Function: Octonion:-associator -returns the associator value of three octonions, Octonion:-commutator -returns the commutator value of two octonions Summary: Function: Octonion:-associator - returns the associator value of three octonions, Octonion:-commutator - returns the commutator value of two octonions Octonion:-Phi - associative 3-form of three octonions Calling Sequence: associator(p1,p2,p3); commutator(p1,p2); Phi(p1,p2,p2); Parameters: p1, p2, p3 - polynomials of type 'octonion' Description: · The associator of three octonions p1, p2, and p3 is defined as: associator(p1,p2,p3) = (p1 &o p2) &o p3 - p1 &o (p2 &o p3). · The commutator of two octonions p1 and p2 is defined as: commutator(p1,p2) = p1 &o p2 - p2 &o p1. · The associative 3-form Phi of three octonions is defined as: Phi(p1,p2,p3) = (1/2)*realpart(p1 &o (p2_bar &o p3) - p3 &o (p2_bar &o p1)) where p2_bar = o_conjug(p2). · For information about type 'octonion' see `type/octonion`. Examples: > restart:with(Clifford):with(Octonion); Collections: Mathematics