Starting week 45 (04.11.2025) – every Tuesday from 10am - 12pm in room B1 – ending week 51, (16.12.2025)

Description of the course:

Computer algebra systems have become essential tools in a physicist’s toolkit, yet their inner workings often remain a mystery. As a result, it is difficult to predict whether a computation will take a few seconds or a few months. Understanding the algorithms behind symbolic computations can help identify bottlenecks and suggest more efficient alternatives. In this course, we will design symbolic mathematical algorithms for computers. These algorithms often differ significantly from the heuristical methods we use in pen-and-paper calculations. We will start from the ground up, with the integer ring, and work our way toward more advanced topics such as finite-field reconstruction, efficient expression evaluation, multivariate polynomial factorization, and symbolic integration. Along the way, we will confront one of the central challenges in computer algebra: intermediate expression swell.

Learning results of the course:

This course is intended for students and researchers interested in modern symbolic computational techniques. By the end of the course, participants will understand the fundamental algorithms that underpin symbolic computations and how they might be implemented efficiently.

Lecturer:

Dr. Ben Ruijl