isGorenstein(Ideal) -- whether the ring is Gorenstein

• Function: isGorenstein

• Usage:

  isGorenstein R or isGorenstein I

• Inputs:
  • I, an ideal, of a polynomial algebra contained in the irrelevant maximal ideal
• Outputs:
  • a Boolean value, whether the local ring obtained by localizing the quotient by I at the irrelevant maximal ideal is Gorenstein

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

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

o2 = false

i3 : isGorenstein (ideal(x^2,y^2))

o3 = true

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

o4 = true