Issue 16: objects with indices (tensors)
http://code.google.com/p/sympy/issues/detail?id=16
Comment #9 by [EMAIL PROTECTED]:
Hi, I've been aware of Sympy for about a year and have kept an eye on it
since then.
I need to do some (and eventually lots) of calculations involving indices.
Playing
around a bit with some of the ideas on this page, I have written some
prototype code
that lets Sympy manipulate indices.
I've attached a patch, and I hope I got the format etc right.
I've used the notation ([i], [j,k]) for example to denote an indexed object
with one
lower index i and two upper indices, j and k.
Example usage:
>>> from sympy.indexed import *
>>> from sympy import *
>>> i, j, k, l = symbols('i', 'j', 'k', 'l')
>>> theta, phi = symbols(r"\theta", r"\phi")
>>> g = Indexed('g', [i,j], components = ((1,0), (0, sin(theta)**2)))
>>> g([2,2])
sin(\theta)**2
>>> g([i,j])
g([i, j])
>>> einstein_sum(g([i,i]))
1 + sin(\theta)**2
>>> einstein_sum(g([i,j]) * g([], [j,k])) # Second list of indices are
superscript
g([i, 1])*g([], [1, k]) + g([i, 2])*g([], [2, k])
There is a fair amount of framework there but not much usability yet. I'm
having
trouble figuring out how to handle differentiation since \delta_1(g_{ij})
really
means the derivative of g^{ij} in the first coordinate direction, but
substituting
the indices in when calculating the einstein sum would give diff(g([i,j]),
1) which
doesn't work as needed.
Is there a neat way I can intercept diff(g([i,j]), 1) to replace 1 with the
required
coordinate? I think anything else is going to be ugly.
The other next step is to allow an expression like einstein_sum(g([i,j]) *
g([],
[j,k])) to be turned into another indexed object with indices, ([i],[j])
I'm not sure if this sort of implementation fits the requirements for a
system in
Sympy but I need it for my own work anyway so I'm happy to develop it
regardless.
Having it able to integrate well into Sympy would be a definite plus
though, so
feedback is appreciated.
Attachments:
indexed_prototype.patch 17.2 KB
0 bytes
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