kone.linearAlgebra/dev.lounres.kone.algebraic.basis/ModuleBasis

ModuleBasis

interface ModuleBasis<out Number, Vector, in Index> : ModuleBasisDecomposition<Number, Vector, Index> (source)

Represents a basis of a module over a ring.

Type Parameters

Number

The type of scalar coefficients (from the underlying ring).

Vector

The type of module elements.

Index

The type used to index basis elements.

Inheritors

Types

interface Finite<out Number, Vector> : ModuleBasis<Number, Vector, UInt> , ModuleBasisDecomposition.Finite<Number, Vector>

A finite version of ModuleBasis indexed by UInt.

Functions

abstract fun decompose(vector: Vector): ModuleBasisDecomposition.Result<Number, Index>

Decomposes a vector into coefficients with respect to the basis.

abstract operator fun get(index: Index): Vector

Returns the basis element at the given index.

toVectorSpaceBasisDecomposition

context(field: Field<Number>)
fun <Number, Vector, Index> ModuleBasisDecomposition<Number, Vector, Index>.toVectorSpaceBasisDecomposition(): VectorSpaceBasisDecomposition<Number, Vector, Index>

Converts a ModuleBasisDecomposition to a VectorSpaceBasisDecomposition over a field by dividing each coefficient by the common scalar.

context(field: Field<Number>)
fun <Number, Vector, Index> ModuleBasis<Number, Vector, Index>.toVectorSpaceBasisDecomposition(): VectorSpaceBasis<Number, Vector, Index>

Converts a ModuleBasis to a VectorSpaceBasis over a field by dividing each decomposition coefficient by the common scalar.