02314_02341_02431_20314_20341_20431_24031
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3121, 17265, 97174, 553228, 3174692, 18322053, 106189146, 617416861, 3598789955, 21017769326, 122941788984, 720056821488, 4221718181323, 24773612115900, 145480732916823, 854846721090033, 5025711372820344, 29559733797698900, 173928218177509662, 1023725558571100573, 6027289850356183760, 35495202568185769241, 209080111554425757773, 1231798540993587548918, 7258395111067882112934, 42776664055659562977552, 252133868469330156926349, 1486301702611427647300328, 8762512400354923876497369, 51664385159327865467101921, 304642506476253925090024258, 1796480585483078059841398456, 10594585545236205726721360468, 62484433522085731441673271197, 368539007159546274256839940862, 2173784436168996199050126836089, 12822383454755661025690177621011, 75637719034329658306084705659614, 446194041594629243832534918090604, 2632226540326035591190786007856668, 15528715838193364444323023674517019, 91613477104561938066255442929840380, 540497411808026359355208061408550771, 3188873482937404759906466904138078981, 18814360630405824615952106184880229096, 111006731523282996687501084193065894108, 654961981102240198493563788750283765890, 3864462591855194670382070163235804004905, 22801727126391370799051103131579755338888, 134540003444673224955428028748360910337873, 793852219416656930426866713026978000942385, 4684162579713524766530316370444093200563882, 27639354508253349243334736718332634156967550, 163089904732402075927018679021464787402978904, 962341357037201749054096592575130284133030417, 5678501984455752326503758819710086976317238364, 33507395678182906354665886401940149905479547785, 197719522169010512547344263573268295835512191633, 1166702596967251604398431516562028190672008921958, 6884498039752005799728077006988098602137515021828, 40624281138482623029346729842004775218900440490972, 239717751896203017418943783748616134700266550819685, 1414541275159865953963894785736477358568980510094378, 8347026852722728898847114281878543151823206591497541, 49254805190728716886037315309470914634964021650109579, 290647018698189448886453654684021204814380485789695534, 1715076457644559109520079635126804749305987574090525496, 10120485092908483170639893764195143687074473792754517256, 59719931225811670636200318100894991180146254012235917603, 352401133811350609832181358136023704172547506186921207500, 2079482334415745401326132200635264894078432534697191512439, 12270804379014023546084728888774453311002942107395549055401, 72408677410945952820725608077932388781471105338628946409632, 427275424442571509030982580977879118467741412750281700796324, 2521302002996746979061506996933639275922752081663911090243678, 14877892696136190370003725879775611399366816802379209885472469, 87792521503495493982784389430785823307183227721964747463813208, 518051724308155591023529678676848819690267085808558286915567417, 3056948922504276129627424803537407108090027248107644148368900829, 18038593019017727775025157387856974061474898869139746742490304014, 106442856916734969547101683605304103079899066284344786774938238078, 628101365157311051067545176022944132308260546501867061748834428800, 3706314566012686827822728392608899703967177156117879530138213380397, 21870268464747125465632786869846386499726997947516412123810559963600, 129052145089038665459747589168251839860666746404641052228327203191537, 761509975279318156667556689051703782294141833693755911899254381566865, 4493504727466230215713405283109460536248754249800569053248370748912178, 26515146470318960540987641086423142936016000253570313499392031530741728, 156459545892982785452483440967943791054051907621977323508803358565584172, 923228697282549551447954444898568597992590400254773297902169601435915245, 5447731695707496507796695897229879331126093169449788011858538684980179726, 32145582548678615175003208159346997853724736793406464135794456545744902961, 189681973342948086627223183707761486096524086544378462069363734145027645659, 1119257413901431808150369106932855073241456883461018462966705871741595805422
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24594/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[9,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[10,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[17,x]
F[11,x] = F[12,x]+F[6,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[9,x]
F[14,x] = F[15,x]+F[5,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[9,x]
F[17,x] = F[18,x]+F[73,x]
F[18,x] = -F[4,x]+F[19,x]
F[19,x] = -F[122,x]+F[20,x]
F[20,x] = F[120,x]+F[21,x]
F[21,x] = F[22,x]+F[87,x]
F[22,x] = F[0,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[9,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[0,x]*F[14,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[5,x]*F[9,x]
F[29,x] = F[30,x]+F[66,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = 1/F[65,x]/F[9,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[23,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[31,x]*F[36,x]*F[9,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]*F[9,x]
F[38,x] = 1/F[64,x]*F[39,x]
F[39,x] = -F[48,x]+F[40,x]
F[40,x] = 1/F[9,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = (1+F[43,x])*x+F[43,x]^2
F[44,x] = -F[2,x]+F[45,x]
F[45,x] = -F[5,x]+F[46,x]
F[46,x] = 1/F[9,x]*F[47,x]
F[47,x] = F[2,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[9,x]*F[50,x]
F[50,x] = F[44,x]
F[51,x] = F[38,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]*F[9,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[1,x]+F[9,x]
F[56,x] = F[52,x]+F[57,x]
F[57,x] = F[58,x]+F[59,x]+F[63,x]
F[58,x] = 0
F[59,x] = F[60,x]*F[9,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[9,x]
F[62,x] = F[57,x]
F[63,x] = F[52,x]*F[9,x]
F[64,x] = F[1,x]+F[52,x]
F[65,x] = F[36,x]+F[5,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[68,x]*F[9,x]
F[68,x] = 1/F[86,x]/F[9,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[83,x]+F[71,x]
F[71,x] = 1/F[9,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[14,x]*F[75,x]*F[9,x]
F[75,x] = F[17,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[31,x]*F[78,x]*F[9,x]
F[78,x] = 1/F[9,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = -F[5,x]+F[81,x]
F[81,x] = 1/F[31,x]/F[9,x]*F[82,x]
F[82,x] = F[18,x]
F[83,x] = F[31,x]*F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[14,x]*F[86,x]*F[9,x]
F[86,x] = F[81,x]+F[84,x]
F[87,x] = F[88,x]
F[88,x] = F[89,x]+F[91,x]
F[89,x] = F[90,x]
F[90,x] = F[20,x]*F[9,x]
F[91,x] = F[92,x]
F[92,x] = F[9,x]*F[93,x]
F[93,x] = F[110,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[9,x]*F[96,x]
F[96,x] = 1/F[9,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = -F[101,x]+F[99,x]
F[99,x] = 1/F[9,x]*F[100,x]
F[100,x] = F[7,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[4,x]*F[43,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[9,x]
F[105,x] = F[106,x]+F[109,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[14,x]*F[9,x]
F[108,x] = F[106,x]+F[96,x]
F[109,x] = F[108,x]*F[43,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[9,x]
F[112,x] = F[113,x]+F[116,x]
F[113,x] = F[114,x]*F[14,x]
F[114,x] = 1/F[9,x]*F[115,x]
