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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)
This is the Gfan program for computing Groebner fans and tropical varieties.
Use the command "gfan list" to view all subcommands.
The command "gfan" is deprecate for computing all Groebner bases of an ideal.
Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end.
LP algorithm being used: "cddgmp".
polymake:  WARNING: created private directory /home/member/dgrayson/.polymake
polymake: used package cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html

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

This is the Gfan program for computing Groebner fans and tropical varieties.
Use the command "gfan list" to view all subcommands.
The command "gfan" is deprecate for computing all Groebner bases of an ideal.
Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end.
LP algorithm being used: "cddgmp".
polymake: used package cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html

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) 
This is the Gfan program for computing Groebner fans and tropical varieties.
Use the command "gfan list" to view all subcommands.
The command "gfan" is deprecate for computing all Groebner bases of an ideal.
Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end.
LP algorithm being used: "cddgmp".
polymake: used package cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html

VERTICES
1 11 13 6 3

This is the Gfan program for computing Groebner fans and tropical varieties.
Use the command "gfan list" to view all subcommands.
The command "gfan" is deprecate for computing all Groebner bases of an ideal.
Please use subcommand "gfan _bases" instead. Awaiting input. <Ctrl>-D to end.
LP algorithm being used: "cddgmp".
polymake: used package cddlib
  Implementation of the double description method of Motzkin et al.
  Copyright by Komei Fukuda.
  http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html

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


o5 = false

Ways to use isStable :