Класс для работы с геометрическими векторами на плоскости

24/08/2017 by Валентин Лавриненко

Задача

9. Напишите класс для работы с геометрическими векторами на плоскости. Реализуйте максимально возможное количество методов.

Тесты

$latex x_1$	$latex y_1$	$latex x_2$	$latex y_2$	$latex x_3$	$latex y_3$	$latex x_4$	$latex y_4$	Ск. пр.	Угол
4	4	61	12	44	65	21	51	-1423	2.7342438697918836

Код

import java.util.*;
import java.lang.Math.*;
import java.io.*;
 
class geomVector
{
	public double x1,x2,y1,y2,xV,yV,xM,yM,vL;
	public void setVector(double a1,double b1, double a2, double b2)
	{
		x1 = a1;
		x2 = a2;
		y1 = b1;
		y2 = b2;
	}
	public void getVectorCoords()
	{
		xV = x2 - x1;
		yV = y2 - y1;
	}
	public void getMiddleCoords()
	{
		getVectorCoords();
		xM = xV/2;
		yM = yV/2;
	}
	public void multiplyVector(double a)
	{
		x1*=a;
		x2*=a;
		y1*=a;
		y2*=a;
		getVectorCoords();
		getMiddleCoords();
	}
	public double getLength()
	{
		return vL = Math.sqrt(xV*xV+yV*yV);
	}
	public void vectorSum(geomVector a,geomVector b)
	{
		a.setVector(a.x1,a.y1,b.x2,b.y2);
	}
	public double scalMult(geomVector a,geomVector b)
	{
		return (a.xV*b.xV+a.yV*b.yV);
	}
	public double getAngle(geomVector a, geomVector b)
	{
		return Math.acos(scalMult(a,b)/(a.getLength()*b.getLength()));
	}
}
 
public class Main {
	public static void main(String[] args)
	{
		double x1,x2,x3,x4,y1,y2,y3,y4;
		Scanner in = new Scanner(System.in);
		x1 = in.nextDouble();
		x2 = in.nextDouble();
		x3 = in.nextDouble();
		x4 = in.nextDouble();
		y1 = in.nextDouble();
		y2 = in.nextDouble();
		y3 = in.nextDouble();
		y4 = in.nextDouble();
		geomVector a = new geomVector();
		geomVector b = new geomVector();
		a.setVector(x1,y1,x2,y2);
		b.setVector(x3,y3,x4,y4);
		a.getVectorCoords();
		b.getVectorCoords();
		System.out.println(b.scalMult(b,a));
		System.out.println(a.getAngle(a,b));
	}
}

import java.util.*;

import java.lang.Math.*;

import java.io.*;

class geomVector

{

public double x1,x2,y1,y2,xV,yV,xM,yM,vL;

public void setVector(double a1,double b1, double a2, double b2)

{

x1 = a1;

x2 = a2;

y1 = b1;

y2 = b2;

}

public void getVectorCoords()

{

xV = x2 - x1;

yV = y2 - y1;

}

public void getMiddleCoords()

{

getVectorCoords();

xM = xV/2;

yM = yV/2;

}

public void multiplyVector(double a)

{

x1*=a;

x2*=a;

y1*=a;

y2*=a;

getVectorCoords();

getMiddleCoords();

}

public double getLength()

{

return vL = Math.sqrt(xV*xV+yV*yV);

}

public void vectorSum(geomVector a,geomVector b)

{

a.setVector(a.x1,a.y1,b.x2,b.y2);

}

public double scalMult(geomVector a,geomVector b)

{

return (a.xV*b.xV+a.yV*b.yV);

}

public double getAngle(geomVector a, geomVector b)

{

return Math.acos(scalMult(a,b)/(a.getLength()*b.getLength()));

}

public class Main {

public static void main(String[] args)

{

double x1,x2,x3,x4,y1,y2,y3,y4;

