue("length( c ) = 1", c.length() == 1);
119        assertTrue("isZERO( c )c" + c, !c.isZERO());
120        assertTrue("isONE( c ) " + c, c.isONE());
121
122        d = fac.getZERO();
123        //System.out.println("d = " + d);
124        assertTrue("length( d ) = 0", d.length() == 0);
125        assertTrue("isZERO( d )", d.isZERO());
126        assertTrue("isONE( d )", !d.isONE());
127    }
128
129
130    /**
131     * Test random polynomial.
132     * 
133     */
134    public void testRandom() {
135        for (int i = 0; i < 7; i++) {
136            a = fac.random(ll + i);
137            //System.out.println("a = " + a);
138
139            // fac.random(rl+i, kl*(i+1), ll+2*i, el+i, q );
140            assertTrue("length( a" + i + " ) <> 0", a.length() >= 0);
141            assertTrue(" not isZERO( a" + i + " )", !a.isZERO());
142            assertTrue(" not isONE( a" + i + " )", !a.isONE());
143        }
144    }
145
146
147    /**
148     * Test addition.
149     * 
150     */
151    public void testAddition() {
152
153        a = fac.random(ll);
154        b = fac.random(ll);
155
156        c = a.sum(b);
157        d = c.subtract(b);
158        assertEquals("a+b-b = a", a, d);
159
160        c = fac.random(ll);
161
162        ExpVector u = ExpVector.EVRAND(rl, el, q);
163        AlgebraicNumber<BigRational> x = cfac.random(kl);
164
165        b = new GenPolynomial<AlgebraicNumber<BigRational>>(fac, x, u);
166        c = a.sum(b);
167        d = a.sum(x, u);
168        assertEquals("a+p(x,u) = a+(x,u)", c, d);
169
170        c = a.subtract(b);
171        d = a.subtract(x, u);
172        assertEquals("a-p(x,u) = a-(x,u)", c, d);
173
174        a = new GenPolynomial<AlgebraicNumber<BigRational>>(fac);
175        b = new GenPolynomial<AlgebraicNumber<BigRational>>(fac, x, u);
176        c = b.sum(a);
177        d = a.sum(x, u);
178        assertEquals("a+p(x,u) = a+(x,u)", c, d);
179
180        c = a.subtract(b);
181        d = a.subtract(x, u);
182        assertEquals("a-p(x,u) = a-(x,u)", c, d);
183
184
185        c = fac.random(ll);
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        c = a.sum(fac.getZERO());
191        d = a.subtract(fac.getZERO());
192        assertEquals("a+0 = a-0", c, d);
193
194        c = fac.getZERO().sum(a);
195        d = fac.getZERO().subtract(a.negate());
196        assertEquals("0+a = 0+(-a)", c, d);
197    }
198
199
200    /**
201     * Test object multiplication.
202     * 
203     */
204
205    public void testMultiplication() {
206
207        a = fac.random(ll);
208        assertTrue("not isZERO( a )", !a.isZERO());
209
210        b = fac.random(ll);
211        assertTrue("not isZERO( b )", !b.isZERO());
212
213        c = b.multiply(a);
214        d = a.multiply(b);
215        assertTrue("not isZERO( c )", !c.isZERO());
216        assertTrue("not isZERO( d )", !d.isZERO());
217
218        //System.out.println("a = " + a);
219        //System.out.println("b = " + b);
220        e = d.subtract(c);
221        assertTrue("isZERO( a*b-b*a ) " + e, e.isZERO());
222
223        assertTrue("a*b = b*a", c.equals(d));
224        assertEquals("a*b = b*a", c, d);
225
226        c = fac.random(ll);
227        //System.out.println("c = " + c);
228        d = a.multiply(b.multiply(c));
229        e = (a.multiply(b)).multiply(c);
230
231        //System.out.println("d = " + d);
232        //System.out.println("e = " + e);
233
234        //System.out.println("d-e = " + d.subtract(c) );
235
236        assertEquals("a(bc) = (ab)c", d, e);
237        assertTrue("a(bc) = (ab)c", d.equals(e));
238
239        AlgebraicNumber<BigRational> z = a.leadingBaseCoefficient();
240        //System.out.println("z = " + z);
241        if (z.isUnit()) {
242            AlgebraicNumber<BigRational> x = z.inverse();
243            //System.out.println("x = " + x);
244            //System.out.println("a = " + a);
245            c = a.monic();
246            //System.out.println("c = " + c);
247            d = a.multiply(x);
248            //System.out.println("d = " + d);
249            assertEquals("a.monic() = a(1/ldcf(a))", c, d);
250        }
251
252        AlgebraicNumber<BigRational> y = b.leadingBaseCoefficient();
253        if (y.isUnit()) {
254            y = y.inverse();
255            c = b.monic();
256            d = b.multiply(y);
257            assertEquals("b.monic() = b(1/ldcf(b))", c, d);
258
259            e = new GenPolynomial<AlgebraicNumber<BigRational>>(fac, y);
260            d = b.multiply(e);
261            assertEquals("b.monic() = b(1/ldcf(b))", c, d);
262
263            d = e.multiply(b);
264            assertEquals("b.monic() = (1/ldcf(b))*b", c, d);
265        }
266    }
267
268
269    /**
270     * Test distributive law.
