001 /*
002 * $Id: ANumGenPolynomialTest.java 2973 2010-01-04 21:59:50Z kredel $
003 */
004
005 package edu.jas.poly;
006
007 import junit.framework.Test;
008 import junit.framework.TestCase;
009 import junit.framework.TestSuite;
010
011 //import edu.jas.structure.RingElem;
012
013 import edu.jas.arith.BigRational;
014
015 import edu.jas.poly.GenPolynomial;
016 import edu.jas.poly.AlgebraicNumber;
017 import edu.jas.poly.AlgebraicNumberRing;
018
019
020 /**
021 * AlgebraicNumber coefficients GenPolynomial tests with JUnit.
022 * @author Heinz Kredel.
023 */
024
025 public class ANumGenPolynomialTest extends TestCase {
026
027 /**
028 * main
029 */
030 public static void main (String[] args) {
031 junit.textui.TestRunner.run( suite() );
032 }
033
034 /**
035 * Constructs a <CODE>ANumGenPolynomialTest</CODE> object.
036 * @param name String.
037 */
038 public ANumGenPolynomialTest(String name) {
039 super(name);
040 }
041
042 /**
043 * suite.
044 */
045 public static Test suite() {
046 TestSuite suite= new TestSuite(ANumGenPolynomialTest.class);
047 return suite;
048 }
049
050 //private final static int bitlen = 100;
051
052 GenPolynomialRing<AlgebraicNumber<BigRational>> fac;
053 AlgebraicNumberRing<BigRational> cfac;
054
055 GenPolynomial<AlgebraicNumber<BigRational>> a;
056 GenPolynomial<AlgebraicNumber<BigRational>> b;
057 GenPolynomial<AlgebraicNumber<BigRational>> c;
058 GenPolynomial<AlgebraicNumber<BigRational>> d;
059 GenPolynomial<AlgebraicNumber<BigRational>> e;
060
061 int rl = 3;
062 int kl = 10;
063 int ll = 5;
064 int el = 5;
065 float q = 0.5f;
066
067 protected void setUp() {
068 a = b = c = d = e = null;
069 BigRational r = new BigRational(1);
070 // univariate minimal polynomial
071 GenPolynomialRing<BigRational> mfac =
072 new GenPolynomialRing<BigRational>(r,1);
073 GenPolynomial<BigRational> modul = mfac.random(3);
074 while ( modul.isZERO() || modul.isUnit() || modul.isConstant() ) {
075 modul = mfac.random(3);
076 }
077 modul = modul.sum( mfac.fromInteger(3L) );
078
079 cfac = new AlgebraicNumberRing<BigRational>( modul.monic() );
080 fac = new GenPolynomialRing<AlgebraicNumber<BigRational>>(cfac,rl);
081 }
082
083 protected void tearDown() {
084 a = b = c = d = e = null;
085 fac = null;
086 }
087
088
089 /**
090 * Test constructor //and toString
091 *
092 */
093 public void testConstruction() {
094 c = fac.getONE();
095 //System.out.println("c = " + c);
096 assertTrue("length( c ) = 1", c.length() == 1);
097 assertTrue("isZERO( c )c"+c, !c.isZERO() );
098 assertTrue("isONE( c ) "+c, c.isONE() );
099
100 d = fac.getZERO();
101 //System.out.println("d = " + d);
102 assertTrue("length( d ) = 0", d.length() == 0);
103 assertTrue("isZERO( d )", d.isZERO() );
104 assertTrue("isONE( d )", !d.isONE() );
105 }
106
107
108 /**
109 * Test random polynomial.
110 *
111 */
112 public void testRandom() {
113 for (int i = 0; i < 7; i++) {
114 a = fac.random(ll+i);
115 //System.out.println("a = " + a);
116
117 // fac.random(rl+i, kl*(i+1), ll+2*i, el+i, q );
118 assertTrue("length( a"+i+" ) <> 0", a.length() >= 0);
119 assertTrue(" not isZERO( a"+i+" )", !a.isZERO() );
120 assertTrue(" not isONE( a"+i+" )", !a.isONE() );
121 }
122 }
123
124
125 /**
126 * Test addition.
