Singular

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)