Thanks for the suggestion. I have now looked at the relativity.py
file and believe it to be a reasonable start. Once I understand more
I will make some related changes and let you know what I get. Another
related area is general relativistic fluid dynamics for which sympy
hopefully can be useful in generating eigenvectors and eigenvalues of
the Jacobian matrix of the conservative variables with respect to the
primitive variables. Also, using sympy to compute the residual of the
equations when studying the accuracy of computations based on
Einstein's equations (Numerical Relativity) could be useful. These
kinds of computations are currently done using Mma. These are just a
few things which it would be nice to demonstrate can be handled by
sympy.
On a related topic, what do you think is the problem with tensor.py?
I can see a need for the approach which seems to be contained therein,
namely evaluation of expressions involving products of various tensors
of various ranks in things like:
T^{abcd}_{ef} * Z_{ad} * W_{b} * Q_{bc} where a,b,c, and d run over
{0,1,2,3}.
Such expressions are used in Numerical Relativity codes and are quite
unwieldy to generate by hand. Having sympy do this would be cool and
maybe even useful.
Comer
On Mar 18, 3:27 pm, Ondrej Certik <[email protected]> wrote:
> Hi Comer,
>
> On Wed, Mar 18, 2009 at 9:17 AM, [email protected]
>
> <[email protected]> wrote:
>
> > I am interested in using Sympy but see on the web page that
> > implementing tensors is rather low on the list of interested
> > additional features. Can the developers give some indication as to
> > when tensor algebra will be added to Sympy?
>
> When we find someone interested in pushing this forward. If you'd be
> interested, play with some very preliminary code here:
>
> $ python examples/advanced/relativity.py
> [...]
> solve the Einstein's equations:
> ⎛ C₂⎞
> λ(r) = -log⎜C₁ + ──⎟
> ⎝ r ⎠
> metric:
> ⎡ C₂ ⎤
> ⎢-C₁ - ── 0 0 0 ⎥
> ⎢ r ⎥
> ⎢ ⎥
> ⎢ 1 ⎥
> ⎢ 0 ─────── 0 0 ⎥
> ⎢ C₂ ⎥
> ⎢ C₁ + ── ⎥
> ⎢ r ⎥
> ⎢ ⎥
> ⎢ 2 ⎥
> ⎢ 0 0 r 0 ⎥
> ⎢ ⎥
> ⎢ 2 2 ⎥
> ⎣ 0 0 0 r ⋅sin (θ)⎦
>
> It allows you to calculate the Schwarzschild metrics pretty easily.
> However, it'd be nice to polish the classes in there, and make it part
> of sympy, write tests for it, more examples etc. If you'd be
> interested in helping out, I fully support it.
>
> > I do general relativity
> > and thus need tensor capability.
>
> Yes, I would love to do more advanced stuff in GR as well with sympy.
>
> Ondrej
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