01324_01342_10324_10342_13024_13042
Counting sequence:
1, 1, 2, 6, 24, 114, 596, 3292, 18806, 109834, 651436, 3907526, 23640140, 143982570, 881673958, 5422800580, 33476506418, 207306959294, 1287223325662, 8011391793164, 49963517051594, 312167835655056, 1953573890960760, 12243569442071516, 76835786689994536, 482776110125912924, 3036765348797076532, 19121511353482248268, 120516296022539366206, 760243934164680158372, 4799745132741622502866, 30326245241925334568638, 191749393312813131257074, 1213237835871169617609818, 7681357240892600153605666, 48662573379872559980480644, 308463392499132723171363842, 1956370814080705596423156836, 12414415358390024420284626280, 78816727455160428750452577412, 500631119804212120741509631456, 3181380466370957743129989542084, 20225690313384465814542651119384, 128639191173292075169672144702104, 818499093442765425265858471694512, 5209922700667771165931997974548508, 33174636974286081335539859746386012, 211318216364487958708691957062116222, 1346535913315206165151646129230295674, 8583094738296689767729242670884518322, 54728033416567674665218848727971499404, 349068800510823508073450570559834018804, 2227116906133788698033906799084604989594, 14213517008220226533369148488804954031068, 90736627504088323598184941782124254059398, 579405264907561524787701871388062910646852, 3700814641553857556816389330567662726885518, 23644158621051342400150402869570079584435194, 151098005581427317249899831089091896041403570, 965825772990497323304410176284502158503999818, 6175057903197174999513828817185451231744689066, 39489586925572431870306339541786101405630006406, 252592651247239954823907112333030786591366628562, 1616042446537613583956636060001719035235573372346, 10341325919755624308933723043929216243386839545718, 66189435748320846526798544202108052781193999427866, 423728623504854886910701256617708123970589581617498, 2713134771352800939402270014506818329782176886153288, 17375496876048727545297711926899860375579712011306026, 111296969642779683131892249658394891946338126740772288, 713029844128234487421222242769582253799825262669543496, 4568866104710007067443485348192013284028048960364366980, 29280849535158873237260029438810858210067866285593878584, 187685907767762394781922233390455078731047818110314134440, 1203235682178519132896096614802743573721105236353407538400, 7715057018638467951875257385397721755913975290135437650864, 49476092281070262703295263737353641213821269997206412452068, 317334962108233981472520743760256393832830485119743818151544, 2035660060905963025473083581241277481731468142887116335239556, 13060384438309360952274834279557043745552714360638162340921508, 83804753904623646089975376470745207507965388751007901900405916, 537826258909220292561543818639289613555878752464695031519618868, 3452031181713323589485711760506375996764890869360183227773760340, 22159784183449939670167536771292646261847391104069840084596507312, 142269970182725683018516320222628867402008375218286081875922597452, 913517095238246062822252436497158018295688297932567383345695005100, 5866440975127996717807608051396352867616862174151812328879250451160, 37677859142644181850891967741124040465051289319362415608715851570030, 242019383045359765192634820574931299736594232299409326777689421453750, 1554767535471587100266268782712469174415737625685960287337966914269034, 9989210296627383082292020821766678476748511650725611306670316676792816, 64186877920179551681436921317108922029432754737313842147085098121169586, 412486561948150413162262071885811510086221474740093180542534252927523022, 2651068169460950120749751782453163584440258121144434091201965193814471194, 17040354739123101386436371636070791952601538321047553387138051334170114032, 109542373313174619664310823576190623958828561295039740538521335051404069076, 704256065482997492135179676161105375629974364838962101095327988183722623830, 4528174581759941370275219584012386492122589887685783005040586808012333448514, 29117832856790663016796268191308866228487718822907319037858359734761492201592, 187256749305885482066745340758937927884556248955717550414670405729645445541692, 1204363825154807065306708242437285432180161524143424676050337969212966118827786
Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25307/
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[33,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = (x*F[7,x,k[0]]^3*k[0]+(2*x*k[0]-1)*F[7,x,k[0]]^2+(x^2*k[0]^2-x*k[0]+1)*F[7,x,k[0]]+k[0]^2*x^2)*(1+F[7,x,k[0]])
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[19,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[121,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[13,x,k[0]]
F[12,x,k[0]] = F[2,x]+F[8,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[19,x,k[0]]*F[24,x,k[0]]
F[16,x,k[0]] = F[0,x]*F[15,x,k[0]]
F[17,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]*F[19,x,k[0]]
F[18,x,k[0]] = F[6,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[20,x,k[0]]+F[23,x,k[0]]
F[22,x,k[0]] = F[19,x,k[0]]*F[21,x,k[0]]
F[22,x,k[0]] = F[8,x,k[0]]
F[23,x,k[0]] = F[15,x,k[0]]*F[2,x]
F[24,x,k[0]] = F[25,x,k[0]]+F[29,x,k[0]]
F[25,x,k[0]] = F[12,x,k[0]]*F[26,x,k[0]]
F[26,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[26,x,k[0]]^2*F[19,x,k[0]]
F[30,x,k[0]] = F[120,x,k[0]]+F[29,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[34,x,k[0]]
F[31,x] = 1/F[33,x]*F[32,x]
F[32,x] = F[2,x]
F[33,x] = x
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[19,x,k[0]]*F[26,x,k[0]]*F[36,x,k[0]]
F[37,x,k[0]] = F[119,x,k[0]]+F[36,x,k[0]]
F[38,x,k[0]] = F[15,x,k[0]]*F[19,x,k[0]]*F[37,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[40,x,k[0]] = F[39,x,k[0]]+F[42,x,k[0]]
F[41,x,k[0]] = F[19,x,k[0]]*F[40,x,k[0]]
F[41,x,k[0]] = F[6,x,k[0]]
F[42,x,k[0]] = F[31,x]+F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[6,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[33,x]*F[46,x,k[0]]
F[46,x,k[0]] = -k[0]*(F[47,x,1]-F[47,x,k[0]])/(-1+k[0])
F[47,x,k[0]] = F[118,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[6,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[33,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[15,x,k[0]]*F[19,x,k[0]]*F[53,x]
F[54,x,k[0]] = F[51,x,k[0]]+F[53,x]
F[55,x,k[0]] = F[33,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[117,x,k[0]]+F[57,x]
F[57,x] = F[111,x]+F[58,x]
F[58,x] = 1/F[33,x]*F[59,x]
F[59,x] = -F[107,x]+F[60,x]
F[60,x] = -F[68,x]+F[61,x]
F[61,x] = 1/F[33,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = -F[67,x]+F[64,x]
F[64,x] = -F[0,x]+F[65,x]
F[65,x] = 1/F[33,x]*F[66,x]
F[66,x] = F[2,x]
F[67,x] = (x*F[67,x]^3+(2*x-1)*F[67,x]^2+(x^2-x+1)*F[67,x]+x^2)*(1+F[67,x])
F[68,x] = F[69,x]
F[69,x] = F[33,x]*F[70,x]
F[70,x] = 1/F[33,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = -F[75,x]+F[73,x]
F[73,x] = 1/F[33,x]*F[74,x]
F[74,x] = F[63,x]
F[75,x] = F[76,x]+F[82,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = (1+F[77,x])*x+F[77,x]^2
F[78,x] = F[67,x]*F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[33,x]*F[81,x]
F[81,x] = F[1,x]+F[79,x]
F[82,x] = F[79,x]*F[83,x]
F[83,x] = -F[106,x]+F[84,x]
F[84,x] = 1/F[102,x]*F[85,x]
F[85,x] = -F[91,x]+F[86,x]
F[86,x] = 1/F[33,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = -F[2,x]+F[89,x]
F[89,x] = -F[90,x]+F[31,x]
F[90,x] = 2+F[90,x]^2+(-2+x)*F[90,x]
F[91,x] = F[92,x]
F[92,x] = F[33,x]*F[93,x]
F[93,x] = 1/F[33,x]*F[94,x]
F[94,x] = F[95,x]
F[95,x] = -F[98,x]+F[96,x]
F[96,x] = 1/F[33,x]*F[97,x]
F[97,x] = F[88,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[67,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[1,x]+F[102,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[33,x]