127 *
128 */
129 public void testAddition() {
130
131 a = fac.random(ll);
132 b = fac.random(ll);
133
134 c = a.sum(b);
135 d = c.subtract(b);
136 assertEquals("a+b-b = a",a,d);
137
138 c = fac.random(ll);
139
140 ExpVector u = ExpVector.EVRAND(rl,el,q);
141 AlgebraicNumber<BigRational> x = cfac.random(kl);
142
143 b = new GenPolynomial<AlgebraicNumber<BigRational>>(fac, x, u);
144 c = a.sum(b);
145 d = a.sum(x,u);
146 assertEquals("a+p(x,u) = a+(x,u)",c,d);
147
148 c = a.subtract(b);
149 d = a.subtract(x,u);
150 assertEquals("a-p(x,u) = a-(x,u)",c,d);
151
152 a = new GenPolynomial<AlgebraicNumber<BigRational>>(fac);
153 b = new GenPolynomial<AlgebraicNumber<BigRational>>(fac,x, u);
154 c = b.sum(a);
155 d = a.sum(x,u);
156 assertEquals("a+p(x,u) = a+(x,u)",c,d);
157
158 c = a.subtract(b);
159 d = a.subtract(x,u);
160 assertEquals("a-p(x,u) = a-(x,u)",c,d);
161
162
163 c = fac.random(ll);
164 d = c.sum( a.sum(b) );
165 e = c.sum( a ).sum(b);
166 assertEquals("c+(a+b) = (c+a)+b",d,e);
167
168 c = a.sum( fac.getZERO() );
169 d = a.subtract( fac.getZERO() );
170 assertEquals("a+0 = a-0",c,d);
171
172 c = fac.getZERO().sum( a );
173 d = fac.getZERO().subtract( a.negate() );
174 assertEquals("0+a = 0+(-a)",c,d);
175 }
176
177
178 /**
179 * Test object multiplication.
180 *
181 */
182
183 public void testMultiplication() {
184
185 a = fac.random(ll);
186 assertTrue("not isZERO( a )", !a.isZERO() );
187
188 b = fac.random(ll);
189 assertTrue("not isZERO( b )", !b.isZERO() );
190
191 c = b.multiply(a);
192 d = a.multiply(b);
193 assertTrue("not isZERO( c )", !c.isZERO() );
194 assertTrue("not isZERO( d )", !d.isZERO() );
195
196 //System.out.println("a = " + a);
197 //System.out.println("b = " + b);
198 e = d.subtract(c);
199 assertTrue("isZERO( a*b-b*a ) " + e, e.isZERO() );
200
201 assertTrue("a*b = b*a", c.equals(d) );
202 assertEquals("a*b = b*a",c,d);
203
204 c = fac.random(ll);
205 //System.out.println("c = " + c);
206 d = a.multiply( b.multiply(c) );
207 e = (a.multiply(b)).multiply(c);
208
209 //System.out.println("d = " + d);
210 //System.out.println("e = " + e);
211
212 //System.out.println("d-e = " + d.subtract(c) );
213
214 assertEquals("a(bc) = (ab)c",d,e);
215 assertTrue("a(bc) = (ab)c", d.equals(e) );
216
217 AlgebraicNumber<BigRational> z = a.leadingBaseCoefficient();
218 //System.out.println("z = " + z);
219 if ( z.isUnit() ) {
220 AlgebraicNumber<BigRational> x = z.inverse();
221 //System.out.println("x = " + x);
222 //System.out.println("a = " + a);
223 c = a.monic();
224 //System.out.println("c = " + c);
225 d = a.multiply(x);
226 //System.out.println("d = " + d);
227 assertEquals("a.monic() = a(1/ldcf(a))",c,d);
228 }
229
230 AlgebraicNumber<BigRational> y = b.leadingBaseCoefficient();
231 if ( y.isUnit() ) {
232 y = y.inverse();
233 c = b.monic();
234 d = b.multiply(y);
235 assertEquals("b.monic() = b(1/ldcf(b))",c,d);
236
237 e = new GenPolynomial<AlgebraicNumber<BigRational>>(fac,y);
238 d = b.multiply(e);
239 assertEquals("b.monic() = b(1/ldcf(b))",c,d);
240
241 d = e.multiply(b);
242 assertEquals("b.monic() = (1/ldcf(b))*b",c,d);
243 }
244 }
245
246
247 /**
248 * Test distributive law.
