> You might consider polishing up the code and submitting for inclusion in
> Sage. I also have an arxiv paper online that includes Sage code, and
> I'm working on polishing up the code for inclusion in Sage. The
> advantage to this is that the tests in the code are run with every
> release, which means that if the code stops working, there is a big fuss
> about it and you (or whoever made the offending change) have a chance to
> update the code to work properly with the current release of Sage.
>
I might consider. But my code is absolutely not a great piece of
programming. My paper study the structure of the algebra so(2,n) : root
spaces, and some of its reductive decompositions in order to work on the
quotient SO(2,n)/SO(1,n).
All my results are proved in the paper by the use of known theorems;
there are no use of Sage or any numerical computation.
The point about Sage is that I hard-coded 10 matrices (a basis of
so(2,3)). For example, the root spaces :
Xpz=matrix([ [0,0,0,0,0],[0,0,0,0,1],[0,0,0,0,0],[0,0,0,0,1],[0,1,0,-1,0] ])
Xmz=matrix([
[0,0,0,0,0],[0,0,0,0,-1],[0,0,0,0,0],[0,0,0,0,1],[0,-1,0,-1,0]] )
Xzp=matrix([ [0,0,0,0,1],[0,0,0,0,0],[0,0,0,0,1],[0,0,0,0,0],[1,0,-1,0,0]] )
Xzm=matrix([
[0,0,0,0,-1],[0,0,0,0,0],[0,0,0,0,1],[0,0,0,0,0],[-1,0,-1,0,0]] )
Xpp=matrix(
[[0,1,0,-1,0],[-1,0,1,0,0],[0,1,0,-1,0],[-1,0,1,0,0],[0,0,0,0,0]] );
Xpm=matrix(
[[0,1,0,-1,0],[-1,0,-1,0,0],[0,-1,0,1,0],[-1,0,-1,0,0],[0,0,0,0,0] ]);
Xmp=matrix(
[[0,1,0,1,0],[-1,0,1,0,0],[0,1,0,1,0],[1,0,-1,0,0],[0,0,0,0,0]] );
Xmm=matrix(
[[0,1,0,1,0],[-1,0,-1,0,0],[0,-1,0,-1,0],[1,0,1,0,0],[0,0,0,0,0] ]);
(don't even try to understand the notation ;) )
Then I implemented some usual functions like the Killing form
def Killing(X,Y):
return (X*Y).trace()
and the Cartan involution I choose :
def theta(X):
return -X.transpose()
My only point was to do some computation on an explicit matrix
representation of so(2,3) before to search for a "real" proof for so(2,n).
I want to publish it, more by intellectual honesty than by conviction
that it will be helpful for anybody.
If someone think that Sage will be improved by knowing 10 matrices of
so(2,3), ok, I will think about making it well. If not, I will follow
the way of Carlo, and register myself in the list of article that cite
Sage :)
have a good night, and thanks for the advices
Laurent
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