(E,T) = extVsCohomology(ff,N)
Given a matrix ff containing a regular sequence in a polynomial ring S over k, set R = S/(ideal ff). If N is a graded R-module, and M is the module N regarded as an S-module, the script returns E = Ext_S(M,k) and T = Tor^S(M,k) as modules over an exterior algebra.
The script prints the Tate resolution of E; and the cohomology table of the sheaf associated to Ext_R(N,k) over the ring of CI operators, which is a polynomial ring over k on c variables.
The output can be used to (sometimes) check whether the submodule of Ext_S(M,k) generated in degree 0 splits (as an exterior module
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The object extVsCohomology is a method function.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/CompleteIntersectionResolutions.m2:2826:0.