polynomial-algebra-0.0: polynomial and exterior algebras Contents Index

Math.Algebra.PolyAlg.Exterior

Synopsis

(<#>) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) newtype ExteriorMonomial symb = EM [symb] type ExteriorTerm symb coeff = (ExteriorMonomial symb, coeff) toExteriorMonomial :: (Ord symb, Num coeff) => [symb] -> Maybe (ExteriorTerm symb coeff) toExteriorTerm :: (Ord symb, Num coeff) => [symb] -> coeff -> Maybe (ExteriorTerm symb coeff) mulExteriorTerm :: (Ord symb, Num coeff) => ExteriorTerm symb coeff -> ExteriorTerm symb coeff -> Maybe (ExteriorTerm symb coeff) showExteriorMonomialWith :: (symb -> String) -> ExteriorMonomial symb -> String exteriorMonomP :: Num c => Parser (ExteriorTerm Symbol c) extAlgP :: Parser (ExtAlg Integer) parseExtAlg :: String -> ExtAlg Integer newtype ExtAlgebra symb coeff = E { unE :: FreeMod (ExteriorMonomial symb) coeff } type ExtAlg c = ExtAlgebra Symbol c (/\) :: (Ord s, Num c) => ExtAlgebra s c -> ExtAlgebra s c -> ExtAlgebra s c fromLinear :: (Ord s, Num c) => FreeMod s c -> ExtAlgebra s c

Documentation

(<#>) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)

newtype ExteriorMonomial symb

Constructors EM [symb] Instances Eq symb => Eq (ExteriorMonomial symb) Ord symb => Ord (ExteriorMonomial symb) Show symb => Show (ExteriorMonomial symb) Pretty symb => Pretty (ExteriorMonomial symb)

type ExteriorTerm symb coeff = (ExteriorMonomial symb, coeff)

toExteriorMonomial :: (Ord symb, Num coeff) => [symb] -> Maybe (ExteriorTerm symb coeff)

The result may be zero if there is a repeated symbol; this case is encoded as Nothing.

toExteriorTerm :: (Ord symb, Num coeff) => [symb] -> coeff -> Maybe (ExteriorTerm symb coeff)

mulExteriorTerm :: (Ord symb, Num coeff) => ExteriorTerm symb coeff -> ExteriorTerm symb coeff -> Maybe (ExteriorTerm symb coeff)

showExteriorMonomialWith :: (symb -> String) -> ExteriorMonomial symb -> String

exteriorMonomP :: Num c => Parser (ExteriorTerm Symbol c)

extAlgP :: Parser (ExtAlg Integer)

parseExtAlg :: String -> ExtAlg Integer

newtype ExtAlgebra symb coeff

Constructors E unE :: FreeMod (ExteriorMonomial symb) coeff Instances (Eq symb, Eq coeff) => Eq (ExtAlgebra symb coeff) (Ord symb, Ord coeff) => Ord (ExtAlgebra symb coeff) (Show symb, Show coeff) => Show (ExtAlgebra symb coeff) (Ord symb, Real coeff, Pretty symb) => Pretty (ExtAlgebra symb coeff) (Ord s, Num c) => FreeModule (ExtAlgebra s c) (Ord s, Num c) => Algebra (ExtAlgebra s c)

type ExtAlg c = ExtAlgebra Symbol c

(/\) :: (Ord s, Num c) => ExtAlgebra s c -> ExtAlgebra s c -> ExtAlgebra s c

fromLinear :: (Ord s, Num c) => FreeMod s c -> ExtAlgebra s c

Produced by Haddock version 2.4.1