MAGMA Computational Algebra System

Introduction

A structure constant algebra A of dimension n over a ring R can be defined in Magma by giving the n³ structure constants a_ij^k ∈R ( 1 ≤i, j, k ≤n) such that, if (e₁, e₂, ..., e_n) is the basis of A, e_i * e_j = ∑_{k = 1}ⁿ a_ij^k * e_k. Structure constant algebras may be defined over any unital ring R. However, many operations require that R be a Euclidean domain or even a field.