001 /*
002 * $Id: RatGenPolynomialTest.java 2831 2009-10-01 21:43:12Z 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 import edu.jas.arith.BigRational;
011
012
013 /**
014 * BigRational coefficients GenPolynomial tests with JUnit.
015 * @author Heinz Kredel.
016 */
017
018 public class RatGenPolynomialTest extends TestCase {
019
020 /**
021 * main.
022 */
023 public static void main (String[] args) {
024 junit.textui.TestRunner.run( suite() );
025 }
026
027 /**
028 * Constructs a <CODE>RatGenPolynomialTest</CODE> object.
029 * @param name String.
030 */
031 public RatGenPolynomialTest(String name) {
032 super(name);
033 }
034
035 /**
036 */
037 public static Test suite() {
038 TestSuite suite= new TestSuite(RatGenPolynomialTest.class);
039 return suite;
040 }
041
042 //private final static int bitlen = 100;
043
044 GenPolynomialRing<BigRational> fac;
045
046 GenPolynomial<BigRational> a;
047 GenPolynomial<BigRational> b;
048 GenPolynomial<BigRational> c;
049 GenPolynomial<BigRational> d;
050 GenPolynomial<BigRational> e;
051
052 int rl = 7;
053 int kl = 10;
054 int ll = 10;
055 int el = 5;
056 float q = 0.5f;
057
058 protected void setUp() {
059 a = b = c = d = e = null;
060 fac = new GenPolynomialRing<BigRational>(new BigRational(1),rl);
061 }
062
063 protected void tearDown() {
064 a = b = c = d = e = null;
065 fac = null;
066 }
067
068
069 /**
070 * Test constructor and toString.
071 *
072 */
073 public void testConstruction() {
074 c = fac.getONE();
075 assertTrue("length( c ) = 1", c.length() == 1);
076 assertTrue("isZERO( c )", !c.isZERO() );
077 assertTrue("isONE( c )", c.isONE() );
078
079 d = fac.getZERO();
080 assertTrue("length( d ) = 0", d.length() == 0);
081 assertTrue("isZERO( d )", d.isZERO() );
082 assertTrue("isONE( d )", !d.isONE() );
083 }
084
085
086 /**
087 * Test random polynomial.
088 */
089 public void testRandom() {
090 for (int i = 0; i < 7; i++) {
091 a = fac.random(ll);
092 //System.out.println("a = " + a);
093
094 // fac.random(rl+i, kl*(i+1), ll+2*i, el+i, q );
095 assertTrue("length( a"+i+" ) <> 0", a.length() >= 0);
096 assertTrue(" not isZERO( a"+i+" )", !a.isZERO() );
097 assertTrue(" not isONE( a"+i+" )", !a.isONE() );
098 }
099 }
100
101
102 /**
103 * Test addition.
104 *
105 */
106 public void testAddition() {
107
108 a = fac.random(ll);
109 b = fac.random(ll);
110
111 c = a.sum(b);
112 d = c.subtract(b);
113 assertEquals("a+b-b = a",a,d);
114
115 c = fac.random(ll);
116
117 ExpVector u = ExpVector.EVRAND(rl,el,q);
118 BigRational x = BigRational.RNRAND(kl);
119
120 b = new GenPolynomial<BigRational>(fac,x, u);
121 c = a.sum(b);
122 d = a.sum(x,u);
123 assertEquals("a+p(x,u) = a+(x,u)",c,d);
124
125 c = a.subtract(b);
126 d = a.subtract(x,u);
127 assertEquals("a-p(x,u) = a-(x,u)",c,d);
128
129 a = new GenPolynomial<BigRational>(fac);
130 b = new GenPolynomial<BigRational>(fac,x, u);
131 c = b.sum(a);
132 d = a.sum(x,u);
133 assertEquals("a+p(x,u) = a+(x,u)",c,d);
134
135 c = a.subtract(b);
136 d = a.subtract(x,u);
137 assertEquals("a-p(x,u) = a-(x,u)",c,d);
138 }
139
140
141 /**
142 * Test object multiplication.
