Inacio Aprendanet

65 Reputation

6 Badges

12 years, 14 days

MaplePrimes Activity


These are replies submitted by Inacio Aprendanet

@Christopher2222 thanks a lot for your help!!!!

@Carl Love thanks for the quick response and the commentary.

 

Thanks a lot!

@John Fredsted I just changed phi to phi_A and it worked!

I will continue to do that, the work cannot stop! 

Thanks a lot for your contribution!

Here´s the file:

Field_A-MaplePrimes.mw
 

 

Initial Definitions:

 

NULL

I wish in this work to express the Maxwell equations deriving from the Lagrangian in the fields phiand "A,"

phi

(1.1)

but expressed in vectorial form;

 

restart; clear; with(Physics); with(Physics[Vectors]); with(Library)interface(imaginaryunit = I)

clear

 

I

(1.2)

Physics:-Coordinates(X = [t, x, y, z])

`Detected \`t\`, the time variable, in position 1. Changing the signature of the spacetime metric accordingly, to: + - - - `

 

`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, x, y, z)}

 

`Systems of spacetime Coordinates are: `*{X = (t, x, y, z)}

 

{X}

(1.3)

Physics:-Vectors:-Setup(math = true, Physics:-Vectors:-diff = X)

`* Partial match of  'math' against keyword 'mathematicalnotation'`

 

`* Partial match of  'Physics:-Vectors:-diff' against keyword 'differentiationvariables'`

 

`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, x, y, z)}

 

[differentiationvariables = [X], mathematicalnotation = true]

(1.4)

NULL

Some definitions

 

 

Defining the Maxwell tensor

 

Physics:-Define(F):NULL

`Defined objects with tensor properties`

(2.1)

 

Defining the field A with their components:

 

A[mu] = Vector(4, [`φ__A`(X), A__1(X), A__2(X), A__3(X)]); Define(%)

A[mu] = Vector[column](%id = 18446744074362908294)

 

`Defined objects with tensor properties`

 

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

(2.2)

Physics:-CompactDisplay(phi__A(X), A__1(X), A__2(X), A__3(X))

phi__A(t, x, y, z)*`will now be displayed as`*phi__A

 

A__1(t, x, y, z)*`will now be displayed as`*A__1

 

A__2(t, x, y, z)*`will now be displayed as`*A__2

 

A__3(t, x, y, z)*`will now be displayed as`*A__3

(2.3)

 

Applying:

 

 

NULL

F[alpha, beta] := Physics:-Vectors:-`+`(Physics:-d_[beta](A[alpha]), -Physics:-d_[alpha](A[beta]));

Physics:-d_[beta](A[alpha], [X])-Physics:-d_[alpha](A[beta], [X])

(3.1)

NULL

 

``

``

Term 1:

 

 

eq1 := Physics:-d_[alpha](F[alpha, beta])

Physics:-d_[alpha](Physics:-d_[beta](A[`~alpha`], [X]), [X])-Physics:-dAlembertian(A[beta], [X])

(4.1)

Physics:-SumOverRepeatedIndices(Physics:-d_[alpha](Physics:-d_[beta](A[`~alpha`], [X]), [X])-Physics:-dAlembertian(A[beta], [X]))

Physics:-d_[beta](diff(phi__A(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X])

(4.2)

Physics:-SubstituteTensorIndices(beta = 4, Physics:-d_[beta](diff(phi__A(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi__A(X), t), z)-(diff(diff(A__1(X), x), z))-(diff(diff(A__2(X), y), z))-(diff(diff(A__3(X), z), z))-Physics:-dAlembertian(A__3(X), [X])

(4.3)

NULL

Physics:-SubstituteTensorIndices(beta = 1, Physics:-d_[beta](diff(phi__A(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi__A(X), t), t)-(diff(diff(A__1(X), t), x))-(diff(diff(A__2(X), t), y))-(diff(diff(A__3(X), t), z))-Physics:-dAlembertian(phi__A(X), [X])

(4.4)

Physics:-SubstituteTensorIndices(beta = 2, Physics:-d_[beta](diff(phi__A(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi__A(X), t), x)-(diff(diff(A__1(X), x), x))-(diff(diff(A__2(X), x), y))-(diff(diff(A__3(X), x), z))-Physics:-dAlembertian(A__1(X), [X])

(4.5)

Physics:-SubstituteTensorIndices(beta = 3, Physics:-d_[beta](diff(phi__A(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi__A(X), t), y)-(diff(diff(A__1(X), x), y))-(diff(diff(A__2(X), y), y))-(diff(diff(A__3(X), y), z))-Physics:-dAlembertian(A__2(X), [X])

(4.6)

Physics:-SubstituteTensorIndices(beta = 4, Physics:-d_[beta](diff(phi__A(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X]))

diff(diff(phi__A(X), t), z)-(diff(diff(A__1(X), x), z))-(diff(diff(A__2(X), y), z))-(diff(diff(A__3(X), z), z))-Physics:-dAlembertian(A__3(X), [X])

(4.7)

eval(op(1, Physics:-d_[beta](diff(phi__A(X), t), [X])-Physics:-d_[beta](diff(A__1(X), x), [X])-Physics:-d_[beta](diff(A__2(X), y), [X])-Physics:-d_[beta](diff(A__3(X), z), [X])-Physics:-dAlembertian(A[beta], [X])), beta = 2);

diff(diff(phi__A(X), t), x)

 

-(diff(diff(A__1(X), x), x))

 

-(diff(diff(A__2(X), x), y))

 

-(diff(diff(A__3(X), x), z))

 

-Physics:-dAlembertian(A__1(X), [X])

(4.8)

``

``

NULL

 

 

``


 

Download Field_A-MaplePrimes.mw

Thanks!

 

 

@John Fredsted thanks for your work! I will try this now and see if I can work something out!

 

Thanks!

Here´s the correct file:edo_solução_A_U.mw

The other has an error.

@Carl Love , thanks a lot, very helpful!

@ecterrab , thanks a lot again for your efforts and help.

@ecterrab , thanks a lot!!!!
Thanks for your efforts and implementations.

@ecterrab thanks a lot for your implementation.

 

It works great, and I have more two question in the subject.

 

Thanks a lot.

 

IdentidadesdeBianchi-somequestions.mw

Thanks for the help!@ecterrab 

 

I have made more calculations with your result...

Identidades_de_Bianchi.mw

Can you give a look for me?

 

 

Thank you!

Thank you!

Thank you!

Thank you!

Thank you for the answer!

1 2 Page 1 of 2