Safe Haskell | None |
---|---|
Language | Haskell2010 |
Synopsis
- data ExtensionField k im
- class IrreducibleMonic k im where
- split :: ExtensionField k im -> Polynomial k
- fromField :: ExtensionField k im -> [k]
- fromList :: forall k im. (GaloisField k, IrreducibleMonic k im) => [k] -> ExtensionField k im
- t :: Polynomial k -> Polynomial (ExtensionField k im)
- x :: GaloisField k => Polynomial k
Documentation
data ExtensionField k im Source #
Extension fields GF(p^q)[X]/<f(X)>
for p
prime, q
positive, and
f(X)
irreducible monic in GF(p^q)[X]
.
Instances
class IrreducibleMonic k im where Source #
Irreducible monic splitting polynomial f(X)
of extension field.
split :: ExtensionField k im -> Polynomial k Source #
Splitting polynomial f(X)
.
fromField :: ExtensionField k im -> [k] Source #
Convert from field element to list representation.
fromList :: forall k im. (GaloisField k, IrreducibleMonic k im) => [k] -> ExtensionField k im Source #
Convert from list representation to field element.
t :: Polynomial k -> Polynomial (ExtensionField k im) Source #
Descend tower of indeterminate variables.
x :: GaloisField k => Polynomial k Source #
Current indeterminate variable.