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.