Question: Substitution Tensor command has problem with number of free indices

July 04 2014 Michael_Watson 35
Maple 18

2

 

I am having trouble with the SubstitutionTensor command.  It kicks out an error message for operand with different free indices, but the operands seems to be fine.  I checked all of the terms and they all seem fine. Thank you for your help.

 

 

restart

with(Physics):

Setup(mathematicalnotation = true, coordinatesystems = X, usephysicsevaluator = false)

[coordinatesystems = {X}, mathematicalnotation = true, usephysicsevaluator = false]

(1)

Define(l[mu]);

{Physics:-Dgamma[mu], Physics:-Psigma[mu], Physics:-d_[mu], eta[mu, nu], Physics:-g_[mu, nu], l[mu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(2)

Define(G[mu, nu] = eta[mu, nu]+Physics:-`*`(l[mu](X), l[nu](X)))

{Physics:-Dgamma[mu], G[mu, nu], Physics:-Psigma[mu], Physics:-d_[mu], eta[mu, nu], Physics:-g_[mu, nu], l[mu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

(3)

declare(l(X))

l(x1, x2, x3, x4)*`will now be displayed as`*l

(4)

``

``

``

``

Setup(metric = rhs(G[]))

[metric = {(1, 1) = 1+l[1](X)^2, (1, 2) = l[1](X)*l[2](X), (1, 3) = l[1](X)*l[3](X), (1, 4) = l[1](X)*l[4](X), (2, 2) = 1+l[2](X)^2, (2, 3) = l[2](X)*l[3](X), (2, 4) = l[2](X)*l[4](X), (3, 3) = 1+l[3](X)^2, (3, 4) = l[3](X)*l[4](X), (4, 4) = -1+l[4](X)^2}]

(5)

g_[];

g[mu, nu] = (Matrix(4, 4, {(1, 1) = 1+l[1](X)^2, (1, 2) = l[1](X)*l[2](X), (1, 3) = l[1](X)*l[3](X), (1, 4) = l[1](X)*l[4](X), (2, 1) = l[1](X)*l[2](X), (2, 2) = 1+l[2](X)^2, (2, 3) = l[2](X)*l[3](X), (2, 4) = l[2](X)*l[4](X), (3, 1) = l[1](X)*l[3](X), (3, 2) = l[2](X)*l[3](X), (3, 3) = 1+l[3](X)^2, (3, 4) = l[3](X)*l[4](X), (4, 1) = l[1](X)*l[4](X), (4, 2) = l[2](X)*l[4](X), (4, 3) = l[3](X)*l[4](X), (4, 4) = -1+l[4](X)^2}))

(6)

``

Christoffel[`~alpha`, mu, nu] = convert(Christoffel[`~alpha`, mu, nu], g_)

Physics:-Christoffel[`~alpha`, mu, nu] = (1/2)*Physics:-g_[`~alpha`, `~beta`]*(Physics:-d_[nu](Physics:-g_[beta, mu], [X])+Physics:-d_[mu](Physics:-g_[beta, nu], [X])-Physics:-d_[beta](Physics:-g_[mu, nu], [X]))

(7)

Christoffel[beta, mu, nu] = convert(Christoffel[beta, mu, nu], g_)

Physics:-Christoffel[beta, mu, nu] = (1/2)*Physics:-d_[nu](Physics:-g_[beta, mu], [X])+(1/2)*Physics:-d_[mu](Physics:-g_[beta, nu], [X])-(1/2)*Physics:-d_[beta](Physics:-g_[mu, nu], [X])

(8)

``

SubstituteTensor(g_[mu, nu] = eta[mu, nu]+Physics:-`*`(l[mu](X), l[nu](X)), Physics:-Christoffel[beta, mu, nu] = (1/2)*Physics:-d_[nu](Physics:-g_[beta, mu], [X])+(1/2)*Physics:-d_[mu](Physics:-g_[beta, nu], [X])-(1/2)*Physics:-d_[beta](Physics:-g_[mu, nu], [X]), evaluateexpression)

Physics:-Christoffel[beta, mu, nu] = (1/2)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)+(1/2)*l[beta](X)*Physics:-d_[nu](l[mu](X), [X])+(1/2)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)+(1/2)*l[beta](X)*Physics:-d_[mu](l[nu](X), [X])-(1/2)*Physics:-d_[beta](l[mu](X), [X])*l[nu](X)-(1/2)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])

