02341_02413_02431_03241_20341_20413_20431_24013_24031_24103
Counting sequence:
1, 1, 2, 6, 24, 110, 531, 2626, 13192, 67074, 344350, 1781898, 9281658, 48617801, 255896339, 1352627962, 7176914051, 38210278249, 204066681023, 1092952427932, 5869106254644, 31593768929505, 170457891882574, 921626057681590, 4992946109851941, 27100151156863389, 147350705662060892, 802519225919075417, 4377659316599081865, 23915276963687464496, 130834469526853220264, 716722501052398952914, 3931270793332970736445, 21589414451208359218760, 118699654754557346213800, 653333713807546984580620, 3599776435681351597677797, 19854092173333006135509458, 109607190482244618607691661, 605653458471002095969313157, 3349563557011453520448062585, 18540218159209552671325191226, 102704322413660280491977910863, 569371086516057479961111909264, 3158793666144068629512877592896, 17536922576059469078120078104312, 97427063276789632065087510224162, 541612186237132976697219325192815, 3012790530647980440193237077190875, 16769141488215454114759407583691434, 93390850522286981394542948567299832, 520403465028214599947051391616539864, 2901413248061240736977880620653503188, 16184683890140875976685000548880744937, 90326702101204507304240050947059637879, 504356776602355112259682826352826942809, 2817488697888828493487823584611770320895, 15746437353232450590760777024167510896112, 88042376573778741891317891753504042134604, 492475179721306774690917778638129363140516, 2755841217630968558542456312655486190953550, 15427504162182926535028249387363593183897148, 86397948294079363378152690878070053470532316, 484030070827741193159617856672432370499993214, 2712673489883934733648254533581426234713312387, 15208076631024744451691826594036365710145561412, 85290012317724004942991047823511539765557874549, 478481219649688687457590270029245032945708859139, 2685161118141976638010236946932221817230066176333, 15073378642362497369221322693125993802858824012993, 84641218467999029424342237251224894754207158477219, 475423484886227735952568516024771825269284998593207, 2671180988387610927222512248867947809548661729843433, 15012279087810984267065778268987961263598995723048034, 84393184910242317141048454698195866970080394306779721, 474550552884383564385360342186321701235458101493567455, 2669125499506001800085133169740134166752620692249828315, 15016339055629855560121356089697420068225598121609749466, 84501605666086926408104638693302608030650423571337564863, 475629788155509022349295236501312860423462700881283417137, 2677773145475316467515900692383762268047009792851589548559, 15079145157752522741377657852882902357873178583550629293937, 84932812865713997031814472768918216776092408261848441470511, 478484488776795656571693949434205413343311191864288588947652, 2696196834625543327259921485342081747118316193277421614105153, 15195835398464798326977482476881852190411657953772187498773405, 85661322510104389563070518418455546216054123962444831020746338, 482981171257033613340456629588779541562921886014031837685554504, 2723697956998701598526585907053252027565837495385967838752342565, 15362757002771955606598295396456180327811082117672427734371625793, 86668057254572500142498093044042143870927213346468310121562460472, 489020332533177561661367726497847034666054514745475600456736498269, 2759758328534652117141830388872565764440042971719448269824712720112, 15577216248134457520075301089368412708252369598422185385094104616332, 87939043166350199275124009203084434193212776940484926964097879322468, 496529656166889695118991292738733699844441727208228286280918240509955, 2804004751914802456045707327702870688737751342015158622741287452061539, 15837293484807772090741022538686785836381806115933727144199329701640380, 89464443624587028969393801619565624117319936151962590163866683413893923, 505458963817895179255740631786231262740386736918288365245438759838619244, 2856182620552141232924620061904476038008676356425844154581133461914271465
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24549/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = 1/F[12,x]*F[11,x]
F[11,x] = F[2,x]
F[12,x] = x
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = F[134,x]+F[16,x]
F[16,x] = F[150,x]+F[17,x]
F[17,x] = F[18,x]*F[53,x]
F[18,x] = -F[146,x]+F[19,x]
F[19,x] = 1/F[12,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[2,x]+F[6,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[116,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[0,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = 1/F[12,x]/F[38,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[10,x]*F[12,x]*F[34,x]*F[38,x]
F[34,x] = 1/F[0,x]/F[12,x]/F[38,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]+F[46,x]
F[37,x] = F[2,x]*F[38,x]
F[38,x] = F[1,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[1,x]+F[12,x]
F[43,x] = F[39,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[39,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[32,x]+F[49,x]
F[49,x] = F[38,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = 1+x^2*F[53,x]^3+(-x^2+x)*F[53,x]^2
F[54,x] = F[12,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[65,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[53,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[12,x]*F[59,x]*F[62,x]
F[62,x] = F[53,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[53,x]^2*F[12,x]
F[65,x] = -F[59,x]+F[66,x]
F[66,x] = 1/F[12,x]/F[4,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = -F[76,x]+F[69,x]
F[69,x] = 1/F[12,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = -F[2,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = 1/F[12,x]*F[75,x]
F[75,x] = F[5,x]
F[76,x] = -F[77,x]+F[74,x]
F[77,x] = -F[80,x]+F[78,x]
F[78,x] = 1/F[12,x]*F[79,x]
F[79,x] = F[5,x]
F[80,x] = F[114,x]+F[81,x]
F[81,x] = -F[87,x]+F[82,x]
F[82,x] = 1/F[12,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[86,x]+F[85,x]
F[85,x] = -F[0,x]+F[10,x]
F[86,x] = x*(1+F[86,x])^2*(x*F[86,x]+1)
F[87,x] = -F[91,x]+F[88,x]
F[88,x] = 1/F[12,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[2,x]+F[84,x]
F[91,x] = F[10,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = 1/F[12,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[9,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[101,x]*F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[2,x]
F[100,x] = F[0,x]*F[2,x]
F[101,x] = 1/F[0,x]/F[12,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]+F[68,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[12,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[4,x]*F[68,x]
F[108,x] = F[0,x]*F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[12,x]*F[4,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[53,x]*F[66,x]
F[113,x] = F[54,x]*F[59,x]
F[114,x] = F[115,x]
F[115,x] = F[109,x]*F[12,x]
F[116,x] = -F[132,x]+F[117,x]
F[117,x] = -F[120,x]+F[118,x]
F[118,x] = 1/F[12,x]*F[119,x]
F[119,x] = F[6,x]
F[120,x] = F[100,x]+F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[12,x]*F[123,x]
F[123,x] = F[124,x]+F[127,x]
F[124,x] = F[125,x]*F[2,x]
F[125,x] = 1/F[12,x]*F[126,x]
F[126,x] = F[22,x]
F[127,x] = F[128,x]
F[128,x] = F[0,x]*F[129,x]*F[50,x]
F[129,x] = F[0,x]+F[130,x]
F[130,x] = F[131,x]
F[131,x] = F[12,x]*F[125,x]
F[132,x] = F[133,x]
F[133,x] = F[12,x]*F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[137,x]+F[138,x]
F[137,x] = F[16,x]*F[53,x]
F[138,x] = F[139,x]*F[53,x]*F[54,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[0,x]^2*F[10,x]
F[141,x] = F[142,x]
F[142,x] = F[0,x]^2*F[12,x]*F[143,x]*F[59,x]
F[143,x] = 1/F[65,x]*F[144,x]
F[144,x] = -F[145,x]+F[101,x]
F[145,x] = F[34,x]*F[59,x]
F[146,x] = -F[149,x]+F[147,x]
F[147,x] = 1/F[12,x]*F[148,x]
F[148,x] = F[23,x]
F[149,x] = F[0,x]*F[10,x]*F[2,x]
