02314_02341_03124_03214_03241_30124_30214_30241
Counting sequence:
1, 1, 2, 6, 24, 112, 563, 2940, 15701, 85120, 466564, 2579219, 14356125, 80360112, 451973241, 2552451469, 14465754770, 82238514176, 468819506023, 2679193555860, 15344847475361, 88062163357603, 506297338359282, 2915703144006045, 16816783563258493, 97129784527290996, 561727638631430729, 3252536943393907453, 18854081569127896894, 109406377379664799989, 635484112446393439549, 3694580153686399753558, 21498088177742123156445, 125195041520201740274860, 729637363590966340178140, 4255410407652360463220635, 24835539094464579171500585, 145040113440270033102909904, 847560898267067815083553517, 4955743897568094993355603713, 28992778814777667743945933330, 169708123730227578074923731535, 993886450388404706246823625169, 5823479057610430276558053702250, 34137427347201751952592248645777, 200204155813686777838818635850713, 1174631014800388937333591556246866, 6894590213125398066985399105012637, 40484340689803571161380857972301157, 237810330761787793472456085873168716, 1397440087518039417762275305294545165, 8214642506000456822835110761645289369, 48304947267379508771562379802934260474, 284142905547340933547249912477074655025, 1671934849668949083967987435605212535797, 9840893702096433658025755448564725032038, 57939929160328480393622778960872089944113, 341228584688392542598289204489599685904889, 2010170443596702175270335983158239625675282, 11845041822436516026487293631185815657984477, 69815674517609522989198136074043877988310749, 411602933556561808582480303538608491414241118, 2427224166096399450001062203732083091466668121, 14316738308110297378363627108598387827682384493, 84465249823944859751196148576747934682582214434, 498435521048696897194529151752031605099840223520, 2941941942527968608303023490787755844002997065923, 17368039480998109134072555442470642716891356622312, 102554939384405792591782564058074519064669149704589, 605688118631136203045927298286909802755220910683727, 3577881198133636198438309649564485889017170007186130, 21139025441363491767965420433217398352949824385587717, 124917727260218464989974675275835565158588219224137081, 738314198783145080960101617414091372567135719893708724, 4364499483995845855726804652490354203842880039268785749, 25804881704638068898613961865701099810074569684633519209, 152595487294979006432314564129846378869077876533382554022, 902510284355672306228764612741471423695121585344217201117, 5338651888121863657278429635598953699544218978279863751993, 31584819973516559111450778472272860478424378245493550883434, 186892128354406784479397899557787933119075879402045772143561, 1106032561623578071872129830277372925966006775669620570436199, 6546477277563808793286518660312345531953246700364487947072970, 38753315687782537228346751024163932934256566466949330604612293, 229440544629522860625133085142557852936463058027857747766923697, 1358595759271358126594833731165009905339752279423602965635618070, 8045774800836614325914631764452768334082123894910349020103491913, 47654267413751190806490107689598093496058797298883629015618044117, 282286980286673546566988095753218560441387136980080903845985998902, 1672375822673140433047283030576758673375185491516881012832674580709, 9908999070959400287544352596602993425319010893970931763160481614217, 58718844078619895307357645938341976729537484876541943672117813781146, 347997377531322882759809403701766605565853001643604105215928099747121, 2062643637009961521152486841567450143709272111636542281711526008626349, 12227036591379785233171005893634241740160648983294030673553707395242958, 72487989708913933648569538228434543397133402088133248360657196831969537, 429791492004964024725338176493709343643711454410251484552189630207368393, 2548564300087519261256484278824861605865083037588980113533984515502514312, 15113969223683133521830133265221855012702210851924451316218879525779646749, 89640813287820457960335772546450184915735060952482104050258430874780805313, 531712098491631128210919288216015025364937034505276154738963480471532689182
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24556/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[22,x]*F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[141,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[23,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[18,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x]
F[21,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
F[22,x] = x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[22,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[26,x]+F[29,x,k[0]]
F[26,x] = F[27,x]
F[27,x] = 1/F[22,x]*F[28,x]
F[28,x] = F[5,x]
F[30,x,k[0]] = F[140,x,k[0]]+F[29,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[32,x,k[0]]+F[88,x,k[0]]+F[90,x,k[0]]
F[31,x] = 0
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[17,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[82,x,k[0]]
F[35,x,k[0]] = F[14,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[25,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = 2*F[31,x]+F[38,x,k[0]]+F[52,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[26,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[1,x]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[17,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[45,x,k[0]] = F[41,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[31,x]+F[47,x,k[0]]+F[51,x,k[0]]
F[47,x,k[0]] = F[17,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[17,x,k[0]]
F[50,x,k[0]] = F[46,x,k[0]]
F[51,x,k[0]] = F[17,x,k[0]]*F[41,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[22,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[56,x]
F[56,x] = F[57,x,1]
F[58,x,k[0]] = F[22,x]*F[57,x,k[0]]*F[62,x]*F[74,x]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = 2*F[31,x]+F[60,x,k[0]]+F[79,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[22,x]*F[62,x]*F[74,x]*F[77,x,k[0]]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[22,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[1,x]+F[22,x]
F[67,x] = F[63,x]+F[68,x]
F[68,x] = F[31,x]+F[69,x]+F[73,x]
F[69,x] = F[22,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[22,x]
F[72,x] = F[68,x]
F[73,x] = F[22,x]*F[63,x]
F[74,x] = F[1,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[22,x]*F[74,x]
F[78,x,k[0]] = F[22,x]*F[77,x,k[0]]
F[78,x,k[0]] = F[19,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[22,x]*F[81,x,k[0]]
F[81,x,k[0]] = (F[59,x,k[0]]*k[0]-F[59,x,1])/(-1+k[0])
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[14,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[17,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[37,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[15,x,k[0]]*F[22,x]*F[26,x]*F[74,x]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[22,x]*F[92,x,k[0]]
F[92,x,k[0]] = -k[0]*(F[93,x,1]-F[93,x,k[0]])/(-1+k[0])
F[93,x,k[0]] = F[94,x,k[0]]
F[95,x,k[0]] = F[136,x]+F[94,x,k[0]]
F[96,x,k[0]] = F[22,x]*F[95,x,k[0]]
F[10,x,k[0]] = F[134,x,k[0]]+F[96,x,k[0]]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[1,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[22,x]
F[101,x] = F[102,x]+F[109,x]
F[102,x] = F[1,x]+F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[22,x]
F[105,x] = F[102,x]+F[106,x]
F[106,x] = F[107,x]+F[22,x]
F[107,x] = F[108,x]
F[108,x] = F[103,x]*F[22,x]
F[109,x] = F[110,x]+F[63,x]
F[110,x] = F[111,x]+F[132,x]+F[31,x]
F[111,x] = F[112,x]*F[22,x]
F[112,x] = F[113,x]+F[117,x]
F[113,x] = F[103,x]+F[114,x]
F[114,x] = F[108,x]+F[115,x]+F[31,x]
F[115,x] = F[116,x]*F[22,x]
F[116,x] = F[106,x]
F[117,x] = F[110,x]+F[118,x]
F[118,x] = F[119,x]+F[123,x]+F[124,x]+F[31,x]
F[119,x] = F[120,x]*F[22,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[114,x]
F[122,x] = F[118,x]
F[123,x] = F[110,x]*F[22,x]
F[124,x] = F[125,x]*F[22,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]+F[68,x]
F[127,x] = 2*F[31,x]+F[123,x]+F[128,x]
F[128,x] = F[129,x]*F[22,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[107,x]
F[131,x] = F[127,x]
F[132,x] = F[133,x]*F[22,x]
F[133,x] = F[109,x]+F[126,x]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[17,x,k[0]]
F[136,x] = F[137,x]
F[137,x] = 1/F[22,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[98,x]+F[4,x]
F[37,x,k[0]] = F[140,x,k[0]]+F[84,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[22,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[57,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[146,x]*F[22,x]*F[40,x,k[0]]*F[86,x]
F[146,x] = F[147,x]+F[74,x]
F[147,x] = F[148,x]+F[75,x]
F[148,x] = F[149,x]+F[151,x]+F[31,x]
F[149,x] = F[150,x]*F[22,x]
F[150,x] = F[148,x]+F[75,x]
F[151,x] = F[147,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{22}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x \right) = x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{26}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{57}\! \left(x , y\right) F_{62}\! \left(x \right) F_{74}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{62}\! \left(x \right) F_{74}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{31}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{22}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right) F_{63}\! \left(x \right)
