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RE: [Axiom-math] Engineering Application

From: Herb Martin
Subject: RE: [Axiom-math] Engineering Application
Date: Mon, 23 Jan 2006 14:44:52 -0600

>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. 

Yes, it is (overly grand), much like a "wagon
train scout" of the pioneer days pulling out
a many-times-folded map of the route from St.
Louis to California and spending an evening
showing the settlers the things they need to
know to prepare for the trip.

> I think your goal to better understand it is
> very laudable. 

Or "overly grand". <grin>  Thanks for the 
encouragement -- it is much appreciated.

I have not yet reach page 200 and I have 
already learned an amazing amount.

> 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?

Please.  I want to discuss everything, but I
am probably not smart enough yet to figure out
how to ask a good question.

So far, I have been trying to learn Axiom & Maxima
in parallel with reading this book and have only
worked out some simple problems (like imaginary roots
and some differentials.)

I am a bit embarrassed to admit that I don't
really understand how much of the work Axiom
can do, nor really what the full capabilities
of Axiom include.

Even before this book I had entertained the 
belief that it might be possible to learn "a
lot of math" by following along through Calculus
and Differential Equations text -- learning to
the IDEAS, and letting the system do the tedious

This probably wouldn't be sufficient for a 
serious mathematician or engineer, but for me
this is just a (serious) hobby.

Perhaps seeing how to use Axiom to graph a
conformal map, or to work through a Fourier
transform would be interesting BUT this is 
merely the first thing that came to mind when
searching (desperately) for something to 
request -- please substitute ANYTHING your
prefer and I will ask for something else as
soon as I have the prerequisites.

> 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.

I know even less of Macaulay, but believe that 
would be useful, and it certainly would be very
gracious of you.

Please note, that I am NOT modest about my abilities
nor about my intelligence, and any seeming "false
modesty" above is in fact just reality:  There is a
LOT of math covered in the book which I have not studied, 
and even my Calculus and Diff Eq is rusty and spotty
in places.

Also:  I have no particular preference for Maxima versus
Axiom, and so with your help I will focus more of my
attention on Axiom (and Macaulay2).

Both of these fine programs do more than I can currently

Herb Martin

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