02314_02341_02431_03214_03241_03421_04231_04321_20314_20341_20431
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2567, 12826, 64770, 329549, 1685981, 8661144, 44634278, 230584632, 1193543777, 6187646990, 32119177351, 166899948827, 868007111240, 4517560151436, 23526027114474, 122579257739147, 638963691128040, 3331953909638794, 17380521506529033, 90687770290105953, 473304709942845781, 2470731938388003043, 12900057915138646591, 67364192256644767625, 351827303613570593221, 1837746856806640965858, 9600442611879775720793, 50158064414697564600672, 262077329360695830780030, 1369471936841624728754432, 7156623206420434363754879, 37401694251251181168057818, 195478798888645815973960307, 1021717411230282462600164476, 5340506421957066303379500972, 27915963443301052217725533721, 145928314517020466535174162805, 762854482087811596394840911338, 3988022682909996630083608945750, 20849039748607991166249720041276, 108999845582072165257755279021917, 569870372303993272360714234260618, 2979447442911145364412885754436829, 15577724125947642615504525468177971, 81447952594478472084618426927737590, 425856759303954065732884255517261814, 2226658003752493313094825075796918156, 11642588252151912474714415865022787209, 60876700356421816452140025774967348130, 318315481045478431458599371668643988648, 1664443632681538858583427500418053482927, 8703315384932156141302139175715075359275, 45509734813445042232852285929739260065513, 237972913919611157680665961096701156434289, 1244383104002806108901982431965598940167737, 6507044468453957799674358060176339687653841, 34026422927401722914760440536210463399252957, 177930930305171896528669128116899167293854699, 930441418710112719636629493116011390214781745, 4865515578630303709598562075059550385338403083, 25443144127342375800071306804978962119402596609, 133049918022481804705924537650854969767657076551, 695761229063551912381627448998544838617875553195, 3638375223069969472772322263452607845713595995647, 19026384724067305070832973846171494871128006283317, 99496196453907561849547463907501253166718378597286, 520304996958157834988160560039911498599736239110445, 2720888427761166486729620030402042393310030214548936, 14228679650590946594400897449569436395696010967622078, 74407980996358002319550673426618753571698158201669422, 389112708824972942014498378217708407188330003257998387, 2034849145285533500234394287943544938052404488096460000, 10641181835103302233609282584624981640471683845127568245, 55647837956123405064323623170693418199492613777360433239, 291009694725880255297897881703092196470073103965413252872, 1521834057239680528905075512160707230819090267273079217880, 7958436836929839157952373042000078350568566740957307398188, 41618731430318217386526417128798294028902514008998975594513, 217645881167957221238637249466436337547412375644496752854994, 1138184270571577241984719747163003479687683344867547464911197, 5952168044533735665031653129851884901817347506688048911999255, 31127069403380105249293721122152867188736321879939042508274203, 162780245788137457327554930210722000070486219172472865002310650, 851266521501024029039685800444047417894772734705366774684679865, 4451739777283944489248318639935044942837450182535036563900252428, 23280608343389070335229129612281670986977291604032673108247192837, 121747259798649446829732864486284860217016876704986117087813961675, 636684622987054812277752161629870253236529602551586751087537503368, 3329582673110133800883582660507062458944458513356744667838051326122, 17412274400864616990591286087436469122112065697023308677440092343447, 91058699535729520667985121983623272756810427733638328689321485697967, 476198047289877302145351886956071821159263052625154485449098191884807, 2490313299044874843607290498029314601437275397123284185370067188094168, 13023285548796884722528871356123335135952298648251675981586420293396322
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24372/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (x*F[6,x]+x-1)*(x*F[6,x]+x-2*F[6,x])
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[16,x]+F[13,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[5,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[4,x]
F[18,x] = 1/F[15,x]/F[66,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[199,x]+F[21,x]
F[21,x] = -F[198,x]+F[22,x]
F[22,x] = F[197,x]+F[23,x]
F[23,x] = F[24,x]+F[26,x]
F[24,x] = F[25,x]*F[6,x]
F[25,x] = F[1,x]+F[15,x]
F[26,x] = F[27,x]
F[27,x] = F[15,x]*F[28,x]
F[28,x] = F[196,x]+F[29,x]
F[29,x] = F[190,x]+F[30,x]
F[30,x] = F[31,x]*F[6,x]
F[31,x] = -F[185,x]+F[32,x]
F[32,x] = -F[180,x]+F[33,x]
F[33,x] = 1/F[15,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[24,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[38,x]
F[38,x] = F[175,x]+F[39,x]
F[39,x] = F[10,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[15,x]*F[4,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = -F[170,x]+F[44,x]
F[44,x] = -F[47,x]+F[45,x]
F[45,x] = 1/F[15,x]*F[46,x]
F[46,x] = F[16,x]
F[47,x] = F[48,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[15,x]*F[50,x]
F[50,x] = F[16,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = -F[53,x]+F[18,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[15,x]*F[6,x]
F[57,x] = F[58,x]
F[58,x] = F[15,x]*F[59,x]
F[59,x] = F[166,x]+F[60,x]
F[60,x] = F[149,x]+F[61,x]
F[61,x] = F[6,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[15,x]*F[64,x]
F[64,x] = F[65,x]+F[69,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = -1+(x^2-2*x)*F[66,x]^2+(2+x)*F[66,x]
F[67,x] = F[68,x]
F[68,x] = F[15,x]*F[42,x]
F[69,x] = 1/F[15,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[56,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[15,x]*F[74,x]
F[74,x] = F[122,x]+F[75,x]
F[75,x] = F[61,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[118,x]*F[120,x]*F[15,x]*F[78,x]
F[78,x] = F[66,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[15,x]*F[66,x]*F[81,x]
F[81,x] = F[11,x]+F[82,x]
F[82,x] = -F[117,x]+F[83,x]
F[83,x] = 1/F[15,x]/F[66,x]*F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[24,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[15,x]*F[88,x]
F[88,x] = F[116,x]+F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[6,x]*F[78,x]
F[91,x] = F[66,x]*F[92,x]
F[92,x] = -F[66,x]+F[93,x]
F[93,x] = 1/F[108,x]*F[94,x]
F[94,x] = -F[100,x]+F[95,x]
F[95,x] = 1/F[15,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = -F[0,x]+F[98,x]
F[98,x] = 1/F[15,x]*F[99,x]
F[99,x] = F[2,x]
F[100,x] = -F[104,x]+F[101,x]
F[101,x] = 1/F[15,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = -F[6,x]+F[97,x]
F[104,x] = F[105,x]*F[93,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[15,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[1,x]+F[105,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[15,x]
F[112,x] = F[1,x]+F[110,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[15,x]
F[115,x] = F[105,x]+F[113,x]
F[116,x] = F[15,x]*F[6,x]*F[78,x]
F[117,x] = F[11,x]*F[25,x]
F[118,x] = 1/F[11,x]/F[15,x]*F[119,x]
F[119,x] = F[82,x]
F[120,x] = F[121,x]
F[121,x] = F[15,x]*F[65,x]
F[122,x] = F[123,x]+F[132,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[15,x]*F[66,x]
F[125,x] = F[126,x]
F[126,x] = -F[130,x]+F[127,x]
F[127,x] = 1/F[15,x]*F[128,x]
F[128,x] = F[129,x]
F[129,x] = F[15,x]*F[18,x]
F[130,x] = 1/F[15,x]*F[131,x]
F[131,x] = F[21,x]
F[132,x] = F[133,x]*F[6,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[15,x]
F[135,x] = -F[138,x]+F[136,x]
F[136,x] = 1/F[15,x]*F[137,x]
F[137,x] = F[67,x]
F[138,x] = -F[142,x]+F[139,x]
F[139,x] = 1/F[15,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = -F[6,x]+F[67,x]
F[142,x] = -F[76,x]+F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[145,x]*F[15,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[118,x]*F[42,x]
F[147,x] = F[148,x]
F[148,x] = F[11,x]*F[118,x]*F[120,x]
F[149,x] = F[150,x]
F[150,x] = F[15,x]*F[151,x]*F[66,x]
F[151,x] = -F[165,x]+F[152,x]
F[152,x] = 1/F[15,x]*F[153,x]
F[153,x] = F[154,x]
F[154,x] = F[15,x]*F[155,x]
F[155,x] = F[156,x]+F[164,x]
F[156,x] = F[120,x]*F[157,x]
F[157,x] = F[158,x]+F[163,x]
F[158,x] = 1/F[15,x]*F[159,x]
F[159,x] = F[160,x]
F[160,x] = F[161,x]+F[67,x]
F[161,x] = F[162,x]
F[162,x] = F[142,x]*F[15,x]
F[163,x] = -F[130,x]+F[18,x]
F[164,x] = F[165,x]
F[165,x] = F[53,x]*F[66,x]
F[166,x] = F[167,x]
F[167,x] = F[132,x]+F[168,x]
F[168,x] = F[169,x]
F[169,x] = F[15,x]*F[53,x]*F[66,x]
F[170,x] = F[171,x]
F[171,x] = -F[172,x]+F[45,x]
F[172,x] = -F[173,x]+F[49,x]
F[173,x] = F[174,x]
F[174,x] = F[163,x]*F[4,x]
F[175,x] = F[176,x]
F[176,x] = F[11,x]*F[177,x]
F[177,x] = F[178,x]
F[178,x] = F[15,x]*F[179,x]
F[179,x] = F[2,x]+F[5,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[15,x]*F[93,x]
F[183,x] = F[184,x]
F[184,x] = F[15,x]*F[179,x]*F[93,x]
F[185,x] = -F[62,x]+F[186,x]
F[186,x] = -F[189,x]+F[187,x]
F[187,x] = 1/F[15,x]*F[188,x]
F[188,x] = F[36,x]
F[189,x] = F[183,x]
F[190,x] = F[191,x]
F[191,x] = F[15,x]*F[192,x]
F[192,x] = F[193,x]+F[195,x]
F[193,x] = F[147,x]+F[194,x]
F[194,x] = F[118,x]*F[42,x]*F[66,x]
F[195,x] = F[66,x]^2*F[163,x]
F[196,x] = F[122,x]
F[197,x] = F[55,x]
F[198,x] = F[71,x]
F[199,x] = F[200,x]
F[200,x] = F[15,x]*F[201,x]
F[201,x] = F[202,x]+F[205,x]
F[202,x] = F[203,x]+F[204,x]
F[203,x] = F[67,x]*F[78,x]
F[204,x] = F[66,x]*F[69,x]
F[205,x] = F[55,x]*F[78,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_{15}\! \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_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{199}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{198}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{197}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{196}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{190}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{185}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{180}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{175}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{170}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{16}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{16}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{18}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{166}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{149}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{6}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = x^{2} F_{66} \left(x \right)^{2}-2 x F_{66} \left(x \right)^{2}+F_{66}\! \left(x \right) x +2 F_{66}\! \left(x \right)-1
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{56}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{122}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{61}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{118}\! \left(x \right) F_{120}\! \left(x \right) F_{15}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{66}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{11}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = \frac{F_{84}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{24}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{15}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{116}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{6}\! \left(x \right) F_{78}\! \left(x \right)
F_{91}\! \left(x \right) = F_{66}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{108}\! \left(x \right)}
