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Hi all

kx,ky is the wavenumber, how can I get the 4 cases of piecewise function according to kx=0,kx≠0 and ky=0,ky≠0. Thanks

J := `assuming`([4*(int(int(JJ*exp(-I*(kx*x+ky*y))*sin(2*l*pi*x/a)*sin(2*k*pi*y/b), x = 0 .. a, AllSolutions), y = 0 .. b, AllSolutions))/(a*b)], [k::posint, l::posint, a > 0, b > 0, JJ > 0])

The following MWE shows what I mean:

with(Physics):Setup(mathematical=true):

Setup(noncommutativeprefix={MX,MY,MZ});

test:=proc()

    local eq;

    eq:=-Commutator(MX,MY)-Commutator(MZ,MY);

    eq:=simplify(subs(MX=-MZ,eq));

    return eq;

end proc:

 

test();  # yields -[-MZ,MY] - [MZ,MY]

 

%  # yields 0

 

 

Any ideas how I can solve this? I would like to return the simplified version.

kappa := Vector(7, [1,w[1]*(1-phi+phi*(1-1/(1+exp(-mu[p]-tau[p3]))))+(1-w[1])*
(1-phi+phi*(1-1/(1+exp(-mu[p]-tau[p3]-eta[p2])))),w[1]*phi/(1+exp(-mu[p]-tau[
p3]))+(1-w[1])*phi/(1+exp(-mu[p]-tau[p3]-eta[p2])),w[1]*(1-phi+phi*(1-1/(1+exp
(-mu[p])))*(1-phi)+phi^2*(1-1/(1+exp(-mu[p])))*(1-1/(1+exp(-mu[p]-tau[p3]))))+
(1-w[1])*(1-phi+phi*(1-1/(1+exp(-mu[p]-eta[p2])))*(1-phi)+phi^2*(1-1/(1+exp(-
mu[p]-eta[p2])))*(1-1/(1+exp(-mu[p]-tau[p3]-eta[p2])))),w[1]*phi^2*(1-1/(1+exp
(-mu[p])))/(1+exp(-mu[p]-tau[p3]))+(1-w[1])*phi^2*(1-1/(1+exp(-mu[p]-eta[p2]))
)/(1+exp(-mu[p]-tau[p3]-eta[p2])),w[1]*(phi/(1+exp(-mu[p]))*(1-phi)+phi^2/(1+
exp(-mu[p]))*(1-1/(1+exp(-mu[p]-tau[p3]))))+(1-w[1])*(phi/(1+exp(-mu[p]-eta[p2
]))*(1-phi)+phi^2/(1+exp(-mu[p]-eta[p2]))*(1-1/(1+exp(-mu[p]-tau[p3]-eta[p2]))
)),w[1]*phi^2/(1+exp(-mu[p]))/(1+exp(-mu[p]-tau[p3]))+(1-w[1])*phi^2/(1+exp(-
mu[p]-eta[p2]))/(1+exp(-mu[p]-tau[p3]-eta[p2]))]);

Download kappa.txt

Here is the expression, I am trying to simplify, given a set of rules. NEW_Cole.mw

I have tried different substitutions, using simplify with side rules, applyrule, eval, subs, algsubs.

But none seem to be working as the way I want them to be.

 

Is there a better way?

 

Thanks!

Hi Maple friends.

Maple tends to spit out results(which comprise of variables) in very complicated forms, and I have to use the context menu to select 'simplify' to reduce them.

Is there a setting which will automatically simplify Maple's output?

Thanks in advance.

I'm working on a complex problem in Composite Materials. I've gotten to a near-result 6x6 matrix, with several cells containing polynomial denominators. I have an equation for simplifying these, which boils the polynomials down to a single variable, but I can't seem to get it to substitute in. Can anyone help me solve this? The problem is also time-sensitive.

 

t := exp(2*(I*Pi*(1/11)))

u := t^10*a[10]+t^9*a[9]+t^8*a[8]+t^7*a[7]+t^6*a[6]+t^5*a[5]+t^4*a[4]+t^3*a[3]+t^2*a[2]+t*a[1]+a[0]

 

How can get maple to simplify expressions like u^3+u^2-1 so that the exponents are between 2*(I*Pi*(1/11)) and 1.

