01243_02143_02413_02431_10243_12043_12403_12430_20143_20413_20431_21043_21403_21430_24013_24031_24103_24130_24301_24310
Counting sequence:
1, 1, 2, 6, 24, 100, 420, 1764, 7392, 30888, 128700, 534820, 2217072, 9170616, 37858184, 156009000, 641865600, 2636997840, 10819447020, 44338518180, 181502706000, 742250539800, 3032623634040, 12379931112120, 50498375129280, 205835768190000, 838437695760600, 3413086373819304, 13885718922546912, 56461243343795248, 229460718022813200, 932085261485772240, 3784466610075565568, 15359135657423615904, 62309220792048078156, 252679995190569300900, 1024309493108660762640, 4150892279216525280984, 16815476530519797609752, 68099092009089422183448, 275704825947730454184000, 1115897609637160312639600, 4515302766800119411388040, 18265736976498044030040120, 73872061393323207970882080, 298689888826068996288186000, 1207431247557503154692242800, 4879888800515010334374542640, 19718181573218839167944497920, 79659355876913342276882160480, 321753350693314945421080155000, 1299358225208023702039251858600, 5246349916369338053410249857312, 21179269307937455957696129325936, 85485555798801255469307598919344, 344988878223673829724144922263600, 1392035931526096692058637289025920, 5616051456215349836207995764102624, 22654222603455151782899170883015472, 91370660675883543216327145963136208, 368473149423492956278584048594763200, 1485758682166931767774155002723629920, 5990124348102526001441374650325104672, 24147391806232446170802537789227008416, 97331422579959967361268600858573993984, 392270738324491435917811201376941320000, 1580775638767253469164948793241116415500, 6369530930473366775754150312346372577700, 25662497299256784820632279955848705075600, 103382237803019979938078328865155209165400, 416437402914978180057476644405676354055000, 1677302947475773398517215453471641364759000, 6755109818244482966744584409796453431995200, 27202795523939930820305949659638065405135600, 109535761885210178059542450265711570820831400, 441022365976179447018705718859538442308975000, 1775532206373288930483956861657212063955268000, 7147607369726576806821907745190594389389049040, 28771196035762003291438287567619555952913267120, 115803345482602508752452408201737453480806746480, 466069939624885137465241759721371120792600992000, 1875636526015716548463759322271100171873261650400, 7547700316726207518169905569065001247186291789480, 30370346080220509203644820270826742446898650160440, 122195350728880168091773399690907951096954545400160, 491620709688050590214320691527534140600914371554000, 1977774967097978312789376406643822220535107060016400, 7956012405264452840750260275481290864166259672618640, 32002693043148753367444511260476467501730520062433920, 128721385785099622674645543332694924274854967973170080, 517712417291960944107678066264030913516079097440610000, 2082095856509766523531178679978713089638822976897854000, 8373126877900570234312930525491928488442524245068097600, 33670531470544744088435155168563218405626615054283632800, 135390482084224097197115834317350276534265785919538815200, 544380627460589912660560692776808764605289679143421340000, 2188739311124862287140511882806107713817281146692653952000, 8799596006765811471523465865676397525748292820683426513600, 35376039101083002389170153366351118747198570665281868015800, 142211230613169140889937748868266531854139088933629423980200, 571659244889053442043658236019624277706805243085090448900000
Generating function in Maple syntax:
(-6*x^3*(-4*x+1)^(1/2)+2*x^2*(-4*x+1)^(1/2)+16*x^3+8*x^2-7*x+1)/(-1+4*x)^2
Generating function in latex syntax:
\frac{-6 x^{3} \sqrt{-4 x +1}+2 x^{2} \sqrt{-4 x +1}+16 x^{3}+8 x^{2}-7 x +1}{\left(-1+4 x \right)^{2}}
Generating function in sympy syntax:
(-6*x**3*sqrt(1 - 4*x) + 16*x**3 + 2*x**2*sqrt(1 - 4*x) + 8*x**2 - 7*x + 1)/(4*x - 1)**2
Implicit equation for the generating function in Maple syntax:
(-1+4*x)^3*F(x)^2-2*(x+1)*(-1+4*x)^3*F(x)+36*x^6+40*x^5+84*x^4-20*x^3-25*x^2+10*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(-1+4 x \right)^{3} F \! \left(x \right)^{2}-2 \left(x +1\right) \left(-1+4 x \right)^{3} F \! \left(x \right)+36 x^{6}+40 x^{5}+84 x^{4}-20 x^{3}-25 x^{2}+10 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+2) = -6*(-3+2*n)/n*a(n)+(-4+7*n)/n*a(n+1), n >= 4
Recurrence in latex format:
a{\left(0 \right)} = 1
a{\left(1 \right)} = 1
a{\left(2 \right)} = 2
a{\left(3 \right)} = 6
a{\left(n + 2 \right)} = - \frac{6 \left(2 n - 3\right) a{\left(n \right)}}{n} + \frac{\left(7 n - 4\right) a{\left(n + 1 \right)}}{n}, \quad n \geq 4
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24664/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = F[6,x]^2*(-1+4*x)+F[6,x]+x^2
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[17,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]^2*F[14,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = x
F[15,x] = 1/F[14,x]*F[16,x]
F[16,x] = F[2,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[14,x]*F[19,x]
F[19,x] = F[110,x]+F[20,x]
F[20,x] = F[21,x]+F[62,x]
F[21,x] = F[22,x]*F[25,x]
