Øyvind, Here is the logic in sympy.physics.quantum that handles the representation of abstract entities in concrete bases:
https://github.com/sympy/sympy/blob/master/sympy/physics/quantum/represent.py I think the code the pretty general, although for now we do assume that the representations are regular matrices (not tensors). But I think it could be generalized quite easily (the idea is super simple). Cheers, Brian On Thu, Mar 17, 2011 at 12:01 PM, Øyvind Jensen <jensen.oyv...@gmail.com> wrote: > to., 17.03.2011 kl. 10.35 -0700, skrev Brian Granger: >> On Thu, Mar 17, 2011 at 1:34 AM, Øyvind Jensen <jensen.oyv...@gmail.com> >> wrote: >> > ma., 14.03.2011 kl. 11.00 -0700, skrev Ondrej Certik: >> >> On Mon, Mar 14, 2011 at 3:11 AM, Øyvind Jensen <jensen.oyv...@gmail.com> >> >> wrote: >> >> > Alexander, All, >> >> > >> >> > How is it going with your tensor implementation? I put together some >> >> > code to implement variance of tensors and uploaded it to github in my >> >> > tensor_contractions branch [0]. If you would like to build on that, >> >> > feel free to do so. If you have already made your own implementation, >> >> > please just choose whatever works best for your framework. >> >> > >> >> > Here is how it works in the advertised branch: >> >> > >> >> > >>> A = IndexedBase('A') >> >> > >>> i = VarIdx('i') >> >> > >>> A[i.up, i.down] >> >> > A[^i, _i] >> >> > >>> get_indices(A[i.up, i.down]) >> >> > (set(), {}) >> >> > >>> get_indices(A[i.up, j.down]*x[j.up]) >> >> > (set([^i]), {}) >> >> >> >> This is great! Once either of these implementations is in sympy, I'll >> >> update the relativity example to use it. >> > >> > That would be very cool! What would be a good way to connect the >> > abstract tensor objects to its concrete representations? Perhaps >> > something like sympy.utilities.implemented_function could work? >> >> Can you say more about what you are thinking. In the quantum stuff we >> now have the notion of abstract objects and then concrete >> representations (in a particular basis). Would this type of thing >> cary over here? > > Perhaps it can be applied here, I am not sure. The current abstract > tensor objects in my branch are nothing but symbols with other symbols > attached to them as indices. Otoh, it seems like the relativity example > calculates the "content" of different tensors, much like the elements of > a matrix or a vector. I think that this corresponds to the > representation in a particular basis, but I don't know exactly how. > > Anyway, I think it could be useful to be able to mix the perspectives, > so that an expression can be manipulated in the abstract formulation > before it is converted to a concrete expression based on the "content". > Something like > > >>> def concretization_handler(inds): > # return an expression determined from the indices > >>> g = IndexedBase('g', content=concretization_handler) > >>> g(i.up, j.down).subs({i:0, j:1}) > # Here we should get the concrete representation of g^0_1. > > I am not sure how this would work, and I am also not sure yet how useful > it would be... How did you implement, and how do you use the abstract > and concrete representations in the quantum module? > > Øyvind > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > > -- Brian E. Granger, Ph.D. Assistant Professor of Physics Cal Poly State University, San Luis Obispo bgran...@calpoly.edu elliso...@gmail.com -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