F[104,x] = F[101,x]+F[105,x]
F[105,x] = F[102,x]
F[106,x] = 1+x*F[106,x]^4+F[106,x]^2*(x^2-2*x+3)+F[106,x]^3*(-1-x)+(-2+2*x)*F[106,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[67,x]*F[81,x]
F[109,x] = F[110,x]*F[33,x]
F[110,x] = (-1+x)^3*F[110,x]^2+(x^4-6*x^3+10*x^2-6*x+2)*F[110,x]+x^2*(-1+x)
F[111,x] = -F[89,x]+F[112,x]
F[112,x] = -F[113,x]+F[96,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[43,x,1]
F[115,x] = F[116,x]
F[116,x] = F[49,x,1]
F[117,x,k[0]] = F[49,x,k[0]]
F[118,x,k[0]] = F[44,x,k[0]]
F[119,x,k[0]] = F[26,x,k[0]]*F[43,x,k[0]]
F[120,x,k[0]] = F[0,x]*F[26,x,k[0]]
F[121,x,k[0]] = F[122,x,k[0]]
F[122,x,k[0]] = F[123,x,k[0]]*F[33,x]
F[124,x,k[0]] = F[123,x,k[0]]*F[19,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+x F_{7}\! \left(x , y\right)^{4} y +2 x^{2} F_{7}\! \left(x , y\right) y^{2}+3 x F_{7}\! \left(x , y\right)^{3} y +y^{2} x^{2}+x F_{7}\! \left(x , y\right)^{2} y -x F_{7}\! \left(x , y\right) y -F_{7}\! \left(x , y\right)^{3}+F_{7}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{121}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{8}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{15}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{26}\! \left(x , y\right)^{2} F_{19}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{34}\! \left(x , y\right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)
F_{33}\! \left(x \right) = x
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{119}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{37}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = -\frac{y \left(F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)\right)}{-1+y}
F_{47}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{53}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{53}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{33}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{111}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{59}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{2}\! \left(x \right)
F_{67}\! \left(x \right) = x F_{67} \left(x \right)^{4}+x^{2} F_{67} \left(x \right)^{2}+3 x F_{67} \left(x \right)^{3}+2 x^{2} F_{67}\! \left(x \right)+x F_{67} \left(x \right)^{2}-F_{67} \left(x \right)^{3}+x^{2}-F_{67}\! \left(x \right) x +F_{67}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{33}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{63}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{82}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{77}\! \left(x \right) x +F_{77} \left(x \right)^{2}+x
F_{78}\! \left(x \right) = F_{67}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{33}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{1}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{79}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{106}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{102}\! \left(x \right)}
F_{85}\! \left(x \right) = -F_{91}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{90}\! \left(x \right)+F_{31}\! \left(x \right)
F_{90}\! \left(x \right) = F_{90}\! \left(x \right) x +F_{90} \left(x \right)^{2}-2 F_{90}\! \left(x \right)+2
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{33}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{33}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{88}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{67}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{1}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{33}\! \left(x \right)
F_{104}\! \left(x \right) = F_{101}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)
F_{106}\! \left(x \right) = x F_{106} \left(x \right)^{4}+x^{2} F_{106} \left(x \right)^{2}-F_{106} \left(x \right)^{3} x -2 x F_{106} \left(x \right)^{2}-F_{106} \left(x \right)^{3}+2 F_{106}\! \left(x \right) x +3 F_{106} \left(x \right)^{2}-2 F_{106}\! \left(x \right)+1