F[22,x] = F[13,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[13,x]^2*F[14,x]*F[22,x]
F[25,x] = 1/F[13,x]*F[26,x]
F[26,x] = -F[46,x]+F[27,x]
F[27,x] = -F[61,x]+F[28,x]
F[28,x] = 1/F[14,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = F[32,x]+F[55,x]
F[32,x] = F[33,x]+F[52,x]
F[33,x] = -F[50,x]+F[34,x]
F[34,x] = 1/F[14,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[14,x]*F[37,x]
F[37,x] = F[38,x]+F[46,x]
F[38,x] = F[13,x]*F[39,x]
F[39,x] = F[40,x]+F[44,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = -1+x^2+4*x+F[41,x]^2*(-1+4*x)+(3-8*x)*F[41,x]
F[42,x] = F[43,x]
F[43,x] = F[14,x]*F[33,x]
F[44,x] = F[45,x]
F[45,x] = F[13,x]^2*F[14,x]
F[46,x] = F[47,x]
F[47,x] = F[13,x]^2*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[14,x]*F[22,x]
F[50,x] = F[51,x]
F[51,x] = F[13,x]^3*F[14,x]
F[52,x] = F[53,x]
F[53,x] = F[13,x]^2*F[54,x]
F[54,x] = F[49,x]
F[55,x] = F[56,x]
F[56,x] = -F[57,x]+F[34,x]
F[57,x] = F[58,x]
F[58,x] = F[13,x]^2*F[59,x]
F[59,x] = F[41,x]+F[60,x]
F[60,x] = F[13,x]*F[14,x]
F[61,x] = F[47,x]
F[62,x] = F[63,x]
F[63,x] = F[13,x]^2*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[14,x]*F[66,x]
F[66,x] = F[22,x]+F[67,x]
F[67,x] = 1/F[14,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[14,x]*F[71,x]
F[71,x] = 1/F[13,x]^2*F[72,x]
F[72,x] = F[73,x]
F[73,x] = -F[99,x]+F[74,x]
F[74,x] = 1/F[14,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[14,x]*F[77,x]
F[77,x] = -F[85,x]+F[78,x]
F[78,x] = 1/F[14,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[14,x]*F[82,x]
F[82,x] = F[7,x]
F[83,x] = F[84,x]
F[84,x] = F[13,x]^2*F[2,x]
F[85,x] = F[86,x]
F[86,x] = F[54,x]*F[87,x]
F[87,x] = 1/F[98,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[96,x]+F[90,x]
F[90,x] = F[91,x]+F[94,x]
F[91,x] = 1/F[14,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[23,x]+F[69,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[87,x]
F[96,x] = 1/F[14,x]*F[97,x]
F[97,x] = F[69,x]
F[98,x] = F[1,x]+F[14,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[13,x]
F[101,x] = -F[103,x]+F[102,x]
F[102,x] = F[21,x]+F[62,x]
F[103,x] = F[104,x]*F[22,x]
F[104,x] = -F[109,x]+F[105,x]
F[105,x] = F[106,x]+F[44,x]
F[106,x] = F[107,x]+F[25,x]
F[107,x] = F[108,x]
F[108,x] = F[13,x]^2*F[14,x]
F[109,x] = F[107,x]+F[39,x]
F[110,x] = F[63,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 4 x F_{6} \left(x \right)^{2}+x^{2}-F_{6} \left(x \right)^{2}+F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{110}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{26}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{55}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{52}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = 4 x F_{41} \left(x \right)^{2}+x^{2}-8 x F_{41}\! \left(x \right)-F_{41} \left(x \right)^{2}+4 x +3 F_{41}\! \left(x \right)-1
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13} \left(x \right)^{3} F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{34}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{41}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{13} \left(x \right)^{2}}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{7}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{54}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{98}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{94}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{23}\! \left(x \right)+F_{69}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{69}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{22}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{44}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{25}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{109}\! \left(x \right) = F_{107}\! \left(x \right)+F_{39}\! \left(x \right)
F_{110}\! \left(x \right) = F_{63}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x**2 + 4*x + (2 - 8*x)*(F_6(x) + 1) + (4*x - 1)*(F_6(x) + 1)**2 + F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_17(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)**2*F_14(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x)/F_14(x))
Eq(F_16(x), F_2(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_14(x)*F_19(x))
Eq(F_19(x), F_110(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_62(x))
Eq(F_21(x), F_22(x)*F_25(x))
Eq(F_22(x), F_13(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_13(x)**2*F_14(x)*F_22(x))
Eq(F_25(x), F_26(x)/F_13(x))
Eq(F_26(x), F_27(x) - F_46(x))
Eq(F_27(x), F_28(x) - F_61(x))
Eq(F_28(x), F_29(x)/F_14(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_55(x))
Eq(F_32(x), F_33(x) + F_52(x))
Eq(F_33(x), F_34(x) - F_50(x))
Eq(F_34(x), F_35(x)/F_14(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_14(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_46(x))
Eq(F_38(x), F_13(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_44(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), x**2 + 4*x + (3 - 8*x)*F_41(x) + (4*x - 1)*F_41(x)**2 - 1)
