01324_01342_03124_03142_03214_03241_03412_03421
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3032, 16768, 95200, 551616, 3248704, 19389824, 117021824, 712934784, 4378663296, 27081760768, 168530142720, 1054464293888, 6629484729344, 41860283723776, 265346078982144, 1687918305128448, 10771600724946944, 68941213290561536, 442427575548461056, 2846278279028277248, 18352802795930714112, 118588983399050477568, 767782177646313963520, 4979949953583054159872, 32355831231314785304576, 210558709598477868859392, 1372283371473310644043776, 8956227437720371727171584, 58530384475270519722344448, 382983331944009873075732480, 2508941882400991929769656320, 16454549025616564077550632960, 108029063908515559257203015680, 709955335647042588246947135488, 4670200441621999823030967074816, 30749210383371183418869593145344, 202631835191481477341835580932096, 1336408589142930743577593910394880, 8820891887800248207842645616099328, 58265606039163432331609113918177280, 385145134336372438153517545014951936, 2547626122504518352345059373749370880, 16862954879453957806433295950799699968, 111688049002357150695437617236627423232, 740191010374927339591042095346440208384, 4908340231496856276155167387891053625344, 32566383524953585451743428317786442563584, 216191815025584682630056511117746832932864, 1435936154519986687271388927327684383473664, 9542210244935909701914535112333926642745344, 63441440797270789570274207083212497542447104, 421987847864035609812611921038977453621510144, 2808165677749896476430412181660982199948673024, 18695400057152198602207487588448805555099664384, 124517318934667876794981726485209358256018817024, 829663030380469516181045468969536049927205945344, 5530253014033277151822501447252768859542807117824, 36876876211546599304952640241147534160671889424384, 245993675479930831097444153196071492613044745273344, 1641532619888105819578474921872098778213883171569664, 10957870017566776973105407282369370881605292622086144, 73172741259813866085843525165796055741778731533860864, 488781499590815166836805313147069246378053989830754304, 3266016193584304781795368579264512180429852251116273664, 21830119367222551518533931442637549583622332430852030464, 145956794906772063908303688832159280080899640502259810304, 976156255610674843557272264494043237596719247573399896064, 6530368897526884156516901341340588540795663316718016528384, 43699464151943991822416314642734234924153890236505455067136, 292503682425016754060674563942105692653276520602464103170048, 1958395155753861178134642484752434547321354421959929815367680, 13115357344387311565189942714961388193723791568257286571819008, 87855288245258220807434419257706594739689863298371489558953984, 588655136964617290378727748345647523048224760353278335983288320, 3945087074043245943220480883373516924524093473530185640451244032, 26445534184872537656159891065987775800859037331423199995782758400, 177315113420178270897337884230405370625266596595435545595983429632, 1189144072556897353149632380542090761485313566766072150285002735616, 7976571139909459540659278969016771924893549063198932776385393983488, 53516644031346094053926692320853113400857456125935108098831390081024, 359128814933435016089195982265693019466937665060517425108183095967744, 2410451231956942090854929022749562369399574571652226108644638813323264, 16181962673932422697324006066082806072538705480272489528566942504321024, 108654292659157748756692409960562400231087476550442681279273807325954048, 729698734574219233499039079740131475511427827391906327937304723961413632, 4901393049759263611751090007430767774012294012253411802436338374951305216, 32928578431873330449020032769024918701977767073681026659850428402339151872, 221259681850061598025738379239459902333741804125566760798692238214534529024, 1486982386224470765974742392790534351529288241405564703964975432734162812928, 9994982631681983889853581814359374515798045147833434066823431563531721375744, 67193835351681822367645151916299435337512265309445122107677199827970631401472, 451800305895479427783024480062272990740768619553108820595092326774304243974144, 3038308670897522420440114885270044773604035642037350319633558033754618737983488, 20435448375693751784554643691894531632637310470282343031794326419655948117213184
Generating function in Maple syntax:
(4*x-5+(8*x^2-8*x+1)^(1/2))/(4*x-4)
Generating function in latex syntax:
