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]
<mailto:[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 <http://moorepants.info>
+01 530-601-9791
On Mon, Feb 17, 2014 at 8:11 PM, Aaron Meurer <[email protected]
<mailto:[email protected]>> wrote:
On Mon, Feb 17, 2014 at 10:39 AM, Alan Bromborsky
<[email protected] <mailto:[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 <http://moorepants.info>
> +01 530-601-9791 <tel:530-601-9791>
>
>
> On Mon, Feb 17, 2014 at 9:22 AM, Sachin Joglekar
<[email protected] <mailto:[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.
>>
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>
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>
> 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).
>
>
>
>
>
>
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--
Rajath S,
M.Sc(Hons.) Physics, B.E.(Hons.) Computer Science
Birla Institute of Technology and Science - Pilani,
Pilani
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