[Axiom-developer] Curiosities with Axiom mathematical structures

[Gabriel Dos Reis]

Hi,

  The recent discussions about Axiom/Aldor being object-oriented or
not, whether Axiom could be made to be "truly categorial" or not
reminded be of a curiosity I found in Axiom's hierarchy for
mathematical structures.

  In the impressive diagram titled "Basic Agebra Hierarchy" displayed
in the Axiom Book (I only have a copy of the edition copyrighted 1992,
NAG), AbelianSemiGroup is not "derived" from SemiGroup, and similarly
AbelianMonoid is not "derived" from Monoid.  I find that curious as it
goes counter the mathematical fact that an AbelianMonoid *is* a
Monoid, with an additional algebraic law (commutation).  


  Does anyone know the reason of those curiosities?

  (A year or so ago, in a discussion with a friend I attributed those
anomalies to object-orientation artifacts.  I would be glad to see
that disproved...)

Thanks,

-- Gaby
PS: libalgebra has similar curiosities