F_{74}\! \left(x \right) = F_{1}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right) F_{74}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = -\frac{-y F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x \right) F_{26}\! \left(x \right) F_{74}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = -\frac{y \left(F_{93}\! \left(x , 1\right)-F_{93}\! \left(x , y\right)\right)}{-1+y}
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{22}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)
F_{102}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{22}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{22}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right) F_{22}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{63}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{132}\! \left(x \right)+F_{31}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{22}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{113}\! \left(x \right) = F_{103}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{108}\! \left(x \right)+F_{115}\! \left(x \right)+F_{31}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{22}\! \left(x \right)
F_{116}\! \left(x \right) = F_{106}\! \left(x \right)
F_{117}\! \left(x \right) = F_{110}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)+F_{124}\! \left(x \right)+F_{31}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{22}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{114}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right)
F_{123}\! \left(x \right) = F_{110}\! \left(x \right) F_{22}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{22}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{123}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{22}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{107}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{22}\! \left(x \right)
F_{133}\! \left(x \right) = F_{109}\! \left(x \right)+F_{126}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x \right) F_{22}\! \left(x \right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{74}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{151}\! \left(x \right)+F_{31}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{22}\! \left(x \right)
F_{150}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_22(x)*F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_141(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_23(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_18(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x))
Eq(F_21(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_22(x), x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_22(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x) + F_29(x, k_0))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)/F_22(x))
Eq(F_28(x), F_5(x))
Eq(F_30(x, k_0), F_140(x, k_0) + F_29(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_32(x, k_0) + F_88(x, k_0) + F_90(x, k_0))
Eq(F_31(x), 0)
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_17(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_82(x, k_0))
Eq(F_35(x, k_0), F_14(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_25(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), 2*F_31(x) + F_38(x, k_0) + F_52(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_26(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_1(x) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_17(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_45(x, k_0), F_41(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_31(x) + F_47(x, k_0) + F_51(x, k_0))
Eq(F_47(x, k_0), F_17(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_17(x, k_0))
Eq(F_50(x, k_0), F_46(x, k_0))
Eq(F_51(x, k_0), F_17(x, k_0)*F_41(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_22(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_56(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_58(x, k_0), F_22(x)*F_57(x, k_0)*F_62(x)*F_74(x))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), 2*F_31(x) + F_60(x, k_0) + F_79(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_22(x)*F_62(x)*F_74(x)*F_77(x, k_0))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_22(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_1(x) + F_22(x))
Eq(F_67(x), F_63(x) + F_68(x))
Eq(F_68(x), F_31(x) + F_69(x) + F_73(x))
Eq(F_69(x), F_22(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_22(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_22(x)*F_63(x))
Eq(F_74(x), F_1(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_22(x)*F_74(x))
Eq(F_78(x, k_0), F_22(x)*F_77(x, k_0))
Eq(F_78(x, k_0), F_19(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_22(x)*F_81(x, k_0))
Eq(F_81(x, k_0), (-k_0*F_59(x, k_0) + F_59(x, 1))/(1 - k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_14(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_17(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_37(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_15(x, k_0)*F_22(x)*F_26(x)*F_74(x))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_22(x)*F_92(x, k_0))
Eq(F_92(x, k_0), -F_93(x, 1) + (-k_0*F_93(x, k_0) + F_93(x, 1))/(1 - k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_95(x, k_0), F_136(x) + F_94(x, k_0))
Eq(F_96(x, k_0), F_22(x)*F_95(x, k_0))
Eq(F_10(x, k_0), F_134(x, k_0) + F_96(x, k_0) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_1(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_22(x))
Eq(F_101(x), F_102(x) + F_109(x))
Eq(F_102(x), F_1(x) + F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_22(x))
Eq(F_105(x), F_102(x) + F_106(x))
Eq(F_106(x), F_107(x) + F_22(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_103(x)*F_22(x))
Eq(F_109(x), F_110(x) + F_63(x))
Eq(F_110(x), F_111(x) + F_132(x) + F_31(x))
Eq(F_111(x), F_112(x)*F_22(x))
Eq(F_112(x), F_113(x) + F_117(x))
Eq(F_113(x), F_103(x) + F_114(x))
Eq(F_114(x), F_108(x) + F_115(x) + F_31(x))
Eq(F_115(x), F_116(x)*F_22(x))
Eq(F_116(x), F_106(x))
Eq(F_117(x), F_110(x) + F_118(x))
Eq(F_118(x), F_119(x) + F_123(x) + F_124(x) + F_31(x))
Eq(F_119(x), F_120(x)*F_22(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_114(x))
Eq(F_122(x), F_118(x))
Eq(F_123(x), F_110(x)*F_22(x))
Eq(F_124(x), F_125(x)*F_22(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x) + F_68(x))
Eq(F_127(x), F_123(x) + F_128(x) + 2*F_31(x))
Eq(F_128(x), F_129(x)*F_22(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_107(x))
Eq(F_131(x), F_127(x))
Eq(F_132(x), F_133(x)*F_22(x))
Eq(F_133(x), F_109(x) + F_126(x))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x)/F_22(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_4(x) - F_98(x))
Eq(F_37(x, k_0), F_140(x, k_0) + F_84(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_22(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_57(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x)*F_22(x)*F_40(x, k_0)*F_86(x))
Eq(F_146(x), F_147(x) + F_74(x))
Eq(F_147(x), F_148(x) + F_75(x))
Eq(F_148(x), F_149(x) + F_151(x) + F_31(x))
Eq(F_149(x), F_150(x)*F_22(x))
Eq(F_150(x), F_148(x) + F_75(x))
Eq(F_151(x), F_147(x)*F_22(x))
Pack JSON:
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Specification JSON:
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{"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 0], [0, 0], [0, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 0], [0, 3], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "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": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24733/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[22,x]*F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[143,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[23,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[18,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x]
F[21,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
F[22,x] = x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[22,x]*F[25,x,k[0]]
F[26,x,k[0]] = F[142,x,k[0]]+F[25,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[83,x,k[0]]
F[27,x,k[0]] = F[28,x]+F[31,x,k[0]]
F[28,x] = F[29,x]
F[29,x] = 1/F[22,x]*F[30,x]
F[30,x] = F[5,x]
F[31,x,k[0]] = k[0]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[22,x]*F[34,x]
F[34,x] = F[35,x]
F[36,x,k[0]] = F[14,x,k[0]]*F[22,x]*F[35,x]*F[41,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = 2*F[38,x]+F[39,x,k[0]]+F[53,x,k[0]]
F[38,x] = 0
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[14,x,k[0]]*F[22,x]*F[28,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[1,x]+F[42,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[17,x,k[0]]*F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[46,x,k[0]] = F[42,x,k[0]]+F[47,x,k[0]]
F[47,x,k[0]] = F[38,x]+F[48,x,k[0]]+F[52,x,k[0]]
F[48,x,k[0]] = F[17,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]+F[51,x,k[0]]
F[50,x,k[0]] = F[17,x,k[0]]
F[51,x,k[0]] = F[47,x,k[0]]
F[52,x,k[0]] = F[17,x,k[0]]*F[42,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[22,x]*F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[14,x,k[0]]*F[22,x]*F[41,x,k[0]]*F[57,x]
F[57,x] = F[58,x,1]
F[59,x,k[0]] = F[22,x]*F[58,x,k[0]]*F[63,x]*F[75,x]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = 2*F[38,x]+F[61,x,k[0]]+F[80,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[22,x]*F[63,x]*F[75,x]*F[78,x,k[0]]