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{67}\! \left(x \right) F_{81}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{33}\! \left(x \right)
F_{110}\! \left(x \right) = x^{4} F_{110}\! \left(x \right)+x^{3} F_{110} \left(x \right)^{2}-6 x^{3} F_{110}\! \left(x \right)-3 x^{2} F_{110} \left(x \right)^{2}+x^{3}+10 x^{2} F_{110}\! \left(x \right)+3 x F_{110} \left(x \right)^{2}-x^{2}-6 F_{110}\! \left(x \right) x -F_{110} \left(x \right)^{2}+2 F_{110}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = -F_{113}\! \left(x \right)+F_{96}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{43}\! \left(x , 1\right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{49}\! \left(x , 1\right)
F_{117}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{121}\! \left(x , y\right) = F_{122}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{33}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{123}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_33(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), k_0*x*(F_7(x, k_0) + 1)**4 + (-k_0*x - 1)*(F_7(x, k_0) + 1)**3 + (2*k_0*x - 3)*(F_7(x, k_0) + 1) + (F_7(x, k_0) + 1)**2*(k_0**2*x**2 - 2*k_0*x + 3) + F_7(x, k_0) + 1)
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_19(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_121(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_13(x, k_0))
Eq(F_12(x, k_0), F_2(x) + F_8(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_19(x, k_0)*F_24(x, k_0))
Eq(F_16(x, k_0), F_0(x)*F_15(x, k_0))
Eq(F_17(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0)*F_19(x, k_0))
Eq(F_18(x, k_0), F_6(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_20(x, k_0) + F_23(x, k_0))
Eq(F_22(x, k_0), F_19(x, k_0)*F_21(x, k_0))
Eq(F_22(x, k_0), F_8(x, k_0))
Eq(F_23(x, k_0), F_15(x, k_0)*F_2(x))
Eq(F_24(x, k_0), F_25(x, k_0) + F_29(x, k_0))
Eq(F_25(x, k_0), F_12(x, k_0)*F_26(x, k_0))
Eq(F_26(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_19(x, k_0)*F_26(x, k_0)**2)
Eq(F_30(x, k_0), F_120(x, k_0) + F_29(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_34(x, k_0))
Eq(F_31(x), F_32(x)/F_33(x))
Eq(F_32(x), F_2(x))
Eq(F_33(x), x)
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_19(x, k_0)*F_26(x, k_0)*F_36(x, k_0))
Eq(F_37(x, k_0), F_119(x, k_0) + F_36(x, k_0))
Eq(F_38(x, k_0), F_15(x, k_0)*F_19(x, k_0)*F_37(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_40(x, k_0), F_39(x, k_0) + F_42(x, k_0))
Eq(F_41(x, k_0), F_19(x, k_0)*F_40(x, k_0))
Eq(F_41(x, k_0), F_6(x, k_0))
Eq(F_42(x, k_0), F_31(x) + F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_6(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_33(x)*F_46(x, k_0))
Eq(F_46(x, k_0), -F_47(x, 1) + (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_47(x, k_0), F_118(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_6(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_33(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_15(x, k_0)*F_19(x, k_0)*F_53(x))
Eq(F_54(x, k_0), F_51(x, k_0) + F_53(x))
Eq(F_55(x, k_0), F_33(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_117(x, k_0) + F_57(x))
Eq(F_57(x), F_111(x) + F_58(x))
Eq(F_58(x), F_59(x)/F_33(x))
Eq(F_59(x), -F_107(x) + F_60(x))
Eq(F_60(x), F_61(x) - F_68(x))
Eq(F_61(x), F_62(x)/F_33(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x) - F_67(x))
Eq(F_64(x), -F_0(x) + F_65(x))
Eq(F_65(x), F_66(x)/F_33(x))
Eq(F_66(x), F_2(x))
Eq(F_67(x), x*(F_67(x) + 1)**4 + (-x - 1)*(F_67(x) + 1)**3 + (2*x - 3)*(F_67(x) + 1) + (F_67(x) + 1)**2*(x**2 - 2*x + 3) + F_67(x) + 1)
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_33(x)*F_70(x))
Eq(F_70(x), F_71(x)/F_33(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x) - F_75(x))
