#!/usr/bin/env cadabra2
{\mu,\nu,\rho,\sigma,\lambda,\kappa,\alpha,\beta,\gamma,\xi}::Indices.
{\mu,\nu,\rho,\sigma,\lambda,\kappa,\alpha,\beta,\gamma,\xi}::Integer(0..3).
\eta_{\mu\nu}::KroneckerDelta.
\delta{#}::KroneckerDelta.
e_{\mu\nu\lambda\rho}::EpsilonTensor(delta=\delta).
J_{\mu\nu}::AntiSymmetric.
J_{\mu\nu}::SelfNonCommuting.
{ J_{\mu\nu}, P_{\mu}, W_{\mu} }::NonCommuting.
{J_{\mu\nu}, P_{\mu}, W_{\mu} }::Depends(\commutator{#}).
def post_process(ex):
   unwrap(ex)
   eliminate_kronecker(ex)
   canonicalise(ex)
   rename_dummies(ex)
   collect_terms(ex)
poincare:= { \commutator{J_{\mu\nu}}{P_{\rho}} -> \eta_{\mu\rho} P_{\nu} - \eta_{\nu\rho} P_{\mu},
             \commutator{J_{\mu\nu}}{J_{\rho\sigma}} -> \eta_{\mu\rho} J_{\nu\sigma} 
                                                      - \eta_{\mu\sigma} J_{\nu\rho}
                                                      - \eta_{\nu\rho} J_{\mu\sigma}
                                                      + \eta_{\nu\sigma} J_{\mu\rho} };
Psq:= \commutator{J_{\mu\nu}}{ P_{\rho}P_{\rho} };
product_rule(_);
substitute(_, poincare);
distribute(_);
Wsq:=\commutator{J_{\mu\nu}}{W_\mu W_\mu};
substitute(_, $W_\mu -> e_{\mu\nu\lambda\rho} P_\nu J_{\lambda\rho}$);
epsilon_to_delta(_);
expand_delta(_);
product_rule(_);
substitute(_, poincare);
distribute(_);