Michel Petitot

Representation for the radical of a finitely generated differential ideal

We give an algorithm which represents the radical J of a finitely generated differential ideal as an intersection of radical differential ideals. The computed representation provides an algorithm for testing membership in J. This algorithm works over either an ordinary or a partial differential polynomial ring of characteristic zero. It has been programmed. We also give a method to obtain a obtain a characteristic set of J, if the ideal is prime.

Computing representations for radicals of finitely generated differential ideals

This paper deals with systems of polynomial differential equations, ordinary or with partial derivatives. The embedding theory is the differential algebra of Ritt and Kolchin. We describe an algorithm, named Rosenfeld–Gröbner, which computes a representation for the radical

Shuffle algebra and polylogarithms

{\mathfrak p}

Computation of the monodromy of generalized polylogarithms

of the differential ideal generated by any such system Σ. The computed representation constitutes a normal simplifier for the equivalence relation modulo

Models of stochastic gene expression and weyl algebra

{\mathfrak p}

New classification techniques for ordinary differential equations

(it permits to test membership in