These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 39.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/39, 1/13, 1/3, 1/1, 3/3, 5/3, 7/3, 9/3, 11/3, 5/1, 7/1, 11/1, 17/1, 19/1
23/1, 25/1, 29/1, 31/1, 35/1, 37/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,0.027678)
( 0.027981,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
(0.027671,0.027685) 54/1951 HST
(0.027678,0.027685) 8/289 HST
(0.027632,0.027723) 9/325 HST
(0.027713,0.027738) 15/541 HST
(0.027722,0.027748) 20/721 HST
(0.027740,0.027756) 27/973 HST
(0.027751,0.027761) 36/1297 HST
(0.027754,0.027767) 47/1693 HST
(0.027765,0.027769) 73/2629 HST
(0.027768,0.027771) 91/3277 HST
(0.027766,0.027775) 111/3997 HST
(0.027772,0.027783) 1/36 EXTENDED HST
(0.027778,0.027820) 19/683 HST
(0.027819,0.027820) 37/1330 HST
(0.027819,0.027820) 55/1977 HST
(0.027820,0.027820) 473/17002 HST
(0.027820,0.027821) 18/647 HST
(0.027821,0.027821) 89/3199 HST
(0.027821,0.027821) 71/2552 HST
(0.027821,0.027822) 177/6362 HST
(0.027821,0.027822) 53/1905 HST
(0.027822,0.027822) 88/3163 HST
(0.027821,0.027822) 545/19589 HST
(0.027822,0.027822) 35/1258 HST
(0.027822,0.027823) 52/1869 HST
(0.027822,0.027823) 86/3091 HST
(0.027823,0.027824) 17/611 HST
(0.027824,0.027824) 67/2408 HST
(0.027824,0.027824) 50/1797 HST
(0.027824,0.027825) 83/2983 HST
(0.027825,0.027825) 33/1186 EXTENDED HST
(0.027824,0.027825) 82/2947 HST
(0.027825,0.027825) 49/1761 HST
(0.027825,0.027827) 16/575 HST
(0.027826,0.027828) 47/1689 HST
(0.027827,0.027828) 31/1114 HST
(0.027828,0.027831) 15/539 HST
(0.027830,0.027837) 14/503 HST
(0.027834,0.027843) 13/467 HST
(0.027840,0.027865) 11/395 HST
(0.027853,0.027857) 10/359 HST
(0.027862,0.027901) 8/287 HST
(0.027887,0.028143) 5/179 HST
(0.027959,0.027987) 4/143 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
-36/1 1 39 Yes Yes No No
0/1 1 39 Yes Yes No No
-1186/33 1 39 Yes Yes No No
-4564/127 1 39 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: 2081
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,0.027737 )
( 0.027737,0.027737 )
( 0.027737,0.027737 )
( 0.027737,0.027737 )
( 0.027737,0.027798 )
( 0.027798,0.027798 )
( 0.027798,0.027805 )
( 0.027805,0.027822 )
( 0.027822,0.027823 )
( 0.027823,0.027823 )
( 0.027823,0.027826 )
( 0.027826,0.027826 )
( 0.027826,0.027826 )
( 0.027826,0.027826 )
( 0.027826,0.027827 )
( 0.027827,0.027827 )
( 0.027827,0.027828 )
( 0.027828,0.027830 )
( 0.027830,0.027835 )
( 0.027835,0.027835 )
( 0.027835,0.027835 )
( 0.027835,0.027835 )
( 0.027835,0.027835 )
( 0.027835,0.027835 )
( 0.027837,0.027838 )
( 0.027842,0.027843 )
( 0.027846,0.027850 )
( 0.027855,0.027855 )
( 0.027860,0.027868 )
( 0.027872,0.027878 )
( 0.027886,0.027891 )
( 0.027906,0.027908 )
( 0.027922,0.027946 )
( 0.027971,0.027973 )
( 0.028015,0.028065 )
( 0.028114,0.028251 )
( 0.028396,0.028908 )
( 0.029369,0.029457 )
( 0.029960,0.030784 )
( 0.030834,0.032833 )
( 0.032980,0.301587 )
( 0.330508,0.336207 )
( 0.388350,18.500000)
(41.013158,infinity )
No nontrivial cycles were found.
The slope function maps every slope to a slope:
no slope maps to the nonslope.
There are 3096 slopes s = p/q with |p| <= 50 and |q| <= 50.
The 1 slopes s in the following list have the property that the
slope function orbit of s contains a slope t whose numerator or
denominator exceeds 1,000,000 in absolute value, and the slopes between
s and t are not among the slopes p/q with |p| <= 50 and |q| <= 50.
40/39
The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50
either contains an extended rational number whose numerator or
denominator exceeds 1,000,000 in absolute value or 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,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,b^-1,b^-1,b^-1,b^-1>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)",
"b=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)",
"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^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)",
"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^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(1,2)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)",
"b=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"c=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)",
"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^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)",
"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^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)",
"c=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)",
"d=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"b=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)",
"c=(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)",
"d=**(1,37)(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)(38,39)",
"a*b*c*d");
****************************INTEGER OVERFLOW REPORT*****************************
Imminent integer overflow halted evaluation of the slope function at
slope -1714847/47565 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -3207393/88964 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1642345/45554 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -33507710/929409 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -33558328/930813 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -37455914/1038921 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -37509344/1040403 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1578099/43835 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1846983/51304 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1847667/51323 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1972618/54835 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1975352/54911 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -2121824/58997 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1143804/31823 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1155090/32137 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1098761/30570 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -3068976/85387 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -930422/25887 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -11461876/318905 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -1342462/37355 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -5357741/149087 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -5366869/149341 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -5366869/149341 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -843765/23479 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -3015198/83905 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -3058896/85121 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -2813774/78303 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -6246754/173847 during the search for all slope function fixed points.
Imminent integer overflow halted evaluation of the slope function at
slope -32205764/896435 during the search for all slope function fixed points.
Imminent integer overflow halted computation of the slope function
at slope -2532813/4129034 during the modular group computation.
This caused the modular group computation to abort.
Imminent integer overflow caused the modular group computation to abort.
**