Computing a holonomic submodule of the partial Weyl closure
For researchers in algebraic analysis and symbolic integration, this algorithm provides a faster method for a key preparatory step, though it is incremental in nature.
The paper introduces a new algorithm for computing a holonomic submodule of the partial Weyl closure, which converts differential operator systems with rational coefficients to polynomial coefficients. The algorithm shows substantial speedups over existing implementations in Singular and Macaulay2.
The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the singularities of the system, it serves as a preparatory step for many algorithms in symbolic integration. A new algorithm is introduced to compute a holonomic submodule of the partial Weyl closure of a finite-rank module, where the closure is taken with respect to a subset of the variables. The method relies on a non-commutative analogue of Rabinowitsch's trick. The algorithm is implemented in the Julia package MultivariateCreativeTelescoping.jl and shows substantial speedups over existing exact Weyl closure algorithms in Singular and Macaulay2.