content: module Numeric.Algebra
    ( 
    -- * Additive
  
    -- ** additive semigroups
      Additive(..)
    , sum1
    -- ** additive Abelian semigroups
    , Abelian
    -- ** additive idempotent semigroups
    , Idempotent
    , sinnum1pIdempotent
    , sinnumIdempotent
    -- ** partitionable additive semigroups
    , Partitionable(..)
    -- ** additive monoids
    , Monoidal(..)
    , sum
    -- ** additive groups
    , Group(..)
  
    -- * Multiplicative
    
    -- ** multiplicative semigroups
    , Multiplicative(..)
    , product1
    -- ** commutative multiplicative semigroups
    , Commutative
    -- ** multiplicative monoids
    , Unital(..)
    , product
    -- ** idempotent multiplicative semigroups
    , Band
    , pow1pBand
    , powBand
    -- ** multiplicative groups
    , Division(..)
    -- ** factorable multiplicative semigroups
    , Factorable(..)
    -- ** involutive multiplicative semigroups
    , InvolutiveMultiplication(..)
    , TriviallyInvolutive
  
    -- * Ring-Structures
    -- ** Semirings 
    , Semiring
    , InvolutiveSemiring
    , Dioid
    -- ** Rngs
    , Rng
    -- ** Rigs
    , Rig(..)
    -- * Rings
    , Ring(..)
    -- ** Division Rings
    , LocalRing
    , DivisionRing
    , Field
  
    -- * Modules
    , LeftModule(..)
    , RightModule(..)
    , Module
  
    -- * Algebras
    -- ** associative algebras over (non-commutative) semirings 
    , Algebra(..)
    , Coalgebra(..)
    -- ** unital algebras
    , UnitalAlgebra(..)
    , CounitalCoalgebra(..)
    , Bialgebra
    -- ** involutive algebras
    , InvolutiveAlgebra(..)
    , InvolutiveCoalgebra(..)
    , InvolutiveBialgebra
    , TriviallyInvolutiveAlgebra
    , TriviallyInvolutiveCoalgebra
    , TriviallyInvolutiveBialgebra
    -- ** idempotent algebras
    , IdempotentAlgebra
    , IdempotentBialgebra
    -- ** commutative algebras
    , CommutativeAlgebra
    , CommutativeBialgebra
    , CocommutativeCoalgebra
    -- ** division algebras
    , DivisionAlgebra(..)
    -- ** Hopf alegebras
    , HopfAlgebra(..)
  
    -- * Ring Properties
    -- ** Characteristic
    , Characteristic(..)
    , charInt, charWord
    -- ** Order
    , Order(..)
    , OrderedRig
    , AdditiveOrder
    , LocallyFiniteOrder
  
    , DecidableZero
    , DecidableUnits
    , DecidableAssociates
  
    -- * Natural numbers
    , Natural
  
    -- * Representable Additive
    , addRep, sinnum1pRep
    -- * Representable Monoidal
    , zeroRep, sinnumRep
    -- * Representable Group
    , negateRep, minusRep, subtractRep, timesRep
    -- * Representable Multiplicative (via Algebra)
    , mulRep
    -- * Representable Unital (via UnitalAlgebra)
    , oneRep
    -- * Representable Rig (via Algebra)
    , fromNaturalRep
    -- * Representable Ring (via Algebra)
    , fromIntegerRep
    
    -- * Norm
    , Quadrance(..)
  
    -- * Covectors
    , Covector(..)
    -- ** Covectors as linear functionals
    , counitM
    , unitM
    , comultM
    , multM
    , invM
    , coinvM
    , antipodeM
    , convolveM
    ) where
  
  import Prelude ()
  import Numeric.Additive.Class
  import Numeric.Additive.Group
  import Numeric.Algebra.Class
  import Numeric.Algebra.Involutive
  import Numeric.Algebra.Idempotent
  import Numeric.Algebra.Commutative
  import Numeric.Algebra.Division
  import Numeric.Algebra.Factorable
  import Numeric.Algebra.Unital
  import Numeric.Algebra.Hopf
  import Numeric.Covector
  import Numeric.Decidable.Units
  import Numeric.Decidable.Associates
  import Numeric.Decidable.Zero
  import Numeric.Dioid.Class
  import Numeric.Module.Representable
  import Numeric.Natural
  import Numeric.Order.Class
  import Numeric.Order.Additive
  import Numeric.Order.LocallyFinite
  import Numeric.Quadrance.Class
  import Numeric.Rig.Class
  import Numeric.Rig.Characteristic
  import Numeric.Rig.Ordered
  import Numeric.Rng.Class
  import Numeric.Ring.Class
  import Numeric.Ring.Local
  import Numeric.Ring.Division
  import Numeric.Field.Class
  