02431_04231_40231
Counting sequence:
1, 1, 2, 6, 24, 117, 652, 3983, 25970, 177635, 1260031, 9195735, 68658450, 522286247, 4035341246, 31591525703, 250129427763, 1999918330696, 16128186650149, 131054251884342, 1072132268711522, 8824173976150632, 73024860281997817, 607320392574055482, 5073703341285612145, 42562468728485058412, 358408407036701417667, 3028667654966753808383, 25676400470676734350463, 218335937959434446524745, 1861808460074824926638664, 15917789468664632335167426, 136425557852917589506619313, 1171947359306971917717109063, 10089277531378037883795312853, 87035647230701003524952875297, 752262857370514211407036294778, 6513761154729601850248783855305, 56499147102852988446851135072259, 490864029612352063211397156244887, 4271241662987175293635209358247608, 37220973343532580870624563648630523, 324811486587467212560414901195789368, 2838289545716220227140446071059051654, 24833460378268745519904292848026379559, 217544621305211715669835928730926341260, 1907950038939671381039691731260444909837, 16752191876767553864684519238123668686626, 147245517832115402180054126208061062032879, 1295565546481993622577897651202860391487006, 11410528452368245605116246092845170943897834, 100592231035607764275949146190235182297900640, 887604834984071399655810437004050879091493982, 7838925424653184517413320577212203049989091552, 69288475813642399245799816803310621064441004015, 612942590104100115512856697891274041620759977086, 5426506572479645444072442456355850497337390808852, 48078476692195888303524625934264367224913530493594, 426284558306243391893148668267877849641350696214301, 3782303004177166007473205284695868152377386584829455, 33582317453266073800964043044243132454508597925916316, 298368485600243870936144712923015350426449426694112498, 2652613411859157978624389665513234645783251552399471233, 23597441359281032461040270828784260794833733423015128911, 210047464265363536550532152512287921563065848391120277933, 1870783619397994900870194594906533434739255244852751971302, 16671536932259423771471119671077069859740113822736074054542, 148650509001813386032619484390284661930301233586111461179834, 1326138491605276871976049101465889999528691108927413064995987, 11836857454594742336278657526922368299295766322175435476344654, 105706728929254214396128725458321072601777295581971194819641719, 944455326833937649447231010228584364134169395036582697791019811, 8442419369241641849156018744296256180521813232937312127345503298, 75501142063713660267255200207805109771282054660802272800666243887, 675516294355523254599929969475664039007090732114370612040636602635, 6046564237908018949057121998989926186585570210945001182468703833132, 54146086752394883625454130854123241140099010920350406147395643226582, 485072060941667764806460566055799785287959029007028124531276066122619, 4347320242781999796228657329413442637712321385947291219367332612175646, 38977032335629874756956534705010720899163466640442515396072625784013908, 349593549811149597932020989950736554608708312480721098573947419257850996, 3136761201269146564359852995119803618539784348063410121631165333757895646, 28155222059350933425875978207133639140887983805637206874732481895717507061, 252808749034652132899970358006318252468735041444051324557448753528012084895, 2270791244821963191809970143694389083466022439787035993590757495147626099620, 20403785339291006095904841310588893476082473448032600099818253486308797360608, 183395755956993247664009223069881538889438257397189045091869117446648974225533, 1648957688991995097207401286725756583021840984475665690772585276297719560921863, 