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resolutions over quotient rings
http://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1296
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Author:  Mathias Schulze (Singular [ Thu Aug 11, 2005 5:31 pm ]
Post subject:  resolutions over quotient rings

> Hello.
>
> I ran into a confusing situation with the Singular v.1.3.8:
> I don't know if this is a bug or maybe I did something wrong, but...
> in a quotient ring mres computes a resolution which is of size 4100.
>
> SINGULAR /
> A Computer Algebra System for Polynomial Computations / version 1-3-8
> 0<
> by: G.-M. Greuel, G. Pfister, H. Schoenemann May 2000
> FB Mathematik der Universitaet, D-67653 Kaiserslautern
> > ring r=0,(a,b,c,d,e,f,g,h,i,j,k,l),Dp;
> > matrix B[2][5]=[h,i,j,k,l, 0,0,d,c,g];
> > print(B);
>
> h,i,j,k,l,
> 0,0,d,c,g
> > resolution rs=mres(B,0);
> > rs;
>
> 2 5 8 7 2 0
> r <-- r <-- r <-- r <-- r <-- r
>
> 0 1 2 3 4 5
>
> > ideal I=jg-dl;
> > qring rI=std(I);
> > matrix bee=imap(r,B);
> > print(bee);
>
> h,i,j,k,l,
> 0,0,d,c,g
>> resolution qrs=mres(bee,0);
> > size(qrs);
>
> 4100
> > qrs;
>
> // the big output omitted...
>
> by the way, using grevlex order, i.e. r=0,(a...),dp;
> seemed to ran into an unending loop.

In general, the resolution is not finite over quotient rings. One has to set a bound up to which the resolution is computed in the second argument of 'mres'. Up to Singular 2.0, unfortunately there is no such bound by default. This will change in Singular 2.1.

email: mschulze@mathematik.uni-kl.de
Posted in old Singular Forum on: 2001-05-28 14:54:45+02

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