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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 24 25 | )abbrev domain FFX FiniteFieldExtension
++ Authors: R.Sutor, J. Grabmeier, A. Scheerhorn
++ Date Created:
++ Date Last Updated: 31 March 1991
++ Reference:
++ Grab92 Finite Fields in Axiom
++ Lidl83 Finite Field, Encyclopedia of Mathematics and Its Applications
++ Description:
++ FiniteFieldExtensionByPolynomial(GF, n) implements an extension
++ of the finite field GF of degree n generated by the extension
++ polynomial constructed by createIrreduciblePoly from
++ \spadtype{FiniteFieldPolynomialPackage}.
FiniteFieldExtension(GF, n) : SIG == CODE where
GF: FiniteFieldCategory
n : PositiveInteger
SIG ==> FiniteAlgebraicExtensionField(GF)
-- MonogenicAlgebra(GF, SUP) with -- have to check this
CODE ==> FiniteFieldExtensionByPolynomial(GF,
createIrreduciblePoly(n)$FiniteFieldPolynomialPackage(GF))
-- old code for generating irreducible polynomials:
-- now "better" order (sparse polys first)
-- generateIrredPoly(n)$IrredPolyOverFiniteField(GF))
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