Davi Rodrigues (Universidade Federal do Espírito Santo, Vitória, Brazil)

This is an introduction to symbolic tensor calculus for gravitational theories using Wolfram Language (WL) / Mathematica and the xAct. It is aimed at participants with a working knowledge of general relativity, and with some basic knowledge of Mathematica (like how to work with a notebook and function definition). The first part introduces essential WL concepts needed for tensor computations, including pattern matching, replacement rules, delayed definitions, and upvalues. The second part focuses on xAct, covering the definition of manifolds, tensors, connections, and curvature, and demonstrating workflows relevant for research in gravity. As core applications, we derive the Einstein field equations from the Einstein–Hilbert action and extend the method to quadratic curvature gravity. The course emphasizes transparent, reproducible computations that can be adapted to general relativity and modified gravity models.