Scanner in = new Scanner(System.in);

x1 = in.nextDouble();

x2 = in.nextDouble();

x3 = in.nextDouble();

x4 = in.nextDouble();

y1 = in.nextDouble();

y2 = in.nextDouble();

y3 = in.nextDouble();

y4 = in.nextDouble();

geomVector a = new geomVector();

geomVector b = new geomVector();

a.setVector(x1,y1,x2,y2);

b.setVector(x3,y3,x4,y4);

a.getVectorCoords();

b.getVectorCoords();

System.out.println(b.scalMult(b,a));

System.out.println(a.getAngle(a,b));

}

Описание решения

Переменные $latex x_1,y_1,x_2,y_2$ являются координатами начала и конца вектора, $latex x_V$ и $latex y_V$ — координаты вектора, $latex x_M$ и $latex y_M$ — координаты середины вектора, $latex v_L$ — длина вектора. Реализованы методы для нахождения середины вектора, длины вектора, умножения вектора на число, сложения векторов, скалярного произведения векторов и нахождения угла между векторами.

Код можно просмотреть на сайте ideone

Класс рациональных дробей

02/09/2016 by Иоанна Васильева

Задача

Напишите класс для работы с не изменяемыми (immutable) рациональными дробями используя статические методы.

Код

import java.lang.*;

class Rational {
    private int n, d;

    /**
     * @param n is a numerator of Fraction
     * @param d is a divider of Fraction
     */
    public Rational(int n, int d) throws ArithmeticException {
        if (d == 0) throw new ArithmeticException("wrong ");
        int divisor = gcd(n, d);
        this.n = n / divisor;
        this.d = d / divisor;
    }

    /**
     * @param n is a numerator of Fraction
     * @param d is a divider of Fraction
     * @return the greatest common divisor of numerator and divider
     */
    private static int gcd(int n, int d) {
        return (d == 0 ? n : gcd(d, n % d));
    }

    /**
     * Check fractions for equality
     *
     * @param x the first fraction
     * @param y the seconds fraction
     * @return true if they are equals, otherwise returns false
     */
    public static boolean equals(Rational x, Rational y) {
        if (x.n != y.n || x.d != y.d) return false;
        else return true;
    }

    /**
     * Add two Fractions x and y
     *
     * @param x the first Fraction
     * @param y the second Fraction
     * @return the result of there addition
     */
    public static Rational add(Rational x, Rational y) {
        return new Rational(x.n * y.d + y.n * x.d, x.d * y.d);
    }

    /**
     * Subtract two Franctions x and y
     *
     * @param x the first Fraction
     * @param y the second Fraction
     * @return the result of there subtraction
     */
    public static Rational sub(Rational x, Rational y) {
        return new Rational(x.n * y.d - y.n * x.d, x.d * y.d);
    }

    /**
     * Multiply two Fractions x and y
     *
     * @param x the first Fraction
     * @param y the seconds Fraction
     * @return the result of there multiplication
     */
    public static Rational mul(Rational x, Rational y) {
        return new Rational(x.n * y.n, x.d * y.d);
    }

    /**
     * Divide two Fractions x and y
     *
     * @param x the first Fraction
     * @param y the second Fraction
     * @return the result of there division
     */
    public static Rational div(Rational x, Rational y) {
        return new Rational(x.n * y.d, x.d * y.n);
    }

    /**
     * Convert fraction to string value
     *
     * @return fraction
     */
    public String toString() {
        return n + "/" + d;
    }

    /**
     * Compare two fractions and write to console a result
     *
     * @param x x the first Fraction
     * @param y the second Fraction
     */
    public static void cmp(Rational x, Rational y) {
        if (!equals(x, y)) {
            if ((x.n * y.d) > (y.n * x.d)) System.out.println(x.toString() + " > " + y.toString());
            else System.out.println(y.toString() + " > " + x.toString());
        } else System.out.println(x.toString() + " = " + y.toString());
    }

    public static void main(String[] args) {
        try {
            Rational a = new Rational(4, 5);
            Rational b = new Rational(1, 2);
            Rational c = new Rational(2, 5);
            System.out.println("Equality - " + equals(a, b));
            System.out.println("Equality - " + equals(mul(a, b), c));
            System.out.println(c.toString() + "+" + b.toString() + "=" + add(c, b));
            System.out.println(a.toString() + "-" + b.toString() + "=" + sub(a, b));
            System.out.println(b.toString() + "-" + a.toString() + "=" + sub(b, a));
            System.out.println(a.toString() + "*" + b.toString() + "=" + mul(c, b));
            System.out.println(a.toString() + "%" + b.toString() + "=" + div(a, b));
            cmp(a, b);
            cmp(b, c);
            cmp(mul(a, b), c);
        } catch (ArithmeticException e) {
            System.out.println("dividing on 0");
        }
    }
}

