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too many parameters - transzendental an finite extations
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1692		 Page 1 of 1
Author:  Guest [ Wed Nov 26, 2008 5:30 pm ]
Post subject:  too many parameters - transzendental an finite extations
hi,

i would like to create a ring like

1) C[a,b][x1,..,x6] or

2) Q[a,b,c][x1,..,x6] minpoly=c^2+c+1;

but at the first case singular tells me there where too many parameters and in the secondcase it doesnt allow me to create the minpoly.

is there any work arroound to get an transzedential and finite ring adjunction at the same time?


kind regards

peter frey

university of mainz
Author:  anne [ Thu Nov 27, 2008 10:26 am ]
Post subject:  Re: too many parameters
Dear Peter,

I suggest that you only adjoin the transcendental parameters as parameters
and use a new ring variable for the algebraic parameter. Doing this, you need
to make sure that you always add your minimal polynomial to the generators of
the ideals you are dealing with or reduce with the principal ideal generated by
your minimal polynomial whenever appropriate. But apart from this inconvenience,
it is the same object you are representing on the computer:
Q(a,b)[c,x1,...,x6]/<c2+c+1>

I hope this help.

Best regards,
Anne
Author:  bulygin [ Fri Dec 05, 2008 6:57 pm ]
Post subject: 
What is said is correct. Just be careful not to forget to do the reduction mod minpoly at the right time. The following simple example illustrates the idea:

// I want to construct Q(a)[b] with b^2-1=0

ring r=(0,a),(x,b),dp;
ideal i=std(b2-1);
poly f=x2-a2+b2-1;
f=reduce(f,i);
factorize(f);

> [1]:
> _[1]=-1
> _[2]=-x+(a)
> _[3]=x+(a)
>[2]:
> 1,1,1

So everything is fine. But the following code fails

ring r=(0,a),(x,b),dp;
ideal i=std(b2-1);
poly f=x2-a2+b2-1;
factorize(f);
// ... and then reduce the anticipated factors mod i

It should be clear when to do the reductions (above it is obvious), in a more complicated example, though, it might be not that transparent. So just be cautious.
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