# isGolod -- whether the ring is Golod

## Synopsis

• Usage:
isGolod R or isGolod I
• Inputs:
• R, , of a polynomial algebra by an ideal contained in the irrelevant maximal ideal
• Outputs:
• , whether the local ring obtained by localizing R at the irrelevant maximal ideal is Golod

## Description

Checks if the local ring obtained by localizing R at the irrelevant maximal ideal is Golod. It is also possible to call the function on the defining ideal of R; see isGolod(Ideal).

 i1 : Q = QQ[x,y,z]; i2 : isGolod (Q/ideal(x^2,x*y,y*z,z^2)) o2 = false i3 : isGolod (Q/ideal(x^2)) o3 = true i4 : isGolod (Q/(ideal(x,y,z))^2) o4 = true

## For the programmer

The object isGolod is .