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

From: Bill Page
Subject: RE: [Axiom-developer] Curiosities with Axiom mathematical structures
Date: Mon, 27 Feb 2006 19:45:33 -0500

On February 26, 2006 12:31 AM Gabriel Dos Reis wrote:
> ... 
>   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).  

The following is a prettier (I think) rendition of these diagrams
done using GraphViz. It also contains a couple of corrections:

When viewed as pdf and in some dvi viewers this diagram includes
live hyperlinks to the appropriate source files.

Bill Page.

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