14830925223292251944323695868303957758365483040707140852683614667202431258559566, 133432736956715421199196568423200772923763146792145899437372456342471167897914082, 1200850589031210702426986887078888657980569622824689093894796164291471526180371230, 10810483104945922855033686933307774999093298851018288916285479434160706945274262790, 97348212739122403296139151553743718516276005487122500561769134033428484840032671620, 876869395759193455723294211825417640740470174434629885117801839877965109118677465936, 7900658235890465628722506879532908945707277009177646768874371389716115801349101633617, 71205007419772273091243010139224836544117759469709058162242245450044998713234315874804, 641910141937039472493340012233889704170790237251397830234948823329033355548465084832116, 5788312886978220378917717303093486129190639825035613238991073941859519040470698521616923, 52208535590571083152385660217937948483409641495981796288342489949170910289302027304479288, 471021289552988328002720658278653559795518923080111714758689654603593101295928683349742075, 4250567357280683596678925578868389774128095292239527975328278386527178080239099456996482591
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/24644/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x]+F[7,x]
F[6,x] = 16*x+(1+x)^3*F[6,x]^2+(8*x^2-20*x)*F[6,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x,1]
F[11,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[2,x]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[4,x]
F[15,x,k[0]] = F[16,x,k[0]]+F[19,x,k[0]]
F[16,x,k[0]] = -k[0]*(F[17,x,1]-F[17,x,k[0]])/(-1+k[0])
F[17,x,k[0]] = F[13,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = x^3*(1+F[18,x,k[0]])^2*k[0]^3+3*x^2*(F[18,x,k[0]]+11/3)*(1+F[18,x,k[0]])*k[0]^2+(3*x*F[18,x,k[0]]^2-14*x*F[18,x,k[0]]-x)*k[0]+F[18,x,k[0]]^2+2*F[18,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[31,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[4,x]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[12,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[32,x,k[0]]
F[27,x,k[0]] = F[10,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]^2*F[31,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[31,x,k[0]] = k[0]*x
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[31,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[78,x,k[0]]
F[35,x,k[0]] = F[10,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0],1]
F[37,x,k[0],k[1]] = F[38,x,k[0],k[0]*k[1]]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[1],1]
F[39,x,k[0],k[1],k[2]] = F[40,x,k[0],k[1],k[1]*k[2]]
F[41,x,k[0],k[1],k[2]] = F[31,x,k[1]]*F[40,x,k[0],k[1],k[2]]*F[48,x,k[0]]
F[41,x,k[0],k[1],k[2]] = F[42,x,k[0],k[1],k[2]]
F[43,x,k[0],k[1],k[2]] = F[42,x,k[0],k[1],k[1]*k[2]]
F[44,x,k[0],k[1],k[2]] = F[43,x,k[0],k[1],k[2]]+F[77,x,k[0],k[1]*k[2]]
F[44,x,k[0],k[1],k[2]] = F[45,x,k[1],k[2]]+F[59,x,k[0],k[1],k[2]]
F[45,x,k[0],k[1]] = F[46,x,k[0],k[0]*k[1]]
F[46,x,k[0],k[1]] = F[47,x,k[0],1,k[1]]
F[47,x,k[0],k[1],k[2]] = F[48,x,k[0]*k[1]]+F[49,x,k[0],k[1],k[2]]
F[48,x,k[0]] = (x*k[0]+1)^3*F[48,x,k[0]]^2+(8*x^2*k[0]^2-20*x*k[0])*F[48,x,k[0]]+16*k[0]*x
F[49,x,k[0],k[1],k[2]] = F[50,x,k[1],k[0],k[2]]
F[50,x,k[0],k[1],k[2]] = F[31,x,k[2]]*F[51,x,k[0],k[1],k[2]]
F[51,x,k[0],k[1],k[2]] = F[52,x,k[1],k[0],k[2]]+F[54,x,k[0],k[1],k[2]]
F[52,x,k[0],k[1],k[2]] = F[53,x,k[0]*k[1],k[1]*k[2]]
F[53,x,k[0],k[1]] = F[30,x,k[1]]*F[46,x,k[0],k[1]]
F[54,x,k[0],k[1],k[2]] = F[55,x,k[0],k[1],k[2]]
