Towards faster real algebraic numbers

AbstractThis paper presents a new encoding scheme for real algebraic number manipulations which enhances current Axiom’s real closure. Algebraic manipulations are performed using different instantiations of sub-resultant-like algorithms instead of Euclidean-like algorithms. We use these algorithms to compute polynomial gcds and Bezout relations, to compute the roots and the signs of algebraic numbers. This allows us to work in the ring of real algebraic integers instead of the field of real algebraic numbers avoiding many denominators

Computing differential characteristic sets by change of ordering

submitted to the Journal of Symbolic ComputationWe describe an algorithm for converting a characteristic set of a prime differential ideal from one ranking into another. This algorithm was implemented in many different languages and has been applied within various software and projects. It permitted to solve formerly unsolved problems