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D.4.3 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.4.3.1 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) |
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