the contraction of 5 gamma matrices cannot work properly for other index

[liulangtian]

Dear Leo,

I download your example Gamma matrices notebook file and it works well on my local laptop.

But I found when I contract 5 gamma matrices with different indexes, the compact results cannot be obtained as showed in my attached screenshot file.
Do you know how to fix this problem?

Best,
Langtian

[duetosymmetry]

Unfortunately, a canonical order does not necessarily mean the simplest expression. The canonical order here involves lexicographically ordering the indices, whereas in your last example, you could get a simpler expression with a different index order. This is a general problem with computer algebra, not specific to xTensor or gamma matrices.

[liulangtian]

OK. Thank you for your explainations.
Actually, I want to build a template for Euclidean Gamma matrices computations based on the Dirac algebra you constructed. Now I am in the first step of testing it in the Minkowskian space.