01243_02143_02413_20143_20413
Counting sequence:
1, 1, 2, 6, 24, 115, 614, 3508, 20983, 129761, 823170, 5328594, 35065285, 233919213, 1578498161, 10756699493, 73923967956, 511785498866, 3566129547594, 24991288175736, 176031591086424, 1245583206794330, 8849901069720812, 63112953715771543, 451613115671208719, 3241566193744570332, 23333058680275347200, 168390777079868917698, 1218168835578256687511, 8832051106050040922012, 64166920940905425354260, 467083098461800868120289, 3406076739311506651851812, 24879488159874591478600859, 182015908885180406691852549, 1333572032636084895880936262, 9784189265406160429697762415, 71878618891170641329323164366, 528699980646240511545463453169, 3893357881652560819974057082269, 28702379739345103162730560090942, 211819139757933175974426028137422, 1564743827922530152372191851069455, 11569931189170706380817115461158961, 85626470631696702667335223612086075, 634244475408150734602854908075857487, 4701751022775621176421231372913340152, 34881961548205100070899877069801409013, 258979630035983726420601128489507562189, 1924153906260347522228022733650061841769, 14305743604795002221030730601218685068736, 106430288615294751100698635046577045908050, 792305552477058201584875775388675318507657, 5901765969066279110213231860322364153685578, 43986852952432228591297212012770050715501120, 328024138498403353236337801914463959685878047, 2447494029685321206655262518495951922021069576, 18270979266902047736649798651486856916693508698, 136464044816105526644673338509305996031544668018, 1019725317891716748960355624873654210408562269786, 7623412678288277717919914380622632288892792485500, 57017742115765977729896193181997289554808052079893, 426636884331155591628618902050800786127633007437233, 3193657567898449184520204103748678157327182251278921, 23916296795978340286388518315369231049384713105857192, 179171741363681279846477519727101365993798017057275747, 1342794994112566179947769430589951695210128016008281719, 10067216451961420552409472536737297110522608983646297215, 75502912318555310638758412537645113622978275648677998736, 566458290754742970884947410109172442113728210793073717916, 4251259820819007142139317496344014326241994558769400548566, 31916008480046772149112999397165072134175053860594160332133, 239682667404156198615395263112821045138168359047256049776952, 1800519858830888523241807614136783459158007660374234694418588, 13529716326626353638997572402784605617359698263628356292937574, 101696350930203075940722166926533541360460708749409530394504968, 764617994169017533346875827556578649073509360559133848612387440, 5750463156167198848958153114368304482925696894359713122136148525, 43259065675384259077496962173450239330161186738086267445908920224, 325510049655566123942455086455571863011862601126620627349071871916, 2449975262128143493734121564528545339003437634457505922112475759297, 18444471539129576874858458006220986190909193100284792978061325682929, 138891365485736661641820909773654643480489092648599801774715119850279, 1046131279761837641955236400253577225570241828522962957979885329139422, 7881275863208693245880448325065285093554474227850190829954149234237990, 59388704897979977755268390470674993619231256671075279983301157874831908, 447616240153428946465412292223818046647495161046798761872629073229244794, 3374428447391656638734304802813108288552956581843335335136174157824967201, 25443968738474516250992268175507660398513630531466026741275386406001460768, 191892337035002128648494250783733502854523598492049431811309110621128363390, 1447493226522041084288848135252534319346877342457981000276391420427717530683, 10920930071479814101821727826118859761462617622778719749431632850831361532274, 82410966013585100659917776694984604964698823760824063406204938732709048916264, 622000671266829156827976773927743704136418752155089753409770366442915420417421, 4695430415103959965793461694011698002991083515798786832642084190798872055060017, 35451691856089393712421403454962108199307602161618277310857118791847104580569775, 267715720313170603918627679319576254818175038107102742052872967038508173495425175, 2022015753500745625572494160053654194073427733620327772634299924187925828896664260, 15274514018736948676259461197634797573228291517672444189378944819941756757377724483, 115404029777544641041344178162289780808564781935014098511739309775198188211007830362, 872054846483343427518663361369071251184899193086059023181099969788820452572747049730
Specification 1
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24477/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[42,x,k[0]]
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[94,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[16,x,k[0],k[1]]+F[17,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[42,x,k[2]]
F[19,x,k[0],k[1],k[2]] = F[20,x,k[0],k[2]]+F[61,x,k[0],k[1],k[2]]+F[63,x,k[0],k[1],k[2]]+F[74,x,k[0],k[1],k[2]]
F[20,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[21,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[42,x,k[0]]
F[22,x,k[0],k[1]] = F[23,x,k[0],1,k[1]]
F[23,x,k[0],k[1],k[2]] = F[24,x,k[0],k[0]*k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = F[24,x,k[0],k[1],k[1]*k[2]]
F[26,x,k[0],k[1],k[2]] = F[25,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],1,k[1],k[2]]