F_{94}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{2}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{97}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{93}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{15}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{1}\! \left(x \right)+F_{105}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{15}\! \left(x \right)
F_{112}\! \left(x \right) = F_{1}\! \left(x \right)+F_{110}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{15}\! \left(x \right)
F_{115}\! \left(x \right) = F_{105}\! \left(x \right)+F_{113}\! \left(x \right)
F_{116}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right) F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{118}\! \left(x \right) = \frac{F_{119}\! \left(x \right)}{F_{11}\! \left(x \right) F_{15}\! \left(x \right)}
F_{119}\! \left(x \right) = F_{82}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{15}\! \left(x \right) F_{65}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{132}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = \frac{F_{128}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{21}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{6}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{15}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{138}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{67}\! \left(x \right)
F_{138}\! \left(x \right) = -F_{142}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{67}\! \left(x \right)
F_{142}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{15}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{118}\! \left(x \right) F_{42}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{11}\! \left(x \right) F_{118}\! \left(x \right) F_{120}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{15}\! \left(x \right) F_{151}\! \left(x \right) F_{66}\! \left(x \right)
F_{151}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = \frac{F_{153}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{15}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{164}\! \left(x \right)
F_{156}\! \left(x \right) = F_{120}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{163}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{67}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{142}\! \left(x \right) F_{15}\! \left(x \right)
F_{163}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{18}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{53}\! \left(x \right) F_{66}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{132}\! \left(x \right)+F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{66}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = -F_{172}\! \left(x \right)+F_{45}\! \left(x \right)
F_{172}\! \left(x \right) = -F_{173}\! \left(x \right)+F_{49}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{163}\! \left(x \right) F_{4}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{11}\! \left(x \right) F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{15}\! \left(x \right) F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{15}\! \left(x \right) F_{93}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{15}\! \left(x \right) F_{179}\! \left(x \right) F_{93}\! \left(x \right)
F_{185}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = \frac{F_{188}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{188}\! \left(x \right) = F_{36}\! \left(x \right)
F_{189}\! \left(x \right) = F_{183}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{15}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{195}\! \left(x \right)
F_{193}\! \left(x \right) = F_{147}\! \left(x \right)+F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{118}\! \left(x \right) F_{42}\! \left(x \right) F_{66}\! \left(x \right)
F_{195}\! \left(x \right) = F_{66} \left(x \right)^{2} F_{163}\! \left(x \right)
F_{196}\! \left(x \right) = F_{122}\! \left(x \right)
F_{197}\! \left(x \right) = F_{55}\! \left(x \right)
F_{198}\! \left(x \right) = F_{71}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{15}\! \left(x \right) F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{205}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)+F_{204}\! \left(x \right)
F_{203}\! \left(x \right) = F_{67}\! \left(x \right) F_{78}\! \left(x \right)
F_{204}\! \left(x \right) = F_{66}\! \left(x \right) F_{69}\! \left(x \right)
F_{205}\! \left(x \right) = F_{55}\! \left(x \right) F_{78}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x*(x - 2)*(F_6(x) + 1)**2 + (x + 1)*(F_6(x) + 1) + F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_5(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_4(x))
Eq(F_18(x), F_19(x)/(F_15(x)*F_66(x)))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_199(x) + F_21(x))
Eq(F_21(x), -F_198(x) + F_22(x))
Eq(F_22(x), F_197(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_26(x))
Eq(F_24(x), F_25(x)*F_6(x))
Eq(F_25(x), F_1(x) + F_15(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_15(x)*F_28(x))
Eq(F_28(x), F_196(x) + F_29(x))
Eq(F_29(x), F_190(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_6(x))
Eq(F_31(x), -F_185(x) + F_32(x))
Eq(F_32(x), -F_180(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_15(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_24(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_38(x))
Eq(F_38(x), F_175(x) + F_39(x))
Eq(F_39(x), F_10(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_4(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), -F_170(x) + F_44(x))
Eq(F_44(x), F_45(x) - F_47(x))
Eq(F_45(x), F_46(x)/F_15(x))
Eq(F_46(x), F_16(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_15(x))
Eq(F_50(x), F_16(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_18(x) - F_53(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_15(x)*F_6(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_15(x)*F_59(x))
Eq(F_59(x), F_166(x) + F_60(x))
Eq(F_60(x), F_149(x) + F_61(x))
Eq(F_61(x), F_6(x)*F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_15(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_69(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), x*(x - 2)*F_66(x)**2 + (x + 2)*F_66(x) - 1)
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_15(x)*F_42(x))
Eq(F_69(x), F_70(x)/F_15(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_56(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_15(x)*F_74(x))
Eq(F_74(x), F_122(x) + F_75(x))
Eq(F_75(x), F_61(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_118(x)*F_120(x)*F_15(x)*F_78(x))
Eq(F_78(x), F_66(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_15(x)*F_66(x)*F_81(x))
Eq(F_81(x), F_11(x) + F_82(x))
Eq(F_82(x), -F_117(x) + F_83(x))
Eq(F_83(x), F_84(x)/(F_15(x)*F_66(x)))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_24(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_15(x)*F_88(x))
Eq(F_88(x), F_116(x) + F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_6(x)*F_78(x))
Eq(F_91(x), F_66(x)*F_92(x))
Eq(F_92(x), -F_66(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_108(x))
Eq(F_94(x), -F_100(x) + F_95(x))
Eq(F_95(x), F_96(x)/F_15(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), -F_0(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_15(x))
Eq(F_99(x), F_2(x))
Eq(F_100(x), F_101(x) - F_104(x))
Eq(F_101(x), F_102(x)/F_15(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), -F_6(x) + F_97(x))
Eq(F_104(x), F_105(x)*F_93(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_15(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_1(x) + F_105(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_15(x))
Eq(F_112(x), F_1(x) + F_110(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_15(x))
Eq(F_115(x), F_105(x) + F_113(x))
Eq(F_116(x), F_15(x)*F_6(x)*F_78(x))
Eq(F_117(x), F_11(x)*F_25(x))
Eq(F_118(x), F_119(x)/(F_11(x)*F_15(x)))
Eq(F_119(x), F_82(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_15(x)*F_65(x))
Eq(F_122(x), F_123(x) + F_132(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_15(x)*F_66(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x) - F_130(x))
Eq(F_127(x), F_128(x)/F_15(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_15(x)*F_18(x))
Eq(F_130(x), F_131(x)/F_15(x))
Eq(F_131(x), F_21(x))
Eq(F_132(x), F_133(x)*F_6(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_15(x))
Eq(F_135(x), F_136(x) - F_138(x))
Eq(F_136(x), F_137(x)/F_15(x))
Eq(F_137(x), F_67(x))
Eq(F_138(x), F_139(x) - F_142(x))
Eq(F_139(x), F_140(x)/F_15(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), -F_6(x) + F_67(x))
Eq(F_142(x), F_143(x) - F_76(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_145(x)*F_15(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_118(x)*F_42(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_11(x)*F_118(x)*F_120(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_15(x)*F_151(x)*F_66(x))
Eq(F_151(x), F_152(x) - F_165(x))
Eq(F_152(x), F_153(x)/F_15(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_15(x)*F_155(x))
Eq(F_155(x), F_156(x) + F_164(x))
Eq(F_156(x), F_120(x)*F_157(x))
Eq(F_157(x), F_158(x) + F_163(x))
Eq(F_158(x), F_159(x)/F_15(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_161(x) + F_67(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_142(x)*F_15(x))
Eq(F_163(x), -F_130(x) + F_18(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_53(x)*F_66(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_132(x) + F_168(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_15(x)*F_53(x)*F_66(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), -F_172(x) + F_45(x))
Eq(F_172(x), -F_173(x) + F_49(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_163(x)*F_4(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_11(x)*F_177(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_15(x)*F_179(x))
Eq(F_179(x), F_2(x) + F_5(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_15(x)*F_93(x))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_15(x)*F_179(x)*F_93(x))
Eq(F_185(x), F_186(x) - F_62(x))
Eq(F_186(x), F_187(x) - F_189(x))
Eq(F_187(x), F_188(x)/F_15(x))
Eq(F_188(x), F_36(x))
Eq(F_189(x), F_183(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_15(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_195(x))
Eq(F_193(x), F_147(x) + F_194(x))
Eq(F_194(x), F_118(x)*F_42(x)*F_66(x))
Eq(F_195(x), F_163(x)*F_66(x)**2)
Eq(F_196(x), F_122(x))
Eq(F_197(x), F_55(x))
Eq(F_198(x), F_71(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_15(x)*F_201(x))
Eq(F_201(x), F_202(x) + F_205(x))
Eq(F_202(x), F_203(x) + F_204(x))
Eq(F_203(x), F_67(x)*F_78(x))
Eq(F_204(x), F_66(x)*F_69(x))
