About the number of generators of an ideal.

Hi!

I am working over the ring R=0,(X,Y,Z),ds; And ideal
Isubset R. I am interested in finding mu(I). For that
initially I used the command minbase(). Then just for the
verification I tried to find out the free reolution of
it (using res and mres). (The answers were tallied.)

Actually I am not interested in the actual generators
which I get by minbase(). I just want mu(I).

Can somebody tell me the algorithm which Singular uses to
compute mu(I) AND/OR res(I)? I tried to look @ the
singular libraries, but it seems these commands are from
the kernel. And I didnt have much patience to look @ the
C++ source code :-(

Thanks in advance.

Vinay Wagh


email: vinay_wagh@yahoo.com
Posted in old Singular Forum on: 2004-06-03 08:47:38+02

Hello, Vinay Wagh



As far as we have understood, under mu(I) you mean the minimal number of generators. We avoid the use this notation, since the Milnor number is also denoted by mu(I).



You can write a procedure, returning the minimal number of generators. Note, that the "mimimal" makes sense only in the local or in the graded case.



This is explained in the SINGULAR book on the page 107, after the definition 2.1.33. The SINGULAR command "prune" provides you with the minimal presentation of a module.



With best regards,
Viktor Levandovskyy and Christoph Lossen, SINGULAR Team