edu.jas.ps.ExamplesMulti Maven / Gradle / Ivy
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/*
* $Id: ExamplesMulti.java 3345 2010-10-15 19:50:36Z kredel $
*/
package edu.jas.ps;
import java.util.ArrayList;
import java.util.List;
import org.apache.log4j.BasicConfigurator;
import edu.jas.arith.BigRational;
import edu.jas.poly.GenPolynomial;
import edu.jas.poly.GenPolynomialRing;
/**
* Examples for multivariate power series implementations.
* @author Heinz Kredel
*/
public class ExamplesMulti {
public static void main(String[] args) {
BasicConfigurator.configure();
if ( args.length > 0 ) {
example1();
example2();
example3();
example4();
example5();
example6();
example7();
example8();
example9();
example10();
}
example11();
}
public static void example1() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x^2 + x y");
GenPolynomial b = pfac.parse("y^2 + x y");
GenPolynomial c = pfac.parse("x^3 + x^2");
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
ReductionSeq red = new ReductionSeq();
MultiVarPowerSeries dp = red.normalform(L, cp);
System.out.println("dp = " + dp);
}
public static void example2() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x - x y");
GenPolynomial b = pfac.parse("y^2 + x^3");
GenPolynomial c = pfac.parse("x^2 + y^2");
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
ReductionSeq red = new ReductionSeq();
MultiVarPowerSeries dp = red.normalform(L, cp);
System.out.println("dp = " + dp);
}
public static void example3() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y", "z" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x");
GenPolynomial b = pfac.parse("y");
GenPolynomial c = pfac.parse("x^2 + y^2 + z^3 + x^4 + y^5");
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
ReductionSeq red = new ReductionSeq();
MultiVarPowerSeries dp = red.normalform(L, cp);
System.out.println("dp = " + dp);
}
public static void example4() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x + x^3 + x^5");
GenPolynomial c = pfac.parse("x + x^2");
System.out.println("a = " + a);
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
//fac.setTruncate(11);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
ReductionSeq red = new ReductionSeq();
MultiVarPowerSeries dp = red.normalform(L, cp);
System.out.println("dp = " + dp);
}
public static void example5() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial c = pfac.parse("x^2 + y^2 - 1");
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
//fac.setTruncate(19);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.getSIN(0);
MultiVarPowerSeries bp = fac.getCOS(1);
MultiVarPowerSeries ep = fac.getCOS(0);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("ep = " + ep);
System.out.println("cp = " + cp);
System.out.println("ap^2 + ep^2 = " + ap.multiply(ap).sum(ep.multiply(ep)));
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
ReductionSeq red = new ReductionSeq();
MultiVarPowerSeries dp = red.normalform(L, cp);
System.out.println("dp = " + dp);
}
public static void example6() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y", "z" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x^5 - x y^6 + z^7");
GenPolynomial b = pfac.parse("x y + y^3 + z^3");
GenPolynomial c = pfac.parse("x^2 + y^2 - z^2");
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
//fac.setTruncate(11);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
L.add(cp);
StandardBaseSeq tm = new StandardBaseSeq();
List> S = tm.STD(L);
for (MultiVarPowerSeries ps : S) {
System.out.println("ps = " + ps);
}
System.out.println("\nS = " + S);
boolean s = tm.isSTD(S);
System.out.println("\nisSTD = " + s);
ReductionSeq red = new ReductionSeq();
s = red.contains(S, L);
System.out.println("S contains L = " + s);
}
public static void example7() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x^10 + x^9 y^2");
GenPolynomial b = pfac.parse("y^8 - x^2 y^7");
System.out.println("a = " + a);
System.out.println("b = " + b);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
fac.setTruncate(12);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
StandardBaseSeq tm = new StandardBaseSeq();
List> S = tm.STD(L);
for (MultiVarPowerSeries ps : S) {
System.out.println("ps = " + ps);
}
System.out.println("\nS = " + S);
boolean s = tm.isSTD(S);
System.out.println("\nisSTD = " + s);
ReductionSeq red = new ReductionSeq();
s = red.contains(S, L);
System.out.println("\nS contains L = " + s);
}
public static void example8() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial c = pfac.parse("x^2 + y^2");
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
//fac.setTruncate(19);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.getSIN(0);