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_14(x)*F_33(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_13(x)**2*F_14(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)**2*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_14(x)*F_22(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_13(x)**3*F_14(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_13(x)**2*F_54(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_34(x) - F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_13(x)**2*F_59(x))
Eq(F_59(x), F_41(x) + F_60(x))
Eq(F_60(x), F_13(x)*F_14(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_13(x)**2*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_14(x)*F_66(x))
Eq(F_66(x), F_22(x) + F_67(x))
Eq(F_67(x), F_68(x)/F_14(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_14(x)*F_71(x))
Eq(F_71(x), F_72(x)/F_13(x)**2)
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x) - F_99(x))
Eq(F_74(x), F_75(x)/F_14(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_14(x)*F_77(x))
Eq(F_77(x), F_78(x) - F_85(x))
Eq(F_78(x), F_79(x)/F_14(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/F_14(x))
Eq(F_82(x), F_7(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_13(x)**2*F_2(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_54(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_98(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_90(x) - F_96(x))
Eq(F_90(x), F_91(x) + F_94(x))
Eq(F_91(x), F_92(x)/F_14(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_23(x) + F_69(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_87(x))
Eq(F_96(x), F_97(x)/F_14(x))
Eq(F_97(x), F_69(x))
Eq(F_98(x), F_1(x) + F_14(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_13(x))
Eq(F_101(x), F_102(x) - F_103(x))
Eq(F_102(x), F_21(x) + F_62(x))
Eq(F_103(x), F_104(x)*F_22(x))
Eq(F_104(x), F_105(x) - F_109(x))
Eq(F_105(x), F_106(x) + F_44(x))
Eq(F_106(x), F_107(x) + F_25(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_13(x)**2*F_14(x))
Eq(F_109(x), F_107(x) + F_39(x))
Eq(F_110(x), F_63(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, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}, {"patt": [3, 2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 0], [1, 0]]}, 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"pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24668/
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[14,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -1+x^2+4*x+F[5,x]^2*(-1+4*x)+(3-8*x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[17,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]^2*F[14,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = x
F[15,x] = 1/F[14,x]*F[16,x]
F[16,x] = F[2,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[14,x]*F[19,x]
F[19,x] = F[127,x]+F[20,x]
F[20,x] = F[21,x]+F[62,x]
F[21,x] = F[22,x]*F[26,x]
F[22,x] = F[13,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[13,x]^2*F[14,x]*F[22,x]
F[26,x] = 1/F[13,x]*F[27,x]
F[27,x] = -F[46,x]+F[28,x]
F[28,x] = -F[61,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = F[33,x]+F[55,x]
F[33,x] = F[34,x]+F[52,x]
F[34,x] = -F[50,x]+F[35,x]
F[35,x] = 1/F[14,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]
F[38,x] = F[39,x]+F[46,x]
F[39,x] = F[13,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]+F[5,x]
F[42,x] = F[43,x]
F[43,x] = F[14,x]*F[34,x]
F[44,x] = F[45,x]
F[45,x] = F[13,x]^2*F[14,x]
F[46,x] = F[47,x]
F[47,x] = F[13,x]^2*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[14,x]*F[22,x]
F[50,x] = F[51,x]
F[51,x] = F[13,x]^3*F[14,x]
F[52,x] = F[53,x]
F[53,x] = F[13,x]^2*F[54,x]
F[54,x] = F[49,x]
F[55,x] = F[56,x]
F[56,x] = -F[57,x]+F[35,x]
F[57,x] = F[58,x]
F[58,x] = F[13,x]^2*F[59,x]
F[59,x] = F[5,x]+F[60,x]
F[60,x] = F[13,x]*F[14,x]
F[61,x] = F[47,x]
F[62,x] = F[63,x]
F[63,x] = F[13,x]^2*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[14,x]*F[66,x]
F[66,x] = F[22,x]+F[67,x]
F[67,x] = 1/F[14,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[14,x]*F[71,x]
F[71,x] = 1/F[13,x]^2*F[72,x]
F[72,x] = F[73,x]
F[73,x] = -F[116,x]+F[74,x]
F[74,x] = 1/F[14,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[14,x]*F[77,x]
F[77,x] = -F[85,x]+F[78,x]
F[78,x] = 1/F[14,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[14,x]*F[82,x]
F[82,x] = F[7,x]
F[83,x] = F[84,x]
F[84,x] = F[13,x]^2*F[2,x]
F[85,x] = F[86,x]
F[86,x] = F[54,x]*F[87,x]
F[87,x] = 1/F[115,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[106,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = -F[103,x]+F[92,x]
F[92,x] = 1/F[14,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[14,x]*F[95,x]
F[95,x] = F[101,x]+F[96,x]
F[96,x] = F[100,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[13,x]*F[22,x]*F[99,x]
F[99,x] = F[13,x]+F[48,x]
F[100,x] = F[13,x]*F[71,x]
F[101,x] = F[102,x]
F[102,x] = F[13,x]^2*F[64,x]
F[103,x] = F[104,x]
F[104,x] = 1/F[14,x]*F[105,x]
F[105,x] = F[69,x]
F[106,x] = F[107,x]
F[107,x] = -F[108,x]+F[92,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = 1/F[14,x]*F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[24,x]+F[69,x]
