i try simplify next expression:
simplify(levicivita[4, sigma, lambda, rho]*levicivita[4, xi, eta, mu]*g_[rho, mu]*qp[sigma]*q[lambda]*qp[xi]*q[eta])
maple gives answer: -2*q[lambda]*q[~lambda
]*qp[sigma]*qp[~sigma
]+2*q[~alpha
]*q[~xi
]*qp[alpha]*qp[xi]
in reality incorrect answer, because indices must run on 1,2,3 not 1,2,3,4!
sumoverrepeatedindices(%) confirms maple mistakes.
my preamble is:
with(physics) setup(mathematicalnotation = true); coordinates(x); setup(spaceindices = lowercaselatin) setup(tensors = q[mu](x)) pdetools:-declare(q(x)) setup(tensors = qp[mu](x)) pdetools:-declare(qp(x))
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