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import java.lang.*;

class Rational {

private int n, d;

/**

* @param n is a numerator of Fraction

* @param d is a divider of Fraction

public Rational(int n, int d) throws ArithmeticException {

if (d == 0) throw new ArithmeticException("wrong ");

int divisor = gcd(n, d);

this.n = n / divisor;

this.d = d / divisor;

}

/**

* @param n is a numerator of Fraction

* @param d is a divider of Fraction

* @return the greatest common divisor of numerator and divider

private static int gcd(int n, int d) {

return (d == 0 ? n : gcd(d, n % d));

}

/**

* Check fractions for equality

* @param x the first fraction

* @param y the seconds fraction

* @return true if they are equals, otherwise returns false

public static boolean equals(Rational x, Rational y) {

if (x.n != y.n || x.d != y.d) return false;

else return true;

}

/**

* Add two Fractions x and y

* @param x the first Fraction

* @param y the second Fraction

* @return the result of there addition

public static Rational add(Rational x, Rational y) {

return new Rational(x.n * y.d + y.n * x.d, x.d * y.d);

}

/**

* Subtract two Franctions x and y

* @param x the first Fraction

* @param y the second Fraction

* @return the result of there subtraction

public static Rational sub(Rational x, Rational y) {

return new Rational(x.n * y.d - y.n * x.d, x.d * y.d);

}

/**

* Multiply two Fractions x and y

* @param x the first Fraction

* @param y the seconds Fraction

* @return the result of there multiplication

public static Rational mul(Rational x, Rational y) {

return new Rational(x.n * y.n, x.d * y.d);

}

/**

* Divide two Fractions x and y

* @param x the first Fraction

* @param y the second Fraction

* @return the result of there division

public static Rational div(Rational x, Rational y) {

return new Rational(x.n * y.d, x.d * y.n);

}

/**

* Convert fraction to string value

* @return fraction

public String toString() {

return n + "/" + d;

}

/**

* Compare two fractions and write to console a result

* @param x x the first Fraction

* @param y the second Fraction

public static void cmp(Rational x, Rational y) {

if (!equals(x, y)) {

if ((x.n * y.d) > (y.n * x.d)) System.out.println(x.toString() + " > " + y.toString());

else System.out.println(y.toString() + " > " + x.toString());

} else System.out.println(x.toString() + " = " + y.toString());

}

public static void main(String[] args) {

try {

Rational a = new Rational(4, 5);

Rational b = new Rational(1, 2);

Rational c = new Rational(2, 5);

System.out.println("Equality - " + equals(a, b));

System.out.println("Equality - " + equals(mul(a, b), c));

System.out.println(c.toString() + "+" + b.toString() + "=" + add(c, b));

System.out.println(a.toString() + "-" + b.toString() + "=" + sub(a, b));

System.out.println(b.toString() + "-" + a.toString() + "=" + sub(b, a));

System.out.println(a.toString() + "*" + b.toString() + "=" + mul(c, b));

System.out.println(a.toString() + "%" + b.toString() + "=" + div(a, b));

cmp(a, b);

cmp(b, c);

cmp(mul(a, b), c);

} catch (ArithmeticException e) {

System.out.println("dividing on 0");

}

Код на Ideone.

Тест

Входящие данные	Операция	Выходящие данные
4/5 1/2	проверка равенства	false
4/5 1/2 2/5	сравнение по равенству дроби и произведения двух других	true
2/5 1/2	сложение	9/10
4/5 1/2	вычитание	3/10
4/5 1/2	вычитание	-3/10
2/5 1/2	умножение	1/5
4/5 1/2	деление	8/5
4/5 1/2	сравнение	4/5 > 1/2
4/5 1/2	сравнение	1/2 > 2/5
4/5 1/2 2/5	сравнение дроби и произведения двух других	2/5 = 2/5

Класс комплексных чисел

26/08/2016 by Дарья Пиндус

Задача.