F[113,x] = F[114,x]
F[114,x] = F[14,x]*F[87,x]
F[115,x] = F[1,x]+F[14,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[13,x]
F[118,x] = -F[120,x]+F[119,x]
F[119,x] = F[21,x]+F[62,x]
F[120,x] = F[121,x]*F[22,x]
F[121,x] = -F[126,x]+F[122,x]
F[122,x] = F[123,x]+F[44,x]
F[123,x] = F[124,x]+F[26,x]
F[124,x] = F[125,x]
F[125,x] = F[13,x]^2*F[14,x]
F[126,x] = F[124,x]+F[40,x]
F[127,x] = F[63,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = 4 F_{5} \left(x \right)^{2} x +x^{2}-8 F_{5}\! \left(x \right) x -F_{5} \left(x \right)^{2}+4 x +3 F_{5}\! \left(x \right)-1
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_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{127}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{26}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \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_{25}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{55}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{52}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{14}\! \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_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13} \left(x \right)^{3} F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{35}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{13} \left(x \right)^{2}}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{7}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{54}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{115}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{106}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = \frac{F_{93}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{14}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{100}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{13}\! \left(x \right)+F_{48}\! \left(x \right)
F_{100}\! \left(x \right) = F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{64}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{69}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{92}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{24}\! \left(x \right)+F_{69}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{115}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{13}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{22}\! \left(x \right)
F_{121}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{44}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{26}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \left(x \right)+F_{40}\! \left(x \right)
F_{127}\! \left(x \right) = F_{63}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 4*x + (3 - 8*x)*F_5(x) + (4*x - 1)*F_5(x)**2 - 1)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_17(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)**2*F_14(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x)/F_14(x))
Eq(F_16(x), F_2(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_14(x)*F_19(x))
Eq(F_19(x), F_127(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_62(x))
Eq(F_21(x), F_22(x)*F_26(x))
Eq(F_22(x), F_13(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_13(x)**2*F_14(x)*F_22(x))
Eq(F_26(x), F_27(x)/F_13(x))
Eq(F_27(x), F_28(x) - F_46(x))
Eq(F_28(x), F_29(x) - F_61(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_55(x))
Eq(F_33(x), F_34(x) + F_52(x))
Eq(F_34(x), F_35(x) - F_50(x))
Eq(F_35(x), F_36(x)/F_14(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_46(x))
Eq(F_39(x), F_13(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x) + F_5(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_14(x)*F_34(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_13(x)**2*F_14(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)**2*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_14(x)*F_22(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_13(x)**3*F_14(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_13(x)**2*F_54(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_35(x) - F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_13(x)**2*F_59(x))
Eq(F_59(x), F_5(x) + F_60(x))
Eq(F_60(x), F_13(x)*F_14(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_13(x)**2*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_14(x)*F_66(x))
Eq(F_66(x), F_22(x) + F_67(x))
Eq(F_67(x), F_68(x)/F_14(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_14(x)*F_71(x))
Eq(F_71(x), F_72(x)/F_13(x)**2)
Eq(F_72(x), F_73(x))
Eq(F_73(x), -F_116(x) + F_74(x))
Eq(F_74(x), F_75(x)/F_14(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_14(x)*F_77(x))
Eq(F_77(x), F_78(x) - F_85(x))
Eq(F_78(x), F_79(x)/F_14(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/F_14(x))
Eq(F_82(x), F_7(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_13(x)**2*F_2(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_54(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_115(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), -F_106(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), -F_103(x) + F_92(x))
