#!/usr/local/bin/cadabra2

from cdb.utils.develop import test_algo


@test_algo($2 * Tr{A B C D}$)
def test01():
	Tr{#}::Trace.
	{A, B, C, D}::NonCommuting.
	ex := Tr{A B C D + C D A B + B C D A} - Tr{D A B C}.
	return young_reduce_trace(ex)
test01()

@test_algo($3 * tr(a^{\mu} b^{\nu} c^{\rho} a^{\mu} b^{\rho} c^{\nu}$)
def test02():
	{\mu,\nu,\rho}::Indices(vector).
	{a^{\mu},b^{\mu},c^{\mu}}::NonCommuting.
	tr{#}::Trace.
	ex := tr(a^{\mu} b^{\nu} c^{\rho} a^{\mu} b^{\rho} c^{\nu} + 
              b^{\mu} c^{\nu} a^{\rho} b^{\nu} c^{\mu} a^{\rho} + 
              c^{\mu} a^{\nu} b^{\mu} c^{\rho} a^{\nu} b^{\rho}).
	return young_reduce_trace(ex)
test02()

@test_algo($0$)
def test03():
	{\mu,\nu}::Indices(vector).
	u^{\mu}::ImplicitIndex.
	u^{\mu}::SelfNonCommuting.
	tr{#}::Trace.
	ex := tr{u^{\mu} u^{\mu} u^{\nu} u^{\nu}} - 
	      tr{u^{\mu} u^{\nu} u^{\nu} u^{\mu}}.
	return young_reduce_trace(ex)
test03()