In hoc signo vinces (Was: Revamping the numeric classes)

Marcin 'Qrczak' Kowalczyk wrote:

JK> Now, signum and abs seem to be quite distincts beasts. Signum seem JK> to require Ord (and a generic zero...).

Signum doesn't require Ord. signum z = z / abs z for complex numbers.

Thank you, I know. And I ignore it. Calling "signum" the result of a vector normalization (on the gauss plane in this case) is something I don't really appreciate, and I wonder why this definition infiltrated the prelude. Just because it conforms to the "normal" definition of signum for reals? Again, a violation of the orthogonality principle. Needing division just to define signum. And of course a completely different approach do define the signum of integers. Or of polynomials... Jerzy Karczmarczuk