These Thurston maps are NET maps for every choice of translation term.
They have degree 32. They are imprimitive, each factoring as a NET map
with degree 16 followed by a Euclidean NET map with degree 2.
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 12.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/32, 2/16, 2/8, 2/4, 2/2, 2/1, 6/2, 10/2, 6/1, 10/1, 14/1, 26/1, 28/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.033525)
( 0.036585,0.038462)
( 0.039181,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
(0.033333,0.033981) 2/59 HST
(0.033938,0.034071) 7/206 HST
(0.034017,0.034126) 20/587 HST
(0.034088,0.034094) 3/88 EXTENDED HST
(0.034091,0.034211) 10/293 HST
(0.034135,0.034272) 4/117 HST
(0.034202,0.034328) 6/175 HST
(0.034246,0.034442) 8/233 HST
(0.034433,0.034452) 30/871 HST
(0.034446,0.034460) 39/1132 HST
(0.034458,0.034467) 57/1654 HST
(0.034462,0.034470) 69/2002 HST
(0.034466,0.034500) 1/29 EXTENDED HST
(0.034499,0.034507) 58/1681 HST
(0.034503,0.034515) 45/1304 HST
(0.034509,0.034511) 44/1275 HST
(0.034510,0.034524) 34/985 HST
(0.034518,0.034536) 27/782 HST
(0.034528,0.034553) 21/608 HST
(0.034539,0.034569) 17/492 HST
(0.034556,0.034600) 13/376 HST
(0.034574,0.034615) 11/318 HST
(0.034598,0.034644) 9/260 HST
(0.034626,0.034704) 6/173 HST
(0.034694,0.034799) 5/144 HST
(0.034742,0.034989) 3/86 HST
(0.034981,0.035001) 19/543 HST
(0.034997,0.035020) 7/200 HST
(0.035012,0.035053) 11/314 HST
(0.035038,0.035075) 19/542 HST
(0.035071,0.035080) 47/1340 HST
(0.035048,0.035109) 77/2195 HST
(0.035081,0.035095) 2/57 EXTENDED HST
(0.035061,0.035235) 13/370 HST
(0.035136,0.035552) 3/85 HST
(0.035427,0.035883) 8/225 HST
(0.035687,0.035743) 1/28 EXTENDED HST
(0.035817,0.036007) 7/195 HST
(0.035919,0.036627) 3/83 HST
(0.036280,0.036834) 2/55 HST
(0.036465,0.036902) 3/82 HST
(0.037706,0.044485) 1/26 EXTENDED HST -> HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 1 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
-29/1 2 16 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: 11227
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,0.035031)
( 0.035031,0.035031)
( 0.035031,0.035032)
( 0.035032,0.035032)
( 0.035032,0.035032)
( 0.035032,0.035032)
( 0.035032,0.035032)
( 0.035032,0.035032)
( 0.035032,infinity)
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 |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=<1,c^-1,d*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*d^-1>(2,32)(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)",
"b=(1,32)(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,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,c>(2,32)(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)",
"d=(1,2)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,32)(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=(1,32)(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,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,c>(2,32)(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 lambda2:
NewSphereMachine(
"a=(1,32)(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,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,c>(2,32)(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)",
"c=(1,32)(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=(1,31)(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)",
"a*b*c*d");
When the translation term of the affine map is lambda1+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=(1,32)(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)(31,32)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2912/83477.
Imminent integer overflow halted evaluation of the slope function at slope
-38361713/1343855 while computing a fixed point excluded interval about 1988257/56756826.
Imminent integer overflow halted evaluation of the slope function at slope
-168949881/5918509 while computing a fixed point excluded interval about 642503/18340904.
Imminent integer overflow halted evaluation of the slope function at
slope -9146573/320415 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -7154803/250641 during the search for all slope function fixed points.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 138857/3963774.
Imminent integer overflow halted evaluation of the slope function at
slope -3936941/137917 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -3936941/137917 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -9488571/332399 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -14549223/509683 during the search for all slope function fixed points.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 3144/89747.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2532/72277.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 9186/262217.
Imminent integer overflow halted evaluation of the slope function at slope
-14390293/504123 while computing a fixed point excluded interval about 171164/4885911.
Imminent integer overflow halted evaluation of the slope function at
slope -8897511/311699 during the search for all slope function fixed points.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 79963/2282560.
Imminent integer overflow halted evaluation of the slope function at
slope -10353773/362715 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -4631865/163081 during the search for all slope function fixed points.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2920/82933.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 2920/82933.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 8526/242153.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 25695/729782.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 25695/729782.
Imminent integer overflow occurred during the computation
of a fixed point excluded interval about 8877/252122.
**