feat: Added a class implemetation of complex numbers along with implementation of all (most) binary operations involved with complex numbers.

math/complex_numbers.cpp

@@ -0,0 +1,183 @@
+/**
+ * Copyright 2020 @author tjgurwara99
+ * @file
+ *
+ * A basic implementation of Complex Number field as a class with operators overloaded to accommodate (mathematical) field operations.
+ */
+
+#include <iostream>
+#include <cmath>
+#include <stdexcept>
+
+/**
+ * Class Complex to represent complex numbers as a field.
+ */
+class Complex {
+    // The real value of the complex number
+    double re;
+    // The imaginary value of the complex number
+    double im;
+
+ public:
+    /**
+     * Complex Constructor which initialises the complex number which takes two arguments.
+     * @param x The real value of the complex number.
+     * @param y The imaginary value of the complex number.
+     */
+    Complex(double x, double y) {
+        this->re = x;
+        this->im = y;
+    }
+    
+    /**
+     * Complex Constructor which initialises the complex number with no arguments.
+     */
+    Complex() {
+        Complex(0.0,0.0);
+    }
+
+    /**
+     * Member function (getter) to access the class' re value.
+     */
+    double real() const {
+        return this->re;
+    }
+
+    /**
+     * Member function (getter) to access the class' im value.
+     */
+    double imag() const {
+        return this->im;
+    }
+
+    /**
+     * Member function to which gives the absolute value (modulus) of our complex number
+     * @return \f$ \sqrt{z \dot \bar{z} \f$ where \f$ z \f$ is our complex number.
+     */
+    double abs() const {
+        return std::sqrt(this->re*this->re + this->im*this->im);
+    }
+
+    /**
+     * Operator overload to be able to add two complex numbers.
+     * @param other The other number that is added to the current number.
+     * @return result current number plus other number
+     */
+    Complex operator+(const Complex& other) {
+        Complex result(this->re + other.re, this->im + other.im);
+        return result;
+    }
+
+    /**
+     * Operator overload to be able to subtract two complex numbers.
+     * @param other The other number being subtracted from the current number.
+     * @return result current number subtract other number
+     */
+    Complex operator-(const Complex& other) {
+        Complex result(this->re - other.re, this->im - other.im);
+        return result;
+    }
+
+    /**
+     * Operator overload to be able to multiple two complex numbers.
+     * @param other The other number to multiply the current number to.
+     * @return result current number times other number.
+     */
+    Complex operator*(const Complex& other) {
+        Complex result(this->re * other.re - this->im * other.im,
+                       this->re * other.im + this->im * other.re);
+        return result;
+    }
+
+    /**
+     * Operator overload of the BITWISE NOT which gives us the conjugate of our complex number.
+     * NOTE: This is overloading the BITWISE operator but its not a BITWISE operation in this definition.
+     * @return result The conjugate of our complex number.
+     */
+    Complex operator~() const {
+        Complex result(this->re, -(this->im));
+        return result;
+    }
+
+    /**
+     * Operator overload to be able to divide two complex numbers. This function would throw an exception if the other number is zero.
+     * @param other The other number we divide our number by.
+     * @return result Current number divided by other number.
+     */
+    Complex operator/(const Complex& other) {
+        Complex result = *this * ~other;
+        double denominator = other.abs() * other.abs();
+        if (denominator != 0) {
+            result = Complex(result.real() / denominator, result.imag() / denominator);
+            return result;
+        }
+        else {
+            throw std::invalid_argument("Undefined Value");
+        }
+    }
+};
+
+/**
+ * Logical Equal overload for our Complex class.
+ * @param a Left hand side of our expression
+ * @param b Right hand side of our expression
+ * @return 'True' If real and imaginary parts of a and b are same
+ * @return 'False' Otherwise.
+ */
+bool operator==(const Complex& a, const Complex& b) {
+    double del_real = a.real() - b.real();
+    double del_imag = a.imag() - b.imag();
+    return ((del_real <= 1e-15 && del_real >= - 1e-15 ) && (del_imag <= 1e-15 && del_imag >= - 1e-15));
+}
+
+/**
+ * Overloaded insersion operator to accommodate the printing of our complex number in their standard form.
+ * @param os The console stream
+ * @param num The complex number.
+ */
+std::ostream& operator<<(std::ostream& os, const Complex& num) {
+    os << num.real();
+    if (num.imag() < 0) {
+        os << " - " << -num.imag();
+    }
+    else {
+        os << " + " << num.imag();
+    }
+    os << "i";
+    return os;
+}
+
+/**
+ * Tests Function
+ */
+void tests() {
+    Complex num1(1,1), num2(1,1);
+    // Test for addition
+    assert(((void)"1 + 1i + 1 + 1i is equal to 2 + 2i but the addition doesn't add up \n",
+            (num1 + num2) == Complex(2,2)));
+    std::cout << "First test passes." << std::endl;
+    // Test for subtraction
+    assert(((void)"1 + 1i - 1 - 1i is equal to 0 but the program says otherwise. \n",
+            (num1 - num2) == Complex(0,0)));
+    std::cout << "Second test passes." << std::endl;
+    // Test for multiplication
+    assert(((void)"(1 + 1i) * (1 + 1i) is equal to 2i but the program says otherwise. \n",
+            (num1 * num2) == Complex(0,2)));
+    std::cout << "Third test passes." << std::endl;
+    // Test for division
+    assert(((void)"(1 + 1i) / (1 + 1i) is equal to 1 but the program says otherwise.\n",
+            (num1 / num2) == Complex(1,0)));
+    std::cout << "Fourth test passes." << std::endl;
+    // Test for conjugates
+    assert(((void)"(1 + 1i) has a conjugate which is equal to (1 - 1i) but the program says otherwise.\n",
+            ~num1 == Complex(1,-1)));
+    std::cout << "Fifth test passes." << std::endl;
+
+}
+/**
+ * Main function
+ */
+int main() {
+    tests();
+    return 0;
+}