A variety is the solution set of a system of polynomial equations, usually in several unknowns. For instance, some famous plane curves are described by one polynomial equation in x and y. A possible project is to discuss how computer algebra, e.g., Maple, can be applied to work with varieties. Interesting operations are, e.g., taking the union of two varieties, projecting a variety onto a coordinate subspace, finding the subvarieties of a variety which are not unions of two proper subvarieties, etc. (The picture shows a conic section.)

Reference:

• D. Cox, J. Little, D. O’Shea, Ideals, Varieties, and Algorithms, Springer, 3rd ed. 2007.

Supervisor: Dr Daniel Robertz