diff options
Diffstat (limited to 'src/algebra/ffcat.spad.pamphlet')
| -rw-r--r-- | src/algebra/ffcat.spad.pamphlet | 27 |
1 files changed, 24 insertions, 3 deletions
diff --git a/src/algebra/ffcat.spad.pamphlet b/src/algebra/ffcat.spad.pamphlet index c87c4c12..b69923d4 100644 --- a/src/algebra/ffcat.spad.pamphlet +++ b/src/algebra/ffcat.spad.pamphlet @@ -117,8 +117,18 @@ ExtensionField(F:Field) : Category == Join(Field,RetractableTo F,VectorSpace F) Frobenius(a,s) == a ** (size()$F ** s) @ + \section{category FAXF FiniteAlgebraicExtensionField} + <<category FAXF FiniteAlgebraicExtensionField>>= +import Boolean +import NonNegativeInteger +import PositiveInteger +import Vector +import Matrix +import SparseUnivariatePolynomial +import OnePointCompletion +import CardinalNumber )abbrev category FAXF FiniteAlgebraicExtensionField ++ Author: J. Grabmeier, A. Scheerhorn ++ Date Created: 11 March 1991 @@ -283,7 +293,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _ m algebraic? a == true transcendent? a == false - extensionDegree() == (#basis()) :: PositiveInteger + extensionDegree(): PositiveInteger == (#basis()) :: PositiveInteger -- degree a == degree(minimalPolynomial a)$SUP(F) :: PI trace a == b := basis() @@ -384,7 +394,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _ for i in 0..extensionDegree()-1] gcd(p,f) = 1 => true false - degree a == + degree(a: %): PositiveInteger == y:$:=Frobenius a deg:PI:=1 while y~=a repeat @@ -475,8 +485,19 @@ DiscreteLogarithmPackage(M): public == private where disclog pretend NonNegativeInteger @ + \section{category FFIELDC FiniteFieldCategory} + <<category FFIELDC FiniteFieldCategory>>= +import Boolean +import Integer +import NonNegativeInteger +import PositiveInteger +import Matrix +import List +import Table +import OnePointCompletion +import SparseUnivariatePolynomial )abbrev category FFIELDC FiniteFieldCategory ++ Author: J. Grabmeier, A. Scheerhorn ++ Date Created: 11 March 1991 @@ -600,7 +621,7 @@ FiniteFieldCategory() : Category ==_ -- equalone := one?(a**(q quo exp.factor)) equalone := ((a**(q quo exp.factor)) = 1) not equalone - order e == + order(e: %): PositiveInteger == e = 0 => error "order(0) is not defined " ord:Integer:= size()-1 -- order e divides ord a:Integer:= 0 |