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Hi again,

 

I am lost... again. I worked with the Physics package and have obtained my result in form of a lengthy equation of commutators of non-commuting objects. So basically my problem is solved, except that I now want to compute some examples to see, if everything is correct. For that purpose I want to replace now the non-commuting objects with explicit matrices, compute the result and see if it agrees with numerical studies. However, I have no clue which command to use, because if I try it with subs, then the multiplication is of the wrong type and Maple won't multiply my matrices. I tried to use eval but wasn't successful.

Here is an exampe to see what I mean.

Test2.mw

 

Thank you for your time

 

NOh

Last week the Physics package was presented in a talk at the Perimeter Institute for Theoretical Physics and in a combined Applied Mathematics and Physics Seminar at the University of Waterloo. The presentation at the Perimeter Institute got recorded. It was a nice opportunity to surprise people with the recent advances in the package. It follows the presentation with sections closed, and at the end there is a link to a pdf with the sections open and to the related worksheet, used to run the computations in real time during the presentation.

COMPUTER ALGEBRA FOR THEORETICAL PHYSICS

 

  

Generally speaking, physicists still experience that computing with paper and pencil is in most cases simpler than computing on a Computer Algebra worksheet. On the other hand, recent developments in the Maple system implemented most of the mathematical objects and mathematics used in theoretical physics computations, and dramatically approximated the notation used in the computer to the one used in paper and pencil, diminishing the learning gap and computer-syntax distraction to a strict minimum. In connection, in this talk the Physics project at Maplesoft is presented and the resulting Physics package illustrated tackling problems in classical and quantum mechanics, general relativity and field theory. In addition to the 10 a.m lecture, there will be a hands-on workshop at 1pm in the Alice Room.

 

... Why computers?

 

 

We can concentrate more on the ideas instead of on the algebraic manipulations

 

We can extend results with ease

 

We can explore the mathematics surrounding a problem

 

We can share results in a reproducible way

 

Representation issues that were preventing the use of computer algebra in Physics

 

 

Notation and related mathematical methods that were missing:


coordinate free representations for vectors and vectorial differential operators,

covariant tensors distinguished from contravariant tensors,

functional differentiation, relativity differential operators and sum rule for tensor contracted (repeated) indices

Bras, Kets, projectors and all related to Dirac's notation in Quantum Mechanics

 

Inert representations of operations, mathematical functions, and related typesetting were missing:

 

inert versus active representations for mathematical operations

ability to move from inert to active representations of computations and viceversa as necessary

hand-like style for entering computations and texbook-like notation for displaying results

 

Key elements of the computational domain of theoretical physics were missing:

 

ability to handle products and derivatives involving commutative, anticommutative and noncommutative variables and functions

ability to perform computations taking into account custom-defined algebra rules of different kinds

(problem related commutator, anticommutator, bracket, etc. rules)

Vector and tensor notation in mechanics, electrodynamics and relativity

   

Dirac's notation in quantum mechanics

   

 

• 

Computer algebra systems were not originally designed to work with this compact notation, having attached so dense mathematical contents, active and inert representations of operations, not commutative and customizable algebraic computational domain, and the related mathematical methods, all this typically present in computations in theoretical physics.

• 

This situation has changed. The notation and related mathematical methods are now implemented.

 

Tackling examples with the Physics package

 

Classical Mechanics

 

Inertia tensor for a triatomic molecule

 

 

Problem: Determine the Inertia tensor of a triatomic molecule that has the form of an isosceles triangle with two masses m[1] in the extremes of the base and mass m[2] in the third vertex. The distance between the two masses m[1] is equal to a, and the height of the triangle is equal to h.

Solution

   

Quantum mechanics

 

Quantization of the energy of a particle in a magnetic field

 


Show that the energy of a particle in a constant magnetic field oriented along the z axis can be written as

H = `ℏ`*`ω__c`*(`#msup(mi("a",mathcolor = "olive"),mo("†"))`*a+1/2)

where `#msup(mi("a",mathcolor = "olive"),mo("†"))`and a are creation and anihilation operators.

Solution

   

The quantum operator components of `#mover(mi("L",mathcolor = "olive"),mo("→",fontstyle = "italic"))` satisfy "[L[j],L[k]][-]=i `ε`[j,k,m] L[m]"

   

Unitary Operators in Quantum Mechanics

 

(with Pascal Szriftgiser, from Laboratoire PhLAM, Université Lille 1, France)

A linear operator U is unitary if 1/U = `#msup(mi("U"),mo("†"))`, in which case, U*`#msup(mi("U"),mo("†"))` = U*`#msup(mi("U"),mo("†"))` and U*`#msup(mi("U"),mo("†"))` = 1.Unitary operators are used to change the basis inside an Hilbert space, which physically means changing the point of view of the considered problem, but not the underlying physics. Examples: translations, rotations and the parity operator.

