next | previous | forward | backward | up | top | index | toc | Macaulay2 website
TorAlgebra :: isGorenstein

isGorenstein -- whether the ring is Gorenstein



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

Ways to use isGorenstein :

For the programmer

The object isGorenstein is a method function.