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BinomialEdgeIdeals :: binomialEdgeIdeal

binomialEdgeIdeal -- Binomial edge ideals

Synopsis

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.

See also

Ways to use binomialEdgeIdeal :

For the programmer

The object binomialEdgeIdeal is a method function with options.