Eq(F_205(x), F_55(x)*F_78(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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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, 1, 4], "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, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], 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0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"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.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], 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[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], 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"pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [1, 3], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 3], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[1, 3]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[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": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "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, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "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": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25118/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (x*F[6,x]+x-2*F[6,x])*(x*F[6,x]+x-1)
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[16,x]+F[13,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[5,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[4,x]
F[18,x] = 1/F[15,x]/F[66,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[199,x]+F[21,x]
F[21,x] = -F[198,x]+F[22,x]
F[22,x] = F[197,x]+F[23,x]
F[23,x] = F[24,x]+F[26,x]
F[24,x] = F[25,x]*F[6,x]
F[25,x] = F[1,x]+F[15,x]
F[26,x] = F[27,x]
F[27,x] = F[15,x]*F[28,x]
F[28,x] = F[196,x]+F[29,x]
F[29,x] = F[190,x]+F[30,x]
F[30,x] = F[31,x]*F[6,x]
F[31,x] = -F[185,x]+F[32,x]
F[32,x] = -F[180,x]+F[33,x]
F[33,x] = 1/F[15,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[24,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[38,x]
F[38,x] = F[175,x]+F[39,x]
F[39,x] = F[10,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[15,x]*F[4,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = -F[170,x]+F[44,x]
F[44,x] = -F[47,x]+F[45,x]
F[45,x] = 1/F[15,x]*F[46,x]
F[46,x] = F[16,x]
F[47,x] = F[48,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[15,x]*F[50,x]
F[50,x] = F[16,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = -F[53,x]+F[18,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[15,x]*F[6,x]
F[57,x] = F[58,x]
F[58,x] = F[15,x]*F[59,x]
F[59,x] = F[166,x]+F[60,x]
F[60,x] = F[149,x]+F[61,x]
F[61,x] = F[6,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[15,x]*F[64,x]
F[64,x] = F[65,x]+F[69,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = -1+(x^2-2*x)*F[66,x]^2+(2+x)*F[66,x]
F[67,x] = F[68,x]
F[68,x] = F[15,x]*F[42,x]
F[69,x] = 1/F[15,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[56,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[15,x]*F[74,x]
F[74,x] = F[122,x]+F[75,x]
F[75,x] = F[61,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[118,x]*F[120,x]*F[15,x]*F[78,x]
F[78,x] = F[66,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[15,x]*F[66,x]*F[81,x]
F[81,x] = F[11,x]+F[82,x]
F[82,x] = -F[117,x]+F[83,x]
F[83,x] = 1/F[15,x]/F[66,x]*F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[24,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[15,x]*F[88,x]
F[88,x] = F[116,x]+F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[6,x]*F[78,x]
F[91,x] = F[66,x]*F[92,x]
F[92,x] = -F[66,x]+F[93,x]
F[93,x] = 1/F[108,x]*F[94,x]
F[94,x] = -F[100,x]+F[95,x]
F[95,x] = 1/F[15,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = -F[0,x]+F[98,x]
F[98,x] = 1/F[15,x]*F[99,x]
F[99,x] = F[2,x]
F[100,x] = -F[104,x]+F[101,x]
F[101,x] = 1/F[15,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = -F[6,x]+F[97,x]
F[104,x] = F[105,x]*F[93,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[15,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[1,x]+F[105,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[15,x]
F[112,x] = F[1,x]+F[110,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[15,x]
F[115,x] = F[105,x]+F[113,x]
F[116,x] = F[15,x]*F[6,x]*F[78,x]
F[117,x] = F[11,x]*F[25,x]
F[118,x] = 1/F[11,x]/F[15,x]*F[119,x]
F[119,x] = F[82,x]
F[120,x] = F[121,x]
F[121,x] = F[15,x]*F[65,x]
F[122,x] = F[123,x]+F[132,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[15,x]*F[66,x]
F[125,x] = F[126,x]
F[126,x] = -F[130,x]+F[127,x]
F[127,x] = 1/F[15,x]*F[128,x]
F[128,x] = F[129,x]
F[129,x] = F[15,x]*F[18,x]
F[130,x] = 1/F[15,x]*F[131,x]
F[131,x] = F[21,x]
F[132,x] = F[133,x]*F[6,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[15,x]
F[135,x] = -F[138,x]+F[136,x]
F[136,x] = 1/F[15,x]*F[137,x]
F[137,x] = F[67,x]
F[138,x] = -F[142,x]+F[139,x]
F[139,x] = 1/F[15,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = -F[6,x]+F[67,x]
F[142,x] = -F[76,x]+F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[145,x]*F[15,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[118,x]*F[42,x]
F[147,x] = F[148,x]
F[148,x] = F[11,x]*F[118,x]*F[120,x]
F[149,x] = F[150,x]
F[150,x] = F[15,x]*F[151,x]*F[66,x]
F[151,x] = -F[165,x]+F[152,x]
F[152,x] = 1/F[15,x]*F[153,x]
F[153,x] = F[154,x]
F[154,x] = F[15,x]*F[155,x]
F[155,x] = F[156,x]+F[164,x]
F[156,x] = F[120,x]*F[157,x]
F[157,x] = F[158,x]+F[163,x]
F[158,x] = 1/F[15,x]*F[159,x]
F[159,x] = F[160,x]
F[160,x] = F[161,x]+F[67,x]
F[161,x] = F[162,x]
F[162,x] = F[142,x]*F[15,x]
F[163,x] = -F[130,x]+F[18,x]
F[164,x] = F[165,x]
F[165,x] = F[53,x]*F[66,x]
F[166,x] = F[167,x]
F[167,x] = F[132,x]+F[168,x]
F[168,x] = F[169,x]
F[169,x] = F[15,x]*F[53,x]*F[66,x]
F[170,x] = F[171,x]
F[171,x] = -F[172,x]+F[45,x]
F[172,x] = -F[173,x]+F[49,x]
F[173,x] = F[174,x]
F[174,x] = F[163,x]*F[4,x]
F[175,x] = F[176,x]
F[176,x] = F[11,x]*F[177,x]
F[177,x] = F[178,x]
F[178,x] = F[15,x]*F[179,x]
F[179,x] = F[2,x]+F[5,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]+F[183,x]
F[182,x] = F[15,x]*F[93,x]
F[183,x] = F[184,x]
F[184,x] = F[15,x]*F[179,x]*F[93,x]
F[185,x] = -F[62,x]+F[186,x]
F[186,x] = -F[189,x]+F[187,x]
F[187,x] = 1/F[15,x]*F[188,x]
F[188,x] = F[36,x]
F[189,x] = F[183,x]
F[190,x] = F[191,x]
F[191,x] = F[15,x]*F[192,x]
F[192,x] = F[193,x]+F[195,x]
F[193,x] = F[147,x]+F[194,x]
F[194,x] = F[118,x]*F[42,x]*F[66,x]
F[195,x] = F[66,x]^2*F[163,x]
F[196,x] = F[122,x]
F[197,x] = F[55,x]
F[198,x] = F[71,x]
F[199,x] = F[200,x]
F[200,x] = F[15,x]*F[201,x]
F[201,x] = F[202,x]+F[205,x]
F[202,x] = F[203,x]+F[204,x]
F[203,x] = F[67,x]*F[78,x]
F[204,x] = F[66,x]*F[69,x]
F[205,x] = F[55,x]*F[78,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_{15}\! \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_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{199}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{198}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{197}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{196}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{190}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{185}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{180}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{175}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{170}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{16}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{16}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{18}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{166}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{149}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{6}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = x^{2} F_{66} \left(x \right)^{2}-2 x F_{66} \left(x \right)^{2}+F_{66}\! \left(x \right) x +2 F_{66}\! \left(x \right)-1
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{56}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{122}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{61}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{118}\! \left(x \right) F_{120}\! \left(x \right) F_{15}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{66}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{11}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = \frac{F_{84}\! \left(x \right)}{F_{15}\! \left(x \right) F_{66}\! \left(x \right)}
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{24}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{15}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{116}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{6}\! \left(x \right) F_{78}\! \left(x \right)
F_{91}\! \left(x \right) = F_{66}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{108}\! \left(x \right)}
F_{94}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{2}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{97}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{93}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{15}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{1}\! \left(x \right)+F_{105}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{15}\! \left(x \right)
F_{112}\! \left(x \right) = F_{1}\! \left(x \right)+F_{110}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{15}\! \left(x \right)
F_{115}\! \left(x \right) = F_{105}\! \left(x \right)+F_{113}\! \left(x \right)
F_{116}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right) F_{78}\! \left(x \right)
F_{117}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{118}\! \left(x \right) = \frac{F_{119}\! \left(x \right)}{F_{11}\! \left(x \right) F_{15}\! \left(x \right)}
F_{119}\! \left(x \right) = F_{82}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{15}\! \left(x \right) F_{65}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{132}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = \frac{F_{128}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{21}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{6}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{15}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{138}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{67}\! \left(x \right)
F_{138}\! \left(x \right) = -F_{142}\! \left(x \right)+F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{67}\! \left(x \right)
F_{142}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{15}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{118}\! \left(x \right) F_{42}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{11}\! \left(x \right) F_{118}\! \left(x \right) F_{120}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{15}\! \left(x \right) F_{151}\! \left(x \right) F_{66}\! \left(x \right)
F_{151}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = \frac{F_{153}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{15}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{164}\! \left(x \right)
F_{156}\! \left(x \right) = F_{120}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{163}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{67}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{142}\! \left(x \right) F_{15}\! \left(x \right)
F_{163}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{18}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{53}\! \left(x \right) F_{66}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{132}\! \left(x \right)+F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{66}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = -F_{172}\! \left(x \right)+F_{45}\! \left(x \right)
F_{172}\! \left(x \right) = -F_{173}\! \left(x \right)+F_{49}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{163}\! \left(x \right) F_{4}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{11}\! \left(x \right) F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{15}\! \left(x \right) F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{183}\! \left(x \right)
