Numeric.Algebra

Additive

additive semigroups

class Additive r

sum1

additive Abelian semigroups

class Abelian r

additive idempotent semigroups

class Idempotent r

sinnum1pIdempotent

sinnumIdempotent

partitionable additive semigroups

class Partitionable m

additive monoids

class Monoidal m

sum

additive groups

class Group r

Multiplicative

multiplicative semigroups

class Multiplicative r

product1

commutative multiplicative semigroups

class Commutative r

multiplicative monoids

class Unital r

product

idempotent multiplicative semigroups

class Band r

pow1pBand

powBand

multiplicative groups

class Division r

factorable multiplicative semigroups

class Factorable m

involutive multiplicative semigroups

class InvolutiveMultiplication r

class TriviallyInvolutive r

Ring-Structures

Semirings

class Semiring r

class InvolutiveSemiring r

class Dioid r

Rngs

class Rng r

Rigs

class Rig r

Rings

class Ring r

Division Rings

class LocalRing r

class DivisionRing r

class Field r

Modules

class LeftModule r m

class RightModule r m

class Module r m

Algebras

associative algebras over (non-commutative) semirings

class Algebra r a

class Coalgebra r c

unital algebras

class UnitalAlgebra r a

class CounitalCoalgebra r c

class Bialgebra r a

involutive algebras

class InvolutiveAlgebra r a

class InvolutiveCoalgebra r c

class InvolutiveBialgebra r h

class TriviallyInvolutiveAlgebra r a

class TriviallyInvolutiveCoalgebra r a

class TriviallyInvolutiveBialgebra r h

idempotent algebras

class IdempotentAlgebra r a

class IdempotentBialgebra r h

commutative algebras

class CommutativeAlgebra r a

class CommutativeBialgebra r h

class CocommutativeCoalgebra r c

division algebras

class DivisionAlgebra r a

Hopf alegebras

class HopfAlgebra r h

Ring Properties

Characteristic

class Characteristic r

charInt

charWord

Order

class Order a

class OrderedRig r

class AdditiveOrder r

class LocallyFiniteOrder a

class DecidableZero r

class DecidableUnits r

class DecidableAssociates r

Natural numbers

data 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

class Quadrance r m

Covectors

data Covector r a

Covectors as linear functionals

counitM

unitM

comultM

multM

invM

coinvM

antipodeM

convolveM