Question: Bugs in covariant differentiation

Hi there.

I found bugs in covariant differentiation of vectors that defined in another coordinate system. I attached three documents - two of them with bugs and one with normal behavior.

In cov_diff_bug_1.mw I defined Killing vector in Minkowski spacetime. Then I transformed metric and this vector to spherical coordinate system and calculated covariant derivative of vector and obtained symmetric tensor matrix. But for Killing vector it should be antisymmetric.

In cov_diff_bug_2.mw I set metric in spherical coordinate system by hand instead of transformation and obtained zero covariant derivative.

And in cov_diff_no_bug.mw I set metric and vector by hand without any transformation and obtained normal results - antisymmetric covariant derivative and zero sum of two covariant derivatives with rearranged indexes.

So in Maple 2020 coordinate transformation don't doing well in combining with covariant differentiation. But in previous versions of Maple this behavior could be opposite)

I'm asking developers to consider this issues.

Thank you.

cov_diff_bug_1.mw

cov_diff_bug_2.mw

cov_diff_no_bug.mw