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These are replies submitted by Hullzie16

You are using multiplications between your partials and your potentials, you need to use d_[mu](A) if you want to have the partial actually evaluate on A. Secondly,  in other spots you are not multiplying two terms together just writing a single term (example gr, should be g*r). 

I think I fixed your problems in the attached code. Also, shouldnt you have some of your indices in a one up one down configuation in F? 



Good luck with whatever you are trying to accomplish.


I was going to post an answer on here for you before I saw this exchange. 

Considering @ecterrab is the head of Maple Physics I would suggest you be much more respectful to his replies in the future. I have had issue with Maple physics in the past where I thought there were bugs but he appropriately responded and showed that some of the issues were my fault and I was not computing things properly. 

Regarding "pre-publication work", I have not once had my work stolen and published before I was done simply by asking for help on this Forum. This is not the kind of place people go scoping for ideas for manuscripts, it is for questions about Maple. 

If you look at my attached sheet you can do what you want.. if I am reading your issues properly.

@Carl Love 

Will use that in the future. 


Not sure how I forgot to mention numeric solutions as I knew that it worked. Thanks for adding that. 

It is all dependent on the system of differential equations you have. Some systems cannot be solved by "analytic" means and must be solved numericlly. 

1) If by connection you are referring to Christoffel symbols then you must remember that they are not tensors, so the error is referring to that portion I believe. 

2) Could you upload your worksheet with the green arrow or tell me your tensor is?

3) I suggest you use the Physics package for this problem, the commands are much simpler to use in my opinion. See attached where I create an expression with a single index contraction of Christoffel and Ricci tensor for a arbitrary static spherically symmetric metric.


Good points, I suppose since I knew how the final answer should look I used symbolic since it would take care of the terms without needing the positive assumption. 

It is quite dodgy sometimes - well most of the time for complex expressions - but the simplicity of this simplification is what made me decide to use it. 

Worksheet from when I updated to Maple 2024 and ran with the updated Physics Package. 





`The "Physics Updates" version in the MapleCloud is 1744 and is the same as the version installed in this computer, created 2024, May 6, 11:8 hours Pacific Time.`






`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: `(`- - - +`)




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

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



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)



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



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





Can you upload your worksheet? 

Or at the very least post what your ODEs are and the initial conditions? 



I would say that I would prefer accuracy over timing here, although a fast result is something desirable to see the rough result. Ofcourse the end goal would always be a quick and accurate code. 

I appreciate this other approach as it could provide some useful insights, although I might need to spend some more time looking at it to make sure i am understanding it correctly. I do enjoy the "smoothness" you mention regarding the fact that my N list is small and creates a course pointplot result. 

I will definetely play around with this and see what it does. 

Thank you. 


I am confused by what you are saying here.. maybe i just need to look at it longer. I think the confusion is maybe on my wording. 

But what I meant by saying "everything appears to work" was that when I looked at the function F[0.1,0.33] outside of the loop in my original file - line 5 - then I did the integration in the same manner - although considering different upper bounds on the integration - it evaluated just fine even when using method = _Dexp. I did not mean everything works as in there was some value for the inequality which was true. 

Thanks for this further insight though. 


Thanks for this. 

I was just showing that everything appeared to work when not inside of the loop. 

I inputted your commands and an answer is returned


Thank you for this. I will upgrade to 2024 as soon as possible and hopefully all my issues will be resolved. 

Regarding the physics, I have been rather opaque as this does not seem like the forum to properly discuss it. However I will say that I agree with everything you have said, I am simply just exploiting some previous knowledge and large amount of symmetry in my problem. Iff I solve the system simulattenously the consistent solution is the one which solves any of the first order ODEs that come from the field equations. 

I appreciate your comments throughout this discusssion. 



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