F[150,x] = F[139,x]*F[54,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_{12}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{134}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{150}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{53}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{146}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{116}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{12}\! \left(x \right) F_{38}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{38}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{46}\! \left(x \right)
F_{37}\! \left(x \right) = F_{2}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{32}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{38}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = x^{2} F_{53} \left(x \right)^{3}-x^{2} F_{53} \left(x \right)^{2}+x F_{53} \left(x \right)^{2}+1
F_{54}\! \left(x \right) = F_{12}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{53}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{53}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{53} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{12}\! \left(x \right) F_{4}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{5}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{5}\! \left(x \right)
F_{80}\! \left(x \right) = F_{114}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{86}\! \left(x \right) = x^{2} F_{86} \left(x \right)^{3}+2 x^{2} F_{86} \left(x \right)^{2}+x^{2} F_{86}\! \left(x \right)+x F_{86} \left(x \right)^{2}+2 x F_{86}\! \left(x \right)+x
F_{87}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{91}\! \left(x \right) = F_{10}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{9}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{2}\! \left(x \right)
F_{100}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{68}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{108}\! \left(x \right) = F_{0}\! \left(x \right) F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{53}\! \left(x \right) F_{66}\! \left(x \right)
F_{113}\! \left(x \right) = F_{54}\! \left(x \right) F_{59}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = -F_{132}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = \frac{F_{119}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{119}\! \left(x \right) = F_{6}\! \left(x \right)
F_{120}\! \left(x \right) = F_{100}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{127}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{2}\! \left(x \right)
F_{125}\! \left(x \right) = \frac{F_{126}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{126}\! \left(x \right) = F_{22}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{0}\! \left(x \right) F_{129}\! \left(x \right) F_{50}\! \left(x \right)
F_{129}\! \left(x \right) = F_{0}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{125}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = F_{16}\! \left(x \right) F_{53}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{53}\! \left(x \right) F_{54}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{10}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{12}\! \left(x \right) F_{143}\! \left(x \right) F_{59}\! \left(x \right)
F_{143}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{65}\! \left(x \right)}
F_{144}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{101}\! \left(x \right)
F_{145}\! \left(x \right) = F_{34}\! \left(x \right) F_{59}\! \left(x \right)
F_{146}\! \left(x \right) = -F_{149}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = \frac{F_{148}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{148}\! \left(x \right) = F_{23}\! \left(x \right)
F_{149}\! \left(x \right) = F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{150}\! \left(x \right) = F_{139}\! \left(x \right) F_{54}\! \left(x \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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x)/F_12(x))
Eq(F_11(x), F_2(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), F_134(x) + F_16(x))
Eq(F_16(x), F_150(x) + F_17(x))
Eq(F_17(x), F_18(x)*F_53(x))
Eq(F_18(x), -F_146(x) + F_19(x))
Eq(F_19(x), F_20(x)/F_12(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_2(x) + F_6(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_116(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_0(x)*F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x)/(F_12(x)*F_38(x)))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_10(x)*F_12(x)*F_34(x)*F_38(x))
Eq(F_34(x), F_35(x)/(F_0(x)*F_12(x)*F_38(x)))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x) + F_46(x))
Eq(F_37(x), F_2(x)*F_38(x))
Eq(F_38(x), F_1(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_1(x) + F_12(x))
Eq(F_43(x), F_39(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_39(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_32(x) + F_49(x))
Eq(F_49(x), F_38(x)*F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), x**2*F_53(x)**3 - x*(x - 1)*F_53(x)**2 + 1)
Eq(F_54(x), F_12(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_65(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_53(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_12(x)*F_59(x)*F_62(x))
Eq(F_62(x), F_53(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_53(x)**2)
Eq(F_65(x), -F_59(x) + F_66(x))
Eq(F_66(x), F_67(x)/(F_12(x)*F_4(x)))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x) - F_76(x))
Eq(F_69(x), F_70(x)/F_12(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), -F_2(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_75(x)/F_12(x))
Eq(F_75(x), F_5(x))
Eq(F_76(x), F_74(x) - F_77(x))
Eq(F_77(x), F_78(x) - F_80(x))
Eq(F_78(x), F_79(x)/F_12(x))
Eq(F_79(x), F_5(x))
Eq(F_80(x), F_114(x) + F_81(x))
Eq(F_81(x), F_82(x) - F_87(x))
Eq(F_82(x), F_83(x)/F_12(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_85(x) - F_86(x))
Eq(F_85(x), -F_0(x) + F_10(x))
Eq(F_86(x), x**2*(F_86(x) + 1)**3 - x*(x - 1)*(F_86(x) + 1)**2)
Eq(F_87(x), F_88(x) - F_91(x))
Eq(F_88(x), F_89(x)/F_12(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_2(x) + F_84(x))
Eq(F_91(x), F_10(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_12(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_9(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_101(x)*F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_2(x))
Eq(F_100(x), F_0(x)*F_2(x))
Eq(F_101(x), F_102(x)/(F_0(x)*F_12(x)))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x) + F_68(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_12(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_4(x)*F_68(x))
Eq(F_108(x), F_0(x)*F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_12(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_53(x)*F_66(x))
Eq(F_113(x), F_54(x)*F_59(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_109(x)*F_12(x))
Eq(F_116(x), F_117(x) - F_132(x))
Eq(F_117(x), F_118(x) - F_120(x))
Eq(F_118(x), F_119(x)/F_12(x))
Eq(F_119(x), F_6(x))
Eq(F_120(x), F_100(x) + F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_12(x)*F_123(x))
Eq(F_123(x), F_124(x) + F_127(x))
Eq(F_124(x), F_125(x)*F_2(x))
Eq(F_125(x), F_126(x)/F_12(x))
Eq(F_126(x), F_22(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_0(x)*F_129(x)*F_50(x))
Eq(F_129(x), F_0(x) + F_130(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_12(x)*F_125(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_12(x)*F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_138(x))
Eq(F_137(x), F_16(x)*F_53(x))
Eq(F_138(x), F_139(x)*F_53(x)*F_54(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_0(x)**2*F_10(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_0(x)**2*F_12(x)*F_143(x)*F_59(x))
Eq(F_143(x), F_144(x)/F_65(x))
Eq(F_144(x), F_101(x) - F_145(x))
Eq(F_145(x), F_34(x)*F_59(x))
Eq(F_146(x), F_147(x) - F_149(x))
