Since the barycentric subdivision of a simplicial complex D is a balanced simplicial complex B, i.e., there exists a dim(D)+1 proper vertex coloring, this colorfulPresentation takes in the barycentric subdivision of a simplicial complex, computes a colorful system of parameters for the Stanley-Reisner ring of B and then returns this quotient ring as an N-graded module over the colorful parameter ring.
i1 : S = QQ[a..e]; |
i2 : F = {a*b*c,c*d,e}
o2 = {a*b*c, c*d, e}
o2 : List
|
i3 : D = simplicialComplex F o3 = | e cd abc | o3 : SimplicialComplex |
i4 : colorfulPresentation D
o4 = cokernel {0} | 0 0 0 0 |
{1} | 0 0 0 0 |
{1} | 0 0 0 0 |
{3} | 0 0 0 0 |
{1} | d 0 0 0 |
{1} | 0 d 0 c |
{2} | 0 0 0 0 |
{2} | 0 0 0 0 |
{2} | 0 0 d 0 |
9
o4 : QQ[b..d]-module, quotient of (QQ[b..d])
|
i5 : M = colorfulPresentation F
o5 = cokernel {0} | 0 0 0 0 |
{1} | 0 0 0 0 |
{1} | 0 0 0 0 |
{3} | 0 0 0 0 |
{1} | d 0 0 0 |
{1} | 0 d 0 c |
{2} | 0 0 0 0 |
{2} | 0 0 0 0 |
{2} | 0 0 d 0 |
9
o5 : QQ[b..d]-module, quotient of (QQ[b..d])
|
i6 : degrees M
o6 = {{0}, {1}, {1}, {3}, {1}, {1}, {2}, {2}, {2}}
o6 : List
|
The object colorfulPresentation is a method function.