\input zb-basic
\input zb-ioport
\iteman{io-port 00014091}
\itemau{White, Neil L.}
\itemti{Multilinear Cayley factorization.}
\itemso{J. Symb. Comput. 11, No.5-6, 421-438 (1991).}
\itemab
The author develops an algorithm which solves the Cayley factorization of a homogeneous bracket polynomial $P$ which is multilinear. The algorithm has seven steps. In step 1 we first find the atomic extensors for the bracket polynomial $P(a,b,\ldots,z)$ of rank $d$ which is multilinear in the $N$ points $a,b,\ldots,z$. In step 2 we rewrite $P$ as a bracket polynomial which is dotted in each atomic extensor. In step 3 we apply straightening with the $d$ elements of $E$ first in the linear order, if there exists an atomic extensor $E$ of step 1. The result must have $E$ as the first row of every resulting tableau. In step 4 we find a primitive factor if any, for pairs of extensors $E=\{e\sb 1,e\sb 2,\ldots,e\sb k\}$, $F=\{f\sb 1,f\sb 2,\ldots,f\sb \ell\}$ such that $k+\ell\ge d$. Step 5 checks if such $E$ and $F$ do not exist. Then no factorization is possible. In step 6 we recompute the atomic extensors by trying to extend the current ones. Finally in step 7 we go to step 2 and repeat. An example is worked out.
\itemrv{J.K.Sengupta (Santa Barbara)}
\itemcc{}
\itemut{multilinear Cayley factorization; algorithm; homogeneous bracket polynomial; atomic extensors; primitive factor}
\itemli{doi:10.1016/S0747-7171(08)80113-7}
\end