Test whether the simplicial monomial algebra K[B] is Buchsbaum.
Note that this condition does not depend on K.
For the defintion of Buchsbaum see:
J. Stueckrad, W. Vogel: Castelnuovo Bounds for Certain Subvarieties in \mathbb{P}^n, Math. Ann. 276 (1987), 341-352.
i1 : R=QQ[x_0..x_3,Degrees=>{{6,0},{0,6},{4,2},{1,5}}]
o1 = R
o1 : PolynomialRing
|
i2 : isBuchsbaumMA R o2 = false |
i3 : decomposeMonomialAlgebra R
o3 = HashTable{| -1 | => {ideal 1, | 5 |} }
| 1 | | 7 |
| -2 | => {ideal 1, | 4 |}
| 2 | | 2 |
0 => {ideal 1, 0}
| 1 | => {ideal 1, | 1 |}
| -1 | | 5 |
| 2 | => {ideal (x , x ), | 2 |}
| -2 | 0 1 | 4 |
| 3 | => {ideal (x , x ), | 3 |}
| 3 | 0 1 | 9 |
o3 : HashTable
|
i4 : R=QQ[x_0..x_3,Degrees=>{{4,0},{0,4},{3,1},{1,3}}]
o4 = R
o4 : PolynomialRing
|
i5 : isBuchsbaumMA R o5 = true |
i6 : decomposeMonomialAlgebra R
o6 = HashTable{| -1 | => {ideal 1, | 3 |} }
| 1 | | 1 |
0 => {ideal 1, 0}
| 1 | => {ideal 1, | 1 |}
| -1 | | 3 |
| 2 | => {ideal (x , x ), | 2 |}
| 2 | 0 1 | 2 |
o6 : HashTable
|
i7 : R=QQ[x_0..x_3,Degrees=>{{5,0},{0,5},{4,1},{1,4}}]
o7 = R
o7 : PolynomialRing
|
i8 : isBuchsbaumMA R o8 = false |
i9 : decomposeMonomialAlgebra R
o9 = HashTable{| -1 | => {ideal 1, | 4 |} }
| 1 | | 1 |
2
| -2 | => {ideal (x , x ), | 3 |}
| 2 | 0 1 | 2 |
0 => {ideal 1, 0}
| 1 | => {ideal 1, | 1 |}
| -1 | | 4 |
2
| 2 | => {ideal (x , x ), | 2 |}
| -2 | 0 1 | 3 |
o9 : HashTable
|
i10 : R=QQ[x_0..x_3,Degrees=>{{5,0},{0,5},{4,1},{1,4}}]
o10 = R
o10 : PolynomialRing
|
i11 : M=monomialAlgebra R
o11 = R
o11 : MonomialAlgebra generated by {{5, 0}, {0, 5}, {4, 1}, {1, 4}}
|
i12 : isBuchsbaumMA M o12 = false |
The object isBuchsbaumMA is a method function.