Eq(F_147(x), F_148(x)/F_12(x))
Eq(F_148(x), F_23(x))
Eq(F_149(x), F_0(x)*F_10(x)*F_2(x))
Eq(F_150(x), F_139(x)*F_54(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": 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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, 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[[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "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}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24834/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = 1/F[12,x]*F[11,x]
F[11,x] = F[2,x]
F[12,x] = x
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = F[134,x]+F[16,x]
F[16,x] = F[150,x]+F[17,x]
F[17,x] = F[18,x]*F[53,x]
F[18,x] = -F[146,x]+F[19,x]
F[19,x] = 1/F[12,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[2,x]+F[6,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[116,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[0,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[30,x]
F[30,x] = 1/F[12,x]/F[38,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[10,x]*F[12,x]*F[34,x]*F[38,x]
F[34,x] = 1/F[0,x]/F[12,x]/F[38,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]+F[46,x]
F[37,x] = F[2,x]*F[38,x]
F[38,x] = F[1,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[1,x]+F[12,x]
F[43,x] = F[39,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[39,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[32,x]+F[49,x]
F[49,x] = F[38,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = 1+x^2*F[53,x]^3+(-x^2+x)*F[53,x]^2
F[54,x] = F[12,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[65,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[53,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[12,x]*F[59,x]*F[62,x]
F[62,x] = F[53,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[53,x]^2*F[12,x]
F[65,x] = -F[59,x]+F[66,x]
F[66,x] = 1/F[12,x]/F[4,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = -F[76,x]+F[69,x]
F[69,x] = 1/F[12,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = -F[2,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = 1/F[12,x]*F[75,x]
F[75,x] = F[5,x]
F[76,x] = -F[77,x]+F[74,x]
F[77,x] = -F[80,x]+F[78,x]
F[78,x] = 1/F[12,x]*F[79,x]
F[79,x] = F[5,x]
F[80,x] = F[114,x]+F[81,x]
F[81,x] = -F[87,x]+F[82,x]
F[82,x] = 1/F[12,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[86,x]+F[85,x]
F[85,x] = -F[0,x]+F[10,x]
F[86,x] = x*(1+F[86,x])^2*(x*F[86,x]+1)
F[87,x] = -F[91,x]+F[88,x]
F[88,x] = 1/F[12,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[2,x]+F[84,x]
F[91,x] = F[10,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = 1/F[12,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[9,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[101,x]*F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[2,x]
F[100,x] = F[0,x]*F[2,x]
F[101,x] = 1/F[0,x]/F[12,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]+F[68,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[12,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[4,x]*F[68,x]
F[108,x] = F[0,x]*F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[12,x]*F[4,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[53,x]*F[66,x]
F[113,x] = F[54,x]*F[59,x]
F[114,x] = F[115,x]
F[115,x] = F[109,x]*F[12,x]
F[116,x] = -F[132,x]+F[117,x]
F[117,x] = -F[120,x]+F[118,x]
F[118,x] = 1/F[12,x]*F[119,x]
F[119,x] = F[6,x]
F[120,x] = F[100,x]+F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[12,x]*F[123,x]
F[123,x] = F[124,x]+F[127,x]
F[124,x] = F[125,x]*F[2,x]
F[125,x] = 1/F[12,x]*F[126,x]
F[126,x] = F[22,x]
F[127,x] = F[128,x]
F[128,x] = F[0,x]*F[129,x]*F[50,x]
F[129,x] = F[0,x]+F[130,x]
F[130,x] = F[131,x]
F[131,x] = F[12,x]*F[125,x]
F[132,x] = F[133,x]
F[133,x] = F[12,x]*F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[137,x]+F[138,x]
F[137,x] = F[16,x]*F[53,x]
F[138,x] = F[139,x]*F[53,x]*F[54,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[0,x]^2*F[10,x]
F[141,x] = F[142,x]
F[142,x] = F[0,x]^2*F[12,x]*F[143,x]*F[59,x]
F[143,x] = 1/F[65,x]*F[144,x]
F[144,x] = -F[145,x]+F[101,x]
F[145,x] = F[34,x]*F[59,x]
F[146,x] = -F[149,x]+F[147,x]
F[147,x] = 1/F[12,x]*F[148,x]
F[148,x] = F[23,x]
F[149,x] = F[0,x]*F[10,x]*F[2,x]
F[150,x] = F[139,x]*F[54,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_{12}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{134}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{150}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{53}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{146}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{116}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{0}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{12}\! \left(x \right) F_{38}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{34}\! \left(x \right) F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{38}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{46}\! \left(x \right)
F_{37}\! \left(x \right) = F_{2}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{32}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{38}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = x^{2} F_{53} \left(x \right)^{3}-x^{2} F_{53} \left(x \right)^{2}+x F_{53} \left(x \right)^{2}+1
F_{54}\! \left(x \right) = F_{12}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{53}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{53}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{53} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{12}\! \left(x \right) F_{4}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{5}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{5}\! \left(x \right)
F_{80}\! \left(x \right) = F_{114}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{86}\! \left(x \right) = x^{2} F_{86} \left(x \right)^{3}+2 x^{2} F_{86} \left(x \right)^{2}+x^{2} F_{86}\! \left(x \right)+x F_{86} \left(x \right)^{2}+2 x F_{86}\! \left(x \right)+x
F_{87}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{91}\! \left(x \right) = F_{10}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{9}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{2}\! \left(x \right)
F_{100}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{68}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{108}\! \left(x \right) = F_{0}\! \left(x \right) F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{53}\! \left(x \right) F_{66}\! \left(x \right)
F_{113}\! \left(x \right) = F_{54}\! \left(x \right) F_{59}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = -F_{132}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = \frac{F_{119}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{119}\! \left(x \right) = F_{6}\! \left(x \right)
F_{120}\! \left(x \right) = F_{100}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{127}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{2}\! \left(x \right)
F_{125}\! \left(x \right) = \frac{F_{126}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{126}\! \left(x \right) = F_{22}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{0}\! \left(x \right) F_{129}\! \left(x \right) F_{50}\! \left(x \right)
F_{129}\! \left(x \right) = F_{0}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{125}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = F_{16}\! \left(x \right) F_{53}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{53}\! \left(x \right) F_{54}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{10}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{12}\! \left(x \right) F_{143}\! \left(x \right) F_{59}\! \left(x \right)
F_{143}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{65}\! \left(x \right)}
F_{144}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{101}\! \left(x \right)