143 *
144 */
145 public void testMultiplication() {
146
147 a = fac.random(ll);
148 assertTrue("not isZERO( a )", !a.isZERO() );
149
150 b = fac.random(ll);
151 assertTrue("not isZERO( b )", !b.isZERO() );
152
153 c = b.multiply(a);
154 d = a.multiply(b);
155 assertTrue("not isZERO( c )", !c.isZERO() );
156 assertTrue("not isZERO( d )", !d.isZERO() );
157
158 //System.out.println("a = " + a);
159 //System.out.println("b = " + b);
160 e = d.subtract(c);
161 assertTrue("isZERO( a*b-b*a ) " + e, e.isZERO() );
162
163 assertTrue("a*b = b*a", c.equals(d) );
164 assertEquals("a*b = b*a",c,d);
165
166 c = fac.random(ll);
167 //System.out.println("c = " + c);
168 d = a.multiply( b.multiply(c) );
169 e = (a.multiply(b)).multiply(c);
170
171 //System.out.println("d = " + d);
172 //System.out.println("e = " + e);
173
174 //System.out.println("d-e = " + d.subtract(c) );
175
176 assertEquals("a(bc) = (ab)c",d,e);
177 assertTrue("a(bc) = (ab)c", d.equals(e) );
178
179 BigRational x = a.leadingBaseCoefficient().inverse();
180 c = a.monic();
181 d = a.multiply(x);
182 assertEquals("a.monic() = a(1/ldcf(a))",c,d);
183
184 BigRational y = b.leadingBaseCoefficient().inverse();
185 c = b.monic();
186 d = b.multiply(y);
187 assertEquals("b.monic() = b(1/ldcf(b))",c,d);
188
189 e = new GenPolynomial<BigRational>(fac,y);
190 d = b.multiply(e);
191 assertEquals("b.monic() = b(1/ldcf(b))",c,d);
192
193 d = e.multiply(b);
194 assertEquals("b.monic() = (1/ldcf(b) (0))*b",c,d);
195 }
196
197
198 /**
199 * Test distributive law.
200 *
201 */
202 public void testDistributive() {
203 a = fac.random(kl,ll,el,q);
204 b = fac.random(kl,ll,el,q);
205 c = fac.random(kl,ll,el,q);
206
207 d = a.multiply( b.sum(c) );
208 e = a.multiply( b ).sum( a.multiply(c) );
209
210 assertEquals("a(b+c) = ab+ac",d,e);
211 }
212
213
214 /**
215 * Test object quotient and remainder.
216 *
217 */
218
219 public void testQuotRem() {
220
221 fac = new GenPolynomialRing<BigRational>(new BigRational(1),1);
222
223 a = fac.random(ll).monic();
224 assertTrue("not isZERO( a )", !a.isZERO() );
225
226 b = fac.random(ll).monic();
227 assertTrue("not isZERO( b )", !b.isZERO() );
228
229 GenPolynomial<BigRational> h = a;
230 GenPolynomial<BigRational> g = fac.random(ll).monic();
231 assertTrue("not isZERO( g )", !g.isZERO() );
232 a = a.multiply(g);
233 b = b.multiply(g);
234 //System.out.println("a = " + a);
235 //System.out.println("b = " + b);
236 //System.out.println("g = " + g);
237
238 GenPolynomial<BigRational>[] qr;
239 qr = b.divideAndRemainder(a);
240 c = qr[0];
241 d = qr[1];
242 //System.out.println("q = " + c);
243 //System.out.println("r = " + d);
244 e = c.multiply(a).sum(d);
245 assertEquals("b = q a + r", b, e );
246
247 qr = a.divideAndRemainder(b);
248 c = qr[0];
249 d = qr[1];
250 //System.out.println("q = " + c);
251 //System.out.println("r = " + d);
252 e = c.multiply(b).sum(d);
253 assertEquals("a = q b + r", a, e );
254
255
256 // gcd tests -------------------------------
257 c = a.gcd(b);
258 //System.out.println("gcd = " + c);
259 assertTrue("a mod gcd(a,b) = 0", a.remainder(c).isZERO() );
260 assertTrue("b mod gcd(a,b) = 0", b.remainder(c).isZERO() );
261 assertEquals("g = gcd(a,b)", c, g );
262
263
264 GenPolynomial<BigRational>[] gst;
265 gst = a.egcd(b);
266 //System.out.println("egcd = " + gst[0]);
267 //System.out.println(", s = " + gst[1] + ", t = " + gst[2]);
268 c = gst[0];
269 d = gst[1];
270 e = gst[2];
271 assertEquals("g = gcd(a,b)", c, g );
272
273 GenPolynomial<BigRational> x;
274 x = a.multiply(d).sum( b.multiply(e) ).monic();
275 //System.out.println("x = " + x);
276 assertEquals("gcd(a,b) = a s + b t", c, x );
277
278
279 gst = a.hegcd(b);
280 //System.out.println("hegcd = " + gst[0]);
281 //System.out.println("s = " + gst[1]);
282 c = gst[0];
283 d = gst[1];
284 assertEquals("g = gcd(a,b)", c, g );
285
286 x = a.multiply(d).remainder(b).monic();
287 //System.out.println("x = " + x);
288 assertEquals("gcd(a,b) = a s mod b", c, x );
289
290 //System.out.println("g = " + g);
291 //System.out.println("h = " + h);
292 c = h.modInverse(g);
293 //System.out.println("c = " + c);
294 x = c.multiply(h).remainder( g ).monic();
295 //System.out.println("x = " + x);
296 assertTrue("h invertible mod g", x.isONE() );
297
298 }
299
300 }