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Hullzie16

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These are questions asked by Hullzie16

Is there a Maple command that can match ...

Hullzie16 232 Maple 2023
solve coefficients
September 17 2024
2 3

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

What does it mean when DESol has an arbi...

Hullzie16 232 Maple 2023
ode dsolve differential-equations
July 23 2024
1 3

I have a thirder order ODE with non polynomial coefficients and I naively thought to try dsolve for fun to see what happens and Maple returned DESol with a second order differential equation and an arbitrary coefficient. I know Maple outputs DESol when it cannot find a solution similar to RootOf but the arbitrary constant is what is throwing me off. 

I am unsure how to interpret this, if a particular solution is found I could reduce the order and see how I could get with the second order ODE but maple doesn't produce a particular solution when I run that command. 

DESol_Question.mw

Is this a bug or does Maple hate me? ...

Hullzie16 232 Maple 2023
physics
May 07 2024
0 1

I am running Maple 2023 - yes I should update - and I found a weird "bug" if you could call it that. For different versions of the Physics package I am getting different answers on the same problem. 
 

This is what I was getting when I run Version 1410:

> 

restart;
> 

with(Physics):

 

> 

Physics:-Version()

`The "Physics Updates" version in the MapleCloud is 1744. The version installed in this computer is 1410 created 2023, March 11, 12:59 hours Pacific Time, found in the directory /Users/b2hull/maple/toolbox/2023/Physics Updates/lib/`

 (1)
> 

Setup(mathematicalnotation=true):
> 

g_[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)}

  

`Setting `*lowercaselatin_is*` letters to represent `*space*` indices`

  

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

  

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

  

_______________________________________________________

 (2)
> 

LG :=(g_[~mu,~nu]*Ricci[mu,nu])*sqrt(-%g_[determinant]);

Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2)

 (3)
> 

SG:=Intc(LG,X)

Int(Int(Int(Int(Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2), x1 = -infinity .. infinity), x2 = -infinity .. infinity), x3 = -infinity .. infinity), x4 = -infinity .. infinity)

 (4)
> 

EQ:=Fundiff(SG,%g_[~delta,~gamma])/sqrt(-%g_[determinant])

((1/2)*%g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*%g_[delta, gamma]*%g_[determinant]/(-%g_[determinant])^(1/2)+Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2)*%g_[delta, `~mu`]*%g_[gamma, `~nu`])/(-%g_[determinant])^(1/2)

 (5)
> 

Simplify(subs(%g_=g_,EQ))

-(1/2)*Physics:-g_[delta, gamma]*Physics:-Ricci[nu, `~nu`]+Physics:-Ricci[delta, gamma]

 (6)
> 

 

> 

 

 

And this is what I get if I used the latet update for 2023, Version 1683:

> 

restart;
> 

with(Physics):
> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1744. The version installed in this computer is 1683 created 2024, March 6, 17:43 hours Pacific Time, found in the directory /Users/b2hull/maple/toolbox/2023/Physics Updates/lib/`

 (1)
> 

Setup(mathematicalnotation=true):
> 

g_[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)}

  

`Setting `*lowercaselatin_is*` letters to represent `*space*` indices`

  

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

  

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

  

_______________________________________________________

 (2)
> 

LG :=(g_[~mu,~nu]*Ricci[mu,nu])*sqrt(-%g_[determinant]);

Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2)

 (3)
> 

SG:=Intc(LG,X)

Int(Int(Int(Int(Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]*(-%g_[determinant])^(1/2), x1 = -infinity .. infinity), x2 = -infinity .. infinity), x3 = -infinity .. infinity), x4 = -infinity .. infinity)

 (4)
> 

EQ:=Fundiff(SG,%g_[~delta,~gamma])/sqrt(-%g_[determinant])

-(1/2)*%g_[delta, gamma]*Physics:-g_[`~mu`, `~nu`]*Physics:-Ricci[mu, nu]

 (5)
> 

Simplify(subs(%g_=g_,EQ))

-(1/2)*Physics:-g_[delta, gamma]*Physics:-Ricci[nu, `~nu`]

 (6)
> 

 

 

Strange right? I bring this up because it makes me wonder about potential errors in other computations...

The answer - equation 6 - in 1410 is the correct answer. This is simply a derivation of the Einstein Tensor. 

Any ideas about why this numeric integra...

Hullzie16 232 Maple 2023
April 22 2024
2 7

I have a double for loop which has a numeric integration located inside of the innermost loop. When I try to run my worksheet I recieve an error in which the numeric integration is not computed for a certain set of values in my loops. If I take these two values and input them into my function and then integrate outside of the loop it appears to work just fine. Not sure what to make of this. Any thoughts would be appreciated. 

Secondly, to avoid any confusion about what I am trying to do and if someone has general comments on my worksheet I added some text in the worksheet to describe what I am interested in doing, even though I am sure most people here would be able to figure that out from the commands alone. 

Thanks. 

LoopError.mw

Can anyone help me with this Physics iss...

Hullzie16 232 Maple 2023
physics
April 06 2024
1 5

I have a complicated tensor expression that is defined wtih all indices down. However if i consider a one-up-one-down configuration it appears to introduce new terms that no longer produce the same result as the all down configuration. Not sure what to make of this. 

IndexQuestion.mw

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