"Source: Text/Geometry/GrpPSL2Shim.text";
"Line: 852";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/GrpPSL2Shim.text, line: 852
// Example: H143E6 ()
print "Example: H143E6";
ei := GetEchoInput();
SetEchoInput(true);
K<z> := CyclotomicField(9);
F := sub<K | z+1/z >;
b := F! (z+1/z);
A<alpha,beta> := QuaternionAlgebra<F | -3, -b>;
G := FuchsianGroup(A);
O := BaseRing(G);
A<alpha,beta> := Algebra(O);
g := G!((1+alpha)/2);
H := UpperHalfPlane();
FixedPoints(g, H);
Matrix(g);
g*H.1;
cH, rH := IsometricCircle(g);
cH;
rH;
CC<I> := ComplexField();
Abs(Matrix(g)[2,1]*(cH+rH*I)+Matrix(g)[2,2]);
D := UnitDisc(: Center := 9/10*H.1);
Matrix(g, D);
cD, rD := IsometricCircle(g, D);
Abs(Matrix(g, D)[2,1]*PlaneToDisc(D, H!(cH+rH*I))+Matrix(g, D)[2,2]);
SetEchoInput(ei);
