Google Summer of Code 2015

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Saim Salman

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Mar 23, 2015, 5:15:20 AM3/23/15
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To Whom It May Concern,

I was applying for the "Google Summer of Code" and was interested in your organization; specifically the project, "Fast Linear Algebra over Extension Fields.". Now before applying I wanted to run the proposal by your team to gauge if I'm eligible and is the project what I understand it to be.

Now I'm doing a Computer Science degree with a minor in Mathematics from Lahore University of Management Sciences (LUMS) hence this project grabbed my attention as it has a lot of maths involved alongside programming.

Now from the project I got to understand that basically I'll be implementing all the basic Matrix functions (Matrix Multiplication, Matrix Addition,  Matrix Subtraction, Column Row Swapping, Gaussian Elimination) but instead of having integer entries there could be polynomial entries. And we'll have to implement all this through some data structure which will treat these matrices as polynomials and the entries as matrices. Is this what is exactly needed in this project?

Now I have a few years experience in C++ (Almost completed my 2nd Year of a 4 Year Degree.) plus I have taken a Linear Algebra Course (also part of my degree plan) hence do meet the requirements.

Now in my deliverables:
1. I thought I would show the data structure I've made and be able to implement basic addition / subtraction / row swapping / column swapping.
2. Would be able to implement matrix - matrix multiplication plus have an idea on how to go about gaussian elimination.
3. Will be able to implement gaussian elimination and if I have time left over implement asymptotically fast gaussian elimination.

(Plus I also know some algorithms like Karatsuba's algorithm in the skills / nice to have).

I plan on using C++ for this, plus if some other programming language / software is needed I'm pretty sure I would be able to implement it. (Know Java (Basic level - OOP), Matlab, Basic Python.)

Also I have no other commitments as such in the summers so I'm pretty sure I would be able to deliver all these deliverables on time.

At the end I would provide the organization with the source code with documentation.

So what I want to know is:
1. Is the project what I have made it out to be.
2. Is this what you want in the deliverables.

Thanks in advance,
Saim Salman.
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