-- -*- M2-comint -*- hash: 7729415327162415280

i1 : G = mixedGraph(digraph {{b,{c,d}},{c,{d}}},bigraph {{a,d}})

o1 = MixedGraph{Bigraph => Bigraph{a => {d}}   }
                                   d => {a}
                Digraph => Digraph{b => {c, d}}
                                   c => {d}
                                   d => {}
                Graph => Graph{}

o1 : MixedGraph

i2 : R = gaussianRing G

o2 = R

o2 : PolynomialRing

i3 : T = trekIdeal(R,G)

o3 = ideal (s   , s   , - s   s    + s   s   , - s   s    + s   s   , -
             a,b   a,c     a,c b,b    a,b b,c     a,c b,b    a,b b,c   
     ------------------------------------------------------------------------
     s   s    + s   s   , s   s    - s   s   )
      a,c b,c    a,b c,c   a,c b,d    a,b c,d

o3 : Ideal of R

i4 : ideal gens gb T

o4 = ideal (s   , s   )
             a,c   a,b

o4 : Ideal of R

i5 : G = graph{{a,b},{b,c},{c,d},{a,d}}

o5 = Graph{a => {b, d}}
           b => {a, c}
           c => {b, d}
           d => {a, c}

o5 : Graph

i6 : R = gaussianRing G

o6 = R

o6 : PolynomialRing

i7 : T = trekIdeal(R,G);

o7 : Ideal of R

i8 : CI = conditionalIndependenceIdeal(R,globalMarkov(G));

o8 : Ideal of R

i9 : T == CI

o9 = true

i10 : H = digraph{{1,{4}},{2,{4}},{3,{4,5}},{4,{5}}}

o10 = Digraph{1 => {4}   }
              2 => {4}
              3 => {4, 5}
              4 => {5}
              5 => {}

o10 : Digraph

i11 : R = gaussianRing H

o11 = R

o11 : PolynomialRing

i12 : T = trekIdeal(R,H);

o12 : Ideal of R

i13 : CI = conditionalIndependenceIdeal(R,globalMarkov(H));

o13 : Ideal of R

i14 : T == CI

o14 = false

i15 : 
