Multiple types of Coordinate Systems for Vectors

[Arihant Parsoya]

Hi All,

    I wanted to work on the idea of Multiple Coordinate Systems. Previously I submitted my PR for the same here. The old PRs related to this idea uses Lame` coeffecients whereas the GSOC ideas page says that there needs to be multiple classes for each coordinate system. Can anyone guide me on whats the right approach implement this idea?

Thanks,

Arihant Parsoya

[Alan Bromborsky]

In 3 dimensions there are 13 separable (orthogonal) coordinate systems.  See link -

https://en.wikipedia.org/wiki/Orthogonal_coordinates

How many do you want to implement?  I would have a coordinate_system class and use it to instantiate a particular coordinate system then when you  instantiate a vector space one of the parameters of  the vector space  instantiation would be the coordinate system.  This way you could have different coordinate systems in the same program. 

For my geometric algebra modules I started with a metric and derived the basis vectors and their derivatives.  If you are interested in this method go to -

github.com/brombo/galgebra

and look at galgebra.pdf in the doc directory.

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[Arihant Parsoya]

Hi Brombo,

I went through galgebra.pdf file and I believe this approach would be good. Initially I want to implement Cartesian and Spherical coordinate systems and get them right before implementing other systems.

On Friday, September 30, 2016 at 10:19:39 PM UTC+5:30, brombo wrote:

In 3 dimensions there are 13 separable (orthogonal) coordinate systems.  See link -

https://en.wikipedia.org/wiki/Orthogonal_coordinates

How many do you want to implement?  I would have a coordinate_system class and use it to instantiate a particular coordinate system then when you  instantiate a vector space one of the parameters of  the vector space  instantiation would be the coordinate system.  This way you could have different coordinate systems in the same program. 

For my geometric algebra modules I started with a metric and derived the basis vectors and their derivatives.  If you are interested in this method go to -

github.com/brombo/galgebra

and look at galgebra.pdf in the doc directory.

On Fri, Sep 30, 2016 at 12:06 PM, Arihant Parsoya <parsoya...@gmail.com> wrote:

Hi All,

    I wanted to work on the idea of Multiple Coordinate Systems. Previously I submitted my PR for the same here. The old PRs related to this idea uses Lame` coeffecients whereas the GSOC ideas page says that there needs to be multiple classes for each coordinate system. Can anyone guide me on whats the right approach implement this idea?

Thanks,

Arihant Parsoya

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[Alan Bromborsky]

If you use the methods in galgebra.pdf remember (this is documented) that for all but rectangular coordinates the basis vectors derived from the metric are not normalized. Especially go over section 2.3.2 is galgebra.pdf.

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[Arihant Parsoya]

Hi,

I am trying to get myself acquainted with geometric algebra by following the book `Geometric Algebra for Physicists` (by Chris Doran). It would be very helpful if you can suggest some other readings which can be helpful in implementing the class `coordinate_system`.

Thanks

[Alan Bromborsky]

My notes base on "Geometric Algebra for Physicists" are at -

https://github.com/brombo/galgebra

Look at bookGA.pdf in the doc directory.

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[Sourabh Garg]

Hey,

I also want to work on it. if you have any link to book's pdf version ,please share with me.

Thanks

Sourabh Garg

[Alan Bromborsky]

Look at my notes.  They may be sufficient.

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[Arihant Parsoya]

Hi, 

I have submitted a PR which implementes classes CoordinateSystem (Super class for remaining coordinate systems), CartesianCoordinateSystem and SphericalCoordinateSystem  using Metric and Lamè coeffecients here. Can you review it?

Thanks.

On Monday, December 12, 2016 at 10:25:18 PM UTC+5:30, brombo wrote:

Look at my notes.  They may be sufficient.

On Mon, Dec 12, 2016 at 12:32 AM, Sourabh Garg <sourabh.8...@gmail.com> wrote:

Hey,

I also want to work on it. if you have any link to book's pdf version ,please share with me.

Thanks

Sourabh Garg

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[Arihant Parsoya]

The link to the PR is https://github.com/sympy/sympy/pull/12020

[Arihant Parsoya]

Hi Brombo,

Can you suggest some API specification for the new coordinate system?

Thanks

[Francesco Bonazzi]

On Sunday, 12 February 2017 20:56:18 UTC+1, Arihant Parsoya wrote:

Hi Brombo,

Can you suggest some API specification for the new coordinate system?

Have you had a look at sympy.diffgeom, there is a CoordSystem class and some tools to connect different kinds of coordinate systems. Unfortunately it's a bit different than the vector module.