F_{145}\! \left(x \right) = F_{34}\! \left(x \right) F_{59}\! \left(x \right)
F_{146}\! \left(x \right) = -F_{149}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = \frac{F_{148}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{148}\! \left(x \right) = F_{23}\! \left(x \right)
F_{149}\! \left(x \right) = F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{150}\! \left(x \right) = F_{139}\! \left(x \right) F_{54}\! \left(x \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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x)/F_12(x))
Eq(F_11(x), F_2(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), F_134(x) + F_16(x))
Eq(F_16(x), F_150(x) + F_17(x))
Eq(F_17(x), F_18(x)*F_53(x))
Eq(F_18(x), -F_146(x) + F_19(x))
Eq(F_19(x), F_20(x)/F_12(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_2(x) + F_6(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_116(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_0(x)*F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_30(x))
Eq(F_30(x), F_31(x)/(F_12(x)*F_38(x)))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_10(x)*F_12(x)*F_34(x)*F_38(x))
Eq(F_34(x), F_35(x)/(F_0(x)*F_12(x)*F_38(x)))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x) + F_46(x))
Eq(F_37(x), F_2(x)*F_38(x))
Eq(F_38(x), F_1(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_1(x) + F_12(x))
Eq(F_43(x), F_39(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_39(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_32(x) + F_49(x))
Eq(F_49(x), F_38(x)*F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), x**2*F_53(x)**3 - x*(x - 1)*F_53(x)**2 + 1)
Eq(F_54(x), F_12(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_65(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_53(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_12(x)*F_59(x)*F_62(x))
Eq(F_62(x), F_53(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_12(x)*F_53(x)**2)
Eq(F_65(x), -F_59(x) + F_66(x))
Eq(F_66(x), F_67(x)/(F_12(x)*F_4(x)))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x) - F_76(x))
Eq(F_69(x), F_70(x)/F_12(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), -F_2(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_75(x)/F_12(x))
Eq(F_75(x), F_5(x))
Eq(F_76(x), F_74(x) - F_77(x))
Eq(F_77(x), F_78(x) - F_80(x))
Eq(F_78(x), F_79(x)/F_12(x))
Eq(F_79(x), F_5(x))
Eq(F_80(x), F_114(x) + F_81(x))
Eq(F_81(x), F_82(x) - F_87(x))
Eq(F_82(x), F_83(x)/F_12(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_85(x) - F_86(x))
Eq(F_85(x), -F_0(x) + F_10(x))
Eq(F_86(x), x**2*(F_86(x) + 1)**3 - x*(x - 1)*(F_86(x) + 1)**2)
Eq(F_87(x), F_88(x) - F_91(x))
Eq(F_88(x), F_89(x)/F_12(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_2(x) + F_84(x))
Eq(F_91(x), F_10(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x)/F_12(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_9(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_101(x)*F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_2(x))
Eq(F_100(x), F_0(x)*F_2(x))
Eq(F_101(x), F_102(x)/(F_0(x)*F_12(x)))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x) + F_68(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_12(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_4(x)*F_68(x))
Eq(F_108(x), F_0(x)*F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_12(x)*F_4(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_53(x)*F_66(x))
Eq(F_113(x), F_54(x)*F_59(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_109(x)*F_12(x))
Eq(F_116(x), F_117(x) - F_132(x))
Eq(F_117(x), F_118(x) - F_120(x))
Eq(F_118(x), F_119(x)/F_12(x))
Eq(F_119(x), F_6(x))
Eq(F_120(x), F_100(x) + F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_12(x)*F_123(x))
Eq(F_123(x), F_124(x) + F_127(x))
Eq(F_124(x), F_125(x)*F_2(x))
Eq(F_125(x), F_126(x)/F_12(x))
Eq(F_126(x), F_22(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_0(x)*F_129(x)*F_50(x))
Eq(F_129(x), F_0(x) + F_130(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_12(x)*F_125(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_12(x)*F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_138(x))
Eq(F_137(x), F_16(x)*F_53(x))
Eq(F_138(x), F_139(x)*F_53(x)*F_54(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_0(x)**2*F_10(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_0(x)**2*F_12(x)*F_143(x)*F_59(x))
Eq(F_143(x), F_144(x)/F_65(x))
Eq(F_144(x), F_101(x) - F_145(x))
Eq(F_145(x), F_34(x)*F_59(x))
Eq(F_146(x), F_147(x) - F_149(x))
Eq(F_147(x), F_148(x)/F_12(x))
Eq(F_148(x), F_23(x))
Eq(F_149(x), F_0(x)*F_10(x)*F_2(x))
Eq(F_150(x), F_139(x)*F_54(x))
Pack JSON:
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Specification JSON:
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"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": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}], "indices": [0, 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": "Rule", "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]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "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], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "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}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24989/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = 1/F[12,x]*F[11,x]
F[11,x] = F[2,x]
F[12,x] = x
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = F[145,x]+F[16,x]
F[16,x] = F[161,x]+F[17,x]
F[17,x] = F[18,x]*F[52,x]
F[18,x] = -F[157,x]+F[19,x]
F[19,x] = 1/F[12,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]+F[5,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[129,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[0,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = 1/F[12,x]/F[37,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[10,x]*F[12,x]*F[33,x]*F[37,x]
F[33,x] = 1/F[0,x]/F[12,x]/F[37,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]+F[45,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[1,x]+F[12,x]
F[42,x] = F[38,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[38,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[31,x]+F[48,x]
F[48,x] = F[37,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = 1+x^2*F[52,x]^3+(-x^2+x)*F[52,x]^2
F[53,x] = F[12,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[64,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[58,x]*F[61,x]
F[61,x] = F[52,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[52,x]^2*F[12,x]
F[64,x] = -F[58,x]+F[65,x]
F[65,x] = 1/F[12,x]/F[4,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[78,x]+F[68,x]
F[68,x] = 1/F[12,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[2,x]+F[71,x]
F[71,x] = -F[0,x]+F[72,x]
F[72,x] = F[0,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = 1/F[12,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[2,x]+F[6,x]
F[78,x] = -F[79,x]+F[75,x]
F[79,x] = -F[82,x]+F[80,x]
F[80,x] = 1/F[12,x]*F[81,x]
F[81,x] = F[77,x]
F[82,x] = F[127,x]+F[83,x]
F[83,x] = -F[88,x]+F[84,x]
F[84,x] = 1/F[12,x]*F[85,x]
F[85,x] = F[86,x]
F[86,x] = -F[2,x]+F[87,x]
F[87,x] = -F[52,x]+F[10,x]
F[88,x] = F[124,x]+F[89,x]
F[89,x] = -F[97,x]+F[90,x]
F[90,x] = 1/F[12,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = -F[2,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = 1/F[12,x]*F[96,x]
F[96,x] = F[87,x]
F[97,x] = -F[98,x]+F[95,x]
F[98,x] = -F[101,x]+F[99,x]
F[99,x] = 1/F[12,x]*F[100,x]
F[100,x] = F[87,x]
F[101,x] = F[102,x]+F[124,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = 1/F[12,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]+F[9,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[111,x]*F[12,x]
F[109,x] = F[110,x]+F[2,x]
F[110,x] = F[0,x]*F[2,x]
