Top
Back: flatteningStrat
Forward: homology
FastBack: grwalk_lib
FastForward: integralbasis_lib
Up: homolog_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.4.7.9 Hom

Procedure from library homolog.lib (see homolog_lib).

Usage:
Hom(M,N,[any]); M,N=modules

Compute:
A presentation of Hom(M',N'), M'=coker(M), N'=coker(N) as follows: let
 
   F1 --M-> F0 -->M' --> 0,    G1 --N-> G0 --> N' --> 0
be presentations of M' and N'. Consider
 
                                  0               0
                                  |^              |^
       0 --> Hom(M',N') ----> Hom(F0,N') ----> Hom(F1,N')
                                  |^              |^
  (A:  induced by M)          Hom(F0,G0) --A-> Hom(F1,G0)
                                  |^              |^
  (B,C:induced by N)              |C              |B
                              Hom(F0,G1) ----> Hom(F1,G1)

Let D=modulo(A,B) and Hom=modulo(D,C), then we have exact sequences
 
   R^p  --D-> Hom(F0,G0) --A-> Hom(F1,G0)/im(B),

 R^q -Hom-> R^p --D-> Hom(F0,G0)/im(C) --A-> Hom(F1,G0)/im(B).
Hence Hom presents Hom(M',N')

Return:
module Hom, a presentation of Hom(M',N'), resp., in case of 3 arguments, a list l (of size <=3):
 
           - l[1] = Hom
           - l[2] = SB of Hom
           - l[3] = kbase of coker(Hom) (if finite dimensional, not 0),
                    represented by elements in Hom(F0,G0) via mapping D

Display:
printlevel >=0: (affine) dimension of Hom (default)
printlevel >=1: D and C and kbase of coker(Hom) in Hom(F0,G0)
printlevel >=2: elements of kbase of coker(Hom) as matrix :F0-->G0

Note:
DISPLAY is as described only for a direct call of 'Hom'. Calling 'Hom' from another proc has the same effect as decreasing printlevel by 1.

Example:
 


Top Back: flatteningStrat Forward: homology FastBack: grwalk_lib FastForward: integralbasis_lib Up: homolog_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-1-6, Dec 2012, generated by texi2html.