Singular Manual: orbitConeOrbits

| #### D.13.3.14 orbitConeOrbits Procedure from library `gitfan.lib` (see gitfan_lib). Usage: orbitConeOrbits(F, Q); F: list, Q: intmat Purpose: Projects a list F of a-face orbits to the orbit cones with respect to Q. The function checks whether the projections are of full dimension and returns an error otherwise. Return: a list of lists of cones Example:
    LIB "gitfan.lib";
    // Note that simplexOrbitRepresentatives and simplexSymmetryGroup are subsets of the actual sets for G25. For the full example see the examples in the documentation
    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 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, 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 simplexSymmetryGroup = permutationFromIntvec(intvec( 1 .. 10 )),
    permutationFromIntvec(intvec( 1, 2, 4, 3, 5, 7, 6, 9, 8, 10 )),
    permutationFromIntvec(intvec( 1, 3, 2, 4, 6, 5, 7, 8, 10, 9 )),
    permutationFromIntvec(intvec( 1, 3, 4, 2, 6, 7, 5, 10, 8, 9 )),
    permutationFromIntvec(intvec( 1, 4, 2, 3, 7, 5, 6, 9, 10, 8 )),
    permutationFromIntvec(intvec( 1, 4, 3, 2, 7, 6, 5, 10, 9, 8 ));
    list fulldimAfaceOrbitRepresentatives=fullDimImages(afaceOrbitRepresentatives,Q);
    list afaceOrbits=computeAfaceOrbits(fulldimAfaceOrbitRepresentatives,simplexSymmetryGroup);
    apply(afaceOrbits,size);
    ==> 3 3 1
    list minAfaceOrbits = minimalAfaceOrbits(afaceOrbits);
    apply(minAfaceOrbits,size);
    ==> 3
    list listOfOrbitConeOrbits = orbitConeOrbits(minAfaceOrbits,Q);

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