RE: [Axiom-math] Engineering Application

[Bill Page]

On January 23, 2006 6:22 AM Herb Martin wrote:
> ... 
> I too am (newly) interested in Algebraic Geometry
> and would prefer to pursue that in Axiom or another
> free CAS (rather than Maple) since this is only a
> hobby interest for me.
> 
> >From the links you (so kindly) offered I also found
> the following:
> 
> Macaulay2 Home Page http://www.math.uiuc.edu/Macaulay2/
>   A software system devoted to supporting research
>   in algebraic geometry and commutative algebra.
>   
> Computations in algebraic geometry with Macaulay 2, 
>  edited by David Eisenbud, Daniel R. Grayson, Michael
>  E. Stillman, and Bernd Sturmfels.  Springer-Verlag
>  September 25, ISBN 3-540-42230-7, $44.95. 
>  http://www.math.uiuc.edu/Macaulay2/Book/  (FREE DOWNLOAD)
> 
> In no way am I trying to move the discussion away
> from Axiom, but I am interest in the subjects no
> matter what the tools (if the price is right.)
>

I think it is entirely appropriate to discuss Macaulay here.
In fact if there is continued interest, I would be very happy
to look into providing a web interface for Macaulay at the
Axiom Wiki, e.g.

  \begin{macaulay}
  R = QQ[x_1..x_4] 
  M = matrix{{x_1,x_2},{x_3,x_4}}
  D = det M
  T = trace M
  I = ideal {D, T}
  J = ideal M^2 
  radical I == radical J 
  \end{macaulay}

with the result displayed on the web page, along with Axiom
and Reduce.
  
> And these links seem related, depending on the
> relationship with Algebraic Topology and if Geometric
> Algebra has the same meaning (do they relate?)

I would yes to Algebraic Topology and not to Geometric Algebra -
although Geometrical is interesting in it's own right.

I think Algebraic Topology is formally related via category
theory, but the methods are very different.

> 
> Algebraic Topology
>   Homotopy & homology spaces are discussed beginning 
>   in Chapter 0 (Geometric introduction)
>   http://www.math.cornell.edu/~hatcher/AT/ATpage.html
>
> Clifford's Geometric Algebra of Physical Space (APS). 
>   http://www.uwindsor.ca/users/b/baylis/main.nsf
>   The intention is to explain the use of paravectors 
>   in the algebra to model spacetime.
>  Relativity in Introductory Physics
>  http://arxiv.org/abs/physics/0406158 
>  Also available: GAWorkBook
> 
> Disclosure:  I am directly trying to gain a (much) 
> better appreciation and understanding of the 
> "The Road to Reality: A Complete Guide to the Laws 
> of the Universe" by Roger Penrose.
>  

Although the title of Penrose's book sounds overly grand, it is
none the less a very serious book on differential geometry as
applied to physics. I think your goal to better understand it is
very laudable. If there is anything in particular in this book
that you would like to discuss, I would be glad participate.
Maybe we can do some examples using Axiom?

Regards,
Bill Page.