Eq(F_92(x), F_93(x)/F_14(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_14(x)*F_95(x))
Eq(F_95(x), F_101(x) + F_96(x))
Eq(F_96(x), F_100(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_13(x)*F_22(x)*F_99(x))
Eq(F_99(x), F_13(x) + F_48(x))
Eq(F_100(x), F_13(x)*F_71(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_13(x)**2*F_64(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)/F_14(x))
Eq(F_105(x), F_69(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), -F_108(x) + F_92(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_111(x)/F_14(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_24(x) + F_69(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_14(x)*F_87(x))
Eq(F_115(x), F_1(x) + F_14(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_13(x))
Eq(F_118(x), F_119(x) - F_120(x))
Eq(F_119(x), F_21(x) + F_62(x))
Eq(F_120(x), F_121(x)*F_22(x))
Eq(F_121(x), F_122(x) - F_126(x))
Eq(F_122(x), F_123(x) + F_44(x))
Eq(F_123(x), F_124(x) + F_26(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_13(x)**2*F_14(x))
Eq(F_126(x), F_124(x) + F_40(x))
Eq(F_127(x), F_63(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, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24826/
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[14,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -1+x^2+4*x+F[5,x]^2*(-1+4*x)+(3-8*x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[17,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]^2*F[14,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = x
F[15,x] = 1/F[14,x]*F[16,x]
F[16,x] = F[2,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[14,x]*F[19,x]
F[19,x] = F[127,x]+F[20,x]
F[20,x] = F[21,x]+F[62,x]
F[21,x] = F[22,x]*F[26,x]
F[22,x] = F[13,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[13,x]^2*F[14,x]*F[22,x]
F[26,x] = 1/F[13,x]*F[27,x]
F[27,x] = -F[46,x]+F[28,x]
F[28,x] = -F[61,x]+F[29,x]
F[29,x] = 1/F[14,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[14,x]*F[32,x]
F[32,x] = F[33,x]+F[55,x]
F[33,x] = F[34,x]+F[52,x]
F[34,x] = -F[50,x]+F[35,x]
F[35,x] = 1/F[14,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]
F[38,x] = F[39,x]+F[46,x]
F[39,x] = F[13,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]+F[5,x]
F[42,x] = F[43,x]
F[43,x] = F[14,x]*F[34,x]
F[44,x] = F[45,x]
F[45,x] = F[13,x]^2*F[14,x]
F[46,x] = F[47,x]
F[47,x] = F[13,x]^2*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[14,x]*F[22,x]
F[50,x] = F[51,x]
F[51,x] = F[13,x]^3*F[14,x]
F[52,x] = F[53,x]
F[53,x] = F[13,x]^2*F[54,x]
F[54,x] = F[49,x]
F[55,x] = F[56,x]
F[56,x] = -F[57,x]+F[35,x]
F[57,x] = F[58,x]
F[58,x] = F[13,x]^2*F[59,x]
F[59,x] = F[5,x]+F[60,x]
F[60,x] = F[13,x]*F[14,x]
F[61,x] = F[47,x]
F[62,x] = F[63,x]
F[63,x] = F[13,x]^2*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[14,x]*F[66,x]
F[66,x] = F[22,x]+F[67,x]
F[67,x] = 1/F[14,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[14,x]*F[71,x]
F[71,x] = 1/F[13,x]^2*F[72,x]
F[72,x] = F[73,x]
F[73,x] = -F[116,x]+F[74,x]
F[74,x] = 1/F[14,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[14,x]*F[77,x]
F[77,x] = -F[85,x]+F[78,x]
F[78,x] = 1/F[14,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[14,x]*F[82,x]
F[82,x] = F[7,x]
F[83,x] = F[84,x]
F[84,x] = F[13,x]^2*F[2,x]
F[85,x] = F[86,x]
F[86,x] = F[54,x]*F[87,x]
F[87,x] = 1/F[115,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[106,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = -F[103,x]+F[92,x]
F[92,x] = 1/F[14,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[14,x]*F[95,x]
F[95,x] = F[101,x]+F[96,x]
F[96,x] = F[100,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[13,x]*F[22,x]*F[99,x]
F[99,x] = F[13,x]+F[48,x]
F[100,x] = F[13,x]*F[71,x]
F[101,x] = F[102,x]
F[102,x] = F[13,x]^2*F[64,x]
F[103,x] = F[104,x]
F[104,x] = 1/F[14,x]*F[105,x]
F[105,x] = F[69,x]
F[106,x] = F[107,x]
F[107,x] = -F[108,x]+F[92,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = 1/F[14,x]*F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[24,x]+F[69,x]
F[113,x] = F[114,x]
F[114,x] = F[14,x]*F[87,x]
F[115,x] = F[1,x]+F[14,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[13,x]
F[118,x] = -F[120,x]+F[119,x]
F[119,x] = F[21,x]+F[62,x]
F[120,x] = F[121,x]*F[22,x]
F[121,x] = -F[126,x]+F[122,x]
F[122,x] = F[123,x]+F[44,x]
F[123,x] = F[124,x]+F[26,x]
F[124,x] = F[125,x]
F[125,x] = F[13,x]^2*F[14,x]
F[126,x] = F[124,x]+F[40,x]
F[127,x] = F[63,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = 4 F_{5} \left(x \right)^{2} x +x^{2}-8 F_{5}\! \left(x \right) x -F_{5} \left(x \right)^{2}+4 x +3 F_{5}\! \left(x \right)-1