Напишите класс для хранения комплексных чисел и реализуйте основные операции работы с ними.

Тесты.

Исходные числа	Операция	Результат
z1 = 2 + 3i z2 = -1 + 2i	+	1.0 + 5.0i
	—	3.0 + i
	*	-8.0 + i
	/	0.8 — 1.4i
3 + 4i	√	2.0 + i, -2.0 -i
-1 + 2i	pow	-3.0 — 4.0i

Код программы

/**
 * <h1>Complex Numbers</h1>
 * The ComplexNumber program implements an application that
 * allows to calculate complex numbers
 **/

public class ComplexNumber {

    /**
     * Represents the real part of a complex number
     */
    private double re;

    /**
     * Represents imaginary part of a complex number
     */
    private double im;

    public ComplexNumber(double re, double im) {
        this.re = re;
        this.im = im;
    }

    public double getRe() {
        return re;
    }

    public double getIm() {
        return im;
    }

    /**
     * @return modulus (or absolute value) of the number
     */
    private double getModule() {
        return Math.sqrt(this.re * this.re + this.im * this.im);
    }

    /**
     * Allows to get the sum of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber sum(ComplexNumber cn1, ComplexNumber cn2) {
        return new ComplexNumber(cn1.getRe() + cn2.getRe(), cn1.getIm() + cn2.getIm());
    }

    /**
     * Allows to get the product of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber multiply(ComplexNumber cn1, ComplexNumber cn2) {
        return new ComplexNumber(cn1.getRe() * cn2.getRe() - cn1.getIm() * cn2.getIm(), cn1.getRe() * cn2.getIm() + cn1.getIm() * cn2.getRe());
    }

    /**
     * Allows to get the difference of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber subtract(ComplexNumber cn1, ComplexNumber cn2) {
        return new ComplexNumber(cn1.getRe() - cn2.getRe(), cn1.getIm() - cn2.getIm());
    }

    /**
     * Allows to get the product of two complex numbers given in the parameters.
     *
     * @return the new complex number
     */
    public static ComplexNumber divide(ComplexNumber cn1, ComplexNumber cn2) {
        ComplexNumber temp = new ComplexNumber(cn2.getRe(), (-1) * cn2.getIm());
        temp = ComplexNumber.multiply(cn1, temp);
        double denominator = cn2.getRe() * cn2.getRe() + cn2.getIm() * cn2.getIm();
        return new ComplexNumber(temp.getRe() / denominator, temp.getIm() / denominator);
    }

    /**
     * This function allows to get the argument of complex number to represent it in trigonometric form
     *
     * @return argument of complex number
     */
    private double GetArg() {
        if (this.re > 0) {
            return Math.atan(im / re);
        } else {
            if (re < 0 && im > 0) {
                return Math.PI + Math.atan(im / re);
            } else {
                return -Math.PI + Math.atan(im / re);
            }
        }
    }

    /**
     * Allows to raise complex number to specified power with the help of de Moivre's formula.
     *
     * @param cn    needed complex number (the base)
     * @param power the exponent
     * @return the new complex number
     */
    public static ComplexNumber pow(ComplexNumber cn, int power) {
        double factor = Math.pow(cn.getModule(), power);
        return new ComplexNumber(factor * Math.cos(power * cn.GetArg()), factor * Math.sin(power * cn.GetArg()));
    }

    /**
     * The function of getting square roots of complex number cn
     *
     * @return an array of pair of square roots
     */
    public static ComplexNumber[] sqrt(ComplexNumber cn) {
        double a = cn.getModule() / 2;
        ComplexNumber pos = new ComplexNumber(Math.sqrt(a + cn.getRe() / 2), Math.signum(cn.getIm()) * Math.sqrt(a - cn.getRe() / 2));
        ComplexNumber neg = new ComplexNumber((-1) * pos.getRe(), (-1) * pos.getIm());
        ComplexNumber[] answer = {pos, neg};
        return answer;
    }

