Source code

001/*
002 * $Id: Examples.java 5861 2018-07-20 10:09:03Z kredel $
003 */
004
005package edu.jas.ufd;
006
007
008import java.util.SortedMap;
009import java.util.ArrayList;
010import java.util.List;
011
012import edu.jas.arith.BigInteger;
013import edu.jas.arith.BigRational;
014import edu.jas.kern.ComputerThreads;
015import edu.jas.poly.AlgebraicNumber;
016import edu.jas.poly.AlgebraicNumberRing;
017import edu.jas.poly.GenPolynomial;
018import edu.jas.poly.GenPolynomialRing;
019import edu.jas.poly.PolyUtil;
020import edu.jas.poly.TermOrder;
021import edu.jas.vector.GenMatrix;
022import edu.jas.vector.GenMatrixRing;
023
024
025/**
026 * Examples for ufd and elementaty integration usage.
027 * @author Heinz Kredel
028 */
029
030public class Examples {
031
032
033    /**
034     * main.
035     */
036    public static void main(String[] args) {
037        //// no go: example6();
038        //example9();
039        example1();
040        example2();
041        example10();
042        ComputerThreads.terminate();
043    }
044
045
046    /**
047     * example1 with GenMatrix. 
048     */
049    public static void example1() {
050        System.out.println("\n\n example 1");
051
052        BigInteger cfac;
053        GenPolynomialRing<BigInteger> fac;
054        QuotientRing<BigInteger> efac;
055        GenPolynomialRing<Quotient<BigInteger>> qfac;
056        GenMatrixRing<GenPolynomial<Quotient<BigInteger>>> mfac;
057
058        cfac = new BigInteger();
059        System.out.println("cfac = " + cfac);
060
061        String[] vc = new String[] {"a", "b"};
062        fac = new GenPolynomialRing<BigInteger>(cfac,vc);
063        System.out.println(" fac = " + fac.toScript());
064
065        efac = new QuotientRing<BigInteger>( fac );
066        System.out.println("efac = " + efac.toScript());
067
068        String[] v = new String[] {"x", "y", "z" };
069        qfac = new GenPolynomialRing<Quotient<BigInteger>>( efac, 3, v );
070        System.out.println("qfac = " + qfac.toScript());
071
072        mfac = new GenMatrixRing<GenPolynomial<Quotient<BigInteger>>>( qfac, 3, 3 );
073        System.out.println("mfac = " + mfac.toScript());
074
075        GenPolynomial<Quotient<BigInteger>> p;
076        p = qfac.random(3,4,2,0.3f);
077        System.out.println("\np = " + p);
078
079        GenMatrix<GenPolynomial<Quotient<BigInteger>>> m;
080        m = mfac.random(3,0.4f);
081        System.out.println("\nm = " + m.toScript());
082    }
083
084
085    /**
086     * example2 with GenPolynomial. 
087     */
088    public static void example2() {
089        System.out.println("\n\n example 2");
090
091        BigInteger fac = new BigInteger();
092        String[] var = new String[]{ "a", "b", "c", "d"};
093        int numvars = var.length;
094        //not needed: TermOrder tord = new TermOrder(TermOrder.INVLEX);
095        GenPolynomialRing<BigInteger> ring = new GenPolynomialRing<BigInteger>(fac,var);
096        List<GenPolynomial<BigInteger>> vars=new ArrayList<GenPolynomial<BigInteger>>();
097        
098        // Build up the polynomial from vars.
099        for(int i=0; i<numvars; i++) vars.add(ring.univariate(i));
100        System.out.println("vars = " + vars);
101        
102        // Silly demo one first. 
103        //  ab+ac+db+dc   ->  (a+d)(b+c)
104        GenPolynomial<BigInteger> tmp=( vars.get(0).multiply(vars.get(1)) ).sum( vars.get(0).multiply(vars.get(2)) )
105        .sum( vars.get(3).multiply(vars.get(1)) ).sum( vars.get(3).multiply(vars.get(2)) );
106        
107        //alternative: tmp = ring.parse("a b + a c + d b + d c");
108        System.out.println("tmp = " +tmp); 
109        
110        Factorization<BigInteger> engine = FactorFactory.getImplementation(fac);
111        SortedMap<GenPolynomial<BigInteger>,Long> factors = engine.factors(tmp);
112        
113        System.out.println("factors = " + factors);
114    }
115
116
117    /**
118     * example6. Partial fraction decomposition.
119     */
120    public static void example6() {
121        System.out.println("\n\nexample 6");
122        // http://www.apmaths.uwo.ca/~rcorless/AM563/NOTES/Nov_16_95/node13.html
123
124        TermOrder to = new TermOrder(TermOrder.INVLEX);
125        BigRational cfac = new BigRational(1);
126        //String[] alpha = new String[] { "alpha" };
127        String[] vars = new String[] { "x" };
128        GenPolynomialRing<BigRational> pfac = new GenPolynomialRing<BigRational>(cfac, 1, to, vars);
129
130        // ( 7 x^6 + 1 ) /  ( x^7 + x + 1 )
131        GenPolynomial<BigRational> D = pfac.parse("x^7 + x + 1");
132        GenPolynomial<BigRational> N = PolyUtil.<BigRational> baseDeriviative(D);
133
134        FactorRational engine = new FactorRational();
135
136        PartialFraction<BigRational> F = engine.baseAlgebraicPartialFraction(N, D);
137        System.out.println("\nintegral " + F);
138    }
139
140
141    /**
142     * example9. Rothstein-Trager and absolute factorization algorithm.