F[63,x] = F[1,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[22,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[1,x]+F[22,x]
F[68,x] = F[64,x]+F[69,x]
F[69,x] = F[38,x]+F[70,x]+F[74,x]
F[70,x] = F[22,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[22,x]
F[73,x] = F[69,x]
F[74,x] = F[22,x]*F[64,x]
F[75,x] = F[1,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[22,x]*F[75,x]
F[79,x,k[0]] = F[22,x]*F[78,x,k[0]]
F[79,x,k[0]] = F[19,x,k[0]]
F[80,x,k[0]] = F[81,x,k[0]]
F[81,x,k[0]] = F[22,x]*F[82,x,k[0]]
F[82,x,k[0]] = (F[60,x,k[0]]*k[0]-F[60,x,1])/(-1+k[0])
F[83,x,k[0]] = F[38,x]+F[84,x,k[0]]+F[90,x,k[0]]+F[92,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[17,x,k[0]]*F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]+F[88,x,k[0]]
F[87,x,k[0]] = F[14,x,k[0]]*F[26,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[14,x,k[0]]*F[31,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[15,x,k[0]]*F[22,x]*F[28,x]*F[75,x]
F[92,x,k[0]] = F[93,x,k[0]]
F[93,x,k[0]] = F[22,x]*F[94,x,k[0]]
F[94,x,k[0]] = -k[0]*(F[95,x,1]-F[95,x,k[0]])/(-1+k[0])
F[95,x,k[0]] = F[96,x,k[0]]
F[97,x,k[0]] = F[138,x]+F[96,x,k[0]]
F[98,x,k[0]] = F[22,x]*F[97,x,k[0]]
F[10,x,k[0]] = F[136,x,k[0]]+F[98,x,k[0]]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[1,x]+F[101,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[22,x]
F[103,x] = F[104,x]+F[111,x]
F[104,x] = F[1,x]+F[105,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[22,x]
F[107,x] = F[104,x]+F[108,x]
F[108,x] = F[109,x]+F[22,x]
F[109,x] = F[110,x]
F[110,x] = F[105,x]*F[22,x]
F[111,x] = F[112,x]+F[64,x]
F[112,x] = F[113,x]+F[134,x]+F[38,x]
F[113,x] = F[114,x]*F[22,x]
F[114,x] = F[115,x]+F[119,x]
F[115,x] = F[105,x]+F[116,x]
F[116,x] = F[110,x]+F[117,x]+F[38,x]
F[117,x] = F[118,x]*F[22,x]
F[118,x] = F[108,x]
F[119,x] = F[112,x]+F[120,x]
F[120,x] = F[121,x]+F[125,x]+F[126,x]+F[38,x]
F[121,x] = F[122,x]*F[22,x]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[116,x]
F[124,x] = F[120,x]
F[125,x] = F[112,x]*F[22,x]
F[126,x] = F[127,x]*F[22,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]+F[69,x]
F[129,x] = 2*F[38,x]+F[125,x]+F[130,x]
F[130,x] = F[131,x]*F[22,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[109,x]
F[133,x] = F[129,x]
F[134,x] = F[135,x]*F[22,x]
F[135,x] = F[111,x]+F[128,x]
F[136,x,k[0]] = F[137,x,k[0]]
F[137,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[17,x,k[0]]
F[138,x] = F[139,x]
F[139,x] = 1/F[22,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = -F[100,x]+F[4,x]
F[142,x,k[0]] = k[0]*F[37,x,k[0]]
F[143,x,k[0]] = F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]*F[22,x]
F[145,x,k[0]] = F[146,x,k[0]]+F[58,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[148,x]*F[22,x]*F[35,x]*F[41,x,k[0]]
F[148,x] = F[149,x]+F[75,x]
F[149,x] = F[150,x]+F[76,x]
F[150,x] = F[151,x]+F[153,x]+F[38,x]
F[151,x] = F[152,x]*F[22,x]
F[152,x] = F[150,x]+F[76,x]
F[153,x] = F[149,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{22}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x \right) = x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{142}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{31}\! \left(x , y\right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = \frac{F_{30}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{30}\! \left(x \right) = F_{5}\! \left(x \right)
F_{31}\! \left(x , y\right) = y F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{22}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{36}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{22}\! \left(x \right) F_{35}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = 2 F_{38}\! \left(x \right)+F_{39}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{22}\! \left(x \right) F_{28}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{48}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{22}\! \left(x \right) F_{41}\! \left(x , y\right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x , 1\right)
F_{59}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{58}\! \left(x , y\right) F_{63}\! \left(x \right) F_{75}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = 2 F_{38}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{63}\! \left(x \right) F_{75}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{63}\! \left(x \right) = F_{1}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{68}\! \left(x \right) = F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{38}\! \left(x \right)+F_{70}\! \left(x \right)+F_{74}\! \left(x \right)
F_{70}\! \left(x \right) = F_{22}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{22}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{22}\! \left(x \right) F_{64}\! \left(x \right)
F_{75}\! \left(x \right) = F_{1}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{22}\! \left(x \right) F_{75}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = -\frac{-y F_{60}\! \left(x , y\right)+F_{60}\! \left(x , 1\right)}{-1+y}
F_{83}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{87}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x \right) F_{28}\! \left(x \right) F_{75}\! \left(x \right)
F_{92}\! \left(x , y\right) = F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = -\frac{y \left(F_{95}\! \left(x , 1\right)-F_{95}\! \left(x , y\right)\right)}{-1+y}
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{138}\! \left(x \right)+F_{96}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{98}\! \left(x , y\right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{22}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{111}\! \left(x \right)
F_{104}\! \left(x \right) = F_{1}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{22}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{22}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right) F_{22}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{64}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{134}\! \left(x \right)+F_{38}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{22}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{119}\! \left(x \right)
F_{115}\! \left(x \right) = F_{105}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{110}\! \left(x \right)+F_{117}\! \left(x \right)+F_{38}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{22}\! \left(x \right)
F_{118}\! \left(x \right) = F_{108}\! \left(x \right)
F_{119}\! \left(x \right) = F_{112}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{125}\! \left(x \right)+F_{126}\! \left(x \right)+F_{38}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{22}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{116}\! \left(x \right)
F_{124}\! \left(x \right) = F_{120}\! \left(x \right)
F_{125}\! \left(x \right) = F_{112}\! \left(x \right) F_{22}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{22}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{69}\! \left(x \right)
F_{129}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{125}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right) F_{22}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{109}\! \left(x \right)
F_{133}\! \left(x \right) = F_{129}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{22}\! \left(x \right)
F_{135}\! \left(x \right) = F_{111}\! \left(x \right)+F_{128}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = \frac{F_{140}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{4}\! \left(x \right)
F_{142}\! \left(x , y\right) = y F_{37}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x \right) F_{22}\! \left(x \right) F_{35}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{75}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{76}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{153}\! \left(x \right)+F_{38}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{22}\! \left(x \right)
F_{152}\! \left(x \right) = F_{150}\! \left(x \right)+F_{76}\! \left(x \right)
F_{153}\! \left(x \right) = F_{149}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_22(x)*F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_143(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_23(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_18(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x))
Eq(F_21(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_22(x), x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_22(x)*F_25(x, k_0))
Eq(F_26(x, k_0), F_142(x, k_0) + F_25(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_83(x, k_0))
Eq(F_27(x, k_0), F_28(x) + F_31(x, k_0))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)/F_22(x))
Eq(F_30(x), F_5(x))
Eq(F_31(x, k_0), k_0*F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_22(x)*F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_36(x, k_0), F_14(x, k_0)*F_22(x)*F_35(x)*F_41(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), 2*F_38(x) + F_39(x, k_0) + F_53(x, k_0))
Eq(F_38(x), 0)
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_14(x, k_0)*F_22(x)*F_28(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_1(x) + F_42(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_17(x, k_0)*F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_46(x, k_0), F_42(x, k_0) + F_47(x, k_0))
Eq(F_47(x, k_0), F_38(x) + F_48(x, k_0) + F_52(x, k_0))
