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Bruna
 Post subject: ideal multiplicity
PostPosted: Wed May 25, 2011 11:55 am 
Please, I'd like to know if I can compute with Singular the Samuel multiplicity of an ideal (which is a system of paramaters but not necessarily a maximal ideal) in a quocient ring.

Thanks,

Bruna


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gorzel
 Post subject: Re: ideal multiplicity
PostPosted: Wed May 25, 2011 2:06 pm 

Joined: Wed Mar 03, 2010 5:08 pm
Posts: 108
Location: Germany, Münster
See mult http://www.singular.uni-kl.de/Manual/la ... htm#SEC315
Quote:
If the input is a standard basis of an ideal in a (local) ring with respect to a local degree ordering then it returns the multiplicity of the ideal (in the sense of Samuel, with respect to the maximal ideal).


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Bruna
 Post subject: Re: ideal multiplicity
PostPosted: Thu May 26, 2011 12:05 pm 
Hello,

if for instance, I put I=x2+y3 in the ring O_2 and mult(I), I will calculate the multiplicity of the maximal ideal in O_2/I, is that right?

But, what I wanna do is calculate the multiplicity of a third ideal, for example J=x, in the quocient ring O_2/I. Is that possible?

Bruna


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hannes
 Post subject: Re: ideal multiplicity
PostPosted: Mon Jun 27, 2011 1:27 pm 

Joined: Wed May 25, 2005 4:16 pm
Posts: 275
yes, that is possible, set the correct basering:
Code:
ring r=....;
ideal I=....;
qring q=std(I);
ideal J=....;
mult(std(J));


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