Macaulay2 » Documentation
Packages » BinomialEdgeIdeals :: parityBinomialEdgeIdeal
next | previous | forward | backward | up | index | toc

parityBinomialEdgeIdeal -- parity binomial edge ideals

Description

This routine returns the (permanental) parity binomial edge ideal of G. 
i1 : G={{1,2},{2,3},{3,1}}

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

o1 : List
 
i2 : I = parityBinomialEdgeIdeal(G,Field=>ZZ/2)

o2 = ideal (x x  + y y , x x  + y y , x x  + y y )
             1 2    1 2   1 3    1 3   2 3    2 3

              ZZ
o2 : Ideal of --[x ..y ]
               2  1   3
 
i3 : J = parityBinomialEdgeIdeal(G)

o3 = ideal (x x  - y y , x x  - y y , x x  - y y )
             1 2    1 2   1 3    1 3   2 3    2 3

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 pbei.

See also

Ways to use parityBinomialEdgeIdeal:

  • parityBinomialEdgeIdeal(List)

For the programmer

The object parityBinomialEdgeIdeal is a method function with options.

The source of this document is in BinomialEdgeIdeals.m2:195:0.