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How can I compute the radical of an ideal? I suppose that there no exist an algorithm for compute it. But in the case of polynomials rings? there exist an algorithm? I need to compute the radical of the ideal generated by $ (x^2y , xy^3) $ in the ring of polynomials $ k[x,y]$ where $k$ is any field.

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    You should look into [Groebner bases](http://en.wikipedia.org/wiki/Groebner_Basis). [This](http://math.stackexchange.com/questions/95217/methods-to-check-if-an-ideal-of-a-polynomial-ring-is-prime-or-at-least-radical/95525#95525) related question might also prove useful.2012-03-28

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