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_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{127}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{26}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \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_{25}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{55}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{52}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{14}\! \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_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{5}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13} \left(x \right)^{3} F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{35}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{13} \left(x \right)^{2}}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{7}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{54}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{115}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{106}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = \frac{F_{93}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{14}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{100}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{13}\! \left(x \right)+F_{48}\! \left(x \right)
F_{100}\! \left(x \right) = F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{64}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{69}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{92}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{24}\! \left(x \right)+F_{69}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{115}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{13}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{120}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{22}\! \left(x \right)
F_{121}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{44}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{26}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \left(x \right)+F_{40}\! \left(x \right)
F_{127}\! \left(x \right) = F_{63}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 4*x + (3 - 8*x)*F_5(x) + (4*x - 1)*F_5(x)**2 - 1)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_17(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)**2*F_14(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x)/F_14(x))
Eq(F_16(x), F_2(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_14(x)*F_19(x))
Eq(F_19(x), F_127(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_62(x))
Eq(F_21(x), F_22(x)*F_26(x))
Eq(F_22(x), F_13(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_13(x)**2*F_14(x)*F_22(x))
Eq(F_26(x), F_27(x)/F_13(x))
Eq(F_27(x), F_28(x) - F_46(x))
Eq(F_28(x), F_29(x) - F_61(x))
Eq(F_29(x), F_30(x)/F_14(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_14(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_55(x))
Eq(F_33(x), F_34(x) + F_52(x))
Eq(F_34(x), F_35(x) - F_50(x))
Eq(F_35(x), F_36(x)/F_14(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_46(x))
Eq(F_39(x), F_13(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x) + F_5(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_14(x)*F_34(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_13(x)**2*F_14(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)**2*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_14(x)*F_22(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_13(x)**3*F_14(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_13(x)**2*F_54(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_35(x) - F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_13(x)**2*F_59(x))
Eq(F_59(x), F_5(x) + F_60(x))
Eq(F_60(x), F_13(x)*F_14(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_13(x)**2*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_14(x)*F_66(x))
Eq(F_66(x), F_22(x) + F_67(x))
Eq(F_67(x), F_68(x)/F_14(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_14(x)*F_71(x))
Eq(F_71(x), F_72(x)/F_13(x)**2)
Eq(F_72(x), F_73(x))
Eq(F_73(x), -F_116(x) + F_74(x))
Eq(F_74(x), F_75(x)/F_14(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_14(x)*F_77(x))
Eq(F_77(x), F_78(x) - F_85(x))
Eq(F_78(x), F_79(x)/F_14(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/F_14(x))
Eq(F_82(x), F_7(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_13(x)**2*F_2(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_54(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_115(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), -F_106(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), -F_103(x) + F_92(x))
Eq(F_92(x), F_93(x)/F_14(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_14(x)*F_95(x))
Eq(F_95(x), F_101(x) + F_96(x))
Eq(F_96(x), F_100(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_13(x)*F_22(x)*F_99(x))
Eq(F_99(x), F_13(x) + F_48(x))
Eq(F_100(x), F_13(x)*F_71(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_13(x)**2*F_64(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)/F_14(x))
Eq(F_105(x), F_69(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), -F_108(x) + F_92(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_111(x)/F_14(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_24(x) + F_69(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_14(x)*F_87(x))
Eq(F_115(x), F_1(x) + F_14(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_13(x))
Eq(F_118(x), F_119(x) - F_120(x))
Eq(F_119(x), F_21(x) + F_62(x))
Eq(F_120(x), F_121(x)*F_22(x))
