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//

// Created by Ari on 12/15/24.

//

#ifndef FINALEXAMPROJECTTWO_TRINION_H

#define FINALEXAMPROJECTTWO_TRINION_H

#include <ostream>

using namespace std;

/**

 * Represents a Trinion number, which is a number that can be expressed

 * as a+bi+cj, where i^2=j^2=-1 and ij=ji=1+i+j.

 * @tparam T The base type of coefficients a,b, and c for the Trinian.

 */

template <typename T>

class Trinion {

 public:

  // CONSTRUCTORS

  Trinion<T>():scalarCoeff(0), iCoeff(0), jCoeff(0) {}

  Trinion<T>(

      const T thePlainCoeff,

      const T theICoeff,

      const T theJCoeff

  ) : scalarCoeff(thePlainCoeff), iCoeff(theICoeff), jCoeff(theJCoeff) {}

  Trinion<T>(const Trinion<T> &second) :

      scalarCoeff(second.scalarCoeff),

      iCoeff(second.iCoeff),

      jCoeff(second.jCoeff) {}

  // OPERATORS

  /**

 * @param second The addend.

 * @return The sum of this Trinion with [second]

 */

  Trinion<T>& operator+(const Trinion<T> &second) const {

    auto *result =

        new Trinion<T>(

            scalarCoeff + second.scalarCoeff,

            iCoeff + second.iCoeff,

            jCoeff + second.jCoeff

        );

    return *result;

  }

  /**

 * @param second The multiplier

 * @return The product of this Trinion with [second]

 */

  Trinion<T> &operator*(const Trinion<T> &second) const {

    T newPlain =

        scalarCoeff * second.scalarCoeff

            - (iCoeff - jCoeff) * (second.iCoeff - second.jCoeff);

    T newI =

        second.iCoeff * (scalarCoeff + jCoeff)

            + iCoeff * (second.scalarCoeff + second.jCoeff);

    T newJ =

        second.jCoeff * (scalarCoeff + iCoeff)

            + jCoeff * (second.scalarCoeff + second.iCoeff);

    Trinion<T> *result = new Trinion<T>(newPlain, newI, newJ);

    return *result;

  }

  /**

 * Sets this to [second].

 * @param second The Trinion to copy into this object.

 * @return *this, after it has been set to [second].

 */

  Trinion<T> &operator=(const Trinion<T> &second) {

    scalarCoeff = second.scalarCoeff;

    iCoeff = second.iCoeff;

    jCoeff = second.jCoeff;

    return *this;

  }

  /**

   * @param second The Trinion to compare.

   * @return true iff this object has the same coefficients as [second]

   */

  bool operator==(const Trinion<T> &second) const {

    return (scalarCoeff == second.scalarCoeff && iCoeff == second.iCoeff && jCoeff == second.jCoeff);

  }

  /**

   * @param exp An exponent.

   * @return This Trinion raised to the exp-th power

   * @example (1+i)^0 == 1

   * @example 2 ^ 9 == 512

   * @example (2i) ^ 3 == -8i

   * @example (1 + i +1.5j) ^ 2 == 0.75 + 5i + 6j

   */

  Trinion<T> &operator^(unsigned int exp);

  // FRIENDS

  /**

   * @return A stream to which ths coefficients of [tri] has been added.

   */

  friend ostream &operator<<(ostream &os, const Trinion<T> &tri) {

    os << tri.scalarCoeff << " + "

    << tri.iCoeff << "i" << " + "

    << tri.jCoeff << "j";

    return os;

  }

  // FIELDS

  T scalarCoeff;

  T iCoeff;

  T jCoeff;

};

#endif //FINALEXAMPROJECTTWO_TRINION_H

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