def tupleInList(fx, x=[]):
	for i in range(len(fx)):
		x.append(i+1)
	return zip(x, fx)

def solve(s):
	return R.lagrange_polynomial(s)

def nextSeq(l, f):
	exec('x = ' + str(l+1))
	exec('f = ' + str(f).replace('^', '**'))
	return f

if __name__ == '__main__':
	R = PolynomialRing(QQ, 'x')
	fx = [1, 4, 9, 16, 25]
	s = tupleInList(fx)
	print s
	f = solve(s)
	l = len(fx)

	print 'Formula: ', f
	print nextSeq(l, f)