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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | )abbrev domain FF FiniteField
++ Author: Mark Botch
++ Date Created: ???
++ Date Last Updated: 29 May 1990
++ Reference:
++ Grab92 Finite Fields in AXIOM.
++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteField(p,n) implements finite fields with p**n elements.
++ This packages checks that p is prime.
++ For a non-checking version, see \spadtype{InnerFiniteField}.
FiniteField(p:PositiveInteger, n:PositiveInteger) : SIG == CODE where
SIG ==> FiniteAlgebraicExtensionField(PrimeField p)
CODE ==>
FiniteFieldExtensionByPolynomial(PrimeField p,_
createIrreduciblePoly(n)$FiniteFieldPolynomialPackage(PrimeField p))
-- old code for generating irreducible polynomials:
-- now "better" order (sparse polys first)
-- generateIrredPoly(n)$IrredPolyOverFiniteField(GF))
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