Further to Alan Bromborsky: The book by Lazenby and Doran is outstanding. However, the formulation of general relativity expressed there is not formally equivalent in all senses to Einstein's relativity, I will have to re-read the papers but I'm pretty sure it is possible to derive results from the Geometric Algebra version which are not derivable in the standard tensor representation of Einstein's theory. Geometric calculus does contain the algebra of tensors as a sub-set, so there are ways to express the same equations as used in standard general relativity (Lazenby and Doran were trying to express relativity in a way more consistent with relativistic quantum mechanics).
I hope this helps (and is accurate!) Tim Varkalis On Wed, Mar 18, 2009 at 10:19 PM, Alan Bromborsky <[email protected]>wrote: > > Ondrej Certik 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 > > > > > > > > > > If you get the latest snapshot of sympy: > > git clone git://git.sympy.org/sympy.git > > There is an extensive geometric algebra/calculus module (numpy required) > with attached documentation > (python-sphinx and dvipng required). The use of geometric algebra in > general relativity is documented in > "Geometric Algebra for Physicists" by Doran and Lasenby (Cambridge > University Press). The main website > is > http://www.mrao.cam.ac.uk/~clifford/<http://www.mrao.cam.ac.uk/%7Eclifford/>. > One of the examples in the book is a one line expression of > the curvature tensor for a rotating black hole using geometric algebra. > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sympy?hl=en -~----------~----~----~----~------~----~------~--~---