F[115,x] = F[88,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[14,x]*F[31,x]
F[118,x] = F[119,x]
F[119,x] = F[78,x]*F[9,x]
F[120,x] = F[121,x]
F[121,x] = F[114,x]*F[9,x]
F[122,x] = F[123,x]
F[123,x] = F[114,x]*F[5,x]*F[9,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_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{73}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{120}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{87}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{66}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{65}\! \left(x \right) F_{9}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{64}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{43}\! \left(x \right) x +F_{43} \left(x \right)^{2}+x
F_{44}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{2}\! \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_{9}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{44}\! \left(x \right)
F_{51}\! \left(x \right) = F_{38}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{9}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{58}\! \left(x \right) = 0
F_{59}\! \left(x \right) = F_{60}\! \left(x \right) F_{9}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{9}\! \left(x \right)
F_{62}\! \left(x \right) = F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = F_{52}\! \left(x \right) F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{65}\! \left(x \right) = F_{36}\! \left(x \right)+F_{5}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{68}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{86}\! \left(x \right) F_{9}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{75}\! \left(x \right) F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{17}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{31}\! \left(x \right) F_{78}\! \left(x \right) F_{9}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{31}\! \left(x \right) F_{9}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{18}\! \left(x \right)
F_{83}\! \left(x \right) = F_{31}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{14}\! \left(x \right) F_{86}\! \left(x \right) F_{9}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{9}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{110}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{9}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{7}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{9}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right)+F_{96}\! \left(x \right)
F_{109}\! \left(x \right) = F_{108}\! \left(x \right) F_{43}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{9}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{116}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{14}\! \left(x \right)
F_{114}\! \left(x \right) = \frac{F_{115}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{115}\! \left(x \right) = F_{88}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{78}\! \left(x \right) F_{9}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{114}\! \left(x \right) F_{9}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{114}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \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_4(x)*F_9(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_10(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_17(x))
Eq(F_11(x), F_12(x) + F_6(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_9(x))
Eq(F_14(x), F_15(x) + F_5(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_9(x))
Eq(F_17(x), F_18(x) + F_73(x))
Eq(F_18(x), F_19(x) - F_4(x))
Eq(F_19(x), -F_122(x) + F_20(x))
Eq(F_20(x), F_120(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_87(x))
Eq(F_22(x), F_0(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_9(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_0(x)*F_14(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_5(x)*F_9(x))
Eq(F_29(x), F_30(x) + F_66(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x)/(F_65(x)*F_9(x)))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_23(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_31(x)*F_36(x)*F_9(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x)*F_9(x))
Eq(F_38(x), F_39(x)/F_64(x))
Eq(F_39(x), F_40(x) - F_48(x))
Eq(F_40(x), F_41(x)/F_9(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), (x - 3)*(F_43(x) + 1) + (F_43(x) + 1)**2 + F_43(x) + 2)
Eq(F_44(x), -F_2(x) + F_45(x))
Eq(F_45(x), F_46(x) - F_5(x))
Eq(F_46(x), F_47(x)/F_9(x))
Eq(F_47(x), F_2(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_9(x))
Eq(F_50(x), F_44(x))
Eq(F_51(x), F_38(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x)*F_9(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_1(x) + F_9(x))
Eq(F_56(x), F_52(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_59(x) + F_63(x))
Eq(F_58(x), 0)
Eq(F_59(x), F_60(x)*F_9(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_9(x))
Eq(F_62(x), F_57(x))
Eq(F_63(x), F_52(x)*F_9(x))
Eq(F_64(x), F_1(x) + F_52(x))
Eq(F_65(x), F_36(x) + F_5(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_68(x)*F_9(x))
Eq(F_68(x), F_69(x)/(F_86(x)*F_9(x)))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_71(x) - F_83(x))
Eq(F_71(x), F_72(x)/F_9(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_14(x)*F_75(x)*F_9(x))
Eq(F_75(x), F_17(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_31(x)*F_78(x)*F_9(x))
Eq(F_78(x), F_79(x)/F_9(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), -F_5(x) + F_81(x))
Eq(F_81(x), F_82(x)/(F_31(x)*F_9(x)))
Eq(F_82(x), F_18(x))
Eq(F_83(x), F_31(x)*F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_14(x)*F_86(x)*F_9(x))
Eq(F_86(x), F_81(x) + F_84(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_89(x) + F_91(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_20(x)*F_9(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_9(x)*F_93(x))
Eq(F_93(x), F_110(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_9(x)*F_96(x))
Eq(F_96(x), F_97(x)/F_9(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), -F_101(x) + F_99(x))
Eq(F_99(x), F_100(x)/F_9(x))
Eq(F_100(x), F_7(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_4(x)*F_43(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_9(x))
Eq(F_105(x), F_106(x) + F_109(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_14(x)*F_9(x))
Eq(F_108(x), F_106(x) + F_96(x))
Eq(F_109(x), F_108(x)*F_43(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_9(x))
Eq(F_112(x), F_113(x) + F_116(x))
Eq(F_113(x), F_114(x)*F_14(x))
Eq(F_114(x), F_115(x)/F_9(x))
