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Using a Defined Tetrad...

Asked by: Michael_Watson 125
define tensor physics
October 09 2015
1  1

 

I am trying to use the Define() funtion for the tetrad form of the Ricci Tensor. I use the Setup() function to define the tetradmetric and the tetrad labels. However, the function continues do some strange things with the d_ . It should be just a simple sum over the repeated indices, but I am getting imaginary terms.

 

  restart; with(Physics); with(Tetrads)

0, "%1 is not a command in the %2 package", Tetrads, Physics

 (1)

Physics:-Setup(coordinatesystems = {X}, spacetimeindices = greek, tetradindices = lowercaselatin, tetradmetric = Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]], shape = symmetric), mathematicalnotation = true)

[coordinatesystems = {X}, mathematicalnotation = true, spacetimeindices = greek, tetradindices = lowercaselatin, tetradmetric = {(1, 2) = 1, (3, 4) = 1}]

 (2)

Physics:-Define(GammaT[a, b, c], RicciT[b, c] = -%d_[c](GammaT[`~a`, b, a])+%d_[a](GammaT[`~a`, b, c])-Physics:-`*`(GammaT[`~m`, b, a], GammaT[`~a`, m, c])+Physics:-`*`(GammaT[`~m`, b, c], GammaT[`~a`, m, a])-Physics:-`*`(GammaT[`~a`, b, m], GammaT[`~m`, c, a]-GammaT[`~m`, a, c]))

{Physics:-Dgamma[mu], GammaT[a, b, c], Physics:-Psigma[mu], RicciT[b, c], Physics:-d_[mu], Physics:-Tetrads:-eta_[a, b], Physics:-g_[mu, nu], Physics:-Tetrads:-l_[mu], Physics:-Tetrads:-m_[mu], Physics:-Tetrads:-mb_[mu], Physics:-Tetrads:-n_[mu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

 (3)

RicciT[1, 2]

-%d_[2](GammaT[`~1`, 1, 1]+GammaT[`~2`, 1, 2]+GammaT[`~3`, 1, 3]+GammaT[`~4`, 1, 4])-GammaT[`~1`, 1, 3]*GammaT[`~3`, 2, 1]-GammaT[`~3`, 1, 3]*GammaT[`~3`, 2, 3]-GammaT[`~4`, 1, 3]*GammaT[`~3`, 2, 4]+GammaT[`~4`, 1, 2]*GammaT[`~1`, 4, 1]+GammaT[`~4`, 1, 2]*GammaT[`~3`, 4, 3]+GammaT[`~4`, 1, 2]*GammaT[`~4`, 4, 4]+GammaT[`~1`, 1, 2]*GammaT[`~3`, 1, 3]+GammaT[`~1`, 1, 2]*GammaT[`~4`, 1, 4]+GammaT[`~2`, 1, 2]*GammaT[`~1`, 2, 1]+GammaT[`~2`, 1, 2]*GammaT[`~3`, 2, 3]+GammaT[`~2`, 1, 2]*GammaT[`~4`, 2, 4]+GammaT[`~3`, 1, 2]*GammaT[`~1`, 3, 1]+GammaT[`~3`, 1, 2]*GammaT[`~3`, 3, 3]+GammaT[`~3`, 1, 2]*GammaT[`~4`, 3, 4]-GammaT[`~1`, 1, 4]*GammaT[`~4`, 2, 1]-GammaT[`~3`, 1, 4]*GammaT[`~4`, 2, 3]-GammaT[`~4`, 1, 4]*GammaT[`~4`, 2, 4]-GammaT[`~1`, 1, 1]*GammaT[`~1`, 2, 1]-GammaT[`~3`, 1, 1]*GammaT[`~1`, 2, 3]-GammaT[`~4`, 1, 1]*GammaT[`~1`, 2, 4]-GammaT[`~1`, 1, 2]*GammaT[`~2`, 2, 1]-GammaT[`~3`, 1, 2]*GammaT[`~2`, 2, 3]-GammaT[`~4`, 1, 2]*GammaT[`~2`, 2, 4]-(1/2)*2^(1/2)*%d_[3](GammaT[`~2`, 1, 2])+(1/2)*2^(1/2)*%d_[3](GammaT[`~1`, 1, 2])+GammaT[`~2`, 3, 2]*GammaT[`~3`, 1, 2]+GammaT[`~2`, 4, 2]*GammaT[`~4`, 1, 2]+GammaT[`~1`, 1, 1]*GammaT[`~1`, 1, 2]+GammaT[`~1`, 1, 2]*GammaT[`~2`, 1, 2]-GammaT[`~1`, 2, 2]*GammaT[`~2`, 1, 1]-GammaT[`~2`, 1, 3]*GammaT[`~3`, 2, 2]-GammaT[`~2`, 1, 4]*GammaT[`~4`, 2, 2]+((1/2)*I)*2^(1/2)*%d_[1](GammaT[`~4`, 1, 2])-((1/2)*I)*2^(1/2)*%d_[4](GammaT[`~4`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[1](GammaT[`~3`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[4](GammaT[`~3`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[2](GammaT[`~2`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[2](GammaT[`~1`, 1, 2])