F[55,x,k[0],k[1],k[2]] = F[31,x,k[1]]*F[47,x,k[1],k[0],k[2]]*F[56,x,k[0],k[1],k[2]]
F[56,x,k[0],k[1],k[2]] = F[57,x,k[0]*k[1],k[0]*k[2]]
F[57,x,k[0],k[1]] = F[58,x,1,k[0],k[1]]
F[58,x,k[0],k[1],k[2]] = F[40,x,k[0]*k[1],k[1],k[2]]
F[59,x,k[0],k[1],k[2]] = F[60,x,k[0],k[1],k[1]*k[2]]
F[60,x,k[0],k[1],k[2]] = F[61,x,k[0],k[1],k[2]]
F[61,x,k[0],k[1],k[2]] = F[31,x,k[0]]*F[62,x,k[0],k[1],k[2]]
F[62,x,k[0],k[1],k[2]] = (F[63,x,k[0],k[1],1]*k[1]-F[63,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[63,x,k[0],k[1],k[2]] = F[64,x,k[0],k[1]*k[2]]+F[74,x,k[0],k[1],k[2]]
F[64,x,k[0],k[1]] = F[30,x,k[1]]*F[65,x,k[0]]
F[65,x,k[0]] = F[30,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[18,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[31,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[71,x,k[0]]
F[70,x,k[0]] = F[30,x,k[0]]*F[66,x,k[0]]
F[71,x,k[0]] = F[72,x,1,k[0]]
F[72,x,k[0],k[1]] = F[73,x,k[0]*k[1],k[1]]
F[73,x,k[0],k[1]] = F[74,x,k[0],k[1],1]
F[74,x,k[0],k[1],k[2]] = F[75,x,k[0],k[1],k[1]*k[2]]
F[75,x,k[0],k[1],k[2]] = F[76,x,k[0],k[1],k[2]]
F[76,x,k[0],k[1],k[2]] = F[31,x,k[1]]*F[40,x,k[0],k[1],k[2]]*F[65,x,k[0]]
F[77,x,k[0],k[1]] = F[30,x,k[1]]*F[48,x,k[0]]
F[78,x,k[0]] = F[5,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,1,k[0]]
F[80,x,k[0],k[1]] = -k[0]*(F[81,x,1,k[1]]-F[81,x,k[0]/k[1],k[1]])/(-k[1]+k[0])
F[81,x,k[0],k[1]] = F[82,x,k[0]*k[1],k[1]]
F[38,x,k[0],k[1]] = F[82,x,k[0],k[1]]+F[83,x,k[1]]
F[84,x,k[0]] = F[31,x,k[0]]*F[83,x,k[0]]
F[84,x,k[0]] = F[66,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{3} F_{6} \left(x \right)^{2}+3 x^{2} F_{6} \left(x \right)^{2}+8 x^{2} F_{6}\! \left(x \right)+3 x F_{6} \left(x \right)^{2}-20 x F_{6}\! \left(x \right)+F_{6} \left(x \right)^{2}+16 x
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{11}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)+F_{2}\! \left(x \right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)+F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = x^{3} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+2 x^{3} F_{18}\! \left(x , y_{0}\right) y_{0}^{3}+x^{3} y_{0}^{3}+3 x^{2} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+14 x^{2} F_{18}\! \left(x , y_{0}\right) y_{0}^{2}+11 y_{0}^{2} x^{2}+3 x F_{18}\! \left(x , y_{0}\right)^{2} y_{0}-14 x F_{18}\! \left(x , y_{0}\right) y_{0}-y_{0} x +F_{18}\! \left(x , y_{0}\right)^{2}+2 F_{18}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)+F_{24}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)^{2} F_{31}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = y_{0} x
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x , y_{0}, 1\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{1}, 1\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{48}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{77}\! \left(x , y_{0}, y_{1} y_{2}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{45}\! \left(x , y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{47}\! \left(x , y_{0}, 1, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{48}\! \left(x , y_{0} y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{48}\! \left(x , y_{0}\right) = x^{3} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{48}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{48}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{48}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{48}\! \left(x , y_{0}\right)^{2}
