我该如何解决旨在解决行列式的功能？

Question

The function can accurately compute 1x1, 2x2, and 3x3 determinants, but it gives wrong values for higher order determinants. I'm thinking there's a problem with the part in the function where I call the function (recursion) to solve lower order determinants as part of the solution.

I suspect it has something to do with variable locality, but I'm not sure why that would be an issue because I thought locality was automatic.

This is Python 2 by the way.

Code:

def is_Det(matrix):
    isdet = True
    if not isinstance(matrix,list): # Is this actually a list?
        isdet = False
    for i in matrix:
        if isinstance(i,list): # Things in matrix are lists?
            if len(i) == len(matrix): # Square shape?
                for j in i: # All numbers?
                    try:
                        j = float(j)
                    except ValueError:
                        isdet = False
            else:
                isdet = False
        else:
            isdet = False
    return isdet

def det_Disp(matrix):
    if is_Det(matrix):
        pass
    else:
        print "Error: Input not a determinant, cannot display"

def det_Eval(matrix):
    print matrix
    except StandardError:
        print "No such value"
    if is_Det(matrix):
        if len(matrix) == 1: # 1x1 determinant
            print matrix[0][0]
            return matrix[0][0]
        elif len(matrix) == 2: # 2x2 determinant
            print matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
            return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0]
        else:
            longdet = matrix # Expands higher-order determinant
            for row1 in longdet:
                for col1 in range(0,len(matrix)-1):
                    row1.append(row1[col1])
            value = 0
            for col2 in range(0,len(matrix)): # Recurse determinant value
                subdet = []
                for row2 in range(1,len(matrix)):
                    subsubdet = []
                    for col3 in range(col2+1,col2+len(matrix)):
                        subsubdet.append(longdet[row2][col3])
                    '''print "Subsubdet:",
                    print subsubdet #***************************'''
                    subdet.append(subsubdet)
                    '''# print "Subdet",
                    print "Subdet:",
                    print subdet #***************************'''
                value += longdet[0][col2] * det_Eval(subdet)
                ##########print value
                '''#print longdet[1][col2],
                #print det_Eval(subdet),
                #print value
            # print longdet'''
            return value
    else:
        print "Error: Input not a determinant, cannot evaluate"

#print det_Eval([[2,3],[4,9]])
#print det_Eval([[6,1,8],[9,9,9],[9,7,4]])
print det_Eval([[8,9,2,3],[4,6,1,8],[9,9,9,9],[1,9,7,4]])

Answer 1

In this line dealing with minors:

 value += longdet[0][col2] * det_Eval(subdet)

you don't take sign into account - sign depends on parity of index of the first line element (col2)