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edu.jas.integrate.Examples Maven / Gradle / Ivy

/*
 * $Id: Examples.java 3356 2010-10-23 16:41:01Z kredel $
 */

package edu.jas.integrate;


import java.util.List;

import edu.jas.arith.BigRational;
import edu.jas.kern.ComputerThreads;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenPolynomialRing;
import edu.jas.poly.TermOrder;
import edu.jas.ufd.Quotient;
import edu.jas.ufd.QuotientRing;


/**
 * Examples related to elementary integration.
 * 
 * @author Axel Kramer
 * @author Heinz Kredel
 */

public class Examples {


    /**
     * Main program.
     * 
     * @param args
     */
    public static void main(String[] args) {
        example1();
        example2();
        example3();
    }


    /**
     * Example rationals.
     */
    public static void example1() {

        BigRational br = new BigRational(0);
        String[] vars = new String[] { "x" };
        GenPolynomialRing fac;
        fac = new GenPolynomialRing(br, vars.length, new TermOrder(TermOrder.INVLEX), vars);

        ElementaryIntegration eIntegrator = new ElementaryIntegration(br);

        GenPolynomial a = fac.parse("x^7 - 24 x^4 - 4 x^2 + 8 x - 8");
        System.out.println("A: " + a.toString());
        GenPolynomial d = fac.parse("x^8 + 6 x^6 + 12 x^4 + 8 x^2");
        System.out.println("D: " + d.toString());
        GenPolynomial gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        List>[] ret = eIntegrator.integrateHermite(a, d);
        System.out.println("Result: " + ret[0] + " , " + ret[1]);

        System.out.println("-----");

        a = fac.parse("10 x^2 - 63 x + 29");
        System.out.println("A: " + a.toString());
        d = fac.parse("x^3 - 11 x^2 + 40 x -48");
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrateHermite(a, d);
        System.out.println("Result: " + ret[0] + " , " + ret[1]);

        System.out.println("-----");

        a = fac.parse("x+3");
        System.out.println("A: " + a.toString());
        d = fac.parse("x^2 - 3 x - 40");
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrateHermite(a, d);
        System.out.println("Result: " + ret[0] + " , " + ret[1]);

        System.out.println("-----");

        a = fac.parse("10 x^2+12 x + 20");
        System.out.println("A: " + a.toString());
        d = fac.parse("x^3 - 8");
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrateHermite(a, d);
        System.out.println("Result: " + ret[0] + " , " + ret[1]);

        System.out.println("------------------------------------------------------\n");
        ComputerThreads.terminate();
    }


    /**
     * Example rational plus logarithm.
     */
    public static void example2() {

        BigRational br = new BigRational(0);
        String[] vars = new String[] { "x" };
        GenPolynomialRing fac;
        fac = new GenPolynomialRing(br, vars.length, new TermOrder(TermOrder.INVLEX), vars);

        ElementaryIntegration eIntegrator = new ElementaryIntegration(br);

        GenPolynomial a = fac.parse("x^7 - 24 x^4 - 4 x^2 + 8 x - 8");
        System.out.println("A: " + a.toString());
        GenPolynomial d = fac.parse("x^8 + 6 x^6 + 12 x^4 + 8 x^2");
        System.out.println("D: " + d.toString());
        GenPolynomial gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        Integral ret = eIntegrator.integrate(a, d);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("10 x^2 - 63 x + 29");
        System.out.println("A: " + a.toString());
        d = fac.parse("x^3 - 11 x^2 + 40 x -48");
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrate(a, d);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("x+3");
        System.out.println("A: " + a.toString());
        d = fac.parse("x^2 - 3 x - 40");
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrate(a, d);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("10 x^2+12 x + 20");
        System.out.println("A: " + a.toString());
        d = fac.parse("x^3 - 8");
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrate(a, d);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("1");
        System.out.println("A: " + a.toString());
        d = fac.parse("(x**5 + x - 7)");
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrate(a, d);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("1");
        d = fac.parse("(x**5 + x - 7)");
        a = a.sum(d);
        System.out.println("A: " + a.toString());
        System.out.println("D: " + d.toString());
        gcd = a.gcd(d);
        System.out.println("GCD: " + gcd.toString());
        ret = eIntegrator.integrate(a, d);
        System.out.println("Result: " + ret);

        System.out.println("-----");
        ComputerThreads.terminate();
    }


    /**
     * Example quotients with rational plus logarithm.
     */
    public static void example3() {

        BigRational br = new BigRational(0);
        String[] vars = new String[] { "x" };
        GenPolynomialRing fac;
        fac = new GenPolynomialRing(br, vars.length, new TermOrder(TermOrder.INVLEX), vars);

        QuotientRing qfac = new QuotientRing(fac);

        ElementaryIntegration eIntegrator = new ElementaryIntegration(br);

        GenPolynomial a = fac.parse("x^7 - 24 x^4 - 4 x^2 + 8 x - 8");
        GenPolynomial d = fac.parse("x^8 + 6 x^6 + 12 x^4 + 8 x^2");
        Quotient q = new Quotient(qfac, a, d);
        System.out.println("q =  " + q);
        QuotIntegral ret = eIntegrator.integrate(q);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("10 x^2 - 63 x + 29");
        d = fac.parse("x^3 - 11 x^2 + 40 x -48");
        q = new Quotient(qfac, a, d);
        System.out.println("q =  " + q);
        ret = eIntegrator.integrate(q);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("x+3");
        d = fac.parse("x^2 - 3 x - 40");
        q = new Quotient(qfac, a, d);
        System.out.println("q =  " + q);
        ret = eIntegrator.integrate(q);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("10 x^2+12 x + 20");
        d = fac.parse("x^3 - 8");
        q = new Quotient(qfac, a, d);
        System.out.println("q =  " + q);
        ret = eIntegrator.integrate(q);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("1");
        d = fac.parse("(x**5 + x - 7)");
        q = new Quotient(qfac, a, d);
        System.out.println("q =  " + q);
        ret = eIntegrator.integrate(q);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        a = fac.parse("1");
        d = fac.parse("(x**5 + x - 7)");
        a = a.sum(d);
        q = new Quotient(qfac, a, d);
        System.out.println("q =  " + q);
        ret = eIntegrator.integrate(q);
        System.out.println("Result: " + ret);

        System.out.println("-----");

        Quotient qi = qfac.random(7);
        //qi = qi.sum( qfac.random(5) );
        q = eIntegrator.deriviative(qi);
        System.out.println("qi =  " + qi);
        System.out.println("q  =  " + q);
        ret = eIntegrator.integrate(q);
        System.out.println("Result: " + ret);
        boolean t = eIntegrator.isIntegral(ret);
        System.out.println("isIntegral = " + t);

        System.out.println("-----");
        ComputerThreads.terminate();
    }


}