#!/usr/local/bin/cadabra2
def post_process(ex):
	sort_product(ex)
	canonicalise(ex)
	collect_terms(ex)
{\mu,\nu,\rho}::Indices(position=free).
x::Coordinate.
\partial{#}::Derivative.

F_{\mu\nu}::AntiSymmetric;
F_{\mu\nu}::Depends(x).
A_{\mu}::Depends(x,\partial{#}).
\delta{#}::Accent;
S:= -1/4 \int{ F_{\mu\nu} F^{\mu\nu} }{x};
rl:= F_{\mu\nu} = \partial_{\mu}{A_{\nu}} - \partial_{\nu}{A_{\mu}};
substitute(S, rl);
vary(S, $A_{\mu} -> \delta{A_{\mu}}$);
distribute(S);
integrate_by_parts(S, $\delta{A_{\mu}}$);
substitute(_, $\partial_{\mu}{A_{\nu}} -> 1/2 \partial_{\mu}{A_{\nu}} + 1/2 F_{\mu\nu} + 1/2 \partial_{\nu}{A_{\mu}}$);
distribute(_);