143     */
144    public static void example9() {
145        System.out.println("\n\nexample 9");
146
147        TermOrder to = new TermOrder(TermOrder.INVLEX);
148        BigRational cfac = new BigRational(1);
149        //String[] alpha = new String[] { "alpha" };
150        String[] vars = new String[] { "x" };
151        GenPolynomialRing<BigRational> pfac = new GenPolynomialRing<BigRational>(cfac, 1, to, vars);
152
153        // 1 / ( x^5 + x - 7 ) 
154        GenPolynomial<BigRational> D = pfac.parse("( x^5 + x - 7 )");
155        GenPolynomial<BigRational> N = pfac.getONE();
156
157        FactorRational engine = new FactorRational();
158
159        PartialFraction<BigRational> F = engine.baseAlgebraicPartialFraction(N, D);
160        System.out.println("\nintegral " + F);
161
162        //PartialFraction<BigRational> Fa = engine.baseAlgebraicPartialFractionIrreducibleAbsolute(N,D);
163        //System.out.println("\nintegral_a " + Fa);
164
165    }
166
167
168    /**
169     * example10. factorization in Q(sqrt(2))(x)(sqrt(x))[y].
170     */
171    public static void example10() {
172        System.out.println("\n\nexample 10");
173
174        TermOrder to = new TermOrder(TermOrder.INVLEX);
175        BigRational cfac = new BigRational(1);
176
177        String[] var_w2 = new String[] { "w2" };
178        GenPolynomialRing<BigRational> pfac = new GenPolynomialRing<BigRational>(cfac, 1, to, var_w2);
179        System.out.println("pfac   = " + pfac.toScript());
180
181        GenPolynomial<BigRational> w2 = pfac.parse(" w2^2 - 2 ");
182        System.out.println("w2     = " + w2);
183
184        AlgebraicNumberRing<BigRational> a2fac = new AlgebraicNumberRing<BigRational>(w2, true);
185        System.out.println("a2fac  = " + a2fac.toScript());
186
187        String[] var_x = new String[] { "x" };
188        GenPolynomialRing<AlgebraicNumber<BigRational>> apfac = new GenPolynomialRing<AlgebraicNumber<BigRational>>(
189                                                                                                                    a2fac, 1, to, var_x);
190        System.out.println("apfac  = " + apfac.toScript());
191
192        QuotientRing<AlgebraicNumber<BigRational>> qfac = new QuotientRing<AlgebraicNumber<BigRational>>(
193                                                                                                         apfac);
194        System.out.println("qfac   = " + qfac.toScript());
195
196        String[] var_wx = new String[] { "wx" };
197        GenPolynomialRing<Quotient<AlgebraicNumber<BigRational>>> pqfac = new GenPolynomialRing<Quotient<AlgebraicNumber<BigRational>>>(
198                                                                                                                                        qfac, 1, to, var_wx);
199        System.out.println("pqfac  = " + pqfac.toScript());
200
201        GenPolynomial<Quotient<AlgebraicNumber<BigRational>>> wx = pqfac.parse(" wx^2 - { x } ");
202        System.out.println("wx     = " + wx);
203
204        AlgebraicNumberRing<Quotient<AlgebraicNumber<BigRational>>> axfac = new AlgebraicNumberRing<Quotient<AlgebraicNumber<BigRational>>>(
205                                                                                                                                            wx, true);
206        System.out.println("axfac  = " + axfac.toScript());
207
208        String[] var_y = new String[] { "y" };
209        GenPolynomialRing<AlgebraicNumber<Quotient<AlgebraicNumber<BigRational>>>> apqfac = new GenPolynomialRing<AlgebraicNumber<Quotient<AlgebraicNumber<BigRational>>>>(
210                                                                                                                                                                           axfac, 1, to, var_y);
211        System.out.println("apqfac = " + apqfac.toScript());
212
213        //  ( y^2 - x ) * ( y^2 - 2 ), need {} for recursive coefficients
214        GenPolynomial<AlgebraicNumber<Quotient<AlgebraicNumber<BigRational>>>> f;
215        f = apqfac.parse(" ( y^2 - { { x } } ) * ( y^2 - 2 )^2 ");
216        System.out.println("f      = " + f);
217
218        FactorAbstract<AlgebraicNumber<Quotient<AlgebraicNumber<BigRational>>>> engine = FactorFactory
219            .getImplementation(axfac);
220        System.out.println("engine = " + engine);
221
222        SortedMap<GenPolynomial<AlgebraicNumber<Quotient<AlgebraicNumber<BigRational>>>>, Long> F = engine
223            .factors(f);
224        System.out.println("factors(f) = " + F);
225    }
226
227}