# torAlgData(Ideal) -- invariants of a local ring and its class (w.r.t. multiplication in homology)

## Synopsis

• Function: torAlgData
• Usage:
torAlgData R or torAlgData I
• Inputs:
• I, an ideal, of a polynomial algebra contained in the irrelevant maximal ideal
• Outputs:
• , with invariants of the local ring obtained by localizing the quotient by I at the irrelevant maximal ideal

## Description

 i1 : Q = QQ[x,y,z]; i2 : data = torAlgData (ideal(x*y,y*z,x^3,x^2*z,x*z^2-y^3,z^3)) 2 3 4 2 + 2T - 2T - T + T o2 = HashTable{BassSeries => ---------------------- } 2 3 4 1 - T - 5T - 2T + T c => 3 Class => G e => 3 h => 0 isCI => false isGolod => false isGorenstein => false m => 6 n => 2 p => 0 2 (1 + T) PoincareSeries => ---------------------- 2 3 4 1 - T - 5T - 2T + T q => 1 r => 3 o2 : HashTable i3 : data#"PoincareSeries" 2 (1 + T) o3 = ---------------------- 2 3 4 1 - T - 5T - 2T + T o3 : Expression of class Divide