homolog.lib
Procedures for Homological Algebra
Gert-Martin Greuel, greuel@mathematik.uni-kl.de, Bernd Martin, martin@math.tu-cottbus.de Christoph Lossen, lossen@mathematik.uni-kl.de
Procedures:
D.4.3.1 cup cup: Ext^1(M’,M’) x Ext^1() –> Ext^2() D.4.3.2 cupproduct cup: Ext^p(M’,N’) x Ext^q(N’,P’) –> Ext^p+q(M’,P’) D.4.3.3 depth depth(I,M’), I ideal, M module, M’=coker(M) D.4.3.4 Ext_R Ext^k(M’,R), M module, R basering, M’=coker(M) D.4.3.5 Ext Ext^k(M’,N’), M,N modules, M’=coker(M), N’=coker(N) D.4.3.6 fitting n-th Fitting ideal of M’=coker(M), M module, n int D.4.3.7 flatteningStrat Flattening stratification of M’=coker(M), M module D.4.3.8 Hom Hom(M’,N’), M,N modules, M’=coker(M), N’=coker(N) D.4.3.9 homology ker(B)/im(A), homology of complex R^k–A->M’–B->N’ D.4.3.10 isCM test if coker(M) is Cohen-Macaulay, M module D.4.3.11 isFlat test if coker(M) is flat, M module D.4.3.12 isLocallyFree test if coker(M) is locally free of constant rank r D.4.3.13 isReg test if I is coker(M)-sequence, I ideal, M module D.4.3.14 kernel ker(M’–A->N’) M,N modules, A matrix D.4.3.15 kohom Hom(R^k,A), A matrix over basering R D.4.3.16 kontrahom Hom(A,R^k), A matrix over basering R D.4.3.17 KoszulHomology n-th Koszul homology H_n(I,coker(M)), I=ideal D.4.3.18 tensorMod Tensor product of modules M’=coker(M), N’=coker(N) D.4.3.19 Tor Tor_k(M’,N’), M,N modules, M’=coker(M), N’=coker(N)