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{50}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{52}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{53}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{1}\right) F_{47}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{57}\! \left(x , y_{0} y_{1}, y_{0} y_{2}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , 1, y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{60}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{63}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{63}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{64}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{1}\right) F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{72}\! \left(x , 1, y_{0}\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{73}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{74}\! \left(x , y_{0}, y_{1}, 1\right)
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{75}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{65}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{1}\right) F_{48}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{79}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{80}\! \left(x , 1, y_{0}\right)
F_{80}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{81}\! \left(x , 1, y_{1}\right)-F_{81}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}
F_{81}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{1}\right)
F_{84}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), 16*x + (x + 1)**3*F_6(x)**2 + (8*x**2 - 20*x)*F_6(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_11(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_2(x))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_4(x))
Eq(F_15(x, k_0), F_16(x, k_0) + F_19(x, k_0))
Eq(F_16(x, k_0), -F_17(x, 1) + (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_13(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), 16*k_0*x + (k_0*x + 1)**3*(F_18(x, k_0) + 1)**2 + (F_18(x, k_0) + 1)*(8*k_0**2*x**2 - 20*k_0*x - 1) + F_18(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_31(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_4(x))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_12(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_32(x, k_0))
Eq(F_27(x, k_0), F_10(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)**2*F_31(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_31(x, k_0), k_0*x)
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_31(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_78(x, k_0))
Eq(F_35(x, k_0), F_10(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0, 1))
Eq(F_37(x, k_0, k_1), F_38(x, k_0, k_0*k_1))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_1, 1))
Eq(F_39(x, k_0, k_1, k_2), F_40(x, k_0, k_1, k_1*k_2))
Eq(F_41(x, k_0, k_1, k_2), F_31(x, k_1)*F_40(x, k_0, k_1, k_2)*F_48(x, k_0))
Eq(F_41(x, k_0, k_1, k_2), F_42(x, k_0, k_1, k_2))
Eq(F_43(x, k_0, k_1, k_2), F_42(x, k_0, k_1, k_1*k_2))
Eq(F_44(x, k_0, k_1, k_2), F_43(x, k_0, k_1, k_2) + F_77(x, k_0, k_1*k_2))
Eq(F_44(x, k_0, k_1, k_2), F_45(x, k_1, k_2) + F_59(x, k_0, k_1, k_2))
Eq(F_45(x, k_0, k_1), F_46(x, k_0, k_0*k_1))
Eq(F_46(x, k_0, k_1), F_47(x, k_0, 1, k_1))
Eq(F_47(x, k_0, k_1, k_2), F_48(x, k_0*k_1) + F_49(x, k_0, k_1, k_2))
Eq(F_48(x, k_0), 16*k_0*x + (k_0*x + 1)**3*F_48(x, k_0)**2 + (8*k_0**2*x**2 - 20*k_0*x)*F_48(x, k_0))
Eq(F_49(x, k_0, k_1, k_2), F_50(x, k_1, k_0, k_2))
Eq(F_50(x, k_0, k_1, k_2), F_31(x, k_2)*F_51(x, k_0, k_1, k_2))
Eq(F_51(x, k_0, k_1, k_2), F_52(x, k_1, k_0, k_2) + F_54(x, k_0, k_1, k_2))
