Cat::LeftAModuleWithBasis – the category of modules over a finite dimensional algebra with a distinguished basis

Cat::LeftAModuleWithBasis(alg) represents the category of the modules over a finite dimensional algebra with a distinguished basis.

Creating the Category

Cat::LeftAModuleWithBasis(alg)

Parameters:

alg: 

A domain which must be from the category Cat::FiniteDimensionalAlgebraWithBasis(coeffRing) with coeffRing a Cat::Ring.

Categories

Cat::ModuleWithBasis(coeffRing), Cat::LeftModule(alg)

Details:

A domain in this category is a left module over a finite dimensional algebra alg, or, equivalently, a representation of alg.

mult2 – left multiplication by elements in alg

Cat::LeftAModuleWithBasis::mult2(alg a, dom x)

Returns the scalar multiplication of a and x.

leftMatrix – compute the matrix of an element

Cat::LeftAModuleWithBasis::leftMatrix(alg math, <vectorBasis v1, math, vectorBasis vk>)

Returns the multiplication matrix of a.

If the basis is provided, it returns the multiplication matrix of a, in the given basis.

Changes in MuPAD 3.1

New Function.