On Friday, February 26, 2016 at 6:00:10 PM UTC+1, Aaron Meurer wrote: > > Does manipulating holonomic functions require solving linear systems > with rational function coefficients, or are there more direct methods? > I ask because if it does a GSoC project for this for SymPy may > require improving SymPy's matrices to support working over rational > function domains. >
Fundamentally, manipulating linear differential operators with rational function coefficients is the same thing as doing linear algebra with rational function coefficients. It has been shown from a complexity point of view that multiplying linear differential operators is equivalent to multiplying matrices (http://arxiv.org/abs/0804.2181). Both the direct and linear algebra point of views are valid. For example, to find an annihilator for f + g given annihilators A, B for f and g, one computes the LCLM (least common left multiple) of A and B. This can be done "directly" by a version of the Euclidean algorithm. It can also be done by solving a linear system, as above. There may be some operations that are more natural to do directly and vice versa; the advantage of linear algebra approach is that as soon as you have translated the problem to linear algebra, it is obvious how to do the actual computation and how to optimize that. Fredrik -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/ff3ea43e-3aa2-4315-b7f0-54e7c2f1bf79%40googlegroups.com. For more options, visit https://groups.google.com/d/optout.
