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Re: [Axiom-developer] Curiosities with Axiom mathematical structures

From: Martin Rubey
Subject: Re: [Axiom-developer] Curiosities with Axiom mathematical structures
Date: 28 Feb 2006 08:38:14 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

This problem was discussed in a thesis at St. Andrews, I forgot by whom but I
can look it up. In fact it seems that this problem cannot be properly solved
with Aldor. There was some discussion on this list, too.

The reason is 

Rng(): Category == Join(AbelianGroup,SemiGroup)

would give a problem...


Gabriel Dos Reis <address@hidden> writes:

> 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
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