Eq(F_115(x), F_88(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_14(x)*F_31(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_78(x)*F_9(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_114(x)*F_9(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_114(x)*F_5(x)*F_9(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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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": [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]]}, {"patt": [2, 4, 0, 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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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], [0, 2]], [[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, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 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[4, 6], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 4], [4, 3], [4, 4]]}, {"patt": [1, 0, 2], "pos": [[4, 4], [4, 3], [4, 6]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 6], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 6], [4, 6], [4, 6]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[4, 4], [4, 4], [4, 3]]}, {"patt": [2, 1, 0], "pos": [[4, 4], [4, 4], [4, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 3], [4, 3], [4, 3], [4, 4]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 3], [4, 3], [4, 3], [4, 6]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 4], [4, 4], [4, 4], [4, 6]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 3], [4, 3], [4, 4], [4, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 3], [4, 4], [4, 3], [4, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 6]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 4]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "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": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"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": [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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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": [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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25147/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[9,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[10,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[17,x]
F[11,x] = F[12,x]+F[6,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[9,x]
F[14,x] = F[15,x]+F[5,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[9,x]
F[17,x] = F[18,x]+F[72,x]
F[18,x] = -F[4,x]+F[19,x]
F[19,x] = -F[121,x]+F[20,x]
F[20,x] = F[119,x]+F[21,x]
F[21,x] = F[22,x]+F[86,x]
F[22,x] = F[0,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[9,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[0,x]*F[14,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[5,x]*F[9,x]
F[29,x] = F[30,x]+F[65,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = 1/F[64,x]/F[9,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[23,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[31,x]*F[36,x]*F[9,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]*F[9,x]
F[38,x] = 1/F[63,x]*F[39,x]
F[39,x] = -F[45,x]+F[40,x]
F[40,x] = 1/F[9,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = -F[0,x]+F[43,x]
F[43,x] = 1/F[9,x]*F[44,x]
F[44,x] = F[2,x]
F[45,x] = -F[50,x]+F[46,x]
F[46,x] = 1/F[9,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[49,x]+F[42,x]
F[49,x] = (1+F[49,x])*x+F[49,x]^2
F[50,x] = F[38,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]*F[9,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[1,x]+F[9,x]
F[55,x] = F[51,x]+F[56,x]
F[56,x] = F[57,x]+F[58,x]+F[62,x]
F[57,x] = 0
F[58,x] = F[59,x]*F[9,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[9,x]
F[61,x] = F[56,x]
F[62,x] = F[51,x]*F[9,x]
F[63,x] = F[1,x]+F[51,x]
F[64,x] = F[36,x]+F[5,x]
F[65,x] = F[66,x]
F[66,x] = F[14,x]*F[67,x]*F[9,x]
F[67,x] = 1/F[85,x]/F[9,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = -F[82,x]+F[70,x]
F[70,x] = 1/F[9,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[14,x]*F[74,x]*F[9,x]
F[74,x] = F[17,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[31,x]*F[77,x]*F[9,x]
F[77,x] = 1/F[9,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = -F[5,x]+F[80,x]
F[80,x] = 1/F[31,x]/F[9,x]*F[81,x]
F[81,x] = F[18,x]
F[82,x] = F[31,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[85,x]*F[9,x]
F[85,x] = F[80,x]+F[83,x]
F[86,x] = F[87,x]
F[87,x] = F[88,x]+F[90,x]
F[88,x] = F[89,x]
F[89,x] = F[20,x]*F[9,x]
F[90,x] = F[91,x]
F[91,x] = F[9,x]*F[92,x]
F[92,x] = F[109,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[9,x]*F[95,x]
F[95,x] = 1/F[9,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = -F[100,x]+F[98,x]
F[98,x] = 1/F[9,x]*F[99,x]
F[99,x] = F[7,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[4,x]*F[49,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[9,x]
F[104,x] = F[105,x]+F[108,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[14,x]*F[9,x]
F[107,x] = F[105,x]+F[95,x]
F[108,x] = F[107,x]*F[49,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[9,x]
F[111,x] = F[112,x]+F[115,x]
F[112,x] = F[113,x]*F[14,x]
F[113,x] = 1/F[9,x]*F[114,x]
F[114,x] = F[87,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[14,x]*F[31,x]
F[117,x] = F[118,x]
F[118,x] = F[77,x]*F[9,x]
F[119,x] = F[120,x]
F[120,x] = F[113,x]*F[9,x]
F[121,x] = F[122,x]
F[122,x] = F[113,x]*F[5,x]*F[9,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_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{72}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{119}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{86}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{65}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{64}\! \left(x \right) F_{9}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{63}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{2}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{49}\! \left(x \right) x +F_{49} \left(x \right)^{2}+x
F_{50}\! \left(x \right) = F_{38}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{9}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = 0
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{9}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{9}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{51}\! \left(x \right) F_{9}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{36}\! \left(x \right)+F_{5}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{14}\! \left(x \right) F_{67}\! \left(x \right) F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{85}\! \left(x \right) F_{9}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right) F_{74}\! \left(x \right) F_{9}\! \left(x \right)
F_{74}\! \left(x \right) = F_{17}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{31}\! \left(x \right) F_{77}\! \left(x \right) F_{9}\! \left(x \right)
F_{77}\! \left(x \right) = \frac{F_{78}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{31}\! \left(x \right) F_{9}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{18}\! \left(x \right)
F_{82}\! \left(x \right) = F_{31}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{85}\! \left(x \right) F_{9}\! \left(x \right)
F_{85}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{9}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{109}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{9}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{7}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{9}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{108}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{95}\! \left(x \right)