    /**
     * Defines and returns the sign required for correct record of a number
     *
     * @return string with appropriate sign
     */
    private String sign() {
        if (im > 0) return " + ";
        else return " - ";
    }

    @Override
    public String toString() {
        String string;
        if (im == 1 || im == -1) {
            if (re == 0) {
                string = sign() + "i";
            } else {
                string = Double.toString(re) + sign() + "i";
            }
        } else {
            string = Double.toString(re) + sign() + Double.toString(Math.abs(im)) + "i";
        }
        return string;
    }

    @Override
    public boolean equals(Object obj) {
        if (this.getClass() != obj.getClass() || obj == null)
            return false;
        return true;
    }

    /**
     * In this function main test on the correctness of this program are done.
     * All operations on complex numbers are shown.
     */
    public static void main(String[] args) {
        ComplexNumber x = new ComplexNumber(2, 3);
        ComplexNumber y = new ComplexNumber(-1, 2);
        System.out.println("z1 = " + x + ",     z2 = " + y);

        ComplexNumber z;
        z = ComplexNumber.sum(x, y);
        System.out.println("+ : " + z);

        z = ComplexNumber.subtract(x, y);
        System.out.println("- : " + z);

        z = ComplexNumber.divide(x, y);
        System.out.println("/ : " + z);

        z = ComplexNumber.multiply(x, y);
        System.out.println(" * :" + z);

        z = ComplexNumber.pow(y, 2);
        System.out.println("Pow 2 of z2 : " + z);

        ComplexNumber b = new ComplexNumber(3, 4);
        ComplexNumber[] ans = ComplexNumber.sqrt(b);
        System.out.println("Sqrt of " + b + " = " + ans[0] + ",  " + ans[1]);

    }
}

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/**

* <h1>Complex Numbers</h1>

* The ComplexNumber program implements an application that

* allows to calculate complex numbers

**/

public class ComplexNumber {

/**

* Represents the real part of a complex number

private double re;

/**

* Represents imaginary part of a complex number

private double im;

public ComplexNumber(double re, double im) {

this.re = re;

this.im = im;

}

public double getRe() {

return re;

}

public double getIm() {

return im;

}

/**

* @return modulus (or absolute value) of the number

private double getModule() {

return Math.sqrt(this.re * this.re + this.im * this.im);

}

/**

* Allows to get the sum of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber sum(ComplexNumber cn1, ComplexNumber cn2) {

return new ComplexNumber(cn1.getRe() + cn2.getRe(), cn1.getIm() + cn2.getIm());

}

/**

* Allows to get the product of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber multiply(ComplexNumber cn1, ComplexNumber cn2) {

return new ComplexNumber(cn1.getRe() * cn2.getRe() - cn1.getIm() * cn2.getIm(), cn1.getRe() * cn2.getIm() + cn1.getIm() * cn2.getRe());

}

/**

* Allows to get the difference of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber subtract(ComplexNumber cn1, ComplexNumber cn2) {

return new ComplexNumber(cn1.getRe() - cn2.getRe(), cn1.getIm() - cn2.getIm());

}

/**

* Allows to get the product of two complex numbers given in the parameters.

* @return the new complex number

public static ComplexNumber divide(ComplexNumber cn1, ComplexNumber cn2) {

ComplexNumber temp = new ComplexNumber(cn2.getRe(), (-1) * cn2.getIm());

temp = ComplexNumber.multiply(cn1, temp);

double denominator = cn2.getRe() * cn2.getRe() + cn2.getIm() * cn2.getIm();

return new ComplexNumber(temp.getRe() / denominator, temp.getIm() / denominator);

}

/**

* This function allows to get the argument of complex number to represent it in trigonometric form

* @return argument of complex number

private double GetArg() {

if (this.re > 0) {

return Math.atan(im / re);

} else {

if (re < 0 && im > 0) {

return Math.PI + Math.atan(im / re);

} else {

return -Math.PI + Math.atan(im / re);

}

/**

* Allows to raise complex number to specified power with the help of de Moivre's formula.

