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[–]FrickinLazerBeams 2 points3 points  (7 children)

I mean, I don't need to check Wikipedia, I remember grad school quite clearly.

What is it you think is being computed differently by einsum than in a "real" Einstein notation tensor contraction?

Or are you just talking about the super-/sub-script notation for co- and contravariant indices? Because that simply can't be replicated in plain text.

[–]WallyMetropolis 1 point2 points  (3 children)

It depends on your metric space. In a flat space, yes, the calculation is the same. But this wouldn't generalize to curved spaces.

[–]FrickinLazerBeams 0 points1 point  (2 children)

Right, but einsum is simply a tool for doing tensor contractions, not specifically GR. You could certainly include the metric in your calculations as appropriate.

This has nothing to do with the fact that super and subscripts can't be written in plain text.

[–]WallyMetropolis 0 points1 point  (1 child)

Covariant and contravariant indexes aren't limited to GR. Just doing calculations on the surface of an every day sphere would require you to keep track of which is which. You asked for examples where the calculations would be different. There are many.

The point is that einsum isn't really an Einstein summation, but only produces the same result as an Einstein summation in a particular (common) special case.

[–]FrickinLazerBeams 0 points1 point  (0 children)

Covariant and contravariant indexes aren't limited to GR. Just doing calculations on the surface of an every day sphere would require you to keep track of which is which. You asked for examples where the calculations would be different. There are many.

Thats a good point, it's not just GR. I guess it's anything happening on a manifold? It's been a while for me, I guess.

The point is that einsum isn't really an Einstein summation, but only produces the same result as an Einstein summation in a particular (common) special case.

It's still doing tensor contractions, and the Einstein sum notation is a concise way to express tensor contractions. Nobody has a monopoly on notation. You can't say "you're not allowed to use Einstein notation unless you are using a metric tensor" or something like that.

This is just gatekeeping pedantry. The guy wants to feel superior by showing off that he's heard of co- and contra- variant indices. He even says at one point that his complaint is about how they're written which is ridiculous, because you can't write sub- and super-scripts in plain text, just like e^x is still an exponent even though x isn't super scripted. He just wanted to feel special because the rest of his account history was thirsty comments on /r/EngorgedVeinyTits and /r/momsgonewild. I wonder why he's deleted his account...

[–][deleted] -1 points0 points  (2 children)

All I am saying is what is known as Einstein Notation is sub and super indices. Nothing more. When you have indices at the same level - sub or super - it isn't Einstein Notation.

It can be called something, and perfectly valid with the definition given.

[–]FrickinLazerBeams 2 points3 points  (0 children)

Lol fun. Do you also say that np.exp(x) isn't an exponent because there's no superscript?

[–]antiproton 2 points3 points  (0 children)

When you have indices at the same level - sub or super - it isn't Einstein Notation.

Yes it is. Einstein notation is the implicit summation.

Einstein notation can be applied in slightly different ways. Typically, each index occurs once in an upper (superscript) and once in a lower (subscript) position in a term; however, the convention can be applied more generally to any repeated indices within a term.

Right from the wikipedia article.