Computes the stellar subdivision of a simplicial complex D by subdividing the face F with a new vertex corresponding to the variable of S. The result is a complex on the variables of R ⊗S. It is a subcomplex of the simplex on the variables of R ⊗S.
i1 : R=QQ[x_0..x_4]; |
i2 : I=monomialIdeal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0); o2 : MonomialIdeal of R |
i3 : betti res I
0 1 2 3
o3 = total: 1 5 5 1
0: 1 . . .
1: . 5 5 .
2: . . . 1
o3 : BettiTally
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i4 : D=simplicialComplex I o4 = | x_2x_4 x_1x_4 x_1x_3 x_0x_3 x_0x_2 | o4 : SimplicialComplex |
i5 : fc=facets(D,useFaceClass=>true)
o5 = {x x , x x , x x , x x , x x }
2 4 1 4 1 3 0 3 0 2
o5 : List
|
i6 : S=QQ[x_5] o6 = S o6 : PolynomialRing |
i7 : D5=stellarSubdivision(D,fc#0,S) o7 = | x_4x_5 x_2x_5 x_1x_4 x_1x_3 x_0x_3 x_0x_2 | o7 : SimplicialComplex |
i8 : I5=ideal D5
o8 = ideal (x x , x x , x x , x x , x x , x x , x x , x x , x x )
0 1 1 2 2 3 0 4 2 4 3 4 0 5 1 5 3 5
o8 : Ideal of QQ[x , x , x , x , x , x ]
0 1 2 3 4 5
|
i9 : betti res I5
0 1 2 3 4
o9 = total: 1 9 16 9 1
0: 1 . . . .
1: . 9 16 9 .
2: . . . . 1
o9 : BettiTally
|
i10 : R=QQ[x_1..x_6] o10 = R o10 : PolynomialRing |
i11 : I=monomialIdeal product gens R
o11 = monomialIdeal(x x x x x x )
1 2 3 4 5 6
o11 : MonomialIdeal of R
|
i12 : D=simplicialComplex I o12 = | x_2x_3x_4x_5x_6 x_1x_3x_4x_5x_6 x_1x_2x_4x_5x_6 x_1x_2x_3x_5x_6 x_1x_2x_3x_4x_6 x_1x_2x_3x_4x_5 | o12 : SimplicialComplex |
i13 : S=QQ[x_7] o13 = S o13 : PolynomialRing |
i14 : Dsigma=stellarSubdivision(D,face {x_1,x_2,x_3},S)
o14 = | x_2x_3x_5x_6x_7 x_1x_3x_5x_6x_7 x_1x_2x_5x_6x_7 x_2x_3x_4x_6x_7 x_1x_3x_4x_6x_7 x_1x_2x_4x_6x_7 x_2x_3x_4x_5x_7 x_1x_3x_4x_5x_7 x_1x_2x_4x_5x_7 x_2x_3x_4x_5x_6 x_1x_3x_4x_5x_6 x_1x_2x_4x_5x_6 |
o14 : SimplicialComplex
|
i15 : betti res ideal Dsigma
0 1 2
o15 = total: 1 2 1
0: 1 . .
1: . . .
2: . 1 .
3: . 1 .
4: . . .
5: . . 1
o15 : BettiTally
|