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D.15.18.6 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
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