(9)

``

``

Christoffel[`~alpha`, mu, nu] = Simplify(Physics:-`*`(eta[`~alpha`, `~beta`]-Physics:-`*`(l[`~alpha`](X), l[`~beta`](X)), rhs(Physics:-Christoffel[beta, mu, nu] = (1/2)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)+(1/2)*l[beta](X)*Physics:-d_[nu](l[mu](X), [X])+(1/2)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)+(1/2)*l[beta](X)*Physics:-d_[mu](l[nu](X), [X])-(1/2)*Physics:-d_[beta](l[mu](X), [X])*l[nu](X)-(1/2)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X]))))

Physics:-Christoffel[`~alpha`, mu, nu] = -(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)*eta[`~alpha`, `~beta`]-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[beta](X)*Physics:-d_[nu](l[mu](X), [X])+(1/2)*l[beta](X)*Physics:-d_[nu](l[mu](X), [X])*eta[`~alpha`, `~beta`]-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)*eta[`~alpha`, `~beta`]-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[beta](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[beta](X)*Physics:-d_[mu](l[nu](X), [X])*eta[`~alpha`, `~beta`]+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])*eta[`~alpha`, `~beta`]+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])*eta[`~alpha`, `~beta`]

(10)

SubstituteTensor({Physics:-`*`(eta[`~mu`, `~nu`], d_[gamma](l[nu](X))) = d_[gamma](l[`~mu`](X)), Physics:-`*`(l[nu](X), eta[`~mu`, `~nu`]) = l[`~mu`](X), Physics:-`*`(l[`~mu`](X), l[mu](X)) = 0}, Physics:-Christoffel[`~alpha`, mu, nu] = -(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)*eta[`~alpha`, `~beta`]-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[beta](X)*Physics:-d_[nu](l[mu](X), [X])+(1/2)*l[beta](X)*Physics:-d_[nu](l[mu](X), [X])*eta[`~alpha`, `~beta`]-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)*eta[`~alpha`, `~beta`]-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[beta](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[beta](X)*Physics:-d_[mu](l[nu](X), [X])*eta[`~alpha`, `~beta`]+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])*eta[`~alpha`, `~beta`]+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])*eta[`~alpha`, `~beta`])

Physics:-Christoffel[`~alpha`, mu, nu] = -(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*l[nu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])*eta[`~alpha`, `~beta`]+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])*eta[`~alpha`, `~beta`]

(11)

Ricci[mu, nu] = convert(Ricci[mu, nu], Christoffel)

Physics:-Ricci[mu, nu] = Physics:-d_[alpha](Physics:-Christoffel[`~alpha`, mu, nu], [X])-Physics:-d_[nu](Physics:-Christoffel[`~alpha`, alpha, mu], [X])+Physics:-Christoffel[`~beta`, mu, nu]*Physics:-Christoffel[`~alpha`, alpha, beta]-Physics:-Christoffel[`~beta`, alpha, mu]*Physics:-Christoffel[`~alpha`, beta, nu]

(12)

SubstituteTensor(Physics:-Christoffel[`~alpha`, mu, nu] = -(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[nu](l[beta](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~beta`](X)*Physics:-d_[mu](l[beta](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*l[nu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[beta](l[mu](X), [X])*eta[`~alpha`, `~beta`]+(1/2)*l[`~alpha`](X)*l[`~beta`](X)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[beta](l[nu](X), [X])*eta[`~alpha`, `~beta`], Physics:-Ricci[mu, nu] = Physics:-d_[alpha](Physics:-Christoffel[`~alpha`, mu, nu], [X])-Physics:-d_[nu](Physics:-Christoffel[`~alpha`, alpha, mu], [X])+Physics:-Christoffel[`~beta`, mu, nu]*Physics:-Christoffel[`~alpha`, alpha, beta]-Physics:-Christoffel[`~beta`, alpha, mu]*Physics:-Christoffel[`~alpha`, beta, nu], evaluateexpression)