Eq(F_52(x, k_0, k_1, k_2), F_53(x, k_0*k_1, k_1*k_2))
Eq(F_53(x, k_0, k_1), F_30(x, k_1)*F_46(x, k_0, k_1))
Eq(F_54(x, k_0, k_1, k_2), F_55(x, k_0, k_1, k_2))
Eq(F_55(x, k_0, k_1, k_2), F_31(x, k_1)*F_47(x, k_1, k_0, k_2)*F_56(x, k_0, k_1, k_2))
Eq(F_56(x, k_0, k_1, k_2), F_57(x, k_0*k_1, k_0*k_2))
Eq(F_57(x, k_0, k_1), F_58(x, 1, k_0, k_1))
Eq(F_58(x, k_0, k_1, k_2), F_40(x, k_0*k_1, k_1, k_2))
Eq(F_59(x, k_0, k_1, k_2), F_60(x, k_0, k_1, k_1*k_2))
Eq(F_60(x, k_0, k_1, k_2), F_61(x, k_0, k_1, k_2))
Eq(F_61(x, k_0, k_1, k_2), F_31(x, k_0)*F_62(x, k_0, k_1, k_2))
Eq(F_62(x, k_0, k_1, k_2), (-k_1*F_63(x, k_0, k_1, 1) + k_2*F_63(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_63(x, k_0, k_1, k_2), F_64(x, k_0, k_1*k_2) + F_74(x, k_0, k_1, k_2))
Eq(F_64(x, k_0, k_1), F_30(x, k_1)*F_65(x, k_0))
Eq(F_65(x, k_0), F_30(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_18(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_31(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_71(x, k_0))
Eq(F_70(x, k_0), F_30(x, k_0)*F_66(x, k_0))
Eq(F_71(x, k_0), F_72(x, 1, k_0))
Eq(F_72(x, k_0, k_1), F_73(x, k_0*k_1, k_1))
Eq(F_73(x, k_0, k_1), F_74(x, k_0, k_1, 1))
Eq(F_74(x, k_0, k_1, k_2), F_75(x, k_0, k_1, k_1*k_2))
Eq(F_75(x, k_0, k_1, k_2), F_76(x, k_0, k_1, k_2))
Eq(F_76(x, k_0, k_1, k_2), F_31(x, k_1)*F_40(x, k_0, k_1, k_2)*F_65(x, k_0))
Eq(F_77(x, k_0, k_1), F_30(x, k_1)*F_48(x, k_0))
Eq(F_78(x, k_0), F_5(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, 1, k_0))
Eq(F_80(x, k_0, k_1), -F_81(x, 1, k_1) + (-k_0*F_81(x, k_0/k_1, k_1) + k_1*F_81(x, 1, k_1))/(-k_0 + k_1))
Eq(F_81(x, k_0, k_1), F_82(x, k_0*k_1, k_1))
Eq(F_38(x, k_0, k_1), F_82(x, k_0, k_1) + F_83(x, k_1))
Eq(F_84(x, k_0), F_31(x, k_0)*F_83(x, k_0))
Eq(F_84(x, k_0), F_66(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [2, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 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"tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 1], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25398/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x]+F[7,x]
F[6,x] = 16*x+(1+x)^3*F[6,x]^2+(8*x^2-20*x)*F[6,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x,1]
F[11,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]+F[2,x]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[4,x]
F[15,x,k[0]] = F[16,x,k[0]]+F[19,x,k[0]]
F[16,x,k[0]] = -k[0]*(F[17,x,1]-F[17,x,k[0]])/(-1+k[0])
F[17,x,k[0]] = F[13,x,k[0]]+F[18,x,k[0]]
F[18,x,k[0]] = x^3*(1+F[18,x,k[0]])^2*k[0]^3+3*x^2*(1+F[18,x,k[0]])*(F[18,x,k[0]]+11/3)*k[0]^2+(3*x*F[18,x,k[0]]^2-14*x*F[18,x,k[0]]-x)*k[0]+F[18,x,k[0]]^2+2*F[18,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[31,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[4,x]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[12,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]*F[4,x]
F[26,x,k[0]] = F[27,x,k[0]]+F[32,x,k[0]]
F[27,x,k[0]] = F[10,x,k[0]]*F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]^2*F[31,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[31,x,k[0]] = k[0]*x
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[31,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[78,x,k[0]]
F[35,x,k[0]] = F[10,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0],1]
F[37,x,k[0],k[1]] = F[38,x,k[0],k[0]*k[1]]
F[38,x,k[0],k[1]] = F[39,x,k[0],k[1],1]
F[39,x,k[0],k[1],k[2]] = F[40,x,k[0],k[1],k[1]*k[2]]
F[41,x,k[0],k[1],k[2]] = F[31,x,k[1]]*F[40,x,k[0],k[1],k[2]]*F[48,x,k[0]]
F[41,x,k[0],k[1],k[2]] = F[42,x,k[0],k[1],k[2]]
