Computing intersection numbers and bases of cohomology groups for   triangulated closed three-dimensional manifolds
  We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing the intersection numbers of 1- and 2-dimensional cycles are developed. By means of these algorithms it is possible to construct a basis of cohomology group from the homology group of two cycles of complementary dimensions. 
E.I. Yakovlev, V.Y. Epifanov
math.GT