homomorphisms between modules
Junyan ยท Wed Jan 30, 2013 12:50 am
we would like to calculate Hom_R(I,R/I) for a polynomial ring R and an ideal I in R. according to the description in the online manual this is done by representing I and R/I as cokernel of matrices B and A by asking for "Hom(B,A)". these matrices are obtained by taking a free resolution of R/I as
R^p --B--> R^q --A--> R --> R/I
but the output of "Hom(B,A)" is an object of SINGULAR data type "module", which is, if we understand correctly, a submodule of a free module (of rank 324 in our example btw..) but this cannot be Hom_R(I,R/I), which is a torsion module.
1) how do we have to interpret "Hom(B,A)?
2) how do we obtain the module Hom_R(I,R/I) we are looking for?
thanks
R^p --B--> R^q --A--> R --> R/I
but the output of "Hom(B,A)" is an object of SINGULAR data type "module", which is, if we understand correctly, a submodule of a free module (of rank 324 in our example btw..) but this cannot be Hom_R(I,R/I), which is a torsion module.
1) how do we have to interpret "Hom(B,A)?
2) how do we obtain the module Hom_R(I,R/I) we are looking for?
thanks