F[111,x] = 1/F[0,x]/F[12,x]*F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]+F[67,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[4,x]*F[67,x]
F[118,x] = F[0,x]*F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[12,x]*F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[52,x]*F[65,x]
F[123,x] = F[53,x]*F[58,x]
F[124,x] = F[125,x]
F[125,x] = F[104,x]*F[12,x]*F[126,x]
F[126,x] = x*(1+F[126,x])^2*(x*F[126,x]+1)
F[127,x] = F[128,x]
F[128,x] = F[119,x]*F[12,x]
F[129,x] = -F[143,x]+F[130,x]
F[130,x] = -F[133,x]+F[131,x]
F[131,x] = 1/F[12,x]*F[132,x]
F[132,x] = F[6,x]
F[133,x] = F[110,x]+F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[137,x]+F[140,x]
F[137,x] = F[138,x]*F[2,x]
F[138,x] = 1/F[12,x]*F[139,x]
F[139,x] = F[5,x]
F[140,x] = F[141,x]
F[141,x] = F[0,x]*F[142,x]*F[49,x]
F[142,x] = F[52,x]+F[93,x]
F[143,x] = F[144,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[146,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[16,x]*F[52,x]
F[149,x] = F[150,x]*F[52,x]*F[53,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[0,x]^2*F[10,x]
F[152,x] = F[153,x]
F[153,x] = F[0,x]^2*F[12,x]*F[154,x]*F[58,x]
F[154,x] = 1/F[64,x]*F[155,x]
F[155,x] = -F[156,x]+F[111,x]
F[156,x] = F[33,x]*F[58,x]
F[157,x] = -F[160,x]+F[158,x]
F[158,x] = 1/F[12,x]*F[159,x]
F[159,x] = F[22,x]
F[160,x] = F[0,x]*F[10,x]*F[2,x]
F[161,x] = F[150,x]*F[53,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_{12}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{145}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{161}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{157}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{129}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{12}\! \left(x \right) F_{37}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{37}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{45}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{37}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = x^{2} F_{52} \left(x \right)^{3}-x^{2} F_{52} \left(x \right)^{2}+x F_{52} \left(x \right)^{2}+1
F_{53}\! \left(x \right) = F_{12}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{64}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{52}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{52} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{12}\! \left(x \right) F_{4}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{0}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{79}\! \left(x \right)+F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{77}\! \left(x \right)
F_{82}\! \left(x \right) = F_{127}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{10}\! \left(x \right)
F_{88}\! \left(x \right) = F_{124}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{97}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{87}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{87}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{124}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{9}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{111}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{2}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{111}\! \left(x \right) = \frac{F_{112}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{67}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{118}\! \left(x \right) = F_{0}\! \left(x \right) F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{52}\! \left(x \right) F_{65}\! \left(x \right)
F_{123}\! \left(x \right) = F_{53}\! \left(x \right) F_{58}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = x^{2} F_{126} \left(x \right)^{3}+2 x^{2} F_{126} \left(x \right)^{2}+x^{2} F_{126}\! \left(x \right)+x F_{126} \left(x \right)^{2}+2 x F_{126}\! \left(x \right)+x
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{129}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{6}\! \left(x \right)
F_{133}\! \left(x \right) = F_{110}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{140}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{2}\! \left(x \right)
F_{138}\! \left(x \right) = \frac{F_{139}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{139}\! \left(x \right) = F_{5}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{0}\! \left(x \right) F_{142}\! \left(x \right) F_{49}\! \left(x \right)
F_{142}\! \left(x \right) = F_{52}\! \left(x \right)+F_{93}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{16}\! \left(x \right) F_{52}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{52}\! \left(x \right) F_{53}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{10}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{12}\! \left(x \right) F_{154}\! \left(x \right) F_{58}\! \left(x \right)
F_{154}\! \left(x \right) = \frac{F_{155}\! \left(x \right)}{F_{64}\! \left(x \right)}
F_{155}\! \left(x \right) = -F_{156}\! \left(x \right)+F_{111}\! \left(x \right)
F_{156}\! \left(x \right) = F_{33}\! \left(x \right) F_{58}\! \left(x \right)
F_{157}\! \left(x \right) = -F_{160}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{22}\! \left(x \right)
F_{160}\! \left(x \right) = F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{161}\! \left(x \right) = F_{150}\! \left(x \right) F_{53}\! \left(x \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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x)/F_12(x))
Eq(F_11(x), F_2(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), F_145(x) + F_16(x))
Eq(F_16(x), F_161(x) + F_17(x))
Eq(F_17(x), F_18(x)*F_52(x))
Eq(F_18(x), -F_157(x) + F_19(x))
Eq(F_19(x), F_20(x)/F_12(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x) + F_5(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_129(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_0(x)*F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x)/(F_12(x)*F_37(x)))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_10(x)*F_12(x)*F_33(x)*F_37(x))
Eq(F_33(x), F_34(x)/(F_0(x)*F_12(x)*F_37(x)))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) + F_45(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_1(x) + F_12(x))
Eq(F_42(x), F_38(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_38(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_31(x) + F_48(x))
Eq(F_48(x), F_37(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), x**2*F_52(x)**3 - x*(x - 1)*F_52(x)**2 + 1)
Eq(F_53(x), F_12(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_64(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_58(x)*F_61(x))
Eq(F_61(x), F_52(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_12(x)*F_52(x)**2)
Eq(F_64(x), -F_58(x) + F_65(x))
Eq(F_65(x), F_66(x)/(F_12(x)*F_4(x)))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x) - F_78(x))
Eq(F_68(x), F_69(x)/F_12(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), -F_2(x) + F_71(x))
Eq(F_71(x), -F_0(x) + F_72(x))
Eq(F_72(x), F_0(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_12(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_2(x) + F_6(x))
Eq(F_78(x), F_75(x) - F_79(x))
Eq(F_79(x), F_80(x) - F_82(x))
Eq(F_80(x), F_81(x)/F_12(x))
Eq(F_81(x), F_77(x))
Eq(F_82(x), F_127(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_88(x))
Eq(F_84(x), F_85(x)/F_12(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), -F_2(x) + F_87(x))
Eq(F_87(x), F_10(x) - F_52(x))
Eq(F_88(x), F_124(x) + F_89(x))
Eq(F_89(x), F_90(x) - F_97(x))
Eq(F_90(x), F_91(x)/F_12(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), -F_2(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_12(x))
Eq(F_96(x), F_87(x))
Eq(F_97(x), F_95(x) - F_98(x))
Eq(F_98(x), -F_101(x) + F_99(x))
Eq(F_99(x), F_100(x)/F_12(x))
Eq(F_100(x), F_87(x))
