Numerical polar calculus and cohomology of line bundles

Let L1,…,Ls be line bundles on a smooth complex variety X⊂Pr and let D1,…,Ds be divisors on X such that Di represents Li. We give a probabilistic algorithm for computing the degree of intersections of polar classes which are in turn used for computing the Euler characteristic of linear combinations of L1,…,Ls. The input consists of generators for the homogeneous ideals IX,IDi⊂C[x0,…,xr] defining X and Di.