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Hello everybody,

I'm trying to solve for a challenging problem : a moving inclined plane with a block

I want to solve for the acceleration components for the block and the plane and the normal force acting on the block.

Let O=(0,0) be an external origin.

Let h be the upper left height of the inclined plane.

Let x1 be the x-position of the center of gravity of the inclined plane.

Let x2 be the x-postion of the center of gravity of the block.

Let y be the y-position of the center of gravity of the block.

Let m1 be the mass of the plane. Let m2 be the mass of the block.

Let  mu[1] be the coeffiction of kinetic friction between the bottom of the inclined plane and the level surface.

Let mu[2]  be the coeffiction of kinetic friction between the block and the upper surface of the inclined plane.

Let theta be the angle of the plane with the horizontal.

Let Fp a force applied to the inclined plane.

 

With those defined variables, I make two separable free body diagrams for the block and for the inclined plane, indicating all of the external forces acting on each. It then comes those two vectorial equations :

Block : m2a2=Wweight of block+Fplan acting on block+Ffriction from plan to block+Nnormal from plan to block

Plane : m1a1=Wweight of plane+Fpushing force+Fblock acting on plane+Ffriction from level to plan+Nnormal from level to plane+Ffriction from block to plane+Nnormal from block to plane

I am quite not sure whether I should include the Ffriction from block to plane and the Nnormal from block to plane into the plane's acceleration calculation. Am I right ?

I notice that from the geometry of the figure, I can write down the relation : tan(theta)=(h-y)/(x2-x1)

This implies the relation : -a2y=tan(theta)(a2x-a1x) (equation 1)

Writing down the equations for the x- and y- components of the accelerations of the block and of the plane , this yields :

( equation 2) : m2a2x=m1 sqrt(a1x2+a1y2) cos(theta) -    mu[2]  N1 sin(theta) +Ncos(theta

 

(equation 3) : m2a2y= m2g+m1 sqrt(a1x2+a1y2) sin(theta) +  mu[2]  N1 cos(theta) +Nsin(theta

(equation 4) : m1a1x=Fp - m2 sqrt(a2x2+a2y2)  sin(theta) +  mu[2]  N1 cos(theta) - Ncos(theta

(equation 5) : m1a1y=-m1g  - m2 sqrt(a2x2+a2y2)  cos(theta) - mu[1] N1 + N1 -  mu[2]  N1 sin(theta) -  mu[2]  N1 cos(theta)

Since N1=m1g,  equation 5 becomes : m1a1y= - m2 sqrt(a2x2+a2y2)  cos(theta)   -  mu[2]  N1 sin(theta) -  mu[2]  N1 cos(theta)

I am confused at this stage because a1y=0, that is to say, the plane remains at the ground level surface.

Where am I wrong ? Does this comes from my previous question ?

 

I want to solve this problem with Maple and plot the solutions. Thank you for any answer !

 

RandomCompositions:= proc(n::posint, k::posint)
local
C,
Compositions:= [seq(C-~1, C= combinat:-composition(n+k, k))],
Rand:= rand(1..nops(Compositions))
;
()-> Compositions[Rand()]
end proc:

R:= RandomCompositions(9,6):
n:= 2^13:
S:= 'R()' $ n:

 

I want to compile statistics each number in a sequence cannot  occur  over twice.

The sequences that do not fit the rule above must be ommitted.

The statistic is  Fermi-Dirac statistics.

confused the Bose-Einstein condensation and Fermi-Dirac statistics.

But the theory is right.

The Interactive Embedded Components in Physics are of great importance today and will be even more in the future. Hereand leave a small tutorial of Embedded Components in Physics applied to physics. I hope that somehow you motives to continue the development of science.

 

  Interactive_Embedded_Components_in_Physics.mw      (in spanish)                 

 

Atte.

Lenin Araujo Castillo

Physics Pure

Computer Science

 

Hi everyone,

I have a question regarding the derivation of tensors/matrices.
Let's assume for simplicity, that I have a vector (6x1) s and a matrix A (6x6)defining Transpose(s)*Inverse(A)*s. From this function I want to calculate the derivative w.r.t. s. My approach would be

restartwith(Physics):
with(LinearAlgebra):
Define(s,A)

Diff(
Transpose(s)*Inverse(A)*s, s)

As a result I get

though I'd rather expect something like Inverse(A)*s + Transpose(s)*Inverse(A)

Now as I'm pretty new to Maple, I can imagine that my approach is wrong, but I don't know any better and can't seem to get any information out of the help documents.

Thanks in advance for any of your suggestions!

Hi everyone,

I was trying to write a Maple sheet to calculate some perturbation theory expension as close to the "book notation" as possible. Lets for example consider a linearly perturbed harmonic oscillator with H = hω(n+1/2) and V = λ(a+a), this is one of the classical examples as it can be solved analytically by completing the square. In the Kato formulation (as used in the appended Maple worksheet), as well as in Rayleigh-Schrödinger perturbation theory one uses the projector onto the complement of the unperturbed state. I would like to do this by defining a projector in Maple. I've read the examples concerning projectors in Maple but it seems I have to use a rather ugly workaround by treating the states "below" the unperturbed state and the ones "above" separately. While this is a little annoying in one dimension it becomes a major nuisance in higher dimensions.