Eq(F_101(x), F_102(x) + F_124(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x)/F_12(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) + F_9(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_111(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_2(x))
Eq(F_110(x), F_0(x)*F_2(x))
Eq(F_111(x), F_112(x)/(F_0(x)*F_12(x)))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x) + F_67(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_4(x)*F_67(x))
Eq(F_118(x), F_0(x)*F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_12(x)*F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_52(x)*F_65(x))
Eq(F_123(x), F_53(x)*F_58(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_104(x)*F_12(x)*F_126(x))
Eq(F_126(x), x**2*(F_126(x) + 1)**3 - x*(x - 1)*(F_126(x) + 1)**2)
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_119(x)*F_12(x))
Eq(F_129(x), F_130(x) - F_143(x))
Eq(F_130(x), F_131(x) - F_133(x))
Eq(F_131(x), F_132(x)/F_12(x))
Eq(F_132(x), F_6(x))
Eq(F_133(x), F_110(x) + F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_140(x))
Eq(F_137(x), F_138(x)*F_2(x))
Eq(F_138(x), F_139(x)/F_12(x))
Eq(F_139(x), F_5(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_0(x)*F_142(x)*F_49(x))
Eq(F_142(x), F_52(x) + F_93(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_16(x)*F_52(x))
Eq(F_149(x), F_150(x)*F_52(x)*F_53(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_0(x)**2*F_10(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_0(x)**2*F_12(x)*F_154(x)*F_58(x))
Eq(F_154(x), F_155(x)/F_64(x))
Eq(F_155(x), F_111(x) - F_156(x))
Eq(F_156(x), F_33(x)*F_58(x))
Eq(F_157(x), F_158(x) - F_160(x))
Eq(F_158(x), F_159(x)/F_12(x))
Eq(F_159(x), F_22(x))
Eq(F_160(x), F_0(x)*F_10(x)*F_2(x))
Eq(F_161(x), F_150(x)*F_53(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": 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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 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[0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, "idx": 1}, {"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, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 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"tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 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": "Rule", "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]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "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], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "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}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25059/
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[12,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[10,x]*F[2,x]
F[10,x] = 1/F[12,x]*F[11,x]
F[11,x] = F[2,x]
F[12,x] = x
F[13,x] = F[14,x]
F[14,x] = F[12,x]*F[15,x]
F[15,x] = F[145,x]+F[16,x]
F[16,x] = F[161,x]+F[17,x]
F[17,x] = F[18,x]*F[52,x]
F[18,x] = -F[157,x]+F[19,x]
F[19,x] = 1/F[12,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]+F[5,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[129,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[0,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = 1/F[12,x]/F[37,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[10,x]*F[12,x]*F[33,x]*F[37,x]
F[33,x] = 1/F[0,x]/F[12,x]/F[37,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]+F[45,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[1,x]+F[12,x]
F[42,x] = F[38,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[38,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[31,x]+F[48,x]
F[48,x] = F[37,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = 1+x^2*F[52,x]^3+(-x^2+x)*F[52,x]^2
F[53,x] = F[12,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[64,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[52,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[58,x]*F[61,x]
F[61,x] = F[52,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[52,x]^2*F[12,x]
F[64,x] = -F[58,x]+F[65,x]
F[65,x] = 1/F[12,x]/F[4,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[78,x]+F[68,x]
F[68,x] = 1/F[12,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[2,x]+F[71,x]
F[71,x] = -F[0,x]+F[72,x]
F[72,x] = F[0,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = 1/F[12,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[2,x]+F[6,x]
F[78,x] = -F[79,x]+F[75,x]
F[79,x] = -F[82,x]+F[80,x]
F[80,x] = 1/F[12,x]*F[81,x]
F[81,x] = F[77,x]
F[82,x] = F[127,x]+F[83,x]
F[83,x] = -F[88,x]+F[84,x]
F[84,x] = 1/F[12,x]*F[85,x]
F[85,x] = F[86,x]
F[86,x] = -F[2,x]+F[87,x]
F[87,x] = -F[52,x]+F[10,x]
F[88,x] = F[124,x]+F[89,x]
F[89,x] = -F[97,x]+F[90,x]
F[90,x] = 1/F[12,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = -F[2,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = 1/F[12,x]*F[96,x]
F[96,x] = F[87,x]
F[97,x] = -F[98,x]+F[95,x]
F[98,x] = -F[101,x]+F[99,x]
F[99,x] = 1/F[12,x]*F[100,x]
F[100,x] = F[87,x]
F[101,x] = F[102,x]+F[124,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = 1/F[12,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]+F[9,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[111,x]*F[12,x]
F[109,x] = F[110,x]+F[2,x]
F[110,x] = F[0,x]*F[2,x]
F[111,x] = 1/F[0,x]/F[12,x]*F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]+F[67,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[4,x]*F[67,x]
F[118,x] = F[0,x]*F[119,x]
F[119,x] = F[120,x]
F[120,x] = F[12,x]*F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[123,x]
F[122,x] = F[52,x]*F[65,x]
F[123,x] = F[53,x]*F[58,x]
F[124,x] = F[125,x]
F[125,x] = F[104,x]*F[12,x]*F[126,x]
F[126,x] = x*(1+F[126,x])^2*(x*F[126,x]+1)
F[127,x] = F[128,x]
F[128,x] = F[119,x]*F[12,x]
F[129,x] = -F[143,x]+F[130,x]
F[130,x] = -F[133,x]+F[131,x]
F[131,x] = 1/F[12,x]*F[132,x]
F[132,x] = F[6,x]
F[133,x] = F[110,x]+F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[137,x]+F[140,x]
F[137,x] = F[138,x]*F[2,x]
F[138,x] = 1/F[12,x]*F[139,x]
F[139,x] = F[5,x]
F[140,x] = F[141,x]
F[141,x] = F[0,x]*F[142,x]*F[49,x]
F[142,x] = F[52,x]+F[93,x]
F[143,x] = F[144,x]
F[144,x] = F[12,x]*F[145,x]
F[145,x] = F[146,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[148,x]+F[149,x]
F[148,x] = F[16,x]*F[52,x]
F[149,x] = F[150,x]*F[52,x]*F[53,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[0,x]^2*F[10,x]
F[152,x] = F[153,x]
F[153,x] = F[0,x]^2*F[12,x]*F[154,x]*F[58,x]
F[154,x] = 1/F[64,x]*F[155,x]
F[155,x] = -F[156,x]+F[111,x]
F[156,x] = F[33,x]*F[58,x]
F[157,x] = -F[160,x]+F[158,x]
F[158,x] = 1/F[12,x]*F[159,x]
F[159,x] = F[22,x]
F[160,x] = F[0,x]*F[10,x]*F[2,x]
F[161,x] = F[150,x]*F[53,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_{12}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{10}\! \left(x \right) = \frac{F_{11}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{11}\! \left(x \right) = F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{145}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{161}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{157}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{129}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{12}\! \left(x \right) F_{37}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right) F_{33}\! \left(x \right) F_{37}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right) F_{37}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{45}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{42}\! \left(x \right) = F_{38}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{31}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{37}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = x^{2} F_{52} \left(x \right)^{3}-x^{2} F_{52} \left(x \right)^{2}+x F_{52} \left(x \right)^{2}+1
