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CodepthThree :: torAlgClass

torAlgClass -- the class (w.r.t. multiplication in homology) of a local ring

Synopsis

Description

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