My question would be: How do I define the projector onto the complement of some state?

 

Cheers, Sören

 

restart; with(Physics); Setup(mathematicalnotation = true)

a := Annihilation(N, 1):

assume(`and`(`in`(m, nonnegint), m > 0)):

Physics:-Ket(N, m)

(1)

H := Physics:-`*`(Physics:-`*`(h, omega), n+1/2):

`ΔE__2` := simplify(value(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Dagger(psi), V), 1/(E(m)-H)), V), psi)))

-lambda^2/(h*omega)

(2)

`ΔE__4,111` := simplify(value(Dagger(psi).V.(1/(E(m)-H)).V.(1/(E(m)-H)).V.(1/(E(m)-H)).V.psi))

Error, (in Physics:-Dagger) numeric exception: division by zero

 

`ΔE__4,201` := -simplify(value(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Physics:-`*`(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Dagger(psi), V), 1/(E(m)-H)^2), V), psi), Dagger(psi)), V), 1/(E(m)-H)), V), psi)))

lambda^4*(2*m+1)/(h^3*omega^3)

(3)

`ΔE__4` := `ΔE__4,111`+`ΔE__4,201`

`ΔE__4,111`+lambda^4*(2*m+1)/(h^3*omega^3)

(4)

``


Download kato_perturbation_theory.mw

 

``

The TensorSubstittuition is not finding all of the eta[~mu,~mu]*l[nu](X)=l[~mu](X) substitutions.

``

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)

NULL

NULL

NULL

NULL

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)

NULL

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)

NULL

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)

NULL

NULL

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[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[`~alpha`](X), [X])*l[nu](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`]

(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)

term1 := 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[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[`~alpha`](X), [X])*l[nu](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:-`*`(Physics:-`*`(d_[alpha](Christoffel[`~alpha`, mu, nu]), l[`~mu`](X)), l[`~nu`](X)))

Physics:-d_[alpha](-(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[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[`~alpha`](X), [X])*l[nu](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`], [X])*l[`~mu`](X)*l[`~nu`](X)

(13)

expand(Physics:-d_[alpha](-(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[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[`~alpha`](X), [X])*l[nu](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`], [X])*l[`~mu`](X)*l[`~nu`](X))

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

(14)

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

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

(15)

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

l[`~lambda`](X)*Physics:-d_[beta](Physics:-d_[lambda](l[mu](X), [X]), [X])*l[alpha](X)*l[`~mu`](X)*eta[`~alpha`, `~beta`]-eta[`~beta`, `~kappa`]*Physics:-d_[beta](l[lambda](X), [X])*Physics:-d_[kappa](l[nu](X), [X])*l[`~lambda`](X)*l[`~nu`](X)+Physics:-d_[alpha](l[`~alpha`](X), [X])*Physics:-d_[kappa](l[nu](X), [X])*l[`~kappa`](X)*l[`~nu`](X)+Physics:-d_[kappa](l[nu](X), [X])*Physics:-d_[mu](l[`~kappa`](X), [X])*l[`~mu`](X)*l[`~nu`](X)

(16)

"SubstituteTensor({l[~mu](X)*l[mu](X)=0,eta[~mu,~nu]*l[nu](X)=l[~mu](X),eta[~mu,~nu]*d_[gamma](l[nu](X))=d_[gamma](l[~mu](X))},l[~lambda](X)*Physics:-d_[beta](Physics:-d_[lambda](l[mu](X),[X]),[X])*l[alpha](X)*l[~mu](X)*eta[~alpha,~beta]-eta[~beta,~kappa]*Physics:-d_[beta](l[lambda](X),[X])*Physics:-d_[kappa](l[nu](X),[X])*l[~lambda](X)*l[~nu](X)+Physics:-d_[alpha](l[~alpha](X),[X])*Physics:-d_[kappa](l[nu](X),[X])*l[~kappa](X)*l[~nu](X)+Physics:-d_[kappa](l[nu](X),[X])*Physics:-d_[mu](l[~kappa](X),[X])*l[~mu](X)*l[~nu](X))"

l[`~lambda`](X)*Physics:-d_[beta](Physics:-d_[lambda](l[mu](X), [X]), [X])*l[alpha](X)*l[`~mu`](X)*eta[`~alpha`, `~beta`]-eta[`~beta`, `~kappa`]*Physics:-d_[beta](l[lambda](X), [X])*Physics:-d_[kappa](l[nu](X), [X])*l[`~lambda`](X)*l[`~nu`](X)+Physics:-d_[alpha](l[`~alpha`](X), [X])*Physics:-d_[kappa](l[nu](X), [X])*l[`~kappa`](X)*l[`~nu`](X)+Physics:-d_[kappa](l[nu](X), [X])*Physics:-d_[mu](l[`~kappa`](X), [X])*l[`~mu`](X)*l[`~nu`](X)

(17)

``

The first term should change eta[~alpha,~beta]*l[alpha] -> l[~beta]. I made eta symmetric so the order should not matter. I notice that the command seems to work when the substitution is at the beginning of the term.  Do I need to use the new RepositionRepeatedIndicesAsIn command?

