ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 12 Aug 2011 05:22:23 -0500Infinite dimensional Lie algebras in Sagehttp://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/Dear Sage community,
I'm considering giving Sage a spin. Having the scripting possibilities that python offers at one's disposal seems very appealing.
But I would first like to know if - short of writing the module I need in python - Sage is currently capable of addressing the kind of problems I am interested in.
I mainly work with infinite dimensional Lie algebras such as the [Virasoro algebra](http://en.wikipedia.org/wiki/Virasoro_algebra). Is there an easy way to implement such algebras in Sage, by specifying structure constants or something like that?Mon, 08 Aug 2011 00:32:34 -0500http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/Answer by niles for <p>Dear Sage community,</p>
<p>I'm considering giving Sage a spin. Having the scripting possibilities that python offers at one's disposal seems very appealing.</p>
<p>But I would first like to know if - short of writing the module I need in python - Sage is currently capable of addressing the kind of problems I am interested in.
I mainly work with infinite dimensional Lie algebras such as the <a href="http://en.wikipedia.org/wiki/Virasoro_algebra">Virasoro algebra</a>. Is there an easy way to implement such algebras in Sage, by specifying structure constants or something like that?</p>
http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?answer=12560#post-id-12560Hi @Gonneman,
Glad to hear you're thinking about Sage :) I am not aware of a general constructor for arbitrary Lie algebras, although there is substantial functionality related to [certain Lie group computations](http://www.sagemath.org/doc/thematic_tutorials/lie.html). Beyond that, the best way to answer your question is probably to browse the [reference manual](http://www.sagemath.org/doc/reference/index.html) (e.g. the section on [Rings](http://www.sagemath.org/doc/reference/rings.html)) and see if there is enough functionality for you to do the computations you're interested in. There is also documentation for various basic [constructions](http://www.sagemath.org/doc/constructions/index.html) in Sage.
Mon, 08 Aug 2011 01:57:49 -0500http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?answer=12560#post-id-12560Comment by Gonneman for <p>Hi <a href="/users/446/gonneman/">@Gonneman</a>,</p>
<p>Glad to hear you're thinking about Sage :) I am not aware of a general constructor for arbitrary Lie algebras, although there is substantial functionality related to <a href="http://www.sagemath.org/doc/thematic_tutorials/lie.html">certain Lie group computations</a>. Beyond that, the best way to answer your question is probably to browse the <a href="http://www.sagemath.org/doc/reference/index.html">reference manual</a> (e.g. the section on <a href="http://www.sagemath.org/doc/reference/rings.html">Rings</a>) and see if there is enough functionality for you to do the computations you're interested in. There is also documentation for various basic <a href="http://www.sagemath.org/doc/constructions/index.html">constructions</a> in Sage.</p>
http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?comment=21406#post-id-21406Thanks a lot for the help Niles and Benjaminfjones. Now I know where to start!Mon, 08 Aug 2011 18:14:18 -0500http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?comment=21406#post-id-21406Answer by benjaminfjones for <p>Dear Sage community,</p>
<p>I'm considering giving Sage a spin. Having the scripting possibilities that python offers at one's disposal seems very appealing.</p>
<p>But I would first like to know if - short of writing the module I need in python - Sage is currently capable of addressing the kind of problems I am interested in.
I mainly work with infinite dimensional Lie algebras such as the <a href="http://en.wikipedia.org/wiki/Virasoro_algebra">Virasoro algebra</a>. Is there an easy way to implement such algebras in Sage, by specifying structure constants or something like that?</p>
http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?answer=12561#post-id-12561As far as I know, facilities for doing Lie theoretic computations directly in a Lie algebra in Sage are sparse. As @Niles mentions, there are facilities for dealing with roots, weights, and Weyl groups, but that's probably not what you're looking for if you are working in the Virasoro algebra.
Of course there is fantastic support for all kinds of linear algebra, which most Lie algebra computations boil down to anyway ...
Here are some other resources, though:
* Sage has a `CombinatorialFreeModule` class which is inherited from to construct many non-commutative / non-associative algebras (e.g. see the documentation and source code for `IwahoriHeckeAlgebraT`). AFAIK, this class is restricted to finite rank modules.
* GAP (which is included in Sage) has several packages (both standard and optional) for doing Lie algebra calculations. See:
- http://www.gap-system.org/Manuals/doc/htm/ref/CHAP061.htm#SECT011
- The SLA package for GAP: http://www.science.unitn.it/~degraaf/sla.html
Also, the folks on the [sage-combinat-devel](http://groups.google.com/group/sage-combinat-devel) and [sage-algebra](https://groups.google.com/group/sage-algebra?hl=en) google groups would probably be interested in this topic if you post your question there.Mon, 08 Aug 2011 08:34:22 -0500http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?answer=12561#post-id-12561Comment by John Palmieri for <p>As far as I know, facilities for doing Lie theoretic computations directly in a Lie algebra in Sage are sparse. As <a href="/users/33/niles/">@niles</a> mentions, there are facilities for dealing with roots, weights, and Weyl groups, but that's probably not what you're looking for if you are working in the Virasoro algebra.</p>
<p>Of course there is fantastic support for all kinds of linear algebra, which most Lie algebra computations boil down to anyway ...</p>
<p>Here are some other resources, though:</p>
<ul>
<li><p>Sage has a <code>CombinatorialFreeModule</code> class which is inherited from to construct many non-commutative / non-associative algebras (e.g. see the documentation and source code for <code>IwahoriHeckeAlgebraT</code>). AFAIK, this class is restricted to finite rank modules.</p></li>
<li><p>GAP (which is included in Sage) has several packages (both standard and optional) for doing Lie algebra calculations. See:</p>
<ul>
<li><a href="http://www.gap-system.org/Manuals/doc/htm/ref/CHAP061.htm#SECT011">http://www.gap-system.org/Manuals/doc...</a></li>
<li>The SLA package for GAP: <a href="http://www.science.unitn.it/~degraaf/sla.html">http://www.science.unitn.it/~degraaf/...</a></li>
</ul></li>
</ul>
<p>Also, the folks on the <a href="http://groups.google.com/group/sage-combinat-devel">sage-combinat-devel</a> and <a href="https://groups.google.com/group/sage-algebra?hl=en">sage-algebra</a> google groups would probably be interested in this topic if you post your question there.</p>
http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?comment=21392#post-id-21392CombinatorialFreeModule is usable with infinite rank modules, as well as finite rank.Fri, 12 Aug 2011 05:22:23 -0500http://ask.sagemath.org/question/8264/infinite-dimensional-lie-algebras-in-sage/?comment=21392#post-id-21392