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D.4.7 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.4.7.1 canonMap  the kernel and the cokernel of the canonical map
D.4.7.2 cup  cup: Ext^1(M',M') x Ext^1() --> Ext^2()
D.4.7.3 cupproduct  cup: Ext^p(M',N') x Ext^q(N',P') --> Ext^p+q(M',P')
D.4.7.4 depth  depth(I,M'), I ideal, M module, M'=coker(M)
D.4.7.5 Ext_R  Ext^k(M',R), M module, R basering, M'=coker(M)
D.4.7.6 Ext  Ext^k(M',N'), M,N modules, M'=coker(M), N'=coker(N)
D.4.7.7 fitting  n-th Fitting ideal of M'=coker(M), M module, n int
D.4.7.8 flatteningStrat  Flattening stratification of M'=coker(M), M module
D.4.7.9 Hom  Hom(M',N'), M,N modules, M'=coker(M), N'=coker(N)
D.4.7.10 homology  ker(B)/im(A), homology of complex R^k--A->M'--B->N'
D.4.7.11 isCM  test if coker(M) is Cohen-Macaulay, M module
D.4.7.12 isFlat  test if coker(M) is flat, M module
D.4.7.13 isLocallyFree  test if coker(M) is locally free of constant rank r
D.4.7.14 isReg  test if I is coker(M)-sequence, I ideal, M module
D.4.7.15 hom_kernel  ker(M'--A->N') M,N modules, A matrix
D.4.7.16 kohom  Hom(R^k,A), A matrix over basering R
D.4.7.17 kontrahom  Hom(A,R^k), A matrix over basering R
D.4.7.18 KoszulHomology  n-th Koszul homology H_n(I,coker(M)), I=ideal
D.4.7.19 tensorMod  Tensor product of modules M'=coker(M), N'=coker(N)
D.4.7.20 Tor  Tor_k(M',N'), M,N modules, M'=coker(M), N'=coker(N)