F[27,x,k[0],k[1],k[2],k[3]] = F[11,x,k[0],k[1]*k[2]]+F[28,x,k[0],k[1],k[2],k[3]]
F[28,x,k[0],k[1],k[2],k[3]] = F[29,x,k[0],k[1],k[2],k[3]]
F[29,x,k[0],k[1],k[2],k[3]] = F[30,x,k[0],k[1],k[2],k[3]]*F[42,x,k[3]]
F[31,x,k[0],k[1],k[2],k[3]] = F[30,x,k[0],k[1],k[2],k[3]]+F[47,x,k[0],k[1],k[2],k[3]]
F[31,x,k[0],k[1],k[2],k[3]] = F[32,x,k[0]*k[1],k[2],k[1],k[3]]
F[32,x,k[0],k[1],k[2],k[3]] = F[33,x,k[0]*k[1],k[2],k[1],k[3]]
F[33,x,k[0],k[1],k[2],k[3]] = F[34,x,k[0],k[1]*k[2],k[2]*k[3]]
F[35,x,k[0],k[1],k[2]] = F[34,x,k[0],k[1],k[2]]*F[42,x,k[2]]
F[35,x,k[0],k[1],k[2]] = F[36,x,k[0],k[1],k[2]]
F[37,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1]]+F[36,x,k[0],k[1],k[2]]
F[37,x,k[0],k[1],k[2]] = F[1,x]+F[38,x,k[0],k[1],k[2]]+F[40,x,k[0],k[1],k[2]]+F[43,x,k[0],k[1],k[2]]+F[46,x,k[0],k[1],k[2]]
F[38,x,k[0],k[1],k[2]] = F[39,x,k[0],k[1],k[2]]*F[8,x]
F[39,x,k[0],k[1],k[2]] = (F[14,x,k[0],k[1]]*k[1]-F[14,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[40,x,k[0],k[1],k[2]] = F[41,x,k[0],k[1],k[2]]*F[42,x,k[0]]
F[41,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[42,x,k[0]] = k[0]*x
F[43,x,k[0],k[1],k[2]] = F[42,x,k[1]]*F[44,x,k[0],k[1],k[2]]
F[44,x,k[0],k[1],k[2]] = (F[45,x,k[0],k[1],1]*k[1]-F[45,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[45,x,k[0],k[1],k[2]] = F[37,x,k[0],k[1],k[1]*k[2]]
F[46,x,k[0],k[1],k[2]] = F[37,x,k[0],k[1],k[2]]*F[42,x,k[2]]
F[47,x,k[0],k[1],k[2],k[3]] = F[48,x,k[0],k[1],k[2],k[3]]*F[57,x,k[2]]
F[48,x,k[0],k[1],k[2],k[3]] = F[49,x,k[0]*k[1],k[2],k[1],k[3]]
F[49,x,k[0],k[1],k[2],k[3]] = F[50,x,k[0]*k[1],k[2],k[1],k[3]]
F[50,x,k[0],k[1],k[2],k[3]] = F[51,x,k[0],k[1]*k[2],k[2]*k[3]]
F[51,x,k[0],k[1],k[2]] = F[52,x,k[0],k[1],k[2]]
F[52,x,k[0],k[1],k[2]] = F[34,x,k[0],k[1],k[2]]*F[42,x,k[1]]*F[53,x,k[2]]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[42,x,k[0]]*F[54,x,k[0]]
F[57,x,k[0]] = F[1,x]+F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[57,x,k[0]]^2*F[42,x,k[0]]
F[60,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[42,x,k[1]]
F[61,x,k[0],k[1],k[2]] = F[62,x,k[0],k[1],k[2]]*F[8,x]
F[62,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[19,x,k[0],k[1],k[2]]*k[0]-F[19,x,1,k[1],k[2]])
F[63,x,k[0],k[1],k[2]] = F[64,x,k[0],k[1],k[2]]
F[64,x,k[0],k[1],k[2]] = F[42,x,k[0]]*F[65,x,k[0],k[1],k[2]]
F[65,x,k[0],k[1],k[2]] = (F[66,x,k[0],1,k[2]]*k[0]-F[66,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[66,x,k[0],k[1],k[2]] = F[67,x,k[0],k[1],k[2]]+F[71,x,k[0],k[1],k[2]]
F[67,x,k[0],k[1],k[2]] = F[68,x,k[0],k[0]*k[1],k[2]]
F[69,x,k[0],k[1],k[2]] = F[42,x,k[2]]*F[68,x,k[0],k[1],k[2]]
F[69,x,k[0],k[1],k[2]] = F[70,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = F[12,x,k[0],k[1]]+F[70,x,k[0],k[1],k[2]]
F[71,x,k[0],k[1],k[2]] = F[57,x,k[1]]*F[72,x,k[0],k[2]]
F[72,x,k[0],k[1]] = F[73,x,k[0],1,k[1]]
F[73,x,k[0],k[1],k[2]] = F[51,x,k[0],k[0]*k[1],k[2]]
F[74,x,k[0],k[1],k[2]] = F[75,x,k[0],k[1],k[2]]
F[75,x,k[0],k[1],k[2]] = F[42,x,k[1]]*F[76,x,k[0],k[1],k[2]]
F[76,x,k[0],k[1],k[2]] = F[77,x,k[0],1,k[1],k[2]]
F[77,x,k[0],k[1],k[2],k[3]] = (F[78,x,k[0],k[1]/k[2],k[2],k[3]]*k[0]*k[1]-F[78,x,k[0],1/k[0],k[2],k[3]]*k[2])/(k[0]*k[1]-k[2])
F[78,x,k[0],k[1],k[2],k[3]] = F[79,x,k[0],k[0]*k[1],k[2],k[3]]
F[79,x,k[0],k[1],k[2],k[3]] = F[80,x,k[0],k[1]*k[2],k[2],k[3]]
F[80,x,k[0],k[1],k[2],k[3]] = F[81,x,k[0],k[1],k[2],k[3]]+F[92,x,k[1],k[2],k[3]]
F[81,x,k[0],k[1],k[2],k[3]] = F[20,x,k[0],k[3]]*F[82,x,k[1],k[2]]
F[83,x,k[0],k[1]] = F[82,x,k[0],k[0]*k[1]]
F[83,x,k[0],k[1]] = F[84,k[0]*x,k[1]]
F[84,x,k[0]] = F[85,x]+F[86,x,k[0]]
F[85,x] = 1+x*F[85,x]^4+F[85,x]^2*(x^2-2*x+3)+F[85,x]^3*(-1-x)+(-2+2*x)*F[85,x]
F[86,x,k[0]] = F[87,x,k[0]]
F[87,x,k[0]] = F[42,x,k[0]]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[90,x,1,k[0]]
F[90,x,k[0],k[1]] = F[82,x,k[0],k[1]]*F[85,x]
F[91,x,k[0]] = F[57,x,k[0]]*F[86,x,k[0]]
F[68,x,k[0],k[1],k[2]] = F[92,x,k[0],k[1],k[2]]+F[93,x,k[0],k[1],k[2]]
F[93,x,k[0],k[1],k[2]] = F[20,x,k[0],k[2]]*F[82,x,k[0],k[1]]
F[94,x,k[0],k[1]] = F[42,x,k[1]]*F[95,x,k[0],k[1]]
F[95,x,k[0],k[1]] = F[96,x,k[0],1,k[1]]
F[96,x,k[0],k[1],k[2]] = F[37,x,k[0],k[1]*k[2],k[2]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{94}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{5}\! \left(x , y_{0}\right) y_{0}-F_{5}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{42}\! \left(x , y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}, y_{2}\right)+F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{42}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = F_{23}\! \left(x , y_{0}, 1, y_{1}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, 1, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{11}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{42}\! \left(x , y_{3}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{32}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}, y_{3}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{33}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}, y_{3}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{34}\! \left(x , y_{0}, y_{1} y_{2}, y_{2} y_{3}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{42}\! \left(x , y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \left(x \right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{14}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{14}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{42}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{22}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{42}\! \left(x , y_{0}\right) = y_{0} x
