In my previous email only the first example uses the metric tensor g to define the coordinate system. In the other examples they defined via the vector manifold function X. X is the position vector written in terms of the rectangular coordinate components where each component is written in terms of the new coordinates. Then the partial derivative of X with respect to each new coordinate defines a basis vector in the new coordinate system (not normalized). From the dot products of these basis vectors the metric tensor g is calculated.
On Thu, Mar 2, 2017 at 12:15 PM, Alan Bromborsky <[email protected]> wrote: > I have attached pdf output of examples of coordinate system api in > galgebra module. g is the metric tensor (in this case only the diagonal > elements since coordinate systems are orthogonal). > > On Mon, Feb 27, 2017 at 2:29 PM, Arihant Parsoya <[email protected] > > wrote: > >> Hi, >> >> I am Arihant Parsoya, sophomore at IIT Bombay. I am interested in >> Computer Science and Mathematics. >> >> I have gone through the idea page >> <https://github.com/sympy/sympy/wiki/GSoC-2017-Student-Instructions> and >> I am interested in working on the project named Implementation of >> multiple types of coordinate systems for vectors >> <https://github.com/sympy/sympy/wiki/GSoC-2017-Ideas#implementation-of-multiple-types-of-coordinate-systems-for-vectors> >> . >> >> I have been contributing to sympy for about a year now. I have submitted >> two PRs related to this idea previously: >> >> [WIP] Multiple Coordinate System >> <https://github.com/sympy/sympy/pull/12020> >> >> Implemented Spherical Coordinate System >> <https://github.com/sympy/sympy/pull/11133> >> >> So far, I have used *Làme *parameters approach to implement multiple >> coordinates. However, I believe that there is better approach to implement >> this idea by using metric tensors and obtaining its Christoffel symbols(as >> suggested by Alan Bromborsky). >> >> It would be very helpful if anyone can give their ideas or tips regarding >> this project(APIs, implementation, etc.) >> >> Thanks, >> Arihant Parsoya, >> IIT Bombay >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at https://groups.google.com/group/sympy. >> To view this discussion on the web visit https://groups.google.com/d/ms >> gid/sympy/2b8ca7d5-c0bc-44ab-a3f6-0452180f954c%40googlegroups.com >> <https://groups.google.com/d/msgid/sympy/2b8ca7d5-c0bc-44ab-a3f6-0452180f954c%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> For more options, visit https://groups.google.com/d/optout. >> > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CALOxT-ncqhVbWP%2B8HYrL%3DbUF1BNv2qaf52VPR5h8s-fVK4pkkw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
