Compute a symbolic determinant in python

symbolic_determinant.py

import functools
import operator


def permutations_impl(xs):
	if len(xs) == 1:
		yield xs, 1
	else:
		for i in range(len(xs)):
			xs[0], xs[i] = xs[i], xs[0]
			for subperm, subsign in permutations_impl(xs[1:]):
				yield [xs[0]] + subperm, subsign * (1 if i == 0 else -1)
			xs[0], xs[i] = xs[i], xs[0]


def permutations(xs):
	xs_copy = list(xs)
	return permutations_impl(xs_copy)


def symbolic_determinant(x):
	v = 0.
	for p, s in permutations(range(len(x))):
		v += s * functools.reduce(operator.mul, [row[pi] for row, pi in zip(x, p)])
	return v

what is this?