Degree?

[clayrat]

For consistency, degree for Ints in Prelude is defined via abs, whereas here you reuse the version for Numbers, which is simply a constant 1.

I'm actually wondering why degree is even required, since (AFAIK) its' only usage is during the proof that a generalized GCD algorithm exists for a chosen ring.

[clayrat]

Ah, I was wrong, it is actually used in the division algorithm itself, e.g., https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Euclidean_division

However, we need not to redefine the division algorithm, as we have to provide div and mod separately. So it seems degree is still extraneous.

[rgrempel]

To be honest, I had not really understood what degree was intended to do -- I will review when I get a chance in light of this discussion:

purescript/purescript-prelude#99

[garyb]

Regardless of the issues brought up in that description, degree for integers is definitely abs. See the examples on Wikipedia for instance:

• ℤ, the ring of integers. Define f(n) = |n|, the absolute value of n.

A constant degree of 1 suggests the type is actually a Field, meaning ∀ x y. x `mod` y = 0.