# Algebraic Geometry Project ideas related to Computer Science

I am a Computer Science Undergrad student with an interest towards Algebraic Geometry.I have just recently started and am currently reading Miles Reids' Undergraduate Algebraic Geometry(I have read Reid's Undergraduate Commutative Algebra).

Apart from "just reading" up some texts, I want to do a specific project related to both computer science and algebraic geometry.

By project , I mean something like a specific problem related to CS which can be solved by algebraic geometric methods or a programming exercise (an example would be a Sudoku-Solver using Grobner Basis). I am not very interested in implementing a particular algorithm (say, Buchberger's Algorithm) and would rather build an application which uses it.

I have seen a few ideas in the appendix to David Cox's Ideals,Varieties and Algorithms but I am not very satisfied.

Any ideas would be extremely helpful.

• It is hard to come upt with project ideas that aren't done before. But some ideas could be: 1) implementing homotopy continuation to solve zero-dimensional systems of equations (docs.lib.purdue.edu/cgi/…), 2) numerical computation of invariants of algebraic varieties (e.g. degree, dimension etc), 3) online Gröbner basis calculator – Fredrik Meyer Jun 22 '16 at 9:11
• By the way: how can you use Gröbner bases to solve sudoku? – Fredrik Meyer Jun 22 '16 at 9:11
• You look at it as a system of 81 (for a 9x9) variables with certain constraints.google.co.in/… – Tushant Mittal Jun 22 '16 at 9:38

Grobner bases are used to test algebraic independence of polynomials. There are still no satisfactory answers for testing algebraic independence over characteristic $p$ fields.