1) Eigenvalues of an unitary operator and exponential of Hermitian operators

   

2) Properties of unitary operators

   

3) Schrödinger equation and unitary transform

   

4) Translation operators

   

Classical Field Theory

 

The field equations for a quantum system of identical particles

 

 

Problem: derive the field equation describing the ground state of a quantum system of identical particles (bosons), that is, the Gross-Pitaevskii equation (GPE). This equation is particularly useful to describe Bose-Einstein condensates (BEC).

Solution

   

The field equations for the lambda*Phi^4 model

   

Maxwell equations departing from the 4-dimensional Action for Electrodynamics

   

General Relativity

 

Given the spacetime metric,

g[mu, nu] = (Matrix(4, 4, {(1, 1) = -exp(lambda(r)), (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = -r^2, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = -r^2*sin(theta)^2, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = exp(nu(r))}))

a) Compute the trace of

"Z[alpha]^(beta)=Phi R[alpha]^(beta)+`𝒟`[alpha]`𝒟`[]^(beta) Phi+T[alpha]^(beta)"

where `≡`(Phi, Phi(r)) is some function of the radial coordinate, R[alpha, `~beta`] is the Ricci tensor, `𝒟`[alpha] is the covariant derivative operator and T[alpha, `~beta`] is the stress-energy tensor

T[alpha, beta] = (Matrix(4, 4, {(1, 1) = 8*exp(lambda(r))*Pi, (1, 2) = 0, (1, 3) = 0, (1, 4) = 0, (2, 1) = 0, (2, 2) = 8*r^2*Pi, (2, 3) = 0, (2, 4) = 0, (3, 1) = 0, (3, 2) = 0, (3, 3) = 8*r^2*sin(theta)^2*Pi, (3, 4) = 0, (4, 1) = 0, (4, 2) = 0, (4, 3) = 0, (4, 4) = 8*exp(nu(r))*Pi*epsilon}))

b) Compute the components of "W[alpha]^(beta)"" ≡"the traceless part of  "Z[alpha]^(beta)" of item a)

c) Compute an exact solution to the nonlinear system of differential equations conformed by the components of  "W[alpha]^(beta)" obtained in b)

Background: paper from February/2013, "Withholding Potentials, Absence of Ghosts and Relationship between Minimal Dilatonic Gravity and f(R) Theories", by P. Fiziev.

a) The trace of "  Z[alpha]^(beta)=Phi R[alpha]^(beta)+`𝒟`[alpha]`𝒟`[]^(beta) Phi+T[alpha]^(beta)"

   

b) The components of "W[alpha]^(beta)"" ≡"the traceless part of " Z[alpha]^(beta)"

   

c) An exact solution for the nonlinear system of differential equations conformed by the components of  "W[alpha]^(beta)"

   

The Physics Project

 

 

"Physics" is a software project at Maplesoft that started in 2006. The idea is to develop a computational symbolic/numeric environment specifically for Physics, targeting educational and research needs in equal footing, and resembling as much as possible the flexible style of computations used with paper and pencil. The main reference for the project is the Landau and Lifshitz Course of Theoretical Physics.

 

A first version of "Physics" with basic functionality appeared in 2007. Since then the package has been growing every year, including now, among other things, a searcheable database of solutions to Einstein equations and a new dedicated programming language for Physics.

 

Since August/2013, weekly updates of the Physics package are distributed on the web, including the new developments related to our plan as well as related to people's feedback.

 

 

Presentation_at_PI_and_UW.pdf     Presentation_at_PI_and_UW.mw

 

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

I am trying the following:

restart; 
with(Physics);
with(Library);
Setup(mathematicalnotation = true);
Setup(op = A);
assume(n::integer);

type(A^n, Physics:-`^`(PhysicsType:-ExtendedQuantumOperator, integer));
type(A^n, PhysicsType:-ExtendedQuantumOperator^integer);

the result is

false
false

However, I expected to get true in both cases. How to construct correct type for A^n?
Thank you.

Hi!