271     * 
272     */
273    public void testDistributive() {
274        a = fac.random(ll);
275        b = fac.random(ll);
276        c = fac.random(ll);
277
278        d = a.multiply(b.sum(c));
279        e = a.multiply(b).sum(a.multiply(c));
280
281        assertEquals("a(b+c) = ab+ac", d, e);
282    }
283
284
285    /**
286     * Test object quotient and remainder.
287     * 
288     */
289
290    public void testQuotRem1() {
291
292        fac = new GenPolynomialRing<AlgebraicNumber<BigRational>>(cfac, 1);
293
294        a = fac.random(2); //.monic();
295        if (a.isZERO()) {
296            return;
297        }
298        assertTrue("not isZERO( a )", !a.isZERO());
299
300        b = fac.random(2); //.monic();
301        if (b.isZERO()) {
302            return;
303        }
304        assertTrue("not isZERO( b )", !b.isZERO());
305
306        GenPolynomial<AlgebraicNumber<BigRational>> g = fac.random(1).monic();
307        if (g.isZERO()) {
308            return;
309        }
310        assertTrue("not isZERO( g )", !g.isZERO());
311        //g = fac.getONE();
312        a = a.multiply(g);
313        b = b.multiply(g);
314        //System.out.println("ta = " + a);
315        //System.out.println("tb = " + b);
316        //System.out.println("tg = " + g);
317
318        GenPolynomial<AlgebraicNumber<BigRational>>[] qr;
319        qr = b.divideAndRemainder(a);
320        c = qr[0];
321        d = qr[1];
322        //System.out.println("q = " + c);
323        //System.out.println("r = " + d);
324        e = c.multiply(a).sum(d);
325        assertEquals("b = q a + r", b, e);
326
327        qr = a.divideAndRemainder(b);
328        c = qr[0];
329        d = qr[1];
330        //System.out.println("q = " + c);
331        //System.out.println("r = " + d);
332        e = c.multiply(b).sum(d);
333        assertEquals("a = q b + r", a, e);
334
335
336        // gcd tests -------------------------------
337        c = a.gcd(b);
338        //System.out.println("gcd = " + c);
339        assertTrue("a mod gcd(a,b) = 0", a.remainder(c).isZERO());
340        assertTrue("b mod gcd(a,b) = 0", b.remainder(c).isZERO());
341        //assertEquals("g = gcd(a,b)", c, g ); 
342
343        GenPolynomial<AlgebraicNumber<BigRational>>[] gst;
344        gst = a.egcd(b);
345        //System.out.println("egcd = " + gst[0]);
346        //System.out.println(", s = " + gst[1] + ", t = " + gst[2]);
347        c = gst[0];
348        d = gst[1];
349        e = gst[2];
350        assertTrue("a mod gcd(a,b) = 0", a.remainder(c).isZERO());
351        assertTrue("b mod gcd(a,b) = 0", b.remainder(c).isZERO());
352        //assertEquals("g = gcd(a,b)", c, g );
353
354        GenPolynomial<AlgebraicNumber<BigRational>> x;
355        x = a.multiply(d).sum(b.multiply(e)).monic();
356        //System.out.println("x = " + x);
357        assertEquals("gcd(a,b) = a s + b t", c, x);
358
359        //System.out.println("a = " + a);
360        //System.out.println("b = " + b);
361        if (a.isZERO() || b.isZERO()) {
362            return;
363        }
364        try {
365            c = a.modInverse(b);
366            //System.out.println("c = " + c);
367            x = c.multiply(a).remainder(b).monic();
368            //System.out.println("x = " + x);
369            assertTrue("a invertible mod b " + x, x.isUnit());
370        } catch (RuntimeException e) {
371            // dann halt nicht
372            // not invertible
373        }
374    }
375
376}