# StructuralConstantsPackage R¶

naalg.spad line 388 [edit on github]

R: Field

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.