Eq(F_73(x), F_74(x)/F_33(x))
Eq(F_74(x), F_63(x))
Eq(F_75(x), F_76(x) + F_82(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), (x - 3)*(F_77(x) + 1) + (F_77(x) + 1)**2 + F_77(x) + 2)
Eq(F_78(x), F_67(x)*F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_33(x)*F_81(x))
Eq(F_81(x), F_1(x) + F_79(x))
Eq(F_82(x), F_79(x)*F_83(x))
Eq(F_83(x), -F_106(x) + F_84(x))
Eq(F_84(x), F_85(x)/F_102(x))
Eq(F_85(x), F_86(x) - F_91(x))
Eq(F_86(x), F_87(x)/F_33(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), -F_2(x) + F_89(x))
Eq(F_89(x), F_31(x) - F_90(x))
Eq(F_90(x), (x - 2)*F_90(x) + F_90(x)**2 + 2)
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_33(x)*F_93(x))
Eq(F_93(x), F_94(x)/F_33(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_96(x) - F_98(x))
Eq(F_96(x), F_97(x)/F_33(x))
Eq(F_97(x), F_88(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_67(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_1(x) + F_102(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_33(x))
Eq(F_104(x), F_101(x) + F_105(x))
Eq(F_105(x), F_102(x))
Eq(F_106(x), x*F_106(x)**4 + (-x - 1)*F_106(x)**3 + (2*x - 2)*F_106(x) + (x**2 - 2*x + 3)*F_106(x)**2 + 1)
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_67(x)*F_81(x))
Eq(F_109(x), F_110(x)*F_33(x))
Eq(F_110(x), (x - 3)*(x - 1)**2*((x - 1)*F_110(x) - 1) + 2*(x - 1)**3 + (x - 1)*((x - 1)*F_110(x) - 1)**2 + F_110(x))
Eq(F_111(x), F_112(x) - F_89(x))
Eq(F_112(x), -F_113(x) + F_96(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_43(x, 1))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_49(x, 1))
Eq(F_117(x, k_0), F_49(x, k_0))
Eq(F_118(x, k_0), F_44(x, k_0))
Eq(F_119(x, k_0), F_26(x, k_0)*F_43(x, k_0))
Eq(F_120(x, k_0), F_0(x)*F_26(x, k_0))
Eq(F_121(x, k_0), F_122(x, k_0))
Eq(F_122(x, k_0), F_123(x, k_0)*F_33(x))
Eq(F_124(x, k_0), F_123(x, k_0)*F_19(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, 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0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 2], [5, 2], [5, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[4, 0], [4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 2]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[5, 0], [5, 0], [5, 2], [5, 0], [5, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], 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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], "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}]}, "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": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], 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0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2]], "symmetry": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2]], "symmetry": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25756/
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[32,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]
F[7,x,k[0]] = F[14,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = F[18,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[0,x]*F[10,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[12,x,k[0]]
F[11,x,k[0]] = 1+F[11,x,k[0]]^2*(x^2*k[0]^2-2*x*k[0]+3)+F[11,x,k[0]]^3*(-x*k[0]-1)+(2*x*k[0]-2)*F[11,x,k[0]]+k[0]*x*F[11,x,k[0]]^4
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]*F[14,x,k[0]]*F[15,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]^2*F[14,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[32,x]
F[20,x,k[0]] = F[21,x,k[0]]+F[25,x,k[0]]
F[21,x,k[0]] = F[11,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[14,x,k[0]]*F[22,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = -k[0]*(F[6,x,1]-F[6,x,k[0]])/(-1+k[0])
F[25,x,k[0]] = F[12,x,k[0]]*F[26,x,k[0]]
F[27,x,k[0]] = F[15,x,k[0]]*F[26,x,k[0]]*F[32,x]
