Relaxed algorithms, p-adic lifting and polynomial system solving

This talk is about computing efficiently p-adic lifting by relaxed algorithms. Our aim is to introduce relaxed algorithms and their application to the computation of recursive p-adics.
To use this framework for the p-adic lifting of various systems of equations, one has to transform the given implicit equations to recursive ones. We will apply these methods both on the case of systems of linear equations, possibly differential, and for the lifting of resolutions of polynomial systems.
In all cases, these new relaxed algorithms are compared to existing algorithms,  both in theory and practice.
This is a compilation of joint works with J. Berthomieu, A. Bostan, M. Chowdhurry, B. Salvy and É. Schost.