cbhexp

 

  
Purpose 		
 
Calculate the exponent corresponding to the composition of flows of
vector fields according to the CBH formula (up to order 4 brackets).





Syntax 		 
z:=cbhexp(x,y);




Description 		 

The function cbhexp computes and returns the exponent $Z$ in
$e^Z=e^X\circ e^Y$, the composition of flows of two vector fields $X$
and $Y$,  calculated according to the Campbell-Baker-Hausdorff (CBH)
formula for the composition of the flows (exponential mappings) acting
on the right.  The exponent $Z$ is approximated by the $4^{\mathit{th}}$
order CBH formula given below (see[43]):

$$\begin{eqnarray*}
Z&=&X+Y+\frac{1}{2}[X,Y]+\frac{1}{12}\left ([X,[X,Y]]-[Y,[X,Y]...
...\\ 
 & & -\frac{1}{48}\left ([Y,[X,[X,Y]]]+[X,[Y,[X,Y]]]\right )
\end{eqnarray*}$$










Arguments 		 
$x, y$  $\parbox{0.64\textwidth}{Lie algebra generators or Lie polynomials, i.e. linear combinations of Lie elements (brackets).}$




Examples 		 

See example for the function reduceLB on page .