These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 40. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/20, 1/40, 1/8, 1/5, 2/10, 3/8, 2/5, 3/5, 2/2, 4/4, 5/5, 6/5, 7/5, 2/1 8/4, 6/2, 6/1, 14/2, 18/2, 14/1, 18/1, 22/1, 26/1, 34/1, 38/1, 39/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.026219) ( 0.026451,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 (0.025665,0.026276) 8/305 HST (0.026250,0.026291) 18/685 HST (0.026291,0.026292) 57/2168 HST (0.026292,0.026292) 29/1103 HST (0.026283,0.026299) 30/1141 HST (0.026295,0.026304) 43/1635 HST (0.026301,0.026307) 59/2243 HST (0.026305,0.026309) 153/5816 HST (0.026307,0.026307) 77/2927 HST (0.026309,0.026309) 97/3687 HST (0.026307,0.026310) 99/3763 HST (0.026309,0.026311) 124/4713 HST (0.026310,0.026312) 154/5853 HST (0.026311,0.026313) 188/7145 HST (0.026312,0.026313) 232/8817 HST (0.026313,0.026318) 1/38 EXTENDED HST (0.026316,0.026334) 39/1481 HST (0.026334,0.026334) 77/2924 HST (0.026334,0.026334) 115/4367 HST (0.026334,0.026334) 38/1443 HST (0.026334,0.026334) 151/5734 HST (0.026334,0.026334) 75/2848 HST (0.026334,0.026334) 112/4253 HST (0.026334,0.026334) 149/5658 HST (0.026334,0.026334) 1153/43783 HST (0.026334,0.026334) 223/8468 HST (0.026334,0.026334) 297/11278 HST (0.026334,0.026335) 927/35201 HST (0.026334,0.026334) 482/18303 HST (0.026335,0.026335) 2407/91401 HST (0.026335,0.026335) 1222/46403 HST (0.026335,0.026335) 1555/59048 HST (0.026335,0.026335) 3739/141981 HST (0.026335,0.026335) 1888/71693 HST (0.026335,0.026335) 1925/73098 HST (0.026335,0.026335) 37/1405 EXTENDED HST (0.026335,0.026335) 221/8392 HST (0.026335,0.026335) 184/6987 HST (0.026335,0.026335) 147/5582 HST (0.026335,0.026335) 477/18113 HST (0.026335,0.026335) 73/2772 HST (0.026335,0.026335) 145/5506 HST (0.026335,0.026335) 36/1367 HST (0.026335,0.026335) 107/4063 HST (0.026335,0.026336) 71/2696 HST (0.026335,0.026336) 35/1329 HST (0.026336,0.026337) 34/1291 HST (0.026336,0.026337) 100/3797 HST (0.026337,0.026337) 33/1253 EXTENDED HST (0.026337,0.026337) 131/4974 HST (0.026337,0.026337) 65/2468 HST (0.026337,0.026338) 97/3683 HST (0.026337,0.026339) 31/1177 HST (0.026338,0.026340) 30/1139 HST (0.026339,0.026343) 28/1063 HST (0.026341,0.026342) 27/1025 HST (0.026342,0.026347) 25/949 HST (0.026344,0.026345) 24/911 HST (0.026346,0.026350) 22/835 HST (0.026347,0.026359) 19/721 HST (0.026353,0.026373) 17/645 HST (0.026359,0.026366) 15/569 HST (0.026363,0.026368) 14/531 HST (0.026368,0.026447) 10/379 HST (0.026390,0.026857) 6/227 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 -38/1 1 40 Yes Yes No No 0/1 1 40 Yes Yes No No -5506/145 1 40 Yes Yes No No -2696/71 1 40 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: 1983 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,0.026330) ( 0.026330,0.026330) ( 0.026330,0.026333) ( 0.026333,0.026333) ( 0.026333,0.026334) ( 0.026334,0.026334) ( 0.026334,0.026334) ( 0.026334,0.026334) ( 0.026334,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026335,0.026335) ( 0.026336,0.026336) ( 0.026336,0.026336) ( 0.026337,0.026337) ( 0.026337,0.026338) ( 0.026338,0.026338) ( 0.026339,0.026339) ( 0.026340,0.026340) ( 0.026340,0.026341) ( 0.026341,0.026341) ( 0.026342,0.026342) ( 0.026343,0.026344) ( 0.026345,0.026345) ( 0.026346,0.026346) ( 0.026347,0.026348) ( 0.026349,0.026349) ( 0.026350,0.026351) ( 0.026352,0.026352) ( 0.026353,0.026356) ( 0.026356,0.026357) ( 0.026358,0.026361) ( 0.026362,0.026362) ( 0.026365,0.026365) ( 0.026369,0.026377) ( 0.026379,0.026379) ( 0.026381,0.026390) ( 0.026393,0.026393) ( 0.026396,0.026446) ( 0.026451,0.026498) ( 0.026547,0.026551) ( 0.026589,0.026816) ( 0.026998,0.027056) ( 0.027219,0.722222) ( 0.953544,1.051282) (41.506329,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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b,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>(2,40)(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)", "b=(1,40)(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,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,c>(2,40)(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)", "d=<1,d,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>(1,2)(3,40)(4,39)(5,38)(6,37)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,40)(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=(1,40)(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,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,c>(2,40)(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 lambda2: NewSphereMachine( "a=(1,40)(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,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,c>(2,40)(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)", "c=(1,40)(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=(1,39)(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)", "a*b*c*d"); When the translation term of the affine map is lambda1+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=(1,40)(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)(39,40)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow halted evaluation of the slope function at slope -799522/21039 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -2045922/53839 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 3043/115595. Imminent integer overflow halted evaluation of the slope function at slope -1494949/39362 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -2271136/59799 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -1339725/35278 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -2386362/62839 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -3465921/91267 while computing a fixed point excluded interval about 86919/3300803. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 8655/328679. Imminent integer overflow halted evaluation of the slope function at slope -3657429/96310 while computing a fixed point excluded interval about 47561/1806157. Imminent integer overflow halted evaluation of the slope function at slope -1639596/43175 while computing a fixed point excluded interval about 44281/1681597. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 4871/184967. Imminent integer overflow halted evaluation of the slope function at slope -3059721/80576 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -1074789/28304 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -2283395/60132 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -864228/22759 while computing a fixed point excluded interval about 22203/843115. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 91003/3455655. Imminent integer overflow halted evaluation of the slope function at slope -4432507/116728 while computing a fixed point excluded interval about 57643/2188875. Imminent integer overflow halted evaluation of the slope function at slope -2353146/61969 while computing a fixed point excluded interval about 57643/2188875. Imminent integer overflow halted evaluation of the slope function at slope -11108646/292541 while computing a fixed point excluded interval about 57643/2188875. Imminent integer overflow halted evaluation of the slope function at slope -1507629/39703 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -1503865/39604 while computing a fixed point excluded interval about 36835/1398719. Imminent integer overflow halted evaluation of the slope function at slope -3587419/94474 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -2125058/55963 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -23946973/630639 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -7123613/187599 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -1561963/41134 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -1708613/44996 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope -4108972/108209 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 912/33745. Imminent integer overflow caused the modular group computation to abort.