# binomialEdgeIdeal -- Binomial edge ideals

## Synopsis

• Usage:
binomialEdgeIdeal G
• Inputs:
• G, a Graph or a List
• Optional inputs:
• Field (missing documentation) => ..., default value QQ,
• Permanental (missing documentation) => ..., default value false,
• TermOrder (missing documentation) => ..., default value Lex,
• Outputs:
• the binomial edge ideal of G

## Description

This routine returns the (permanental) binomial edge ideal of G.
 i1 : G={{1,2},{2,3},{3,1}} o1 = {{1, 2}, {2, 3}, {3, 1}} o1 : List i2 : I = binomialEdgeIdeal(G,Field=>ZZ/2) o2 = ideal (x y + x y , x y + x y , x y + x y ) 1 2 2 1 1 3 3 1 2 3 3 2 ZZ o2 : Ideal of --[x ..y ] 2 1 3 i3 : J = binomialEdgeIdeal(G,Permanental=>true) o3 = ideal (x y + x y , x y + x y , x y + x y ) 1 2 2 1 1 3 3 1 2 3 3 2 o3 : Ideal of QQ[x ..y ] 1 3 i4 : needsPackage("Graphs") o4 = Graphs o4 : Package i5 : H=graph({{1,2},{2,3},{3,1}}) o5 = Graph{1 => {2, 3}} 2 => {1, 3} 3 => {1, 2} o5 : Graph i6 : I = binomialEdgeIdeal(H) o6 = ideal (x y - x y , x y - x y , x y - x y ) 1 2 2 1 1 3 3 1 2 3 3 2 o6 : Ideal of QQ[x ..y ] 1 3
A synonym for this function is bei.