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#!/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()
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