// For each of the following inputs run the  commands
// The funciton "q2Extension" and the procedure "OrbitDivisors" are defined in the file Skript.txt

G0:=sub<G|gv>;
H,e,Orb:=q2Extension(G0); // constructing a bigger automorphism group
for w in Orb do OrbitDivisors(G,genus,G0,H,e,w); end for;



/* We are considering Hurwitz orbits (see Script) of generating vectors for the following reason.
It is possible that:
1) 2 different generating vectors gv_1, gv_2 for G^0 <G  define non-isomorphic curves C1 and C2 of the same genus;
2) the groups H1, H2 we have to consider are equal (H1=H2=:H);
3) we cannot use the input to distinguish between a generating vector for the covering C1-> C1/H=P^1 and a generating vector for the covering C2-> C2/H.

In this situation the g.v. w_1 for the first covering and the g.v. w_2 for the second covering
are in different Hurwitz orbit (since C1 and C2 are not isomorphic) of generating vectors of H of given type.
Whence considering OrbitDivisors(G,genus,q,G0,H,e,w_i) for i=1,2 we deal both cases simultaneously.

If one of the three conditions 1)-3) is not satisfied, then we have get only one orbit.
*/



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


// Input 1
G:=SmallGroup(12, 4);
gv:=[ G.1 * G.2 * G.3^2, Id(G), G.3^2, G.3 ];
genus:=7;


//-------------------------//-------------------------//-------------------------
//-------------------------//-------------------------//-------------------------
//CASEK^2=2 p_g=q=2
//-------------------------//-------------------------//-------------------------

// Input 1
G:=SmallGroup(16,13); genus:=9;
gv:= [ G.1 * G.3, G.2 * G.3, G.2 * G.3 * G.4, G.1 * G.3 * G.4 ];


// Input 2-3:  here we are in the situation described above

G:=SmallGroup(16,11); genus:=9;
gv:= [ Id(G), G.1 * G.2 * G.4, Id(G), G.1 ];

gv:= [ G.2 * G.3, G.1 * G.4, G.2 * G.3, G.1 * G.2 * G.3 * G.4 ];