Hullzie16

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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. 

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

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

I asked a question a while ago

https://www.mapleprimes.com/questions/235734-How-Can-The-Functional-Derivativevariation

Which did not get any immediate responses but one late one which i had replied to, but nothing else since then. 

Is it appropriate to delete and repost and try to get more responses/exposure and see if anyone else has any ideas? 

Since @ecterrab is the one who responded I consider this an interesting problem that I would like to continue discussing. 

I have a pretty ugly nested integral (in my opinion) that I am trying to compute. I thought that I simplified the problem to an easier siutation however during my attempted calculations I am recieving: "Error, (in evalf/int) cannot handle unevaluated name `L` in evalhf

I am unsure where this is coming from, I would assume something in procedure or my attempted use of unapply is incorrect. Any comments are welcome, including those that state I am doing this entirely incorrectly. 

Thanks. 

NestedError.mw

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