F_{182}\! \left(x \right) = F_{15}\! \left(x \right) F_{93}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)
F_{184}\! \left(x \right) = F_{15}\! \left(x \right) F_{179}\! \left(x \right) F_{93}\! \left(x \right)
F_{185}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = \frac{F_{188}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{188}\! \left(x \right) = F_{36}\! \left(x \right)
F_{189}\! \left(x \right) = F_{183}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{15}\! \left(x \right) F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{195}\! \left(x \right)
F_{193}\! \left(x \right) = F_{147}\! \left(x \right)+F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{118}\! \left(x \right) F_{42}\! \left(x \right) F_{66}\! \left(x \right)
F_{195}\! \left(x \right) = F_{66} \left(x \right)^{2} F_{163}\! \left(x \right)
F_{196}\! \left(x \right) = F_{122}\! \left(x \right)
F_{197}\! \left(x \right) = F_{55}\! \left(x \right)
F_{198}\! \left(x \right) = F_{71}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)
F_{200}\! \left(x \right) = F_{15}\! \left(x \right) F_{201}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)+F_{205}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)+F_{204}\! \left(x \right)
F_{203}\! \left(x \right) = F_{67}\! \left(x \right) F_{78}\! \left(x \right)
F_{204}\! \left(x \right) = F_{66}\! \left(x \right) F_{69}\! \left(x \right)
F_{205}\! \left(x \right) = F_{55}\! \left(x \right) F_{78}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x*(x - 2)*(F_6(x) + 1)**2 + (x + 1)*(F_6(x) + 1) + F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_5(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_4(x))
Eq(F_18(x), F_19(x)/(F_15(x)*F_66(x)))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_199(x) + F_21(x))
Eq(F_21(x), -F_198(x) + F_22(x))
Eq(F_22(x), F_197(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_26(x))
Eq(F_24(x), F_25(x)*F_6(x))
Eq(F_25(x), F_1(x) + F_15(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_15(x)*F_28(x))
Eq(F_28(x), F_196(x) + F_29(x))
Eq(F_29(x), F_190(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_6(x))
Eq(F_31(x), -F_185(x) + F_32(x))
Eq(F_32(x), -F_180(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_15(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_24(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_38(x))
Eq(F_38(x), F_175(x) + F_39(x))
Eq(F_39(x), F_10(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_4(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), -F_170(x) + F_44(x))
Eq(F_44(x), F_45(x) - F_47(x))
Eq(F_45(x), F_46(x)/F_15(x))
Eq(F_46(x), F_16(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_15(x))
Eq(F_50(x), F_16(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_18(x) - F_53(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_15(x)*F_6(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_15(x)*F_59(x))
Eq(F_59(x), F_166(x) + F_60(x))
Eq(F_60(x), F_149(x) + F_61(x))
Eq(F_61(x), F_6(x)*F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_15(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_69(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), x*(x - 2)*F_66(x)**2 + (x + 2)*F_66(x) - 1)
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_15(x)*F_42(x))
Eq(F_69(x), F_70(x)/F_15(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_56(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_15(x)*F_74(x))
Eq(F_74(x), F_122(x) + F_75(x))
Eq(F_75(x), F_61(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_118(x)*F_120(x)*F_15(x)*F_78(x))
Eq(F_78(x), F_66(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_15(x)*F_66(x)*F_81(x))
Eq(F_81(x), F_11(x) + F_82(x))
Eq(F_82(x), -F_117(x) + F_83(x))
Eq(F_83(x), F_84(x)/(F_15(x)*F_66(x)))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_24(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_15(x)*F_88(x))
Eq(F_88(x), F_116(x) + F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_6(x)*F_78(x))
Eq(F_91(x), F_66(x)*F_92(x))
Eq(F_92(x), -F_66(x) + F_93(x))
Eq(F_93(x), F_94(x)/F_108(x))
Eq(F_94(x), -F_100(x) + F_95(x))
Eq(F_95(x), F_96(x)/F_15(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), -F_0(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_15(x))
Eq(F_99(x), F_2(x))
Eq(F_100(x), F_101(x) - F_104(x))
Eq(F_101(x), F_102(x)/F_15(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), -F_6(x) + F_97(x))
Eq(F_104(x), F_105(x)*F_93(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_15(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_1(x) + F_105(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_15(x))
Eq(F_112(x), F_1(x) + F_110(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_15(x))
Eq(F_115(x), F_105(x) + F_113(x))
Eq(F_116(x), F_15(x)*F_6(x)*F_78(x))
Eq(F_117(x), F_11(x)*F_25(x))
Eq(F_118(x), F_119(x)/(F_11(x)*F_15(x)))
Eq(F_119(x), F_82(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_15(x)*F_65(x))
Eq(F_122(x), F_123(x) + F_132(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_15(x)*F_66(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x) - F_130(x))
Eq(F_127(x), F_128(x)/F_15(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_15(x)*F_18(x))
Eq(F_130(x), F_131(x)/F_15(x))
Eq(F_131(x), F_21(x))
Eq(F_132(x), F_133(x)*F_6(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_15(x))
Eq(F_135(x), F_136(x) - F_138(x))
Eq(F_136(x), F_137(x)/F_15(x))
Eq(F_137(x), F_67(x))
Eq(F_138(x), F_139(x) - F_142(x))
Eq(F_139(x), F_140(x)/F_15(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), -F_6(x) + F_67(x))
Eq(F_142(x), F_143(x) - F_76(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_145(x)*F_15(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_118(x)*F_42(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_11(x)*F_118(x)*F_120(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_15(x)*F_151(x)*F_66(x))
Eq(F_151(x), F_152(x) - F_165(x))
Eq(F_152(x), F_153(x)/F_15(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_15(x)*F_155(x))
Eq(F_155(x), F_156(x) + F_164(x))
Eq(F_156(x), F_120(x)*F_157(x))
Eq(F_157(x), F_158(x) + F_163(x))
Eq(F_158(x), F_159(x)/F_15(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_161(x) + F_67(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_142(x)*F_15(x))
Eq(F_163(x), -F_130(x) + F_18(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_53(x)*F_66(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_132(x) + F_168(x))
Eq(F_168(x), F_169(x))
Eq(F_169(x), F_15(x)*F_53(x)*F_66(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), -F_172(x) + F_45(x))
Eq(F_172(x), -F_173(x) + F_49(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_163(x)*F_4(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_11(x)*F_177(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_15(x)*F_179(x))
Eq(F_179(x), F_2(x) + F_5(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x) + F_183(x))
Eq(F_182(x), F_15(x)*F_93(x))
Eq(F_183(x), F_184(x))
Eq(F_184(x), F_15(x)*F_179(x)*F_93(x))
Eq(F_185(x), F_186(x) - F_62(x))
Eq(F_186(x), F_187(x) - F_189(x))
Eq(F_187(x), F_188(x)/F_15(x))
Eq(F_188(x), F_36(x))
Eq(F_189(x), F_183(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_15(x)*F_192(x))
Eq(F_192(x), F_193(x) + F_195(x))
Eq(F_193(x), F_147(x) + F_194(x))
Eq(F_194(x), F_118(x)*F_42(x)*F_66(x))
Eq(F_195(x), F_163(x)*F_66(x)**2)
Eq(F_196(x), F_122(x))
Eq(F_197(x), F_55(x))
Eq(F_198(x), F_71(x))
Eq(F_199(x), F_200(x))
Eq(F_200(x), F_15(x)*F_201(x))
Eq(F_201(x), F_202(x) + F_205(x))
Eq(F_202(x), F_203(x) + F_204(x))
Eq(F_203(x), F_67(x)*F_78(x))
Eq(F_204(x), F_66(x)*F_69(x))
Eq(F_205(x), F_55(x)*F_78(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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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, 1, 4], "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, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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"Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[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": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "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, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "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": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25234/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (x*F[6,x]+x-1)*(x*F[6,x]+x-2*F[6,x])
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[16,x]+F[13,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[5,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[4,x]
F[18,x] = 1/F[15,x]/F[90,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[206,x]+F[21,x]
F[21,x] = -F[205,x]+F[22,x]
F[22,x] = F[204,x]+F[23,x]
F[23,x] = F[24,x]+F[26,x]
F[24,x] = F[25,x]*F[6,x]
F[25,x] = F[1,x]+F[15,x]
F[26,x] = F[27,x]
F[27,x] = F[15,x]*F[28,x]
F[28,x] = F[203,x]+F[29,x]
F[29,x] = F[192,x]+F[30,x]
F[30,x] = F[31,x]*F[6,x]
F[31,x] = -F[187,x]+F[32,x]
F[32,x] = -F[182,x]+F[33,x]
F[33,x] = 1/F[15,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[24,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[38,x]
F[38,x] = F[177,x]+F[39,x]
F[39,x] = F[10,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[15,x]*F[4,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = -F[56,x]+F[44,x]
F[44,x] = -F[51,x]+F[45,x]
F[45,x] = 1/F[15,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[50,x]+F[48,x]
F[48,x] = 1/F[15,x]*F[49,x]
F[49,x] = F[7,x]
F[50,x] = F[4,x]*F[6,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = -F[54,x]+F[18,x]
F[54,x] = 1/F[15,x]*F[55,x]
F[55,x] = F[21,x]
F[56,x] = F[57,x]
F[57,x] = -F[58,x]+F[45,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = -F[60,x]+F[18,x]
F[60,x] = 1/F[15,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[15,x]*F[6,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[66,x]
F[66,x] = F[173,x]+F[67,x]
F[67,x] = F[157,x]+F[68,x]
F[68,x] = F[6,x]*F[69,x]
F[69,x] = F[70,x]+F[76,x]
F[70,x] = F[15,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[15,x]*F[73,x]
F[73,x] = F[6,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[15,x]*F[42,x]
F[76,x] = 1/F[118,x]*F[77,x]
F[77,x] = -F[82,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[121,x]*F[15,x]*F[80,x]
F[80,x] = 1/F[15,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[63,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[15,x]*F[85,x]
F[85,x] = F[133,x]+F[86,x]
F[86,x] = F[68,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[131,x]*F[15,x]*F[70,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = -1+(x^2-2*x)*F[90,x]^2+(2+x)*F[90,x]
F[91,x] = F[92,x]
F[92,x] = F[15,x]*F[90,x]*F[93,x]
F[93,x] = F[11,x]+F[94,x]
F[94,x] = -F[130,x]+F[95,x]
F[95,x] = 1/F[15,x]/F[90,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[24,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[15,x]
F[100,x] = F[101,x]+F[129,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[6,x]*F[89,x]
F[103,x] = F[104,x]*F[90,x]
F[104,x] = -F[90,x]+F[105,x]
F[105,x] = 1/F[121,x]*F[106,x]
F[106,x] = -F[114,x]+F[107,x]
F[107,x] = 1/F[15,x]*F[108,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]+F[6,x]
F[110,x] = -F[2,x]+F[111,x]