F[43,x,k[0],k[1],k[2]] = F[42,x,k[0],k[1],k[1]*k[2]]
F[44,x,k[0],k[1],k[2]] = F[43,x,k[0],k[1],k[2]]+F[77,x,k[0],k[1]*k[2]]
F[44,x,k[0],k[1],k[2]] = F[45,x,k[1],k[2]]+F[59,x,k[0],k[1],k[2]]
F[45,x,k[0],k[1]] = F[46,x,k[0],k[0]*k[1]]
F[46,x,k[0],k[1]] = F[47,x,k[0],1,k[1]]
F[47,x,k[0],k[1],k[2]] = F[48,x,k[0]*k[1]]+F[49,x,k[0],k[1],k[2]]
F[48,x,k[0]] = (x*k[0]+1)^3*F[48,x,k[0]]^2+(8*x^2*k[0]^2-20*x*k[0])*F[48,x,k[0]]+16*k[0]*x
F[49,x,k[0],k[1],k[2]] = F[50,x,k[1],k[0],k[2]]
F[50,x,k[0],k[1],k[2]] = F[31,x,k[2]]*F[51,x,k[0],k[1],k[2]]
F[51,x,k[0],k[1],k[2]] = F[52,x,k[1],k[0],k[2]]+F[54,x,k[0],k[1],k[2]]
F[52,x,k[0],k[1],k[2]] = F[53,x,k[0]*k[1],k[1]*k[2]]
F[53,x,k[0],k[1]] = F[30,x,k[1]]*F[46,x,k[0],k[1]]
F[54,x,k[0],k[1],k[2]] = F[55,x,k[0],k[1],k[2]]
F[55,x,k[0],k[1],k[2]] = F[31,x,k[1]]*F[47,x,k[1],k[0],k[2]]*F[56,x,k[0],k[1],k[2]]
F[56,x,k[0],k[1],k[2]] = F[57,x,k[0]*k[1],k[0]*k[2]]
F[57,x,k[0],k[1]] = F[58,x,1,k[0],k[1]]
F[58,x,k[0],k[1],k[2]] = F[40,x,k[0]*k[1],k[1],k[2]]
F[59,x,k[0],k[1],k[2]] = F[60,x,k[0],k[1],k[1]*k[2]]
F[60,x,k[0],k[1],k[2]] = F[61,x,k[0],k[1],k[2]]
F[61,x,k[0],k[1],k[2]] = F[31,x,k[0]]*F[62,x,k[0],k[1],k[2]]
F[62,x,k[0],k[1],k[2]] = (F[63,x,k[0],k[1],1]*k[1]-F[63,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[63,x,k[0],k[1],k[2]] = F[64,x,k[0],k[1]*k[2]]+F[74,x,k[0],k[1],k[2]]
F[64,x,k[0],k[1]] = F[30,x,k[1]]*F[65,x,k[0]]
F[65,x,k[0]] = F[30,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[18,x,k[0]]+F[67,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[31,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[71,x,k[0]]
F[70,x,k[0]] = F[30,x,k[0]]*F[66,x,k[0]]
F[71,x,k[0]] = F[72,x,1,k[0]]
F[72,x,k[0],k[1]] = F[73,x,k[0]*k[1],k[1]]
F[73,x,k[0],k[1]] = F[74,x,k[0],k[1],1]
F[74,x,k[0],k[1],k[2]] = F[75,x,k[0],k[1],k[1]*k[2]]
F[75,x,k[0],k[1],k[2]] = F[76,x,k[0],k[1],k[2]]
F[76,x,k[0],k[1],k[2]] = F[31,x,k[1]]*F[40,x,k[0],k[1],k[2]]*F[65,x,k[0]]
F[77,x,k[0],k[1]] = F[30,x,k[1]]*F[48,x,k[0]]
F[78,x,k[0]] = F[5,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,1,k[0]]
F[80,x,k[0],k[1]] = -k[0]*(F[81,x,1,k[1]]-F[81,x,k[0]/k[1],k[1]])/(-k[1]+k[0])
F[81,x,k[0],k[1]] = F[82,x,k[0]*k[1],k[1]]
F[38,x,k[0],k[1]] = F[82,x,k[0],k[1]]+F[83,x,k[1]]
F[84,x,k[0]] = F[31,x,k[0]]*F[83,x,k[0]]
F[84,x,k[0]] = F[66,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{3} F_{6} \left(x \right)^{2}+3 x^{2} F_{6} \left(x \right)^{2}+8 x^{2} F_{6}\! \left(x \right)+3 x F_{6} \left(x \right)^{2}-20 x F_{6}\! \left(x \right)+F_{6} \left(x \right)^{2}+16 x
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{11}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)+F_{2}\! \left(x \right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{17}\! \left(x , 1\right)-F_{17}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)+F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = x^{3} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+2 x^{3} F_{18}\! \left(x , y_{0}\right) y_{0}^{3}+x^{3} y_{0}^{3}+3 x^{2} F_{18}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+14 x^{2} F_{18}\! \left(x , y_{0}\right) y_{0}^{2}+11 y_{0}^{2} x^{2}+3 x F_{18}\! \left(x , y_{0}\right)^{2} y_{0}-14 x F_{18}\! \left(x , y_{0}\right) y_{0}-y_{0} x +F_{18}\! \left(x , y_{0}\right)^{2}+2 F_{18}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)+F_{24}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{32}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)^{2} F_{31}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}\right) = y_{0} x
