algebra

Constructive abstract algebra

LTS Haskell 24.18:	4.3.1@rev:3
Stackage Nightly 2025-11-04:	4.3.1@rev:3
Latest on Hackage:	4.3.1@rev:3

See all snapshots algebra appears in

BSD-3-Clause licensed by Edward A. Kmett

Maintained by Edward A. Kmett

This version can be pinned in stack with:algebra-4.3.1@sha256:5bb7e0db14ee455e54005a6948fb9dd4440a1e5dc766480c2ac46cda01a6d2b1,4129

Module documentation for 4.3.1

Numeric
- Numeric.Additive
  - Numeric.Additive.Class
  - Numeric.Additive.Group
- Numeric.Algebra
  - Numeric.Algebra.Class
  - Numeric.Algebra.Commutative
  - Numeric.Algebra.Complex
    - Numeric.Algebra.Complex.Class
  - Numeric.Algebra.Distinguished
    - Numeric.Algebra.Distinguished.Class
  - Numeric.Algebra.Division
  - Numeric.Algebra.Dual
    - Numeric.Algebra.Dual.Class
  - Numeric.Algebra.Factorable
  - Numeric.Algebra.Hopf
  - Numeric.Algebra.Hyperbolic
  - Numeric.Algebra.Idempotent
  - Numeric.Algebra.Incidence
  - Numeric.Algebra.Involutive
  - Numeric.Algebra.Quaternion
    - Numeric.Algebra.Quaternion.Class
  - Numeric.Algebra.Unital
    - Numeric.Algebra.Unital.UnitNormalForm
- Numeric.Band
  - Numeric.Band.Class
  - Numeric.Band.Rectangular
- Numeric.Coalgebra
  - Numeric.Coalgebra.Categorical
  - Numeric.Coalgebra.Dual
  - Numeric.Coalgebra.Geometric
  - Numeric.Coalgebra.Hyperbolic
    - Numeric.Coalgebra.Hyperbolic.Class
  - Numeric.Coalgebra.Incidence
  - Numeric.Coalgebra.Quaternion
  - Numeric.Coalgebra.Trigonometric
    - Numeric.Coalgebra.Trigonometric.Class
- Numeric.Covector
- Numeric.Decidable
  - Numeric.Decidable.Associates
  - Numeric.Decidable.Nilpotent
  - Numeric.Decidable.Units
  - Numeric.Decidable.Zero
- Numeric.Dioid
  - Numeric.Dioid.Class
- Numeric.Domain
  - Numeric.Domain.Class
  - Numeric.Domain.Euclidean
  - Numeric.Domain.GCD
  - Numeric.Domain.Integral
  - Numeric.Domain.PID
  - Numeric.Domain.UFD
- Numeric.Exp
- Numeric.Field
  - Numeric.Field.Class
  - Numeric.Field.Fraction
- Numeric.Log
- Numeric.Map
- Numeric.Module
  - Numeric.Module.Class
  - Numeric.Module.Representable
- Numeric.Order
  - Numeric.Order.Additive
  - Numeric.Order.Class
  - Numeric.Order.LocallyFinite
- Numeric.Partial
  - Numeric.Partial.Group
  - Numeric.Partial.Monoid
  - Numeric.Partial.Semigroup
- Numeric.Quadrance
  - Numeric.Quadrance.Class
- Numeric.Rig
  - Numeric.Rig.Characteristic
  - Numeric.Rig.Class
  - Numeric.Rig.Ordered
- Numeric.Ring
  - Numeric.Ring.Class
  - Numeric.Ring.Division
  - Numeric.Ring.Endomorphism
  - Numeric.Ring.Local
  - Numeric.Ring.Opposite
  - Numeric.Ring.Rng
- Numeric.Rng
  - Numeric.Rng.Class
  - Numeric.Rng.Zero
- Numeric.Semiring
  - Numeric.Semiring.Involutive
  - Numeric.Semiring.ZeroProduct

Depends on 12 packages(full list with versions):

adjunctions, array, base, containers, distributive, mtl, nats, semigroupoids, semigroups, tagged, transformers, void

algebra

This is a package for exploring constructive abstract algebra in Haskell.

Contact Information

Contributions and bug reports are welcome!

Please feel free to contact me through github or on the #haskell IRC channel on irc.freenode.net.

-Edward Kmett

Changes

4.3.1

Compatibility with GHC 8.4.x: added Semigroup (End r) instance.

4.3

Compatibility with GHC 8.0.x
Dropped incomplete instance for Algebra r (Map a b) instance
Restructured Ring hierarchy (Thanks @dfoxfranke!)
Added DecidableNilpotence class (Thanks @dfoxfranke!)

4.2

Support for nats version 1 and base 4.8’s version of Numeric.Natural. This required monomorphizing some stuff to Natural, but that is more accurate than the previous hack anyways.

4.1

Added Euclidean domains and the field of fractions.

4.0

Compatibility with GHC 7.8.x
Removed keyed and representable-tries dependencies

3.0.2

Started CHANGELOG