Abstract
Among the fundamental objects studied in algebraic geometry are algebraic varieties which are aggregates of common zeros of polynomial sets, viewed as points in an affine space. In contrast, ideals generated by polynomial sets are typical examples dealt with in commutative algebra. Elimination algorithms provide powerful constructive tools for many problems in these two related areas. In this chapter, we investigate some computational aspects of a few such problems.KeywordsAlgebraic GeometryIrreducible ComponentAlgebraic VarietyPolynomial IdealGeneric ZeroThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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