# Singular

#### D.15.16.6 GITcone

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

Usage:
GITcone(OCcones, w); OCcones: list of orbit cones, w: bigintmat with one row

Purpose:
Returns the intersection of all orbit cones containing w.

Return:
cone,intvec with the GIT cone containing w, and the hash of this cone (the indices of the orbit cones contributing to the intersection)

Example:
 ```LIB "gitfan.lib"; 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; list AF= afaces(J,nrows(Q)); AF=fullDimImages(AF,Q); AF = minimalAfaces(AF); list OC = orbitCones(AF,Q); bigintmat w[1][nrows(Q)]; for(int i = 1; i <= nrows(Q); i++){ w = w + Q[1..nrows(Q),i]; } GITcone(OC,w); ==> AMBIENT_DIM ==> 5 ==> FACETS ==> 0,0,0,0,1, ==> 0,1,0,0,0 ==> LINEAR_SPAN ==> 1,0,0,0,-1, ==> 0,0,1,0,-1, ==> 0,0,0,1,-1 ==> 3,5,6,8,10,11,12,14,16,17,18,19,20,21,22,23,24,25 ```