# removeLowestDimension -- remove components of lowest dimension

## Synopsis

• Usage:
removeLowestDimension M
• Inputs:
• Outputs:

## Description

This function yields the intersection of the primary components of M except those of lowest dimension, and thus returns the ambient free module of M (or unit ideal) if M is pure dimensional. For a very brief description of the method used, see topComponents.

As an example we remove the lowest dimensional component of an ideal I:

 i1 : R = ZZ/32003[a..d]; i2 : I = intersect(ideal(a*b+a^2,b^2), ideal(a^2,b^2,c^2), ideal(b^3,c^3,d^3)) 3 2 3 2 3 2 3 3 2 3 3 3 2 2 3 2 3 o2 = ideal (b , b d , b c , a c + a*b*c , a b*d , a d , a c d + a*b*c d ) o2 : Ideal of R i3 : removeLowestDimension I 2 2 o3 = ideal (b , a + a*b) o3 : Ideal of R