F_{108}\! \left(x \right) = F_{107}\! \left(x \right) F_{49}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{9}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{115}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{14}\! \left(x \right)
F_{113}\! \left(x \right) = \frac{F_{114}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{114}\! \left(x \right) = F_{87}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{77}\! \left(x \right) F_{9}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{113}\! \left(x \right) F_{9}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{113}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \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_4(x)*F_9(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_10(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_17(x))
Eq(F_11(x), F_12(x) + F_6(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_9(x))
Eq(F_14(x), F_15(x) + F_5(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_9(x))
Eq(F_17(x), F_18(x) + F_72(x))
Eq(F_18(x), F_19(x) - F_4(x))
Eq(F_19(x), -F_121(x) + F_20(x))
Eq(F_20(x), F_119(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_86(x))
Eq(F_22(x), F_0(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_9(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_0(x)*F_14(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_5(x)*F_9(x))
Eq(F_29(x), F_30(x) + F_65(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x)/(F_64(x)*F_9(x)))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_23(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_31(x)*F_36(x)*F_9(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x)*F_9(x))
Eq(F_38(x), F_39(x)/F_63(x))
Eq(F_39(x), F_40(x) - F_45(x))
Eq(F_40(x), F_41(x)/F_9(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), -F_0(x) + F_43(x))
Eq(F_43(x), F_44(x)/F_9(x))
Eq(F_44(x), F_2(x))
Eq(F_45(x), F_46(x) - F_50(x))
Eq(F_46(x), F_47(x)/F_9(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_42(x) - F_49(x))
Eq(F_49(x), (x - 3)*(F_49(x) + 1) + (F_49(x) + 1)**2 + F_49(x) + 2)
Eq(F_50(x), F_38(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x)*F_9(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_1(x) + F_9(x))
Eq(F_55(x), F_51(x) + F_56(x))
Eq(F_56(x), F_57(x) + F_58(x) + F_62(x))
Eq(F_57(x), 0)
Eq(F_58(x), F_59(x)*F_9(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_9(x))
Eq(F_61(x), F_56(x))
Eq(F_62(x), F_51(x)*F_9(x))
Eq(F_63(x), F_1(x) + F_51(x))
Eq(F_64(x), F_36(x) + F_5(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_14(x)*F_67(x)*F_9(x))
Eq(F_67(x), F_68(x)/(F_85(x)*F_9(x)))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x) - F_82(x))
Eq(F_70(x), F_71(x)/F_9(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_14(x)*F_74(x)*F_9(x))
Eq(F_74(x), F_17(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_31(x)*F_77(x)*F_9(x))
Eq(F_77(x), F_78(x)/F_9(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), -F_5(x) + F_80(x))
Eq(F_80(x), F_81(x)/(F_31(x)*F_9(x)))
Eq(F_81(x), F_18(x))
Eq(F_82(x), F_31(x)*F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_85(x)*F_9(x))
Eq(F_85(x), F_80(x) + F_83(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_88(x) + F_90(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_20(x)*F_9(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_9(x)*F_92(x))
Eq(F_92(x), F_109(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_9(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_9(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), -F_100(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_9(x))
Eq(F_99(x), F_7(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_4(x)*F_49(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_9(x))
Eq(F_104(x), F_105(x) + F_108(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_14(x)*F_9(x))
Eq(F_107(x), F_105(x) + F_95(x))
Eq(F_108(x), F_107(x)*F_49(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_9(x))
Eq(F_111(x), F_112(x) + F_115(x))
Eq(F_112(x), F_113(x)*F_14(x))
Eq(F_113(x), F_114(x)/F_9(x))
Eq(F_114(x), F_87(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_14(x)*F_31(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_77(x)*F_9(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_113(x)*F_9(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_113(x)*F_5(x)*F_9(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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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:
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"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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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": [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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25252/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[9,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[10,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[17,x]
F[11,x] = F[12,x]+F[6,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[9,x]
F[14,x] = F[15,x]+F[5,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[9,x]
F[17,x] = F[18,x]+F[73,x]
F[18,x] = -F[4,x]+F[19,x]
F[19,x] = -F[122,x]+F[20,x]
F[20,x] = F[120,x]+F[21,x]
F[21,x] = F[22,x]+F[87,x]
F[22,x] = F[0,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[9,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[0,x]*F[14,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[5,x]*F[9,x]
F[29,x] = F[30,x]+F[66,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = 1/F[65,x]/F[9,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[23,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[31,x]*F[36,x]*F[9,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]*F[9,x]
F[38,x] = 1/F[64,x]*F[39,x]
F[39,x] = -F[48,x]+F[40,x]
F[40,x] = 1/F[9,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = (1+F[43,x])*x+F[43,x]^2
F[44,x] = -F[2,x]+F[45,x]
F[45,x] = -F[5,x]+F[46,x]
F[46,x] = 1/F[9,x]*F[47,x]
F[47,x] = F[2,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[9,x]*F[50,x]
F[50,x] = F[44,x]
F[51,x] = F[38,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]*F[9,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[1,x]+F[9,x]
F[56,x] = F[52,x]+F[57,x]
F[57,x] = F[58,x]+F[59,x]+F[63,x]
F[58,x] = 0
F[59,x] = F[60,x]*F[9,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[9,x]
F[62,x] = F[57,x]
F[63,x] = F[52,x]*F[9,x]
F[64,x] = F[1,x]+F[52,x]
F[65,x] = F[36,x]+F[5,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[68,x]*F[9,x]
F[68,x] = 1/F[86,x]/F[9,x]*F[69,x]
F[69,x] = F[70,x]
F[70,x] = -F[83,x]+F[71,x]
F[71,x] = 1/F[9,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[14,x]*F[75,x]*F[9,x]
F[75,x] = F[17,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[31,x]*F[78,x]*F[9,x]
F[78,x] = 1/F[9,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = -F[5,x]+F[81,x]
F[81,x] = 1/F[31,x]/F[9,x]*F[82,x]
F[82,x] = F[18,x]
F[83,x] = F[31,x]*F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[14,x]*F[86,x]*F[9,x]
F[86,x] = F[81,x]+F[84,x]
F[87,x] = F[88,x]
F[88,x] = F[89,x]+F[91,x]
F[89,x] = F[90,x]
F[90,x] = F[20,x]*F[9,x]
F[91,x] = F[92,x]
