Hello,

My name is Zhang Shuai. I'm a first year graduate at Peking University 
major in math, and I would like to join GSoC 2018 this year.

I have ~9 years of programming experience (participated in algorithm 
competitions in high school). Very familiar with python, C and a subset of 
C++.

I'm interested in algebraic number theory and arithmetic geometry. I've 
read Commutative Algebra by Atiyah-Macdonald, a fourth of Algebraic Geometry
by Hartshorne and several papers in The LLL Algorithm - Survey and 
Applications.

I'm particularly interested in the idea `Univariate polynomials over 
algebraic domains', namely factorization, GCD for algebraic number fields 
and function
fields. It seems that a lot has already been done, so could anybody please 
tell me what exactly I should do? Besides, where can I read about how
algebraic/transcendental extensions to Q/F_p and their elements are 
represented in SymPy?

Thanks in advance,
Zhang Shuai

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