Abstract   Let  X  be a projective scheme and let  M  and  N  be two coherent O   X   -modules. Given an integer  m , we present an algorithm for computing the global extension module  Ext   X    m  ( M ,  N ). As a consequence, one may calculate the sheaf cohomology  H   m  ( X ,  N ) and construct the sheaf corresponding to an element of the module  Ext   X   1 ( M ,  N ). This algorithm depends only on the computation of Grobner bases and syzygies and has been implemented in the computer algebra system Macaulay2.
['Gregory G. Smith']
Computing global extension modules