F[92,x] = F[9,x]*F[93,x]
F[93,x] = F[110,x]+F[94,x]
F[94,x] = F[95,x]
F[95,x] = F[9,x]*F[96,x]
F[96,x] = 1/F[9,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = -F[101,x]+F[99,x]
F[99,x] = 1/F[9,x]*F[100,x]
F[100,x] = F[7,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[4,x]*F[43,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[9,x]
F[105,x] = F[106,x]+F[109,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[14,x]*F[9,x]
F[108,x] = F[106,x]+F[96,x]
F[109,x] = F[108,x]*F[43,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[9,x]
F[112,x] = F[113,x]+F[116,x]
F[113,x] = F[114,x]*F[14,x]
F[114,x] = 1/F[9,x]*F[115,x]
F[115,x] = F[88,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[14,x]*F[31,x]
F[118,x] = F[119,x]
F[119,x] = F[78,x]*F[9,x]
F[120,x] = F[121,x]
F[121,x] = F[114,x]*F[9,x]
F[122,x] = F[123,x]
F[123,x] = F[114,x]*F[5,x]*F[9,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_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{73}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{122}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{120}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{87}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{66}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{65}\! \left(x \right) F_{9}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{64}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{43}\! \left(x \right) x +F_{43} \left(x \right)^{2}+x
F_{44}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{2}\! \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_{9}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{44}\! \left(x \right)
F_{51}\! \left(x \right) = F_{38}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{9}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{58}\! \left(x \right) = 0
F_{59}\! \left(x \right) = F_{60}\! \left(x \right) F_{9}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{9}\! \left(x \right)
F_{62}\! \left(x \right) = F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = F_{52}\! \left(x \right) F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{65}\! \left(x \right) = F_{36}\! \left(x \right)+F_{5}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{68}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{86}\! \left(x \right) F_{9}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{14}\! \left(x \right) F_{75}\! \left(x \right) F_{9}\! \left(x \right)
F_{75}\! \left(x \right) = F_{17}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{31}\! \left(x \right) F_{78}\! \left(x \right) F_{9}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{31}\! \left(x \right) F_{9}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{18}\! \left(x \right)
F_{83}\! \left(x \right) = F_{31}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{14}\! \left(x \right) F_{86}\! \left(x \right) F_{9}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{9}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{110}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{9}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = -F_{101}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{7}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{9}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{109}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right)+F_{96}\! \left(x \right)
F_{109}\! \left(x \right) = F_{108}\! \left(x \right) F_{43}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{9}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{116}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{14}\! \left(x \right)
F_{114}\! \left(x \right) = \frac{F_{115}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{115}\! \left(x \right) = F_{88}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{78}\! \left(x \right) F_{9}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{114}\! \left(x \right) F_{9}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{114}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \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_4(x)*F_9(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_10(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_17(x))
Eq(F_11(x), F_12(x) + F_6(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_9(x))
Eq(F_14(x), F_15(x) + F_5(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_9(x))
Eq(F_17(x), F_18(x) + F_73(x))
Eq(F_18(x), F_19(x) - F_4(x))
Eq(F_19(x), -F_122(x) + F_20(x))
Eq(F_20(x), F_120(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_87(x))
Eq(F_22(x), F_0(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_9(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_0(x)*F_14(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_5(x)*F_9(x))
Eq(F_29(x), F_30(x) + F_66(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x)/(F_65(x)*F_9(x)))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_23(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_31(x)*F_36(x)*F_9(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x)*F_9(x))
Eq(F_38(x), F_39(x)/F_64(x))
Eq(F_39(x), F_40(x) - F_48(x))
Eq(F_40(x), F_41(x)/F_9(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), (x - 3)*(F_43(x) + 1) + (F_43(x) + 1)**2 + F_43(x) + 2)
Eq(F_44(x), -F_2(x) + F_45(x))
Eq(F_45(x), F_46(x) - F_5(x))
Eq(F_46(x), F_47(x)/F_9(x))
Eq(F_47(x), F_2(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_9(x))
Eq(F_50(x), F_44(x))
Eq(F_51(x), F_38(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x)*F_9(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_1(x) + F_9(x))
Eq(F_56(x), F_52(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_59(x) + F_63(x))
Eq(F_58(x), 0)
Eq(F_59(x), F_60(x)*F_9(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_9(x))
Eq(F_62(x), F_57(x))
Eq(F_63(x), F_52(x)*F_9(x))
Eq(F_64(x), F_1(x) + F_52(x))
Eq(F_65(x), F_36(x) + F_5(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_68(x)*F_9(x))
Eq(F_68(x), F_69(x)/(F_86(x)*F_9(x)))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_71(x) - F_83(x))
Eq(F_71(x), F_72(x)/F_9(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_14(x)*F_75(x)*F_9(x))
Eq(F_75(x), F_17(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_31(x)*F_78(x)*F_9(x))
Eq(F_78(x), F_79(x)/F_9(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), -F_5(x) + F_81(x))
Eq(F_81(x), F_82(x)/(F_31(x)*F_9(x)))
Eq(F_82(x), F_18(x))
Eq(F_83(x), F_31(x)*F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_14(x)*F_86(x)*F_9(x))
Eq(F_86(x), F_81(x) + F_84(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_89(x) + F_91(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_20(x)*F_9(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_9(x)*F_93(x))
Eq(F_93(x), F_110(x) + F_94(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_9(x)*F_96(x))
Eq(F_96(x), F_97(x)/F_9(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), -F_101(x) + F_99(x))
Eq(F_99(x), F_100(x)/F_9(x))
Eq(F_100(x), F_7(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_4(x)*F_43(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_9(x))
