-- Copyright 1995 by Daniel R. Grayson -- also see Complexes/Tor.m2 Tor(ZZ, Module, Module) := Module => opts -> (i,M,N) -> ( if ring M =!= ring N then error "expected the same ring"; R := ring M; if not isCommutative R then error "'Tor' not implemented yet for noncommutative rings."; if i < 0 then R^0 else if i === 0 then M ** N else ( C := resolution(M,LengthLimit=>i+1); N = minimalPresentation N; b := C.dd; complete b; if b#?i then ( if b#?(i+1) then homology(b_i ** N, b_(i+1) ** N) else kernel (b_i ** N)) else ( if b#?(i+1) then error "internal error" else C_i ** N)))

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