* @param cn needed complex number (the base)

* @param power the exponent

* @return the new complex number

public static ComplexNumber pow(ComplexNumber cn, int power) {

double factor = Math.pow(cn.getModule(), power);

return new ComplexNumber(factor * Math.cos(power * cn.GetArg()), factor * Math.sin(power * cn.GetArg()));

}

/**

* The function of getting square roots of complex number cn

* @return an array of pair of square roots

public static ComplexNumber[] sqrt(ComplexNumber cn) {

double a = cn.getModule() / 2;

ComplexNumber pos = new ComplexNumber(Math.sqrt(a + cn.getRe() / 2), Math.signum(cn.getIm()) * Math.sqrt(a - cn.getRe() / 2));

ComplexNumber neg = new ComplexNumber((-1) * pos.getRe(), (-1) * pos.getIm());

ComplexNumber[] answer = {pos, neg};

return answer;

}

/**

* Defines and returns the sign required for correct record of a number

* @return string with appropriate sign

private String sign() {

if (im > 0) return " + ";

else return " - ";

}

@Override

public String toString() {

String string;

if (im == 1 || im == -1) {

if (re == 0) {

string = sign() + "i";

} else {

string = Double.toString(re) + sign() + "i";

}

} else {

string = Double.toString(re) + sign() + Double.toString(Math.abs(im)) + "i";

}

return string;

}

@Override

public boolean equals(Object obj) {

if (this.getClass() != obj.getClass() || obj == null)

return false;

return true;

}

/**

* In this function main test on the correctness of this program are done.

* All operations on complex numbers are shown.

public static void main(String[] args) {

ComplexNumber x = new ComplexNumber(2, 3);

ComplexNumber y = new ComplexNumber(-1, 2);

System.out.println("z1 = " + x + ", z2 = " + y);

ComplexNumber z;

z = ComplexNumber.sum(x, y);

System.out.println("+ : " + z);

z = ComplexNumber.subtract(x, y);

System.out.println("- : " + z);

z = ComplexNumber.divide(x, y);

System.out.println("/ : " + z);

z = ComplexNumber.multiply(x, y);

System.out.println(" * :" + z);

z = ComplexNumber.pow(y, 2);

System.out.println("Pow 2 of z2 : " + z);

ComplexNumber b = new ComplexNumber(3, 4);

ComplexNumber[] ans = ComplexNumber.sqrt(b);

System.out.println("Sqrt of " + b + " = " + ans[0] + ", " + ans[1]);

}

Ссылка на Ideone.

Quaternion

09/07/2016 by Владислав Козачков

Условие

Кватернионы (от лат. quaterni, по четыре) — система гиперкомплексных чисел, образующая векторное пространство размерностью четыре над полем вещественных чисел. Обычно обозначаются символом $H$ . Предложены Уильямом Гамильтоном в 1843 году.
Кватернионы удобны для описания изометрий трёх- и четырёхмерного евклидовых пространств, и поэтому получили широкое распространение в механике. Также их используют в вычислительной математике, например, при создании трёхмерной графики.
Источник: Кватернионы — Википедия.

Код на Java:

Описание класса:

import java.util.*;
import java.lang.*;
import java.io.*;

class Quaternion {
	private double a;
	private double b;
	private double c;
	private double d;
	
	public Quaternion() {
		a = 0;
		b = 0;
		c = 0;
		d = 0;
	}
	public Quaternion(double a) {
		this.a = a;
		b = 0;
		c = 0;
		d = 0;
	}
	public Quaternion(double a, double b, double c, double d) {
		this.a = a;
		this.b = b;
		this.c = c;
		this.d = d;
	}
	
	public Quaternion conjug() {
		return new Quaternion(a, -b, -c, -d);
	}
	public double abs() {
		return Math.sqrt(a * a  + b * b + c * c + d * d);
	}
	public Quaternion inverse() throws ArithmeticException {
		return Quaternion.divide(this.conjug(), this.abs() * this.abs());
	}
	public boolean isZero() {
		return (a == 0 && b == 0 && c == 0 && d == 0);
	}
	
