These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 33.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0} {lambda1} {lambda2,lambda1+lambda2}
These pure modular group Hurwitz classes each contain
infinitely many Thurston equivalence classes.
The number of pure modular group Hurwitz classes
in this modular group Hurwitz class is 7.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/33, 1/11, 1/3, 1/1, 3/3, 5/3, 7/3, 9/3, 5/1, 7/1, 13/1, 17/1, 19/1, 23/1
25/1, 29/1, 31/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.033186)
( 0.033645,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
(0.032983,0.033268) 8/241 HST
(0.033251,0.033288) 18/541 HST
(0.033279,0.033298) 25/751 HST
(0.033284,0.033311) 32/961 HST
(0.033273,0.033333) 50/1501 HST
(0.033322,0.033342) 1/30 EXTENDED HST
(0.033333,0.033405) 16/479 HST
(0.033404,0.033406) 31/928 HST
(0.033405,0.033407) 46/1377 HST
(0.033407,0.033408) 15/449 HST
(0.033408,0.033410) 44/1317 HST
(0.033409,0.033411) 29/868 HST
(0.033411,0.033412) 43/1287 HST
(0.033410,0.033412) 128/3831 HST
(0.033412,0.033414) 14/419 HST
(0.033414,0.033416) 41/1227 HST
(0.033415,0.033417) 27/808 HST
(0.033415,0.033420) 53/1586 HST
(0.033418,0.033422) 13/389 HST
(0.033420,0.033426) 25/748 HST
(0.033425,0.033427) 12/359 HST
(0.033427,0.033431) 35/1047 HST
(0.033429,0.033432) 23/688 HST
(0.033428,0.033437) 34/1017 HST
(0.033433,0.033476) 10/299 HST
(0.033456,0.033694) 7/209 HST
(0.033517,0.046932) 4/119 HST
The supplemental half-space computation shows that these NET maps are rational.
SLOPE FUNCTION INFORMATION
NUMBER OF FIXED POINTS FOUND: 5 EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
-30/1 1 33 Yes Yes No No
0/1 1 33 Yes Yes No No
-6734/225 1 33 Yes Yes No No
-8646/289 1 33 Yes Yes No No
-6722/225 1 33 Yes Yes No No
NUMBER OF EQUATORS FOUND: 5 5 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: 1293
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,0.033410)
( 0.033410,0.033410)
( 0.033410,0.033411)
( 0.033411,0.033413)
( 0.033413,0.033414)
( 0.033414,0.033414)
( 0.033414,0.033420)
( 0.033420,0.033420)
( 0.033420,infinity)
NONTRIVIAL CYCLES
-389/13 -> -419/14 -> -389/13
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=(2,33)(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)",
"b=**(1,33)(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,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*d>(2,33)(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)",
"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^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(1,2)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=****(1,33)(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=(1,33)(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,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*d>(2,33)(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 lambda2:
NewSphereMachine(
"a=(1,33)(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,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*d>(2,33)(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)",
"c=****(1,33)(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=****(1,32)(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)",
"a*b*c*d");
When the translation term of the affine map is lambda1+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=(1,33)(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)(32,33)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow halted evaluation of the slope function at
slope -12246278/409153 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -12219460/408257 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1916268/64025 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -2443544/81645 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1067393/35666 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -27379971/914878 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -2456685/82088 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1800028/60157 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -2637759/88154 during the search for all slope function fixed points.
**