Eq(F_48(x, k_0), F_17(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0) + F_51(x, k_0))
Eq(F_50(x, k_0), F_17(x, k_0))
Eq(F_51(x, k_0), F_47(x, k_0))
Eq(F_52(x, k_0), F_17(x, k_0)*F_42(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_22(x)*F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_14(x, k_0)*F_22(x)*F_41(x, k_0)*F_57(x))
Eq(F_57(x), F_58(x, 1))
Eq(F_59(x, k_0), F_22(x)*F_58(x, k_0)*F_63(x)*F_75(x))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), 2*F_38(x) + F_61(x, k_0) + F_80(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_22(x)*F_63(x)*F_75(x)*F_78(x, k_0))
Eq(F_63(x), F_1(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_22(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_1(x) + F_22(x))
Eq(F_68(x), F_64(x) + F_69(x))
Eq(F_69(x), F_38(x) + F_70(x) + F_74(x))
Eq(F_70(x), F_22(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_22(x))
Eq(F_73(x), F_69(x))
Eq(F_74(x), F_22(x)*F_64(x))
Eq(F_75(x), F_1(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_22(x)*F_75(x))
Eq(F_79(x, k_0), F_22(x)*F_78(x, k_0))
Eq(F_79(x, k_0), F_19(x, k_0))
Eq(F_80(x, k_0), F_81(x, k_0))
Eq(F_81(x, k_0), F_22(x)*F_82(x, k_0))
Eq(F_82(x, k_0), (-k_0*F_60(x, k_0) + F_60(x, 1))/(1 - k_0))
Eq(F_83(x, k_0), F_38(x) + F_84(x, k_0) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_17(x, k_0)*F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0) + F_88(x, k_0))
Eq(F_87(x, k_0), F_14(x, k_0)*F_26(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_14(x, k_0)*F_31(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_15(x, k_0)*F_22(x)*F_28(x)*F_75(x))
Eq(F_92(x, k_0), F_93(x, k_0))
Eq(F_93(x, k_0), F_22(x)*F_94(x, k_0))
Eq(F_94(x, k_0), -F_95(x, 1) + (-k_0*F_95(x, k_0) + F_95(x, 1))/(1 - k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_97(x, k_0), F_138(x) + F_96(x, k_0))
Eq(F_98(x, k_0), F_22(x)*F_97(x, k_0))
Eq(F_10(x, k_0), F_136(x, k_0) + F_98(x, k_0) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_1(x) + F_101(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_22(x))
Eq(F_103(x), F_104(x) + F_111(x))
Eq(F_104(x), F_1(x) + F_105(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_22(x))
Eq(F_107(x), F_104(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_22(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_105(x)*F_22(x))
Eq(F_111(x), F_112(x) + F_64(x))
Eq(F_112(x), F_113(x) + F_134(x) + F_38(x))
Eq(F_113(x), F_114(x)*F_22(x))
Eq(F_114(x), F_115(x) + F_119(x))
Eq(F_115(x), F_105(x) + F_116(x))
Eq(F_116(x), F_110(x) + F_117(x) + F_38(x))
Eq(F_117(x), F_118(x)*F_22(x))
Eq(F_118(x), F_108(x))
Eq(F_119(x), F_112(x) + F_120(x))
Eq(F_120(x), F_121(x) + F_125(x) + F_126(x) + F_38(x))
Eq(F_121(x), F_122(x)*F_22(x))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_116(x))
Eq(F_124(x), F_120(x))
Eq(F_125(x), F_112(x)*F_22(x))
Eq(F_126(x), F_127(x)*F_22(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x) + F_69(x))
Eq(F_129(x), F_125(x) + F_130(x) + 2*F_38(x))
Eq(F_130(x), F_131(x)*F_22(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_109(x))
Eq(F_133(x), F_129(x))
Eq(F_134(x), F_135(x)*F_22(x))
Eq(F_135(x), F_111(x) + F_128(x))
Eq(F_136(x, k_0), F_137(x, k_0))
Eq(F_137(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)/F_22(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), -F_100(x) + F_4(x))
Eq(F_142(x, k_0), k_0*F_37(x, k_0))
Eq(F_143(x, k_0), F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0)*F_22(x))
Eq(F_145(x, k_0), F_146(x, k_0) + F_58(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x)*F_22(x)*F_35(x)*F_41(x, k_0))
Eq(F_148(x), F_149(x) + F_75(x))
Eq(F_149(x), F_150(x) + F_76(x))
Eq(F_150(x), F_151(x) + F_153(x) + F_38(x))
Eq(F_151(x), F_152(x)*F_22(x))
Eq(F_152(x), F_150(x) + F_76(x))
Eq(F_153(x), F_149(x)*F_22(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": "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": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24825/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[22,x]*F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[141,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[23,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[18,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x]
F[21,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
F[22,x] = x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[22,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[26,x]+F[29,x,k[0]]
F[26,x] = F[27,x]
F[27,x] = 1/F[22,x]*F[28,x]
F[28,x] = F[5,x]
F[30,x,k[0]] = F[140,x,k[0]]+F[29,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[32,x,k[0]]+F[88,x,k[0]]+F[90,x,k[0]]
F[31,x] = 0
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[17,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[82,x,k[0]]
F[35,x,k[0]] = F[14,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[25,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = 2*F[31,x]+F[38,x,k[0]]+F[52,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[26,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[1,x]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[17,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[45,x,k[0]] = F[41,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[31,x]+F[47,x,k[0]]+F[51,x,k[0]]
F[47,x,k[0]] = F[17,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[17,x,k[0]]
F[50,x,k[0]] = F[46,x,k[0]]
F[51,x,k[0]] = F[17,x,k[0]]*F[41,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[22,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[56,x]
F[56,x] = F[57,x,1]
F[58,x,k[0]] = F[22,x]*F[57,x,k[0]]*F[62,x]*F[74,x]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = 2*F[31,x]+F[60,x,k[0]]+F[79,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[22,x]*F[62,x]*F[74,x]*F[77,x,k[0]]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[22,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[1,x]+F[22,x]
F[67,x] = F[63,x]+F[68,x]
F[68,x] = F[31,x]+F[69,x]+F[73,x]
F[69,x] = F[22,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[22,x]
F[72,x] = F[68,x]
F[73,x] = F[22,x]*F[63,x]
F[74,x] = F[1,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[22,x]*F[74,x]
F[78,x,k[0]] = F[22,x]*F[77,x,k[0]]
F[78,x,k[0]] = F[19,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[22,x]*F[81,x,k[0]]
F[81,x,k[0]] = (F[59,x,k[0]]*k[0]-F[59,x,1])/(-1+k[0])
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[14,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[17,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[37,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[15,x,k[0]]*F[22,x]*F[26,x]*F[74,x]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[22,x]*F[92,x,k[0]]
F[92,x,k[0]] = -k[0]*(F[93,x,1]-F[93,x,k[0]])/(-1+k[0])
F[93,x,k[0]] = F[94,x,k[0]]
F[95,x,k[0]] = F[136,x]+F[94,x,k[0]]
F[96,x,k[0]] = F[22,x]*F[95,x,k[0]]
F[10,x,k[0]] = F[134,x,k[0]]+F[96,x,k[0]]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[1,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[22,x]
F[101,x] = F[102,x]+F[109,x]
F[102,x] = F[1,x]+F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[22,x]
F[105,x] = F[102,x]+F[106,x]
F[106,x] = F[107,x]+F[22,x]
F[107,x] = F[108,x]
F[108,x] = F[103,x]*F[22,x]
F[109,x] = F[110,x]+F[63,x]
F[110,x] = F[111,x]+F[132,x]+F[31,x]
F[111,x] = F[112,x]*F[22,x]
F[112,x] = F[113,x]+F[117,x]
F[113,x] = F[103,x]+F[114,x]
F[114,x] = F[108,x]+F[115,x]+F[31,x]
F[115,x] = F[116,x]*F[22,x]
F[116,x] = F[106,x]
F[117,x] = F[110,x]+F[118,x]
F[118,x] = F[119,x]+F[123,x]+F[124,x]+F[31,x]
F[119,x] = F[120,x]*F[22,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[114,x]
F[122,x] = F[118,x]
F[123,x] = F[110,x]*F[22,x]
F[124,x] = F[125,x]*F[22,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]+F[68,x]
F[127,x] = 2*F[31,x]+F[123,x]+F[128,x]
F[128,x] = F[129,x]*F[22,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[107,x]
F[131,x] = F[127,x]
F[132,x] = F[133,x]*F[22,x]
F[133,x] = F[109,x]+F[126,x]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[17,x,k[0]]
F[136,x] = F[137,x]
F[137,x] = 1/F[22,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[98,x]+F[4,x]
F[37,x,k[0]] = F[140,x,k[0]]+F[84,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[22,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[57,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[146,x]*F[22,x]*F[40,x,k[0]]*F[86,x]
F[146,x] = F[147,x]+F[74,x]
F[147,x] = F[148,x]+F[75,x]
F[148,x] = F[149,x]+F[151,x]+F[31,x]
F[149,x] = F[150,x]*F[22,x]
F[150,x] = F[148,x]+F[75,x]
F[151,x] = F[147,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{22}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x \right) = x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{26}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{57}\! \left(x , y\right) F_{62}\! \left(x \right) F_{74}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{62}\! \left(x \right) F_{74}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{31}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{22}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right) F_{63}\! \left(x \right)
