These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 25.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0} {lambda1,lambda2,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 2.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/5, 2/5, 4/5
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
(-101.622777,-2.014921 )
( -1.985298,-1.009938 )
( -0.990160,-0.503703 )
( -0.496297,-0.009840 )
( 0.009840,0.992649 )
( 1.007405,101.622777)
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 3 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
1/1 2 5 No No No No
1/0 2 5 No No No No
0/1 2 5 No No No No
NUMBER OF EQUATORS FOUND: 0 0 0 0
The fixed point finder is unable to determine whether
there are any more slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 5336
Here is their union. There are no more slope function fixed points
whose negative reciprocals lie in any of the following intervals.
EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION
( -infinity,-2.611431)
( -2.611431,-1.620566)
( -1.620566,-0.617068)
( -0.617068,-0.617068)
( -0.617068,-0.617068)
( -0.617068,-0.617068)
( -0.617068,-0.617068)
( -0.617044,-0.617003)
( -0.615793,-0.615152)
( -0.602722,-0.598425)
( -0.502140,-0.497860)
( -0.002418,0.002418 )
(413.568627,infinity )
There are no equators because both elementary divisors are greater than 1.
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 either one of the above cycles or the nonslope.
If the slope function maps slope p/q to slope p'/q', then |p'| <= |p|
for every slope p/q with |p| <= 50 and |q| <= 50.
If the slope function maps slope p/q to slope p'/q', then |q'| <= |q|
for every slope p/q with |p| <= 50 and |q| <= 50.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=(2,8)(3,22)(4,10)(5,24)(6,21)(7,13)(9,15)(11,16)(12,18)(14,20)(17,23)(19,25)",
"b=**(1,21)(2,3)(4,5)(6,16)(7,8)(9,10)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"c=<1,1,1,1,c^-1,1,1,c,c^-1,c^-1,1,1,1,1,1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(5,25)(6,7)(8,9)(10,20)(11,12)(13,14)(16,17)(18,19)(21,22)(23,24)",
"d=(1,22)(2,6)(3,24)(4,8)(7,11)(9,13)(10,25)(12,16)(14,18)(15,20)(17,21)(19,23)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,6)(2,8)(3,22)(4,10)(5,24)(7,13)(9,15)(11,21)(12,18)(14,20)(17,23)(19,25)",
"b=(2,3)(4,5)(6,21)(7,8)(9,10)(11,16)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"c=<1,1,1,1,1,1,1,1,1,c^-1,1,1,1,1,c^-1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(6,7)(8,9)(10,25)(11,12)(13,14)(15,20)(16,17)(18,19)(21,22)(23,24)",
"d=(1,22)(2,6)(3,24)(4,8)(5,10)(7,11)(9,13)(12,16)(14,18)(15,25)(17,21)(19,23)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=<1,a*b,1,c^-1,c^-1,1,1,1,1,c^-1,1,1,1,1,c,1,1,1,1,c,c*d,1,c,1,1>(1,7)(2,21)(3,9)(4,23)(5,20)(6,12)(8,14)(10,15)(11,17)(13,19)(16,22)(18,24)",
"b=<1,1,1,1,c^-1,1,1,c,c^-1,c^-1,1,1,1,1,1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(5,25)(6,7)(8,9)(10,20)(11,12)(13,14)(16,17)(18,19)(21,22)(23,24)",
"c=****(1,21)(2,3)(4,5)(6,16)(7,8)(9,10)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"d=****(1,16)(2,23)(3,7)(4,25)(5,9)(6,11)(8,12)(10,14)(13,17)(15,19)(18,22)(20,24)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=<1,a*b,1,c^-1,c^-1,1,1,c^-1,1,c^-1,1,1,1,c,1,1,1,1,1,c,c*d,1,c,1,c>(1,7)(2,21)(3,9)(4,23)(5,25)(6,12)(8,14)(10,20)(11,17)(13,19)(16,22)(18,24)",
"b=<1,1,1,1,1,1,1,1,1,c^-1,1,1,1,1,c^-1,1,1,1,1,c,1,1,1,1,c>(1,2)(3,4)(6,7)(8,9)(10,25)(11,12)(13,14)(15,20)(16,17)(18,19)(21,22)(23,24)",
"c=(2,3)(4,5)(6,21)(7,8)(9,10)(11,16)(12,13)(14,15)(17,18)(19,20)(22,23)(24,25)",
"d=****(1,21)(2,23)(3,7)(4,25)(5,9)(6,16)(8,12)(10,14)(13,17)(15,19)(18,22)(20,24)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at slope
448797935/1172004989 while computing a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at slope
813703491/2124930791 while computing a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at slope
799623434/2088161689 while computing a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at slope
434717878/1135235887 while computing a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at slope
83892379/219079187 while computing a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at slope
757383263/1977854383 while computing a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at slope
69812322/182310085 while computing a fixed point excluded interval about -439693799/168372721.
Imminent integer overflow halted evaluation of the slope function at
slope 566278663/917692125 during the search for all slope function fixed points.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow halted evaluation of the slope function at slope
1172004989/723207054 while computing a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow halted evaluation of the slope function at slope
2124930791/1311227300 while computing a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow halted evaluation of the slope function at slope
2088161689/1288538255 while computing a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow halted evaluation of the slope function at slope
1135235887/700518009 while computing a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow halted evaluation of the slope function at slope
219079187/135186808 while computing a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow halted evaluation of the slope function at slope
1977854383/1220471120 while computing a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about -271321078/439693799.
Imminent integer overflow halted evaluation of the slope function at slope
182310085/112497763 while computing a fixed point excluded interval about -271321078/439693799.
**