F_{32}\! \left(x , y_{0}\right) = F_{33}\! \left(x , y_{0}\right)
F_{33}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)
F_{34}\! \left(x , y_{0}\right) = F_{35}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)
F_{36}\! \left(x , y_{0}\right) = F_{37}\! \left(x , y_{0}, 1\right)
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{38}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{1}, 1\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{48}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{77}\! \left(x , y_{0}, y_{1} y_{2}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{45}\! \left(x , y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{47}\! \left(x , y_{0}, 1, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{48}\! \left(x , y_{0} y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{48}\! \left(x , y_{0}\right) = x^{3} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{3}+3 x^{2} F_{48}\! \left(x , y_{0}\right)^{2} y_{0}^{2}+8 x^{2} F_{48}\! \left(x , y_{0}\right) y_{0}^{2}+3 x F_{48}\! \left(x , y_{0}\right)^{2} y_{0}-20 x F_{48}\! \left(x , y_{0}\right) y_{0}+16 y_{0} x +F_{48}\! \left(x , y_{0}\right)^{2}
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{50}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{52}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{53}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{1}\right) F_{47}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{57}\! \left(x , y_{0} y_{1}, y_{0} y_{2}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{58}\! \left(x , 1, y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{40}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{60}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{63}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{63}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{64}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{64}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{1}\right) F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{72}\! \left(x , 1, y_{0}\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{73}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}\right) = F_{74}\! \left(x , y_{0}, y_{1}, 1\right)
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{75}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{65}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{1}\right) F_{48}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{79}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{80}\! \left(x , 1, y_{0}\right)
F_{80}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{81}\! \left(x , 1, y_{1}\right)-F_{81}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}
F_{81}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{1}\right)
F_{84}\! \left(x , y_{0}\right) = F_{31}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), 16*x + (x + 1)**3*F_6(x)**2 + (8*x**2 - 20*x)*F_6(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x, 1))
Eq(F_11(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0) + F_2(x))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_4(x))
Eq(F_15(x, k_0), F_16(x, k_0) + F_19(x, k_0))
Eq(F_16(x, k_0), -F_17(x, 1) + (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_13(x, k_0) + F_18(x, k_0))
Eq(F_18(x, k_0), 16*k_0*x + (k_0*x + 1)**3*(F_18(x, k_0) + 1)**2 + (F_18(x, k_0) + 1)*(8*k_0**2*x**2 - 20*k_0*x - 1) + F_18(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_31(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_4(x))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_12(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0)*F_4(x))
