Memorial University of Newfoundland
Atlantic Algebra Centre
October 4 – 9, 2010

Mini Course

Computing in Commutative Algebra

Professor Dr. Gerhard Pfister
(University of Keiserlautern, Germany)

First lecture: Gröbner bases and SINGULAR
Monday, October 4, 2010, 10-10:50 a.m., C-2010
The notion of a Gröbner basis (with respect to any ordering) will be explained as the basis for computations in localizations of factor-rings of polynomial rings. The computer algebra system SINGULAR and its use will be explained as a basis for further applications in commutative algebra and other fields.

Second lecture: Polynomial solving and primary decomposition
Tuesday, October 5, 2010, 10-10:50 a.m., SN-3060
Triangular sets as a symbolic pre-processing to solve polynomial systems of equations will be discussed. The computation of a primary decomposition – one of the most difficult task in computer algebra – will be explained. The computation of the normalization of a ring will be included.

Third lecture: Invariants
Thursday, October 7, 2010, 10-10:50 a.m., A-1049
The computation of many invariants in commutative algebra as Hilbert function, Hilbert polynomial, dimension, degree, multiplicity will be discussed and explained.

Fourth lecture: Homological Algebra
Friday, October 8, 2010, 10-10:50 a.m., SN-3060
Important notions in homological algebra as for instance depth and Cohen-Macaulayness will be analyzed and it will be explained how to check and respectively compute it.

The notes of this mini course are available here.