F_{74}\! \left(x \right) = F_{1}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right) F_{74}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = -\frac{-y F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x \right) F_{26}\! \left(x \right) F_{74}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = -\frac{y \left(F_{93}\! \left(x , 1\right)-F_{93}\! \left(x , y\right)\right)}{-1+y}
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{22}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)
F_{102}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{22}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{22}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right) F_{22}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{63}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{132}\! \left(x \right)+F_{31}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{22}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{113}\! \left(x \right) = F_{103}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{108}\! \left(x \right)+F_{115}\! \left(x \right)+F_{31}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{22}\! \left(x \right)
F_{116}\! \left(x \right) = F_{106}\! \left(x \right)
F_{117}\! \left(x \right) = F_{110}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)+F_{124}\! \left(x \right)+F_{31}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{22}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{114}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right)
F_{123}\! \left(x \right) = F_{110}\! \left(x \right) F_{22}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{22}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{123}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{22}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{107}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{22}\! \left(x \right)
F_{133}\! \left(x \right) = F_{109}\! \left(x \right)+F_{126}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x \right) F_{22}\! \left(x \right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{74}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{151}\! \left(x \right)+F_{31}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{22}\! \left(x \right)
F_{150}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_22(x)*F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_141(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_23(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_18(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x))
Eq(F_21(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_22(x), x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_22(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x) + F_29(x, k_0))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)/F_22(x))
Eq(F_28(x), F_5(x))
Eq(F_30(x, k_0), F_140(x, k_0) + F_29(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_32(x, k_0) + F_88(x, k_0) + F_90(x, k_0))
Eq(F_31(x), 0)
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_17(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_82(x, k_0))
Eq(F_35(x, k_0), F_14(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_25(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), 2*F_31(x) + F_38(x, k_0) + F_52(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_26(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_1(x) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_17(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_45(x, k_0), F_41(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_31(x) + F_47(x, k_0) + F_51(x, k_0))
Eq(F_47(x, k_0), F_17(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_17(x, k_0))
Eq(F_50(x, k_0), F_46(x, k_0))
Eq(F_51(x, k_0), F_17(x, k_0)*F_41(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_22(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_56(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_58(x, k_0), F_22(x)*F_57(x, k_0)*F_62(x)*F_74(x))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), 2*F_31(x) + F_60(x, k_0) + F_79(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_22(x)*F_62(x)*F_74(x)*F_77(x, k_0))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_22(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_1(x) + F_22(x))
Eq(F_67(x), F_63(x) + F_68(x))
Eq(F_68(x), F_31(x) + F_69(x) + F_73(x))
Eq(F_69(x), F_22(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_22(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_22(x)*F_63(x))
Eq(F_74(x), F_1(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_22(x)*F_74(x))
Eq(F_78(x, k_0), F_22(x)*F_77(x, k_0))
Eq(F_78(x, k_0), F_19(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_22(x)*F_81(x, k_0))
Eq(F_81(x, k_0), (-k_0*F_59(x, k_0) + F_59(x, 1))/(1 - k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_14(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_17(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_37(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_15(x, k_0)*F_22(x)*F_26(x)*F_74(x))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_22(x)*F_92(x, k_0))
Eq(F_92(x, k_0), -F_93(x, 1) + (-k_0*F_93(x, k_0) + F_93(x, 1))/(1 - k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_95(x, k_0), F_136(x) + F_94(x, k_0))
Eq(F_96(x, k_0), F_22(x)*F_95(x, k_0))
Eq(F_10(x, k_0), F_134(x, k_0) + F_96(x, k_0) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_1(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_22(x))
Eq(F_101(x), F_102(x) + F_109(x))
Eq(F_102(x), F_1(x) + F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_22(x))
Eq(F_105(x), F_102(x) + F_106(x))
Eq(F_106(x), F_107(x) + F_22(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_103(x)*F_22(x))
Eq(F_109(x), F_110(x) + F_63(x))
Eq(F_110(x), F_111(x) + F_132(x) + F_31(x))
Eq(F_111(x), F_112(x)*F_22(x))
Eq(F_112(x), F_113(x) + F_117(x))
Eq(F_113(x), F_103(x) + F_114(x))
Eq(F_114(x), F_108(x) + F_115(x) + F_31(x))
Eq(F_115(x), F_116(x)*F_22(x))
Eq(F_116(x), F_106(x))
Eq(F_117(x), F_110(x) + F_118(x))
Eq(F_118(x), F_119(x) + F_123(x) + F_124(x) + F_31(x))
Eq(F_119(x), F_120(x)*F_22(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_114(x))
Eq(F_122(x), F_118(x))
Eq(F_123(x), F_110(x)*F_22(x))
Eq(F_124(x), F_125(x)*F_22(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x) + F_68(x))
Eq(F_127(x), F_123(x) + F_128(x) + 2*F_31(x))
Eq(F_128(x), F_129(x)*F_22(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_107(x))
Eq(F_131(x), F_127(x))
Eq(F_132(x), F_133(x)*F_22(x))
Eq(F_133(x), F_109(x) + F_126(x))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x)/F_22(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_4(x) - F_98(x))
Eq(F_37(x, k_0), F_140(x, k_0) + F_84(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_22(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_57(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x)*F_22(x)*F_40(x, k_0)*F_86(x))
Eq(F_146(x), F_147(x) + F_74(x))
Eq(F_147(x), F_148(x) + F_75(x))
Eq(F_148(x), F_149(x) + F_151(x) + F_31(x))
Eq(F_149(x), F_150(x)*F_22(x))
Eq(F_150(x), F_148(x) + F_75(x))
Eq(F_151(x), F_147(x)*F_22(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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{"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 1], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 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{"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 1], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 1], [0, 2], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[2, 2], [2, 1], [2, 1], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [2, 1], [2, 2], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 1], [2, 2], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 2], [0, 1], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 2], [0, 1], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 2], [2, 1], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [2, 2], [2, 1], [2, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 2], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 2], [0, 2], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 2], [2, 2], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [2, 2], [2, 2], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [2, 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[0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 1], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 3], [0, 0], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 3], [0, 3], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 3], [0, 0], [0, 0], [0, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 3], [0, 0], [0, 3], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[0, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "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": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25050/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[22,x]*F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[141,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[23,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[18,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x]
F[21,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
F[22,x] = x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[22,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[26,x]+F[29,x,k[0]]
F[26,x] = F[27,x]
F[27,x] = 1/F[22,x]*F[28,x]
