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StatePolytope :: isStable

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

Synopsis

Description

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)
polymake: used package cdd
  cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www-oldurls.inf.ethz.ch/personal/fukudak/cdd_home/

VERTICES
1 9 6 6 9
1 6 12 3 9
1 4 14 5 7
1 3 14 8 5
1 9 3 12 6
1 7 5 14 4
1 5 8 14 3
1 3 12 12 3

polymake: used package cdd
  cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www-oldurls.inf.ethz.ch/personal/fukudak/cdd_home/

VERTICES
1 9 6 6 9
1 6 12 3 9
1 4 14 5 7
1 3 14 8 5
1 9 3 12 6
1 7 5 14 4
1 5 8 14 3
1 3 12 12 3


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

o4 : Ideal of R
i5 : isStable(3,I) 
polymake: used package cdd
  cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www-oldurls.inf.ethz.ch/personal/fukudak/cdd_home/

VERTICES
1 11 13 6 3

polymake: used package cdd
  cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www-oldurls.inf.ethz.ch/personal/fukudak/cdd_home/

VERTICES
1 33/4 33/4 33/4 33/4
1 11 13 6 3


o5 = false

Ways to use isStable :

For the programmer

The object isStable is a method function.