python求矩阵的行列式_python行列式算法?

from itertools import combinations,permutations
#检测
#生成一个排序函数
#计算逆序数
#计算行列式

Matrix = [[1,5,3],[7,4,3],[2,4,232]]
#检测
def test(Matrix):
    #检测是否是一个方阵
    for i in Matrix:
        if len(i)==len(Matrix):
            pass
            for ii in i:
                if type(ii)==type(101):
                    pass

                else:
                    try:
                        b = 3/0
                    except:
                        print("请检查您输入的矩阵")
                        print("不可靠的结果")
                        break
        else:
            try:
                b = 3/0

            except:
                print("请检查您输入的矩阵")
                print("不可靠的结果")
                break
            
    #输出行列式阶数和n!
    sum = 1
    for i in range(len(Matrix)+1):
        sum *= i
        
    return len(Matrix),sum


def InversionNumber(l):
    sum = 0
    l0 = []
    for i in range(len(l)):
        if l[i] < l[i-1] and i-1 >= 0:
           l0.append(l[i-1])
           sum += 1

        for k in range(i-1):
            if l[i] < l[k]:
                sum += 1

    return (-1)**sum


def Permute(n):
    #返回一个列表,包含整个序列,最后一位表明(-1)^ε
    l = []
    for k in range(1,n+1):
            l.append(k)
    L = list(permutations(l, len(l)))
    for i in L:
        L[L.index(i)]=list(i)

    for i in L:
        i.append(InversionNumber(i))

    return L

def main(Matrix):
    l,S = test(Matrix)
    L = Permute(l)
    sum = 0
    for i in L:
        sum1 = 1
        for ii in range(len(Matrix)):
            sum1 *= Matrix[ii][i[ii]-1]
        sum1 *= i[-1]
        sum += sum1
    return sum

if __name__ == "__main__":
    det = main(Matrix)