F[28,x] = F[5,x]
F[30,x,k[0]] = F[140,x,k[0]]+F[29,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[32,x,k[0]]+F[88,x,k[0]]+F[90,x,k[0]]
F[31,x] = 0
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[17,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[82,x,k[0]]
F[35,x,k[0]] = F[14,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[25,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = 2*F[31,x]+F[38,x,k[0]]+F[52,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[26,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[1,x]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[17,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[45,x,k[0]] = F[41,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[31,x]+F[47,x,k[0]]+F[51,x,k[0]]
F[47,x,k[0]] = F[17,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[17,x,k[0]]
F[50,x,k[0]] = F[46,x,k[0]]
F[51,x,k[0]] = F[17,x,k[0]]*F[41,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[22,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[56,x]
F[56,x] = F[57,x,1]
F[58,x,k[0]] = F[22,x]*F[57,x,k[0]]*F[62,x]*F[74,x]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = 2*F[31,x]+F[60,x,k[0]]+F[79,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[22,x]*F[62,x]*F[74,x]*F[77,x,k[0]]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[22,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[1,x]+F[22,x]
F[67,x] = F[63,x]+F[68,x]
F[68,x] = F[31,x]+F[69,x]+F[73,x]
F[69,x] = F[22,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[22,x]
F[72,x] = F[68,x]
F[73,x] = F[22,x]*F[63,x]
F[74,x] = F[1,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[22,x]*F[74,x]
F[78,x,k[0]] = F[22,x]*F[77,x,k[0]]
F[78,x,k[0]] = F[19,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[22,x]*F[81,x,k[0]]
F[81,x,k[0]] = (F[59,x,k[0]]*k[0]-F[59,x,1])/(-1+k[0])
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[14,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[17,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[37,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[15,x,k[0]]*F[22,x]*F[26,x]*F[74,x]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[22,x]*F[92,x,k[0]]
F[92,x,k[0]] = -k[0]*(F[93,x,1]-F[93,x,k[0]])/(-1+k[0])
F[93,x,k[0]] = F[94,x,k[0]]
F[95,x,k[0]] = F[136,x]+F[94,x,k[0]]
F[96,x,k[0]] = F[22,x]*F[95,x,k[0]]
F[10,x,k[0]] = F[134,x,k[0]]+F[96,x,k[0]]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[1,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[22,x]
F[101,x] = F[102,x]+F[109,x]
F[102,x] = F[1,x]+F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[22,x]
F[105,x] = F[102,x]+F[106,x]
F[106,x] = F[107,x]+F[22,x]
F[107,x] = F[108,x]
F[108,x] = F[103,x]*F[22,x]
F[109,x] = F[110,x]+F[63,x]
F[110,x] = F[111,x]+F[132,x]+F[31,x]
F[111,x] = F[112,x]*F[22,x]
F[112,x] = F[113,x]+F[117,x]
F[113,x] = F[103,x]+F[114,x]
F[114,x] = F[108,x]+F[115,x]+F[31,x]
F[115,x] = F[116,x]*F[22,x]
F[116,x] = F[106,x]
F[117,x] = F[110,x]+F[118,x]
F[118,x] = F[119,x]+F[123,x]+F[124,x]+F[31,x]
F[119,x] = F[120,x]*F[22,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[114,x]
F[122,x] = F[118,x]
F[123,x] = F[110,x]*F[22,x]
F[124,x] = F[125,x]*F[22,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]+F[68,x]
F[127,x] = 2*F[31,x]+F[123,x]+F[128,x]
F[128,x] = F[129,x]*F[22,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[107,x]
F[131,x] = F[127,x]
F[132,x] = F[133,x]*F[22,x]
F[133,x] = F[109,x]+F[126,x]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[17,x,k[0]]
F[136,x] = F[137,x]
F[137,x] = 1/F[22,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[98,x]+F[4,x]
F[37,x,k[0]] = F[140,x,k[0]]+F[84,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[22,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[57,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[146,x]*F[22,x]*F[40,x,k[0]]*F[86,x]
F[146,x] = F[147,x]+F[74,x]
F[147,x] = F[148,x]+F[75,x]
F[148,x] = F[149,x]+F[151,x]+F[31,x]
F[149,x] = F[150,x]*F[22,x]
F[150,x] = F[148,x]+F[75,x]
F[151,x] = F[147,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{22}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x \right) = x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{26}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{57}\! \left(x , y\right) F_{62}\! \left(x \right) F_{74}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{62}\! \left(x \right) F_{74}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{31}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{22}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right) F_{63}\! \left(x \right)
F_{74}\! \left(x \right) = F_{1}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right) F_{74}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = -\frac{-y F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x \right) F_{26}\! \left(x \right) F_{74}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = -\frac{y \left(F_{93}\! \left(x , 1\right)-F_{93}\! \left(x , y\right)\right)}{-1+y}
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{22}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)
F_{102}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{22}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{22}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right) F_{22}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{63}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{132}\! \left(x \right)+F_{31}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{22}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{113}\! \left(x \right) = F_{103}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{108}\! \left(x \right)+F_{115}\! \left(x \right)+F_{31}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{22}\! \left(x \right)
F_{116}\! \left(x \right) = F_{106}\! \left(x \right)
F_{117}\! \left(x \right) = F_{110}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)+F_{124}\! \left(x \right)+F_{31}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{22}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{114}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right)
F_{123}\! \left(x \right) = F_{110}\! \left(x \right) F_{22}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{22}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{123}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{22}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{107}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{22}\! \left(x \right)
F_{133}\! \left(x \right) = F_{109}\! \left(x \right)+F_{126}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x \right) F_{22}\! \left(x \right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{74}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{151}\! \left(x \right)+F_{31}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{22}\! \left(x \right)
F_{150}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_22(x)*F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_141(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_23(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_18(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x))
Eq(F_21(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_22(x), x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_22(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x) + F_29(x, k_0))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)/F_22(x))
Eq(F_28(x), F_5(x))
Eq(F_30(x, k_0), F_140(x, k_0) + F_29(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_32(x, k_0) + F_88(x, k_0) + F_90(x, k_0))
Eq(F_31(x), 0)
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_17(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_82(x, k_0))
Eq(F_35(x, k_0), F_14(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_25(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), 2*F_31(x) + F_38(x, k_0) + F_52(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_26(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_1(x) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_17(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_45(x, k_0), F_41(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_31(x) + F_47(x, k_0) + F_51(x, k_0))
Eq(F_47(x, k_0), F_17(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_17(x, k_0))
Eq(F_50(x, k_0), F_46(x, k_0))
Eq(F_51(x, k_0), F_17(x, k_0)*F_41(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_22(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_56(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_58(x, k_0), F_22(x)*F_57(x, k_0)*F_62(x)*F_74(x))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), 2*F_31(x) + F_60(x, k_0) + F_79(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_22(x)*F_62(x)*F_74(x)*F_77(x, k_0))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_22(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_1(x) + F_22(x))
Eq(F_67(x), F_63(x) + F_68(x))
Eq(F_68(x), F_31(x) + F_69(x) + F_73(x))
Eq(F_69(x), F_22(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_22(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_22(x)*F_63(x))
Eq(F_74(x), F_1(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_22(x)*F_74(x))
Eq(F_78(x, k_0), F_22(x)*F_77(x, k_0))