\frac{4 x -5+\sqrt{8 x^{2}-8 x +1}}{4 x -4}
Generating function in sympy syntax:
(4*x + sqrt(8*x**2 - 8*x + 1) - 5)/(4*x - 4)
Implicit equation for the generating function in Maple syntax:
(2*x-2)*F(x)^2+(-4*x+5)*F(x)+x-3 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -2\right) F \! \left(x \right)^{2}+\left(-4 x +5\right) F \! \left(x \right)+x -3 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3032
a(8) = 16768
a(9) = 95200
a(10) = 551616
a(n+3) = 8*n/(n+3)*a(n)-4*(3+4*n)/(n+3)*a(n+1)+3*(5+3*n)/(n+3)*a(n+2), n >= 11
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3032
a(8) = 16768
a(9) = 95200
a(10) = 551616
a{\left(n + 3 \right)} = \frac{8 n a{\left(n \right)}}{n + 3} + \frac{3 \left(3 n + 5\right) a{\left(n + 2 \right)}}{n + 3} - \frac{4 \left(4 n + 3\right) a{\left(n + 1 \right)}}{n + 3}, \quad n \geq 11
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/24474/
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[38,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (-1+x*(1+F[7,x,k[0]])*k[0])*(x*(1+F[7,x,k[0]])*k[0]-2*F[7,x,k[0]])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[38,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[105,x,k[0]]*F[14,x,k[0]]*F[34,x,k[0]]
F[15,x,k[0]] = F[103,x,k[0]]*F[14,x,k[0]]*F[34,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[98,x,k[0]]
F[17,x,k[0]] = F[18,k[0]*x]
F[18,x] = -F[20,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = -1+(x^2-2*x)*F[20,x]^2+(2+x)*F[20,x]
F[21,x] = 1/F[41,x]*F[22,x]
F[22,x] = -F[94,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[38,x]
F[25,x] = 1/F[38,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[39,x]+F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[30,x,k[0]]+F[58,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[56,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[35,x]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = k[0]*x
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[39,x]
F[38,x] = x
F[39,x] = F[40,x]+F[45,x]
F[40,x] = F[1,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[38,x]*F[43,x]
F[43,x] = F[40,x]+F[44,x]
F[44,x] = F[41,x]
F[45,x] = F[36,x]+F[46,x]
F[46,x] = F[47,x]+F[48,x]+F[50,x]
F[47,x] = 0
F[48,x] = F[38,x]*F[49,x]
F[49,x] = F[41,x]
F[50,x] = F[38,x]*F[51,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[38,x]+F[53,x]
F[53,x] = F[47,x]+F[50,x]+F[54,x]
F[54,x] = F[38,x]*F[41,x]
F[55,x] = F[53,x]
F[56,x,k[0]] = F[40,x]*F[57,x,k[0]]
F[57,x,k[0]] = x*(x^4*F[57,x,k[0]]^2*k[0]^2-3*k[0]*((F[57,x,k[0]]+2/3)*k[0]+2/3*F[57,x,k[0]]-1/3)*F[57,x,k[0]]*x^3+((3*F[57,x,k[0]]^2+4*F[57,x,k[0]]+1)*k[0]^2+(6*F[57,x,k[0]]^2+F[57,x,k[0]]-1)*k[0]+F[57,x,k[0]]-1)*x^2+(-(F[57,x,k[0]]+1)^2*k[0]^2+(-6*F[57,x,k[0]]^2-5*F[57,x,k[0]])*k[0]-3*F[57,x,k[0]]+2)*x+(2*F[57,x,k[0]]^2+3*F[57,x,k[0]]+1)*k[0]+3*F[57,x,k[0]]-1)
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[38,x]*F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[93,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[92,x,k[0]]
F[62,x,k[0]] = F[32,x,k[0]]*F[63,x]
F[63,x] = F[64,x]+F[77,x]
F[64,x] = F[65,x]+F[67,x]
F[65,x] = F[1,x]+F[66,x]
F[66,x] = F[38,x]*F[65,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[69,x]
F[69,x] = F[38,x]*F[70,x]
F[70,x] = F[1,x]+F[68,x]
F[71,x] = F[47,x]+F[72,x]+F[76,x]
F[72,x] = F[38,x]*F[73,x]
F[73,x] = F[71,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[38,x]*F[65,x]
F[76,x] = F[38,x]*F[67,x]
F[77,x] = F[78,x]+F[82,x]
F[78,x] = F[38,x]+F[79,x]
F[79,x] = F[47,x]+F[80,x]+F[81,x]
F[80,x] = F[38,x]*F[74,x]
F[81,x] = F[38,x]*F[78,x]
F[82,x] = F[83,x]+F[87,x]
F[83,x] = F[47,x]+F[84,x]+F[85,x]
F[84,x] = F[38,x]*F[68,x]
F[85,x] = F[38,x]*F[86,x]
F[86,x] = F[38,x]+F[83,x]
F[87,x] = F[47,x]+F[88,x]+F[89,x]+F[91,x]
F[88,x] = F[38,x]*F[71,x]
F[89,x] = F[38,x]*F[90,x]
F[90,x] = F[79,x]+F[87,x]
F[91,x] = F[38,x]*F[82,x]
F[92,x,k[0]] = F[57,x,k[0]]*F[64,x]
F[93,x,k[0]] = F[32,x,k[0]]*F[38,x]*F[64,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[36,x]*F[65,x]
F[96,x] = F[41,x]*F[97,x]
F[97,x] = (x^4*F[97,x]^2+(-5*F[97,x]^2-F[97,x])*x^3+(9*F[97,x]^2+6*F[97,x]-1)*x^2+(-7*F[97,x]^2-10*F[97,x]+1)*x+2*F[97,x]^2+6*F[97,x])*x
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[14,x,k[0]]*F[34,x,k[0]]
F[101,x,k[0]] = F[100,x,k[0]]+F[98,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]
