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## [Axiom-developer] Curiosities with Axiom mathematical structures

**From**: |
Gabriel Dos Reis |

**Subject**: |
[Axiom-developer] Curiosities with Axiom mathematical structures |

**Date**: |
26 Feb 2006 06:30:45 +0100 |

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

**[Axiom-developer] Curiosities with Axiom mathematical structures**,
*Gabriel Dos Reis* **<=**
**Re: [Axiom-developer] Curiosities with Axiom mathematical structures**, *William Sit*, `2006/02/26`
**Re: [Axiom-developer] Curiosities with Axiom mathematical structures**, *Gabriel Dos Reis*, `2006/02/26`
**RE: [Axiom-developer] Curiosities with Axiom mathematical structures**, *Bill Page*, `2006/02/26`
**Re: [Axiom-developer] Curiosities with Axiom mathematical structures**, *Gabriel Dos Reis*, `2006/02/26`
**Re: [Axiom-developer] Curiosities with Axiom mathematical structures**, *Ralf Hemmecke*, `2006/02/27`
**Re: [Axiom-developer] Curiosities with Axiom mathematical structures**, *Gabriel Dos Reis*, `2006/02/27`
**RE: [Axiom-developer] Curiosities with Axiom mathematical structures**, *Bill Page*, `2006/02/28`

**Re: [Axiom-developer] Curiosities with Axiom mathematical structures**, *Andrey G. Grozin*, `2006/02/26`