# isGorenstein -- whether the ring is Gorenstein

## Synopsis

• Usage:
isGorenstein R or isGorenstein 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 Gorenstein

## Description

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

 i1 : Q = QQ[x,y,z]; i2 : isGorenstein (Q/ideal(x^2,x*y,y*z,z^2)) o2 = false i3 : isGorenstein (Q/ideal(x^2,y^2)) o3 = true i4 : isGorenstein (Q/ideal(x*z+y*z,x*y+y*z,x^2-y*z,y*z^2+z^3,y^3-z^3)) o4 = true

## For the programmer

The object isGorenstein is .