Computer Algebra is the art of using a computer to perform exact mathematical computations.
This course will cover the following notions:
- Fast multiplication (Karatsuba, FFT);
- Fast division (symbolic Newton iteration, evaluation-interpolation);
- Euclidean algorithm (gcd and applications, fast gcd);
- Resultant (elimination in two variables);
- D-finite power series (automatic proofs of identities);
- linear algebra (fast matrix multiplication and equivalent problems);
- linear algebra over polynomial matrices (minimal bases and applications);
- symbolic summation (Gosper’s algorithm, Zeilberger’s algorithm, Petkovsek’s algorithm);
- Gröbner bases (algorithms for polynomial systems and applications).
The aim of this course is to cover these fundamental algorithms while providing the students with a practical familiarity with their uses and applications through tutorials using Maple. After this course, no student will think of using pen-and-paper for long mathematical derivations.