F[27,x,k[0]] = F[28,x,k[0]]
F[29,x,k[0]] = F[28,x,k[0]]+F[79,x,k[0]]
F[29,x,k[0]] = F[30,x]+F[33,x,k[0]]
F[30,x] = 1/F[32,x]*F[31,x]
F[31,x] = F[2,x]
F[32,x] = x
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[14,x,k[0]]*F[15,x,k[0]]*F[35,x,k[0]]
F[36,x,k[0]] = F[35,x,k[0]]+F[78,x,k[0]]
F[37,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[36,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]
F[39,x,k[0]] = F[38,x,k[0]]+F[41,x,k[0]]
F[40,x,k[0]] = F[14,x,k[0]]*F[39,x,k[0]]
F[40,x,k[0]] = F[6,x,k[0]]
F[41,x,k[0]] = F[30,x]+F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[6,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[32,x]*F[45,x,k[0]]
F[45,x,k[0]] = -k[0]*(F[46,x,1]-F[46,x,k[0]])/(-1+k[0])
F[46,x,k[0]] = F[47,x,k[0]]+F[77,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[14,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0],1]
F[50,x,k[0],k[1]] = F[51,x,k[0],k[0]*k[1]]
F[52,x,k[0],k[1]] = (F[51,x,k[0],k[1]]*k[1]-F[51,x,k[0],1])/(-1+k[1])
F[53,x,k[0],k[1]] = F[32,x]*F[52,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[54,x,k[0],k[1]]
F[54,x,k[0],k[1]] = F[55,x,k[1]]+F[57,x,k[0],k[1]]
F[55,x,k[0]] = F[43,x,k[0]]+F[56,x]
F[56,x] = -F[0,x]+F[30,x]
F[57,x,k[0],k[1]] = F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[10,x,k[0]]*F[14,x,k[0]]*F[59,x,k[1]]
F[60,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[59,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[38,x,k[0]] = F[61,x,k[0]]+F[62,x,k[0]]
F[63,x,k[0]] = F[5,x,k[0]]+F[62,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[64,x,k[0]] = F[11,x,k[0]]+F[65,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[10,x,k[0]]*F[11,x,k[0]]*F[14,x,k[0]]*F[15,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[32,x]*F[69,x,k[0]]
F[70,x,k[0]] = F[14,x,k[0]]*F[69,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[72,x,k[0]] = F[71,x,k[0]]+F[76,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[74,x,k[0]]
F[73,x,k[0]] = F[11,x,k[0]]*F[4,x]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[14,x,k[0]]*F[20,x,k[0]]
F[76,x,k[0]] = (F[5,x,k[0]]*k[0]-F[5,x,1])/(-1+k[0])
F[77,x,k[0]] = F[43,x,k[0]]
F[78,x,k[0]] = F[15,x,k[0]]*F[42,x,k[0]]
F[79,x,k[0]] = F[0,x]*F[15,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = x^{2} F_{11}\! \left(x , y\right)^{2} y^{2}+y x F_{11}\! \left(x , y\right)^{4}-x F_{11}\! \left(x , y\right)^{3} y -2 x F_{11}\! \left(x , y\right)^{2} y +2 x F_{11}\! \left(x , y\right) y -F_{11}\! \left(x , y\right)^{3}+3 F_{11}\! \left(x , y\right)^{2}-2 F_{11}\! \left(x , y\right)+1
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{32}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{33}\! \left(x , y\right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{32}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = x
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{6}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = -\frac{y \left(F_{46}\! \left(x , 1\right)-F_{46}\! \left(x , y\right)\right)}{-1+y}
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y , 1\right)
F_{50}\! \left(x , y , z\right) = F_{51}\! \left(x , y , y z \right)
F_{52}\! \left(x , y , z\right) = -\frac{-F_{51}\! \left(x , y , z\right) z +F_{51}\! \left(x , y , 1\right)}{-1+z}
F_{53}\! \left(x , y , z\right) = F_{32}\! \left(x \right) F_{52}\! \left(x , y , z\right)
F_{53}\! \left(x , y , z\right) = F_{54}\! \left(x , y , z\right)
F_{54}\! \left(x , y , z\right) = F_{55}\! \left(x , z\right)+F_{57}\! \left(x , y , z\right)
F_{55}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{30}\! \left(x \right)
F_{57}\! \left(x , y , z\right) = F_{58}\! \left(x , y , z\right)
F_{58}\! \left(x , y , z\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{59}\! \left(x , z\right)