Eq(F_26(x, k_0), F_27(x, k_0) + F_32(x, k_0))
Eq(F_27(x, k_0), F_10(x, k_0)*F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)**2*F_31(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_31(x, k_0), k_0*x)
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_31(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_78(x, k_0))
Eq(F_35(x, k_0), F_10(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0, 1))
Eq(F_37(x, k_0, k_1), F_38(x, k_0, k_0*k_1))
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_1, 1))
Eq(F_39(x, k_0, k_1, k_2), F_40(x, k_0, k_1, k_1*k_2))
Eq(F_41(x, k_0, k_1, k_2), F_31(x, k_1)*F_40(x, k_0, k_1, k_2)*F_48(x, k_0))
Eq(F_41(x, k_0, k_1, k_2), F_42(x, k_0, k_1, k_2))
Eq(F_43(x, k_0, k_1, k_2), F_42(x, k_0, k_1, k_1*k_2))
Eq(F_44(x, k_0, k_1, k_2), F_43(x, k_0, k_1, k_2) + F_77(x, k_0, k_1*k_2))
Eq(F_44(x, k_0, k_1, k_2), F_45(x, k_1, k_2) + F_59(x, k_0, k_1, k_2))
Eq(F_45(x, k_0, k_1), F_46(x, k_0, k_0*k_1))
Eq(F_46(x, k_0, k_1), F_47(x, k_0, 1, k_1))
Eq(F_47(x, k_0, k_1, k_2), F_48(x, k_0*k_1) + F_49(x, k_0, k_1, k_2))
Eq(F_48(x, k_0), 16*k_0*x + (k_0*x + 1)**3*F_48(x, k_0)**2 + (8*k_0**2*x**2 - 20*k_0*x)*F_48(x, k_0))
Eq(F_49(x, k_0, k_1, k_2), F_50(x, k_1, k_0, k_2))
Eq(F_50(x, k_0, k_1, k_2), F_31(x, k_2)*F_51(x, k_0, k_1, k_2))
Eq(F_51(x, k_0, k_1, k_2), F_52(x, k_1, k_0, k_2) + F_54(x, k_0, k_1, k_2))
Eq(F_52(x, k_0, k_1, k_2), F_53(x, k_0*k_1, k_1*k_2))
Eq(F_53(x, k_0, k_1), F_30(x, k_1)*F_46(x, k_0, k_1))
Eq(F_54(x, k_0, k_1, k_2), F_55(x, k_0, k_1, k_2))
Eq(F_55(x, k_0, k_1, k_2), F_31(x, k_1)*F_47(x, k_1, k_0, k_2)*F_56(x, k_0, k_1, k_2))
Eq(F_56(x, k_0, k_1, k_2), F_57(x, k_0*k_1, k_0*k_2))
Eq(F_57(x, k_0, k_1), F_58(x, 1, k_0, k_1))
Eq(F_58(x, k_0, k_1, k_2), F_40(x, k_0*k_1, k_1, k_2))
Eq(F_59(x, k_0, k_1, k_2), F_60(x, k_0, k_1, k_1*k_2))
Eq(F_60(x, k_0, k_1, k_2), F_61(x, k_0, k_1, k_2))
Eq(F_61(x, k_0, k_1, k_2), F_31(x, k_0)*F_62(x, k_0, k_1, k_2))
Eq(F_62(x, k_0, k_1, k_2), (-k_1*F_63(x, k_0, k_1, 1) + k_2*F_63(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_63(x, k_0, k_1, k_2), F_64(x, k_0, k_1*k_2) + F_74(x, k_0, k_1, k_2))
Eq(F_64(x, k_0, k_1), F_30(x, k_1)*F_65(x, k_0))
Eq(F_65(x, k_0), F_30(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_18(x, k_0) + F_67(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_31(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_71(x, k_0))
Eq(F_70(x, k_0), F_30(x, k_0)*F_66(x, k_0))
Eq(F_71(x, k_0), F_72(x, 1, k_0))
Eq(F_72(x, k_0, k_1), F_73(x, k_0*k_1, k_1))
Eq(F_73(x, k_0, k_1), F_74(x, k_0, k_1, 1))
Eq(F_74(x, k_0, k_1, k_2), F_75(x, k_0, k_1, k_1*k_2))
Eq(F_75(x, k_0, k_1, k_2), F_76(x, k_0, k_1, k_2))
Eq(F_76(x, k_0, k_1, k_2), F_31(x, k_1)*F_40(x, k_0, k_1, k_2)*F_65(x, k_0))
Eq(F_77(x, k_0, k_1), F_30(x, k_1)*F_48(x, k_0))
Eq(F_78(x, k_0), F_5(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, 1, k_0))
Eq(F_80(x, k_0, k_1), -F_81(x, 1, k_1) + (-k_0*F_81(x, k_0/k_1, k_1) + k_1*F_81(x, 1, k_1))/(-k_0 + k_1))
Eq(F_81(x, k_0, k_1), F_82(x, k_0*k_1, k_1))
Eq(F_38(x, k_0, k_1), F_82(x, k_0, k_1) + F_83(x, k_1))
Eq(F_84(x, k_0), F_31(x, k_0)*F_83(x, k_0))
Eq(F_84(x, k_0), F_66(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 4, 3, 1], [0, 4, 2, 3, 1], [4, 0, 2, 3, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], 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