These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 31.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0,lambda1} {lambda2,lambda1+lambda2}
These pure modular group Hurwitz classes each contain only
finitely many Thurston equivalence classes.
However, this modular group Hurwitz class contains
infinitely many Thurston equivalence classes.
The number of pure modular group Hurwitz classes
in this modular group Hurwitz class is 10.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/31, 1/1, 3/1, 5/1, 7/1, 9/1, 11/1, 13/1, 15/1, 17/1, 19/1, 21/1, 23/1
25/1, 27/1, 29/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.035531)
( 0.036129,infinity)
The half-space computation does not determine rationality.
EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION
INTERVAL COMPUTED FOR HST OR EXTENDED HST
(0.035446,0.035591) 7/197 HST
(0.035545,0.035635) 11/309 HST
(0.035556,0.035672) 17/477 HST
(0.035661,0.035682) 30/841 HST
(0.035674,0.035688) 39/1093 HST
(0.035683,0.035694) 50/1401 HST
(0.035689,0.035699) 63/1765 HST
(0.035696,0.035702) 83/2325 HST
(0.035699,0.035704) 104/2913 HST
(0.035703,0.035706) 131/3669 HST
(0.035705,0.035708) 161/4509 HST
(0.035707,0.035722) 1/28 EXTENDED HST
(0.035714,0.035802) 15/419 HST
(0.035801,0.035803) 29/810 HST
(0.035802,0.035804) 43/1201 HST
(0.035804,0.035807) 14/391 HST
(0.035806,0.035808) 55/1536 HST
(0.035808,0.035810) 27/754 HST
(0.035809,0.035811) 40/1117 HST
(0.035811,0.035814) 13/363 HST
(0.035814,0.035815) 64/1787 HST
(0.035814,0.035815) 51/1424 HST
(0.035815,0.035818) 25/698 HST
(0.035818,0.035819) 37/1033 HST
(0.035817,0.035820) 49/1368 HST
(0.035819,0.035822) 12/335 HST
(0.035822,0.035825) 35/977 HST
(0.035825,0.035826) 23/642 HST
(0.035826,0.035838) 11/307 HST
(0.035837,0.035839) 31/865 HST
(0.035836,0.035844) 92/2567 HST
(0.035840,0.035844) 10/279 HST
(0.035836,0.035866) 29/809 HST
(0.035848,0.035850) 19/530 HST
(0.035853,0.035859) 9/251 HST
(0.035862,0.035994) 7/195 HST
(0.035904,0.035976) 6/167 HST
(0.035940,0.036534) 4/111 HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 4 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
-28/1 1 31 Yes Yes No No
0/1 1 31 Yes Yes No No
-6728/241 1 31 Yes Yes No No
-6724/241 1 31 Yes Yes No No
NUMBER OF EQUATORS FOUND: 4 4 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: 1458
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,0.035629)
( 0.035629,0.035823)
( 0.035823,infinity)
NONTRIVIAL CYCLES
-307/11 -> -391/14 -> -363/13 -> -335/12 -> -307/11
The slope function maps every slope to a slope:
no slope maps to the nonslope.
The slope function orbit of every slope p/q with |p| <= 50
and |q| <= 50 ends in one of the above cycles.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=<1,a*b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)",
"b=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)",
"c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)",
"d=<1,1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(1,2)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)",
"b=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)",
"c=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)",
"d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)",
"b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)",
"c=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)",
"d=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)",
"b=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)",
"c=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)",
"d=**(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)(30,31)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow halted evaluation of the slope function at
slope -76201614/2715007 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1398888/50113 during the search for all slope function fixed points.
**