resLengthThreeTorAlgClass -- the class (w.r.t. multiplication in homology) of an ideal

Synopsis

• Usage:

  resLengthThreeTorAlgClass F

• Inputs:
  • F, a chain complex, a length three free resolution of a cyclic module
  • I, an ideal, an ideal of codepth 3
• Outputs:
  • a string, the (parametrized) class of the ideal I

Description

Classifies the ideal $I$ as belonging to one of the (parametrized) classes B , C(c), G(r), H(p,q) , T, provided that it is codepth 3.

i1 : Q = QQ[x,y,z];

i2 : resLengthThreeTorAlgClass ideal (x*y,x^2,y*z,z^2)

o2 = B

i3 : resLengthThreeTorAlgClass ideal (x^2,y^2,z^2)

o3 = C(3)

i4 : resLengthThreeTorAlgClass ideal (x*y,y*z,x^3,x^2*z,x*z^2-y^3,z^3)

o4 = G(3)

i5 : resLengthThreeTorAlgClass ideal (x*z+y*z,x*y+y*z,x^2-y*z,y*z^2+z^3,y^3-z^3)

o5 = G(5)

i6 : resLengthThreeTorAlgClass ideal (x^2,y^2,z^2,x*z)

o6 = H(3,2)

i7 : resLengthThreeTorAlgClass ideal (x^2,y^2,z^2,x*y*z)

o7 = T

Caveat