We introduce a new method for finding non-realizability certificate of simplicial sphere Σ. It enables us to prove the first time balanced 2-neighborly 3-sphere by Zheng, family highly neighborly centrally symmetric spheres Novik and several combinatorial prismatoids introduced Criado Santos. The method, implemented in polymake framework, uses integer programming find monomial combination class...

Integer programs with a fixed number of constraints are solvable in pseudo-polynomial time the largest coefficient any constraint. We give new algorithm which improves running state art. Moreover, we show that improving on our for is equivalent to over quadratic (min, +)-convolution. This strong evidence algorithm’s best possible. also present specialized testing feasibility an integer program ...