F[111,x] = -F[90,x]+F[112,x]
F[112,x] = 1/F[15,x]*F[113,x]
F[113,x] = F[2,x]
F[114,x] = -F[117,x]+F[115,x]
F[115,x] = 1/F[15,x]*F[116,x]
F[116,x] = F[110,x]
F[117,x] = F[105,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[15,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[1,x]+F[118,x]
F[122,x] = F[123,x]+F[126,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[15,x]
F[125,x] = F[1,x]+F[123,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[15,x]
F[128,x] = F[118,x]+F[126,x]
F[129,x] = F[15,x]*F[6,x]*F[89,x]
F[130,x] = F[11,x]*F[25,x]
F[131,x] = 1/F[11,x]/F[15,x]*F[132,x]
F[132,x] = F[94,x]
F[133,x] = F[134,x]+F[138,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[15,x]*F[90,x]
F[136,x] = 1/F[15,x]*F[137,x]
F[137,x] = F[82,x]
F[138,x] = F[139,x]*F[6,x]
F[139,x] = F[140,x]
F[140,x] = F[141,x]*F[15,x]
F[141,x] = -F[145,x]+F[142,x]
F[142,x] = 1/F[15,x]*F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[74,x]
F[145,x] = -F[149,x]+F[146,x]
F[146,x] = 1/F[15,x]*F[147,x]
F[147,x] = F[148,x]
F[148,x] = -F[6,x]+F[74,x]
F[149,x] = -F[87,x]+F[150,x]
F[150,x] = F[151,x]
F[151,x] = F[15,x]*F[152,x]
F[152,x] = F[153,x]+F[155,x]
F[153,x] = F[131,x]*F[154,x]
F[154,x] = 1/F[15,x]*F[144,x]
F[155,x] = F[156,x]
F[156,x] = F[131,x]*F[70,x]*F[89,x]
F[157,x] = F[158,x]
F[158,x] = F[15,x]*F[159,x]*F[90,x]
F[159,x] = -F[172,x]+F[160,x]
F[160,x] = 1/F[15,x]*F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[15,x]*F[163,x]
F[163,x] = F[164,x]+F[171,x]
F[164,x] = F[165,x]*F[70,x]
F[165,x] = F[166,x]+F[53,x]
F[166,x] = 1/F[15,x]*F[167,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]+F[74,x]
F[169,x] = F[170,x]
F[170,x] = F[149,x]*F[15,x]
F[171,x] = F[172,x]
F[172,x] = F[60,x]*F[90,x]
F[173,x] = F[174,x]
F[174,x] = F[138,x]+F[175,x]
F[175,x] = F[176,x]
F[176,x] = F[15,x]*F[60,x]*F[90,x]
F[177,x] = F[178,x]
F[178,x] = F[11,x]*F[179,x]
F[179,x] = F[180,x]
F[180,x] = F[15,x]*F[181,x]
F[181,x] = F[2,x]+F[5,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]+F[185,x]
F[184,x] = F[105,x]*F[15,x]
F[185,x] = F[186,x]
F[186,x] = F[105,x]*F[15,x]*F[181,x]
F[187,x] = -F[69,x]+F[188,x]
F[188,x] = -F[191,x]+F[189,x]
F[189,x] = 1/F[15,x]*F[190,x]
F[190,x] = F[36,x]
F[191,x] = F[185,x]
F[192,x] = -F[201,x]+F[193,x]
F[193,x] = F[194,x]+F[200,x]
F[194,x] = F[195,x]
F[195,x] = F[15,x]*F[196,x]*F[90,x]
F[196,x] = F[197,x]+F[199,x]
F[197,x] = F[172,x]+F[198,x]
F[198,x] = F[131,x]*F[42,x]
F[199,x] = F[53,x]*F[90,x]
F[200,x] = F[87,x]
F[201,x] = F[202,x]
F[202,x] = F[90,x]^2*F[15,x]*F[60,x]
F[203,x] = F[133,x]
F[204,x] = F[62,x]
F[205,x] = F[82,x]
F[206,x] = F[207,x]
F[207,x] = F[15,x]*F[208,x]
F[208,x] = F[209,x]+F[212,x]
F[209,x] = F[210,x]+F[211,x]
F[210,x] = F[74,x]*F[89,x]
F[211,x] = F[80,x]*F[90,x]
F[212,x] = F[62,x]*F[89,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_{15}\! \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_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{15}\! \left(x \right) F_{90}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{206}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{205}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{204}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{203}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{192}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{182}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{177}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{18}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{21}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{45}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{18}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{173}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{157}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{6}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{76}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{6}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{118}\! \left(x \right)}
F_{77}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{121}\! \left(x \right) F_{15}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{63}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{15}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{133}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{68}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{131}\! \left(x \right) F_{15}\! \left(x \right) F_{70}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = x^{2} F_{90} \left(x \right)^{2}-2 x F_{90} \left(x \right)^{2}+F_{90}\! \left(x \right) x +2 F_{90}\! \left(x \right)-1
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right) F_{90}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{15}\! \left(x \right) F_{90}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{24}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{15}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{129}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{6}\! \left(x \right) F_{89}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{90}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{121}\! \left(x \right)}
F_{106}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{6}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = \frac{F_{113}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{113}\! \left(x \right) = F_{2}\! \left(x \right)
F_{114}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = \frac{F_{116}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{116}\! \left(x \right) = F_{110}\! \left(x \right)
F_{117}\! \left(x \right) = F_{105}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{15}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{126}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{15}\! \left(x \right)
F_{125}\! \left(x \right) = F_{1}\! \left(x \right)+F_{123}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{15}\! \left(x \right)
F_{128}\! \left(x \right) = F_{118}\! \left(x \right)+F_{126}\! \left(x \right)
F_{129}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right) F_{89}\! \left(x \right)
F_{130}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{11}\! \left(x \right) F_{15}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{94}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{138}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{15}\! \left(x \right) F_{90}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{82}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{6}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{15}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = \frac{F_{143}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{74}\! \left(x \right)
F_{145}\! \left(x \right) = -F_{149}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = \frac{F_{147}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{74}\! \left(x \right)
F_{149}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{15}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{155}\! \left(x \right)
F_{153}\! \left(x \right) = F_{131}\! \left(x \right) F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{131}\! \left(x \right) F_{70}\! \left(x \right) F_{89}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{15}\! \left(x \right) F_{159}\! \left(x \right) F_{90}\! \left(x \right)
F_{159}\! \left(x \right) = -F_{172}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = \frac{F_{161}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{15}\! \left(x \right) F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{171}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{70}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{53}\! \left(x \right)
F_{166}\! \left(x \right) = \frac{F_{167}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{74}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{149}\! \left(x \right) F_{15}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{60}\! \left(x \right) F_{90}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{138}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{15}\! \left(x \right) F_{60}\! \left(x \right) F_{90}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{11}\! \left(x \right) F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{15}\! \left(x \right) F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{185}\! \left(x \right)
F_{184}\! \left(x \right) = F_{105}\! \left(x \right) F_{15}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{105}\! \left(x \right) F_{15}\! \left(x \right) F_{181}\! \left(x \right)
F_{187}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = -F_{191}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = \frac{F_{190}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{190}\! \left(x \right) = F_{36}\! \left(x \right)
F_{191}\! \left(x \right) = F_{185}\! \left(x \right)
F_{192}\! \left(x \right) = -F_{201}\! \left(x \right)+F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{200}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{15}\! \left(x \right) F_{196}\! \left(x \right) F_{90}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{199}\! \left(x \right)
F_{197}\! \left(x \right) = F_{172}\! \left(x \right)+F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{131}\! \left(x \right) F_{42}\! \left(x \right)
F_{199}\! \left(x \right) = F_{53}\! \left(x \right) F_{90}\! \left(x \right)
F_{200}\! \left(x \right) = F_{87}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{90} \left(x \right)^{2} F_{15}\! \left(x \right) F_{60}\! \left(x \right)
F_{203}\! \left(x \right) = F_{133}\! \left(x \right)
F_{204}\! \left(x \right) = F_{62}\! \left(x \right)
F_{205}\! \left(x \right) = F_{82}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{15}\! \left(x \right) F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{212}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{211}\! \left(x \right)
F_{210}\! \left(x \right) = F_{74}\! \left(x \right) F_{89}\! \left(x \right)
F_{211}\! \left(x \right) = F_{80}\! \left(x \right) F_{90}\! \left(x \right)
F_{212}\! \left(x \right) = F_{62}\! \left(x \right) F_{89}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x*(x - 2)*(F_6(x) + 1)**2 + (x + 1)*(F_6(x) + 1) + F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_5(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_4(x))
Eq(F_18(x), F_19(x)/(F_15(x)*F_90(x)))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_206(x) + F_21(x))
Eq(F_21(x), -F_205(x) + F_22(x))
Eq(F_22(x), F_204(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_26(x))
Eq(F_24(x), F_25(x)*F_6(x))
Eq(F_25(x), F_1(x) + F_15(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_15(x)*F_28(x))
Eq(F_28(x), F_203(x) + F_29(x))
Eq(F_29(x), F_192(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_6(x))
Eq(F_31(x), -F_187(x) + F_32(x))
Eq(F_32(x), -F_182(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_15(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_24(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_38(x))
Eq(F_38(x), F_177(x) + F_39(x))
Eq(F_39(x), F_10(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_4(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x) - F_56(x))
Eq(F_44(x), F_45(x) - F_51(x))
Eq(F_45(x), F_46(x)/F_15(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x) - F_50(x))
