This method returns the n × n matrix of direct causal effect indeterminates. This matrix has the parameter l(i,j) in the (i,j) position if there is a directed edge i →j, and 0 otherwise. Note that this matrix is not symmetric. The documentation of gaussianRing further describes the indeterminates l(i,j).
i1 : G = mixedGraph(digraph {{b,{c,d}},{c,d}},bigraph {{a,d}})
o1 = MixedGraph{Bigraph => Bigraph{a => set {d}} }
d => set {a}
Digraph => Digraph{b => set {c, d}}
c => set {d}
d => set {}
Graph => Graph{}
o1 : MixedGraph
|
i2 : R = gaussianRing G o2 = R o2 : PolynomialRing |
i3 : compactMatrixForm =false; |
i4 : directedEdgesMatrix R
o4 = | 0 0 0 0 |
| |
| 0 0 l l |
| b,c b,d |
| |
| 0 0 0 l |
| c,d |
| |
| 0 0 0 0 |
4 4
o4 : Matrix R <--- R
|
To obtain the directed edges matrix of a digraph, it should first be embedded into a mixed graph as follows.
i5 : D = digraph{{a,b},{c,d}}
o5 = Digraph{a => set {b}}
b => set {}
c => set {d}
d => set {}
o5 : Digraph
|
i6 : Dembedded = mixedGraph(D, bigraph{})
o6 = MixedGraph{Bigraph => Bigraph{} }
Digraph => Digraph{a => set {b}}
b => set {}
c => set {d}
d => set {}
Graph => Graph{}
o6 : MixedGraph
|
i7 : directedEdgesMatrix gaussianRing Dembedded
o7 = | 0 0 0 0 |
| |
| 0 0 l l |
| b,c b,d |
| |
| 0 0 0 l |
| c,d |
| |
| 0 0 0 0 |
4 4
o7 : Matrix R <--- R
|