Re: [sage-devel] Re: Exterior algebras.

[David Joyner]

On Tue, Apr 7, 2015 at 9:12 AM, kcrisman  wrote:
> Sorry for dredging this up from the depths...
>
> So I see that http://trac.sagemath.org/ticket/14418 has a more explicit
> interface.  What gets me wondering about the current state in Sage is an
> article in the most recent Notices which contains a reference to
> https://sites.google.com/site/grassmannalgebra/thegrassmannalgebrabook which
> has a fairly fully-featured (apparently) computational set of Mma extensions
> for all sorts of Grassmann algebra types - including the "internal product"
> and "regressive product".  Just putting this out there in case anyone knows
> anything about it - or even the author, in the event that it were possible
> to just "port" things to Sage.
>

Sympy (in Sage) as a lot of this stuff:
http://docs.sympy.org/0.7.4/modules/galgebra/GA.html

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Re: [sage-devel] Re: Exterior algebras.

[kcrisman]

Sorry for dredging this up from the depths...

So I see that http://trac.sagemath.org/ticket/14418 has a more explicit 
interface.  What gets me wondering about the current state in Sage is an 
article in the most recent Notices which contains a reference 
to https://sites.google.com/site/grassmannalgebra/thegrassmannalgebrabook 
which has a fairly fully-featured (apparently) computational set of Mma 
extensions for all sorts of Grassmann algebra types - including the 
"internal product" and "regressive product".  Just putting this out there 
in case anyone knows anything about it - or even the author, in the event 
that it were possible to just "port" things to Sage.

>

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Re: [sage-devel] Re: Exterior algebras.

[Michael Brickenstein]

Hi!

For  the simple case of  exterior algebras
there exists already ring creation code in
the track ticket.
It might be a little bit hacky, but it works for now.
What is mainly needed, is cleaning the construction for Sage
class hierarchies and coercions.

Cheers,
Michael

Am 25.03.2010 um 10:10 schrieb mmarco:

> Ok, i have seen how to define them in singular properly. Something
> like this:
> 
> ring r=0,(x,y,z),lp;
> def a=nc_algebra(-1,0);
> setring a;
> ideal i=x2,y2z2;
> i=std(i);
> qring e=i;
> setring e;
> 
> creates an exterior algebra. The command Exterior() from the package
> nctools.lib does essentially the same.
> 
> I think the best way to implement this in sage would be to build a
> class that wraps this singular cosntruction in the same way that
> PolynomialRing wraps the singular rings. Any suggesttion in that sense?
> 
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Re: [sage-devel] Re: Exterior algebras.

[Nicolas M. Thiery]

On Fri, Mar 19, 2010 at 01:00:38PM -0700, bump wrote:
> > I hope other people respond, too.  I would suggest looking at
> >
> > 
> >
> > and the code in sage/algebras/quatalg (for quaternion algebras): use
> > this as one model for how to implement a noncommutative algebra.
> 
> Another place to look is algebras/iwahori_hecke_algebra.py,
> showing how to an algebra as a subclass of CombinatorialFreeModule.

Yup. And the canonical example to look at shall be:

sage: A = AlgebrasWithBasis(QQ).example()
sage: A??

(suggestions, or better patches, to improve that example are welcome)

Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" 
http://Nicolas.Thiery.name/

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Re: [sage-devel] Re: Exterior algebras.

[Mike Hansen]

On Fri, Mar 19, 2010 at 1:00 PM, bump  wrote:
>> I hope other people respond, too.  I would suggest looking at
>>
>> 
>>
>> and the code in sage/algebras/quatalg (for quaternion algebras): use
>> this as one model for how to implement a noncommutative algebra.
>
> Another place to look is algebras/iwahori_hecke_algebra.py,
> showing how to an algebra as a subclass of CombinatorialFreeModule.

There's also some code up at
http://trac.sagemath.org/sage_trac/ticket/4539 which has some code for
exterior algebras provided by Singular.

--Mike

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