// The function "q1Extension" and the procedure "OrbitDivisors" are defined in the file script.txt, which must be load in advance.
// Then, for each of the following inputs run the following commands.


G0:=sub<G|gv>;
H,e,HOrb:=q1Extension(G0,gv); // constructing a bigger automorphism group
for w in HOrb do OrbitDivisors(G,genus,G0,H,e,w); end for;

/* 

HOrb stands for Hurwitz orbits.
As explained in [CF18, Section 6.2], (see also [BC04, BCG08]), generating vectors for a group H, 
of type (0; m_1,..., m_r), which differ by a Huwitz move or an automorphism of H yield isomorphic covers
C->C/H = P^1, hence we shall consider only one representative for each orbit of the group action induced by automorphisms and Huwitz moves.

As expected, in each case we shall indeed get a single orbit.
*/


//-------------------------//-------------------------//-------------------------
//-------------------------//-------------------------//-------------------------
// CASE K^2=4, p_g=q=1
//-------------------------//-------------------------//-------------------------

// Input 1
G:=SmallGroup(48,38); genus:=13;
gv:= [ G.1 * G.5, G.2 * G.4, G.1 * G.2 * G.5^2, G.1 * G.2 * G.5^2 ];


// Intput 2
G:=SmallGroup(48,37); genus:=13;
gv:=[ G.4 * G.5^2, G.2 * G.4 * G.5, G.1 * G.2 * G.3 * G.4 * G.5, G.1 * G.2 * G.3 * G.4 * G.5 ];


//-------------------------//-------------------------//-------------------------
//-------------------------//-------------------------//-------------------------
// CASE K^2=2, p_g=q=1
//-------------------------//-------------------------//-------------------------

// Input 1
G:=SmallGroup(64, 153); genus:=17;
gv:=[ G.1 * G.2 * G.3 * G.4, G.1, G.1, G.1 * G.4 * G.5 ];


// Input 2
G:=SmallGroup(64, 150); genus:=17;
gv:=[ G.2 * G.3 * G.4 * G.6, G.2 * G.3 * G.4 * G.5, G.1 * G.2 * G.6, G.1 * G.2 * G.6 ];


// Input 3
G:=SmallGroup(64, 147); genus:=17;
gv:= [ G.2 * G.3 * G.4 * G.6, G.2 * G.3 * G.4 * G.5, G.1 * G.2 * G.6, G.1 * G.2 * G.6 ]; 


// Input 4
G:=SmallGroup(64, 128); genus:=17;
gv:=[ G.1 * G.2 * G.3 * G.4 * G.6, G.1, G.1 * G.4, G.1 * G.5 ];


// Input 5
G:=SmallGroup(64, 130); genus:=17;
gv:= [ G.4 * G.6, G.1 * G.2 * G.3 * G.6, G.1 * G.5 * G.6, G.1 * G.5 * G.6 ];


// Input 6
G:=SmallGroup(64, 134); genus:=17;
gv:=[ G.1 * G.2 * G.3 * G.6, G.5, G.1 * G.4, G.1 * G.4 * G.6 ];


// Input 7
G:=SmallGroup(64, 227); genus:=17;
gv:= [ G.2 * G.3 * G.6, G.1 * G.2 * G.4 * G.6, G.2 * G.5 * G.6, G.2 * G.5 ];


// Input 8
G:=SmallGroup(64, 227); genus:=17;
gv:= [ G.1 * G.4 * G.6, G.3 * G.6, G.3 * G.4 * G.5, G.3 * G.4 * G.5 * G.6 ];


// Input 9
G:=SmallGroup(64, 228); genus:=17;
gv:=[ G.1 * G.2 * G.3 * G.4 * G.5 * G.6, G.1 * G.2 * G.4, G.2 * G.5 * G.6, G.2 * G.5 ];


// Input 10
G:=SmallGroup(64, 234); genus:=17;
gv:=[ G.4 * G.5, G.2, G.3 * G.6, G.3 * G.5 * G.6 ];


// Input 11
G:=SmallGroup(64, 234); genus:=17;
gv:=[ G.1 * G.2 * G.4 * G.5, G.2 * G.5, G.1, G.1 ];


// Input 12
G:=SmallGroup(64, 236); genus:=17;
gv:= [ G.2 * G.3 * G.4 * G.5, G.2 * G.4 * G.5, G.3 * G.4 * G.5, G.3 * G.4 * G.5 ];


// Input 13
G:=SmallGroup(64, 219); genus:=17;
gv:=[ G.1 * G.3, G.1 * G.3 * G.4 * G.6, G.1 * G.2 * G.3 * G.5, G.1 * G.2 * G.3 ];

 
// Input 14
G:=SmallGroup(64, 221); genus:=17;
gv:=[ G.1 * G.3, G.1 * G.3 * G.4 * G.6, G.1 * G.2 * G.3 * G.5, G.1 * G.2 * G.3 ];

 
// Input 15
G:=SmallGroup(64, 213); genus:=17;
gv:= [ G.1 * G.2 * G.4 * G.6, G.1 * G.2 * G.3 * G.6, G.1 * G.2 * G.3 * G.4 * G.5 * G.6, G.1 * G.2 * G.3 * G.4 * G.5 ];


// Input 16
G:=SmallGroup(64, 206); genus:=17;
gv:=[ G.1 * G.2 * G.3 * G.4 * G.5, G.1 * G.2 * G.5 * G.6, G.1 * G.2 * G.4, G.1 * G.2 * G.4 * G.6 ];