On Mon, Feb 17, 2014 at 10:39 AM, Alan Bromborsky <[email protected]> wrote: > On 02/17/2014 10:46 AM, Jason Moore wrote: > > Another approach would be to write a traditional vector calculus module that > uses the geometric algebra package in the background. I don't know enough > about geometric algebra to know if that is actually possible. But maybe. > Alan could probably comment. > > The sympy.physics.vector module can be improved, but keep in mind that > Prasoon's work is essentially what that is. We'd ideally need a vector > calculus package that is in the top level name space of sympy which would > replace sympy.physics.vector functionality. The main hurdle is the fact that > we rely heavily on immutability in sympy.physics.vector and the new vector > classes should be immutable and based on core SymPy classes. > > > Jason > moorepants.info > +01 530-601-9791 > > > On Mon, Feb 17, 2014 at 9:22 AM, Sachin Joglekar <[email protected]> > wrote: >> >> Thats definitely a plan. I am going to send a PR soon with the grad, curl, >> divergence and scalar potential functions that a basic electrostatics module >> would need. What further enhancements can you think of to the module? Have a >> look at the code and share your ideas. >> About implementing a vector module for SymPy, there are various upsides to >> that. First off, having a core based on SymPy's architecture would probably >> be much faster than the current implementation (Provided we can provide it >> as much flexibility as the current one has, with the constraint of >> immutability). Second, we would like the physics vector-related stuff to be >> more homogeneous with the rest of SymPy, which it currently is not. However, >> last summer we did realise that's not an easy job. I would still suggest you >> look at Prasoon's code (and the the small amount I tried) and see whether >> you can build such a module. >> >> >> On Monday, February 10, 2014 7:09:44 PM UTC+5:30, Rajath Shashidhara >> wrote: >>> >>> Hello, >>> >>> I'm interested in implementing electrodynamics in sympy. >>> Any thoughts about this? >>> >>> I don't seem to find any documentation about grad, divergence, and curl. >>> Are they implemented? >>> I'm willing to do this as well. >>> >>> Please give me feedback. >>> >>> Thanks. >> >> -- >> 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 http://groups.google.com/group/sympy. >> For more options, visit https://groups.google.com/groups/opt_out. > > > -- > 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 http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > > The main problem with the current GA module is that it only allows one > instance of a geometric algebra at a time. That is you can have a geometric > algebra with space time coordinate system that is (t,x,y,z) or (t,r,theta,z) > or (t,r,theta,phi) or any other by defining an appropriate metric tensor > (you are also not limited to > space time 4D). But only one instance of the algebra at a time is allowed > in the current GA module (I am developing a revised GA module that does not > have this limitation). The problem I see with this limitation is if one > needs to map one coordinate system into another. > > The map from geometric algebra/calculus to 3d vector calculus is simple. > When the geometric algebra is instantiated a special vector 'grad' and the > pseudo scalar 'I' is defined and the operations dot (|), wedge (^), and > geometric (*) products implemented. Then if U(x) and V(x) are vector fields > and f(x) is a scalar field we have - > > 1. U \cdot V = U|V (dot product) > 2. U \times V = -I*(U^V) (vector product) > 3. \nabla \cdot U = grad|U (divergence) > 4. \nabla \times U = -I*(grad ^ U) (curl) > 5. \nabla f = grad*f (gradient of scalar function) > > Of course 2 and 3 are only valid in a 3d vector space and with dealing with > relativity it is much nicer to deal with a 4d Minkowski space. > > My new implementation is functional and includes some new objects such as > multivector differential operators. I have not made a branch of it yet > since the api has changed some and I need to fix the documentation. My > biggest problem in revising the GA module is doing the documentation in > Sphinx. I have been using LaTeX for 30 years and writing docs in Sphinx > makes me feel like I am documenting while wearing blinders.
Tools like pandoc claim to be able to convert any markup format to any other markup format. I wonder if it would produce anything useful if you told it to convert LaTeX to rst. It may at least tell you about some feature of rst that you didn't know about. I agree that rst can be hard to work with. There's a nice little cheatsheet at http://openalea.gforge.inria.fr/doc/openalea/doc/_build/html/source/sphinx/rest_syntax.html. Aaron Meurer > > If anyone is interested the new code is at https://github.com/brombo/GA and > includes documentation in LaTeX and a set of introductory notes (in > progress) for geometric algebra and calculus. > > I would be very interested in what you (plural) think should be the > functionality required for a physics module. I think the only thing > currently missing from my new GA module is a mapping from one instance > (coordinate system) of a geometric algebra to another, assuming each > geometric algebra are based on the same vector space (dimension and > signature). > > > > > > > -- > 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 http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. -- 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 http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
