# extractInclusionMinimalIdeals -- Extract inclusion minimal ideals from a list of ideals

## Synopsis

• Usage:
extractInclusionMinimalIdeals L
• Inputs:
• L, a list of ideals
• Optional inputs:
• Verbose => ..., default value false, generate informative output
• Outputs:
• the list with some redundant ideals removed

## Description

 i1 : R = QQ[a,b] o1 = R o1 : PolynomialRing i2 : L = {ideal(a^4),ideal(a^3),ideal(a^5),ideal(b^2*a) } 4 3 5 2 o2 = {ideal a , ideal a , ideal a , ideal(a*b )} o2 : List i3 : extractInclusionMinimalIdeals L 5 2 o3 = {ideal a , ideal(a*b )} o3 : List
This function is mostly for internal purposes.

## Caveat

The resulting list may be not irredundant, because I_1 \subset I_2 \cap I_3 is not checked.

## Ways to use extractInclusionMinimalIdeals :

• "extractInclusionMinimalIdeals(List)"

## For the programmer

The object extractInclusionMinimalIdeals is .