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primaryComponent -- find a primary component corresponding to an associated prime

Synopsis

Description

The output Q is topComponents(I + P^m) for sufficiently large m. The criterion that Q is primary is given in Eisenbud-Huneke-Vasconcelos, Invent. Math. 110 (1992) 207-235. However, we use localize(Ideal,Ideal).

The Strategy option value sets the strategy option for localize, and should be one of the following:

  • Strategy => 0 -- Uses localize Strategy 0
  • Strategy => 1 -- Uses localize Strategy 1
  • Strategy => 2 -- Uses localize Strategy 2

The Increment option value should be an integer. The algorithm given in Eisenbud-Huneke-Vasconcelos, Invent. Math. 110 (1992) 207-235, relies on topComponents(I + P^m) for $m$ sufficiently large. The algorithm begins with $m = 1$, and increases $m$ by the value of the Increment option until m is sufficiently large. The default value is 1.

Authored by C. Yackel. Last modified June, 2000.

See also

Ways to use primaryComponent:

For the programmer

The object primaryComponent is a method function with options.