F[102,x,k[0]] = F[14,x,k[0]]*F[38,x]*F[4,x]
F[103,x,k[0]] = F[100,x,k[0]]+F[104,x,k[0]]
F[104,x,k[0]] = x^2*F[104,x,k[0]]^2*k[0]^2-2*x*F[104,x,k[0]]^2*k[0]+x*F[104,x,k[0]]*k[0]+2*F[104,x,k[0]]-1
F[105,x,k[0]] = (F[106,x,k[0]]*k[0]-F[106,x,1])/(-1+k[0])
F[106,x,k[0]] = F[0,x]+F[6,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_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{7}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{7}\! \left(x , y\right)^{2} y -3 x F_{7}\! \left(x , y\right) y -y x +2 F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(y x \right)
F_{18}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = x^{2} F_{20} \left(x \right)^{2}-2 x F_{20} \left(x \right)^{2}+F_{20}\! \left(x \right) x +2 F_{20}\! \left(x \right)-1
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{22}\! \left(x \right) = -F_{94}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{38}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = y x
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = x
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{45}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{36}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = 0
F_{48}\! \left(x \right) = F_{38}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{41}\! \left(x \right)
F_{50}\! \left(x \right) = F_{38}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{38}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{38}\! \left(x \right) F_{41}\! \left(x \right)
F_{55}\! \left(x \right) = F_{53}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -x^{2} y^{2}+y x +x^{5} F_{57}\! \left(x , y\right)^{2} y^{2}-3 x^{4} F_{57}\! \left(x , y\right)^{2} y^{2}-2 x^{4} F_{57}\! \left(x , y\right)^{2} y -2 x^{4} F_{57}\! \left(x , y\right) y^{2}+3 x^{3} F_{57}\! \left(x , y\right)^{2} y^{2}+x^{4} F_{57}\! \left(x , y\right) y +6 x^{3} F_{57}\! \left(x , y\right)^{2} y +4 x^{3} F_{57}\! \left(x , y\right) y^{2}-x^{2} F_{57}\! \left(x , y\right)^{2} y^{2}+x^{3} F_{57}\! \left(x , y\right) y -6 x^{2} F_{57}\! \left(x , y\right)^{2} y -2 x^{2} F_{57}\! \left(x , y\right) y^{2}-5 x^{2} F_{57}\! \left(x , y\right) y +2 x F_{57}\! \left(x , y\right)^{2} y +3 x F_{57}\! \left(x , y\right) y +x^{3} F_{57}\! \left(x , y\right)-3 x^{2} F_{57}\! \left(x , y\right)+3 F_{57}\! \left(x , y\right) x -x^{3} y +x^{3} y^{2}-x +2 x^{2}-x^{3}
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{77}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{38}\! \left(x \right) F_{65}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{38}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{1}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{47}\! \left(x \right)+F_{72}\! \left(x \right)+F_{76}\! \left(x \right)
F_{72}\! \left(x \right) = F_{38}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{38}\! \left(x \right) F_{65}\! \left(x \right)
F_{76}\! \left(x \right) = F_{38}\! \left(x \right) F_{67}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{82}\! \left(x \right)
F_{78}\! \left(x \right) = F_{38}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{47}\! \left(x \right)+F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{38}\! \left(x \right) F_{74}\! \left(x \right)
F_{81}\! \left(x \right) = F_{38}\! \left(x \right) F_{78}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{47}\! \left(x \right)+F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{38}\! \left(x \right) F_{68}\! \left(x \right)
F_{85}\! \left(x \right) = F_{38}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{38}\! \left(x \right)+F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{47}\! \left(x \right)+F_{88}\! \left(x \right)+F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{38}\! \left(x \right) F_{71}\! \left(x \right)
F_{89}\! \left(x \right) = F_{38}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{79}\! \left(x \right)+F_{87}\! \left(x \right)
F_{91}\! \left(x \right) = F_{38}\! \left(x \right) F_{82}\! \left(x \right)
F_{92}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{93}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{38}\! \left(x \right) F_{64}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{36}\! \left(x \right) F_{65}\! \left(x \right)
