Hello, Vinay Wagh
Quote:
> 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.)
>
> 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.)
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).
Quote:
> Actually I am not interested in the actual generators
> which I get by minbase(). I just want mu(I).
> which I get by minbase(). I just want 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.
Quote:
> 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
> 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
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.
Quote:
> Thanks in advance.
> Vinay Wagh
>
> Vinay Wagh
>
With best regards,
Viktor Levandovskyy and Christoph Lossen, SINGULAR Team