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{1}\right) F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{45}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{45}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{37}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{42}\! \left(x , y_{2}\right)
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{48}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{57}\! \left(x , y_{2}\right)
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{49}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}, y_{3}\right)
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{50}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}, y_{3}\right)
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{51}\! \left(x , y_{0}, y_{1} y_{2}, y_{2} y_{3}\right)
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{42}\! \left(x , y_{1}\right) F_{53}\! \left(x , y_{2}\right)
F_{53}\! \left(x , y_{0}\right) = F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{56}\! \left(x , y_{0}\right)
F_{56}\! \left(x , y_{0}\right) = F_{42}\! \left(x , y_{0}\right) F_{54}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{58}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}\right) = F_{59}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{57}\! \left(x , y_{0}\right)^{2} F_{42}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right) F_{42}\! \left(x , y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \left(x \right)
F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{19}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{0}\right) F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{66}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{66}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{68}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{2}\right) F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{57}\! \left(x , y_{1}\right) F_{72}\! \left(x , y_{0}, y_{2}\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = F_{73}\! \left(x , y_{0}, 1, y_{1}\right)
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{51}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{1}\right) F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{77}\! \left(x , y_{0}, 1, y_{1}, y_{2}\right)
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = -\frac{-y_{0} y_{1} F_{78}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}, y_{3}\right)+y_{2} F_{78}\! \left(x , y_{0}, \frac{1}{y_{0}}, y_{2}, y_{3}\right)}{y_{0} y_{1}-y_{2}}
F_{78}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{79}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}, y_{3}\right)
F_{79}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{80}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}, y_{3}\right)
F_{80}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{81}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{92}\! \left(x , y_{1}, y_{2}, y_{3}\right)
F_{81}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{20}\! \left(x , y_{0}, y_{3}\right) F_{82}\! \left(x , y_{1}, y_{2}\right)
F_{83}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{83}\! \left(x , y_{0}, y_{1}\right) = F_{84}\! \left(y_{0} x , y_{1}\right)
F_{84}\! \left(x , y_{0}\right) = F_{85}\! \left(x \right)+F_{86}\! \left(x , y_{0}\right)
F_{85}\! \left(x \right) = x F_{85} \left(x \right)^{4}+x^{2} F_{85} \left(x \right)^{2}-F_{85} \left(x \right)^{3} x -2 x F_{85} \left(x \right)^{2}-F_{85} \left(x \right)^{3}+2 F_{85}\! \left(x \right) x +3 F_{85} \left(x \right)^{2}-2 F_{85}\! \left(x \right)+1
F_{86}\! \left(x , y_{0}\right) = F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{42}\! \left(x , y_{0}\right) F_{88}\! \left(x , y_{0}\right)
F_{88}\! \left(x , y_{0}\right) = F_{89}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{90}\! \left(x , 1, y_{0}\right)
F_{90}\! \left(x , y_{0}, y_{1}\right) = F_{82}\! \left(x , y_{0}, y_{1}\right) F_{85}\! \left(x \right)
F_{91}\! \left(x , y_{0}\right) = F_{57}\! \left(x , y_{0}\right) F_{86}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{92}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{93}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{93}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{20}\! \left(x , y_{0}, y_{2}\right) F_{82}\! \left(x , y_{0}, y_{1}\right)
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{1}\right) F_{95}\! \left(x , y_{0}, y_{1}\right)
F_{95}\! \left(x , y_{0}, y_{1}\right) = F_{96}\! \left(x , y_{0}, 1, y_{1}\right)
F_{96}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{37}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_42(x, k_0))
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_21(x, k_0, k_1) + F_94(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_16(x, k_0, k_1) + F_17(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_42(x, k_2))