Essentially it keeps outputting things like exp(2*(I*Pi*(1/11)))^12 and not simplifying it as it is a root of unity

Hi There

I'm getting started with maple and facing a doubt about using subs, somehow it does not seem to work, this is my expression:

 

> restart;
> theta := omega*t-k*x;
                                omega t - k x
> phi[1] := -(1/2)*H*c*cosh(k*(z+h))*sin(theta)/sinh(k*h);
                   H c cosh(k (z + h)) sin(-omega t + k x)
                   ---------------------------------------
                                 2 sinh(k h)              
> diff(phi[1], t, t);
                                                             2
                H c cosh(k (z + h)) sin(-omega t + k x) omega
              - ----------------------------------------------
                                 2 sinh(k h)                  
> td := simplify(subs(z = 0, %));
                                                          2
                   H c cosh(k h) sin(-omega t + k x) omega
                 - ----------------------------------------
                                 2 sinh(k h)               
> simplify(subs(cosh(k*h)/sinh(k*h) = 1/tanh(k*h), %));
                                                          2
                   H c cosh(k h) sin(-omega t + k x) omega
                 - ----------------------------------------
                                 2 sinh(k h)               
I cannot subs cosh/sinh = tanh. I would like to know why.

Any tips? Thank you

Hi there

I am stuck with the expression

 

> e := (3+2*sinh(x)^2)/(sinh(x)^2*tanh(x));
                                            2
                               3 + 2 sinh(x)  
                              ----------------
                                     2        
                              sinh(x)  tanh(x)

its simplified way, which i cannot find, is


> f := 3*coth(x)^3-coth(x);
                                     3          
                            3 coth(x)  - coth(x)
> simplify(e-f);
                                      0

I would appreciate immensely if someone could give me some pointers on how to solve it.

 

best regards

 

nvc

 

Hi all. I am using Maple 18.

1. Does Maple only output an answer, or can it be made to display the steps it took to achieve the result, in a way that is logical and understandable by the user? For example, I would like to see it display steps when integrating or differentiating, or dividing a polynomial by another polynomial. Basically any process that involve simplifyinf or factorisation.

2. I am trying to divide x^2 + 5x + 9 by x+2, but all Maple displays is the expression

How can I make it do the polynomial division and output the steps it took? I tried using simplify and evaluate from the context menu but the output is still just the expression.

3. Has something happened to this site? It was working fine in Opera until two days ago, and has sinmce started displaying "Error generating page" where the replies to questions should be. No problems with the "posts" section, only in the "questions" section.

Thanks in advance.

 

Well, I'm having issues getting this expression to simplify.  I have a bunch of polynomial results I store in an array, and the simplify command isn't cancelling obvious terms which should cancel out.

June_18.mw

Curiously, it will simplify if I use the command by selecting it from the drop down menu when I select the expression (see lines (7) vs. (8))

Hello,

I am writing a program in C that uses the open maple library. It is not the first time that I use it but now I am facing a strange problem that involves the simplify command: suppose a,x,y are symbols that are not previously used in maple, the following lines

1)  EvalMapleStatement(kv, "simplify((a*x^2-y^2)/(x^2*y^2-1));");

2)  EvalMapleStatement(kv, "simplify((2*x^2-y^2)/(x^2*y^2-1));");

only differ by the fact that the parameter a is replaced by 2 in the second line. But they return the following output:

1) (a*x^2-y^2)/(x^2*y^2-1)

that is correct, nothing to simplify..

2) Error, (in gcd/LinZip) input must be polynomials over the integers

I must be doing something wrong but I am getting nowhere...

Thanks...

 

P.S. This is the complete listing 

 

#include <stdio.h>

#include <stdlib.h>

 

#include "maplec.h"

 

static void M_DECL textCallBack( void *data, int tag, char *output )

{

    printf("%s\n",output);

}

 

int main( int argc, char *argv[] )

{

    char err[2048];  /* command input and error string buffers */

    MKernelVector kv;  /* Maple kernel handle */

    MCallBackVectorDesc cb = {  textCallBack,

                                0,   /* errorCallBack not used */

                                0,   /* statusCallBack not used */

                                0,   /* readLineCallBack not used */

                                0,   /* redirectCallBack not used */

                                0,   /* streamCallBack not used */

                                0,   /* queryInterrupt not used */

                                0    /* callBackCallBack not used */

                            };

    ALGEB r, l;  /* Maple data-structures */

        char *myargv[]={"maple"};

        int myargc=1;

 

    if( (kv=StartMaple(myargc,myargv,&cb,NULL,NULL,err)) == NULL ) {

        printf("Fatal error, %s\n",err);

        return( 1 );

    }

 

EvalMapleStatement(kv, "simplify((a*x^2-y^2)/(x^2*y^2-1));");

 

EvalMapleStatement(kv, "simplify((2*x^2-y^2)/(x^2*y^2-1));");

 

    StopMaple(kv);

 

    return( 0 );

}

 

compiled with

gcc prova.c -I /Library/Frameworks/Maple.framework/Versions/Current/extern/include/ -L /Library/Frameworks/Maple.framework/Versions/Current/bin.APPLE_UNIVERSAL_OSX/ -l maplec

Hello

 

I have a nasty expression which I want to simplify in terms of another expression/function I have defined. 