 (4)

 

``

 

Download Problem_with_Defined_Tetrad_Function.mw

How to do a color inversion in maple...

Asked by: ccAndrew 688
October 08 2015
3  12

How can I do a color inversion on a jpg image in Maple?

Activation of new packages ? ...

Asked by: shadi alomari 10
package
October 08 2015
2  8

Hello 

I have maple 13, and I installed two new packages, the problem that I don't know where should I saved them and how to make them active to start using there routines ??? 

So pleas any one know how to add packages to maple 13, help me    :) 

 

I found a bug in Maple...

Asked by: MDD 367
polynomialideals
October 08 2015
0  3

I think that I found a bug in Maple! Please run the following command:

I need the Generators of above Ideal. What is your idea?!

indefinite integration...

Asked by: Vishal 5
integration
October 08 2015
0  0

I have a problem about the integration of a function. The maple returns mathematical form of the given command

the function is

fn :=(-4.079067798*10^(-16)+3.422708023*10^(-16)*I)*(3.363377947*10^(-11)+5.977507284*10^(-12038)*I+(3.363377947*10^(-11)+4.678081798*10^(-22)*I)*erf(1.664331698*10^15*qq-0.2503507367e-1-4.649313602*I)) *exp(-2.77*(qq/(tau*tau))^2)*exp(-I*w0*qq)*exp(-(ss-qq)/T_pop)

qq is the integration variable qq=-inf..ss

w0=10^15

tau=10^(-15)

T_pop=30e-15

Problem with Expansion...

Asked by: abbeykabir 85
expand
October 08 2015
1  1

Real part of a matrix...

Asked by: jaimeperez 15
matrix real
October 08 2015
0  6

I have this matrix

A := Matrix([[x+I*y, z+I*w], [-z+I*w, x-I*y]])

and I want a matrix which components are de real parte of the components of A. I have tried this:

Re(A)

but it doesn't work.

What is wrong?

Thank you so much.

Check two matrices are the same...

Asked by: jaimeperez 15
matrix eval evalb
October 08 2015
0  7

I have this two matrices

uA := Matrix([[-w^2+x^2+y^2-z^2, -2*(w*y+x*z), 2*(-w*x+y*z)], [2*(-w*y+x*z), w^2+x^2-y^2-z^2, -2*(w*z+x*y)], [2*(w*x+y*z), 2*(-w*z+x*y), -w^2+x^2-y^2+z^2]])

and

 

UA := eval(uA, {w = -w, x = -x, y = -y, z = -z})

 

and I want to check that their are the same. I have tried

evalb(uA = UA)

 

but it says it false. It should say that is true, because - I think- this two matrices are the same.