Physics:-Ricci[mu, nu] = (1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])+l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X]))+(-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`])*(-(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[beta](l[lambda](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/2)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])*eta[`~alpha`, `~lambda`]+(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])-(1/2)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`])-(-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)+(1/2)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])-(1/2)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])-(1/2)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`])*(-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/2)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])-(1/2)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`])+(1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])+l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X]))-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[alpha](l[`~alpha`](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[mu](l[alpha](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[alpha](X)-(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[nu](l[alpha](X), [X])-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X]))-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X]))+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[alpha](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[mu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[nu](l[`~alpha`](X), [X]), [X])*l[mu](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[kappa](X), [X]), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*Physics:-d_[alpha](l[nu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*Physics:-d_[alpha](l[mu](X), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[kappa](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[alpha](X)*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*l[alpha](X)*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X])+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[tau](X), [X]), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*Physics:-d_[nu](l[mu](X), [X])+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*Physics:-d_[nu](l[alpha](X), [X])+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*Physics:-d_[mu](l[tau](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](Physics:-d_[mu](l[tau](X), [X]), [X])*l[alpha](X)

(13)

SubstituteTensor({Physics:-`*`(eta[`~mu`, `~nu`], d_[gamma](l[nu](X))) = d_[gamma](l[`~mu`](X)), Physics:-`*`(l[nu](X), eta[`~mu`, `~nu`]) = l[`~mu`](X), Physics:-`*`(l[`~mu`](X), l[mu](X)) = 0}, Physics:-Ricci[mu, nu] = (1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])+l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X]))+(-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`])*(-(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[beta](l[lambda](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/2)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])*eta[`~alpha`, `~lambda`]+(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])-(1/2)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`])-(-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)+(1/2)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])-(1/2)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])-(1/2)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`])*(-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/2)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])-(1/2)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`])+(1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])+l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X]))-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[alpha](l[`~alpha`](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[mu](l[alpha](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[alpha](X)-(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[nu](l[alpha](X), [X])-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X]))-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X]))+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[alpha](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[mu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[nu](l[`~alpha`](X), [X]), [X])*l[mu](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[kappa](X), [X]), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*Physics:-d_[alpha](l[nu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*Physics:-d_[alpha](l[mu](X), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[kappa](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[alpha](X)*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*l[alpha](X)*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X])+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[tau](X), [X]), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*Physics:-d_[nu](l[mu](X), [X])+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*Physics:-d_[nu](l[alpha](X), [X])+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*Physics:-d_[mu](l[tau](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](Physics:-d_[mu](l[tau](X), [X]), [X])*l[alpha](X))

Physics:-Ricci[mu, nu] = (1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*Physics:-d_[nu](l[alpha](X), [X])+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[kappa](X), [X]), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*Physics:-d_[alpha](l[nu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*Physics:-d_[alpha](l[mu](X), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[kappa](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[alpha](X)*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X])+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[tau](X), [X]), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*Physics:-d_[nu](l[mu](X), [X])+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`])*((1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/2)*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/2)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`])+(1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])+l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X]))-(-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)+(1/2)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])-(1/2)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])-(1/2)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`])*(-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/2)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])-(1/2)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`])+(1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])+l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X]))-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[alpha](l[`~alpha`](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[mu](l[alpha](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[alpha](X)-(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[nu](l[alpha](X), [X])-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X]))-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X]))+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[alpha](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[mu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[nu](l[`~alpha`](X), [X]), [X])*l[mu](X)

(14)

