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 Post subject: List the elements of a finite ring
PostPosted: Sat Apr 16, 2016 7:29 pm 
How can I list the elements of a finite ring?


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 Post subject: Re: List the elements of a finite ring
PostPosted: Fri Apr 22, 2016 11:19 am 

Joined: Wed May 25, 2005 4:16 pm
Posts: 178
finite fields as Z/pZ (p prime), Z/mZ (m not prime), extensions of Z/pZ
with p^k elements are part of the kernel of Singular
(see http://www.singular.uni-kl.de/Manual/4-0-3/sing_28.htm
http://www.singular.uni-kl.de/Manual/4-0-3/sing_30.htm
with the following limits:
http://www.singular.uni-kl.de/Manual/4-0-3/sing_455.htm
)
If you want to list all elements of Z/pZ or Z/mZ,
simply start with number(0) and add 1 until you get again 0.
The elements of GF(p^k) are 0 and all powers of a (till you get 1).
For OTHER extensions of Z/pZ (given by a minpoly) there is no easy way
to list all elements (beside all possible polynomials in a with debree <
degree(minpoly)).


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