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Question: Is this a bug or does Maple hate me?

Question:Is this a bug or does Maple hate me?

Hullzie16 333 Maple 2023
physics
May 07 2024
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. 
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