Gsoc Idea 2016 Series Expansion

[Abhishek Verma]

Hello everyone , I am abhishek Verma and series expansion will be idea for gsoc 2016.

What is my  present status 

1. I have read the book On Computing Limits in a

Symbolic Manipulation System by gruntz.

and have probably understood code of gruntz.py and limits.py

2.I have read Power Series in Computer Algebra

WOLFRAM KOEPF understood what the algorithm thet are using to obtained the formal series.

3.I am reading the book "A New Algorithm Computing for Asymptotic Series" by Dominik Gruntz "

 >>> there are three things that I want to know 

1. What is exactly status of series expansion in sympy?

2. What have done with work of Avichal Dayal  on formal power and improvement of aysmtotic expansion?

3. Should polys/ring_series will be implementation of series expansion?

Topic on which i will work -

1. Formal Power series and aymtotic expansion

2.extension of gruntz .py able to calculate the all types of limits (limits with occilating funtion) 

 https://groups.google.com/forum/#!msg/sympy/h3aVz3y3n7g/JtqyPMakotMJ

3. operation with infinte series and series of multiple variable

Anyone reply will be very helpful for me. I think there is a lot of room for improvement in series expansion. But probably scattered here and there.
so need some direction.

Cheers
Abhishek Verma

[Jason Moore]

I would try using the series expansion modules in SymPy and see if you can discover some of the things it can't do. You can search the mailing list and github issues to find out problems or suggestions for series expansions.

Jason
moorepants.info
+01 530-601-9791

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[Abhishek Verma]

On Wednesday, March 16, 2016 at 4:18:29 AM UTC+5:30, Jason Moore wrote:

I would try using the series expansion modules in SymPy and see if you can discover some of the things it can't do. You can search the mailing list and github issues to find out problems or suggestions for series expansions.

 

 

I have gone through the mailing list discussion and found work of Avichal Dayal ,https://groups.google.com/forum/#!msg/sympy/o214NoJ7tJY/JbU7M_MbZesJ

    And would like to continue his work but , what happened to his work that he did in Gsoc 2014?? 

   there are also work can be done like :  

  1.No separate functions for taylor, laurent, asymptotic etc.

  2.Asymptotic Expansion:

    Many special and elementary functions do not have it implemented. I plan to do

    it for all whose expansion is possible.

    

    In general also SymPy does not do it properly.

    For e.g.:-

        series(sin(1/x+exp(-x))-sin(1/x), x, oo, 2) currently gives O(1/x**2)

    It can be better expanded as:-

        1/exp(x) - 1/(2*exp(x)*x**2) + O(1/(exp(x)*x**4))

   3.There was some paper about computing limits with oscillating 

      functions.so I would also want to work on that. 

[Abhishek Verma]

there is also user interface given here 

 

https://github.com/sympy/sympy/wiki/UD-series-user-interface

 

   which definitely implemented yet. 

[Sartaj Singh]

Hi,

I did some work on the series module as part of my GSoC project last year. I specifically worked on Formal Power Series and limits of sequences. You can see sympy.series.formal, sympy.series.fourier, sympy.series.limitseq.

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Regards

Sartaj Singh

Mathematics and Computing,

Indian Institute of Technology,

Varanasi - 221 005 INDIA

E-mail: singhs...@gmail.com, sartaj.si...@itbhu.ac.in

[Aaron Meurer]

A good place to start would be to look through the issues labeled
"series" on the issue tracker. That should give you an idea of what
sorts of things don't work.

Aaron Meurer

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[Abhishek Verma]

Who Suggested the book on idea page of series Expansion
1.Symbolic Asymptotics: Functions of Two Variables, Implicit Functions" by Bruno Savly and John Shackell
2."Symbolic Asymptotics: Multiseries of Inverse Functions" by Bruno Savly and John Shackell
Actually I am going through these book and want some discussion.

[Abhishek Verma]

I have shared my proposal with sympy on series expansion.
Here is link Series Expansion . So Mentor should reviewing it.and suggest if it need some changes.

[Sartaj Singh]

I gave it a quick read. I have added some comments.

On 24 March 2016 at 02:04, Abhishek Verma <iamverma...@gmail.com> wrote:

I have shared my proposal with sympy on series expansion.
Here is link Series Expansion . So Mentor should reviewing it.and suggest if it need some changes.

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