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:
* cup:: cup: Ext^1(M',M') x Ext^1() -> Ext^2()
* cupproduct:: cup: Ext^p(M',N') x Ext^q(N',P') -> Ext^p+q(M',P')
* depth:: depth(I,M'), I ideal, M module, M'=coker(M)
* Ext_R:: Ext^k(M',R), M module, R basering, M'=coker(M)
* Ext:: Ext^k(M',N'), M,N modules, M'=coker(M), N'=coker(N)
* fitting:: n-th Fitting ideal of M'=coker(M), M module, n int
* flatteningStrat:: Flattening stratification of M'=coker(M), M module
* Hom:: Hom(M',N'), M,N modules, M'=coker(M), N'=coker(N)
* homology:: ker(B)/im(A), homology of complex R^k-A->M'-B->N'
* isCM:: test if coker(M) is Cohen-Macaulay, M module
* isFlat:: test if coker(M) is flat, M module
* isLocallyFree:: test if coker(M) is locally free of constant rank r
* isReg:: test if I is coker(M)-sequence, I ideal, M module
* kernel:: ker(M'-A->N') M,N modules, A matrix
* kohom:: Hom(R^k,A), A matrix over basering R
* kontrahom:: Hom(A,R^k), A matrix over basering R
* KoszulHomology:: n-th Koszul homology H_n(I,coker(M)), I=ideal
* tensorMod:: Tensor product of modules M'=coker(M), N'=coker(N)
* Tor:: Tor_k(M',N'), M,N modules, M'=coker(M), N'=coker(N)

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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