here's why it cannot be done: data TwoByTwoMatrix = TTM Integer Integer Integer Integer instance Num TwoByTwoMatrix where fromInteger i = TTM i 0 0 i (TTM a b c d) + (TTM e f g h) = TTM (a+e) (b+f) (c+g) (d+h) negate m = (fromInteger (-1)) * m (TTM a b c d) * (TTM e f g h) = TTM (b*g+a*e) (a*f+b*h) (d*g+c*e) (c*f+d*h) It should follow that the above is a (non-abelian) ring, as required (all definitions follow the standard matrix addition/multiplication/addition convensions). n = (TTM 0 1 0 0) then: n * (n + 1) = n. Since n has odd entries, it cannot be divided by 2 (more precisely: we cannot find an m s.t. n * 2 = m). Best, Sebastiaan On Wed, Dec 16, 2020 at 6:14 PM Henning Thielemann < lemming@henning-thielemann.de> wrote:
On Wed, 16 Dec 2020, Tom Smeding wrote:
You say 'abs x = x/2', but what's that (/)? For example, what is 'abs' supposed to give when called on (the representation of) the polynomial X^2 + 3X + 2?
I meant it this way:
instance (Fractional a) => Num (Polynomial a) where abs = fmap (/2) _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.