#include "iostream.h"
#include "math.h"

void main()
{
    //program d1r6
    //driver program for routine vander
    int i, j, n = 5;
    double x[6], q[6], w[6], term[6];
	double sum1;
    //輸入已知的方程組的系數矩陣的x
    x[1] = 1.0; x[2] = 1.5; x[3] = 2.0; x[4] = 2.5; x[5] = 3.0;
    //輸入已知的方程組的右端向量b
    q[1] = 1.0; q[2] = 1.5; q[3] = 2.0; q[4] = 2.5; q[5] = 3.0;
    cout<<"已知的方程組的右端向量"<<endl;
	cout.setf(ios::fixed|ios::right);
	cout.precision(5);
    cout<<"       "<<q[1]<<endl;
    cout<<"       "<<q[2]<<endl;
    cout<<"       "<<q[3]<<endl;
    cout<<"       "<<q[4]<<endl;
    cout<<"       "<<q[5]<<endl;
    vander(x, w, q, n);
    //輸出方程組的解w
    cout<<endl;
    cout<<" 計算出的方程組的解"<<endl;
	cout.width(15);
    cout<<w[1]<<endl;
	cout.width(15);
    cout<<w[2]<<endl;
	cout.width(15);
    cout<<w[3]<<endl;
	cout.width(15);
    cout<<w[4]<<endl;
	cout.width(15);
    cout<<w[5]<<endl;
    //將計算出的解乘以系數矩陣，以驗證計算結果正確
    cout<<endl;
    cout<<"將計算出的解乘以系數矩陣，以驗證計算結果正確"<<endl;
    cout<<endl;
    cout<<"解乘以系數矩陣     方程組的右端向量"<<endl;
    sum1 = 0;
    for (i = 1; i<=n; i++)
	{
        term[i] = w[i];
        sum1 = sum1 + w[i];
    }

    cout<<"   "<<sum1<<"             "<<q[1]<<endl;
    for (i = 2; i<=n; i++)
	{
        sum1 = 0;
        for (j = 1; j<=n; j++)
		{
           term[j] = term[j] * x[j];
           sum1 = sum1 + term[j];
        }
        cout<<"   "<<sum1<<"             "<<q[i]<<endl;
    }
}