expand(Physics:-`*`(Physics:-`*`(Physics:-Ricci[mu, nu] = (1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*Physics:-d_[alpha](l[tau](X), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*Physics:-d_[nu](l[alpha](X), [X])+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*Physics:-d_[mu](l[tau](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[mu](X)*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*l[nu](X)*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[mu](l[kappa](X), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[kappa](X), [X]), [X])*l[nu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*Physics:-d_[alpha](l[nu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*Physics:-d_[alpha](l[mu](X), [X])-(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[kappa](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[alpha](X)*Physics:-d_[tau](l[mu](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[`~tau`](X)*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[`~tau`](X), [X])*l[mu](X)*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~tau`](X)*l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X])+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[tau](X), [X]), [X])*l[mu](X)+(1/2)*l[`~alpha`](X)*l[`~tau`](X)*Physics:-d_[alpha](l[tau](X), [X])*Physics:-d_[nu](l[mu](X), [X])+(-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)+(1/2)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])-(1/2)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])-(1/2)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]+(1/2)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])-(1/2)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`])*((1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/2)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/2)*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/2)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`])+(1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])+l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X]))-(-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)+(1/2)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)+(1/2)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)+(1/2)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)+(1/2)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])-(1/2)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]+(1/2)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])-(1/2)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`])*(-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])-(1/2)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/2)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)+(1/2)*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/2)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/2)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])-(1/2)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`])+(1/2)*eta[`~alpha`, `~tau`]*(Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])+l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X]))-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[mu](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[alpha](l[`~alpha`](X), [X]), [X])*l[mu](X)-(1/2)*Physics:-d_[nu](l[`~alpha`](X), [X])*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[mu](l[alpha](X), [X]), [X])-(1/2)*Physics:-d_[nu](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[alpha](X)-(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[nu](l[alpha](X), [X])-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])+l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X]))-(1/2)*eta[`~alpha`, `~kappa`]*(Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])+l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X]))+(1/2)*Physics:-d_[alpha](l[`~alpha`](X), [X])*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[nu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[nu](X)+(1/2)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[alpha](l[nu](X), [X])+(1/2)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[mu](X), [X]), [X])+(1/2)*Physics:-d_[alpha](Physics:-d_[nu](l[`~alpha`](X), [X]), [X])*l[mu](X), l[`~mu`](X)), l[`~nu`](X)))

Physics:-Ricci[mu, nu]*l[`~mu`](X)*l[`~nu`](X) = (1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*Physics:-d_[alpha](l[mu](X), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[`~kappa`](X)*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*Physics:-d_[alpha](l[`~kappa`](X), [X])*Physics:-d_[nu](l[kappa](X), [X])*l[mu](X)-(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[kappa](X), [X]), [X])*l[mu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*Physics:-d_[alpha](l[`~alpha`](X), 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[X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]

(15)

