Can someone please explain to me these two concepts and how they differ from each other? I'm taking a class entitled Math & Computers which emphasizes algebraic geometry in a symbolic-computational setting. That being said, the class is not very oriented towards explaining and understanding these ideas as it is assumed that I've already had experience in dealing with them.(adsbygoogle = window.adsbygoogle || []).push({});

Most specifically, I'm talking about affine varieties and vanishing ideals in the realm of polynomial rings. Is the vanishing ideal a subset of the affine variety?

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# Affine Varieties and the Vanishing Ideal

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