249 *
250 */
251 public void testDistributive() {
252 a = fac.random( ll );
253 b = fac.random( ll );
254 c = fac.random( ll );
255
256 d = a.multiply( b.sum(c) );
257 e = a.multiply( b ).sum( a.multiply(c) );
258
259 assertEquals("a(b+c) = ab+ac",d,e);
260 }
261
262
263 /**
264 * Test object quotient and remainder.
265 *
266 */
267
268 public void testQuotRem1() {
269
270 fac = new GenPolynomialRing<AlgebraicNumber<BigRational>>(cfac,1);
271
272 a = fac.random(2); //.monic();
273 if ( a.isZERO() ) {
274 return;
275 }
276 assertTrue("not isZERO( a )", !a.isZERO() );
277
278 b = fac.random(2); //.monic();
279 if ( b.isZERO() ) {
280 return;
281 }
282 assertTrue("not isZERO( b )", !b.isZERO() );
283
284 GenPolynomial<AlgebraicNumber<BigRational>> h = a;
285 GenPolynomial<AlgebraicNumber<BigRational>> g = fac.random(1).monic();
286 if ( g.isZERO() ) {
287 return;
288 }
289 assertTrue("not isZERO( g )", !g.isZERO() );
290 //g = fac.getONE();
291 a = a.multiply(g);
292 b = b.multiply(g);
293 //System.out.println("ta = " + a);
294 //System.out.println("tb = " + b);
295 //System.out.println("tg = " + g);
296
297 GenPolynomial<AlgebraicNumber<BigRational>>[] qr;
298 qr = b.divideAndRemainder(a);
299 c = qr[0];
300 d = qr[1];
301 //System.out.println("q = " + c);
302 //System.out.println("r = " + d);
303 e = c.multiply(a).sum(d);
304 assertEquals("b = q a + r", b, e );
305
306 qr = a.divideAndRemainder(b);
307 c = qr[0];
308 d = qr[1];
309 //System.out.println("q = " + c);
310 //System.out.println("r = " + d);
311 e = c.multiply(b).sum(d);
312 assertEquals("a = q b + r", a, e );
313
314
315 // gcd tests -------------------------------
316 c = a.gcd(b);
317 //System.out.println("gcd = " + c);
318 assertTrue("a mod gcd(a,b) = 0", a.remainder(c).isZERO() );
319 assertTrue("b mod gcd(a,b) = 0", b.remainder(c).isZERO() );
320 //assertEquals("g = gcd(a,b)", c, g );
321
322 GenPolynomial<AlgebraicNumber<BigRational>>[] gst;
323 gst = a.egcd(b);
324 //System.out.println("egcd = " + gst[0]);
325 //System.out.println(", s = " + gst[1] + ", t = " + gst[2]);
326 c = gst[0];
327 d = gst[1];
328 e = gst[2];
329 assertTrue("a mod gcd(a,b) = 0", a.remainder(c).isZERO() );
330 assertTrue("b mod gcd(a,b) = 0", b.remainder(c).isZERO() );
331 //assertEquals("g = gcd(a,b)", c, g );
332
333 GenPolynomial<AlgebraicNumber<BigRational>> x;
334 x = a.multiply(d).sum( b.multiply(e) ).monic();
335 //System.out.println("x = " + x);
336 assertEquals("gcd(a,b) = a s + b t", c, x );
337
338 //System.out.println("a = " + a);
339 //System.out.println("b = " + b);
340 if ( a.isZERO() || b.isZERO() ) {
341 return;
342 }
343 try {
344 c = a.modInverse(b);
345 //System.out.println("c = " + c);
346 x = c.multiply(a).remainder( b ).monic();
347 //System.out.println("x = " + x);
348 assertTrue("a invertible mod b "+x, x.isUnit() );
349 } catch (RuntimeException e) {
350 // dann halt nicht
351 // not invertible
352 }
353 }
354
355 }