Oh yes, I wasn't suggesting it is not a good thing, just that maybe you
might find good stuff there that is useful to you. For example I would
be surprised if there wasn't an implementation of the levi-civita symbol
somewhere around there.
On 27.03.2012 18:45, Comer Duncan wrote:
Hi Tom,
Thanks for the reply. I have taken a cursory look at the quantum stuff
and do not think at present that there is much overlap. My use of
dual is in the context of cartesian coordinate components of the
antisymmetric 2nd rank tensor. The tensor and its dual really live in
different spaces. In the quantum formalism the states (ket vectors)
live in a vector space while the dual states (bra vectors) are really
functionals, ie they map vectors to the complex numbers. While
strictly speaking the dual tensor really lives as an element of a
space dual to the space of the tensor, my usage does not exploit that
very much. My use of dual is in the context of its utility in writing
down Maxwell's equations in two equations, one for the four divergence
of the Maxwell tensor and another for the four divergence of the dual
of the Maxwell tensor. It provides an elegant and computationally
useful formulation of Maxwell electrodynamics. My entire use is to
the practical end of working with Maxwell's equations and studying the
hyperbolicity of the system of PDE. Having a method which can yield
the dual of a given symbolic antisymmetric matrix would save time
when such a thing needs to be constructed. In other words adding the
dual method simply adds to the available set of utilities, which I
think is a good thing.
Cheers,
Comer
On Tue, Mar 27, 2012 at 1:12 PM, Tom Bachmann<e_mc...@web.de> wrote:
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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