Eq(F_121(x), F_122(x) - F_126(x))
Eq(F_122(x), F_123(x) + F_44(x))
Eq(F_123(x), F_124(x) + F_26(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_13(x)**2*F_14(x))
Eq(F_126(x), F_124(x) + F_40(x))
Eq(F_127(x), F_63(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, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 4]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25151/
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[7,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[6,x,k[0]] = -1+k[0]^2*x^2+F[6,x,k[0]]^2*(4*x*k[0]-1)+(-8*x*k[0]+3)*F[6,x,k[0]]+4*k[0]*x
F[7,x] = x
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{6}\! \left(x , y\right) = y^{2} x^{2}+4 x F_{6}\! \left(x , y\right)^{2} y -8 x F_{6}\! \left(x , y\right) y +4 y x -F_{6}\! \left(x , y\right)^{2}+3 F_{6}\! \left(x , y\right)-1
F_{7}\! \left(x \right) = x
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_7(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_6(x, k_0), k_0**2*x**2 + 4*k_0*x + (-8*k_0*x + 3)*F_6(x, k_0) + (4*k_0*x - 1)*F_6(x, k_0)**2 - 1)
Eq(F_7(x), x)
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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1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25332/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (-1+4*x)*F[6,x]^2+F[6,x]+x^2
F[7,x] = F[8,x]
F[8,x] = F[14,x]*F[9,x]
F[9,x] = F[10,x]+F[17,x]
F[10,x] = F[11,x]*F[15,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]^2*F[14,x]
F[13,x] = F[1,x]+F[11,x]
F[14,x] = x
F[15,x] = 1/F[14,x]*F[16,x]
F[16,x] = F[2,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[14,x]*F[19,x]
F[19,x] = F[110,x]+F[20,x]
F[20,x] = F[21,x]+F[62,x]
F[21,x] = F[22,x]*F[25,x]
F[22,x] = F[13,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[13,x]^2*F[14,x]*F[22,x]
F[25,x] = 1/F[13,x]*F[26,x]
F[26,x] = -F[46,x]+F[27,x]
F[27,x] = -F[61,x]+F[28,x]
F[28,x] = 1/F[14,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[14,x]*F[31,x]
F[31,x] = F[32,x]+F[55,x]
F[32,x] = F[33,x]+F[52,x]
F[33,x] = -F[50,x]+F[34,x]
F[34,x] = 1/F[14,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[14,x]*F[37,x]
F[37,x] = F[38,x]+F[46,x]
F[38,x] = F[13,x]*F[39,x]
F[39,x] = F[40,x]+F[44,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = -1+x^2+4*x+F[41,x]^2*(-1+4*x)+(3-8*x)*F[41,x]
F[42,x] = F[43,x]
F[43,x] = F[14,x]*F[33,x]
F[44,x] = F[45,x]
F[45,x] = F[13,x]^2*F[14,x]
F[46,x] = F[47,x]
F[47,x] = F[13,x]^2*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[14,x]*F[22,x]
F[50,x] = F[51,x]
F[51,x] = F[13,x]^3*F[14,x]
F[52,x] = F[53,x]
F[53,x] = F[13,x]^2*F[54,x]
F[54,x] = F[49,x]
F[55,x] = F[56,x]
F[56,x] = -F[57,x]+F[34,x]
F[57,x] = F[58,x]
F[58,x] = F[13,x]^2*F[59,x]
F[59,x] = F[41,x]+F[60,x]
F[60,x] = F[13,x]*F[14,x]
F[61,x] = F[47,x]
F[62,x] = F[63,x]
F[63,x] = F[13,x]^2*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[14,x]*F[66,x]
F[66,x] = F[22,x]+F[67,x]
F[67,x] = 1/F[14,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[13,x]*F[14,x]*F[71,x]
F[71,x] = 1/F[13,x]^2*F[72,x]
F[72,x] = F[73,x]
F[73,x] = -F[99,x]+F[74,x]
F[74,x] = 1/F[14,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[14,x]*F[77,x]
F[77,x] = -F[85,x]+F[78,x]
F[78,x] = 1/F[14,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = -F[83,x]+F[81,x]
F[81,x] = 1/F[14,x]*F[82,x]
F[82,x] = F[7,x]
F[83,x] = F[84,x]
F[84,x] = F[13,x]^2*F[2,x]
F[85,x] = F[86,x]
F[86,x] = F[54,x]*F[87,x]
F[87,x] = 1/F[98,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[96,x]+F[90,x]
F[90,x] = F[91,x]+F[94,x]
F[91,x] = 1/F[14,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[23,x]+F[69,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[87,x]
F[96,x] = 1/F[14,x]*F[97,x]
F[97,x] = F[69,x]
F[98,x] = F[1,x]+F[14,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[13,x]
F[101,x] = -F[103,x]+F[102,x]
F[102,x] = F[21,x]+F[62,x]
F[103,x] = F[104,x]*F[22,x]
F[104,x] = -F[109,x]+F[105,x]
F[105,x] = F[106,x]+F[44,x]
F[106,x] = F[107,x]+F[25,x]
F[107,x] = F[108,x]
F[108,x] = F[13,x]^2*F[14,x]
F[109,x] = F[107,x]+F[39,x]
F[110,x] = F[63,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = 4 x F_{6} \left(x \right)^{2}+x^{2}-F_{6} \left(x \right)^{2}+F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{110}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{26}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{55}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{52}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{46}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = 4 F_{41} \left(x \right)^{2} x +x^{2}-8 F_{41}\! \left(x \right) x -F_{41} \left(x \right)^{2}+4 x +3 F_{41}\! \left(x \right)-1
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13} \left(x \right)^{3} F_{14}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{34}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{41}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right)
F_{61}\! \left(x \right) = F_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = \frac{F_{68}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{13} \left(x \right)^{2}}