Eq(F_48(x), F_49(x)/F_15(x))
Eq(F_49(x), F_7(x))
Eq(F_50(x), F_4(x)*F_6(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_18(x) - F_54(x))
Eq(F_54(x), F_55(x)/F_15(x))
Eq(F_55(x), F_21(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_45(x) - F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_18(x) - F_60(x))
Eq(F_60(x), F_61(x)/F_15(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_15(x)*F_6(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_66(x))
Eq(F_66(x), F_173(x) + F_67(x))
Eq(F_67(x), F_157(x) + F_68(x))
Eq(F_68(x), F_6(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_76(x))
Eq(F_70(x), F_15(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_15(x)*F_73(x))
Eq(F_73(x), F_6(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_15(x)*F_42(x))
Eq(F_76(x), F_77(x)/F_118(x))
Eq(F_77(x), F_78(x) - F_82(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_121(x)*F_15(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_15(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_63(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_15(x)*F_85(x))
Eq(F_85(x), F_133(x) + F_86(x))
Eq(F_86(x), F_68(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_131(x)*F_15(x)*F_70(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), x*(x - 2)*F_90(x)**2 + (x + 2)*F_90(x) - 1)
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_15(x)*F_90(x)*F_93(x))
Eq(F_93(x), F_11(x) + F_94(x))
Eq(F_94(x), -F_130(x) + F_95(x))
Eq(F_95(x), F_96(x)/(F_15(x)*F_90(x)))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_24(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_15(x))
Eq(F_100(x), F_101(x) + F_129(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_6(x)*F_89(x))
Eq(F_103(x), F_104(x)*F_90(x))
Eq(F_104(x), F_105(x) - F_90(x))
Eq(F_105(x), F_106(x)/F_121(x))
Eq(F_106(x), F_107(x) - F_114(x))
Eq(F_107(x), F_108(x)/F_15(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x) + F_6(x))
Eq(F_110(x), F_111(x) - F_2(x))
Eq(F_111(x), F_112(x) - F_90(x))
Eq(F_112(x), F_113(x)/F_15(x))
Eq(F_113(x), F_2(x))
Eq(F_114(x), F_115(x) - F_117(x))
Eq(F_115(x), F_116(x)/F_15(x))
Eq(F_116(x), F_110(x))
Eq(F_117(x), F_105(x)*F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_15(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_1(x) + F_118(x))
Eq(F_122(x), F_123(x) + F_126(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_15(x))
Eq(F_125(x), F_1(x) + F_123(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_15(x))
Eq(F_128(x), F_118(x) + F_126(x))
Eq(F_129(x), F_15(x)*F_6(x)*F_89(x))
Eq(F_130(x), F_11(x)*F_25(x))
Eq(F_131(x), F_132(x)/(F_11(x)*F_15(x)))
Eq(F_132(x), F_94(x))
Eq(F_133(x), F_134(x) + F_138(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_15(x)*F_90(x))
Eq(F_136(x), F_137(x)/F_15(x))
Eq(F_137(x), F_82(x))
Eq(F_138(x), F_139(x)*F_6(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_141(x)*F_15(x))
Eq(F_141(x), F_142(x) - F_145(x))
Eq(F_142(x), F_143(x)/F_15(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_74(x))
Eq(F_145(x), F_146(x) - F_149(x))
Eq(F_146(x), F_147(x)/F_15(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), -F_6(x) + F_74(x))
Eq(F_149(x), F_150(x) - F_87(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_15(x)*F_152(x))
Eq(F_152(x), F_153(x) + F_155(x))
Eq(F_153(x), F_131(x)*F_154(x))
Eq(F_154(x), F_144(x)/F_15(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_131(x)*F_70(x)*F_89(x))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_15(x)*F_159(x)*F_90(x))
Eq(F_159(x), F_160(x) - F_172(x))
Eq(F_160(x), F_161(x)/F_15(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_15(x)*F_163(x))
Eq(F_163(x), F_164(x) + F_171(x))
Eq(F_164(x), F_165(x)*F_70(x))
Eq(F_165(x), F_166(x) + F_53(x))
Eq(F_166(x), F_167(x)/F_15(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x) + F_74(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_149(x)*F_15(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_60(x)*F_90(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_138(x) + F_175(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_15(x)*F_60(x)*F_90(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_11(x)*F_179(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_15(x)*F_181(x))
Eq(F_181(x), F_2(x) + F_5(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x) + F_185(x))
Eq(F_184(x), F_105(x)*F_15(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_105(x)*F_15(x)*F_181(x))
Eq(F_187(x), F_188(x) - F_69(x))
Eq(F_188(x), F_189(x) - F_191(x))
Eq(F_189(x), F_190(x)/F_15(x))
Eq(F_190(x), F_36(x))
Eq(F_191(x), F_185(x))
Eq(F_192(x), F_193(x) - F_201(x))
Eq(F_193(x), F_194(x) + F_200(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_15(x)*F_196(x)*F_90(x))
Eq(F_196(x), F_197(x) + F_199(x))
Eq(F_197(x), F_172(x) + F_198(x))
Eq(F_198(x), F_131(x)*F_42(x))
Eq(F_199(x), F_53(x)*F_90(x))
Eq(F_200(x), F_87(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_15(x)*F_60(x)*F_90(x)**2)
Eq(F_203(x), F_133(x))
Eq(F_204(x), F_62(x))
Eq(F_205(x), F_82(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_15(x)*F_208(x))
Eq(F_208(x), F_209(x) + F_212(x))
Eq(F_209(x), F_210(x) + F_211(x))
Eq(F_210(x), F_74(x)*F_89(x))
Eq(F_211(x), F_80(x)*F_90(x))
Eq(F_212(x), F_62(x)*F_89(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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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, 1, 4], "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, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], 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1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25342/
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[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (x*F[6,x]+x-2*F[6,x])*(x*F[6,x]+x-1)
F[7,x] = F[8,x]
F[8,x] = F[18,x]*F[9,x]
F[9,x] = F[10,x]+F[24,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = F[12,x,1]
F[12,x,k[0]] = F[13,x]+F[14,x,k[0]]
F[13,x] = -1+(x^2-2*x)*F[13,x]^2+(2+x)*F[13,x]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[12,x,k[0]]*F[16,x,k[0]]
F[16,x,k[0]] = k[0]*F[17,x]
F[17,x] = F[18,x]*F[19,x]
F[18,x] = x
F[19,x] = F[20,x,1]
F[20,x,k[0]] = F[13,x]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[13,x]*F[20,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = k[0]*x
F[24,x] = F[25,x]
F[25,x] = F[18,x]*F[26,x]*F[4,x]
F[26,x] = 1/F[18,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[11,x]+F[29,x]
F[29,x] = F[1,x]+F[30,x]+F[62,x]+F[63,x]
F[30,x] = F[18,x]*F[31,x]
F[31,x] = F[29,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[18,x]*F[34,x]
F[34,x] = 1/F[18,x]*F[35,x]
F[35,x] = -F[38,x]-F[61,x]+F[36,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = F[13,x]*F[38,x]
F[38,x] = F[29,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[18,x]*F[36,x]
F[41,x] = F[42,x]*F[47,x]
F[42,x] = F[43,x]
F[43,x] = F[18,x]*F[44,x]
F[44,x] = F[45,x,1]
F[45,x,k[0]] = (F[46,x,k[0]]*k[0]-F[46,x,1])/(-1+k[0])
F[46,x,k[0]] = x^2*F[46,x,k[0]]^2*k[0]^2-2*x*F[46,x,k[0]]^2*k[0]+x*F[46,x,k[0]]*k[0]+2*F[46,x,k[0]]-1
F[47,x] = F[48,x]+F[59,x]
F[48,x] = F[11,x]+F[49,x]
F[49,x] = F[42,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[18,x]*F[52,x]
F[52,x] = F[53,x]+F[57,x]
F[53,x] = F[42,x]*F[54,x]
F[54,x] = F[11,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[11,x]*F[18,x]*F[19,x]
F[57,x] = F[58,x]
F[58,x] = F[13,x]*F[49,x]
F[59,x] = F[60,x]
F[60,x] = F[18,x]*F[19,x]*F[48,x]
F[61,x] = F[13,x]*F[18,x]*F[47,x]
F[62,x] = F[18,x]*F[38,x]
F[63,x] = F[18,x]*F[64,x]
F[64,x] = F[65,x]+F[74,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[13,x]+F[42,x]
F[67,x] = F[68,x]
F[68,x] = F[18,x]*F[69,x]
F[69,x] = F[70,x]+F[73,x]
F[70,x] = F[13,x]*F[71,x]
F[71,x] = F[65,x]+F[72,x]
F[72,x] = F[55,x]
F[73,x] = F[19,x]*F[42,x]
F[74,x] = F[49,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_{18}\! \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_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x , 1\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{14}\! \left(x , y\right)
F_{13}\! \left(x \right) = x^{2} F_{13} \left(x \right)^{2}-2 x F_{13} \left(x \right)^{2}+F_{13}\! \left(x \right) x +2 F_{13}\! \left(x \right)-1
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = y F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = F_{20}\! \left(x , 1\right)
F_{20}\! \left(x , y\right) = F_{13}\! \left(x \right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = y x
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right) F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{30}\! \left(x \right) = F_{18}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{35}\! \left(x \right) = -F_{38}\! \left(x \right)-F_{61}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{29}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right) F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{47}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{18}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x , 1\right)
F_{45}\! \left(x , y\right) = -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}
F_{46}\! \left(x , y\right) = x^{2} F_{46}\! \left(x , y\right)^{2} y^{2}-2 y x F_{46}\! \left(x , y\right)^{2}+x F_{46}\! \left(x , y\right) y +2 F_{46}\! \left(x , y\right)-1
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{59}\! \left(x \right)
F_{48}\! \left(x \right) = F_{11}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{42}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{18}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{57}\! \left(x \right)
F_{53}\! \left(x \right) = F_{42}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13}\! \left(x \right) F_{49}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right) F_{48}\! \left(x \right)
F_{61}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right) F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{63}\! \left(x \right) = F_{18}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{74}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{13}\! \left(x \right)+F_{42}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{65}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{55}\! \left(x \right)
F_{73}\! \left(x \right) = F_{19}\! \left(x \right) F_{42}\! \left(x \right)
F_{74}\! \left(x \right) = F_{49}\! \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_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x*(x - 2)*(F_6(x) + 1)**2 + (x + 1)*(F_6(x) + 1) + F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_18(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_24(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_12(x, 1))
Eq(F_12(x, k_0), F_13(x) + F_14(x, k_0))
Eq(F_13(x), x*(x - 2)*F_13(x)**2 + (x + 2)*F_13(x) - 1)
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_12(x, k_0)*F_16(x, k_0))
Eq(F_16(x, k_0), k_0*F_17(x))
Eq(F_17(x), F_18(x)*F_19(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x, 1))
Eq(F_20(x, k_0), F_13(x) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_13(x)*F_20(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), k_0*x)
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_18(x)*F_26(x)*F_4(x))
Eq(F_26(x), F_27(x)/F_18(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), -F_11(x) + F_29(x))