Please can you tell me how to do this?

A simple example would be:

 

myFunction := a^2 + b^2

horribleFunction:= a^2 + b^2 + ...

I want it to simplify so I get something like

 

A(myFunction)^n  + .....

 

Above is just a simplifcation to try and explain what I mean

 

Thanks

 

Hi , everyone who love Maple and dsolve command, 

my ODE is :

sys_ode := diff(d11(m), m) = -(3*sin(m)^2-1)*d31(m)/a^(3/2)+(-3*cos(m)*sin(m)/a^(3/2))*d41(m), diff(d21(m), m) = (-3*cos(m)*sin(m)/a^(3/2))*d31(m)-(3*cos(m)^2-1)*d41(m)/a^(3/2), diff(d31(m), m) = -a^(3/2)*d11(m), diff(d41(m), m) = -a^(3/2)*d21(m)

using " dsolve([sys_ode]) " command could get the solution easily, and the solution contains "I" (imaginary domain).

However, when we substitute the solution into the ODE "sys_ode", find not correct !

we use the following command to check the solution :

 simplify(  -diff(d11(m), m) -(3*sin(m)^2-1)*d31(m)/a^(3/2)+(-3*cos(m)*sin(m)/a^(3/2))*d41(m)  )

the upper expression is supposed to be zero, but not ! Is it a bug in Maple dsolve ?

After using Simplify the indices are are arranged in the tensor.  I am using the April 14th update from the Physics R&D page.

 


restart

with(Physics):

Setup(mathematicalnotation = true, coordinatesystems = X)

[coordinatesystems = {X}, mathematicalnotation = true]

(1)

Define(l[mu], eta[mu, nu] = -rhs(g_[Minkowski]))

{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)

declare(l(X))

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

(3)

InitialMetric := g_[mu, nu] = eta[mu, nu]+Physics:-`*`(l[mu](X), l[nu](X)); 1; Define(G[mu, nu] = rhs(InitialMetric))

{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)}

(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)

NULL

We first define the Christoffel symbol in terms of the metric,   `g__&mu;,&nu;`.

``

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

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

(6)

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

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

(7)

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

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

(8)

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

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

(9)

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

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

(10)

NULL

NULL

Now we can substitute into the null condition for the Ricci tensor, `R__&mu;&nu;`*`#mi("l")`^mu*l^nu = 0.

convert(Physics:-`*`(Physics:-`*`(Ricci[mu, nu], l[`~mu`](X)), l[`~nu`](X)), Christoffel)

(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])*l[`~mu`](X)*l[`~nu`](X)

(11)

NULL

SubstituteTensorIndices(alpha = rho, (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])*l[`~mu`](X)*l[`~nu`](X))

(Physics:-d_[rho](Physics:-Christoffel[`~rho`, mu, nu], [X])-Physics:-d_[nu](Physics:-Christoffel[`~rho`, mu, rho], [X])+Physics:-Christoffel[`~beta`, mu, nu]*Physics:-Christoffel[`~rho`, beta, rho]-Physics:-Christoffel[`~beta`, mu, rho]*Physics:-Christoffel[`~rho`, beta, nu])*l[`~mu`](X)*l[`~nu`](X)

(12)

  Do the first term

 

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

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

(13)

NULL

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

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

(14)

 

 

Do same thing with the first term but use the Simplify command

 

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

Physics:-d_[rho](Physics:-Christoffel[`~rho`, mu, nu], [X])*l[`~mu`](X)*l[`~nu`](X) = -Physics:-d_[alpha2](l[`~alpha3`](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[`~alpha5`](X)*l[`~rho`](X)*l[rho](X)+Physics:-d_[alpha4](l[`~alpha5`](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[alpha2](X)*l[`~alpha3`](X)*l[`~alpha4`](X)-Physics:-d_[alpha](l[alpha3](X), [X])*eta[`~alpha`, `~alpha1`]*Physics:-d_[alpha1](l[alpha2](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+eta[`~alpha`, `~alpha5`]*Physics:-d_[alpha2](l[alpha](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)-eta[`~alpha5`, `~alpha3`]*Physics:-d_[alpha3](Physics:-d_[alpha5](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[alpha2](X)*l[`~alpha6`](X)+eta[`~alpha6`, `~alpha5`]*Physics:-d_[alpha3](Physics:-d_[alpha5](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[alpha2](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](l[alpha3](X), [X])*Physics:-d_[rho](l[`~rho`](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](Physics:-d_[alpha3](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)*l[`~alpha6`](X)

(15)

