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

## Synopsis

• Usage:
resLengthThreeTorAlgClass F
• Inputs:
• F, , a length three free resolution of a cyclic module
• I, an ideal, an ideal of codepth 3
• Outputs:
• , 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

The codepth of the ideal I must be exactly 3, and the length of the complex F must be exactly 3.

## Ways to use resLengthThreeTorAlgClass :

• "resLengthThreeTorAlgClass(ChainComplex)"
• "resLengthThreeTorAlgClass(Ideal)"

## For the programmer

The object resLengthThreeTorAlgClass is .