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


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