F_{96}\! \left(x \right) = F_{41}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = x^{5} F_{97} \left(x \right)^{2}-5 x^{4} F_{97} \left(x \right)^{2}-x^{4} F_{97}\! \left(x \right)+9 x^{3} F_{97} \left(x \right)^{2}+6 x^{3} F_{97}\! \left(x \right)-7 x^{2} F_{97} \left(x \right)^{2}-x^{3}-10 x^{2} F_{97}\! \left(x \right)+2 x F_{97} \left(x \right)^{2}+x^{2}+6 F_{97}\! \left(x \right) x
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{104}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = x^{2} F_{104}\! \left(x , y\right)^{2} y^{2}-2 y x F_{104}\! \left(x , y\right)^{2}+x F_{104}\! \left(x , y\right) y +2 F_{104}\! \left(x , y\right)-1
F_{105}\! \left(x , y\right) = -\frac{-y F_{106}\! \left(x , y\right)+F_{106}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\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_38(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(k_0*x - 2)*(F_7(x, k_0) + 1)**2 + (k_0*x + 1)*(F_7(x, k_0) + 1) + F_7(x, k_0) - 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_38(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_105(x, k_0)*F_14(x, k_0)*F_34(x, k_0))
Eq(F_15(x, k_0), F_103(x, k_0)*F_14(x, k_0)*F_34(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_98(x, k_0))
Eq(F_17(x, k_0), F_18(k_0*x))
Eq(F_18(x), F_19(x) - F_20(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), x*(x - 2)*F_20(x)**2 + (x + 2)*F_20(x) - 1)
Eq(F_21(x), F_22(x)/F_41(x))
Eq(F_22(x), F_23(x) - F_94(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_38(x))
Eq(F_25(x), F_26(x)/F_38(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x) - F_39(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_30(x, k_0) + F_58(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_56(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_35(x))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), k_0*x)
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_39(x))
Eq(F_38(x), x)
Eq(F_39(x), F_40(x) + F_45(x))
Eq(F_40(x), F_1(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_38(x)*F_43(x))
Eq(F_43(x), F_40(x) + F_44(x))
Eq(F_44(x), F_41(x))
Eq(F_45(x), F_36(x) + F_46(x))
Eq(F_46(x), F_47(x) + F_48(x) + F_50(x))
Eq(F_47(x), 0)
Eq(F_48(x), F_38(x)*F_49(x))
Eq(F_49(x), F_41(x))
Eq(F_50(x), F_38(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_38(x) + F_53(x))
Eq(F_53(x), F_47(x) + F_50(x) + F_54(x))
Eq(F_54(x), F_38(x)*F_41(x))
Eq(F_55(x), F_53(x))
Eq(F_56(x, k_0), F_40(x)*F_57(x, k_0))
Eq(F_57(x, k_0), k_0*x*(x - 1)*(k_0*x - 2)*((x - 1)*F_57(x, k_0) - 1)**2 - (x - 1)**3 + (x - 1)**2*(k_0*x + 1)*((x - 1)*F_57(x, k_0) - 1) + F_57(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_38(x)*F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_93(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_92(x, k_0))
Eq(F_62(x, k_0), F_32(x, k_0)*F_63(x))
Eq(F_63(x), F_64(x) + F_77(x))
Eq(F_64(x), F_65(x) + F_67(x))
Eq(F_65(x), F_1(x) + F_66(x))
Eq(F_66(x), F_38(x)*F_65(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_38(x)*F_70(x))
Eq(F_70(x), F_1(x) + F_68(x))
Eq(F_71(x), F_47(x) + F_72(x) + F_76(x))
Eq(F_72(x), F_38(x)*F_73(x))
Eq(F_73(x), F_71(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_38(x)*F_65(x))
Eq(F_76(x), F_38(x)*F_67(x))
Eq(F_77(x), F_78(x) + F_82(x))
Eq(F_78(x), F_38(x) + F_79(x))
Eq(F_79(x), F_47(x) + F_80(x) + F_81(x))
Eq(F_80(x), F_38(x)*F_74(x))
Eq(F_81(x), F_38(x)*F_78(x))
Eq(F_82(x), F_83(x) + F_87(x))
Eq(F_83(x), F_47(x) + F_84(x) + F_85(x))
Eq(F_84(x), F_38(x)*F_68(x))
Eq(F_85(x), F_38(x)*F_86(x))
Eq(F_86(x), F_38(x) + F_83(x))
Eq(F_87(x), F_47(x) + F_88(x) + F_89(x) + F_91(x))
Eq(F_88(x), F_38(x)*F_71(x))
Eq(F_89(x), F_38(x)*F_90(x))
Eq(F_90(x), F_79(x) + F_87(x))
Eq(F_91(x), F_38(x)*F_82(x))
Eq(F_92(x, k_0), F_57(x, k_0)*F_64(x))
Eq(F_93(x, k_0), F_32(x, k_0)*F_38(x)*F_64(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_36(x)*F_65(x))
Eq(F_96(x), F_41(x)*F_97(x))
Eq(F_97(x), x*(x - 2)*(x - 1)*((x - 1)*F_97(x) - 1)**2 - (x - 1)**3 + (x - 1)**2*(x + 1)*((x - 1)*F_97(x) - 1) + F_97(x))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_14(x, k_0)*F_34(x, k_0))
Eq(F_101(x, k_0), F_100(x, k_0) + F_98(x, k_0))
Eq(F_101(x, k_0), F_102(x, k_0))
Eq(F_102(x, k_0), F_14(x, k_0)*F_38(x)*F_4(x))
Eq(F_103(x, k_0), F_100(x, k_0) + F_104(x, k_0))
Eq(F_104(x, k_0), k_0*x*(k_0*x - 2)*F_104(x, k_0)**2 + (k_0*x + 2)*F_104(x, k_0) - 1)
