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D.13.3.30 gitCone

Procedure from library gitfan.lib (see gitfan_lib).

Usage:
gitCone(a, Q, w); a: ideal, Q:bigintmat, w:bigintmat

Purpose:
Returns the GIT-cone lambda(w), i.e. the intersection of all orbit cones containing the vector w.

Note:
call this only if you are interested in a single GIT-cone.

Return:
a cone.

Example:
 
LIB "gitfan.lib";
intmat Q[3][4] =
1,0,1,0,
0,1,0,1,
0,0,1,1;
ring R = 0,T(1..4),dp;
ideal a = 0;
bigintmat w[1][3] = 3,3,1;
cone lambda = gitCone(a, Q, w);
==> (T(1),T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
rays(lambda);
==> 1,0,0,
==> 0,1,0,
==> 1,1,1
bigintmat w2[1][3] = 1,1,1;
cone lambda2 = gitCone(a, Q, w2);
==> (T(1),T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
rays(lambda2);
==> 1,1,1