1\cdbalgorithm{projweyl}{} 2 3Projects an expression onto Weyl spinors of positive chirality (this 4algorithm only works in even dimensions). On such a subspace, we have 5\begin{equation} 6\label{e:g10toeps} 7\Gamma^{r_1 \cdots r_{d}}\Big|_{\text{Weyl}} = \frac{1}{\sqrt{-g}}\epsilon^{r_1\cdots 8r_{d}} 9\, ,\quad \epsilon^{0\cdots (d-1)} = +1\, , 10\end{equation} 11and therefore all gamma matrices with more than $d/2$ indices can be 12converted to their ``dual'' gamma matrices. By repeated contraction 13of~\eqref{e:g10toeps} with gamma matrices on the left one deduces that 14\begin{equation} 15\Gamma^{r_1\cdots r_n}\Big|_{\text{Weyl}} = \frac{1}{\sqrt{-g}} \frac{(-1)^{\frac{1}{2}n(n+1)+1}}{(d-n)!} 16\Gamma_{s_1\cdots s_{d-n}}\Big|_{\text{Weyl}} \epsilon^{s_1\cdots s_{d-n} r_1\cdots r_n}\, . 17\end{equation} 18Here is an example: 19\begin{screen}{1,2} 20{m,n,p,q,r,s,t}::Indices. 21{m,n,p,q,r,s,t}::Integer(0..5). 22\Gamma{#}::GammaMatrix. 23\Gamma_{m n p q}; 24@projweyl!(%); 25\end{screen} 26 27\cdbseeprop{GammaMatrix} 28\cdbseealgo{join} 29