GSoC 2018 - Univariate polynomials over algebraic domains

[Shuai Zhang]

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

[Kalevi Suominen]

Hi,

Transcendental extensions of Q can be created by  QQ.frac_field(self, *symbols, **kwargs) and their elements are of type `FracElement`. Transcendental extensions of F_p can be created similarly. Algebraic extensions of Q are created by QQ.algebraic_field(self, *extension) and their elements are of type ANP. There is no construction of algebraic extensions of F_p yet.

Kalevi Suominen