Eq(F_105(x), F_106(x) + F_109(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_14(x)*F_9(x))
Eq(F_108(x), F_106(x) + F_96(x))
Eq(F_109(x), F_108(x)*F_43(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_9(x))
Eq(F_112(x), F_113(x) + F_116(x))
Eq(F_113(x), F_114(x)*F_14(x))
Eq(F_114(x), F_115(x)/F_9(x))
Eq(F_115(x), F_88(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_14(x)*F_31(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_78(x)*F_9(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_114(x)*F_9(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_114(x)*F_5(x)*F_9(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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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": [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]]}, {"patt": [2, 4, 0, 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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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], [0, 2]], [[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, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 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[4, 6], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 4], [4, 3], [4, 4]]}, {"patt": [1, 0, 2], "pos": [[4, 4], [4, 3], [4, 6]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 6], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 6], [4, 6], [4, 6]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[4, 4], [4, 4], [4, 3]]}, {"patt": [2, 1, 0], "pos": [[4, 4], [4, 4], [4, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 3], [4, 3], [4, 3], [4, 4]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 3], [4, 3], [4, 3], [4, 6]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 4], [4, 4], [4, 4], [4, 6]]}, {"patt": [1, 2, 0, 3], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 3], [4, 3], [4, 4], [4, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 3], [4, 4], [4, 3], [4, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 4]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 6]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 3]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 4]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 6]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 4]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, "idx": 0}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "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": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"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": [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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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": [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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25492/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[9,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[10,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[17,x]
F[11,x] = F[12,x]+F[6,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]*F[9,x]
F[14,x] = F[15,x]+F[5,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]^2*F[9,x]
F[17,x] = F[18,x]+F[72,x]
F[18,x] = -F[4,x]+F[19,x]
F[19,x] = -F[121,x]+F[20,x]
F[20,x] = F[119,x]+F[21,x]
F[21,x] = F[22,x]+F[86,x]
F[22,x] = F[0,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[9,x]
F[25,x] = F[26,x]+F[27,x]
F[26,x] = F[0,x]*F[14,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[5,x]*F[9,x]
F[29,x] = F[30,x]+F[65,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = 1/F[64,x]/F[9,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[23,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[31,x]*F[36,x]*F[9,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]*F[9,x]
F[38,x] = 1/F[63,x]*F[39,x]
F[39,x] = -F[45,x]+F[40,x]
F[40,x] = 1/F[9,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = -F[0,x]+F[43,x]
F[43,x] = 1/F[9,x]*F[44,x]
F[44,x] = F[2,x]
F[45,x] = -F[50,x]+F[46,x]
F[46,x] = 1/F[9,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = -F[49,x]+F[42,x]
F[49,x] = (1+F[49,x])*x+F[49,x]^2
F[50,x] = F[38,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]*F[9,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[1,x]+F[9,x]
F[55,x] = F[51,x]+F[56,x]
F[56,x] = F[57,x]+F[58,x]+F[62,x]
F[57,x] = 0
F[58,x] = F[59,x]*F[9,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[9,x]
F[61,x] = F[56,x]
F[62,x] = F[51,x]*F[9,x]
F[63,x] = F[1,x]+F[51,x]
F[64,x] = F[36,x]+F[5,x]
F[65,x] = F[66,x]
F[66,x] = F[14,x]*F[67,x]*F[9,x]
F[67,x] = 1/F[85,x]/F[9,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = -F[82,x]+F[70,x]
F[70,x] = 1/F[9,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[14,x]*F[74,x]*F[9,x]
F[74,x] = F[17,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[31,x]*F[77,x]*F[9,x]
F[77,x] = 1/F[9,x]*F[78,x]
F[78,x] = F[79,x]
F[79,x] = -F[5,x]+F[80,x]
F[80,x] = 1/F[31,x]/F[9,x]*F[81,x]
F[81,x] = F[18,x]
F[82,x] = F[31,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[85,x]*F[9,x]
F[85,x] = F[80,x]+F[83,x]
F[86,x] = F[87,x]
F[87,x] = F[88,x]+F[90,x]
F[88,x] = F[89,x]
F[89,x] = F[20,x]*F[9,x]
F[90,x] = F[91,x]
F[91,x] = F[9,x]*F[92,x]
F[92,x] = F[109,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[9,x]*F[95,x]
F[95,x] = 1/F[9,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = -F[100,x]+F[98,x]
F[98,x] = 1/F[9,x]*F[99,x]
F[99,x] = F[7,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[4,x]*F[49,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[9,x]
F[104,x] = F[105,x]+F[108,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[14,x]*F[9,x]
F[107,x] = F[105,x]+F[95,x]
F[108,x] = F[107,x]*F[49,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[9,x]
F[111,x] = F[112,x]+F[115,x]
F[112,x] = F[113,x]*F[14,x]
F[113,x] = 1/F[9,x]*F[114,x]
F[114,x] = F[87,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[14,x]*F[31,x]
F[117,x] = F[118,x]
F[118,x] = F[77,x]*F[9,x]
F[119,x] = F[120,x]
F[120,x] = F[113,x]*F[9,x]
F[121,x] = F[122,x]
F[122,x] = F[113,x]*F[5,x]*F[9,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_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{5}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{72}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{119}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{86}\! \left(x \right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{14}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{65}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{64}\! \left(x \right) F_{9}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{63}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{2}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{49}\! \left(x \right) x +F_{49} \left(x \right)^{2}+x
F_{50}\! \left(x \right) = F_{38}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right) F_{9}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = 0
