Speaker
Description
With a view toward Feynman Integral Reduction, I discuss fundamental algorithms in commutative algebra as implemented in the open source computer algebra system Singular. I introduce a highly efficient framework for massively parallel computations in computer algebra, which combines Singular with the workflow management system GPI-Space and is based on the idea of separating coordination and computation. I also give an outlook on the potential of cross border methods in the next generation computer algebra system OSCAR, which integrates Singular with the systems GAP for group theory, polymake for polyhedral geometry, and Antic for number theory. Using commutative algebra methods, I address the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals with degree-four numerators.