F_{60}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{5}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{32}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{77}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{15}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_32(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0))
Eq(F_7(x, k_0), F_14(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), F_18(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_0(x)*F_10(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_12(x, k_0))
Eq(F_11(x, k_0), k_0*x*F_11(x, k_0)**4 + (-k_0*x - 1)*F_11(x, k_0)**3 + (2*k_0*x - 2)*F_11(x, k_0) + (k_0**2*x**2 - 2*k_0*x + 3)*F_11(x, k_0)**2 + 1)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_10(x, k_0)*F_11(x, k_0)*F_14(x, k_0)*F_15(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_14(x, k_0)*F_15(x, k_0)**2)
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_32(x))
Eq(F_20(x, k_0), F_21(x, k_0) + F_25(x, k_0))
Eq(F_21(x, k_0), F_11(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_14(x, k_0)*F_22(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), -F_6(x, 1) + (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_12(x, k_0)*F_26(x, k_0))
Eq(F_27(x, k_0), F_15(x, k_0)*F_26(x, k_0)*F_32(x))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_29(x, k_0), F_28(x, k_0) + F_79(x, k_0))
Eq(F_29(x, k_0), F_30(x) + F_33(x, k_0))
Eq(F_30(x), F_31(x)/F_32(x))
Eq(F_31(x), F_2(x))
Eq(F_32(x), x)
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_14(x, k_0)*F_15(x, k_0)*F_35(x, k_0))
Eq(F_36(x, k_0), F_35(x, k_0) + F_78(x, k_0))
Eq(F_37(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_36(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_39(x, k_0), F_38(x, k_0) + F_41(x, k_0))
Eq(F_40(x, k_0), F_14(x, k_0)*F_39(x, k_0))
Eq(F_40(x, k_0), F_6(x, k_0))
Eq(F_41(x, k_0), F_30(x) + F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_6(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_32(x)*F_45(x, k_0))
Eq(F_45(x, k_0), -F_46(x, 1) + (-k_0*F_46(x, k_0) + F_46(x, 1))/(1 - k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_77(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_14(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0, 1))
Eq(F_50(x, k_0, k_1), F_51(x, k_0, k_0*k_1))
Eq(F_52(x, k_0, k_1), (-k_1*F_51(x, k_0, k_1) + F_51(x, k_0, 1))/(1 - k_1))
Eq(F_53(x, k_0, k_1), F_32(x)*F_52(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_54(x, k_0, k_1))
Eq(F_54(x, k_0, k_1), F_55(x, k_1) + F_57(x, k_0, k_1))
Eq(F_55(x, k_0), F_43(x, k_0) + F_56(x))
Eq(F_56(x), -F_0(x) + F_30(x))
Eq(F_57(x, k_0, k_1), F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_10(x, k_0)*F_14(x, k_0)*F_59(x, k_1))
Eq(F_60(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_59(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_38(x, k_0), F_61(x, k_0) + F_62(x, k_0))
Eq(F_63(x, k_0), F_5(x, k_0) + F_62(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_64(x, k_0), F_11(x, k_0) + F_65(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_10(x, k_0)*F_11(x, k_0)*F_14(x, k_0)*F_15(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_32(x)*F_69(x, k_0))
Eq(F_70(x, k_0), F_14(x, k_0)*F_69(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_72(x, k_0), F_71(x, k_0) + F_76(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_74(x, k_0))
Eq(F_73(x, k_0), F_11(x, k_0)*F_4(x))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_14(x, k_0)*F_20(x, k_0))
Eq(F_76(x, k_0), (-k_0*F_5(x, k_0) + F_5(x, 1))/(1 - k_0))
Eq(F_77(x, k_0), F_43(x, k_0))
Eq(F_78(x, k_0), F_15(x, k_0)*F_42(x, k_0))
Eq(F_79(x, k_0), F_0(x)*F_15(x, k_0))
Pack JSON:
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Specification JSON:
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