Does anyone know what is wrong?

 

Many thanks

Error in shadebetween...

Asked by: DJJerome1976 540
shadebetween
October 07 2015
2  16

Can anyone offer an explanation why the following error occurs, and how it can be avoided? Thanks!

 

plots:-shadebetween(2, 1/sqrt(-x^2+1), x = 0 .. (1/2)*sqrt(3))

Error, (in t) invalid input: nops expects 1 argument, but received 0

  

``

 

Download error.mw

Finding contravariant bases vectors and its compon...

Asked by: lemelinm 1540
October 07 2015
1  2

In preparation for learning GR, I need somme trick on how to use the DifferentialGEometry package or else. So I want to show you what I want to do (see the link to the document below) and I would like some help on how to do it with tensor.  That would help me a lot.  Then, I will extansion it on a 3-D problem and next in 4-D.

 

Thank you in advance dor your help

 

here is the file : Finding_covariant_and_contravariant.mw

 

--------------------------------------
Mario Lemelin
Maple 2015 Ubuntu 14.04 - 64 bits
Maple 2015 Win 10 -  64 bits
messagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987

How to display all steps of solution?...

Asked by: KarryWC 0
step-by-step
October 07 2015
0  3

For the life of me I cannot find the method to do so.

 

So the solution would look like:

1. Euation

2 Step 2

3 Step 3

4 step 3+n

where n is the number of steps reuired.

Any help will be appreciated so very much.

.

.TIA

Larry C

 

 

Check that a segment is a subset of another segmen...

Asked by: Kitonum 21500
October 07 2015
0  4

Is there in Maple a command to verify that one segment on the real axis is a subset of another segment?  For example  RealRange(2, 4)  is subset of  RealRange(2, 5) . 

Of course easy to write a procedure that makes it:

Subset:=proc(r1::RealRange, r2::RealRange)

local a, b, c, d;

a, c:= op~(1,[r1, r2])[];

b, d:= op~(2,[r1, r2])[];

if a>=c and b<=d then true else false fi;

end proc:

 

Example of use:

Subset(RealRange(2,4), RealRange(2,5));

Subset(RealRange(2,5), RealRange(2,4));

                            true

                            false

 

How can I evaluate a matrix?...

Asked by: jaimeperez 15
matrix evaluation
October 07 2015
1  2

I have this matrix

 

uA := Matrix([[-w^2+x^2+y^2-z^2, -2*(w*y+x*z), 2*(-w*x+y*z)], [2*(-w*y+x*z), w^2+x^2-y^2-z^2, -2*(w*z+x*y)], [2*(w*x+y*z), 2*(-w*z+x*y), -w^2+x^2-y^2+z^2]])

and I would like to evaluate the variables like this

 

x = -x, y = -y, z = -z, w = -w

I tried this

Eval(uA, x = -x, y = -y, z = -z, w = -w)

but it didnt work.

 

Any suggestions??

 

Thank you so much

 

 

How can I assign a value to an expression?...

Asked by: jaimeperez 15
October 07 2015
2  1

I want to compute some matrix multiplications and i need this expression to be 1 always, i.e,

x^2+y^2+z^2+w^2=1

for every calculation I do.

I have tried x^2+y^2+z^2+w^2:=1 and assign(x^2+y^2+z^2+w^2,1) but it doesn't work.

What I should type to make it work?

 

Thank you

 

 

Convergence problem of ODE system...

Asked by: samiyare 195
ode dsolve convergence
October 07 2015
1  3

Hi,

In line with my previous questions

http://www.mapleprimes.com/questions/201944-Convergence-Problem-In-My-Algorithm-DSOLVE

I write a code with different variables and odes. However I tried to get the solution, I cannot get the results. I think it should be some problems with my Guess procedure. The code is attached. I would be most grateful if you help me on this problem.

code.mw

Thank you.

Amir

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