I noticed the following strange behavior which I cannot explain.
I wanted to compute the integral closure of the following ring,
$$ A = \mathbb{F}_5[x,t]/(t^2 (1 - x^4) - x^5) $$
Call the integral closure $S$. Then I computed the degree of $S/tS$ which of course should be $5$ since this is the normalization of a degree $5$ cover of $k[t]$. However, the answer I get depends on the order in which I enter the variables.
where as if I define my polynomial ring with variables in the other order I get the correct answer,
I have tried this in Macaulay2, version 1.19.1 and version 1.22 and I reproduced the behavior on two different Linux machines.
Does anyone have any idea what is going on?