Test whether the simplicial monomial algebra K[B] is Buchsbaum.
Note that this condition does not depend on K.
i1 : R=QQ[x_0..x_3,Degrees=>{{6,0},{0,6},{4,2},{1,5}}]
o1 = R
o1 : PolynomialRing
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i2 : isBuchsbaumMA R o2 = false |
i3 : decomposeMonomialAlgebra R
o3 = HashTable{| -1 | => {ideal 1, | 5 |} }
| 1 | | 7 |
| -2 | => {ideal 1, | 4 |}
| 2 | | 2 |
| 1 | => {ideal 1, | 1 |}
| -1 | | 5 |
| 2 | => {ideal (x , x ), | 2 |}
| -2 | 0 1 | 4 |
| 3 | => {ideal (x , x ), | 3 |}
| 3 | 0 1 | 9 |
0 => {ideal 1, 0}
o3 : HashTable
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i4 : R=QQ[x_0..x_3,Degrees=>{{4,0},{0,4},{3,1},{1,3}}]
o4 = R
o4 : PolynomialRing
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i5 : isBuchsbaumMA R o5 = true |
i6 : decomposeMonomialAlgebra R
o6 = HashTable{| -1 | => {ideal 1, | 3 |} }
| 1 | | 1 |
| 1 | => {ideal 1, | 1 |}
| -1 | | 3 |
| 2 | => {ideal (x , x ), | 2 |}
| 2 | 0 1 | 2 |
0 => {ideal 1, 0}
o6 : HashTable
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i7 : R=QQ[x_0..x_3,Degrees=>{{5,0},{0,5},{4,1},{1,4}}]
o7 = R
o7 : PolynomialRing
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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 |
| 1 | => {ideal 1, | 1 |}
| -1 | | 4 |
2
| 2 | => {ideal (x , x ), | 2 |}
| -2 | 0 1 | 3 |
0 => {ideal 1, 0}
o9 : HashTable
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