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

## Synopsis

• 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.

• 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 .