# Singular

#### D.15.16.14 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); ```