load "ovalfunc.mgm";

/*
G := AlternatingGroup(5);
c := G!(1,2)(3,4);
b := G!(1,2,3,4,5);
a := (b*c) ^(-1);
*/

/*
G :=CyclicGroup(16);
x := G.1;
a := x^4;
b := x;
c := (a*b)^(-1);
*/

/*
G :=CyclicGroup(24);
x := G.1;
a := x^4;
b := x;
c := (a*b)^(-1);
*/

/*
G :=CyclicGroup(6);
x := G.1;
a := x;
b := x^4;
c := (a*b)^(-1);
*/


/*
k := 7;
G :=CyclicGroup(2*k);
x := G.1;
a := x^k;
b := x^(k-1);
c := (a*b)^(-1);
*/

/*
s := 16;
G :=DirectProduct(CyclicGroup(3),DihedralGroup(s));
w := G.1;
r := G.2;
f := G.3;
a := f;
b := w*r;
c := (a*b)^(-1);
*/

G := AlternatingGroup(7);
a := G!(1,2,3);
b := G!(1,7,6,5,4,3,2);
c := (a*b) ^(-1);
#G/#sub<G|a,b>;


lmn := getLMN(a,b,c);
lamunu := getLaMuNu(lmn);
RPQ := getRPQ(a,b,c,G); 
R := RPQ[1];
P := RPQ[2];
Q := RPQ[3];
H := OvalRotpqr(a,b,c);

ovals := Ovalspqr(a,b,c,G);
Op := ovals[1];
Oq := ovals[2];
Or := ovals[3];


SetLogFile("rez.txt":Overwrite:=true);


"lmn",lmn;
"lammnu",lamunu;
"Hords",[Order(H[1]),Order(H[2]),Order(H[3])]; 
"Onums",[#Op,#Oq,#Or];

[OvalIntersectionPattern(Oq,Oq,R,G), OvalIntersectionPattern(Oq,Op,R,G),OvalIntersectionPattern(Op,Op,R,G)];
[OvalIntersectionPattern(Or,Or,P,G), OvalIntersectionPattern(Or,Oq,P,G),OvalIntersectionPattern(Oq,Oq,P,G)];
[OvalIntersectionPattern(Op,Op,Q,G), OvalIntersectionPattern(Op,Or,Q,G),OvalIntersectionPattern(Or,Or,Q,G)];



UnsetLogFile();