Calculating differentials of Weyman Complexes in Macaulay2

Resultants are useful for applications in robotics and control theory, but often they become extensive multivariate polynomials. Therefore, it is useful to represent them implicitly as determinants of matrices. Gelfand, Kapranov and Zelevinsky associated resultants with a Koszul complex of sheaves. They consider the spectral sequence of the double complex arising from the sheaf cohomologies and specified resultants via determinants of the corresponding Weyman complexes. This complex depend on an additional line bundle. It can be chosen in a way that all higher sheaf cohomologies vanish, but the resulting complex often contains several terms. Thus, to calculate its determinant, a fraction of multivariate polynomials must be evaluated. To avoid this, we consider as Dickenstein and Emiris line bundles which yield Weyman complexes with only two terms. For this, higher sheaf cohomologies must also be taken into account. Here, we determine their higher differentials.