InverseMetric is not symmetric?

Question

Hi And as always many thanks for $C_{δβ}$.

Is this a bug or a feature, please?

g^{\mu\nu}::InverseMetric.

if InverseMetric.get($g^{\gamma\kappa}$):
    print('yes')  # <-- actually prints yes
else:
    print('no')

if Symmetric.get($g^{\gamma\kappa}$):
    print('yes')
else:
    print('no')  # <-- actually prints no

Thanks GPN

Answer 1

Hi GPN.

I was not able of reproducing your results. Let me show you my trial code.

First, I assign some basic properties:

{\mu,\nu}::Indices;
g_{\mu\nu}::Metric;
g^{\mu\nu}::InverseMetric;

Then I check if the inverse metric is symmetric:

if Symmetric.get($g^{\mu\nu}$):
    print("True")
else:
    print("False")

I'm getting that it is True!

Just as a cross check I ask if it is antisymmetric:

if AntiSymmetric.get($g^{\mu\nu}$):
    print("True")
else:
    print("False")

And I got False!

If you are not getting the same results it might be that you are using an older version of the software, were the inheritance of the symmetries was buggy or miscompiled.

Regards, Dox.

Comments

Thanks Dox. I will try to find a more detailed difference between your code and mine, but so far I haven't been able to reproduce. So I accept your answer, thanks!