Réal

Rewriting is the part of computer algebra that studies the transformations of mathematical expressions induced by admissible rules. The examples range from elementary situations, like the relation (a + b)² = a² + 2ab + b² in a ring, to computation in complex algebraic structures, like the Jacobi rule [[x,y],z] = [x,[y,z]] - [[x,z],y] in a Lie algebra.

The Réal project proposes to explore the connexions between rewriting and algebra. Our goal is to understand the algebraic foundations of rewriting, to integrate similar computational mechanisms that are known in algebra, and to develop new computational tools for applications in three domains of mathematics: combinatorial and higher algebra, the theory of groups and representations, and the study of algebraic systems and varieties.