On Nov. 17, Feifei Li wrote
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Thanks for the pauli matrices implementation.
Maybe I didn't make it clear enough that I am looking for a general way to
simplify commutators based on a few elementary commutation rules, for
example:
given a set of elementary rules, e.g., [A, B]=iC, [B, C]=iA, [C, A]=iB,
can we simplify arbitrary commutators like [A^10+A^5.B^10, C^3+B^5]
I think the key should be to specify customized rules and let Maxima
simplify expressions according to those rules. However as I go through the
documentation, I can not find good example indicating this is doable.
Since my problem involves spin operators Jx, Jy, Jz that are 10X10 in
dimension. You implementation of pauli matrices give me a hint that I can
actually use 10X10 matrices to represent Jx, Jy, Jz such that the
calculation turns into linear algebra. I will try this out before I find the
more general way. If you know of any general way of doing the commutator,
please let me know
Thanks again for the code and suggestion!
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Hi Fiefei,
You should try the explicit matrix method, at least as an
easy check on any symbolic method you use.
Matrix methods are almost bug free compared to symbolic
methods, and much easier to get up and running
quickly. You know, usually, that you can use a
variety of matrix representations in any given
problem, so using matrices is not a serious
restriction, unless you want the output to take a
special form which is easier to achieve with
a symbolic method.
In working on Ch. 12, Dirac Algebra and QED, I
found that the matrix methods were easier to set
up, almost always were faster, and were an invaluable
check on the symbolic methods I spent a lot of
time developing.
>From the mathematician's point of view, getting
a self consistent and reliable simplification of abstract
objects is always more fun than simply getting the
right answer ( the latter is often what physicists really
want and care about).
There are probably folks on the mailing list with
some code ideas for a symbolic approach.
Ted