primaryComponent(Ideal,Ideal) -- find a primary component corresponding to an associated prime

primaryComponent(Ideal,Ideal) -- find a primary component corresponding to an associated prime

Synopsis:

Usage: Q = primaryComponent(I,P)

Function: primaryComponent

Input:

I, an instance of class Ideal: an ideal in a (quotient of a) polynomial ring R.

P, an instance of class Ideal: an associated prime of I.

Output:

Q, an instance of class Ideal: a P-primary ideal of I.

Optional arguments :

primaryComponent(..., Increment => ...)

primaryComponent(..., PrintLevel => ...)

primaryComponent(..., Strategy => ...) -- specify a computational strategy

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

Caveat:

Author and maintainer: C. Yackel, cyackel@math.indiana.edu. Last modified June 2000.

See also:

ass Ideal -- find the associated primes of an ideal

primaryDecomposition Ideal -- find a primary decomposition of an ideal

radical -- compute the radical of an ideal

decompose -- irreducible components of an ideal

top -- compute the top dimensional components

removeLowestDimension -- remove components of lower dimension

Code:

     -- ../../../Macaulay2/m2/primdecomp-EHV.m2:293-300
     primaryComponent(Ideal,Ideal) := Ideal => o -> (I,P) -> (
          localizefcn := if o.Strategy === 1 then
               SYlocalize ass1
          else if o.Strategy === 2 then
               SYlocalize ass2
          else EHVlocalize;
          (primarycomponent localizefcn)(I,P,o.PrintLevel,
               o.Increment))