Different fields of mathematics make use of the algebraic notion of valuation to filter objects. In this talk, we will present two recent works involving symbolic algorithms with valuations.
The first one concerns adapting modern algorithms for Gröbner bases to the case of Tate series, that is convergent power series with coefficients in a valued ring. The second one concerns generalizing results and algorithms for computing integral elements in algebraic field extensions or differential Ore algebras to general valued vector spaces, and in particular to recurrence Ore algebras.
The first part is a joint work with X. Caruso and T. Vaccon, and the second part with S. Chen, L. Du and M. Kauers.