A Prototype for Integral Elimination

We present in this extended abstract some ongoing work which has been presented in [13]. This extended abstract contains no new results w.r.t. [13], and is intended to present our prototype integral_elimination for performing Integral Elimination. This prototype is a first step to the generalization of the differential elimination algorithms for the integral case, where the differentiation is replaced by an integration operator. Our approach is incomplete and still needs an important theoretical development. However it is already sufficient to handle nontrivial examples The originality of our approach consists in using new types of reductions and introducing exponential terms during the computations. Our prototype has been implemented in Python using SymPy. We briefly motivate the context, and present some examples treated by our prototype.