## Section: New Results

### Formalization of a Newton Series Representation of Polynomials

Participants : Boris Djalal, Cyril Cohen.

We formalize an algorithm to change the representation of a polynomial to a Newton power series. This provides a way to compute efficiently polynomials whose roots are the sums or products of roots of other polynomials, and hence provides a base component of efficient computation for algebraic numbers. In order to achieve this, we formalize a notion of truncated power series and develop an abstract theory of poles of fractions. This work is described in [13] .