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I'm wondering if there's an algorithm, or a program I can use, to compute integral closures. Specifically, what I have in mind are variants of questions of the sort: what is the integral closure of ℤ[x] in Quot(ℚ[x,y]/fℚ[x,y]), for some specific f(x,y).

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The first five results Google returns for "integral closure algorithm" are links to (different) papers titled "An algorithm for computing the integral closure," for example . – Qiaochu Yuan Jan 14 '10 at 0:14
up vote 2 down vote accepted

If you are looking for prepackaged software, Macaulay II can do the job.

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for the link:"Gone The requested resource /Macaulay2/doc/Macaulay2-1.3.1/share/doc/Macaulay2/IntegralClosure/html/‌​ml is no longer available on this server and there is no forwarding address. Please remove all references to this resource." – user 1 Mar 25 '15 at 7:02

In addition to all the papers, there's even a book! "Integral closure: rees algebras, multiplicities, algorithms" by Vasconcelos.

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