Eq(F_19(x, k_0, k_1, k_2), F_20(x, k_0, k_2) + F_61(x, k_0, k_1, k_2) + F_63(x, k_0, k_1, k_2) + F_74(x, k_0, k_1, k_2))
Eq(F_20(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_21(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_42(x, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, k_0, 1, k_1))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_0, k_0*k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_24(x, k_0, k_1, k_1*k_2))
Eq(F_26(x, k_0, k_1, k_2), F_25(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, 1, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2, k_3), F_11(x, k_0, k_1*k_2) + F_28(x, k_0, k_1, k_2, k_3))
Eq(F_28(x, k_0, k_1, k_2, k_3), F_29(x, k_0, k_1, k_2, k_3))
Eq(F_29(x, k_0, k_1, k_2, k_3), F_30(x, k_0, k_1, k_2, k_3)*F_42(x, k_3))
Eq(F_31(x, k_0, k_1, k_2, k_3), F_30(x, k_0, k_1, k_2, k_3) + F_47(x, k_0, k_1, k_2, k_3))
Eq(F_31(x, k_0, k_1, k_2, k_3), F_32(x, k_0*k_1, k_2, k_1, k_3))
Eq(F_32(x, k_0, k_1, k_2, k_3), F_33(x, k_0*k_1, k_2, k_1, k_3))
Eq(F_33(x, k_0, k_1, k_2, k_3), F_34(x, k_0, k_1*k_2, k_2*k_3))
Eq(F_35(x, k_0, k_1, k_2), F_34(x, k_0, k_1, k_2)*F_42(x, k_2))
Eq(F_35(x, k_0, k_1, k_2), F_36(x, k_0, k_1, k_2))
Eq(F_37(x, k_0, k_1, k_2), F_12(x, k_0, k_1) + F_36(x, k_0, k_1, k_2))
Eq(F_37(x, k_0, k_1, k_2), F_1(x) + F_38(x, k_0, k_1, k_2) + F_40(x, k_0, k_1, k_2) + F_43(x, k_0, k_1, k_2) + F_46(x, k_0, k_1, k_2))
Eq(F_38(x, k_0, k_1, k_2), F_39(x, k_0, k_1, k_2)*F_8(x))
Eq(F_39(x, k_0, k_1, k_2), (-k_1*F_14(x, k_0, k_1) + k_2*F_14(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_40(x, k_0, k_1, k_2), F_41(x, k_0, k_1, k_2)*F_42(x, k_0))
Eq(F_41(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_42(x, k_0), k_0*x)
Eq(F_43(x, k_0, k_1, k_2), F_42(x, k_1)*F_44(x, k_0, k_1, k_2))
Eq(F_44(x, k_0, k_1, k_2), (-k_1*F_45(x, k_0, k_1, 1) + k_2*F_45(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_45(x, k_0, k_1, k_2), F_37(x, k_0, k_1, k_1*k_2))
Eq(F_46(x, k_0, k_1, k_2), F_37(x, k_0, k_1, k_2)*F_42(x, k_2))
Eq(F_47(x, k_0, k_1, k_2, k_3), F_48(x, k_0, k_1, k_2, k_3)*F_57(x, k_2))
Eq(F_48(x, k_0, k_1, k_2, k_3), F_49(x, k_0*k_1, k_2, k_1, k_3))
Eq(F_49(x, k_0, k_1, k_2, k_3), F_50(x, k_0*k_1, k_2, k_1, k_3))
Eq(F_50(x, k_0, k_1, k_2, k_3), F_51(x, k_0, k_1*k_2, k_2*k_3))
Eq(F_51(x, k_0, k_1, k_2), F_52(x, k_0, k_1, k_2))
Eq(F_52(x, k_0, k_1, k_2), F_34(x, k_0, k_1, k_2)*F_42(x, k_1)*F_53(x, k_2))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_42(x, k_0)*F_54(x, k_0))
Eq(F_57(x, k_0), F_1(x) + F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_42(x, k_0)*F_57(x, k_0)**2)
Eq(F_60(x, k_0, k_1), F_20(x, k_0, k_1)*F_42(x, k_1))
Eq(F_61(x, k_0, k_1, k_2), F_62(x, k_0, k_1, k_2)*F_8(x))
Eq(F_62(x, k_0, k_1, k_2), (k_0*F_19(x, k_0, k_1, k_2) - F_19(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_63(x, k_0, k_1, k_2), F_64(x, k_0, k_1, k_2))
Eq(F_64(x, k_0, k_1, k_2), F_42(x, k_0)*F_65(x, k_0, k_1, k_2))
Eq(F_65(x, k_0, k_1, k_2), (-k_0*F_66(x, k_0, 1, k_2) + k_1*F_66(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_66(x, k_0, k_1, k_2), F_67(x, k_0, k_1, k_2) + F_71(x, k_0, k_1, k_2))
Eq(F_67(x, k_0, k_1, k_2), F_68(x, k_0, k_0*k_1, k_2))
Eq(F_69(x, k_0, k_1, k_2), F_42(x, k_2)*F_68(x, k_0, k_1, k_2))
Eq(F_69(x, k_0, k_1, k_2), F_70(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), F_12(x, k_0, k_1) + F_70(x, k_0, k_1, k_2))
Eq(F_71(x, k_0, k_1, k_2), F_57(x, k_1)*F_72(x, k_0, k_2))
Eq(F_72(x, k_0, k_1), F_73(x, k_0, 1, k_1))
Eq(F_73(x, k_0, k_1, k_2), F_51(x, k_0, k_0*k_1, k_2))
Eq(F_74(x, k_0, k_1, k_2), F_75(x, k_0, k_1, k_2))
Eq(F_75(x, k_0, k_1, k_2), F_42(x, k_1)*F_76(x, k_0, k_1, k_2))
Eq(F_76(x, k_0, k_1, k_2), F_77(x, k_0, 1, k_1, k_2))
Eq(F_77(x, k_0, k_1, k_2, k_3), (-k_0*k_1*F_78(x, k_0, k_1/k_2, k_2, k_3) + k_2*F_78(x, k_0, 1/k_0, k_2, k_3))/(-k_0*k_1 + k_2))
Eq(F_78(x, k_0, k_1, k_2, k_3), F_79(x, k_0, k_0*k_1, k_2, k_3))
Eq(F_79(x, k_0, k_1, k_2, k_3), F_80(x, k_0, k_1*k_2, k_2, k_3))
Eq(F_80(x, k_0, k_1, k_2, k_3), F_81(x, k_0, k_1, k_2, k_3) + F_92(x, k_1, k_2, k_3))
Eq(F_81(x, k_0, k_1, k_2, k_3), F_20(x, k_0, k_3)*F_82(x, k_1, k_2))
Eq(F_83(x, k_0, k_1), F_82(x, k_0, k_0*k_1))
Eq(F_83(x, k_0, k_1), F_84(k_0*x, k_1))
Eq(F_84(x, k_0), F_85(x) + F_86(x, k_0))
Eq(F_85(x), x*F_85(x)**4 + (-x - 1)*F_85(x)**3 + (2*x - 2)*F_85(x) + (x**2 - 2*x + 3)*F_85(x)**2 + 1)
Eq(F_86(x, k_0), F_87(x, k_0))
Eq(F_87(x, k_0), F_42(x, k_0)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_90(x, 1, k_0))
Eq(F_90(x, k_0, k_1), F_82(x, k_0, k_1)*F_85(x))
Eq(F_91(x, k_0), F_57(x, k_0)*F_86(x, k_0))
Eq(F_68(x, k_0, k_1, k_2), F_92(x, k_0, k_1, k_2) + F_93(x, k_0, k_1, k_2))
Eq(F_93(x, k_0, k_1, k_2), F_20(x, k_0, k_2)*F_82(x, k_0, k_1))
Eq(F_94(x, k_0, k_1), F_42(x, k_1)*F_95(x, k_0, k_1))
Eq(F_95(x, k_0, k_1), F_96(x, k_0, 1, k_1))
Eq(F_96(x, k_0, k_1, k_2), F_37(x, k_0, k_1*k_2, k_2))
Pack JSON:
{"name": "point_and_row_and_col_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": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3]], "symmetry": true}, {"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": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "assumption": {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, "sub_assumption": {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false, "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 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0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [4, 1], [4, 1]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 2
Strategy pack name: row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24617/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[36,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[121,x,k[0],k[1]]+F[19,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[15,x,k[0],k[1]]+F[16,x,k[0],k[1],k[2]]
F[15,x,k[0],k[1]] = (F[4,x,k[0]]*k[0]-F[4,x,k[1]]*k[1])/(-k[1]+k[0])
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[36,x,k[2]]
F[17,x,k[0],k[1],k[2]] = F[18,x,k[0],k[2]]+F[51,x,k[0],k[1],k[2]]+F[53,x,k[0],k[1],k[2]]+F[66,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[19,x,k[0],k[1]]+F[50,x,k[0],k[1]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[36,x,k[0]]
F[20,x,k[0],k[1]] = F[21,x,k[0],1,k[1]]
F[21,x,k[0],k[1],k[2]] = F[22,x,k[0],k[0]*k[1],k[2]]
F[22,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1]]+F[23,x,k[0],k[1],k[2]]
F[23,x,k[0],k[1],k[2]] = F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0],k[1],k[2]]*F[36,x,k[2]]
F[25,x,k[0],k[1],k[2]] = F[26,x,k[2],k[0],k[1]]
F[27,x,k[0],k[1],k[2]] = F[26,x,k[0],k[1],k[2]]+F[41,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = F[28,x,k[1],k[2],k[0]]
F[29,x,k[0],k[1],k[2]] = F[28,x,k[0],k[1],k[2]]*F[36,x,k[2]]
F[29,x,k[0],k[1],k[2]] = F[30,x,k[0],k[1],k[2]]
F[31,x,k[0],k[1],k[2]] = F[11,x,k[0],k[1]]+F[30,x,k[0],k[1],k[2]]
F[31,x,k[0],k[1],k[2]] = F[1,x]+F[32,x,k[0],k[1],k[2]]+F[34,x,k[0],k[1],k[2]]+F[37,x,k[0],k[1],k[2]]+F[40,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[33,x,k[0],k[1],k[2]]*F[7,x]
F[33,x,k[0],k[1],k[2]] = (F[13,x,k[0],k[1]]*k[1]-F[13,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[34,x,k[0],k[1],k[2]] = F[35,x,k[0],k[1],k[2]]*F[36,x,k[0]]
F[35,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1]]*k[1]-F[20,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[36,x,k[0]] = k[0]*x
F[37,x,k[0],k[1],k[2]] = F[36,x,k[1]]*F[38,x,k[0],k[1],k[2]]
F[38,x,k[0],k[1],k[2]] = (F[39,x,k[0],k[1],1]*k[1]-F[39,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[39,x,k[0],k[1],k[2]] = F[31,x,k[0],k[1],k[1]*k[2]]
F[40,x,k[0],k[1],k[2]] = F[31,x,k[0],k[1],k[2]]*F[36,x,k[2]]
F[41,x,k[0],k[1],k[2]] = F[42,x,k[0],k[1],k[2]]
F[42,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]*F[36,x,k[2]]*F[43,x,k[2]]*F[46,x,k[0]]
F[43,x,k[0]] = F[1,x]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[43,x,k[0]]^2*F[36,x,k[0]]
F[46,x,k[0]] = F[1,x]+F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[46,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = k[0]*x
F[50,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[36,x,k[1]]
F[51,x,k[0],k[1],k[2]] = F[52,x,k[0],k[1],k[2]]*F[7,x]
F[52,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[17,x,k[0],k[1],k[2]]*k[0]-F[17,x,1,k[1],k[2]])
F[53,x,k[0],k[1],k[2]] = F[54,x,k[0],k[1],k[2]]
F[54,x,k[0],k[1],k[2]] = F[36,x,k[0]]*F[55,x,k[0],k[1],k[2]]
F[55,x,k[0],k[1],k[2]] = (F[56,x,k[0],1,k[2]]*k[0]-F[56,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[56,x,k[0],k[1],k[2]] = F[57,x,k[0],k[1],k[2]]+F[58,x,k[0],k[1],k[2]]
F[57,x,k[0],k[1],k[2]] = F[25,x,k[0],k[0]*k[1],k[2]]
F[58,x,k[0],k[1],k[2]] = F[59,x,k[0],k[1],k[2]]
F[59,x,k[0],k[1],k[2]] = F[36,x,k[0]]*F[43,x,k[1]]*F[60,x,k[0],k[2]]*F[62,x,k[2]]
F[60,x,k[0],k[1]] = F[61,x,k[0],1,k[1]]
F[61,x,k[0],k[1],k[2]] = F[28,x,k[0],k[0]*k[1],k[2]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[1,x]+F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[36,x,k[0]]*F[63,x,k[0]]
F[66,x,k[0],k[1],k[2]] = F[67,x,k[0],k[1],k[2]]
F[67,x,k[0],k[1],k[2]] = F[36,x,k[1]]*F[68,x,k[0],k[1],k[2]]
F[68,x,k[0],k[1],k[2]] = F[69,x,k[0],1,k[1],k[2]]
F[69,x,k[0],k[1],k[2],k[3]] = (F[70,x,k[0],k[1]/k[2],k[2],k[3]]*k[0]*k[1]-F[70,x,k[0],1/k[0],k[2],k[3]]*k[2])/(k[0]*k[1]-k[2])
F[70,x,k[0],k[1],k[2],k[3]] = F[71,x,k[0],k[0]*k[1],k[2],k[3]]
F[71,x,k[0],k[1],k[2],k[3]] = F[72,x,k[0],k[1]*k[2],k[2],k[3]]
F[72,x,k[0],k[1],k[2],k[3]] = F[119,x,k[0],k[1],k[2],k[3]]+F[73,x,k[1],k[2],k[3]]
F[25,x,k[0],k[1],k[2]] = F[73,x,k[0],k[1],k[2]]+F[74,x,k[0],k[1],k[2]]
F[74,x,k[0],k[1],k[2]] = F[75,x,k[0],k[1],k[2]]
F[75,x,k[0],k[1],k[2]] = F[106,x,k[0],k[1]]*F[36,x,k[0]]*F[62,x,k[2]]*F[76,x,k[0],k[2]]
F[77,x,k[0],k[1]] = F[76,x,k[0]*k[1],k[1]]
F[77,x,k[0],k[1]] = F[78,x,k[0],k[1]]+F[79,x,k[0],k[1]]+F[99,x,k[0],k[1]]
F[78,x,k[0],k[1]] = F[18,x,k[0]*k[1],k[1]]
F[79,x,k[0],k[1]] = F[7,x]*F[80,x,k[0],k[1]]
F[81,x,k[0],k[1]] = F[36,x,k[1]]*F[80,x,k[0],k[1]]
F[82,x,k[0],k[1]] = F[81,x,k[0],k[1]]+F[83,x,k[1]]
F[82,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[83,x,k[0]] = F[84,x,1,k[0]]
F[84,x,k[0],k[1]] = F[1,x]+F[50,x,k[0],k[1]]+F[85,x,k[0],k[1]]+F[87,x,k[0],k[1]]
F[85,x,k[0],k[1]] = F[7,x]*F[86,x,k[0],k[1]]
F[86,x,k[0],k[1]] = 1/(-1+k[0])*(F[84,x,k[0],k[1]]*k[0]-F[84,x,1,k[1]])
F[87,x,k[0],k[1]] = F[36,x,k[0]]*F[88,x,k[0],k[1]]
