Hullzie16

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These are questions asked by Hullzie16

Has anyone had any success in turning off the scrollable matrix feature on Mac? I found the post

 https://www.mapleprimes.com/questions/238061-How-To-Disable-The-New-Scrollable-Matrices

and tried to follow the steps outlined by Acer, but I cannot get it to work. Specifically, I greated a preference file at the location:

 //Users/$USER/Library/Preferences/Maple/<version>/Maple preferences which has the statement 

ScrollableMathTableOutput=false

Any success stories, or tips, will be greatly appreciated. 

Thanks. 

I am looking at the d'Almbert operator for the Minkowski metric in cartesian coordinates. When using the dAlmbertian command and converting to partial derivatives it gets the coefficients wrong, the negatives are not in the correct place based on the metric. But when I manually write the operator with the metric and derivative operator it returns the correct answer. Any thoughts on this? 

See attached, thank you. 

restart;

with(Physics):

Setup(coordinatesystems=cartesian,signature=`-+++`,metric=Minkowski)

 

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

 

_______________________________________________________

 

`The Minkowski metric in coordinates `*[t, x, y, z]

 

`Signature: `(`- + + +`)

 

_______________________________________________________

 

Physics:-g_[mu, nu] = Matrix(%id = 36893488152289591652)

 

[coordinatesystems = {X}, metric = {(1, 1) = -1, (2, 2) = 1, (3, 3) = 1, (4, 4) = 1}, signature = `- + + +`]

(1)

g_[lineelement]

-Physics:-d_(t)^2+Physics:-d_(x)^2+Physics:-d_(y)^2+Physics:-d_(z)^2

(2)

CompactDisplay(phi(t,x,y,z))

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

(3)

dAlembertian(phi(X))

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

(4)

convert(%,diff)

-(diff(diff(phi(X), t), t))-(diff(diff(phi(X), x), x))-(diff(diff(phi(X), y), y))+diff(diff(phi(X), z), z)

(5)

g_[~mu,~nu]*d_[nu](d_[mu](phi(X)))

Physics:-g_[`~mu`, `~nu`]*Physics:-d_[mu](Physics:-d_[nu](phi(X), [X]), [X])

(6)

SumOverRepeatedIndices((6))

-(diff(diff(phi(X), t), t))+diff(diff(phi(X), x), x)+diff(diff(phi(X), y), y)+diff(diff(phi(X), z), z)

(7)
 

 

dAlmbert.mw

Suppose I have a metric g, and I want to perform a conformal transformation g = exp(2Phi(X))*g, is there a straightforward way to do this for curvature quantitieies (Christoffel, Ricci Scalar etc)? I was able to do it rather easily for the Christoffel symbols, as seen below, but it required me making a substitution for each index pair. While this isn't horrible, it would be nice if there was a way to do it without this procedure.

** Edited to make it Phi(X) 

restart;

with(Physics):CompactDisplay(Phi(X)):

Phi(X)*`will now be displayed as`*Phi

(1)

Setup(metric=arbitrary):

_______________________________________________________

 

`Systems of spacetime coordinates are:`*{X = (x1, x2, x3, x4)}

 

`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x1, x2, x3, x4)}

 

`The arbitrary metric in coordinates `*[x1, x2, x3, x4]

 

`Signature: `(`- - - +`)

 

_______________________________________________________

 

Physics:-g_[mu, nu] = Matrix(%id = 36893488152300428092)

(2)

Christoffel[~alpha,beta,nu,definition]

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

(3)

Simplify(eval((3),[g_[mu,beta]=exp(2*Phi(X))*g_[mu,beta],g_[mu,nu]=exp(2*Phi(X))*g_[mu,nu],g_[beta,nu]=exp(2*Phi(X))*g_[beta,nu]]))

Physics:-Christoffel[`~alpha`, beta, nu] = exp(2*Phi(X))*(Physics:-d_[nu](Phi(X), [X])*Physics:-g_[beta, `~alpha`]+Physics:-d_[beta](Phi(X), [X])*Physics:-g_[nu, `~alpha`]-Physics:-d_[`~alpha`](Phi(X), [X])*Physics:-g_[beta, nu]+Physics:-Christoffel[`~alpha`, beta, nu])

(4)

expand((4))

Physics:-Christoffel[`~alpha`, beta, nu] = (exp(Phi(X)))^2*Physics:-d_[nu](Phi(X), [X])*Physics:-g_[beta, `~alpha`]+(exp(Phi(X)))^2*Physics:-d_[beta](Phi(X), [X])*Physics:-g_[nu, `~alpha`]-(exp(Phi(X)))^2*Physics:-d_[`~alpha`](Phi(X), [X])*Physics:-g_[beta, nu]+(exp(Phi(X)))^2*Physics:-Christoffel[`~alpha`, beta, nu]

(5)
 

 

Any thoughts appreciated, thank you!

MyConformal.mw

I have a procedure that I am trying to run that would be an improvement/more sophisticated way of solving a problem that I have previously solved. When I try and run my procedure I am getting an error, and from what I gather with the error is that there are some values when inserted into my procedure that cannot be evaluated. Just for context it is a procedure that contains numerical solutions to a system of DEs and and contains inequalities. 

I would like to know is there an easy method to figure out what values are giving me this error? 

Or a follow up, is there something wrong with my procedure that is giving me this error? I have included some commentary in my workshet as well to hopefully make everything clear. 

Thanks. 

Proc_Error.mw

I have a differential equation which I am looking for a series solution in inverse powers of r. I am doing this by matching inverse powers between the RHS and LHS of the differential equation and then finding the coefficient in the series solution that would solve this. I have written a little procedure which returns the coefficients, I am just curious if there is a command that will do this for me or if i can improve on this technique? I tried the Solve command in PDETools but it just kept evaluating and did not return an answer. 

Thanks in advance. 

 

EDIT: More detail provided in the first reply. 

coefficient_question.mw

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