	public static Quaternion sum(Quaternion a, Quaternion b) {
		return new Quaternion(a.a + b.a, a.b + b.b, a.c + b.c, a.d + b.d);
	}
	public static Quaternion sub(Quaternion a, Quaternion b) {
		return new Quaternion(a.a - b.a, a.b - b.b, a.c - b.c, a.d - b.d);
	}
	public static Quaternion mul(Quaternion a, double mult) {
		return new Quaternion(a.a * mult, a.b * mult, a.c * mult, a.d * mult);
	}
	public static Quaternion mul(Quaternion a, Quaternion b) {
		return new Quaternion(a.a * b.a - a.b * b.b - a.c * b.c - a.d * b.d,
							  a.a * b.b + a.b * b.a + a.c * b.d - a.d * b.c,
							  a.a * b.c - a.b * b.d + a.c * b.a + a.d * b.b,
							  a.a * b.d + a.b * b.c - a.c * b.b + a.d * b.a);
	}
	public static Quaternion divide(Quaternion a, double divider) throws ArithmeticException {
		if (divider == 0) throw new ArithmeticException("Zero divider");
		return new Quaternion(a.a / divider, a.b / divider, a.c / divider, a.d / divider);
	}
	public static Quaternion divide(Quaternion a, Quaternion b) throws ArithmeticException {
		if (b.isZero()) throw new ArithmeticException("Zero divider");
		return Quaternion.mul(a, b.inverse());
	}
	
	public String toString() {
		return new String(a +
						  ((b < 0)? " - " : " + ") + Math.abs(b) + "*i" +
						  ((c < 0)? " - " : " + ") + Math.abs(c) + "*j" +
						  ((d < 0)? " - " : " + ") + Math.abs(d) + "*k\n");
	}
}

import java.util.*;

import java.lang.*;

import java.io.*;

class Quaternion {

private double a;

private double b;

private double c;

private double d;

public Quaternion() {

a = 0;

b = 0;

c = 0;

d = 0;

}

public Quaternion(double a) {

this.a = a;

b = 0;

c = 0;

d = 0;

}

public Quaternion(double a, double b, double c, double d) {

this.a = a;

this.b = b;

this.c = c;

this.d = d;

}

public Quaternion conjug() {

return new Quaternion(a, -b, -c, -d);

}

public double abs() {

return Math.sqrt(a * a + b * b + c * c + d * d);

}

public Quaternion inverse() throws ArithmeticException {

return Quaternion.divide(this.conjug(), this.abs() * this.abs());

}

public boolean isZero() {

return (a == 0 && b == 0 && c == 0 && d == 0);

}

public static Quaternion sum(Quaternion a, Quaternion b) {

return new Quaternion(a.a + b.a, a.b + b.b, a.c + b.c, a.d + b.d);

}

public static Quaternion sub(Quaternion a, Quaternion b) {

return new Quaternion(a.a - b.a, a.b - b.b, a.c - b.c, a.d - b.d);

}

public static Quaternion mul(Quaternion a, double mult) {

return new Quaternion(a.a * mult, a.b * mult, a.c * mult, a.d * mult);

}

public static Quaternion mul(Quaternion a, Quaternion b) {

return new Quaternion(a.a * b.a - a.b * b.b - a.c * b.c - a.d * b.d,

a.a * b.b + a.b * b.a + a.c * b.d - a.d * b.c,

a.a * b.c - a.b * b.d + a.c * b.a + a.d * b.b,

a.a * b.d + a.b * b.c - a.c * b.b + a.d * b.a);

}

public static Quaternion divide(Quaternion a, double divider) throws ArithmeticException {

if (divider == 0) throw new ArithmeticException("Zero divider");

return new Quaternion(a.a / divider, a.b / divider, a.c / divider, a.d / divider);

}

public static Quaternion divide(Quaternion a, Quaternion b) throws ArithmeticException {

if (b.isZero()) throw new ArithmeticException("Zero divider");

return Quaternion.mul(a, b.inverse());

}

public String toString() {

return new String(a +

((b < 0)? " - " : " + ") + Math.abs(b) + "*i" +

((c < 0)? " - " : " + ") + Math.abs(c) + "*j" +

((d < 0)? " - " : " + ") + Math.abs(d) + "*k\n");

