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primary and secondary invariants
http://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2285
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Author:  johnunmx [ Thu Sep 26, 2013 8:00 am ]
Post subject:  primary and secondary invariants

Hi, all:

I am new to Singular, and what I want to do is to generate all primary and secondary invariants of a polynomial within some total degree, which is symmetrized under a known group. For instance, v=f(r12,r13,r23), and the group is s3, whose elements are just the same as in the permutation group of S3. My script is following as:

ring R=0,(x,y,z),dp;
> matrix A1[3][3]=1,0,0,0,1,0,0,0,1;
> matrix A2[3][3]=1,0,0,0,0,1,0,1,0;
> matrix A3[3][3]=0,0,1, 0,1,0, 1,0,0;
> matrix A4[3][3]=0,1,0, 1,0,0, 0,0,1;
> matrix A5[3][3]=0,0,1, 1,0,0, 0,1,0;
> matrix A6[3][3]=0,1,0, 0,0,1, 1,0,0;

Then I do not know how to make S=(A1, A2, A3, A4, A5, A6). After this, I think I can get the invariants using
B(1..3)=invariant_ring(S);

Am I right? Thanks in advance.

Best

John

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