F[88,x,k[0],k[1]] = F[1,x]+F[89,x,k[0],k[1]]+F[92,x,k[0],k[1]]+F[95,x,k[0],k[1]]+F[98,x,k[0],k[1]]
F[89,x,k[0],k[1]] = F[7,x]*F[90,x,k[0],k[1]]
F[90,x,k[0],k[1]] = (F[91,x,k[0],1]*k[0]-F[91,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[91,x,k[0],k[1]] = F[13,x,k[0],k[0]*k[1]]
F[92,x,k[0],k[1]] = F[36,x,k[0]]*F[93,x,k[0],k[1]]
F[93,x,k[0],k[1]] = (F[94,x,k[0],1]*k[0]-F[94,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[94,x,k[0],k[1]] = F[20,x,k[0],k[0]*k[1]]
F[95,x,k[0],k[1]] = F[36,x,k[0]]*F[96,x,k[0],k[1]]
F[96,x,k[0],k[1]] = (F[97,x,k[0],1]*k[0]-F[97,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[97,x,k[0],k[1]] = F[88,x,k[0],k[0]*k[1]]
F[98,x,k[0],k[1]] = F[36,x,k[1]]*F[88,x,k[0],k[1]]
F[99,x,k[0],k[1]] = F[100,x,k[0],k[1]]
F[100,x,k[0],k[1]] = F[101,x,k[0]*k[1],k[1]]
F[101,x,k[0],k[1]] = F[102,x,k[0],k[1]]*F[36,x,k[0]]
F[102,x,k[0],k[1]] = F[103,x,k[0],k[1]]+F[104,x,k[0],k[1]]
F[103,x,k[0],k[1]] = F[57,x,k[0],1,k[1]]
F[104,x,k[0],k[1]] = F[105,x,k[0],k[1]]
F[105,x,k[0],k[1]] = F[102,x,k[0],k[1]]*F[36,x,k[0]]*F[43,x,k[0]]
F[107,x,k[0],k[1]] = F[106,x,k[0],k[0]*k[1]]
F[107,x,k[0],k[1]] = F[108,k[0]*x,k[1]]
F[108,x,k[0]] = F[109,x]+F[110,x,k[0]]
F[109,x] = 1+x*F[109,x]^4+F[109,x]^2*(x^2-2*x+3)+F[109,x]^3*(-1-x)+(-2+2*x)*F[109,x]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[36,x,k[0]]
F[112,x,k[0]] = F[113,x,k[0]]+F[114,x,k[0]]
F[113,x,k[0]] = F[108,x,k[0]]*F[43,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]
F[115,x,k[0]] = F[109,x]*F[116,x,k[0]]*F[7,x]
F[117,x,k[0]] = F[116,x,k[0]]*F[7,x]
F[117,x,k[0]] = F[118,x,k[0]]
F[108,x,k[0]] = F[118,x,k[0]]+F[43,x,k[0]]
F[119,x,k[0],k[1],k[2],k[3]] = F[120,x,k[0],k[1],k[2],k[3]]
F[120,x,k[0],k[1],k[2],k[3]] = F[106,x,k[1],k[2]]*F[36,x,k[0]]*F[62,x,k[3]]*F[76,x,k[0],k[3]]
F[121,x,k[0],k[1]] = F[122,x,k[0],k[1]]*F[36,x,k[1]]
F[122,x,k[0],k[1]] = F[123,x,k[0],1,k[1]]
F[123,x,k[0],k[1],k[2]] = F[31,x,k[0],k[1]*k[2],k[2]]
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{5}\! \left(x , y_{0}\right) = F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y_{0}\right) = -\frac{-F_{4}\! \left(x , y_{0}\right) y_{0}+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , 1, y_{0}\right)
F_{10}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{121}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{1}\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{4}\! \left(x , y_{0}\right) y_{0}-F_{4}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{36}\! \left(x , y_{2}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{18}\! \left(x , y_{0}, y_{2}\right)+F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{50}\! \left(x , y_{0}, y_{1}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{21}\! \left(x , y_{0}, 1, y_{1}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{36}\! \left(x , y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{36}\! \left(x , y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{13}\! \left(x , y_{0}, y_{1}\right)-F_{13}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{36}\! \left(x , y_{0}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{20}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{36}\! \left(x , y_{0}\right) = y_{0} x
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{1}\right) F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{39}\! \left(x , y_{0}, y_{1}, 1\right)-F_{39}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{36}\! \left(x , y_{2}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{36}\! \left(x , y_{2}\right) F_{43}\! \left(x , y_{2}\right) F_{46}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{44}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{45}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{43}\! \left(x , y_{0}\right)^{2} F_{36}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{46}\! \left(x , y_{0}\right) F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = y_{0} x
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{1}\right)
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{7}\! \left(x \right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0}\right) F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{56}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{56}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{1}\right) F_{60}\! \left(x , y_{0}, y_{2}\right) F_{62}\! \left(x , y_{2}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = F_{61}\! \left(x , y_{0}, 1, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{62}\! \left(x , y_{0}\right) = F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{64}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{36}\! \left(x , y_{0}\right) F_{63}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{36}\! \left(x , y_{1}\right) F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{69}\! \left(x , y_{0}, 1, y_{1}, y_{2}\right)
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = -\frac{-F_{70}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}, y_{3}\right) y_{0} y_{1}+F_{70}\! \left(x , y_{0}, \frac{1}{y_{0}}, y_{2}, y_{3}\right) y_{2}}{y_{0} y_{1}-y_{2}}
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{71}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}, y_{3}\right)
