Hello Alan, I don't understand what you mean.
I mean to say, sympy must be able to symbolically convert a surface integral into volume integral(vice versa) using divergence theorem(line integral to area integral using stokes theorem). In this case, I'm talking about prasoon's vector module. Using the geometric algebra module, as you have mentioned, this would be equivalent to moving to a coordinate set on the surface and integrating over a rectangular patch. Sorry, if I have misunderstood. [I'm only a student and still inexperienced]. On Tue, Feb 18, 2014 at 7:31 PM, Alan Bromborsky <[email protected]>wrote: > What do you mean in regard to divergence theorem, and stokes theorem > being supported. In the multiple integral section docs for sympy definite > multidimensional integrals are only supported on rectangular integration > ranges. That is limits of integration are independent of each other along > each axis. This restriction would severely limit the application of the > divergence theorem, and stokes theorem. In order to compute a surface > integral you would need the metric tensor for that surface and then you > would still be restricted to a integrating over a rectangular coordinate > patch. > > > On 02/18/2014 08:16 AM, Rajath Shashidhara wrote: > > Hello Sachin, > > In addition to the features you have mentioned, (vector integration is > implemented in prasoon's PR), > I think divergence theorem, and stokes theorem must also be supported. > Also, a module for solving/simplifying vector equations might also help. > [support for BAC-CAB rule, div of curl, grad of div, .... ]. > > > > On Tue, Feb 18, 2014 at 7:19 AM, Jason Moore <[email protected]> wrote: > >> Here is an example of a math heavy page I wrote in with rst + Sphinx: >> >> https://raw2.github.com/moorepants/dissertation/master/eom.rst >> >> :math:`...` is the same as \(...\) or $...$ >> >> and >> >> .. math:: gives you the amsmath align environment. >> >> It worked out pretty well, ended up with a nice html and latex document. >> >> pandoc does an ok job converting latex to rst, but I've found it misses a >> lot too and/or outputs poor rst representations of what you want. >> >> >> Jason >> moorepants.info >> +01 530-601-9791 >> >> >> On Mon, Feb 17, 2014 at 8:11 PM, Aaron Meurer <[email protected]> wrote: >> >>> 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. >>> >> >> -- >> You received this message because you are subscribed to a topic in the >> Google Groups "sympy" group. >> To unsubscribe from this topic, visit >> https://groups.google.com/d/topic/sympy/77KcEdT6rXE/unsubscribe. >> To unsubscribe from this group and all its topics, 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. >> > > > > -- > Rajath S, > M.Sc(Hons.) Physics, B.E.(Hons.) Computer Science > Birla Institute of Technology and Science - Pilani, > Pilani > -- > 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 a topic in the > Google Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/77KcEdT6rXE/unsubscribe. > To unsubscribe from this group and all its topics, 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. > -- Rajath S, M.Sc(Hons.) Physics, B.E.(Hons.) Computer Science Birla Institute of Technology and Science - Pilani, Pilani -- 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.