F_{53}\! \left(x \right) = F_{12}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{64}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{52}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{52} \left(x \right)^{2} F_{12}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{12}\! \left(x \right) F_{4}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{0}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{79}\! \left(x \right)+F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{77}\! \left(x \right)
F_{82}\! \left(x \right) = F_{127}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{10}\! \left(x \right)
F_{88}\! \left(x \right) = F_{124}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{97}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{87}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{87}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{124}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{9}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{111}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{2}\! \left(x \right)
F_{110}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{111}\! \left(x \right) = \frac{F_{112}\! \left(x \right)}{F_{0}\! \left(x \right) F_{12}\! \left(x \right)}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{67}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{118}\! \left(x \right) = F_{0}\! \left(x \right) F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{123}\! \left(x \right)
F_{122}\! \left(x \right) = F_{52}\! \left(x \right) F_{65}\! \left(x \right)
F_{123}\! \left(x \right) = F_{53}\! \left(x \right) F_{58}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = x^{2} F_{126} \left(x \right)^{3}+2 x^{2} F_{126} \left(x \right)^{2}+x^{2} F_{126}\! \left(x \right)+x F_{126} \left(x \right)^{2}+2 x F_{126}\! \left(x \right)+x
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{129}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{6}\! \left(x \right)
F_{133}\! \left(x \right) = F_{110}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{140}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{2}\! \left(x \right)
F_{138}\! \left(x \right) = \frac{F_{139}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{139}\! \left(x \right) = F_{5}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{0}\! \left(x \right) F_{142}\! \left(x \right) F_{49}\! \left(x \right)
F_{142}\! \left(x \right) = F_{52}\! \left(x \right)+F_{93}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{149}\! \left(x \right)
F_{148}\! \left(x \right) = F_{16}\! \left(x \right) F_{52}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{52}\! \left(x \right) F_{53}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{10}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{0} \left(x \right)^{2} F_{12}\! \left(x \right) F_{154}\! \left(x \right) F_{58}\! \left(x \right)
F_{154}\! \left(x \right) = \frac{F_{155}\! \left(x \right)}{F_{64}\! \left(x \right)}
F_{155}\! \left(x \right) = -F_{156}\! \left(x \right)+F_{111}\! \left(x \right)
F_{156}\! \left(x \right) = F_{33}\! \left(x \right) F_{58}\! \left(x \right)
F_{157}\! \left(x \right) = -F_{160}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{12}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{22}\! \left(x \right)
F_{160}\! \left(x \right) = F_{0}\! \left(x \right) F_{10}\! \left(x \right) F_{2}\! \left(x \right)
F_{161}\! \left(x \right) = F_{150}\! \left(x \right) F_{53}\! \left(x \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_12(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_2(x))
Eq(F_10(x), F_11(x)/F_12(x))
Eq(F_11(x), F_2(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)*F_15(x))
Eq(F_15(x), F_145(x) + F_16(x))
Eq(F_16(x), F_161(x) + F_17(x))
Eq(F_17(x), F_18(x)*F_52(x))
Eq(F_18(x), -F_157(x) + F_19(x))
Eq(F_19(x), F_20(x)/F_12(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x) + F_5(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_129(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_0(x)*F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x)/(F_12(x)*F_37(x)))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_10(x)*F_12(x)*F_33(x)*F_37(x))
Eq(F_33(x), F_34(x)/(F_0(x)*F_12(x)*F_37(x)))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x) + F_45(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_1(x) + F_12(x))
Eq(F_42(x), F_38(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_38(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_31(x) + F_48(x))
Eq(F_48(x), F_37(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), x**2*F_52(x)**3 - x*(x - 1)*F_52(x)**2 + 1)
Eq(F_53(x), F_12(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_64(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_52(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_58(x)*F_61(x))
Eq(F_61(x), F_52(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_12(x)*F_52(x)**2)
Eq(F_64(x), -F_58(x) + F_65(x))
Eq(F_65(x), F_66(x)/(F_12(x)*F_4(x)))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x) - F_78(x))
Eq(F_68(x), F_69(x)/F_12(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), -F_2(x) + F_71(x))
Eq(F_71(x), -F_0(x) + F_72(x))
Eq(F_72(x), F_0(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_12(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_2(x) + F_6(x))
Eq(F_78(x), F_75(x) - F_79(x))
Eq(F_79(x), F_80(x) - F_82(x))
Eq(F_80(x), F_81(x)/F_12(x))
Eq(F_81(x), F_77(x))
Eq(F_82(x), F_127(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_88(x))
Eq(F_84(x), F_85(x)/F_12(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), -F_2(x) + F_87(x))
Eq(F_87(x), F_10(x) - F_52(x))
Eq(F_88(x), F_124(x) + F_89(x))
Eq(F_89(x), F_90(x) - F_97(x))
Eq(F_90(x), F_91(x)/F_12(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), -F_2(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_12(x))
Eq(F_96(x), F_87(x))
Eq(F_97(x), F_95(x) - F_98(x))
Eq(F_98(x), -F_101(x) + F_99(x))
Eq(F_99(x), F_100(x)/F_12(x))
Eq(F_100(x), F_87(x))
Eq(F_101(x), F_102(x) + F_124(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x)/F_12(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) + F_9(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_111(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_2(x))
Eq(F_110(x), F_0(x)*F_2(x))
Eq(F_111(x), F_112(x)/(F_0(x)*F_12(x)))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x) + F_67(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_4(x)*F_67(x))
Eq(F_118(x), F_0(x)*F_119(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_12(x)*F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_123(x))
Eq(F_122(x), F_52(x)*F_65(x))
Eq(F_123(x), F_53(x)*F_58(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_104(x)*F_12(x)*F_126(x))
Eq(F_126(x), x**2*(F_126(x) + 1)**3 - x*(x - 1)*(F_126(x) + 1)**2)
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_119(x)*F_12(x))
Eq(F_129(x), F_130(x) - F_143(x))
Eq(F_130(x), F_131(x) - F_133(x))
Eq(F_131(x), F_132(x)/F_12(x))
Eq(F_132(x), F_6(x))
Eq(F_133(x), F_110(x) + F_134(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_137(x) + F_140(x))
Eq(F_137(x), F_138(x)*F_2(x))
Eq(F_138(x), F_139(x)/F_12(x))
Eq(F_139(x), F_5(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_0(x)*F_142(x)*F_49(x))
Eq(F_142(x), F_52(x) + F_93(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_12(x)*F_145(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_149(x))
Eq(F_148(x), F_16(x)*F_52(x))
Eq(F_149(x), F_150(x)*F_52(x)*F_53(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_0(x)**2*F_10(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_0(x)**2*F_12(x)*F_154(x)*F_58(x))
Eq(F_154(x), F_155(x)/F_64(x))
Eq(F_155(x), F_111(x) - F_156(x))
Eq(F_156(x), F_33(x)*F_58(x))
Eq(F_157(x), F_158(x) - F_160(x))
Eq(F_158(x), F_159(x)/F_12(x))
Eq(F_159(x), F_22(x))
