A p -adic Descartes solver: the Strassman solver

par Dr Josué Tonelli-Cueto (INRIA Paris - IMJ PRG)

jeudi 16 juin 2022, 14:00 → 15:00 Europe/Paris

https://bbb.unilim.fr/b/vac-m6r-7dv

Solving polynomials is a fundamental computational problem in mathematics. In the real setting, we can use Descartes’ rule of signs to efficiently isolate the real roots of a square-free real polynomial. In this talk, we show how to translate this method into the p-adic worlds. We show how the p-adic analog of Descartes’ rule of signs, Strassman’s theorem, leads to an algorithm to isolate the p-adic roots of a square-free p-adic polynomial and provide some complexity estimates adapting the condition-based complexity framework from real/complex numerical algebraic geometry to the p-adic case.