Back to Forum | View unanswered posts | View active topics
|
Page 1 of 1
|
[ 3 posts ] |
|
Author |
Message |
Guest
|
Post subject: too many parameters - transzendental an finite extations Posted: Wed Nov 26, 2008 5:30 pm |
|
|
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
|
|
Top |
|
|
anne
|
Post subject: Re: too many parameters Posted: Thu Nov 27, 2008 10:26 am |
|
|
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
|
|
Top |
|
|
bulygin
|
Post subject: Posted: Fri Dec 05, 2008 6:57 pm |
|
Joined: Fri Dec 05, 2008 4:48 pm Posts: 5
|
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.
_________________ Dr. Stanislav Bulygin Post Doctoral researcher Working group Cryptographic Primitives Department Secure Data Center for Advanced Security Reseach Darmstadt http://www.mathematik.uni-kl.de/~bulygin/
|
|
Top |
|
|
|
Page 1 of 1
|
[ 3 posts ] |
|
|
You can post new topics in this forum You can reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum
|
|
It is currently Fri May 13, 2022 11:05 am
|
|