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East African Summer School on Commutative Algebra and Algebraic Geometry

August 9-20, 2004

University of Nairobi, Kenya

Day 1:

- Getting started on CoCoA
- Using help
- Solve problems from class

Day 2:

- Ideal membership
- Algebra membership problem (e.g. write x^4+y^4+z^4 as algebraic combination of e1=x+y+z, e2=xy+xz+yz, e3=xyz)
- Polynomial invariants of a group of matricies
- Reynolds operator

- Plüker coordinates
- Calculating the quadratic relations on the coordinates

Day 4:

- Calculate the Hilbert series of a ring of invariants using Molien's Theorem
- Compare dimensions of invariants found by Reynolds operators to
Hilbert series

- Determine generators for the ring of invariants of the group