Test whether the monomial algebra K[B] is simplicial, that is, the cone C(B) is spanned by linearly independent vectors.
Note that this condition does not depend on K.
i1 : B={{1,0,0},{0,2,0},{0,0,2},{1,0,1},{0,1,1}}
o1 = {{1, 0, 0}, {0, 2, 0}, {0, 0, 2}, {1, 0, 1}, {0, 1, 1}}
o1 : List
|
i2 : R=QQ[x_0..x_4,Degrees=>B] o2 = R o2 : PolynomialRing |
i3 : isSimplicialMA R o3 = true |
i4 : isSimplicialMA B o4 = true |
i5 : B={{1,0,1},{0,1,1},{1,1,1},{0,0,1}}
o5 = {{1, 0, 1}, {0, 1, 1}, {1, 1, 1}, {0, 0, 1}}
o5 : List
|
i6 : R=QQ[x_0..x_3,Degrees=>B] o6 = R o6 : PolynomialRing |
i7 : isSimplicialMA R o7 = false |
i8 : isSimplicialMA B o8 = false |
i9 : B={{1,0,1},{0,1,1},{1,1,1},{0,0,1}}
o9 = {{1, 0, 1}, {0, 1, 1}, {1, 1, 1}, {0, 0, 1}}
o9 : List
|
i10 : M=monomialAlgebra B
ZZ
o10 = ---[x ..x ]
101 0 3
o10 : MonomialAlgebra generated by {{1, 0, 1}, {0, 1, 1}, {1, 1, 1}, {0, 0, 1}}
|
i11 : isSimplicialMA M o11 = false |
The object isSimplicialMA is a method function.