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Module resolutions
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2115		 Page 1 of 1
Author:  TrevorM [ Mon Jul 02, 2012 9:40 pm ]
Post subject:  Module resolutions
Hi everyone, I am having a little trouble with the one set of commands I use Singular for, and I would love to see if there is a way to 'fix' it.

My problem is that I use Singular to calculate minimal resolutions of ideals of a specific form (or rather, the module R/I, where I is my ideal). The ideals I am using are generated by 3 binomial terms and 3 monomial terms. It is very important for my research that I know exactly how each generator is interacting, but Singular keeps feeling the need to change one of my monomial generators to an ideal-equivalent version. I can work around this, but it slows me down substantially to figure out all the conversions and then rewrite the resolution.

So my question is can I make Singular stick with only the generators I plug in? I included a piece of an example below.


ideal I=x4y4-z7,x4z3-y7,y3z4-x8,xy2z6,x3y4z5,x8y3z3;
rs=minres(rs);
print(rs[1]);
y7-x4z3,
x4y4-z7,
x8-y3z4,
xy2z6,
x3y4z5,
y6z7

It changes the monomial x8y3z3 into y6z7 which doesn't change anything ring-theoretically, but it makes my attempts at finding what I'm looking for quite difficult, so I would love to make it keep that 6th generator unchanged.

For the record, I am quite Singular-illiterate, but I am not so Ludditic that I won't use technology when it can compete things like resolutions easily for me!

Thanks in advance!
Author:  hannes [ Tue Jul 03, 2012 9:49 am ]
Post subject:  Re: Module resolutions
Using nres and not minres may help:
Code:
ideal I=x4y4-z7,x4z3-y7,y3z4-x8,xy2z6,x3y4z5,x8y3z3;
rresolution rs=nres(I,0);
print(rs[1]);

rs is a free resolution, which is minimized from
the second module on.
See http://www.singular.uni-kl.de/Manual/3-1-4/sing_326.htm
Author:  TrevorM [ Tue Jul 03, 2012 2:45 pm ]
Post subject:  Re: Module resolutions
Perfection! That is exactly what I was looking for. Thanks.
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