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

[Bill Page]

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:

http://wiki.axiom-developer.org/book--main--1/Endpaper3

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

Regards,
Bill Page.