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# findMins -- calculates the minimal elements of a subset of ZZ^r

- Usage:
    `findMins L`
- Inputs:
  - L, a list, subset of $\ZZ^r$
- Outputs:
  - a list, minimal elements

## Description

Given a list L of elements in $\ZZ^r$, this function will return the minimal elements of L under the partial order where $c\leq d$ if and only if $c_i\leq d_i$ for all $1\leq i\leq r$.

    i1 : L = {{1,2},{3,1},{3,2},{1,4}}

    o1 = {{1, 2}, {3, 1}, {3, 2}, {1, 4}}

    o1 : List

    i2 : findMins L

    o2 = {{1, 2}, {3, 1}}

    o2 : List

The algorithm constructs a monomial ideal by using the elements of the list as exponents. Such an ideal can also be given directly.

## See also

- findRegion -- finds minimal multidegree(s) in a given region where an ideal or module satisfies a Boolean function

## Ways to use findMins:

- `findMins(Ideal)`
- `findMins(List)`

## For the programmer

The object findMins is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LinearTruncations.m2:889:0.