 

 

NULL

 

Download Maple_Question_7.7.14.mw

 

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

``


Download Maple_Question_7.3.14.mw

Hi,
The FunctionAdvisor project is currently developing at full speed. During the last two months, a significant amount of new conversion routines and mathematical information for Jacobi elliptic and Jacobi Theta functions, on identities, periodicity, transformations, etc. got added to the conversion network for mathematical functions and to the FunctionAdvisor. The previous months was the turn of the set of complex components, added to the network. Developments regarding the simplification and integration of special functions (e.g SphericalY for computing spherical harmonics or Dirac), as well as fixes to the numerical evaluation of JacobiAM, `assuming` and to differential equation subroutines are also part of the update.

These developments are available to everybody as usual in the Maplesoft R&D Differential Equations and Mathematical Functions webpage. Below there is a list of the latest developments as seen in the worksheet that comes in the zip with the DEsAndMathematicalFunctions update.

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hi,
An interesting sequence of enhancements and new developments happened in the Physics package during this first half of the year. During the last month, improvements happened in the handling of Vectorial expressions and quantum mechanics using Dirac’s notation. During April and part of May it was the turn of general relativity enhancements.

Some of the developments are also interesting beyond Physics. For example: it is now possible to multiply equations. Suppose you have A = B   (1), and C = D   (2), multiplying as in (1) (2) now results in lhs((1)) lhs((2)) = rhs((1)) rhs((2)), saving a lot of typing. You can also perform (1)/(2) or (1)^2. Some enhancements in Physics related simplification, integration, `assuming`, and typesetting - e.g. the simplification and integration of spherical harmonics (SphericalY function) are also part of the update.

These developments are available to everybody as usual in the Maplesoft R&D Physics webpage. Below there is a list of the developments for the last month as seen in the worksheet that comes in the zip with the Physics update.

 

Edgardo S. Cheb-Terrab
Physics, Differential Equations and Mathematical Functions, Maplesoft

Hello,

I wanted to ask whether it's possible to use the taylor command together with vectors from the physics package, maybe I am just doing something wrong here. I tried the following:

and get an error message that diff cannot handle vectors. Of course I could do the expansion by hand an enter the result in Maple but I think it would be a very nice feature because an expansion of vector fields which vary in space and time is such a common problem e.g. in classical electrodynamics. I think of an expansion with non-projected vectors such as

+ higher order terms.

Thanks a lot!

Peter

Is it within the Physics environment possible to specify two sets, A and B, say, of quantities for which the following holds?

1.) any two elements of A anticommute,

2.) any two elements of B anticommute (as well), but

3.) any quantity from A commutes (not anticommutes) with any quantity from B.

Consider the following code:

with(LinearAlgebra):
with(Physics):
Setup(anticommutativeprefix = psi):
psiFermi := Vector(2,symbol = psi):
psiBose  := Vector(2,symbol = phi):
A := Matrix([[0,1],[1,0]]):
Transpose(psiFermi) . A;
Transpose(psiBose ) . A;

It produces the following output:

Why is the first line, for anticommuting components, not evaluated to the same form as the second line, for commuting components? The actual choice of the matrix A seems immaterial; the odd behaviour is present even if A is chosen to be the identity matrix!

In comparison, the 'contracted' (scalarly) expressions

Transpose(psiFermi) . A . psiFermi,
Transpose(psiBose ) . A . psiBose;

produce the following completely sensible output:

This is one is for Edgardo: In the "mini course", there is a command "PlotExpression" used that does not seem to do anything, at least for me. This is in a fresh Maple 18.01 installation on Linux with the latest version of Physics pulled off the Web today.

I cannot find any reference to PlotExpression in the Maple Help files, so where is this thing supposed to be defined? I >am< running a .mapleinit file of my own, configuring some of the plots[setoptions] parameters to my liking, but it should not clobber anything from the system mapleinit.

Another person managed to get the definition of PlotExpression and send it to me. From that I can see that the underlying plots:-plotcompare command seems to work, at least in part.

???

USPAS

 

hello guys

i have a 2-sphere metric (ds^2=dθ^2+sinθ^2 dφ^2) , how to calculate R^abcd R_abcd . 

 

thank you very much

For context, I'm designing a work sheet based around quantum tunneling. Currently I'm looking at the boundary conditions.

What I want to be able to do is to set the expression psi[1] equal to psi[2], but only for the value x = 0. Is this possible? I've tried using if statements, and I've considered converting these expressions into functions for this purpose, but I'm not having much luck. 

Thanks

Blanky

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