polynomial_field_test1.1.py

num_points = int(input("How many data points do you have? "))
point_list = [] #Creates an empty list containing tuples of the points.
augmented_matrix = [[0]*(num_points+1)]*num_points

for i in range (num_points): #Gets input from user, and stores the x and y values into a tuple.
    x = int(input("X value: "))
    y = int(input("Y value: "))
    ith_point = (x, y)
    point_list.append(ith_point)


# Now for the actual testing
for i in range (num_points): # column
    power = num_points # Gets the power based on amount of points given, then fills each row with x^(n-1) points, with the exponent decrasing every collumn for the coefficient matrix.

    row = [0] * (num_points + 1) # Placeholder row to fill up
    for j in range(num_points):  # row
        x_value = point_list[i][0]
        row[j] = pow(x_value, (power - 1))
        power -= 1
    augmented_matrix[i] = row
    augmented_matrix[i][num_points] = point_list[i][1]  # Sets the final column to be equal to the y-values of the points, to satisfy the system of equations

#Prints out the augmented matrix
print("Points in matrix form:")
for i in range (num_points):
    print(augmented_matrix[i])