Fix some nN, and let x=(x1,x2,,xn) be a tuple of length n, containing only numerical data. We define the symmetric part of x to be the tuple: (2x1+xn,2x2+xn1,,2xn+x1) and the anti-symmetric part of x to be the tuple: (2x1xn,2x2xn1,,2xnx1) Define a function symmetric which accepts a tuple x, and returns a list containing two items: the symmetric part of x, followed by the anti-symmetric part of x