"SubstituteTensor({l[~mu](X)*l[mu](X)=0,l[nu](X)*eta[~mu,~nu]=l[~mu](X),eta[~mu,~nu]*d_[gamma](l[nu](X))=d_[gamma](l[~mu](X))},rhs(Physics:-Ricci[mu,nu]*l[~mu](X)*l[~nu](X) = -1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*Physics:-d_[nu](Physics:-d_[alpha](l[mu](X),[X]),[X])-1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[nu](Physics:-d_[alpha](l[~alpha](X),[X]),[X])*l[mu](X)-1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[nu](l[~alpha](X),[X])*Physics:-d_[mu](l[alpha](X),[X])-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*Physics:-d_[nu](Physics:-d_[mu](l[alpha](X),[X]),[X])-1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[nu](Physics:-d_[mu](l[~alpha](X),[X]),[X])*l[alpha](X)-1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~alpha](X),[X])*Physics:-d_[nu](l[alpha](X),[X])+1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](l[~alpha](X),[X])*Physics:-d_[mu](l[nu](X),[X])+1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*Physics:-d_[alpha](Physics:-d_[mu](l[nu](X),[X]),[X])+1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](Physics:-d_[mu](l[~alpha](X),[X]),[X])*l[nu](X)+1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~alpha](X),[X])*Physics:-d_[alpha](l[nu](X),[X])+1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*Physics:-d_[alpha](Physics:-d_[nu](l[mu](X),[X]),[X])+1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](Physics:-d_[nu](l[~alpha](X),[X]),[X])*l[mu](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X),[X])*l[~alpha](X)*l[~chi](X)*Physics:-d_[nu](l[chi](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X),[X])*l[~alpha](X)*l[~chi](X)*l[nu](X)*Physics:-d_[chi](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X),[X])*l[~alpha](X)*l[~chi](X)*l[beta](X)*Physics:-d_[chi](l[nu](X),[X])+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*Physics:-d_[nu](l[iota](X),[X])*l[mu](X)*l[~alpha](X)*l[~lambda](X)*Physics:-d_[alpha](l[lambda](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*Physics:-d_[nu](l[iota](X),[X])*l[mu](X)*l[~alpha](X)*l[~lambda](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X),[X])+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*Physics:-d_[mu](l[iota](X),[X])*l[nu](X)*l[~alpha](X)*l[~lambda](X)*Physics:-d_[alpha](l[lambda](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X),[X])*l[~alpha](X)*l[~chi](X)*Physics:-d_[beta](l[chi](X),[X])*l[nu](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X),[X])*l[~alpha](X)*l[~chi](X)*l[nu](X)*Physics:-d_[chi](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X),[X])*l[~alpha](X)*l[~chi](X)*l[beta](X)*Physics:-d_[chi](l[nu](X),[X])+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X),[X])*l[~alpha](X)*l[~chi](X)*Physics:-d_[nu](l[chi](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X),[X])*l[~alpha](X)*l[~chi](X)*Physics:-d_[beta](l[chi](X),[X])*l[nu](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*Physics:-d_[mu](l[iota](X),[X])*l[nu](X)*l[~alpha](X)*l[~lambda](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*l[nu](X)*Physics:-d_[iota](l[mu](X),[X])*l[~alpha](X)*l[~lambda](X)*Physics:-d_[alpha](l[lambda](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*l[nu](X)*Physics:-d_[iota](l[mu](X),[X])*l[~alpha](X)*l[~lambda](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*l[mu](X)*Physics:-d_[iota](l[nu](X),[X])*l[~alpha](X)*l[~lambda](X)*Physics:-d_[alpha](l[lambda](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~iota](X)*l[mu](X)*Physics:-d_[iota](l[nu](X),[X])*l[~alpha](X)*l[~lambda](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[mu](l[omega](X),[X])*l[alpha](X)*l[~alpha](X)*l[~chi](X)*Physics:-d_[nu](l[chi](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[mu](l[omega](X),[X])*l[alpha](X)*l[~alpha](X)*l[~chi](X)*Physics:-d_[beta](l[chi](X),[X])*l[nu](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[mu](l[omega](X),[X])*l[alpha](X)*l[~alpha](X)*l[~chi](X)*l[nu](X)*Physics:-d_[chi](l[beta](X),[X])+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[mu](l[omega](X),[X])*l[alpha](X)*l[~alpha](X)*l[~chi](X)*l[beta](X)*Physics:-d_[chi](l[nu](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[alpha](l[omega](X),[X])*l[mu](X)*l[~alpha](X)*l[~chi](X)*Physics:-d_[nu](l[chi](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[alpha](l[omega](X),[X])*l[mu](X)*l[~alpha](X)*l[~chi](X)*Physics:-d_[beta](l[chi](X),[X])*l[nu](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[alpha](l[omega](X),[X])*l[mu](X)*l[~alpha](X)*l[~chi](X)*l[nu](X)*Physics:-d_[chi](l[beta](X),[X])+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*l[~omega](X)*Physics:-d_[alpha](l[omega](X),[X])*l[mu](X)*l[~alpha](X)*l[~chi](X)*l[beta](X)*Physics:-d_[chi](l[nu](X),[X])+1/2*l[~mu](X)*l[~nu](X)*eta[~alpha,