Reduces a chordal network, by prunning the arcs that do not belong to the top $k$ dimensional parts of the variety.
i1 : R = QQ[a..j,MonomialOrder=>Lex]; |
i2 : I = ideal {a*d - b*c, c*f - d*e, e*h - f*g, g*j - h*i, a*j - b*i};
o2 : Ideal of R
|
i3 : N = chordalNet I; |
i4 : chordalTria N; |
i5 : codimCount N
7 6 5 4
o5 = 2t + 17t + 14t + t
o5 : ZZ[t]
|
i6 : reduceDimension(N,2); |
i7 : codimCount N
5 4
o7 = 14t + t
o7 : ZZ[t]
|
i8 : reduceDimension(N,1); |
i9 : codimCount N
4
o9 = t
o9 : ZZ[t]
|
The method topComponents(ChordalNet) is equivalent to reduceDimension(N,1).
An arc is removed only if all the chains through it have small dimension. If an arc belongs to a chain of large dimenson and a chain of small dimension, then the arc will not be removed.
The object reduceDimension is a function closure.