Eq(F_160(x), F_0(x)*F_10(x)*F_2(x))
Eq(F_161(x), F_150(x)*F_53(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"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.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": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": 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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "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": 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"pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 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"tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "indices": [0, 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": "Rule", "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]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "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], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "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}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 3], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 2], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 4], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[2, 0]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": 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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25138/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[0,x]*F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[60,x]
F[15,x] = F[16,x]*F[56,x]
F[16,x] = 1/F[11,x]/F[31,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[0,x]*F[11,x]*F[19,x]*F[31,x]
F[19,x] = F[20,x]+F[22,x]
F[20,x] = 1/F[11,x]*F[21,x]
F[21,x] = F[2,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]*F[20,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = 1+x^2*F[25,x]^3+(-x^2+x)*F[25,x]^2
F[26,x] = F[27,x]
F[27,x] = F[11,x]*F[28,x]
F[28,x] = F[29,x,1]
F[29,x,k[0]] = (F[30,x,k[0]]*k[0]-F[30,x,1])/(-1+k[0])
F[30,x,k[0]] = (1+x*F[30,x,k[0]]*(F[30,x,k[0]]-1)*k[0])*(x*F[30,x,k[0]]*k[0]+1)
F[31,x] = F[32,x]+F[40,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[1,x]+F[11,x]
F[37,x] = F[33,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[11,x]*F[33,x]
F[40,x] = F[41,x]
F[41,x] = F[11,x]*F[32,x]*F[42,x]
F[42,x] = F[43,x,1]
F[43,x,k[0]] = (F[44,x,k[0]]*k[0]-F[44,x,1])/(-1+k[0])
F[44,x,k[0]] = F[45,x,k[0]]+F[54,x,k[0]]
F[45,x,k[0]] = F[1,x]+F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]*F[49,x,k[0]]
F[48,x,k[0]] = k[0]*x
F[49,x,k[0]] = F[50,x,k[0]]+F[51,x,k[0]]
F[50,x,k[0]] = F[1,x]+F[48,x,k[0]]
F[51,x,k[0]] = F[46,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[46,x,k[0]]*F[48,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[11,x]*F[43,x,k[0]]*F[45,x,k[0]]
F[56,x] = F[57,x,1]
F[58,x,k[0]] = F[48,x,k[0]]*F[57,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = k[0]*x*(1+F[59,x,k[0]])^2*(x*F[59,x,k[0]]*k[0]+1)
F[60,x] = F[61,x]
F[61,x] = F[0,x]*F[62,x]*F[65,x]
F[62,x] = F[63,x]+F[9,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[25,x]*F[9,x]
F[65,x] = F[66,x]
F[66,x] = F[11,x]*F[67,x]
F[67,x] = F[68,x,1]
F[68,x,k[0]] = (F[57,x,k[0]]*k[0]-F[57,x,1])/(-1+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_{11}\! \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 \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{60}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{56}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{11}\! \left(x \right) F_{31}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{0}\! \left(x \right) F_{11}\! \left(x \right) F_{19}\! \left(x \right) F_{31}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{2}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = x^{2} F_{25} \left(x \right)^{3}-x^{2} F_{25} \left(x \right)^{2}+x F_{25} \left(x \right)^{2}+1
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \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) = -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}
F_{30}\! \left(x , y\right) = y^{2} x^{2} F_{30}\! \left(x , y\right)^{3}-x^{2} F_{30}\! \left(x , y\right)^{2} y^{2}+y x F_{30}\! \left(x , y\right)^{2}+1
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{40}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{33}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = -\frac{-F_{44}\! \left(x , y\right) y +F_{44}\! \left(x , 1\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = y x
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{46}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{43}\! \left(x , y\right) F_{45}\! \left(x , y\right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = F_{48}\! \left(x , y\right) F_{57}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = x^{2} F_{59}\! \left(x , y\right)^{3} y^{2}+2 x^{2} F_{59}\! \left(x , y\right)^{2} y^{2}+x^{2} F_{59}\! \left(x , y\right) y^{2}+x F_{59}\! \left(x , y\right)^{2} y +2 x F_{59}\! \left(x , y\right) y +y x
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{0}\! \left(x \right) F_{62}\! \left(x \right) F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{9}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x , 1\right)
F_{68}\! \left(x , y\right) = -\frac{-y F_{57}\! \left(x , y\right)+F_{57}\! \left(x , 1\right)}{-1+y}
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_11(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_0(x)*F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_60(x))
Eq(F_15(x), F_16(x)*F_56(x))
Eq(F_16(x), F_17(x)/(F_11(x)*F_31(x)))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_0(x)*F_11(x)*F_19(x)*F_31(x))
Eq(F_19(x), F_20(x) + F_22(x))
Eq(F_20(x), F_21(x)/F_11(x))
Eq(F_21(x), F_2(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_20(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), x**2*F_25(x)**3 - x*(x - 1)*F_25(x)**2 + 1)
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_11(x)*F_28(x))
Eq(F_28(x), F_29(x, 1))
Eq(F_29(x, k_0), (-k_0*F_30(x, k_0) + F_30(x, 1))/(1 - k_0))
Eq(F_30(x, k_0), k_0**2*x**2*F_30(x, k_0)**3 - k_0*x*(k_0*x - 1)*F_30(x, k_0)**2 + 1)
Eq(F_31(x), F_32(x) + F_40(x))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_1(x) + F_11(x))
Eq(F_37(x), F_33(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_11(x)*F_33(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_11(x)*F_32(x)*F_42(x))
Eq(F_42(x), F_43(x, 1))
Eq(F_43(x, k_0), (-k_0*F_44(x, k_0) + F_44(x, 1))/(1 - k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_54(x, k_0))
Eq(F_45(x, k_0), F_1(x) + F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0)*F_49(x, k_0))
Eq(F_48(x, k_0), k_0*x)
Eq(F_49(x, k_0), F_50(x, k_0) + F_51(x, k_0))
Eq(F_50(x, k_0), F_1(x) + F_48(x, k_0))
Eq(F_51(x, k_0), F_46(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_46(x, k_0)*F_48(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_11(x)*F_43(x, k_0)*F_45(x, k_0))
Eq(F_56(x), F_57(x, 1))
Eq(F_58(x, k_0), F_48(x, k_0)*F_57(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), k_0**2*x**2*(F_59(x, k_0) + 1)**3 - k_0*x*(k_0*x - 1)*(F_59(x, k_0) + 1)**2)
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_0(x)*F_62(x)*F_65(x))
Eq(F_62(x), F_63(x) + F_9(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_25(x)*F_9(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_11(x)*F_67(x))
Eq(F_67(x), F_68(x, 1))
Eq(F_68(x, k_0), (-k_0*F_57(x, k_0) + F_57(x, 1))/(1 - k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "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": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, "idx": 1}, {"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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 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