Python实现行列式计算

数学公式：
　　

代码：

# 逆序数

def getInversion(numlist):

    count = 0

    for i in range(1,len(numlist)):

        subscript = numlist[i]

        for j in range(i):

            if subscript < numlist[j]:

                count += 1

    return count

D = 0

# 全排列，求每项的积

def permutation(dd,ilist,jlist,index):

    global D

    for i in range(index,len(jlist)):

        if index == len(jlist)-1:

            term = 1

            for ii in range(len(ilist)):

                i = ilist[ii]

                j = jlist[ii]

                term *= dd[i][j]

            if getInversion(jlist) % 2 == 0:

                D += term

            else:D -= term

            return

        tmp = jlist[index]

        jlist[index] = jlist[i]

        jlist[i] = tmp

        permutation(dd,ilist,jlist,index+1)

        tmp = jlist[index]

        jlist[index] = jlist[i]

        jlist[i] = tmp

if __name__ == '__main__':

    dd = [[1, 2, -4], [-2, 2, 1], [-3, 4, -2]]

    dd =[[1,1,1,1],[-1,2,1,3],[1,4,1,9],[-1,8,1,27]]

    jlist = []

    ilist = []

    for ii in range(len(dd)):

        ilist.append(ii)

        jlist.append(ii)

    permutation(dd,ilist,jlist,0)

    print(D)