Hi,

Yes, those algorithms are relevant to SymPy. For the first one, you might 
be interested in completing this PR: 
https://github.com/sympy/sympy/pull/2449. It should be possible to make it 
work also with finite fields and rings.

Kalevi Suominen


On Sunday, February 16, 2020 at 7:52:26 PM UTC+2, ABHINAV ANAND wrote:
>
> Hey sympy community, my name is Abhinav and i am from India. I have posted 
> a rough draft of gsoc proposal earlier and i need to confirm that if this 
> can be a Gsoc proposal.
> Currently sympy uses special case factorization algorithms like pollard 
> rho etc. for integer factorization which works well if the number is made 
> of small factors or the number is limited to 10-15 digits long.
> I propose to implement two new algorithms:
>
> (1) Lenstra elliptic-curve factorization
> (2) Self initializing multiple polynomial quadratic sieve
>
> Currently the fastest known algorithm for factorization is General number 
> field sieve but its efficiency is seen when the numbers are more than 100 
> digits long and in general impractical as it takes hours to factorize 
> those. Instead the algorithms that i proposed are used to factorize 
> integers in the range of 20 - 60 digits long. 
> Quadratic sieve is the second fastest known algorithm and elliptic-curve 
> factorization is the third fastest known algorithm. 
> So, i was wondering if this is relevant to Sympy and can this be a 
> proposal for this year Gsoc. Looking forward to hear from the community. 
>

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