SubstituteTensor(Physics:-`*`(l[`~nu`](X), l[nu](X)) = 0, Physics:-d_[rho](Physics:-Christoffel[`~rho`, mu, nu], [X])*l[`~mu`](X)*l[`~nu`](X) = -Physics:-d_[alpha2](l[`~alpha3`](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[`~alpha5`](X)*l[`~rho`](X)*l[rho](X)+Physics:-d_[alpha4](l[`~alpha5`](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[alpha2](X)*l[`~alpha3`](X)*l[`~alpha4`](X)-Physics:-d_[alpha](l[alpha3](X), [X])*eta[`~alpha`, `~alpha1`]*Physics:-d_[alpha1](l[alpha2](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+eta[`~alpha`, `~alpha5`]*Physics:-d_[alpha2](l[alpha](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)-eta[`~alpha5`, `~alpha3`]*Physics:-d_[alpha3](Physics:-d_[alpha5](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[alpha2](X)*l[`~alpha6`](X)+eta[`~alpha6`, `~alpha5`]*Physics:-d_[alpha3](Physics:-d_[alpha5](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[alpha2](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](l[alpha3](X), [X])*Physics:-d_[rho](l[`~rho`](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](Physics:-d_[alpha3](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)*l[`~alpha6`](X))

Physics:-d_[rho](Physics:-Christoffel[`~rho`, mu, nu], [X])*l[`~mu`](X)*l[`~nu`](X) = -Physics:-d_[alpha](l[alpha3](X), [X])*eta[`~alpha`, `~alpha1`]*Physics:-d_[alpha1](l[alpha2](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+eta[`~alpha`, `~alpha5`]*Physics:-d_[alpha2](l[alpha](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](l[alpha3](X), [X])*Physics:-d_[rho](l[`~rho`](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](Physics:-d_[alpha3](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)*l[`~alpha6`](X)

(16)

 

Simplify command does make the algebra easier, but the indices are not the same. Now, equation 16 should correspond to equation 14, but there is no combination of alphas that is consistent.  The variables alpha1 and alpha5 must be rho. One term is always wrong when I try to change the other indices.

alpha2 and alpha3 must be either mu or nu based on the first term.  But alpha6 should also be either mu or nu based on the last term, however that will make alpha2 and alpha3 either (nu and rho) or (mu and rho).  Neither combination makes all of the terms consistent with (14).  Very frustrating.

 

SubstituteTensorIndices({alpha1 = rho, alpha5 = rho}, Physics:-d_[rho](Physics:-Christoffel[`~rho`, mu, nu], [X])*l[`~mu`](X)*l[`~nu`](X) = -Physics:-d_[alpha](l[alpha3](X), [X])*eta[`~alpha`, `~alpha1`]*Physics:-d_[alpha1](l[alpha2](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+eta[`~alpha`, `~alpha5`]*Physics:-d_[alpha2](l[alpha](X), [X])*Physics:-d_[alpha5](l[alpha3](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](l[alpha3](X), [X])*Physics:-d_[rho](l[`~rho`](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](Physics:-d_[alpha3](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)*l[`~alpha6`](X))

Physics:-d_[rho](Physics:-Christoffel[`~rho`, mu, nu], [X])*l[`~mu`](X)*l[`~nu`](X) = -Physics:-d_[alpha](l[alpha3](X), [X])*eta[`~alpha`, `~rho`]*Physics:-d_[rho](l[alpha2](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+eta[`~alpha`, `~rho`]*Physics:-d_[alpha2](l[alpha](X), [X])*Physics:-d_[rho](l[alpha3](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](l[alpha3](X), [X])*Physics:-d_[rho](l[`~rho`](X), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)+Physics:-d_[alpha2](Physics:-d_[alpha3](l[alpha6](X), [X]), [X])*l[`~alpha2`](X)*l[`~alpha3`](X)*l[`~alpha6`](X)

(17)

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``

``


Download Vacuum_Solutions_(Kerr-Schild)_3.mw

Hello,

I have to simplify a piecewise function and Maple gets a more complicated solution than needed.




I don't know how to handle this kind of problems with Maple?
I don't understand why Maple doesn't see this?
Am I doing something wrong?

Thanks in advance for your help / advice.


# the code of my example
restart:
Mf(x):=piecewise(x<=L/2,1/2*x*F,x>1/2*L,1/2*x*F-F*(x-1/2*L));
# Make a dimensionless function:
# -    Mf(x):= Mf(xi)*F*L
# -    variable ξ  ( xi:=x/L )
eq[1]:=Mf(xi)*F*L=Mf(x);
Mf(xi):=solve(eq[1],Mf(xi));
Mf(xi):=subs(x=xi*L,Mf(xi));
# F is the Force and L is the Length of the beam:
Mf(xi):=simplify(Mf(xi)) assuming F>0,L>0;
print("When I simplify this function by hand it will be");
Mf(xi):=piecewise(xi<=1/2,1/2*xi,xi>1/2,-1/2*xi+1/2);




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