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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 arxiv.org/abs/alg-geom/9704017 . –  Qiaochu Yuan Jan 14 '10 at 0:14
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up vote 2 down vote accepted

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

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

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