Singular

D.15.16.7 GITfan

Procedure from library `gitfan.lib` (see gitfan_lib).

Usage:
GITfan(J,Q [, G]); J:ideal, Q:intmat, G:list

Purpose:
Computes the GIT fan associated to J and Q. Optionally a symmetry group action on the column space of Q can be specified.

Return:
a fan, the GIT fan.

Note:
The proceduce uses parallel computation for the construction of the GIT-cones. The a-faces are not computed in parallel. This can be done by calling the aface procedure specifying a list of simplex faces. If used with the optional argument G, the orbit decomposition of the simplex of columns of Q is computed. Refer to the Singular documentation on how to do this more efficiently using GAP.

Example:
 ```LIB "gitfan.lib"; setcores(4); ==> 4 ring R = 0,T(1..10),wp(1,1,1,1,1,1,1,1,1,1); ideal J = T(5)*T(10)-T(6)*T(9)+T(7)*T(8), T(1)*T(9)-T(2)*T(7)+T(4)*T(5), T(1)*T(8)-T(2)*T(6)+T(3)*T(5), T(1)*T(10)-T(3)*T(7)+T(4)*T(6), T(2)*T(10)-T(3)*T(9)+T(4)*T(8); intmat Q[5][10] = 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 1; fan GIT = GITfan(J,Q); intmat Q[5][10] = ==> // ** redefining Q (intmat Q[5][10] =) 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 1, 0, 0, 0, 1, 1, -1, 0, 0, 0, 0, 1; list simplexSymmetryGroup = G25Action(); fan GIT2 = GITfan(J,Q,simplexSymmetryGroup); ```