GSoC 2017 : Vector Integration

[Mohit Chandra]

Hello , I'm Mohit Chandra , second year CS undergrad at IIIT Hyderabad . Actually, I went through the GSoC wiki and I'm interested in Vector Integration idea. It would be really nice if someone could guide me on this issue. Thanks.

[Alan Bromborsky]

You should look at -

http://www.ime.unicamp.br/~marcio/ps2009/spivak

which covers differential forms and the generalized Stokes theorem which includes all the vector integration theorems.

even more general is the fundamental (integration) theorem of geometric calculus -

https://arxiv.org/abs/math/9807024

On Tue, Mar 7, 2017 at 2:06 AM, Mohit Chandra <mohitcha...@gmail.com> wrote:

Hello , I'm Mohit Chandra , second year CS undergrad at IIIT Hyderabad . Actually, I went through the GSoC wiki and I'm interested in Vector Integration idea. It would be really nice if someone could guide me on this issue. Thanks.

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[Mohit Chandra]

@brombo , Thank you for your help . I have taken Vector mathematics course in previous semester and thus I am familiar with some of the topics, so this issue of vector integration is of great interest to me. Actually, I wanted to know whether any previous work on vector integration has been done in sympy or not and also some If you can suggest starting point in terms of understanding the code base of vector mathematics in sympy . Thanks.

On Tuesday, March 7, 2017 at 10:41:25 PM UTC+5:30, brombo wrote:

You should look at -

http://www.ime.unicamp.br/~marcio/ps2009/spivak

which covers differential forms and the generalized Stokes theorem which includes all the vector integration theorems.

even more general is the fundamental (integration) theorem of geometric calculus -

https://arxiv.org/abs/math/9807024

On Tue, Mar 7, 2017 at 2:06 AM, Mohit Chandra <mohitcha...@gmail.com> wrote:

Hello , I'm Mohit Chandra , second year CS undergrad at IIIT Hyderabad . Actually, I went through the GSoC wiki and I'm interested in Vector Integration idea. It would be really nice if someone could guide me on this issue. Thanks.

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[Mohit Chandra]

Sir, I have started working on my proposal kindly have a look at that and please provide your reviews , thanks.

Link : https://github.com/sympy/sympy/wiki/GSoC-2017-Application-Mohit-Chandra:-Implementation-of-vector-integration

On Tuesday, March 7, 2017 at 10:41:25 PM UTC+5:30, brombo wrote:

You should look at -

http://www.ime.unicamp.br/~marcio/ps2009/spivak

which covers differential forms and the generalized Stokes theorem which includes all the vector integration theorems.

even more general is the fundamental (integration) theorem of geometric calculus -

https://arxiv.org/abs/math/9807024

On Tue, Mar 7, 2017 at 2:06 AM, Mohit Chandra <mohitcha...@gmail.com> wrote:

Hello , I'm Mohit Chandra , second year CS undergrad at IIIT Hyderabad . Actually, I went through the GSoC wiki and I'm interested in Vector Integration idea. It would be really nice if someone could guide me on this issue. Thanks.

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[Arif Ahmed]

Maybe one of the important things in this project would be the implementation of a parameterization algorithm : http://ac.els-cdn.com/S0747717108801447/1-s2.0-S0747717108801447-main.pdf?_tid=62782f0c-0da3-11e7-8706-00000aacb360&acdnat=1490038284_68e1059b544113dca2f588d62087ca9d

Once a certain curve has been parameterized then the existing integrate functions can work on it.

[Mohit Chandra]

Yes , I agree with you and I have tried to keep this part in consideration . What I think that this proposal should achieve is that it should be able to perform vector integration on 3-dimension (maybe we can neglect higher dimension co-ordinates as sympy [as of now doesn't support more than 3-dimension coordinates]) . I have looked into conditions of parametrization as :

1. single symbol 't' for parametric coordinates for line integrals.
2. symbols 't' and 's' for parametric coordinated for surface integrals.