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GF(ZZ,ZZ) -- make a finite field of a given prime power order

Synopsis

Description

The generator of this ring is a primitive element: it generates the multiplicative group of non-zero elements.

If the single argument form GF(q) is given, q should be a prime power q = p^n

i1 : A = GF(3,2,Variable=>b);
i2 : ambient A

        ZZ
        --[b]
         3
o2 = ----------
      2
     b  + b - 1

o2 : QuotientRing
i3 : b^8

o3 = 1

o3 : A
i4 : b^4

o4 = -1

o4 : A
i5 : K = GF 8

o5 = K

o5 : GaloisField
i6 : x = K_0

o6 = a

o6 : K
i7 : x^3+x

o7 = 1

o7 : K

Caveat

A table of size q is created, so this routine should only be used with relatively small finite fields.

See also