package org.jlinalg.demo;

import org.jlinalg.FieldElement;
import org.jlinalg.FieldP;
import org.jlinalg.Matrix;
import org.jlinalg.Vector;

/**
 * This demonstration of the class FieldP shows that in vector spaces over
 * finite fields there can be linear dependent vectors which are all orthogonal
 * to each other.
 * 
 * @author Andreas Lochbihler
 */
public class FieldPDemo {

	public static void main(String[] args) {
		int prime = 7;
		FieldElement p1, p2, p3, p4, p5, p6;
		p1 = new FieldP(1, prime);
		p2 = new FieldP(2, prime);
		p3 = new FieldP(3, prime);
		p4 = new FieldP(4, prime);
		p5 = new FieldP(5, prime);
		p6 = new FieldP(6, prime);

		Vector u = new Vector(new FieldElement[] { p1, p1, p5 });
		Vector v = new Vector(new FieldElement[] { p1, p3, p2 });
		Vector w = new Vector(new FieldElement[] { p6, p4, p5, });
		Matrix matrix = new Matrix(new Vector[] { u, v, w });

		System.out.println(matrix);

		/*
		 * Now we will see that the vectors are linear dependent, because the
		 * rank of the their matrix is smaller than 3.
		 */
		System.out.println("Rank: " + matrix.rank());

		/*
		 * Let us check now, if they are all orthogonal to each other. Two
		 * vectors a, b are orthogonal on each other if <a, b> = 0, where < , >
		 * is the scalar product.
		 */

		// <u, v> =
		System.out.println(" < " + u + ", " + v + " > = " + u.multiply(v));
		// <u, w> =
		System.out.println(" < " + u + ", " + w + " > = " + u.multiply(w));
		// <v, w> =
		System.out.println(" < " + v + ", " + w + " > = " + v.multiply(w));
	}
}