Computing with semi-algebraic sets in Sage (math)
Semi-algebraic sets are subsets of R^n specified by polynomial inequalities. The project will extend capabilities of Sage (http://www.sagemath.org) to deal with them, such as CADs computations or sums of squares based (i.e. semi-definite programming based) methods. There might be a possibility for participation in Google Summer of Code (GSoC) or Google Semester of Code with Sage as a GSoC organisation.
Interest in open source software, some knowledge of Python, appropriate maths background.