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{72}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}, y_{3}\right)
F_{72}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{119}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{73}\! \left(x , y_{1}, y_{2}, y_{3}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{106}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{2}\right) F_{76}\! \left(x , y_{0}, y_{2}\right)
F_{77}\! \left(x , y_{0}, y_{1}\right) = F_{76}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{77}\! \left(x , y_{0}, y_{1}\right) = F_{78}\! \left(x , y_{0}, y_{1}\right)+F_{79}\! \left(x , y_{0}, y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)
F_{78}\! \left(x , y_{0}, y_{1}\right) = F_{18}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{79}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x \right) F_{80}\! \left(x , y_{0}, y_{1}\right)
F_{81}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{1}\right) F_{80}\! \left(x , y_{0}, y_{1}\right)
F_{82}\! \left(x , y_{0}, y_{1}\right) = F_{81}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{1}\right)
F_{82}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{83}\! \left(x , y_{0}\right) = F_{84}\! \left(x , 1, y_{0}\right)
F_{84}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y_{0}, y_{1}\right)+F_{85}\! \left(x , y_{0}, y_{1}\right)+F_{87}\! \left(x , y_{0}, y_{1}\right)
F_{85}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x \right) F_{86}\! \left(x , y_{0}, y_{1}\right)
F_{86}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{84}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{84}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{87}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}\right) F_{88}\! \left(x , y_{0}, y_{1}\right)
F_{88}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{89}\! \left(x , y_{0}, y_{1}\right)+F_{92}\! \left(x , y_{0}, y_{1}\right)+F_{95}\! \left(x , y_{0}, y_{1}\right)+F_{98}\! \left(x , y_{0}, y_{1}\right)
F_{89}\! \left(x , y_{0}, y_{1}\right) = F_{7}\! \left(x \right) F_{90}\! \left(x , y_{0}, y_{1}\right)
F_{90}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{91}\! \left(x , y_{0}, 1\right) y_{0}-F_{91}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{91}\! \left(x , y_{0}, y_{1}\right) = F_{13}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{92}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}\right) F_{93}\! \left(x , y_{0}, y_{1}\right)
F_{93}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{94}\! \left(x , y_{0}, 1\right) y_{0}-F_{94}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{94}\! \left(x , y_{0}, y_{1}\right) = F_{20}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{95}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}\right) F_{96}\! \left(x , y_{0}, y_{1}\right)
F_{96}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{97}\! \left(x , y_{0}, 1\right)-y_{1} F_{97}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}
F_{97}\! \left(x , y_{0}, y_{1}\right) = F_{88}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{98}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{1}\right) F_{88}\! \left(x , y_{0}, y_{1}\right)
F_{99}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = F_{101}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{101}\! \left(x , y_{0}, y_{1}\right) = F_{102}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{0}\right)
F_{102}\! \left(x , y_{0}, y_{1}\right) = F_{103}\! \left(x , y_{0}, y_{1}\right)+F_{104}\! \left(x , y_{0}, y_{1}\right)
F_{103}\! \left(x , y_{0}, y_{1}\right) = F_{57}\! \left(x , y_{0}, 1, y_{1}\right)
F_{104}\! \left(x , y_{0}, y_{1}\right) = F_{105}\! \left(x , y_{0}, y_{1}\right)
F_{105}\! \left(x , y_{0}, y_{1}\right) = F_{102}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{106}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(y_{0} x , y_{1}\right)
F_{108}\! \left(x , y_{0}\right) = F_{109}\! \left(x \right)+F_{110}\! \left(x , y_{0}\right)
F_{109}\! \left(x \right) = x F_{109} \left(x \right)^{4}+x^{2} F_{109} \left(x \right)^{2}-F_{109} \left(x \right)^{3} x -2 x F_{109} \left(x \right)^{2}-F_{109} \left(x \right)^{3}+2 F_{109}\! \left(x \right) x +3 F_{109} \left(x \right)^{2}-2 F_{109}\! \left(x \right)+1
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right)
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{113}\! \left(x , y_{0}\right)+F_{114}\! \left(x , y_{0}\right)
F_{113}\! \left(x , y_{0}\right) = F_{108}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}\right)
F_{114}\! \left(x , y_{0}\right) = F_{115}\! \left(x , y_{0}\right)
F_{115}\! \left(x , y_{0}\right) = F_{109}\! \left(x \right) F_{116}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{117}\! \left(x , y_{0}\right) = F_{116}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)
F_{117}\! \left(x , y_{0}\right) = F_{118}\! \left(x , y_{0}\right)
F_{108}\! \left(x , y_{0}\right) = F_{118}\! \left(x , y_{0}\right)+F_{43}\! \left(x , y_{0}\right)
F_{119}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{120}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{120}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{106}\! \left(x , y_{1}, y_{2}\right) F_{36}\! \left(x , y_{0}\right) F_{62}\! \left(x , y_{3}\right) F_{76}\! \left(x , y_{0}, y_{3}\right)
