[sage-devel] Re: Anyone developing Differential System and Cartan--Kaehler in sage?

[Paul Leopardi]

Back in 2008, I said I was interested in adding support for Clifford 
algebras / Geometric Algebra to Sage. Since then I have found out that 
there is some support available in Axiom. Now that there is renewed 
interest in Exterior algebras, I would like to better understand how to 
incorporate both the Exterior algebras and the Clifford algebras into Sage 
in a way that makes sense both in terms of coercion and in terms of 
Categories, Is there an existing structure we could bolt our 
implementations into, or do we need to define these ourselves? I would much 
prefer elegance and logical consistency over convention. I do know that 
there are lots of conventions hanging around Clifford algebras and spinors, 
but I don't want these to get in the way. 

As a prototype, I added a Python interface to GluCat , 
implemented via Cython code. (GluCat implements both the Clifford and the 
exterior product, as well as inner products and the left contraction.) I 
began the Python interface at Sage Days 10 in Nancy, and am still refining 
this interface in anticipation of Cython v0.16. I did not try to add this 
to Sage (1) because it only implements a special case (up to 64 generators, 
Real field via float, double, dd_real or qd_real), (2) because it employs 
its own convention for generators and basis elements (signed index sets), 
(3) because I did not understand coercion or Categories in Sage, (4) 
because my ARC grant applications which included this work were 
unsuccessful, but mostly (5) because I did not make the time to do this.

-- 
To post to this group, send an email to sage-devel@googlegroups.com
To unsubscribe from this group, send an email to 
sage-devel+unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URL: http://www.sagemath.org

[sage-devel] Re: Anyone developing Differential System and Cartan--Kaehler in sage?

[Joris Vankerschaver]

Hi Abraham,

This sounds like a great project -- I've always wanted to read the
Bryant/Griffiths books on EDS but I've always been too lazy to do the
computations myself and get a proper grip on the subjects.  Such a
Sage package could be a great help.

I'm not entirely happy with the way that the current implementation of
DifferentialForms relies so much on CoordinatePatch, and I'm sure
there's room for improvement here.

All the best,
Joris




On Dec 15, 5:42 pm, adsmith  wrote:
> On Dec 15, 8:48 am, Jason Grout  wrote:
>
> > On 12/15/11 7:38 AM, adsmith wrote:
>
> > I'm not an expert in the area, but 
> > ishttp://www.sagemath.org/doc/reference/tensor.htmlusefulto you?  You
> > can see fromhttp://trac.sagemath.org/sage_trac/ticket/9650someof the
> > people involved in that code.
>
> > Thanks,
>
> > Jason
>
> Hi Jason,
>
> Thanks for the tip.  That is a start, and I'll dig into that code a
> bit.
>
> The great advantage of the packages I want to emulate is that they
> have no notion of coordinates at all, just a graded ideal defined by a
> set of generators.  Now, I'm sure with Tensor's coordinate patch
> system, one could make an interface that automatically generates and
> completely hides the underlying coordinates, but ideally they need not
> exist at all.

-- 
To post to this group, send an email to sage-devel@googlegroups.com
To unsubscribe from this group, send an email to 
sage-devel+unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URL: http://www.sagemath.org

[sage-devel] Re: Anyone developing Differential System and Cartan--Kaehler in sage?

[adsmith]

On Dec 15, 8:48 am, Jason Grout  wrote:
> On 12/15/11 7:38 AM, adsmith wrote:
>
> I'm not an expert in the area, but 
> ishttp://www.sagemath.org/doc/reference/tensor.htmluseful to you?  You
> can see fromhttp://trac.sagemath.org/sage_trac/ticket/9650some of the
> people involved in that code.
>
> Thanks,
>
> Jason

Hi Jason,

Thanks for the tip.  That is a start, and I'll dig into that code a
bit.

The great advantage of the packages I want to emulate is that they
have no notion of coordinates at all, just a graded ideal defined by a
set of generators.  Now, I'm sure with Tensor's coordinate patch
system, one could make an interface that automatically generates and
completely hides the underlying coordinates, but ideally they need not
exist at all.

-- 
To post to this group, send an email to sage-devel@googlegroups.com
To unsubscribe from this group, send an email to 
sage-devel+unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URL: http://www.sagemath.org

[sage-devel] Re: Anyone developing Differential System and Cartan--Kaehler in sage?

[Jason Grout]

On 12/15/11 7:38 AM, adsmith wrote:

Hi everyone,

I am in need of a package to carry out computations in exterior
algebra, differential ideals, and various aspects of the Cartan--
Kähler theorem.

I have used Jeanne Clelland's "Cartan" package for Maple[1]
extensively, and I have been thinking about reproducing it in sage
(with Jeanne's blessing).  I am new to sage but very experienced in
python and capable of producing an adequate solution for myself and my
immediate colleagues.  But, before I jump headlong into it, I was
wondering whether anyone else working on similar packages.  Basic
functionality for
alternating forms in a coordinate-free manner is the first
infrastructure I'd be looking for, analogous to "difforms" in Maple,
or the "Forms" package by Yu&  Clelland [1].


[1]: http://euclid.colorado.edu/~jnc/Maple.html



I'm not an expert in the area, but is 
http://www.sagemath.org/doc/reference/tensor.html useful to you?  You 
can see from http://trac.sagemath.org/sage_trac/ticket/9650 some of the 
people involved in that code.


Thanks,

Jason



--
To post to this group, send an email to sage-devel@googlegroups.com
To unsubscribe from this group, send an email to 
sage-devel+unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URL: http://www.sagemath.org