Eq(F_105(x, k_0), (-k_0*F_106(x, k_0) + F_106(x, 1))/(1 - k_0))
Eq(F_106(x, k_0), F_0(x) + F_6(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_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.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": 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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"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}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 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": [[1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], 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[[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": []}, "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [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": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]], "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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/25246/
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[20,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[6,x,k[0]]+F[7,x,k[0]]
F[6,x,k[0]] = x^2*F[6,x,k[0]]^2*k[0]^2-2*x*F[6,x,k[0]]^2*k[0]+x*F[6,x,k[0]]*k[0]+2*F[6,x,k[0]]-1
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[20,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[11,x,k[0]]
F[10,x,k[0]] = (F[5,x,k[0]]*k[0]-F[5,x,1])/(-1+k[0])
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[10,x,k[0]]*F[13,x,k[0]]*F[19,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]*F[19,x,k[0]]*F[6,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[16,x,k[0]] = F[15,x,k[0]]+F[6,x,k[0]]
F[17,x,k[0]] = F[16,x,k[0]]*F[19,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = (x*(1+F[18,x,k[0]])*k[0]-2*F[18,x,k[0]])*(-1+x*(1+F[18,x,k[0]])*k[0])
F[19,x,k[0]] = k[0]*x
F[20,x] = x
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_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = x^{2} F_{6}\! \left(x , y\right)^{2} y^{2}-2 y x F_{6}\! \left(x , y\right)^{2}+x F_{6}\! \left(x , y\right) y +2 F_{6}\! \left(x , y\right)-1
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{20}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{11}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = x^{2} F_{18}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{18}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{18}\! \left(x , y\right)^{2} y -3 x F_{18}\! \left(x , y\right) y -y x +2 F_{18}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x \right) = x
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_20(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_6(x, k_0) + F_7(x, k_0))
Eq(F_6(x, k_0), k_0*x*(k_0*x - 2)*F_6(x, k_0)**2 + (k_0*x + 2)*F_6(x, k_0) - 1)
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_20(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_11(x, k_0))
Eq(F_10(x, k_0), (-k_0*F_5(x, k_0) + F_5(x, 1))/(1 - k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_10(x, k_0)*F_13(x, k_0)*F_19(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0)*F_19(x, k_0)*F_6(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_16(x, k_0), F_15(x, k_0) + F_6(x, k_0))
Eq(F_17(x, k_0), F_16(x, k_0)*F_19(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x*(k_0*x - 2)*(F_18(x, k_0) + 1)**2 + (k_0*x + 1)*(F_18(x, k_0) + 1) + F_18(x, k_0) - 1)
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x), x)
Pack JSON:
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Specification JSON:
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"workable": true}}, "idx": 0}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"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, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"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": []}, "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [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": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 3, 1, 2, 4], [0, 3, 1, 4, 2], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 1, 2], [0, 3, 4, 2, 1]], "symmetry": false}}, {"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"}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25920/
