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matrix-ts

typeclasses overview

A collection of typeclasses that add additional laws to existing fp-ts typeclasses.

Added in v1.0.0

Table of contents

Typeclasses

AbelianGroup (interface)

An AbelianGroup is a Group that abides the following laws:

  • Commutativity: a * b = b * a

Signature

export interface AbelianGroup<A> extends Grp.Group<A> {}

Added in v1.0.0

Bimodule (interface)

Signature

export interface Bimodule<A, L, R = L> extends LeftModule<A, L>, RightModule<A, R> {}

Added in v1.0.0

CommutativeRing (interface)

Adapted from: https://pursuit.purescript.org/packages/purescript-prelude/6.0.0/docs/Data.CommutativeRing

A Ring structure with commutativity of multiplcation

  • Commutativity: a * b = b * a

Signature

export interface CommutativeRing<A> extends Rng.Ring<A> {}

Added in v1.0.0

DivisionRing (interface)

Adapted from: https://pursuit.purescript.org/packages/purescript-prelude/6.0.0/docs/Data.DivisionRing

A ring structure with division

  • One != zero
  • Nonzero multiplicative inverse

Signature

export interface DivisionRing<A> extends Rng.Ring<A> {
  readonly recip: (x: A) => A
}

Added in v1.0.0

EuclidianRing (interface)

Adapted from: https://pursuit.purescript.org/packages/purescript-prelude/6.0.0/docs/Data.EuclideanRing

Signature

export interface EuclidianRing<A> extends CommutativeRing<A> {
  readonly degree: (a: A) => number
  readonly div: (x: A, y: A) => A
  readonly mod: (x: A, y: A) => A
}

Added in v1.0.0

LeftModule (interface)

A Module over a Ring R extends an Abelian Group A follows all the laws for an Abelian Group and the following:

  • Distributivity over the Abelian Group: r * (x + y) = r * x + r * y
  • Distributivity over the Ring R: (r + s) * x = r * x + s * x
  • Associativity over the Ring R: (r * s) * x = r * (s * x)
  • Unital element over the Ring R: 1 * x = x

Signature

export interface LeftModule<A, L> extends AbelianGroup<A> {
  readonly leftScalarMul: (r: L, x: A) => A
}

Added in v1.0.0

RightModule (interface)

See LeftModule for Module laws

Signature

export interface RightModule<A, R> extends AbelianGroup<A> {
  readonly rightScalarMul: (x: A, r: R) => A
}

Added in v1.0.0