[GAP Forum] Fields & Polynomials

[Marco Costantini]

Dear Forum,

On Monday 08 May 2006 10:18, Joachim Schittenhelm asked:
> with given F=GF(q) and an irreducible polynomial f over F of degree n,
> how can i create the field of polynomials over F of degree at most n-1 that
> is isomorphic to GF(q^n).

The requested field of polynomial is isomorphic to an algebraic extension of 
the field. See the chapter "65 Algebraic extensions of fields" 
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP065.htm
of Gap reference manual.

You can also create the field with q^n elements with the command 
GF(q^n);
but this field may not be related to the given polynomial f.
To use f you can use:
GF(q^n, f);

See "57.3 Creating Finite Fields"
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP057.htm#SECT003


For any remark concerning this mail, please do not reply to me, but write to
support at gap-system.org .

Best regards,
Marco Costantini