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[38,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (-1+x*(1+F[7,x,k[0]])*k[0])*(x*(1+F[7,x,k[0]])*k[0]-2*F[7,x,k[0]])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[38,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[104,x,k[0]]*F[14,x,k[0]]*F[34,x,k[0]]
F[15,x,k[0]] = F[102,x,k[0]]*F[14,x,k[0]]*F[34,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[97,x,k[0]]
F[17,x,k[0]] = F[18,k[0]*x]
F[18,x] = -F[20,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = -1+(x^2-2*x)*F[20,x]^2+(2+x)*F[20,x]
F[21,x] = 1/F[41,x]*F[22,x]
F[22,x] = -F[93,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[38,x]
F[25,x] = 1/F[38,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[39,x]+F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = F[30,x,k[0]]+F[58,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[56,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]*F[35,x]
F[32,x,k[0]] = F[1,x]+F[33,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = k[0]*x
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[39,x]
F[38,x] = x
F[39,x] = F[40,x]+F[45,x]
F[40,x] = F[1,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[38,x]*F[43,x]
F[43,x] = F[40,x]+F[44,x]
F[44,x] = F[41,x]
F[45,x] = F[36,x]+F[46,x]
F[46,x] = F[47,x]+F[48,x]+F[50,x]
F[47,x] = 0
F[48,x] = F[38,x]*F[49,x]
F[49,x] = F[41,x]
F[50,x] = F[38,x]*F[51,x]
F[51,x] = F[52,x]+F[55,x]
F[52,x] = F[38,x]+F[53,x]
F[53,x] = F[47,x]+F[50,x]+F[54,x]
F[54,x] = F[38,x]*F[41,x]
F[55,x] = F[53,x]
F[56,x,k[0]] = F[40,x]*F[57,x,k[0]]
F[57,x,k[0]] = (x^4*F[57,x,k[0]]^2*k[0]^2-3*((F[57,x,k[0]]+2/3)*k[0]+2/3*F[57,x,k[0]]-1/3)*F[57,x,k[0]]*k[0]*x^3+((3*F[57,x,k[0]]^2+4*F[57,x,k[0]]+1)*k[0]^2+(6*F[57,x,k[0]]^2+F[57,x,k[0]]-1)*k[0]+F[57,x,k[0]]-1)*x^2+(-(F[57,x,k[0]]+1)^2*k[0]^2+(-6*F[57,x,k[0]]^2-5*F[57,x,k[0]])*k[0]-3*F[57,x,k[0]]+2)*x+(2*F[57,x,k[0]]^2+3*F[57,x,k[0]]+1)*k[0]+3*F[57,x,k[0]]-1)*x
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[38,x]*F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[92,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]+F[91,x,k[0]]
F[62,x,k[0]] = F[32,x,k[0]]*F[63,x]
F[63,x] = F[64,x]+F[76,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = F[1,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[38,x]*F[65,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[70,x]
F[70,x] = F[38,x]*F[71,x]
F[71,x] = F[1,x]+F[69,x]
F[72,x] = F[47,x]+F[73,x]+F[75,x]
F[73,x] = F[38,x]*F[74,x]
F[74,x] = F[66,x]+F[72,x]
F[75,x] = F[38,x]*F[68,x]
F[76,x] = F[77,x]+F[81,x]
F[77,x] = F[38,x]+F[78,x]
F[78,x] = F[47,x]+F[79,x]+F[80,x]
F[79,x] = F[38,x]*F[66,x]
F[80,x] = F[38,x]*F[77,x]
F[81,x] = F[82,x]+F[86,x]
F[82,x] = F[47,x]+F[83,x]+F[84,x]
F[83,x] = F[38,x]*F[69,x]
F[84,x] = F[38,x]*F[85,x]
F[85,x] = F[38,x]+F[82,x]
F[86,x] = F[47,x]+F[87,x]+F[88,x]+F[90,x]
F[87,x] = F[38,x]*F[72,x]
F[88,x] = F[38,x]*F[89,x]
F[89,x] = F[78,x]+F[86,x]
F[90,x] = F[38,x]*F[81,x]
F[91,x,k[0]] = F[57,x,k[0]]*F[64,x]
F[92,x,k[0]] = F[32,x,k[0]]*F[38,x]*F[64,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[36,x]*F[65,x]
F[95,x] = F[41,x]*F[96,x]
F[96,x] = x*(x^4*F[96,x]^2+(-5*F[96,x]^2-F[96,x])*x^3+(9*F[96,x]^2+6*F[96,x]-1)*x^2+(-7*F[96,x]^2-10*F[96,x]+1)*x+2*F[96,x]^2+6*F[96,x])
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[14,x,k[0]]*F[34,x,k[0]]*F[99,x,k[0]]
F[100,x,k[0]] = F[97,x,k[0]]+F[99,x,k[0]]
F[100,x,k[0]] = F[101,x,k[0]]
F[101,x,k[0]] = F[14,x,k[0]]*F[38,x]*F[4,x]
F[102,x,k[0]] = F[103,x,k[0]]+F[99,x,k[0]]
F[103,x,k[0]] = x^2*F[103,x,k[0]]^2*k[0]^2-2*x*F[103,x,k[0]]^2*k[0]+x*F[103,x,k[0]]*k[0]+2*F[103,x,k[0]]-1
F[104,x,k[0]] = (F[105,x,k[0]]*k[0]-F[105,x,1])/(-1+k[0])
F[105,x,k[0]] = F[0,x]+F[6,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_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{7}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{7}\! \left(x , y\right)^{2} y -3 x F_{7}\! \left(x , y\right) y -y x +2 F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{38}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(y x \right)
F_{18}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = x^{2} F_{20} \left(x \right)^{2}-2 x F_{20} \left(x \right)^{2}+F_{20}\! \left(x \right) x +2 F_{20}\! \left(x \right)-1
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{41}\! \left(x \right)}
