# StructuralConstantsPackage R¶

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 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.

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.