[sage-devel] Re: Exterior algebras.

2015-04-08 Thread kcrisman


 Exterior algebras were included as part of 
 http://trac.sagemath.org/ticket/15300 (which was merged into Sage 6.4).

 sage: E.x,y = ExteriorAlgebra(QQ)
 sage: a = x * y + x - 3*y / 2; a
 x^y + x - 3/2*y
 sage: a.interior_product(x)
 y + 1
 sage: a.interior_product(y)
 -x - 3/2


Great.  Any other Grassmann stuff beyond this?  (E.g. regressive 
product.)  Is this interface with similar functionality in Singular or 
elsewhere (and/or the differential forms/manifolds folks)?

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[sage-devel] Re: Exterior algebras.

2015-04-08 Thread Travis Scrimshaw



 Great.  Any other Grassmann stuff beyond this?  (E.g. regressive 
 product.)  Is this interface with similar functionality in Singular or 
 elsewhere (and/or the differential forms/manifolds folks)?


I didn't implement anything like that as I wanted to do the relationship 
with Lie algebras (the boundary/coboundary methods, which might deserve 
some alias...). There are likely many improvements and extensions that can 
be made to this implementation.

Best,
Travis

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

2015-04-07 Thread David Joyner
On Tue, Apr 7, 2015 at 9:12 AM, kcrisman kcris...@gmail.com 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.

2015-04-07 Thread 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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[sage-devel] Re: Exterior algebras.

2015-04-07 Thread Travis Scrimshaw
Exterior algebras were included as part of 
http://trac.sagemath.org/ticket/15300 (which was merged into Sage 6.4).

sage: E.x,y = ExteriorAlgebra(QQ)
sage: a = x * y + x - 3*y / 2; a
x^y + x - 3/2*y
sage: a.interior_product(x)
y + 1
sage: a.interior_product(y)
-x - 3/2

Best,
Travis

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[sage-devel] Re: Exterior algebras.

2010-03-25 Thread 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.

2010-03-25 Thread 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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[sage-devel] Re: Exterior algebras.

2010-03-24 Thread Michael Brickenstein
Singular includes all necessary stuff, see #4539.
Cheers,
Michael

On 24 Mrz., 00:31, javier vengor...@gmail.com wrote:
 Somebody wrote [1] a Reduce (cf. [2]) interface some time ago. If it
 works properly one could try to load Bergmann [3] from it. That would
 give access to plenty of Groebner basis, Hilbert series, Hochschild
 cohomology and many other ring theoretical methods for big families of
 noncommutative algebras. Since Bergmann is written in Lisp, maybe it
 can also be loaded directly from ECL. I don't have any clue how
 complicated interfacing Bergmann could get, though, but if we don't
 have many noncommutative algebra stuff, it might be worth giving it a
 shot.

 Cheers
 J

 [1]http://groups.google.com/group/sage-devel/browse_thread/thread/87e888...

 [1]http://www.reduce-algebra.com/

 [2]http://servus.math.su.se/bergman/

 On Mar 23, 4:34 pm, mmarco mma...@unizar.es wrote:

  Thanks for the code. From what  i see, it does not inherit ideals or
  groebner basis. I will try to take a look at that.



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[sage-devel] Re: Exterior algebras.

2010-03-23 Thread mmarco
Thanks for the code. From what  i see, it does not inherit ideals or
groebner basis. I will try to take a look at that.

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[sage-devel] Re: Exterior algebras.

2010-03-23 Thread javier
Somebody wrote [1] a Reduce (cf. [2]) interface some time ago. If it
works properly one could try to load Bergmann [3] from it. That would
give access to plenty of Groebner basis, Hilbert series, Hochschild
cohomology and many other ring theoretical methods for big families of
noncommutative algebras. Since Bergmann is written in Lisp, maybe it
can also be loaded directly from ECL. I don't have any clue how
complicated interfacing Bergmann could get, though, but if we don't
have many noncommutative algebra stuff, it might be worth giving it a
shot.

Cheers
J

[1] 
http://groups.google.com/group/sage-devel/browse_thread/thread/87e88893228aed59/a71d7372949fbfe2?lnk=gstq=reduce#a71d7372949fbfe2

[1] http://www.reduce-algebra.com/

[2] http://servus.math.su.se/bergman/

On Mar 23, 4:34 pm, mmarco mma...@unizar.es wrote:
 Thanks for the code. From what  i see, it does not inherit ideals or
 groebner basis. I will try to take a look at that.

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[sage-devel] Re: Exterior algebras.

2010-03-21 Thread bump
 (suggestions, or better patches, to improve that example are welcome)

Earlier I posted code to construct exterior algebras in Sage here:

http://sporadic.stanford.edu/bump/exterior.sage

This uses CombinatorialAlgebras. Currently the preferred method of
constructing a ring is to implement it as a subclass of
CombinatorialFreeModule
using convenient hooks that are provided there. I reimplemented the
exterior
algebra that way and for comparison, here it is:

http://sporadic.stanford.edu/bump/exterior1.sage

Both methods are about the same number of lines of code, but the
second method
is cleaner and easier if you know how to do it. I think both rings
have identical behavior.

I would like to comment on the deprecation warnings in
combinatorial_algebra.py.

The method of constructing a ring in combinatorial_algebra.py is quick
and convenient. I do agree that the preferred method is better. I
think
that any construation that is to be put into sage should not use
CombinatorialAlgebras.

However I think the deprecation warning (just deprecated - don't
use!)
in combinatorial_algebras.py is not helpful. After all,
the old method does work and is convenient and
quick. If I want a quick and dirty ring for some experiment I might
use it.

There is the deprecation warning but no pointer towards a better way.

Dan



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

2010-03-20 Thread 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
 
  http://www.sagemath.org/doc/reference/coercion.html
 
  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 nthi...@users.sf.net
http://Nicolas.Thiery.name/

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[sage-devel] Re: Exterior algebras.

2010-03-19 Thread bump
 I hope other people respond, too.  I would suggest looking at

 http://www.sagemath.org/doc/reference/coercion.html

 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.

Dan

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

2010-03-19 Thread Mike Hansen
On Fri, Mar 19, 2010 at 1:00 PM, bump b...@match.stanford.edu wrote:
 I hope other people respond, too.  I would suggest looking at

 http://www.sagemath.org/doc/reference/coercion.html

 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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[sage-devel] Re: Exterior algebras.

2010-03-19 Thread bump
On Mar 19, 10:46 am, mmarco wrote:
 I would need to deal with exterior algebras, and as far as i have
 seen, they are not defined in sage. I could try working on
 implementing them, but i have no idea how to build the corresponding
 class in sage.

 What should be the appropiate aproach? Is there some documentation
 about how to build new ring classes?.

Here is an implementation of exterior algebras in sage:

http://sporadic.stanford.edu/bump/exterior.sage

This uses combinatorial_algebra.py. That has a deprecation
warning (do not use). I think that means that you should not
use it for code that is going into Sage itself, but it sure is
handy to be able to implement a ring in just a few lines.

The exterior algebra on [0, 1, 2, 3]

After attaching the file, you can do this:

sage: E = ExteriorAlgebra(4); E
sage: [x0, x1, x2, x3] = E.generators()
sage: x0*x1
x0*x1
sage: x1*x0
-x0*x1
sage: (x0+x1*x2+x3)*x0
-x0*x3 + x0*x1*x2

Daniel Bump

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