GSoC 2015 Karr Algorithm

[Ramana Venkata]

Hi, 

I want to implement Karr Algorithm for GSoC 2015. I have read the Karr's original paper and Brucin Erocal's thesis Algebraic extensions for symbolic summations to get an overview of the algorithm. I found Karr's original paper is a little hard to read from So I am currently reading Carsten Schneider Thesis . Who will be possible mentor for this project? Can somebody help me how should I proceed forward? 

Erocal Thesis mentions of an existing implementation of Karr algorithm using Sage. But I couldn't find it anywhere. 

[someone]

Hi,


> I want to implement Karr Algorithm for GSoC 2015. I have read the
> Karr's original paper

This is just for Background and basic definition.
It is not complete enough for a modern implementation.

> and Brucin Erocal's thesis

> <http://www.sagemath.org/files/thesis/erocal-thesis-2011.pdf>

He has a very good itroduction to the topic.
However, his focus was algebraic extensions
of the difference fields. For an implementation
I would go after transcendental ones first.
Algebraic extensions are always most difficult.
(Compare also to Risch integration.)

> I found Karr's original paper is a little hard to read
> from So I am currently reading Carsten Schneider Thesis

> <file:///home/vramana/Downloads/SymbSumTHESIS.pdf> .

Perfect. But this assumes the same algebraic setting
of difference algebra.

> Erocal Thesis mentions of an existing implementation of Karr
> algorithm using Sage. But I couldn't find it anywhere.

The Code was never merged into Sage and is not online.

[Aaron Meurer]

Wasn't there an implementation in Maple? Is it online?

Aaron Meurer

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[Ramana Venkata]

I couldn't find a maple implementation. Carsten's implementation in Mathematica is available but is password protected. I'll write to them to give me access to it.

[Ramana Venkata]

On Saturday, March 7, 2015 at 10:57:32 PM UTC+5:30, rl wrote:

Hi,


> I want to implement Karr Algorithm for GSoC 2015. I have read the
> Karr's original paper

This is just for Background and basic definition.
It is not complete enough for a modern implementation.

Yeah. It was very much unreadable for me in the later portions.

 

> and Brucin Erocal's thesis
> <http://www.sagemath.org/files/thesis/erocal-thesis-2011.pdf>

He has a very good itroduction to the topic.
However, his focus was algebraic extensions
of the difference fields. For an implementation
I would go after transcendental ones first.
Algebraic extensions are always most difficult.
(Compare also to Risch integration.)

You suggested this one and the carsten's thesis on an old thread 

from there I picked these ones. I didn't look at Algebraic extensions 

as such. There seems to be a lot of issues in implementing just the
transcendental ones.  I think Erocal's implementation uses a lot of 

Sage's Field module which is currently non-existent in sympy afaik.

So I have to see how of it do I need for this project. 

 

> I found Karr's original paper is a little hard to read
> from So I am currently reading Carsten Schneider Thesis
> <file:///home/vramana/Downloads/SymbSumTHESIS.pdf> .

Perfect. But this assumes the same algebraic setting
of difference algebra.

I am currently struggling to see how do I start the implementation and 

what are the things I need to implement before it. Can you tell me what 

will be the high level approach to this project?  

So, for now I'll read this thoroughly and get a better understanding.