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 Post subject: About the number of generators of an ideal.
PostPosted: Thu Aug 11, 2005 5:32 pm 
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


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 Post subject: Re: About the number of generators of an ideal.
PostPosted: Thu Aug 11, 2005 8:22 pm 

Joined: Thu Aug 11, 2005 8:03 pm
Posts: 37
Location: RWTH Aachen, Germany
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.)


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).


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 :-(


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
>


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

_________________
Viktor Levandovskyy


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