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| List the elements of a finite ring https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2524 |
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| Author: | sejwal [ Sat Apr 16, 2016 7:29 pm ] |
| Post subject: | List the elements of a finite ring |
How can I list the elements of a finite ring? |
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| Author: | hannes [ Fri Apr 22, 2016 11:19 am ] |
| Post subject: | Re: List the elements of a finite ring |
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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