Symbolic Computation Group

Factoring linear ODEs is an important step in their simplification and solution. As well as opening the door to (differential) Galois-theoretic methods, factoring can reduce a problem's size, making it more amenable to ad hoc techniques. While ``effective'' algorithms (i.e., algorithms which can be shown to terminate) for differential factoring have been known for a century, they are still extremely costly. On the other hand, for the related problem of factoring usual polynomials, great success has been achieved through modular methods: factor the polynomial modulo one or more primes and reconstruct a global factorization. In this talk I will discuss the problem of factoring linear ODEs via modular methods. I will present efficient algorithms for the first part of the problem, factoring ODEs and difference equations where the coefficients are from a function field over a finite field.