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retnev
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- TL;DR Summary
- Maple Physics metrics contraction indices
I have been using Maple for a decade, but only recently started using the Physics Package.
I unfortunately ran into trouble to contract indices ( Maple calls it SumOverRepeatedIndices ).
Below I give an example that will execute if you paste it into a Maple worksheet.
A metric is defined. A contraction involving the metric is then further defined.
Result is the contraction command fails to contract and I cannot find a solution to this in the Maple help files.
1) Paste the code above into a maple worksheet with a Maple version that supports the Physics package.
2) Execute the worksheet.
3) Observe that the last command "ContractOverIndices fails, as e.g. the nu index should be Summed out for the four coordinates (rho, z, phi, t).
Any idea what I do wrong that prevents Maple from contracting the index nu ?
Result
No contraction over tensors take place using e.g. nu as coordinate to contract.
So what is the reason that Maple refuses to contract over indices in the example shown?
I unfortunately ran into trouble to contract indices ( Maple calls it SumOverRepeatedIndices ).
Below I give an example that will execute if you paste it into a Maple worksheet.
A metric is defined. A contraction involving the metric is then further defined.
Result is the contraction command fails to contract and I cannot find a solution to this in the Maple help files.
Instructions to replicate the problemwith(Physics):
Coordinates(X = (rho, z, phi, t));
ds := 1*dt^2 - 2*drho^2 - 3*dz^2 - 4*dphi^2;
Setup(metric = ds);
g_[~mu, ~nu]*Diff(Phi(rho, z), nu, mu);
SumOverRepeatedIndices(%, nu);
1) Paste the code above into a maple worksheet with a Maple version that supports the Physics package.
2) Execute the worksheet.
3) Observe that the last command "ContractOverIndices fails, as e.g. the nu index should be Summed out for the four coordinates (rho, z, phi, t).
Any idea what I do wrong that prevents Maple from contracting the index nu ?
Result
No contraction over tensors take place using e.g. nu as coordinate to contract.
So what is the reason that Maple refuses to contract over indices in the example shown?
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