F_{22}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{38}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{38}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{39}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x , 1\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{35}\! \left(x \right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = y x
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = x
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{45}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{41}\! \left(x \right)
F_{45}\! \left(x \right) = F_{36}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = 0
F_{48}\! \left(x \right) = F_{38}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{41}\! \left(x \right)
F_{50}\! \left(x \right) = F_{38}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{55}\! \left(x \right)
F_{52}\! \left(x \right) = F_{38}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{38}\! \left(x \right) F_{41}\! \left(x \right)
F_{55}\! \left(x \right) = F_{53}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{40}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -x^{3} y +x^{3} y^{2}+x^{3} F_{57}\! \left(x , y\right)-3 x^{2} F_{57}\! \left(x , y\right)+3 F_{57}\! \left(x , y\right) x -x^{2} y^{2}+y x -2 x^{4} F_{57}\! \left(x , y\right) y^{2}+x^{5} F_{57}\! \left(x , y\right)^{2} y^{2}-3 x^{4} F_{57}\! \left(x , y\right)^{2} y^{2}+6 x^{3} F_{57}\! \left(x , y\right)^{2} y +4 x^{3} F_{57}\! \left(x , y\right) y^{2}+3 x^{3} F_{57}\! \left(x , y\right)^{2} y^{2}+x^{4} F_{57}\! \left(x , y\right) y -2 x^{4} F_{57}\! \left(x , y\right)^{2} y +x^{3} F_{57}\! \left(x , y\right) y +2 x F_{57}\! \left(x , y\right)^{2} y -x^{2} F_{57}\! \left(x , y\right)^{2} y^{2}-2 x^{2} F_{57}\! \left(x , y\right) y^{2}-5 x^{2} F_{57}\! \left(x , y\right) y +3 x F_{57}\! \left(x , y\right) y -6 x^{2} F_{57}\! \left(x , y\right)^{2} y -x +2 x^{2}-x^{3}
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{38}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{76}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{38}\! \left(x \right) F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{38}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{47}\! \left(x \right)+F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{38}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{38}\! \left(x \right) F_{68}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{81}\! \left(x \right)
F_{77}\! \left(x \right) = F_{38}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{47}\! \left(x \right)+F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{38}\! \left(x \right) F_{66}\! \left(x \right)
F_{80}\! \left(x \right) = F_{38}\! \left(x \right) F_{77}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{47}\! \left(x \right)+F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{38}\! \left(x \right) F_{69}\! \left(x \right)
F_{84}\! \left(x \right) = F_{38}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{38}\! \left(x \right)+F_{82}\! \left(x \right)
F_{86}\! \left(x \right) = F_{47}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{38}\! \left(x \right) F_{72}\! \left(x \right)
F_{88}\! \left(x \right) = F_{38}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{38}\! \left(x \right) F_{81}\! \left(x \right)
F_{91}\! \left(x , y\right) = F_{57}\! \left(x , y\right) F_{64}\! \left(x \right)
F_{92}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{38}\! \left(x \right) F_{64}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{36}\! \left(x \right) F_{65}\! \left(x \right)
F_{95}\! \left(x \right) = F_{41}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = x^{5} F_{96} \left(x \right)^{2}-5 x^{4} F_{96} \left(x \right)^{2}-x^{4} F_{96}\! \left(x \right)+9 x^{3} F_{96} \left(x \right)^{2}+6 x^{3} F_{96}\! \left(x \right)-7 x^{2} F_{96} \left(x \right)^{2}-x^{3}-10 x^{2} F_{96}\! \left(x \right)+2 x F_{96} \left(x \right)^{2}+x^{2}+6 F_{96}\! \left(x \right) x
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{34}\! \left(x , y\right) F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{97}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = x^{2} F_{103}\! \left(x , y\right)^{2} y^{2}-2 y x F_{103}\! \left(x , y\right)^{2}+x F_{103}\! \left(x , y\right) y +2 F_{103}\! \left(x , y\right)-1
F_{104}\! \left(x , y\right) = -\frac{-y F_{105}\! \left(x , y\right)+F_{105}\! \left(x , 1\right)}{-1+y}
