Test whether the simplicial monomial algebra K[B] is Cohen-Macaulay.
Note that this condition does not depend on K.
i1 : a=3 o1 = 3 |
i2 : B={{a, 0}, {0, a}, {1, a-1}, {a-1, 1}} o2 = {{3, 0}, {0, 3}, {1, 2}, {2, 1}} o2 : List |
i3 : R=QQ[x_0..x_3,Degrees=>B] o3 = R o3 : PolynomialRing |
i4 : isCohenMacaulayMA R o4 = true |
i5 : decomposeMA R o5 = HashTable{| -1 | => {ideal 1, | 2 |}} | 1 | | 1 | | 1 | => {ideal 1, | 1 |} | -1 | | 2 | 0 => {ideal 1, 0} o5 : HashTable |
i6 : a=4 o6 = 4 |
i7 : B={{a, 0}, {0, a}, {1, a-1}, {a-1, 1}} o7 = {{4, 0}, {0, 4}, {1, 3}, {3, 1}} o7 : List |
i8 : R=QQ[x_0..x_3,Degrees=>B] o8 = R o8 : PolynomialRing |
i9 : isCohenMacaulayMA R o9 = false |
i10 : decomposeMA R o10 = HashTable{| -1 | => {ideal 1, | 3 |} } | 1 | | 1 | | 1 | => {ideal 1, | 1 |} | -1 | | 3 | | 2 | => {ideal (x , x ), | 2 |} | 2 | 1 0 | 2 | 0 => {ideal 1, 0} o10 : HashTable |