A Jordan algebra is a non-associative algebra over the reals with a bilinear multiplication that satisfies the following identities:
(the second identity is known as the Jordan identity). In literature
one usually indicates multiplication by juxtaposition but one sometimes
sees . Package idiom is to use an asterisk, as in
x*y. There are five types of Jordan algebras, all of which
have their own representation in the package, which uses S4 methods.
For more detail, see the package vignette
vignette("jordan")