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radical ideal algorithms

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mri...@drake.edu

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Sep 11, 2008, 8:42:45 PM9/11/08
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The book by Cox, Little and O'Shea, "Ideals, Varieties, and
Algorithms," discusses the radical membership algorithm. However, I
would like a nice algorithm the starts with a finite set of
polynomials in several variables, considers the radical of the ideal
generated by this set, and produces a small set of generators for this
radical, possibly a Groebner basis. Any clues? Thanks in advance.

DavidA

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Sep 17, 2008, 4:00:55 PM9/17/08
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Determining the radical of an ideal in the general case is quite hard.
It goes roughly like this:
1. Find a primary decomposition for the ideal
2. From this, calculate the minimal associated primes of the ideal.
3. Then the radical is the intersection of the minimal associated
primes
The hard part is the primary decomposition.

For more, see
Schenck, Computational Algebraic Geometry, chapter 1, or
Eisenbud, Commutative Algebra, chapter 3.
(Eisenbud gives references to the papers in which the algorithm for
primary decomposition is described.)

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