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{83}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{7}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{54}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{98}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{94}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{23}\! \left(x \right)+F_{69}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{69}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{21}\! \left(x \right)+F_{62}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{22}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{109}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{44}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{25}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{109}\! \left(x \right) = F_{107}\! \left(x \right)+F_{39}\! \left(x \right)
F_{110}\! \left(x \right) = F_{63}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x**2 + 4*x + (2 - 8*x)*(F_6(x) + 1) + (4*x - 1)*(F_6(x) + 1)**2 + F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_14(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_17(x))
Eq(F_10(x), F_11(x)*F_15(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)**2*F_14(x))
Eq(F_13(x), F_1(x) + F_11(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x)/F_14(x))
Eq(F_16(x), F_2(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_14(x)*F_19(x))
Eq(F_19(x), F_110(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_62(x))
Eq(F_21(x), F_22(x)*F_25(x))
Eq(F_22(x), F_13(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_13(x)**2*F_14(x)*F_22(x))
Eq(F_25(x), F_26(x)/F_13(x))
Eq(F_26(x), F_27(x) - F_46(x))
Eq(F_27(x), F_28(x) - F_61(x))
Eq(F_28(x), F_29(x)/F_14(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_14(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_55(x))
Eq(F_32(x), F_33(x) + F_52(x))
Eq(F_33(x), F_34(x) - F_50(x))
Eq(F_34(x), F_35(x)/F_14(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_14(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_46(x))
Eq(F_38(x), F_13(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_44(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), x**2 + 4*x + (3 - 8*x)*F_41(x) + (4*x - 1)*F_41(x)**2 - 1)
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_14(x)*F_33(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_13(x)**2*F_14(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)**2*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_14(x)*F_22(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_13(x)**3*F_14(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_13(x)**2*F_54(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_34(x) - F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_13(x)**2*F_59(x))
Eq(F_59(x), F_41(x) + F_60(x))
Eq(F_60(x), F_13(x)*F_14(x))
Eq(F_61(x), F_47(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_13(x)**2*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_14(x)*F_66(x))
Eq(F_66(x), F_22(x) + F_67(x))
Eq(F_67(x), F_68(x)/F_14(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_13(x)*F_14(x)*F_71(x))
Eq(F_71(x), F_72(x)/F_13(x)**2)
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x) - F_99(x))
Eq(F_74(x), F_75(x)/F_14(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_14(x)*F_77(x))
Eq(F_77(x), F_78(x) - F_85(x))
Eq(F_78(x), F_79(x)/F_14(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_81(x) - F_83(x))
Eq(F_81(x), F_82(x)/F_14(x))
Eq(F_82(x), F_7(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_13(x)**2*F_2(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_54(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_98(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_90(x) - F_96(x))
Eq(F_90(x), F_91(x) + F_94(x))
Eq(F_91(x), F_92(x)/F_14(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_23(x) + F_69(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_87(x))
Eq(F_96(x), F_97(x)/F_14(x))
Eq(F_97(x), F_69(x))
Eq(F_98(x), F_1(x) + F_14(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_13(x))
Eq(F_101(x), F_102(x) - F_103(x))
Eq(F_102(x), F_21(x) + F_62(x))
Eq(F_103(x), F_104(x)*F_22(x))
Eq(F_104(x), F_105(x) - F_109(x))
Eq(F_105(x), F_106(x) + F_44(x))
Eq(F_106(x), F_107(x) + F_25(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_13(x)**2*F_14(x))
Eq(F_109(x), F_107(x) + F_39(x))
Eq(F_110(x), F_63(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, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [0, 2, 4, 3, 1], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [1, 2, 4, 3, 0], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 0, 4, 3, 1], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 1, 4, 3, 0], [2, 4, 0, 1, 3], [2, 4, 0, 3, 1], [2, 4, 1, 0, 3], [2, 4, 1, 3, 0], [2, 4, 3, 0, 1], [2, 4, 3, 1, 0]], "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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], 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