Eq(F_78(x, k_0), F_19(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_22(x)*F_81(x, k_0))
Eq(F_81(x, k_0), (-k_0*F_59(x, k_0) + F_59(x, 1))/(1 - k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_14(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_17(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_37(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_15(x, k_0)*F_22(x)*F_26(x)*F_74(x))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_22(x)*F_92(x, k_0))
Eq(F_92(x, k_0), -F_93(x, 1) + (-k_0*F_93(x, k_0) + F_93(x, 1))/(1 - k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_95(x, k_0), F_136(x) + F_94(x, k_0))
Eq(F_96(x, k_0), F_22(x)*F_95(x, k_0))
Eq(F_10(x, k_0), F_134(x, k_0) + F_96(x, k_0) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_1(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_22(x))
Eq(F_101(x), F_102(x) + F_109(x))
Eq(F_102(x), F_1(x) + F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_22(x))
Eq(F_105(x), F_102(x) + F_106(x))
Eq(F_106(x), F_107(x) + F_22(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_103(x)*F_22(x))
Eq(F_109(x), F_110(x) + F_63(x))
Eq(F_110(x), F_111(x) + F_132(x) + F_31(x))
Eq(F_111(x), F_112(x)*F_22(x))
Eq(F_112(x), F_113(x) + F_117(x))
Eq(F_113(x), F_103(x) + F_114(x))
Eq(F_114(x), F_108(x) + F_115(x) + F_31(x))
Eq(F_115(x), F_116(x)*F_22(x))
Eq(F_116(x), F_106(x))
Eq(F_117(x), F_110(x) + F_118(x))
Eq(F_118(x), F_119(x) + F_123(x) + F_124(x) + F_31(x))
Eq(F_119(x), F_120(x)*F_22(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_114(x))
Eq(F_122(x), F_118(x))
Eq(F_123(x), F_110(x)*F_22(x))
Eq(F_124(x), F_125(x)*F_22(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x) + F_68(x))
Eq(F_127(x), F_123(x) + F_128(x) + 2*F_31(x))
Eq(F_128(x), F_129(x)*F_22(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_107(x))
Eq(F_131(x), F_127(x))
Eq(F_132(x), F_133(x)*F_22(x))
Eq(F_133(x), F_109(x) + F_126(x))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x)/F_22(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_4(x) - F_98(x))
Eq(F_37(x, k_0), F_140(x, k_0) + F_84(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_22(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_57(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x)*F_22(x)*F_40(x, k_0)*F_86(x))
Eq(F_146(x), F_147(x) + F_74(x))
Eq(F_147(x), F_148(x) + F_75(x))
Eq(F_148(x), F_149(x) + F_151(x) + F_31(x))
Eq(F_149(x), F_150(x)*F_22(x))
Eq(F_150(x), F_148(x) + F_75(x))
Eq(F_151(x), F_147(x)*F_22(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", 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{"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 1], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 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{"patt": [3, 0, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 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"pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 1], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": 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"comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[0, 2]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 1]]}]}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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": "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": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_and_row_placements_tracked_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25903/
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[22,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[22,x]*F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[141,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[23,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[18,x,k[0]]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0]] = F[11,x,k[0]]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x]
F[21,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
F[22,x] = x
F[23,x,k[0]] = F[24,x,k[0]]
F[24,x,k[0]] = F[22,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[26,x]+F[29,x,k[0]]
F[26,x] = F[27,x]
F[27,x] = 1/F[22,x]*F[28,x]
F[28,x] = F[5,x]
F[30,x,k[0]] = F[140,x,k[0]]+F[29,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[32,x,k[0]]+F[88,x,k[0]]+F[90,x,k[0]]
F[31,x] = 0
F[32,x,k[0]] = F[33,x,k[0]]
F[33,x,k[0]] = F[17,x,k[0]]*F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[82,x,k[0]]
F[35,x,k[0]] = F[14,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[25,x,k[0]]+F[37,x,k[0]]
F[37,x,k[0]] = 2*F[31,x]+F[38,x,k[0]]+F[52,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[26,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[1,x]+F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[17,x,k[0]]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]+F[45,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[45,x,k[0]] = F[41,x,k[0]]+F[46,x,k[0]]
F[46,x,k[0]] = F[31,x]+F[47,x,k[0]]+F[51,x,k[0]]
F[47,x,k[0]] = F[17,x,k[0]]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[17,x,k[0]]
F[50,x,k[0]] = F[46,x,k[0]]
F[51,x,k[0]] = F[17,x,k[0]]*F[41,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[22,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[56,x]
F[56,x] = F[57,x,1]
F[58,x,k[0]] = F[22,x]*F[57,x,k[0]]*F[62,x]*F[74,x]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = 2*F[31,x]+F[60,x,k[0]]+F[79,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[22,x]*F[62,x]*F[74,x]*F[77,x,k[0]]
F[62,x] = F[1,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[22,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[1,x]+F[22,x]
F[67,x] = F[63,x]+F[68,x]
F[68,x] = F[31,x]+F[69,x]+F[73,x]
F[69,x] = F[22,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[22,x]
F[72,x] = F[68,x]
F[73,x] = F[22,x]*F[63,x]
F[74,x] = F[1,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[22,x]*F[74,x]
F[78,x,k[0]] = F[22,x]*F[77,x,k[0]]
F[78,x,k[0]] = F[19,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[22,x]*F[81,x,k[0]]
F[81,x,k[0]] = (F[59,x,k[0]]*k[0]-F[59,x,1])/(-1+k[0])
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[14,x,k[0]]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]
F[85,x,k[0]] = F[17,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[14,x,k[0]]*F[17,x,k[0]]*F[40,x,k[0]]*F[86,x]
F[87,x,k[0]] = F[37,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[15,x,k[0]]*F[22,x]*F[26,x]*F[74,x]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[22,x]*F[92,x,k[0]]
F[92,x,k[0]] = -k[0]*(F[93,x,1]-F[93,x,k[0]])/(-1+k[0])
F[93,x,k[0]] = F[94,x,k[0]]
F[95,x,k[0]] = F[136,x]+F[94,x,k[0]]
F[96,x,k[0]] = F[22,x]*F[95,x,k[0]]
F[10,x,k[0]] = F[134,x,k[0]]+F[96,x,k[0]]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[1,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[22,x]
F[101,x] = F[102,x]+F[109,x]
F[102,x] = F[1,x]+F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[22,x]
F[105,x] = F[102,x]+F[106,x]
F[106,x] = F[107,x]+F[22,x]
F[107,x] = F[108,x]
F[108,x] = F[103,x]*F[22,x]
F[109,x] = F[110,x]+F[63,x]
F[110,x] = F[111,x]+F[132,x]+F[31,x]
F[111,x] = F[112,x]*F[22,x]
F[112,x] = F[113,x]+F[117,x]
F[113,x] = F[103,x]+F[114,x]
F[114,x] = F[108,x]+F[115,x]+F[31,x]
F[115,x] = F[116,x]*F[22,x]
F[116,x] = F[106,x]
F[117,x] = F[110,x]+F[118,x]
F[118,x] = F[119,x]+F[123,x]+F[124,x]+F[31,x]
F[119,x] = F[120,x]*F[22,x]
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[114,x]
F[122,x] = F[118,x]
F[123,x] = F[110,x]*F[22,x]
F[124,x] = F[125,x]*F[22,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]+F[68,x]
F[127,x] = 2*F[31,x]+F[123,x]+F[128,x]
F[128,x] = F[129,x]*F[22,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[107,x]
F[131,x] = F[127,x]
F[132,x] = F[133,x]*F[22,x]
F[133,x] = F[109,x]+F[126,x]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[10,x,k[0]]*F[14,x,k[0]]*F[17,x,k[0]]
F[136,x] = F[137,x]
F[137,x] = 1/F[22,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[98,x]+F[4,x]
F[37,x,k[0]] = F[140,x,k[0]]+F[84,x,k[0]]
F[141,x,k[0]] = F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[22,x]
F[143,x,k[0]] = F[144,x,k[0]]+F[57,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]
F[145,x,k[0]] = F[146,x]*F[22,x]*F[40,x,k[0]]*F[86,x]
F[146,x] = F[147,x]+F[74,x]
F[147,x] = F[148,x]+F[75,x]
F[148,x] = F[149,x]+F[151,x]+F[31,x]
F[149,x] = F[150,x]*F[22,x]
F[150,x] = F[148,x]+F[75,x]
F[151,x] = F[147,x]*F[22,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_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{22}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{21}\! \left(x , y\right) = -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}
F_{22}\! \left(x \right) = x
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{5}\! \left(x \right)
F_{30}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{26}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{41}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{41}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{58}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{57}\! \left(x , y\right) F_{62}\! \left(x \right) F_{74}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{62}\! \left(x \right) F_{74}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{62}\! \left(x \right) = F_{1}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{67}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{31}\! \left(x \right)+F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{22}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right)
