Hey, my name is Abhinav Anand. I am a third year undergraduate from IIT 
Guwahati, India. I am interested in taking part in Gsoc this year in sympy. 
I have been contributing for past few months. 

As suggested by contributors that fixing bugs can be a proposal for Gsoc, 
but rather than that i would like to improve the speed of sympy by 
implementing faster algorithms and reshaping some of the algorithms if they 
can be made faster. While contributing i found that the calculation of 
inverse of a matrix can be made really fast if we remove the checking of 
invertiblity of a matrix by determinant, instead a check can be introduced 
within the decomposition algorithms. I have already started to implement 
this in #18608 <https://github.com/sympy/sympy/pull/18608> .
Another algorithm for is fast exponentiation using cayley hamilton theorem. 
I already implemented this in #18595 
<https://github.com/sympy/sympy/pull/18595>. 
I will likely finish these two pr in a few days.
Another faster algorithm i found in this discussion #12409 
<https://github.com/sympy/sympy/issues/12409> and #18341 
<https://github.com/sympy/sympy/issues/18341>. I thought of implementing 
quadratic sieve algorithm but after i researched about this i found it 
difficult to implement this while my classes are going on, as it is a big 
and complicated algorithm. It will require a lot of time to implement it 
which i found difficult while my classes are going on. I would really like 
to implement this during Gsoc.
I am sure that there are some places in sympy which can use better 
algorithms or probably can be made faster. 
So do you think that this can be a good Gsoc proposal. If yes then i will 
start looking through the codebase and look for better solutions, before 
the student application period begins.

Thank you

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