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{9}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{9}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{51}\! \left(x \right) F_{9}\! \left(x \right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{36}\! \left(x \right)+F_{5}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{14}\! \left(x \right) F_{67}\! \left(x \right) F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{85}\! \left(x \right) F_{9}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right) F_{74}\! \left(x \right) F_{9}\! \left(x \right)
F_{74}\! \left(x \right) = F_{17}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{31}\! \left(x \right) F_{77}\! \left(x \right) F_{9}\! \left(x \right)
F_{77}\! \left(x \right) = \frac{F_{78}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{31}\! \left(x \right) F_{9}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{18}\! \left(x \right)
F_{82}\! \left(x \right) = F_{31}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{85}\! \left(x \right) F_{9}\! \left(x \right)
F_{85}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{9}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{109}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{9}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{7}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{9}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{108}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{95}\! \left(x \right)
F_{108}\! \left(x \right) = F_{107}\! \left(x \right) F_{49}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{9}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{115}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{14}\! \left(x \right)
F_{113}\! \left(x \right) = \frac{F_{114}\! \left(x \right)}{F_{9}\! \left(x \right)}
F_{114}\! \left(x \right) = F_{87}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{77}\! \left(x \right) F_{9}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{113}\! \left(x \right) F_{9}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{113}\! \left(x \right) F_{5}\! \left(x \right) F_{9}\! \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_4(x)*F_9(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_10(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_17(x))
Eq(F_11(x), F_12(x) + F_6(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x)*F_9(x))
Eq(F_14(x), F_15(x) + F_5(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)**2*F_9(x))
Eq(F_17(x), F_18(x) + F_72(x))
Eq(F_18(x), F_19(x) - F_4(x))
Eq(F_19(x), -F_121(x) + F_20(x))
Eq(F_20(x), F_119(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_86(x))
Eq(F_22(x), F_0(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_9(x))
Eq(F_25(x), F_26(x) + F_27(x))
Eq(F_26(x), F_0(x)*F_14(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_5(x)*F_9(x))
Eq(F_29(x), F_30(x) + F_65(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x)/(F_64(x)*F_9(x)))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_23(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_31(x)*F_36(x)*F_9(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x)*F_9(x))
Eq(F_38(x), F_39(x)/F_63(x))
Eq(F_39(x), F_40(x) - F_45(x))
Eq(F_40(x), F_41(x)/F_9(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), -F_0(x) + F_43(x))
Eq(F_43(x), F_44(x)/F_9(x))
Eq(F_44(x), F_2(x))
Eq(F_45(x), F_46(x) - F_50(x))
Eq(F_46(x), F_47(x)/F_9(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_42(x) - F_49(x))
Eq(F_49(x), (x - 3)*(F_49(x) + 1) + (F_49(x) + 1)**2 + F_49(x) + 2)
Eq(F_50(x), F_38(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x)*F_9(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_1(x) + F_9(x))
Eq(F_55(x), F_51(x) + F_56(x))
Eq(F_56(x), F_57(x) + F_58(x) + F_62(x))
Eq(F_57(x), 0)
Eq(F_58(x), F_59(x)*F_9(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_9(x))
Eq(F_61(x), F_56(x))
Eq(F_62(x), F_51(x)*F_9(x))
Eq(F_63(x), F_1(x) + F_51(x))
Eq(F_64(x), F_36(x) + F_5(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_14(x)*F_67(x)*F_9(x))
Eq(F_67(x), F_68(x)/(F_85(x)*F_9(x)))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x) - F_82(x))
Eq(F_70(x), F_71(x)/F_9(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_14(x)*F_74(x)*F_9(x))
Eq(F_74(x), F_17(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_31(x)*F_77(x)*F_9(x))
Eq(F_77(x), F_78(x)/F_9(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), -F_5(x) + F_80(x))
Eq(F_80(x), F_81(x)/(F_31(x)*F_9(x)))
Eq(F_81(x), F_18(x))
Eq(F_82(x), F_31(x)*F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_85(x)*F_9(x))
Eq(F_85(x), F_80(x) + F_83(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_88(x) + F_90(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_20(x)*F_9(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_9(x)*F_92(x))
Eq(F_92(x), F_109(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_9(x)*F_95(x))
Eq(F_95(x), F_96(x)/F_9(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), -F_100(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_9(x))
Eq(F_99(x), F_7(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_4(x)*F_49(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_9(x))
Eq(F_104(x), F_105(x) + F_108(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_14(x)*F_9(x))
Eq(F_107(x), F_105(x) + F_95(x))
Eq(F_108(x), F_107(x)*F_49(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_9(x))
Eq(F_111(x), F_112(x) + F_115(x))
Eq(F_112(x), F_113(x)*F_14(x))
Eq(F_113(x), F_114(x)/F_9(x))
Eq(F_114(x), F_87(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_14(x)*F_31(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_77(x)*F_9(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_113(x)*F_9(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_113(x)*F_5(x)*F_9(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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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:
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"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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 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": [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], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 4, 0, 3, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25926/
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[34,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (x^2*k[0]^2+4*x*k[0]-1)*F[7,x,k[0]]^2+(4*x^2*k[0]^2-5*x*k[0]+2)*F[7,x,k[0]]+4*k[0]^2*x^2-k[0]*x
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[34,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = F[4,x]*F[7,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[19,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[23,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]
F[17,x,k[0]] = F[16,x,k[0]]*F[19,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[20,x,k[0]]^2*F[19,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,1,k[0]]
F[25,x,k[0],k[1]] = F[26,x,k[0]*k[1],k[1]]
F[26,x,k[0],k[1]] = F[0,x]*F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0],k[1]]+F[43,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[29,x]*F[35,x,k[0],k[1]]
F[29,x] = F[30,x,1]
F[30,x,k[0]] = F[20,x,k[0]]+F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[20,x,k[0]]*F[33,x,k[0]]*F[34,x]
