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

From: Gabriel Dos Reis
Subject: Re: [Axiom-developer] Curiosities with Axiom mathematical structures
Date: 02 Mar 2006 20:42:13 +0100

"Bill Page" <address@hidden> writes:

| 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.

Thanks; I'll send it to friends with whom we are looking at "concepts".
That will save me from having to scan that page of the book.

-- Gaby

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