}

Стандартное определение

Кватернионы можно определить как формальную сумму a + bi + cj + dk, где a, b, c, d — вещественные числа, а i, j, k — мнимые единицы со следующим свойством: i² = j² = k² = ijk = −1.
Таким образом, таблица умножения базисных кватернионов — 1, i, j, k — выглядит так:

×	1	i	j	k
1	1	i	j	k
i	i	-1	k	-j
j	j	-k	-1	i
k	k	j	-1	-1

Сопряжение

Для кватерниона q сопряжённым называется:
$conj(q) = a - bi - cj - dk$

Модуль

Так же, как и для комплексных чисел,
$abs(q) = sqrt(q*conj(q)) = sqrt(a^2 + b^2 + c^2 + d^2)$
называется модулем q.

Обращение умножения (деление)

Кватернион, обратный по умножению к q, вычисляется так:
$q^-1 = conj(q)/abs(q)^2$ .

Основная программа:

class Main {
	public static void main (String[] args) {
		Quaternion qt1 = new Quaternion();
		Quaternion qt2 = new Quaternion(5);
		Quaternion qt3 = new Quaternion(1, 2, 3, 4);
		Quaternion qt4 = new Quaternion(0.1, 1.4, -2.5, -1.7);
		if (!qt1.isZero()) {
			System.out.print(Quaternion.sum(qt3, qt4));
		} else {
			System.out.print(Quaternion.mul(qt3, qt4));
		}
		do {
			qt2 = Quaternion.sub(qt2, qt3);
			System.out.print(qt2);
			System.out.print(qt2.conjug());
			System.out.print(qt2.inverse());
		} while (qt2.isZero());
		try {
			System.out.print(Quaternion.divide(qt3, qt4));
		} catch (ArithmeticException e) {
			System.out.print(e.getMessage());
		}
		System.out.print(Quaternion.mul(qt3, 17.2));
	}
}

class Main {

public static void main (String[] args) {

Quaternion qt1 = new Quaternion();

Quaternion qt2 = new Quaternion(5);

Quaternion qt3 = new Quaternion(1, 2, 3, 4);

Quaternion qt4 = new Quaternion(0.1, 1.4, -2.5, -1.7);

if (!qt1.isZero()) {

System.out.print(Quaternion.sum(qt3, qt4));

} else {

System.out.print(Quaternion.mul(qt3, qt4));

}

do {

qt2 = Quaternion.sub(qt2, qt3);

System.out.print(qt2);

System.out.print(qt2.conjug());

System.out.print(qt2.inverse());

} while (qt2.isZero());

try {

System.out.print(Quaternion.divide(qt3, qt4));

} catch (ArithmeticException e) {

System.out.print(e.getMessage());

}

System.out.print(Quaternion.mul(qt3, 17.2));

}

Ход выполнения

При выполнении происходит проверка функций класса: логических, арифметических, построения объектов, производных от исходного (таких, как сопряженное и обратное значение), функции строкового отображения объекта.

Вывод программы:

11.600000000000001 + 6.5*i + 6.8*j - 10.499999999999998*k

4.0 - 2.0*i - 3.0*j - 4.0*k

4.0 + 2.0*i + 3.0*j + 4.0*k

0.08888888888888888 + 0.04444444444444444*i + 0.06666666666666665*j + 0.08888888888888888*k

-1.026102610261026 - 0.5490549054905489*i - 0.5580558055805579*j + 1.017101710171017*k

17.2 + 34.4*i + 51.599999999999994*j + 68.8*k

Ссылки:

Рабочий код для тестирования на Ideone.com: Ideone.com

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Tag Archives: объекты

Класс для работы с геометрическими векторами на плоскости

Задача

Тесты

Код

Описание решения

Класс рациональных дробей

Задача

Код

Тест

Класс комплексных чисел

Quaternion

Условие

Код на Java:

Описание класса:

Стандартное определение

Сопряжение

Модуль

Обращение умножения (деление)

Основная программа:

Ход выполнения

Вывод программы:

Ссылки: