Symbolic computation of Drazin inverses by specializations

In this paper, we show how to reduce the computation of Drazin inverses over certain computable fields to the computation of Drazin inverses of matrices with rational functions as entries. As a consequence we derive a symbolic algorithm to compute the Drazin inverse of matrices whose entries are elements of a finite transcendental field extension of a computable field. The algorithm is applied to matrices over the field of meromorphic functions, in several complex variables, on a connected domain and to matrices over the field of Laurent formal power series.