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Date: Sun, 07 Feb 2016 17:46:18 -0500
From: daly <daly@axiom-developer.com>
To: Ralf Hemmecke <ralf@hemmecke.org>
Subject: Re: [Axiom-developer] [fricas-devel] Bug in conditional exports

>> No, LinGroebnerPackage is not Groebner walk.  It is an older method
>> which is limited to zero dimensional ideals (it has name attached but
>> ATM I have no reference handy).

>You probably mean FGLM.
>http://www-polsys.lip6.fr/~jcf/Papers/FGLM.pdf

>I should have stated that in the first place, but I was desparately
>looking for Gr=C3=B6bner Walk and wrote the mail to quickly.

>> And even in case of zero dimensional ideals it is likely to be less
>> efficient than Groebner walk.

>Since I need(ed) something for non-zero dimensional ideal, I haven't
>actually looked intensively into the code. Maybe LinGroebnerPackage
>actually implements FGLM, but I wonder why someone would not put FGLM ther=
e.

>Maybe it was implemented by one of the authors of the paper. Tere are at
>least a number of files that carry the name Gianni in them.
>Tim, do you happen to know the history?

I will check with Gianni and get back to you if she replies.

>Anyway, it would be good if someone implements Groebner Walk in FriCAS.
>Perhaps a nice little project for GSoC 2016.

>Ralf

Tim Daly

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Date: Sun, 28 Feb 2016 18:59:45 -0500 (EST)
From: daly <daly@axiom-developer.com>
To: axiom-developer@nongnu.org
Subject: [Axiom-developer] Towards an exploratory medium for mathematics

In this blog post, the author makes the point that things like music
notation, photoshop, and other media recording and manipulation
decisions have changed the way the world thought. Music notation
allowed music to be captured and reproduced without hearing the
original. Photoshop adds memes like the lasso, the stamper, and the
eyedropper as ways of manipulating images. The result is an explosion
of creativity not possible in other ways.

The author makes the point that we can, and need to, exploit the
new media in order to foster exploratory mathematics.

Towards an exploratory medium for mathematics
http://cognitivemedium.com/emm/emm.html

It would be interesting to connect his SVD example to the Axiom
Browser, the interpreter, and use it to drive a canvas on a web
page. Note that Axiom now has a connection to COQ, although that
is not explicitly exposed at the algebra level (yet).

In any case, this seems worth thinking about.

Tim
http://daly.axiom-developer.org



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