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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);

  

Source: Ablamowicz, Rafal - Department of Mathematics, Tennessee Technological University

 

Collections: Mathematics