StructuralConstantsPackage(R)

naalg.spad line 463 [edit on github]

StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.

coordinates : (Matrix(R), List(Matrix(R))) -> Vector(R)

coordinates(a, [v1, ..., vn]) returns the coordinates of a with respect to the R-module basis v1, ..., vn.

structuralConstants : List(Matrix(R)) -> Vector(Matrix(R))

structuralConstants(basis) takes the basis of a matrix algebra, e.g. the result of basisOfCentroid and calculates the structural constants. Note, that the it is not checked, whether basis really is a basis of a matrix algebra.

structuralConstants : (List(Symbol), Matrix(Fraction(Polynomial(R)))) -> Vector(Matrix(Fraction(Polynomial(R))))

structuralConstants(ls, mt) determines the structural constants of an algebra with generators ls and multiplication table mt, the entries of which must be given as linear polynomials in the indeterminates given by ls. The result is in particular useful as fourth argument for AlgebraGivenByStructuralConstants and GenericNonAssociativeAlgebra.

structuralConstants : (List(Symbol), Matrix(Polynomial(R))) -> Vector(Matrix(Polynomial(R)))

structuralConstants(ls, mt) determines the structural constants of an algebra with generators ls and multiplication table mt, the entries of which must be given as linear polynomials in the indeterminates given by ls. The result is in particular useful as fourth argument for AlgebraGivenByStructuralConstants and GenericNonAssociativeAlgebra.