#### D.13.3.15 minimalOrbitConeOrbits

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

Usage:
  minimalOrbitConeOrbits(listOfOrbits); listOfOrbits: list of lists of cones

Purpose:
  Minimizes a list of orbit cone orbits.

Return:
  a list of lists of cones

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 simplexSymmetryGroup = G25Action();
    list simplexOrbitRepresentatives = intvec( 1, 2, 3, 4, 5 ),
    intvec( 1, 2, 3, 5, 6 ),
    intvec( 1, 2, 3, 5, 7 ),
    intvec( 1, 2, 3, 5, 10 ),
    intvec( 1, 2, 3, 7, 9 ),
    intvec( 1, 2, 6, 9, 10 ),
    intvec( 1, 2, 3, 4, 5, 6 ),
    intvec( 1, 2, 3, 4, 5, 10 ),
    intvec( 1, 2, 3, 5, 6, 8 ),
    intvec( 1, 2, 3, 5, 6, 9 ),
    intvec( 1, 2, 3, 5, 7, 10 ),
    intvec( 1, 2, 3, 7, 9, 10 ),
    intvec( 1, 2, 3, 4, 5, 6, 7 ),
    intvec( 1, 2, 3, 4, 5, 6, 8 ),
    intvec( 1, 2, 3, 4, 5, 6, 9 ),
    intvec( 1, 2, 3, 5, 6, 9, 10 ),
    intvec( 1, 2, 3, 4, 5, 6, 7, 8 ),
    intvec( 1, 2, 3, 4, 5, 6, 9, 10 ),
    intvec( 1, 2, 3, 4, 5, 6, 7, 8, 9 ),
    intvec( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 );
    list afaceOrbitRepresentatives=afaces(J,simplexOrbitRepresentatives);
    list fulldimAfaceOrbitRepresentatives=fullDimImages(afaceOrbitRepresentatives,Q);
    list afaceOrbits=computeAfaceOrbits(fulldimAfaceOrbitRepresentatives,simplexSymmetryGroup);
    apply(afaceOrbits,size);
    ==> 10 15 10 1
    list minAfaceOrbits = minimalAfaceOrbits(afaceOrbits);
    apply(minAfaceOrbits,size);
    ==> 10 15
    list listOfOrbitConeOrbits = orbitConeOrbits(minAfaceOrbits,Q);
    apply(listOfOrbitConeOrbits,size);
    ==> 10 15
    list listOfMinimalOrbitConeOrbits = minimalOrbitConeOrbits(listOfOrbitConeOrbits);
    size(listOfMinimalOrbitConeOrbits);
    ==> 2

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