Automated Combinatorial Solving and Its Applications in Computational Algebra

Computer science develops a number of highly engineered solving techniques for combinatorial problems such as satisfiability (SAT). We will give an overview of these techniques and look at some concrete applications in computational algebra. In the first application, we consider calculating the smallest generating set of finite magma. In the second application, we consider calculating the lexicographically smallest magma isomorphic to a given one.