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::PostDefaultRules( @@eliminate_kr!(%), @@collect_terms!(%) ).
D{#}::Derivative.
\bar{#}::DiracBar.
\partial{#}::PartialDerivative.
\delta{A??}::Derivative.
{m,n,p,q,r,s,t}::Indices(flat).
{\mu,\nu,\rho,\sigma,\kappa}::Indices(curved,position=fixed).
e^{m \mu}::Vielbein.
e_{m \mu}::InverseVielbein.
\delta_{\mu}^{\rho}::KroneckerDelta.
\delta_{m n}::KroneckerDelta.
\delta^{m n}::KroneckerDelta.
\psi_{\mu}::Spinor(dimension=4, type=Majorana).
\epsilon::Spinor(dimension=4, type=Majorana).
\Gamma_{#}::GammaMatrix(metric=\delta).
{\psi_{\mu}, \epsilon}::AntiCommuting.
\psi_{\mu}::SelfAntiCommuting.
{\epsilon,\psi_{\mu}}::SortOrder.
{\epsilon,\psi_{\mu}}::Depends(\bar,\partial,D).
\Gamma_{#}::Depends(\bar).
# @vary[ e_{m \mu} e^{n \mu} ]( e_{m \mu} -> \bar{\epsilon}\Gamma_m \psi_\mu,
# e^{n \mu} -> \delta{e^{n \mu}} );
#
# @distribute[ @(%)*e^{m \rho} ]: @substitute!(%)( e_{m \mu} e^{m \rho} -> \delta_{\mu}^{\rho} );
#
L:= -1/2 e R - 1/2 e \bar{\psi_\mu} \Gamma^{\mu\nu\rho} D_{\nu}{\psi_{\rho}};
@rewrite_indices!(%){ \Gamma^{m n p} }{ e^{n \mu} };
@vary!(%)( e^{n \mu} -> -\bar{\epsilon} \Gamma^m \psi^\nu e^{m \mu} e^{n \nu},
e -> e \bar{\epsilon} \Gamma^n \psi_\mu e_n^\mu,
R -> -2 R_{\mu\rho} e^{n \mu} \bar{\epsilon} \Gamma^n \psi^\rho,
\psi_\mu -> D_{\mu}{\epsilon} );
@take_match[@(%)]( \bar{D_{\mu}{\epsilon}}*A?? );
@substitute!(%)( D_{\mu}{\epsilon} -> \partial_{\mu}{\epsilon} + 1/4 \omega_{\mu m n} \Gamma^{m n} \epsilon );
@distribute!(%): @unwrap!(%): @rewrite_diracbar!(%);
@substitute!(%)( \Gamma^{q r}\Gamma^{m n p} -> \Gamma^{m n p}\Gamma^{q r}
- @join![ \Gamma^{q r}\Gamma^{m n p} - \Gamma^{m n p} \Gamma^{q r} ]{expand} );
@canonicalise!(%);
@distribute!(%);
# NOW we need to raise/lower indices.
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