Reading course for Ph.D. students at IMPA.
Contents: The purpose of the course is to learn the very basics on the use of Gröbner basis for programming on the commutative algebra software SINGULAR.
Reference: A Singular introduction to commutative algebra, Gert-Martin Greuel and Gerhard Pfister.
Notes: My lecture notes and some solved exercises.
Lecture 1: Ring in SINGULAR.
Lecture 2: Monomial orderings.
Lecture 3: Gröbner basis.
Lecture 4: Weak normal forms.
Lecture 5: Elimination theory.
Lecture 6: Modules.
Lecture 7: Computations on modules.
Lecture 8: Computing syzygies.