isGolod -- whether the ring is Golod

Synopsis

Usage:

isGolod R or isGolod I
Inputs:
- R, a quotient ring, of a polynomial algebra by an ideal contained in the irrelevant maximal ideal
Outputs:
- a Boolean value, 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

Ways to use isGolod:

isGolod(QuotientRing)
isGolod(Ideal) -- whether the ring is Golod

For the programmer

The object isGolod is a method function.