F_{72}\! \left(x \right) = F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right) F_{63}\! \left(x \right)
F_{74}\! \left(x \right) = F_{1}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right) F_{74}\! \left(x \right)
F_{78}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = -\frac{-y F_{59}\! \left(x , y\right)+F_{59}\! \left(x , 1\right)}{-1+y}
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{22}\! \left(x \right) F_{26}\! \left(x \right) F_{74}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = -\frac{y \left(F_{93}\! \left(x , 1\right)-F_{93}\! \left(x , y\right)\right)}{-1+y}
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{136}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{22}\! \left(x \right) F_{95}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{134}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{22}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{109}\! \left(x \right)
F_{102}\! \left(x \right) = F_{1}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{22}\! \left(x \right)
F_{105}\! \left(x \right) = F_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{22}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right) F_{22}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{63}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{132}\! \left(x \right)+F_{31}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{22}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{117}\! \left(x \right)
F_{113}\! \left(x \right) = F_{103}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{108}\! \left(x \right)+F_{115}\! \left(x \right)+F_{31}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{22}\! \left(x \right)
F_{116}\! \left(x \right) = F_{106}\! \left(x \right)
F_{117}\! \left(x \right) = F_{110}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{123}\! \left(x \right)+F_{124}\! \left(x \right)+F_{31}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{22}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{114}\! \left(x \right)
F_{122}\! \left(x \right) = F_{118}\! \left(x \right)
F_{123}\! \left(x \right) = F_{110}\! \left(x \right) F_{22}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{22}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{123}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{22}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{107}\! \left(x \right)
F_{131}\! \left(x \right) = F_{127}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{22}\! \left(x \right)
F_{133}\! \left(x \right) = F_{109}\! \left(x \right)+F_{126}\! \left(x \right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{4}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{140}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{22}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{145}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = F_{146}\! \left(x \right) F_{22}\! \left(x \right) F_{40}\! \left(x , y\right) F_{86}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{74}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{151}\! \left(x \right)+F_{31}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{22}\! \left(x \right)
F_{150}\! \left(x \right) = F_{148}\! \left(x \right)+F_{75}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right) F_{22}\! \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_22(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_22(x)*F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_141(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_23(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_18(x, k_0))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_14(x, k_0)*F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0), F_11(x, k_0) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x))
Eq(F_21(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_22(x), x)
Eq(F_23(x, k_0), F_24(x, k_0))
Eq(F_24(x, k_0), F_22(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x) + F_29(x, k_0))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)/F_22(x))
Eq(F_28(x), F_5(x))
Eq(F_30(x, k_0), F_140(x, k_0) + F_29(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_32(x, k_0) + F_88(x, k_0) + F_90(x, k_0))
Eq(F_31(x), 0)
Eq(F_32(x, k_0), F_33(x, k_0))
Eq(F_33(x, k_0), F_17(x, k_0)*F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_82(x, k_0))
Eq(F_35(x, k_0), F_14(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_25(x, k_0) + F_37(x, k_0))
Eq(F_37(x, k_0), 2*F_31(x) + F_38(x, k_0) + F_52(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_26(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_1(x) + F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_17(x, k_0)*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0) + F_45(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_45(x, k_0), F_41(x, k_0) + F_46(x, k_0))
Eq(F_46(x, k_0), F_31(x) + F_47(x, k_0) + F_51(x, k_0))
Eq(F_47(x, k_0), F_17(x, k_0)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_17(x, k_0))
Eq(F_50(x, k_0), F_46(x, k_0))
Eq(F_51(x, k_0), F_17(x, k_0)*F_41(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_22(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_56(x))
Eq(F_56(x), F_57(x, 1))
Eq(F_58(x, k_0), F_22(x)*F_57(x, k_0)*F_62(x)*F_74(x))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), 2*F_31(x) + F_60(x, k_0) + F_79(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_22(x)*F_62(x)*F_74(x)*F_77(x, k_0))
Eq(F_62(x), F_1(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_22(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_1(x) + F_22(x))
Eq(F_67(x), F_63(x) + F_68(x))
Eq(F_68(x), F_31(x) + F_69(x) + F_73(x))
Eq(F_69(x), F_22(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_22(x))
Eq(F_72(x), F_68(x))
Eq(F_73(x), F_22(x)*F_63(x))
Eq(F_74(x), F_1(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_22(x)*F_74(x))
Eq(F_78(x, k_0), F_22(x)*F_77(x, k_0))
Eq(F_78(x, k_0), F_19(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_22(x)*F_81(x, k_0))
Eq(F_81(x, k_0), (-k_0*F_59(x, k_0) + F_59(x, 1))/(1 - k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_14(x, k_0)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0))
Eq(F_85(x, k_0), F_17(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_14(x, k_0)*F_17(x, k_0)*F_40(x, k_0)*F_86(x))
Eq(F_87(x, k_0), F_37(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_15(x, k_0)*F_22(x)*F_26(x)*F_74(x))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_22(x)*F_92(x, k_0))
Eq(F_92(x, k_0), -F_93(x, 1) + (-k_0*F_93(x, k_0) + F_93(x, 1))/(1 - k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_95(x, k_0), F_136(x) + F_94(x, k_0))
Eq(F_96(x, k_0), F_22(x)*F_95(x, k_0))
Eq(F_10(x, k_0), F_134(x, k_0) + F_96(x, k_0) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_1(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_22(x))
Eq(F_101(x), F_102(x) + F_109(x))
Eq(F_102(x), F_1(x) + F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_22(x))
Eq(F_105(x), F_102(x) + F_106(x))
Eq(F_106(x), F_107(x) + F_22(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_103(x)*F_22(x))
Eq(F_109(x), F_110(x) + F_63(x))
Eq(F_110(x), F_111(x) + F_132(x) + F_31(x))
Eq(F_111(x), F_112(x)*F_22(x))
Eq(F_112(x), F_113(x) + F_117(x))
Eq(F_113(x), F_103(x) + F_114(x))
Eq(F_114(x), F_108(x) + F_115(x) + F_31(x))
Eq(F_115(x), F_116(x)*F_22(x))
Eq(F_116(x), F_106(x))
Eq(F_117(x), F_110(x) + F_118(x))
Eq(F_118(x), F_119(x) + F_123(x) + F_124(x) + F_31(x))
Eq(F_119(x), F_120(x)*F_22(x))
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_114(x))
Eq(F_122(x), F_118(x))
Eq(F_123(x), F_110(x)*F_22(x))
Eq(F_124(x), F_125(x)*F_22(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x) + F_68(x))
Eq(F_127(x), F_123(x) + F_128(x) + 2*F_31(x))
Eq(F_128(x), F_129(x)*F_22(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_107(x))
Eq(F_131(x), F_127(x))
Eq(F_132(x), F_133(x)*F_22(x))
Eq(F_133(x), F_109(x) + F_126(x))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_10(x, k_0)*F_14(x, k_0)*F_17(x, k_0))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x)/F_22(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_4(x) - F_98(x))
Eq(F_37(x, k_0), F_140(x, k_0) + F_84(x, k_0))
Eq(F_141(x, k_0), F_142(x, k_0))
Eq(F_142(x, k_0), F_143(x, k_0)*F_22(x))
Eq(F_143(x, k_0), F_144(x, k_0) + F_57(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0))
Eq(F_145(x, k_0), F_146(x)*F_22(x)*F_40(x, k_0)*F_86(x))
Eq(F_146(x), F_147(x) + F_74(x))
Eq(F_147(x), F_148(x) + F_75(x))
Eq(F_148(x), F_149(x) + F_151(x) + F_31(x))
Eq(F_149(x), F_150(x)*F_22(x))
Eq(F_150(x), F_148(x) + F_75(x))
Eq(F_151(x), F_147(x)*F_22(x))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_req_corrob_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.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]], "symmetry": true}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 3, 1, 2, 4], [0, 3, 2, 1, 4], [0, 3, 2, 4, 1], [3, 0, 1, 2, 4], [3, 0, 2, 1, 4], [3, 0, 2, 4, 1]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, 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