Singular

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)