scallopedpancake

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These are replies submitted by scallopedpancake

@ecterrab Thanks for letting me know: sorry I completely blanked on the format! Hopefull thius should work SmallExample.mw This is just an example of Euclidean gravity. The momentum of the h[4,4] field should vanish, but it doesn't vanish for the right reasons in the code. In particular, Eq. 10 is clearly wrong: symbol is a bug that I don't understand; Eq. 11-12 would be fine but Maple doesn't seem to be differentiating indies correctly, since there should be some delta[mu,4]s there but there aren't

@Hullzie16 Hi, here's a short example of 4D Euclidean linearised gravity, where it fails. SmallExample.maple 

@janhardo I appreciate the sentiment, but that code is wrong. By writing coordindates=[t,x1,x2,x3], it has defined four coordinate systems.

@acer Thanks for that, I thought it would just recognise ++ and +=. I'll do some more reading on the compiler: I don't think I considered it being a strict compiler since I've not had any issues in the past.

I've added my MWE in an edit. Alternatively, here (MWE.mw) it is as a worksheet.

From https://www.mapleprimes.com/posts/209047-Minimize-The-Number-Of-Tensor-Components, it appears Maple cannot use identities when reducing the number of components. Maybe this is the issue?

@tomleslie As mentioned by @acer it's a subpackage.
 

restart;

#Import physics package and establish dimension

with(Physics):

Setup(dimension=3):

"`Warning, unable to define the Pauli sigma matrices (Psigma) as a tensor in a spacetime with dimension = `3` where the metric is not Euclidean. You can still refer to the Pauli matrices using `Psigma[x]`, `Psigma[y]` and `Psigma[z]"

 

`The dimension and signature of the tensor space are set to `[3, `- - +`]

(1)

#Define the tensor. N.B.: Here it would be equally correct to add ',minimizetensorcomponents' to the argument and it would do the same as the Library:-MinimizeTensorComponents command below (or at least, has the same outcome)

Define(T[mu,nu,alpha],symmetric={{mu,nu}},antisymmetric={{nu,alpha}});

`Defined objects with tensor properties`

 

{Physics:-Dgamma[mu], Physics:-Psigma[mu], T[mu, nu, alpha], Physics:-d_[mu], Physics:-g_[mu, nu], Physics:-LeviCivita[alpha, mu, nu]}

(2)

#Reduces the number of tensor components based on symmetries, and finds the number of independent components

Library:-MinimizeTensorComponents(T[mu,nu,alpha]);
Library:-NumberOfIndependentTensorComponents(T[mu,nu,alpha]);

_rtable[18446746145787512342]

 

4

(3)

 

 

Download MWE.mw

This is also the case in Maple 2020 as I have just verified.

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