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StatePolytope :: isStable

isStable -- determines whether the mth Hilbert point of I is GIT stable



Bayer and Morrison showed that GIT stability of the mth Hilbert point of I with respect to the maximal torus acting on a polynomial ring by scaling the variables can be tested by whether Statem(I) contains a certain point.
i1 : R = QQ[a..d];
i2 : I = ideal(a*c-b^2,a*d-b*c,b*d-c^2);

o2 : Ideal of R
i3 : isStable(3,I)

o3 = true
i4 : I = ideal(a^2,b^2,b*c);

o4 : Ideal of R
i5 : isStable(3,I) 

o5 = false

Ways to use isStable :

For the programmer

The object isStable is a method function.