# Singular

#### D.15.18.13 minimalAfaceOrbits

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

Usage:
minimalAfaceOrbits(afaceOrbits); afaceOrbits: list

Purpose:
Returns a list of all minimal a-face orbits.

Return:
a list of intvecs

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 ```