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question about finite fields
https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2396		 Page 1 of 1
Author:  jack [ Mon Apr 14, 2014 1:36 pm ]
Post subject:  question about finite fields
Hello,


when defining a ring over a finite field, e.g.
Code:
ring rng = (49,a),x,dp;
basering;
//   # ground field : 49
//   primitive element : a
//   minpoly        : 1*a^3+6*a^2+4*a^0
//   number of vars : 1
//        block   1 : ordering dp
//                  : names    x
//        block   2 : ordering C


howto
- check, that the coefficient ring is a (finite) field
- get a generator of the finite coefficient field
- get the cardinality of the finite coefficient field
(without parsing the string output above)

?
Author:  malex [ Wed Apr 16, 2014 5:51 am ]
Post subject:  Re: question about finite fields
i would try something along the following lines :

Code:
if ( !( (char(basering) == 0) || (npars(basering) > 1) || ( (npars(basering) == 1)&&(string(minpoly) == "0") ) ) )
{
  "field is finite..."; 
}


ps: here i don't consider the case of integer coeff. rings

for the cardinality one will need the degree of minpoly: just watch the powers: par(1)^i until reduction happen.

O.
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