# idealsFromGeneratingSets -- creates ideals from sets of monomials

## Synopsis

• Usage:
idealsFromGeneratingSets(List)
• Inputs:
• B, a list, of sets of monomials
• Optional inputs:
• IncludeZeroIdeals => ..., default value true, optional input to choose whether zero ideals should be included
• Verbose => ..., default value false, optional input to request verbose feedback
• Outputs:
• a list, of monomial ideals

## Description

Given a list of sets of monomials, the function converts each set into a monomial ideal.

 i1 : n=4; D=2; p=1.0; N=3; i5 : B=randomMonomialSets(n,D,p,N); B/print 2 2 2 2 {x , x , x , x , x , x x , x x , x x , x , x x , x x , x , x x , x } 1 2 3 4 1 1 2 1 3 1 4 2 2 3 2 4 3 3 4 4 2 2 2 2 {x , x , x , x , x , x x , x x , x x , x , x x , x x , x , x x , x } 1 2 3 4 1 1 2 1 3 1 4 2 2 3 2 4 3 3 4 4 2 2 2 2 {x , x , x , x , x , x x , x x , x x , x , x x , x x , x , x x , x } 1 2 3 4 1 1 2 1 3 1 4 2 2 3 2 4 3 3 4 4 o6 = {, , } o6 : List i7 : idealsFromGeneratingSets(B) o7 = {monomialIdeal (x , x , x , x ), monomialIdeal (x , x , x , x ), 1 2 3 4 1 2 3 4 ------------------------------------------------------------------------ monomialIdeal (x , x , x , x )} 1 2 3 4 o7 : List

In case the option IncludeZeroIdeals is set to false, the function also counts how many sets are converted to the zero ideal.