Calculating a determinant in Lua - math

Question

I'm trying to calculate determinants with any order using Lua. I can calculate determinants for order less than 4, but not for greater equals than 4 ones.
I have a 4x4 matrix and its determinant with the program is 0, but the real solution is 56.
I don't know if the problem is in getSubmatrix method or is in detMat method, because I don't have any error message from the console.
I've ported the methods from my own java code, where it works fine.
Here's all my code:
function numMat(n, A)
local S = {}
for i = 1, #A, 1 do
local T = {}
S[i] = T
for j =1, #A[1], 1 do
T[j] = n * A[i][j]
end
end
return S
end
function sumMat(A, B)
local C = {}
for i = 1, #A do
local D = {}
C[i] = D
for j = 1, #A[1] do
D[j] = A[i][j] + B[i][j]
end
end
return C
end
function subMat(A, B)
return sumMat(A, numMat(-1, B))
end
function printMatrix(A)
for i, v in ipairs(A) do
for j, w in ipairs(v) do
print(w)
end
end
end
function escalarProduct(u, v)
local w = 0
for i = 1, #u do
w = w + u[i] * v[i]
end
return w
end
function prodMat(A, B)
local C = {}
for i = 1, #A do
C[i] = {}
for j = 1, #B[1] do
local num = A[i][1] * B[1][j]
for k = 2, #A[1] do
num = num + A[i][k] * B[k][j]
end
C[i][j] = num
end
end
return C
end
function powMat(A, power)
local B = {}
local C = {}
C = A
for i = 1, power - 1 do
B = prodMat(C, A)
C = B
end
return B
end
function trasposeMat(A)
local B = {}
for i = 1, #A do
local C = {}
B[i] = C
for j = 1, #A[1] do
C[j] = A[j][i]
end
end
return B
end
function productDiag(m)
local prod = 1
for i = 1, #m do
for j = 1, #m do
if i == j then prod = prod * m[i][i] end
end
end
return prod
end
function isDiagonal(A)
for i = 1, #A do
for j = 1, #A do
if i ~= j and A[i][j] ~= 0 then return false end
end
end
return true
end
function isTriangSup(m)
for i = 1, #m do
for j = 1, i do
if m[i][j] == 0 then return true end
end
end
return false
end
function isTriangInf(m)
return isTriangSup(trasposeMat(m))
end
function isTriang(m)
if(isTriangSup(m)) then return true
else
return false
end
end
function getSubmatrix(A, rows, cols, col)
local submatrix = {}
local k = 1
for j = 1, cols do
--local D = {}
--submatrix[j] = D
if j == col then
break
end
for i = 2, rows do
submatrix[i-1][k] = A[i][j]
--D[k] = A[i][j]
end
k = k + 1
end
return submatrix
end
function det2Mat(A)
assert(#A == 2 and #A == #A[1], 'Error: The matrix must be squared, order 2.')
return A[1][1] * A[2][2] - A[1][2] * A[2][1]
end
function det3Mat(A)
assert(#A == 3 and #A == #A[1], 'Error: The matrix must be squared, order 3.')
s1 = A[1][1] * A[2][2] * A[3][3] + A[2][1] * A[3][2] * A[1][3] + A[1][2] * A[2][3] * A[3][1]
s2 = A[1][3] * A[2][2] * A[3][1] + A[1][2] * A[2][1] * A[3][3] + A[2][3] * A[3][2] * A[1][1]
return s1 - s2
end
function detMat(A)
local submatrix = {}
local det
local sign = 1
local rows = #A
local cols = #A[1]
assert(rows == cols, 'Error: The matrix must be squared.')
if rows == 1 then
return A[1][1]
end
if rows == 2 then
return det2Mat(A)
end
if rows == 3 then
return det3Mat(A)
end
if isDiagonal(A) or isTriang(A) then return productDiag(A) end
if rows > 3 then
for column = 1, cols do
submatrix = getSubmatrix(A, rows, cols, column)
det = det + sign * A[1][column] * detMat(submatrix)
sign = -sign
end
end
return det
end
A = {{1, 3}, {5, 6}}
B = {{2, 4}, {3, 1}}
C = {{2, 3, 4}, {-5, 4, 7}, {7, 1, 0}}
D = {{2, 0, 0, 0}, {0, 4, 0, 0}, {0, 0, 7, 0}, {0, 0, 0, 6}}
E = {{2, 3, 4, -3}, {-5, 4, 7, -2}, {7, 1, 0, 5}, {3, 4, 5, 6}}
--printMatrix(numMat(-1, A))
--printMatrix(sumMat(A, B))
--printMatrix(subMat(A, B))
--print(escalarProduct({1, 3}, {5, 6}))
--printMatrix(prodMat(A, B))
--printMatrix(trasposeMat(A))
--printMatrix(powMat(A, 2))
--printMatrix(powMat(A, 3))
print(detMat(A))
print(detMat(B))
print(detMat(C))
print(detMat(D))
print(detMat(E)) --The solution must be 56
And the console solution is:
-9
-10
1
336
0
The error is when I want to find out the determinant of the matrix E.