Classifies the local ring obtained by localizing R at the irrelevant maximal ideal as belonging to one of the (parametrized) classes B, C(c), G(r), H(p,q), S, or T, provided that it is codepth at most 3
i1 : Q = QQ[x,y,z]; |
i2 : torAlgClass (Q/ideal (x^2,x*y,y*z,z^2)) o2 = B |
i3 : torAlgClass (Q/ideal (x^2,y^2)) o3 = C(2) |
i4 : torAlgClass (Q/ideal (x*y,y*z,x^3,x^2*z,x*z^2-y^3,z^3)) o4 = G(3) |
i5 : torAlgClass (Q/ideal (x^2,y^2,z^2,x*y)) o5 = H(3,2) |
i6 : torAlgClass (Q/ideal (x^2,y^2,x*y)) o6 = S |
i7 : torAlgClass (Q/ideal (x^2,y^2,z^2,x*y*z)) o7 = T |
If the local ring has codepth more than 3, then the function returns "codepth > 3".
i8 : Q = QQ[w,x,y,z]; |
i9 : torAlgClass (Q/ideal (w^4,x^2,y^2,z^2)) o9 = codepth > 3 |
If the defining ideal of R is not contained in the irrelevant maximal ideal, then the resulting local ring is zero, and the function returns "zero ring".
i10 : Q = QQ[x,y,z]; |
i11 : torAlgClass (Q/ideal (x^2-1)) o11 = zero ring |