I seem to run into problems with (quantum) perturbation theory. In the following minimal working example, an energy denominator, as occuring in perturbation theory is not evaluated if I previously assume that the quantum number is a positive integer. It's supposed to return an error, as the energy denominator is 0.

restart; with(Physics)

a := Annihilation(N, 1, notation = explicit):

psi := Ket(N, m);

Physics:-Ket(N, m)

(1)

E := proc (g) options operator, arrow; (1/2)*g*(g-1)-mu*g end proc:

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

-I/(Im(m)*(2*Re(m)-1-2*mu))

(2)

assume(`in`(m, nonnegint), m > 0);

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

-2*Physics:-Bracket(Physics:-Bra(N, m), 1/(-2*mu*Physics:-`*`(`a-`[N[1]], `a+`[N[1]])+2*mu*m-m^2+Physics:-`*`(Physics:-`^`(`a-`[N[1]], 2), Physics:-`^`(`a+`[N[1]], 2))-4*Physics:-`*`(`a-`[N[1]], `a+`[N[1]])+2*mu+m+2), Physics:-Ket(N, m))

(3)

Parse:-ConvertTo1D, "invalid input %1", `.`(Dagger(psi), 1/(E-H), psi)

2/(2*mu*m-m^2+2*E+m)

(4)

``

Download energy_denominator.mw

 

Best regards,

Sören

Hello everyone,

I've been trying to do some perturbation theory and ran into some problems I don't quite understand. I implemented the Hamiltonian of the Bose-Hubbard model and treated the hopping as a perturbation. Calculating the second order energy shift is easily accomplished, but when I'm only interested in one of the two occuring terms, I run into problems. The calculation takes minutes to finally fail, giving me an "too many levels of recursion"-error. I need to be able to just pick a few terms for some calculations, I'm doing, and can't figure out what I might be doing wrong. Here is the source code (download is below):

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

a__1 := Annihilation(N, 1):

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

Physics:-Ket(N, m, m)

(1)

H := Physics:-`*`(Physics:-`*`(1/2, n__1), n__1-1)+Physics:-`*`(Physics:-`*`(1/2, n__2), n__2-1):

`ΔE__2` := Physics:-`*`(Physics:-`*`(2, d), simplify(value(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Typesetting:-delayDotProduct(Dagger(psi), V), 1/(E(m, m)-H)), V), psi))))

-4*d*J^2*m*(m+1)

(2)

simplify(value(((Dagger(psi).c__2)*a__1.(1/(E(m, m)-H)).c__1)*a__2.psi))

Error, (in PatternMatching:-AlgStruct:-Match) too many levels of recursion

 

``

Download too_many_levels_of_recursion.mw

It would be great, if someone could point out the mistake, I'm making. I copy/pasted the last line, so there shouldn't be any typos.

Thanks in advance,

Sören

Hi, 

I'm trying to set up the dirac algebra using the Physics package in maple 18. There are dirac gamma matricies (Dgamma) already specified, but I can't seem to manipulate their commutation relations. 

So I've tried building my own: 

restart;
with(Physics);

Setup(noncommutativeprefix = {gamma});

g[1] := gamma[1]; g[2] := gamma[2]; g[3] := gamma[3]; g[4] := gamma[0];

InverseMetric := rhs(g_[`~mu`, `~nu`, matrix])

Algebra :=  (a, b) -> %AntiCommutator(g[a], g[b]) = 2*InverseMetric[a, b];

Rules := Matrix(4, 4, Algebra);

Setup(algebrarules = Rules);

Error, (in Physics:-Setup) unable to set AntiCommutator(gamma[0], gamma[1]) = 0 because, taking into account {AntiCommutator(gamma[0], gamma[0]) = 2}, we would have gamma[0] and gamma[0] anticommutative and AntiCommutator(gamma[0], gamma[0]) <> 0

It seems like Maple can't handle the Dirac Algebra? Or have I done something obviously wrong?

Any help is appreciated. 

Thanks

I have been learning to use the Physics package in Maple 18.  I just updated to the latest version of the Physics package to see if it would fix the problem by my results are the same.

When I take a covariant derivative in spherical coordinates it does not appear to have a scale factor such as g_kk below.  

 A_(j;k)=1/(g_(kk))(partialA_j)/(partialx_k)-Gamma_(jk)^iA_i,

This definition of comes from the Mathworld web site.  I think they have a typo such that it should actually read h_k which is the scale factor instead of g_kk which is the metric.  They are related by h_k^2 = g_kk.

Why doesn't Maple's covariant derivative have the scale factor when I am differentiating in spherical coordinates?

Thanks!

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):

`&Delta;E__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)

`&Delta;E__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

 

`&Delta;E__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)

`&Delta;E__4` := `&Delta;E__4,111`+`&Delta;E__4,201`

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

(15)

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

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