MultiVarPowerSeries bp = fac.getTAN(0);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
//L.add(cp);
System.out.println("\nL = " + L);
StandardBaseSeq tm = new StandardBaseSeq();
List> S = tm.STD(L);
for (MultiVarPowerSeries ps : S) {
System.out.println("ps = " + ps);
}
System.out.println("\nS = " + S);
boolean s = tm.isSTD(S);
System.out.println("\nisSTD = " + s);
ReductionSeq red = new ReductionSeq();
s = red.contains(S, L);
System.out.println("S contains L = " + s);
}
public static void example9() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y", "z" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x z - y z - y^2 z");
GenPolynomial b = pfac.parse("x z - y z + y^2 z");
GenPolynomial c = pfac.parse("z + y^2 z");
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
fac.setTruncate(11);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
L.add(cp);
StandardBaseSeq tm = new StandardBaseSeq();
List> S = tm.STD(L);
for (MultiVarPowerSeries ps : S) {
System.out.println("ps = " + ps);
}
System.out.println("\nS = " + S);
boolean s = tm.isSTD(S);
System.out.println("\nisSTD = " + s);
ReductionSeq red = new ReductionSeq();
s = red.contains(S, L);
System.out.println("S contains L = " + s);
}
public static void example10() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y", "z" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x^2 z^2 - y^6");
GenPolynomial b = pfac.parse("x y z^2 + y^4 z - x^5 z - x^4 y^3");
GenPolynomial c = pfac.parse("x z - y^3 + x^2 z - x y^3");
GenPolynomial d = pfac.parse("y z + x y z - x^4 - x^5");
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
System.out.println("d = " + d);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
fac.setTruncate(9);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
MultiVarPowerSeries dp = fac.fromPolynomial(d);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
System.out.println("dp = " + dp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
L.add(cp);
L.add(dp);
StandardBaseSeq tm = new StandardBaseSeq();
List> S = tm.STD(L);
for (MultiVarPowerSeries ps : S) {
System.out.println("ps = " + ps);
}
System.out.println("\nS = " + S);
boolean s = tm.isSTD(S);
System.out.println("\nisSTD = " + s);
ReductionSeq red = new ReductionSeq();
s = red.contains(S, L);
System.out.println("S contains L = " + s);
List> R = red.totalNormalform(S);
System.out.println("R = " + R);
s = red.contains(R, L);
System.out.println("R contains L = " + s);
s = red.contains(R, S);
System.out.println("R contains S = " + s);
}
public static void example11() {
BigRational br = new BigRational(1);
String[] vars = new String[] { "x", "y", "z" };
GenPolynomialRing pfac = new GenPolynomialRing(br, vars);
System.out.println("pfac = " + pfac.toScript());
GenPolynomial a = pfac.parse("x^5 - x y^6 - z^7");
GenPolynomial b = pfac.parse("x y + y^3 + z^3");
GenPolynomial c = pfac.parse("x^2 + y^2 - z^2");
System.out.println("a = " + a);
System.out.println("b = " + b);
System.out.println("c = " + c);
MultiVarPowerSeriesRing fac = new MultiVarPowerSeriesRing(pfac);
//fac.setTruncate(9);
System.out.println("fac = " + fac.toScript());
MultiVarPowerSeries ap = fac.fromPolynomial(a);
MultiVarPowerSeries bp = fac.fromPolynomial(b);
MultiVarPowerSeries cp = fac.fromPolynomial(c);
System.out.println("ap = " + ap);
System.out.println("bp = " + bp);
System.out.println("cp = " + cp);
List> L = new ArrayList>();
L.add(ap);
L.add(bp);
L.add(cp);
StandardBaseSeq tm = new StandardBaseSeq();
List> S = tm.STD(L);
for (MultiVarPowerSeries ps : S) {
System.out.println("ps = " + ps);
}
System.out.println("\nS = " + S);
boolean s = tm.isSTD(S);
System.out.println("\nisSTD = " + s);
ReductionSeq red = new ReductionSeq();
s = red.contains(S, L);
System.out.println("S contains L = " + s);
List> R = red.totalNormalform(S);
for (MultiVarPowerSeries ps : R) {
System.out.println("ps = " + ps);
}
System.out.println("\nR = " + R);
s = tm.isSTD(R);
System.out.println("\nisSTD = " + s);
s = red.contains(R, L);
System.out.println("R contains L = " + s);
s = red.contains(R, S);
System.out.println("R contains S = " + s);
s = red.contains(S,R);
System.out.println("S contains R = " + s);
s = red.contains(S,L);
System.out.println("S contains L = " + s);
List> Rs = tm.STD(R);
for (MultiVarPowerSeries ps : Rs) {
System.out.println("ps = " + ps);
}
System.out.println("\nRs = " + Rs);
s = tm.isSTD(Rs);
System.out.println("\nisSTD = " + s);
s = red.contains(Rs, R);
System.out.println("Rs contains R = " + s);
s = red.contains(Rs, S);
System.out.println("Rs contains S = " + s);
}
}
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