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](X)*l[~nu](X)*Physics:-d_[nu](l[~beta](X),[X])*l[mu](X)*Physics:-d_[lambda](l[~alpha](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[nu](l[mu](X),[X])*Physics:-d_[beta](l[~alpha](X),[X])*l[alpha](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[nu](l[mu](X),[X])*l[~alpha](X)*Physics:-d_[beta](l[alpha](X),[X])+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[nu](l[mu](X),[X])*Physics:-d_[alpha](l[~alpha](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[nu](l[mu](X),[X])*l[~alpha](X)*Physics:-d_[alpha](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[nu](l[mu](X),[X])*Physics:-d_[lambda](l[~alpha](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~beta](X),[X])*l[nu](X)*l[~alpha](X)*Physics:-d_[beta](l[alpha](X),[X])+1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~beta](X),[X])*l[nu](X)*Physics:-d_[alpha](l[~alpha](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~beta](X),[X])*l[nu](X)*l[~alpha](X)*Physics:-d_[alpha](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~beta](X),[X])*l[nu](X)*Physics:-d_[lambda](l[~alpha](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[nu](X),[X])*Physics:-d_[beta](l[~alpha](X),[X])*l[alpha](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[nu](X),[X])*l[~alpha](X)*Physics:-d_[beta](l[alpha](X),[X])+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[nu](X),[X])*Physics:-d_[alpha](l[~alpha](X),[X])*l[beta](X)+1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[nu](X),[X])*l[~alpha](X)*Physics:-d_[alpha](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[nu](X),[X])*Physics:-d_[lambda](l[~alpha](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~beta](X),[X])*l[alpha](X)*Physics:-d_[nu](l[~alpha](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~beta](X),[X])*l[alpha](X)*l[~alpha](X)*Physics:-d_[nu](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[mu](l[~beta](X),[X])*l[alpha](X)*l[~alpha](X)*Physics:-d_[beta](l[nu](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[alpha](X),[X])*Physics:-d_[nu](l[~alpha](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[alpha](X),[X])*l[~alpha](X)*Physics:-d_[nu](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[alpha](X),[X])*Physics:-d_[beta](l[~alpha](X),[X])*l[nu](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[mu](l[alpha](X),[X])*l[~alpha](X)*Physics:-d_[beta](l[nu](X),[X])-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](l[~beta](X),[X])*l[mu](X)*Physics:-d_[nu](l[~alpha](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](l[~beta](X),[X])*l[mu](X)*l[~alpha](X)*Physics:-d_[nu](l[beta](X),[X])-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](l[~beta](X),[X])*l[mu](X)*Physics:-d_[beta](l[~alpha](X),[X])*l[nu](X)-1/4*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](l[~beta](X),[X])*l[mu](X)*l[~alpha](X)*Physics:-d_[beta](l[nu](X),[X])-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[alpha](l[mu](X),[X])*Physics:-d_[nu](l[~alpha](X),[X])*l[beta](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[alpha](l[mu](X),[X])*l[~alpha](X)*Physics:-d_[nu](l[beta](X),[X])-1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[nu](l[~alpha](X),[X])*l[~tau](X)*l[alpha](X)*Physics:-d_[tau](l[mu](X),[X])-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*l[~tau](X)*Physics:-d_[nu](l[alpha](X),[X])*Physics:-d_[tau](l[mu](X),[X])-1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[nu](l[~alpha](X),[X])*l[~tau](X)*l[mu](X)*Physics:-d_[tau](l[alpha](X),[X])-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*Physics:-d_[nu](l[~tau](X),[X])*l[mu](X)*Physics:-d_[tau](l[alpha](X),[X])-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*l[~tau](X)*Physics:-d_[nu](l[mu](X),[X])*Physics:-d_[tau](l[alpha](X),[X])-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*l[~tau](X)*l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X),[X]),[X])+1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*l[~tau](X)*Physics:-d_[nu](Physics:-d_[alpha](l[tau](X),[X]),[X])*l[mu](X)-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*l[~kappa](X)*Physics:-d_[nu](l[kappa](X),[X])*Physics:-d_[alpha](l[mu](X),[X])-1/2*l[~mu](X)*l[~nu](X)*Physics:-d_[alpha](l[~alpha](X),[X])*l[~kappa](X)*Physics:-d_[nu](l[kappa](X),[X])*l[mu](X)-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*Physics:-d_[alpha](l[~kappa](X),[X])*Physics:-d_[nu](l[kappa](X),[X])*l[mu](X)-1/2*l[~mu](X)*l[~nu](X)*l[~alpha](X)*l[~kappa](X)*Physics:-d_[alpha](Physics:-d_[nu](l[kappa](X),[X]),[X])*l[mu](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[alpha](l[mu](X),[X])*Physics:-d_[beta](l[~alpha](X),[X])*l[nu](X)-1/4*l[~mu](X)*l[~nu](X)*l[~beta](X)*Physics:-d_[alpha](l[mu](X),[X])*l[~alpha](X)*Physics:-d_[beta](l[nu](X),[X])))"

