Program for Determinant, characteristic equation,etc.

.cpp

//Program to solve questions based on eigen value and eigen vector.
//This is going to be a menu driven program. Following operations would be made possible by this code:
//1. Find Determinant of an inserted matrix.
//2. See if Matrix is consistant or not.
//3. Finding sqquare of a Matrics .
//4. Finding cube of a Matrix.
//5. Finding product of two Matrix.
//6. Finding Characteristic equation of a matrix.

char const p_2= 253;        //power to 2 superscript.
//char const p_3= 254;
#include<iostream>
using namespace std;
class game
{
    private:
        int order, A[5][5],B[5][5],result[5][5],choice;
    public:
        game()
        {
            order= 5;
            for(int i=0;i<order;i++)
            {
                for(int j=0;j<order;j++)
                {
                    result[i][j]=0;
                    B[i][j]=0;
                }
            }
        }
        void menu();
        void display();
        void Det();
        void sq();
        void cube();
        void mul();
        void char_eq();
};
void game::display()
{
    system("cls");
    cout<<"Program to Simplify MTT Questions by reducing Time in lathargic calculation."<<endl;
}
void game::menu()
{
    display();
    cout<<"MENU:"<<endl;
    cout<<"\nOperations available are:"<<endl;
    cout<<"1. To find Determinant of a Given Matrix."<<endl;
    cout<<"2. To find the Characteristic Equation of a given Matrix."<<endl;
    cout<<"3. To find the Square of a Matrix."<<endl;
    cout<<"4. To find the Cube of a given Matrix."<<endl;
    cout<<"5. To find the product of two Matrix."<<endl;
    cout<<"Enter the your choice:";
    cin>>choice;
    if(choice==1)
        Det();
    else if(choice==2)
        char_eq();
    else if(choice==3)
        sq();
    else if(choice==4)
        cube();
    else if(choice==5)
        mul();
    else
    {
            exit(0);
    }
}
void game::Det()
{
    display();
    cout<<"\n\nOperation Number: 1, Finding Determinant of a Matrix."<<endl;
    cout<<"\nEnter Order of the Matrix:";
    cin>>order;
    cout<<"Enter the Matrix:"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
            cin>>A[i][j];
    }
    if(order==2)
        cout<<"The Determinant of the given Matrix is: "<<((A[0][0]*A[1][1])-(A[0][1]*A[1][0]))<<endl;
    else if(order==3)
        cout<<"The Determinant of the given Matrix is: "<<((A[0][0]*((A[1][1]*A[2][2])-(A[1][2]*A[2][1]))) - (A[1][0]*((A[0][1]*A[2][2])-(A[0][2]*A[2][1]))) + (A[2][0]*((A[0][1]*A[1][2])-(A[0][2]*A[1][1]))))<<endl;
    else
        cout<<"Sorry the Program is not designed to find determinant of matrix of order greater than 3, yet."<<endl;
    
}
void game::char_eq()
{
    display();
    cout<<"\nOperation to find the Characteristic equation of a given Matrix."<<endl;
    cout<<"Enter the order of the Matrix:";
    cin>>order;
    cout<<"Enter the Matrix A:"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
            cin>>A[i][j];
    }
    if(order==2)
    {
        cout<<"The Characteristic Equation of the given Matrix is: A"<<(char)p_2<<" - "<<(A[0][0]+A[1][1])<<"A +"<<((A[0][0]*A[1][1])-(A[0][1]*A[1][0]))<<endl;
    }
    else if(order==3)
    {
        int n=((A[0][0]*((A[1][1]*A[2][2])-(A[1][2]*A[2][1]))) - (A[1][0]*((A[0][1]*A[2][2])-(A[0][2]*A[2][1]))) + (A[2][0]*((A[0][1]*A[1][2])-(A[0][2]*A[1][1]))));
        int q= ((A[0][0]*A[1][1]) + (A[1][1]*A[2][2]) + (A[0][0]*A[2][2])-(A[0][1]*A[1][0]) - (A[0][2]*A[2][0]) - (A[1][2]*A[2][1]));
        cout<<"The Characteristic Equation of the given Matrix is: A^3 + ("<<-1*(A[0][0]+A[1][1]+A[2][2])<<")A"<<(char)p_2<<" + ("<<q<<")A +("<<-1*n<<")"<<endl;
    }
}
void game::sq()
{
    display();
    cout<<"\nOperation to find square of a given matrix."<<endl;
    cout<<"Enter the order of the Matrix:";
    cin>>order;
    cout<<"Enter the Matrix A:"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
            cin>>A[i][j];
    }
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
        {
            for(int k=0;k<order;k++)
            {
                result[i][j]+=(A[i][k]*A[k][j]);
            }
        }
    }
    cout<<"The Square of the Matrix is:"<<endl;
    cout<<"A"<<(char)p_2<<":"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
        {
            cout<<result[i][j]<<" ";
        }
        cout<<endl;
    }
}
void game::cube()
{
    display();
    cout<<"\nOperation to find Cube of a given matrix."<<endl;
    cout<<"Enter the order of the Matrix:";
    cin>>order;
    cout<<"Enter the Matrix A:"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
            cin>>A[i][j];
    }
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
        {
            for(int k=0;k<order;k++)
            {
                B[i][j]+=(A[i][k]*A[k][j]);
            }
        }
    }
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
        {
            for(int k=0;k<order;k++)
            {
                result[i][j]+=(A[i][k]*B[k][j]);
            }
        }
    }
    cout<<"The Cube of the Matrix is:"<<endl;
    cout<<"A^3"<<":"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
        {
            cout<<result[i][j]<<" ";
        }
        cout<<endl;
    }
}
void game::mul()
{
    display();
    cout<<"\nOperation to find product of a two given matrix."<<endl;
    cout<<"Enter the order of the Matrix:";
    cin>>order;
    cout<<"Enter the Matrix A:"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
            cin>>A[i][j];
    }
    cout<<"Enter the Matrix B:"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
            cin>>B[i][j];
    }
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
        {
            for(int k=0;k<order;k++)
            {
                result[i][j]+=(A[i][k]*B[k][j]);
            }
        }
    }
    cout<<"The Product of the two Matrix is:"<<endl;
    cout<<"A.B"<<":"<<endl;
    for(int i=0;i<order;i++)
    {
        for(int j=0;j<order;j++)
        {
            cout<<result[i][j]<<" ";
        }
        cout<<endl;
    }
}
int main()
{
    char ch;
    do
    {
        game o;
        o.menu();
        cout<<"Do you want to Quit?(y-Yes/n-No):";
        cin>>ch;
    } while (ch=='n'||ch=='N');
    return 0;
}