F_{105}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\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_38(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(k_0*x - 2)*(F_7(x, k_0) + 1)**2 + (k_0*x + 1)*(F_7(x, k_0) + 1) + F_7(x, k_0) - 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_38(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_104(x, k_0)*F_14(x, k_0)*F_34(x, k_0))
Eq(F_15(x, k_0), F_102(x, k_0)*F_14(x, k_0)*F_34(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_97(x, k_0))
Eq(F_17(x, k_0), F_18(k_0*x))
Eq(F_18(x), F_19(x) - F_20(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), x*(x - 2)*F_20(x)**2 + (x + 2)*F_20(x) - 1)
Eq(F_21(x), F_22(x)/F_41(x))
Eq(F_22(x), F_23(x) - F_93(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_38(x))
Eq(F_25(x), F_26(x)/F_38(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x) - F_39(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), F_30(x, k_0) + F_58(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_56(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0)*F_35(x))
Eq(F_32(x, k_0), F_1(x) + F_33(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), k_0*x)
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_39(x))
Eq(F_38(x), x)
Eq(F_39(x), F_40(x) + F_45(x))
Eq(F_40(x), F_1(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_38(x)*F_43(x))
Eq(F_43(x), F_40(x) + F_44(x))
Eq(F_44(x), F_41(x))
Eq(F_45(x), F_36(x) + F_46(x))
Eq(F_46(x), F_47(x) + F_48(x) + F_50(x))
Eq(F_47(x), 0)
Eq(F_48(x), F_38(x)*F_49(x))
Eq(F_49(x), F_41(x))
Eq(F_50(x), F_38(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_55(x))
Eq(F_52(x), F_38(x) + F_53(x))
Eq(F_53(x), F_47(x) + F_50(x) + F_54(x))
Eq(F_54(x), F_38(x)*F_41(x))
Eq(F_55(x), F_53(x))
Eq(F_56(x, k_0), F_40(x)*F_57(x, k_0))
Eq(F_57(x, k_0), k_0*x*(x - 1)*(k_0*x - 2)*((x - 1)*F_57(x, k_0) - 1)**2 - (x - 1)**3 + (x - 1)**2*(k_0*x + 1)*((x - 1)*F_57(x, k_0) - 1) + F_57(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_38(x)*F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_92(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0) + F_91(x, k_0))
Eq(F_62(x, k_0), F_32(x, k_0)*F_63(x))
Eq(F_63(x), F_64(x) + F_76(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), F_1(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_38(x)*F_65(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_38(x)*F_71(x))
Eq(F_71(x), F_1(x) + F_69(x))
Eq(F_72(x), F_47(x) + F_73(x) + F_75(x))
Eq(F_73(x), F_38(x)*F_74(x))
Eq(F_74(x), F_66(x) + F_72(x))
Eq(F_75(x), F_38(x)*F_68(x))
Eq(F_76(x), F_77(x) + F_81(x))
Eq(F_77(x), F_38(x) + F_78(x))
Eq(F_78(x), F_47(x) + F_79(x) + F_80(x))
Eq(F_79(x), F_38(x)*F_66(x))
Eq(F_80(x), F_38(x)*F_77(x))
Eq(F_81(x), F_82(x) + F_86(x))
Eq(F_82(x), F_47(x) + F_83(x) + F_84(x))
Eq(F_83(x), F_38(x)*F_69(x))
Eq(F_84(x), F_38(x)*F_85(x))
Eq(F_85(x), F_38(x) + F_82(x))
Eq(F_86(x), F_47(x) + F_87(x) + F_88(x) + F_90(x))
Eq(F_87(x), F_38(x)*F_72(x))
Eq(F_88(x), F_38(x)*F_89(x))
Eq(F_89(x), F_78(x) + F_86(x))
Eq(F_90(x), F_38(x)*F_81(x))
Eq(F_91(x, k_0), F_57(x, k_0)*F_64(x))
Eq(F_92(x, k_0), F_32(x, k_0)*F_38(x)*F_64(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_36(x)*F_65(x))
Eq(F_95(x), F_41(x)*F_96(x))
Eq(F_96(x), x*(x - 2)*(x - 1)*((x - 1)*F_96(x) - 1)**2 - (x - 1)**3 + (x - 1)**2*(x + 1)*((x - 1)*F_96(x) - 1) + F_96(x))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_14(x, k_0)*F_34(x, k_0)*F_99(x, k_0))
Eq(F_100(x, k_0), F_97(x, k_0) + F_99(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0))
Eq(F_101(x, k_0), F_14(x, k_0)*F_38(x)*F_4(x))
Eq(F_102(x, k_0), F_103(x, k_0) + F_99(x, k_0))
Eq(F_103(x, k_0), k_0*x*(k_0*x - 2)*F_103(x, k_0)**2 + (k_0*x + 2)*F_103(x, k_0) - 1)
Eq(F_104(x, k_0), (-k_0*F_105(x, k_0) + F_105(x, 1))/(1 - k_0))
Eq(F_105(x, k_0), F_0(x) + F_6(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_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.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": 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": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"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}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 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", 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