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# removeLowestDimension -- remove components of lowest dimension

- Usage:
    `removeLowestDimension M`
- Inputs:
  - M, an ideal or a module,
- Outputs:
  - an ideal or a module,

## 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

## See also

- topComponents -- compute top dimensional component of an ideal or module
- saturate -- saturation of ideal or submodule
- Ideal : Ideal -- ideal or submodule quotient
- radical -- the radical of an ideal
- minimalPrimes -- minimal primes of an ideal

## Ways to use removeLowestDimension:

- `removeLowestDimension(Ideal)`
- `removeLowestDimension(Module)`

## For the programmer

The object removeLowestDimension is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PrimaryDecomposition/doc.m2:750:0.