Eq(F_29(x), F_1(x) + F_30(x) + F_62(x) + F_63(x))
Eq(F_30(x), F_18(x)*F_31(x))
Eq(F_31(x), F_29(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_18(x)*F_34(x))
Eq(F_34(x), F_35(x)/F_18(x))
Eq(F_35(x), F_36(x) - F_38(x) - F_61(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), F_13(x)*F_38(x))
Eq(F_38(x), F_29(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_18(x)*F_36(x))
Eq(F_41(x), F_42(x)*F_47(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_18(x)*F_44(x))
Eq(F_44(x), F_45(x, 1))
Eq(F_45(x, k_0), (-k_0*F_46(x, k_0) + F_46(x, 1))/(1 - k_0))
Eq(F_46(x, k_0), k_0*x*(k_0*x - 2)*F_46(x, k_0)**2 + (k_0*x + 2)*F_46(x, k_0) - 1)
Eq(F_47(x), F_48(x) + F_59(x))
Eq(F_48(x), F_11(x) + F_49(x))
Eq(F_49(x), F_42(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_18(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_57(x))
Eq(F_53(x), F_42(x)*F_54(x))
Eq(F_54(x), F_11(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_11(x)*F_18(x)*F_19(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_13(x)*F_49(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_18(x)*F_19(x)*F_48(x))
Eq(F_61(x), F_13(x)*F_18(x)*F_47(x))
Eq(F_62(x), F_18(x)*F_38(x))
Eq(F_63(x), F_18(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_74(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_13(x) + F_42(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_18(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_73(x))
Eq(F_70(x), F_13(x)*F_71(x))
Eq(F_71(x), F_65(x) + F_72(x))
Eq(F_72(x), F_55(x))
Eq(F_73(x), F_19(x)*F_42(x))
Eq(F_74(x), F_49(x))
Pack JSON:
{"name": "point_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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"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": "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, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "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": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25510/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (x*F[6,x]+x-1)*(x*F[6,x]+x-2*F[6,x])
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[11,x]*F[2,x]
F[11,x] = 1/F[0,x]*F[12,x]
F[12,x] = -F[16,x]+F[13,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[5,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[4,x]
F[18,x] = 1/F[15,x]/F[90,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[206,x]+F[21,x]
F[21,x] = -F[205,x]+F[22,x]
F[22,x] = F[204,x]+F[23,x]
F[23,x] = F[24,x]+F[26,x]
F[24,x] = F[25,x]*F[6,x]
F[25,x] = F[1,x]+F[15,x]
F[26,x] = F[27,x]
F[27,x] = F[15,x]*F[28,x]
F[28,x] = F[203,x]+F[29,x]
F[29,x] = F[192,x]+F[30,x]
F[30,x] = F[31,x]*F[6,x]
F[31,x] = -F[187,x]+F[32,x]
F[32,x] = -F[182,x]+F[33,x]
F[33,x] = 1/F[15,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[24,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[38,x]
F[38,x] = F[177,x]+F[39,x]
F[39,x] = F[10,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[15,x]*F[4,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = -F[56,x]+F[44,x]
F[44,x] = -F[51,x]+F[45,x]
F[45,x] = 1/F[15,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[50,x]+F[48,x]
F[48,x] = 1/F[15,x]*F[49,x]
F[49,x] = F[7,x]
F[50,x] = F[4,x]*F[6,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = -F[54,x]+F[18,x]
F[54,x] = 1/F[15,x]*F[55,x]
F[55,x] = F[21,x]
F[56,x] = F[57,x]
F[57,x] = -F[58,x]+F[45,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = -F[60,x]+F[18,x]
F[60,x] = 1/F[15,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[15,x]*F[6,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[66,x]
F[66,x] = F[173,x]+F[67,x]
F[67,x] = F[157,x]+F[68,x]
F[68,x] = F[6,x]*F[69,x]
F[69,x] = F[70,x]+F[76,x]
F[70,x] = F[15,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[15,x]*F[73,x]
F[73,x] = F[6,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[15,x]*F[42,x]
F[76,x] = 1/F[118,x]*F[77,x]
F[77,x] = -F[82,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[121,x]*F[15,x]*F[80,x]
F[80,x] = 1/F[15,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[63,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[15,x]*F[85,x]
F[85,x] = F[133,x]+F[86,x]
F[86,x] = F[68,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[131,x]*F[15,x]*F[70,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = -1+(x^2-2*x)*F[90,x]^2+(2+x)*F[90,x]
F[91,x] = F[92,x]
F[92,x] = F[15,x]*F[90,x]*F[93,x]
F[93,x] = F[11,x]+F[94,x]
F[94,x] = -F[130,x]+F[95,x]
F[95,x] = 1/F[15,x]/F[90,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[24,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[15,x]
F[100,x] = F[101,x]+F[129,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[6,x]*F[89,x]
F[103,x] = F[104,x]*F[90,x]
F[104,x] = -F[90,x]+F[105,x]
F[105,x] = 1/F[121,x]*F[106,x]
F[106,x] = -F[114,x]+F[107,x]
F[107,x] = 1/F[15,x]*F[108,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]+F[6,x]
F[110,x] = -F[2,x]+F[111,x]
F[111,x] = -F[90,x]+F[112,x]
F[112,x] = 1/F[15,x]*F[113,x]
F[113,x] = F[2,x]
F[114,x] = -F[117,x]+F[115,x]
F[115,x] = 1/F[15,x]*F[116,x]
F[116,x] = F[110,x]
F[117,x] = F[105,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[15,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[1,x]+F[118,x]
F[122,x] = F[123,x]+F[126,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]*F[15,x]
F[125,x] = F[1,x]+F[123,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[15,x]
F[128,x] = F[118,x]+F[126,x]
F[129,x] = F[15,x]*F[6,x]*F[89,x]
F[130,x] = F[11,x]*F[25,x]
F[131,x] = 1/F[11,x]/F[15,x]*F[132,x]
F[132,x] = F[94,x]
F[133,x] = F[134,x]+F[138,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[15,x]*F[90,x]
F[136,x] = 1/F[15,x]*F[137,x]
F[137,x] = F[82,x]
F[138,x] = F[139,x]*F[6,x]
F[139,x] = F[140,x]
F[140,x] = F[141,x]*F[15,x]
F[141,x] = -F[145,x]+F[142,x]
F[142,x] = 1/F[15,x]*F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[74,x]
F[145,x] = -F[149,x]+F[146,x]
F[146,x] = 1/F[15,x]*F[147,x]
F[147,x] = F[148,x]
F[148,x] = -F[6,x]+F[74,x]
F[149,x] = -F[87,x]+F[150,x]
F[150,x] = F[151,x]
F[151,x] = F[15,x]*F[152,x]
F[152,x] = F[153,x]+F[155,x]
F[153,x] = F[131,x]*F[154,x]
F[154,x] = 1/F[15,x]*F[144,x]
F[155,x] = F[156,x]
F[156,x] = F[131,x]*F[70,x]*F[89,x]
F[157,x] = F[158,x]
F[158,x] = F[15,x]*F[159,x]*F[90,x]
F[159,x] = -F[172,x]+F[160,x]
F[160,x] = 1/F[15,x]*F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[15,x]*F[163,x]
F[163,x] = F[164,x]+F[171,x]
F[164,x] = F[165,x]*F[70,x]
F[165,x] = F[166,x]+F[53,x]
F[166,x] = 1/F[15,x]*F[167,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]+F[74,x]
F[169,x] = F[170,x]
F[170,x] = F[149,x]*F[15,x]
F[171,x] = F[172,x]
F[172,x] = F[60,x]*F[90,x]
F[173,x] = F[174,x]
F[174,x] = F[138,x]+F[175,x]
F[175,x] = F[176,x]
F[176,x] = F[15,x]*F[60,x]*F[90,x]
F[177,x] = F[178,x]
F[178,x] = F[11,x]*F[179,x]
F[179,x] = F[180,x]
F[180,x] = F[15,x]*F[181,x]
F[181,x] = F[2,x]+F[5,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]+F[185,x]
F[184,x] = F[105,x]*F[15,x]
F[185,x] = F[186,x]
F[186,x] = F[105,x]*F[15,x]*F[181,x]
F[187,x] = -F[69,x]+F[188,x]
F[188,x] = -F[191,x]+F[189,x]
F[189,x] = 1/F[15,x]*F[190,x]
F[190,x] = F[36,x]
F[191,x] = F[185,x]
F[192,x] = -F[201,x]+F[193,x]
F[193,x] = F[194,x]+F[200,x]
F[194,x] = F[195,x]
F[195,x] = F[15,x]*F[196,x]*F[90,x]
F[196,x] = F[197,x]+F[199,x]
F[197,x] = F[172,x]+F[198,x]
F[198,x] = F[131,x]*F[42,x]
F[199,x] = F[53,x]*F[90,x]
F[200,x] = F[87,x]
F[201,x] = F[202,x]
F[202,x] = F[90,x]^2*F[15,x]*F[60,x]
F[203,x] = F[133,x]
F[204,x] = F[62,x]
F[205,x] = F[82,x]
F[206,x] = F[207,x]
F[207,x] = F[15,x]*F[208,x]
F[208,x] = F[209,x]+F[212,x]
F[209,x] = F[210,x]+F[211,x]
F[210,x] = F[74,x]*F[89,x]
F[211,x] = F[80,x]*F[90,x]
F[212,x] = F[62,x]*F[89,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_{15}\! \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_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}+2 x^{2} F_{6}\! \left(x \right)-2 x F_{6} \left(x \right)^{2}+x^{2}-3 x F_{6}\! \left(x \right)-x +2 F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{15}\! \left(x \right) F_{90}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{206}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{205}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{204}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{203}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{192}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{182}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{177}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{10}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{54}\! \left(x \right)+F_{18}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{21}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{45}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{18}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{173}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{157}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{6}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{76}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{15}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{6}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{15}\! \left(x \right) F_{42}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{118}\! \left(x \right)}
F_{77}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{121}\! \left(x \right) F_{15}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{63}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{15}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{133}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{68}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{131}\! \left(x \right) F_{15}\! \left(x \right) F_{70}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = x^{2} F_{90} \left(x \right)^{2}-2 x F_{90} \left(x \right)^{2}+F_{90}\! \left(x \right) x +2 F_{90}\! \left(x \right)-1
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right) F_{90}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{15}\! \left(x \right) F_{90}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{24}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{15}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{129}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{6}\! \left(x \right) F_{89}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{90}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{121}\! \left(x \right)}
F_{106}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{6}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = \frac{F_{113}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{113}\! \left(x \right) = F_{2}\! \left(x \right)
F_{114}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = \frac{F_{116}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{116}\! \left(x \right) = F_{110}\! \left(x \right)
F_{117}\! \left(x \right) = F_{105}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{15}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{1}\! \left(x \right)+F_{118}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{126}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{15}\! \left(x \right)
F_{125}\! \left(x \right) = F_{1}\! \left(x \right)+F_{123}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{15}\! \left(x \right)
