I wonder if any of the tensor and/or quantum algebra code would be
helpful to use? (I have never used any of it myself but I would think
this sort of object is fairly common.)
On 27.03.2012 18:02, Comer Duncan wrote:
I forgot to say something about the dual of a matrix. In my present
context in the ipython notebooks I am using the following definition:
Given a 4x4 antisymmetric matrix F (so F_{ab} = - F_{ba}) the dual to
F is defined to be
\sideset{^{*}}{^{ab}}{\mathbf{F}} =\frac{1}{2}
\mathbf{\epsilon}^{abcd} \mathbf{F}_{cd}
where \mathbf{\epsilon}^{abcd} is the Levi-Civita pseudo-tensor,
whose value is +1 if abcd is an even permutation of 0123 and -1 if
abcd is an odd permutation of 0123 and has the value 0 if two or more
of the indices abcd are equal. The Levi-Civita pseudo-tensor is
already implemented in sympy.functions.special.tensor_functions.
I think having the dual of an antisymmetric matrix available would be
a help for anyone who would need to construct such a beast.
I hope this helps explain better what I am wanting to do with the
dual. Note that there is a lot more that can be done with such things
and that my implementation is for a cartesian (Minkowski spacetime)
coordinate basis. And I would put the dual in the same place as
sympy.functions.special.tensor_functions rather than in the matrices.
Comer
On Tue, Mar 27, 2012 at 10:30 AM, Matthew Rocklin<mrock...@gmail.com> wrote:
1. create a new method for testing the antisymmetry of a matrix: new "
is_anti_symmetric() " method
This sounds good to me.
2. create a new method for calculating the symbolic determinant using LU
decomposition: new "det_lu_decomposition() " method
This also sounds good to me. Is anyone familiar with symbolic methods to
compute the determinant? There are a couple floating around in matrices.py.
Comer's LU decomposition method seems to be quite fast for the couple simple
matrices I've tried. When is one method preferable to another?
3. create a new method for calculating the dual of a square matrix: new
"dual_matrix" method
Can you define dual matrix?
If this is ok, I would appreciate some guidance on doing this, as I have
not done it before.
This wiki page is an excellent starting point
https://github.com/sympy/sympy/wiki/Development-workflow#wiki-workflow-process
When you get stuck with that I would suggest the IRC channel. I suspect
about half of the conversation on there at this point must be about using
git and github.
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