F[33,x,k[0]] = 1/(-1+k[0])*(F[30,x,k[0]]*k[0]-F[30,x,1])
F[34,x] = x
F[36,x,k[0],k[1]] = F[20,x,k[0]]+F[35,x,k[0],k[1]]
F[36,x,k[0],k[1]] = F[37,x,k[1]]+F[38,x,k[0],k[1]]
F[37,x,k[0]] = -2+k[0]^2*x^2+F[37,x,k[0]]^2*(x^2*k[0]^2+4*x*k[0]-1)+(2*x^2*k[0]^2-13*x*k[0]+4)*F[37,x,k[0]]+8*k[0]*x
F[38,x,k[0],k[1]] = F[39,x,k[0],k[1]]
F[39,x,k[0],k[1]] = F[19,x,k[0]]*F[20,x,k[0]]*F[40,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[36,x,k[0],k[1]]+F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = F[42,x,k[0],k[1]]*F[7,x,k[1]]
F[42,x,k[0],k[1]] = (F[20,x,k[0]]*k[0]-F[20,x,k[1]]*k[1])/(-k[1]+k[0])
F[43,x,k[0],k[1]] = F[44,x,k[1]]*F[55,x,k[0],k[1]]
F[45,x,k[0]] = F[29,x]+F[44,x,k[0]]
F[45,x,k[0]] = F[46,x,1,k[0]]
F[47,x,k[0],k[1]] = F[46,x,k[0]*k[1],k[1]]
F[47,x,k[0],k[1]] = F[48,x,k[0],k[1]]+F[49,x,k[0],k[1]]
F[48,x,k[0],k[1]] = F[36,x,k[0]*k[1],k[1]]
F[49,x,k[0],k[1]] = F[50,x,k[0],k[1]]
F[50,x,k[0],k[1]] = F[34,x]*F[51,x,k[0],k[1]]
F[51,x,k[0],k[1]] = F[52,x,k[0],k[1]]+F[54,x,k[0],k[1]]
F[52,x,k[0],k[1]] = F[20,x,k[1]]*F[53,x,k[0],k[1]]
F[53,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[47,x,k[0],k[1]]*k[0]*k[1]-F[47,x,1/k[1],k[1]])
F[54,x,k[0],k[1]] = F[27,x,k[0]*k[1],k[1]]
F[55,x,k[0],k[1]] = k[1]*(F[21,x,k[0]]-F[21,x,k[1]])/(-k[1]+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+4 x^{2} F_{7}\! \left(x , y\right) y^{2}+4 y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -5 x F_{7}\! \left(x , y\right) y -y x -F_{7}\! \left(x , y\right)^{2}+2 F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y\right) = F_{1}\! \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_{20}\! \left(x , y\right)^{2} F_{19}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , 1, y\right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y z , z\right)
F_{26}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{27}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right)+F_{43}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{29}\! \left(x \right) F_{35}\! \left(x , y , z\right)
F_{29}\! \left(x \right) = F_{30}\! \left(x , 1\right)
F_{30}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{34}\! \left(x \right)
F_{33}\! \left(x , y\right) = -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x \right) = x
F_{36}\! \left(x , y , z\right) = F_{20}\! \left(x , y\right)+F_{35}\! \left(x , y , z\right)
F_{36}\! \left(x , y , z\right) = F_{37}\! \left(x , z\right)+F_{38}\! \left(x , y , z\right)
F_{37}\! \left(x , y\right) = x^{2} F_{37}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{37}\! \left(x , y\right) y^{2}+y^{2} x^{2}+4 x F_{37}\! \left(x , y\right)^{2} y -13 x F_{37}\! \left(x , y\right) y +8 y x -F_{37}\! \left(x , y\right)^{2}+4 F_{37}\! \left(x , y\right)-2
F_{38}\! \left(x , y , z\right) = F_{39}\! \left(x , y , z\right)
F_{39}\! \left(x , y , z\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{40}\! \left(x , y , z\right)
F_{40}\! \left(x , y , z\right) = F_{36}\! \left(x , y , z\right)+F_{41}\! \left(x , y , z\right)
F_{41}\! \left(x , y , z\right) = F_{42}\! \left(x , y , z\right) F_{7}\! \left(x , z\right)
F_{42}\! \left(x , y , z\right) = \frac{y F_{20}\! \left(x , y\right)-F_{20}\! \left(x , z\right) z}{-z +y}
F_{43}\! \left(x , y , z\right) = F_{44}\! \left(x , z\right) F_{55}\! \left(x , y , z\right)
F_{45}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{44}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , 1, y\right)
F_{47}\! \left(x , y , z\right) = F_{46}\! \left(x , y z , z\right)
F_{47}\! \left(x , y , z\right) = F_{48}\! \left(x , y , z\right)+F_{49}\! \left(x , y , z\right)
F_{48}\! \left(x , y , z\right) = F_{36}\! \left(x , y z , z\right)
F_{49}\! \left(x , y , z\right) = F_{50}\! \left(x , y , z\right)
F_{50}\! \left(x , y , z\right) = F_{34}\! \left(x \right) F_{51}\! \left(x , y , z\right)
F_{51}\! \left(x , y , z\right) = F_{52}\! \left(x , y , z\right)+F_{54}\! \left(x , y , z\right)
F_{52}\! \left(x , y , z\right) = F_{20}\! \left(x , z\right) F_{53}\! \left(x , y , z\right)
F_{53}\! \left(x , y , z\right) = \frac{y z F_{47}\! \left(x , y , z\right)-F_{47}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{54}\! \left(x , y , z\right) = F_{27}\! \left(x , y z , z\right)
F_{55}\! \left(x , y , z\right) = \frac{z \left(F_{21}\! \left(x , y\right)-F_{21}\! \left(x , z\right)\right)}{-z +y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_34(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0**2*x**2 + 8*k_0*x + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 + 4*k_0*x - 1) + (F_7(x, k_0) + 1)*(2*k_0**2*x**2 - 13*k_0*x + 3) + F_7(x, k_0) - 2)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_34(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), F_4(x)*F_7(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_19(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_23(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_20(x, k_0))
Eq(F_17(x, k_0), F_16(x, k_0)*F_19(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), -F_6(x, 1) + (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_19(x, k_0)*F_20(x, k_0)**2)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, 1, k_0))
Eq(F_25(x, k_0, k_1), F_26(x, k_0*k_1, k_1))
Eq(F_26(x, k_0, k_1), F_0(x)*F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_1) + F_43(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_29(x)*F_35(x, k_0, k_1))
Eq(F_29(x), F_30(x, 1))
Eq(F_30(x, k_0), F_20(x, k_0) + F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_20(x, k_0)*F_33(x, k_0)*F_34(x))
Eq(F_33(x, k_0), (k_0*F_30(x, k_0) - F_30(x, 1))/(k_0 - 1))
Eq(F_34(x), x)
Eq(F_36(x, k_0, k_1), F_20(x, k_0) + F_35(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), F_37(x, k_1) + F_38(x, k_0, k_1))
Eq(F_37(x, k_0), k_0**2*x**2 + 8*k_0*x + (k_0**2*x**2 + 4*k_0*x - 1)*F_37(x, k_0)**2 + (2*k_0**2*x**2 - 13*k_0*x + 4)*F_37(x, k_0) - 2)
Eq(F_38(x, k_0, k_1), F_39(x, k_0, k_1))
Eq(F_39(x, k_0, k_1), F_19(x, k_0)*F_20(x, k_0)*F_40(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_36(x, k_0, k_1) + F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, k_0, k_1)*F_7(x, k_1))
Eq(F_42(x, k_0, k_1), (-k_0*F_20(x, k_0) + k_1*F_20(x, k_1))/(-k_0 + k_1))
Eq(F_43(x, k_0, k_1), F_44(x, k_1)*F_55(x, k_0, k_1))
Eq(F_45(x, k_0), F_29(x) + F_44(x, k_0))
Eq(F_45(x, k_0), F_46(x, 1, k_0))
Eq(F_47(x, k_0, k_1), F_46(x, k_0*k_1, k_1))
Eq(F_47(x, k_0, k_1), F_48(x, k_0, k_1) + F_49(x, k_0, k_1))
Eq(F_48(x, k_0, k_1), F_36(x, k_0*k_1, k_1))
Eq(F_49(x, k_0, k_1), F_50(x, k_0, k_1))
Eq(F_50(x, k_0, k_1), F_34(x)*F_51(x, k_0, k_1))
Eq(F_51(x, k_0, k_1), F_52(x, k_0, k_1) + F_54(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), F_20(x, k_1)*F_53(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), (k_0*k_1*F_47(x, k_0, k_1) - F_47(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_54(x, k_0, k_1), F_27(x, k_0*k_1, k_1))
Eq(F_55(x, k_0, k_1), -F_21(x, k_0) + (-k_0*F_21(x, k_0) + k_1*F_21(x, k_1))/(-k_0 + k_1))
Pack JSON:
{"name": "point_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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