op(32, rhs(Physics:-Ricci[mu, nu]*l[`~mu`](X)*l[`~nu`](X) = -(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[beta](l[`~alpha`](X), 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[X])*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)))

(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]

(16)

op(17, rhs(Physics:-Ricci[mu, nu]*l[`~mu`](X)*l[`~nu`](X) = (1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)-(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*l[`~kappa`](X)*Physics:-d_[mu](l[kappa](X), [X])*Physics:-d_[alpha](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), 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[X])*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[nu](X), [X]), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[nu](X)+(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[alpha](l[nu](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[mu](X), [X]), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[`~alpha`](X), [X]), [X])*l[mu](X)-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*Physics:-d_[alpha](l[nu](X), [X])*Physics:-d_[kappa](l[mu](X), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*l[nu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[mu](X), [X]), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*Physics:-d_[nu](l[alpha](X), [X])*Physics:-d_[tau](l[mu](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*l[alpha](X)*Physics:-d_[nu](Physics:-d_[tau](l[mu](X), [X]), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*Physics:-d_[nu](l[mu](X), [X])*Physics:-d_[tau](l[alpha](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~tau`]*l[mu](X)*Physics:-d_[nu](Physics:-d_[tau](l[alpha](X), [X]), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*Physics:-d_[alpha](l[mu](X), [X])*Physics:-d_[kappa](l[nu](X), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*eta[`~alpha`, `~kappa`]*l[mu](X)*Physics:-d_[alpha](Physics:-d_[kappa](l[nu](X), [X]), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]))

(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])

(17)

op(77, rhs(Physics:-Ricci[mu, nu]*l[`~mu`](X)*l[`~nu`](X) = (1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[nu](l[mu](X), [X])*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[nu](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[nu](X), [X])*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)-(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[mu](X), [X]), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](Physics:-d_[alpha](l[`~alpha`](X), [X]), [X])*l[mu](X)-(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~alpha`](X), [X])*Physics:-d_[mu](l[alpha](X), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*Physics:-d_[nu](Physics:-d_[mu](l[alpha](X), [X]), [X])-(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[alpha](X)-(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[nu](l[alpha](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](l[`~alpha`](X), [X])*Physics:-d_[mu](l[nu](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[nu](X), [X]), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](Physics:-d_[mu](l[`~alpha`](X), [X]), [X])*l[nu](X)+(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~alpha`](X), [X])*Physics:-d_[alpha](l[nu](X), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*l[`~alpha`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[mu](X), [X]), [X])+(1/2)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](Physics:-d_[nu](l[`~alpha`](X), [X]), [X])*l[mu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[nu](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[mu](l[omega](X), [X])*l[alpha](X)*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*Physics:-d_[beta](l[`~alpha`](X), [X])*l[alpha](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~omega`](X)*Physics:-d_[alpha](l[omega](X), [X])*l[mu](X)*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), 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`~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[beta](l[chi](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[nu](l[iota](X), [X])*l[mu](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*Physics:-d_[mu](l[iota](X), [X])*l[nu](X)*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*l[`~lambda`](X)*Physics:-d_[alpha](l[lambda](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[nu](X)*Physics:-d_[iota](l[mu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*l[`~lambda`](X)*l[beta](X)*Physics:-d_[lambda](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*l[`~iota`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*l[alpha](X)*Physics:-d_[lambda](l[beta](X), [X])*eta[`~alpha`, `~lambda`]-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*Physics:-d_[beta](l[alpha](X), [X])-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[alpha](l[`~alpha`](X), [X])*l[beta](X)-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*l[`~alpha`](X)*Physics:-d_[alpha](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[iota](l[nu](X), [X])*eta[`~beta`, `~iota`]*Physics:-d_[lambda](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[mu](l[`~beta`](X), [X])*l[alpha](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[mu](l[alpha](X), [X])*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*Physics:-d_[alpha](l[`~beta`](X), [X])*l[mu](X)*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])*l[nu](X)*Physics:-d_[chi](l[beta](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[`~beta`](X)*Physics:-d_[alpha](l[mu](X), [X])*l[beta](X)*Physics:-d_[chi](l[nu](X), [X])*eta[`~alpha`, `~chi`]+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*Physics:-d_[beta](l[`~alpha`](X), [X])*l[nu](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[mu](X)*Physics:-d_[omega](l[alpha](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*Physics:-d_[beta](l[nu](X), [X])+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*Physics:-d_[nu](l[`~alpha`](X), [X])*l[beta](X)+(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*Physics:-d_[nu](l[beta](X), [X])))

-(1/4)*l[`~mu`](X)*l[`~nu`](X)*l[alpha](X)*Physics:-d_[omega](l[mu](X), [X])*eta[`~beta`, `~omega`]*l[`~alpha`](X)*l[`~chi`](X)*Physics:-d_[nu](l[chi](X), [X])*l[beta](X)

(18)

``


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