5

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.

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where as if I define my polynomial ring with variables in the other order I get the correct answer,

enter image description here

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?

Ben C
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    Probably you would get a quicker response on the Macaulay discussion group. This forum isn't really for software questions, even if they research-linked. https://groups.google.com/g/macaulay2 – Ryan Budney Dec 28 '23 at 06:08
  • @RyanBudney thank you for the suggestion, I will repost there – Ben C Dec 28 '23 at 22:48

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