These Thurston maps are primitive and have degree 4.
There are exactly three postcritical points
if the translation term b = lambda2.
For this value of b, this Thurston map is not a NET map.
All other choices of b among 0, lambda1, lambda2,
lambda1+lambda2 yield NET maps.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0} {lambda1} {lambda1+lambda2}
Since no Thurston multiplier is 1, this modular group Hurwitz class
contains only finitely many Thurston equivalence classes.
The number of pure modular group Hurwitz classes
in this modular group Hurwitz class is 9.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/2, 1/2
Since every Thurston multiplier is less than 1, every
NET map in this modular group Hurwitz class is rational.
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.994023)
( 1.005892,infinity)
SLOPE FUNCTION INFORMATION
There are no slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 28
No nontrivial cycles were found.
The slope function maps some slope to the nonslope.
The slope function orbit of every slope p/q with |p| <= 50
and |q| <= 50 ends in the nonslope.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=",
"b=(1,4)(2,3)",
"c=<1,1,1,1>(1,2)(3,4)",
"d=<1,b^-1*a*b,c,1>(1,3)(2,4)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,3)(2,4)",
"b=",
"c=<1,c,a,1>(1,2)(3,4)",
"d=(1,4)(2,3)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=**(1,4)(2,3)",
"b=<1,c,a,1>(1,2)(3,4)",
"c=",
"d=<1,b^-1,b,b>(1,3)(2,4)",
"a*b*c*d");
**