### D.4.8 homolog_lib

Library:
  homolog.lib
Purpose:
  Procedures for Homological Algebra
Authors:
  Gert-Martin Greuel, greuel@mathematik.uni-kl.de,
  Bernd Martin, martin@math.tu-cottbus.de
  Christoph Lossen, lossen@mathematik.uni-kl.de

Procedures:

> D.4.8.1 canonMap |  | the kernel and the cokernel of the canonical map
> D.4.8.2 cup |  | cup: Ext^1(M',M') x Ext^1() --> Ext^2()
> D.4.8.3 cupproduct |  | cup: Ext^p(M',N') x Ext^q(N',P') --> Ext^p+q(M',P')
> D.4.8.4 depth |  | depth(I,M'), I ideal, M module, M'=coker(M)
> D.4.8.5 Ext_R |  | Ext^k(M',R), M module, R basering, M'=coker(M)
> D.4.8.6 Ext |  | Ext^k(M',N'), M,N modules, M'=coker(M), N'=coker(N)
> D.4.8.7 fitting |  | n-th Fitting ideal of M'=coker(M), M module, n int
> D.4.8.8 flatteningStrat |  | Flattening stratification of M'=coker(M), M module
> D.4.8.9 Hom |  | Hom(M',N'), M,N modules, M'=coker(M), N'=coker(N)
> D.4.8.10 homology |  | ker(B)/im(A), homology of complex R^k--A->M'--B->N'
> D.4.8.11 isCM |  | test if coker(M) is Cohen-Macaulay, M module
> D.4.8.12 isFlat |  | test if coker(M) is flat, M module
> D.4.8.13 isLocallyFree |  | test if coker(M) is locally free of constant rank r
> D.4.8.14 isReg |  | test if I is coker(M)-sequence, I ideal, M module
> D.4.8.15 hom_kernel |  | ker(M'--A->N') M,N modules, A matrix
> D.4.8.16 kohom |  | Hom(R^k,A), A matrix over basering R
> D.4.8.17 kontrahom |  | Hom(A,R^k), A matrix over basering R
> D.4.8.18 KoszulHomology |  | n-th Koszul homology H_n(I,coker(M)), I=ideal
> D.4.8.19 tensorMod |  | Tensor product of modules M'=coker(M), N'=coker(N)
> D.4.8.20 Tor |  | Tor_k(M',N'), M,N modules, M'=coker(M), N'=coker(N)

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