Computing the Zariski closure of a finitely generated matrix group

We describe an algorithm for determining the algebraic subgroup of G L ( n , C ) \mathrm {GL}(n,\mathbb {C}) that is defined as the closure of the group generated by a finite number of elements of G L ( n , C ) \mathrm {GL}(n,\mathbb {C}) . The algorithm avoids the use of Gröbner bases and can be used on nontrivial examples. In the last section we report on an implementation of the algorithm in the computer algebra system OSCAR .