Computational Commutative Algebra

Description: This is a short reading course for Ph.D. students at IMPA. 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.