F_{128}\! \left(x \right) = F_{118}\! \left(x \right)+F_{126}\! \left(x \right)
F_{129}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right) F_{89}\! \left(x \right)
F_{130}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{11}\! \left(x \right) F_{15}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{94}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{138}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{15}\! \left(x \right) F_{90}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{82}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{6}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{15}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = \frac{F_{143}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{74}\! \left(x \right)
F_{145}\! \left(x \right) = -F_{149}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = \frac{F_{147}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{74}\! \left(x \right)
F_{149}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{15}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{155}\! \left(x \right)
F_{153}\! \left(x \right) = F_{131}\! \left(x \right) F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{131}\! \left(x \right) F_{70}\! \left(x \right) F_{89}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{15}\! \left(x \right) F_{159}\! \left(x \right) F_{90}\! \left(x \right)
F_{159}\! \left(x \right) = -F_{172}\! \left(x \right)+F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = \frac{F_{161}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{15}\! \left(x \right) F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{171}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right) F_{70}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{53}\! \left(x \right)
F_{166}\! \left(x \right) = \frac{F_{167}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{74}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{149}\! \left(x \right) F_{15}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{60}\! \left(x \right) F_{90}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = F_{138}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{15}\! \left(x \right) F_{60}\! \left(x \right) F_{90}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)
F_{178}\! \left(x \right) = F_{11}\! \left(x \right) F_{179}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{15}\! \left(x \right) F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{185}\! \left(x \right)
F_{184}\! \left(x \right) = F_{105}\! \left(x \right) F_{15}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{105}\! \left(x \right) F_{15}\! \left(x \right) F_{181}\! \left(x \right)
F_{187}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = -F_{191}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = \frac{F_{190}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{190}\! \left(x \right) = F_{36}\! \left(x \right)
F_{191}\! \left(x \right) = F_{185}\! \left(x \right)
F_{192}\! \left(x \right) = -F_{201}\! \left(x \right)+F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{200}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{15}\! \left(x \right) F_{196}\! \left(x \right) F_{90}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{199}\! \left(x \right)
F_{197}\! \left(x \right) = F_{172}\! \left(x \right)+F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{131}\! \left(x \right) F_{42}\! \left(x \right)
F_{199}\! \left(x \right) = F_{53}\! \left(x \right) F_{90}\! \left(x \right)
F_{200}\! \left(x \right) = F_{87}\! \left(x \right)
F_{201}\! \left(x \right) = F_{202}\! \left(x \right)
F_{202}\! \left(x \right) = F_{90} \left(x \right)^{2} F_{15}\! \left(x \right) F_{60}\! \left(x \right)
F_{203}\! \left(x \right) = F_{133}\! \left(x \right)
F_{204}\! \left(x \right) = F_{62}\! \left(x \right)
F_{205}\! \left(x \right) = F_{82}\! \left(x \right)
F_{206}\! \left(x \right) = F_{207}\! \left(x \right)
F_{207}\! \left(x \right) = F_{15}\! \left(x \right) F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)+F_{212}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right)+F_{211}\! \left(x \right)
F_{210}\! \left(x \right) = F_{74}\! \left(x \right) F_{89}\! \left(x \right)
F_{211}\! \left(x \right) = F_{80}\! \left(x \right) F_{90}\! \left(x \right)
F_{212}\! \left(x \right) = F_{62}\! \left(x \right) F_{89}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x*(x - 2)*(F_6(x) + 1)**2 + (x + 1)*(F_6(x) + 1) + F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_11(x)*F_2(x))
Eq(F_11(x), F_12(x)/F_0(x))
Eq(F_12(x), F_13(x) - F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_5(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_4(x))
Eq(F_18(x), F_19(x)/(F_15(x)*F_90(x)))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_206(x) + F_21(x))
Eq(F_21(x), -F_205(x) + F_22(x))
Eq(F_22(x), F_204(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_26(x))
Eq(F_24(x), F_25(x)*F_6(x))
Eq(F_25(x), F_1(x) + F_15(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_15(x)*F_28(x))
Eq(F_28(x), F_203(x) + F_29(x))
Eq(F_29(x), F_192(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_6(x))
Eq(F_31(x), -F_187(x) + F_32(x))
Eq(F_32(x), -F_182(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_15(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_24(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_38(x))
Eq(F_38(x), F_177(x) + F_39(x))
Eq(F_39(x), F_10(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_15(x)*F_4(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x) - F_56(x))
Eq(F_44(x), F_45(x) - F_51(x))
Eq(F_45(x), F_46(x)/F_15(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x) - F_50(x))
Eq(F_48(x), F_49(x)/F_15(x))
Eq(F_49(x), F_7(x))
Eq(F_50(x), F_4(x)*F_6(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_18(x) - F_54(x))
Eq(F_54(x), F_55(x)/F_15(x))
Eq(F_55(x), F_21(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_45(x) - F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_18(x) - F_60(x))
Eq(F_60(x), F_61(x)/F_15(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_15(x)*F_6(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_66(x))
Eq(F_66(x), F_173(x) + F_67(x))
Eq(F_67(x), F_157(x) + F_68(x))
Eq(F_68(x), F_6(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_76(x))
Eq(F_70(x), F_15(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_15(x)*F_73(x))
Eq(F_73(x), F_6(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_15(x)*F_42(x))
Eq(F_76(x), F_77(x)/F_118(x))
Eq(F_77(x), F_78(x) - F_82(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_121(x)*F_15(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_15(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_63(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_15(x)*F_85(x))
Eq(F_85(x), F_133(x) + F_86(x))
Eq(F_86(x), F_68(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_131(x)*F_15(x)*F_70(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), x*(x - 2)*F_90(x)**2 + (x + 2)*F_90(x) - 1)
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_15(x)*F_90(x)*F_93(x))
Eq(F_93(x), F_11(x) + F_94(x))
Eq(F_94(x), -F_130(x) + F_95(x))
Eq(F_95(x), F_96(x)/(F_15(x)*F_90(x)))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_24(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_15(x))
Eq(F_100(x), F_101(x) + F_129(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_6(x)*F_89(x))
Eq(F_103(x), F_104(x)*F_90(x))
Eq(F_104(x), F_105(x) - F_90(x))
Eq(F_105(x), F_106(x)/F_121(x))
Eq(F_106(x), F_107(x) - F_114(x))
Eq(F_107(x), F_108(x)/F_15(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x) + F_6(x))
Eq(F_110(x), F_111(x) - F_2(x))
Eq(F_111(x), F_112(x) - F_90(x))
Eq(F_112(x), F_113(x)/F_15(x))
Eq(F_113(x), F_2(x))
Eq(F_114(x), F_115(x) - F_117(x))
Eq(F_115(x), F_116(x)/F_15(x))
Eq(F_116(x), F_110(x))
Eq(F_117(x), F_105(x)*F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_15(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_1(x) + F_118(x))
Eq(F_122(x), F_123(x) + F_126(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x)*F_15(x))
Eq(F_125(x), F_1(x) + F_123(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_15(x))
Eq(F_128(x), F_118(x) + F_126(x))
Eq(F_129(x), F_15(x)*F_6(x)*F_89(x))
Eq(F_130(x), F_11(x)*F_25(x))
Eq(F_131(x), F_132(x)/(F_11(x)*F_15(x)))
Eq(F_132(x), F_94(x))
Eq(F_133(x), F_134(x) + F_138(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_15(x)*F_90(x))
Eq(F_136(x), F_137(x)/F_15(x))
Eq(F_137(x), F_82(x))
Eq(F_138(x), F_139(x)*F_6(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_141(x)*F_15(x))
Eq(F_141(x), F_142(x) - F_145(x))
Eq(F_142(x), F_143(x)/F_15(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_74(x))
Eq(F_145(x), F_146(x) - F_149(x))
Eq(F_146(x), F_147(x)/F_15(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), -F_6(x) + F_74(x))
Eq(F_149(x), F_150(x) - F_87(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_15(x)*F_152(x))
Eq(F_152(x), F_153(x) + F_155(x))
Eq(F_153(x), F_131(x)*F_154(x))
Eq(F_154(x), F_144(x)/F_15(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_131(x)*F_70(x)*F_89(x))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_15(x)*F_159(x)*F_90(x))
Eq(F_159(x), F_160(x) - F_172(x))
Eq(F_160(x), F_161(x)/F_15(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_15(x)*F_163(x))
Eq(F_163(x), F_164(x) + F_171(x))
Eq(F_164(x), F_165(x)*F_70(x))
Eq(F_165(x), F_166(x) + F_53(x))
Eq(F_166(x), F_167(x)/F_15(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x) + F_74(x))
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_149(x)*F_15(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_60(x)*F_90(x))
Eq(F_173(x), F_174(x))
Eq(F_174(x), F_138(x) + F_175(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_15(x)*F_60(x)*F_90(x))
Eq(F_177(x), F_178(x))
Eq(F_178(x), F_11(x)*F_179(x))
Eq(F_179(x), F_180(x))
Eq(F_180(x), F_15(x)*F_181(x))
Eq(F_181(x), F_2(x) + F_5(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x) + F_185(x))
Eq(F_184(x), F_105(x)*F_15(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_105(x)*F_15(x)*F_181(x))
Eq(F_187(x), F_188(x) - F_69(x))
Eq(F_188(x), F_189(x) - F_191(x))
Eq(F_189(x), F_190(x)/F_15(x))
Eq(F_190(x), F_36(x))
Eq(F_191(x), F_185(x))
Eq(F_192(x), F_193(x) - F_201(x))
Eq(F_193(x), F_194(x) + F_200(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_15(x)*F_196(x)*F_90(x))
Eq(F_196(x), F_197(x) + F_199(x))
Eq(F_197(x), F_172(x) + F_198(x))
Eq(F_198(x), F_131(x)*F_42(x))
Eq(F_199(x), F_53(x)*F_90(x))
Eq(F_200(x), F_87(x))
Eq(F_201(x), F_202(x))
Eq(F_202(x), F_15(x)*F_60(x)*F_90(x)**2)
Eq(F_203(x), F_133(x))
Eq(F_204(x), F_62(x))
Eq(F_205(x), F_82(x))
Eq(F_206(x), F_207(x))
Eq(F_207(x), F_15(x)*F_208(x))
Eq(F_208(x), F_209(x) + F_212(x))
Eq(F_209(x), F_210(x) + F_211(x))
Eq(F_210(x), F_74(x)*F_89(x))
Eq(F_211(x), F_80(x)*F_90(x))
Eq(F_212(x), F_62(x)*F_89(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, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1]], "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, 1, 4], "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, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], 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