F_{121}\! \left(x , y_{0}, y_{1}\right) = F_{122}\! \left(x , y_{0}, y_{1}\right) F_{36}\! \left(x , y_{1}\right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = F_{123}\! \left(x , y_{0}, 1, y_{1}\right)
F_{123}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{31}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\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)*F_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_36(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_121(x, k_0, k_1) + F_19(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_15(x, k_0, k_1) + F_16(x, k_0, k_1, k_2))
Eq(F_15(x, k_0, k_1), (-k_0*F_4(x, k_0) + k_1*F_4(x, k_1))/(-k_0 + k_1))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_36(x, k_2))
Eq(F_17(x, k_0, k_1, k_2), F_18(x, k_0, k_2) + F_51(x, k_0, k_1, k_2) + F_53(x, k_0, k_1, k_2) + F_66(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_19(x, k_0, k_1) + F_50(x, k_0, k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_36(x, k_0))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, 1, k_1))
Eq(F_21(x, k_0, k_1, k_2), F_22(x, k_0, k_0*k_1, k_2))
Eq(F_22(x, k_0, k_1, k_2), F_11(x, k_0, k_1) + F_23(x, k_0, k_1, k_2))
Eq(F_23(x, k_0, k_1, k_2), F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0, k_1, k_2)*F_36(x, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_26(x, k_2, k_0, k_1))
Eq(F_27(x, k_0, k_1, k_2), F_26(x, k_0, k_1, k_2) + F_41(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, k_1, k_2, k_0))
Eq(F_29(x, k_0, k_1, k_2), F_28(x, k_0, k_1, k_2)*F_36(x, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_30(x, k_0, k_1, k_2))
Eq(F_31(x, k_0, k_1, k_2), F_11(x, k_0, k_1) + F_30(x, k_0, k_1, k_2))
Eq(F_31(x, k_0, k_1, k_2), F_1(x) + F_32(x, k_0, k_1, k_2) + F_34(x, k_0, k_1, k_2) + F_37(x, k_0, k_1, k_2) + F_40(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_33(x, k_0, k_1, k_2)*F_7(x))
Eq(F_33(x, k_0, k_1, k_2), (-k_1*F_13(x, k_0, k_1) + k_2*F_13(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_34(x, k_0, k_1, k_2), F_35(x, k_0, k_1, k_2)*F_36(x, k_0))
Eq(F_35(x, k_0, k_1, k_2), (-k_1*F_20(x, k_0, k_1) + k_2*F_20(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_36(x, k_0), k_0*x)
Eq(F_37(x, k_0, k_1, k_2), F_36(x, k_1)*F_38(x, k_0, k_1, k_2))
Eq(F_38(x, k_0, k_1, k_2), (-k_1*F_39(x, k_0, k_1, 1) + k_2*F_39(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_39(x, k_0, k_1, k_2), F_31(x, k_0, k_1, k_1*k_2))
Eq(F_40(x, k_0, k_1, k_2), F_31(x, k_0, k_1, k_2)*F_36(x, k_2))
Eq(F_41(x, k_0, k_1, k_2), F_42(x, k_0, k_1, k_2))
Eq(F_42(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2)*F_36(x, k_2)*F_43(x, k_2)*F_46(x, k_0))
Eq(F_43(x, k_0), F_1(x) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_36(x, k_0)*F_43(x, k_0)**2)
Eq(F_46(x, k_0), F_1(x) + F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_46(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), k_0*x)
Eq(F_50(x, k_0, k_1), F_18(x, k_0, k_1)*F_36(x, k_1))
Eq(F_51(x, k_0, k_1, k_2), F_52(x, k_0, k_1, k_2)*F_7(x))
Eq(F_52(x, k_0, k_1, k_2), (k_0*F_17(x, k_0, k_1, k_2) - F_17(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_53(x, k_0, k_1, k_2), F_54(x, k_0, k_1, k_2))
Eq(F_54(x, k_0, k_1, k_2), F_36(x, k_0)*F_55(x, k_0, k_1, k_2))
Eq(F_55(x, k_0, k_1, k_2), (-k_0*F_56(x, k_0, 1, k_2) + k_1*F_56(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_56(x, k_0, k_1, k_2), F_57(x, k_0, k_1, k_2) + F_58(x, k_0, k_1, k_2))
Eq(F_57(x, k_0, k_1, k_2), F_25(x, k_0, k_0*k_1, k_2))
Eq(F_58(x, k_0, k_1, k_2), F_59(x, k_0, k_1, k_2))
Eq(F_59(x, k_0, k_1, k_2), F_36(x, k_0)*F_43(x, k_1)*F_60(x, k_0, k_2)*F_62(x, k_2))
Eq(F_60(x, k_0, k_1), F_61(x, k_0, 1, k_1))
Eq(F_61(x, k_0, k_1, k_2), F_28(x, k_0, k_0*k_1, k_2))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_1(x) + F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_36(x, k_0)*F_63(x, k_0))
Eq(F_66(x, k_0, k_1, k_2), F_67(x, k_0, k_1, k_2))
Eq(F_67(x, k_0, k_1, k_2), F_36(x, k_1)*F_68(x, k_0, k_1, k_2))
Eq(F_68(x, k_0, k_1, k_2), F_69(x, k_0, 1, k_1, k_2))
Eq(F_69(x, k_0, k_1, k_2, k_3), (-k_0*k_1*F_70(x, k_0, k_1/k_2, k_2, k_3) + k_2*F_70(x, k_0, 1/k_0, k_2, k_3))/(-k_0*k_1 + k_2))
Eq(F_70(x, k_0, k_1, k_2, k_3), F_71(x, k_0, k_0*k_1, k_2, k_3))
Eq(F_71(x, k_0, k_1, k_2, k_3), F_72(x, k_0, k_1*k_2, k_2, k_3))
Eq(F_72(x, k_0, k_1, k_2, k_3), F_119(x, k_0, k_1, k_2, k_3) + F_73(x, k_1, k_2, k_3))
Eq(F_25(x, k_0, k_1, k_2), F_73(x, k_0, k_1, k_2) + F_74(x, k_0, k_1, k_2))
Eq(F_74(x, k_0, k_1, k_2), F_75(x, k_0, k_1, k_2))
Eq(F_75(x, k_0, k_1, k_2), F_106(x, k_0, k_1)*F_36(x, k_0)*F_62(x, k_2)*F_76(x, k_0, k_2))
Eq(F_77(x, k_0, k_1), F_76(x, k_0*k_1, k_1))
Eq(F_77(x, k_0, k_1), F_78(x, k_0, k_1) + F_79(x, k_0, k_1) + F_99(x, k_0, k_1))
Eq(F_78(x, k_0, k_1), F_18(x, k_0*k_1, k_1))
Eq(F_79(x, k_0, k_1), F_7(x)*F_80(x, k_0, k_1))
Eq(F_81(x, k_0, k_1), F_36(x, k_1)*F_80(x, k_0, k_1))
Eq(F_82(x, k_0, k_1), F_81(x, k_0, k_1) + F_83(x, k_1))
Eq(F_82(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_83(x, k_0), F_84(x, 1, k_0))
Eq(F_84(x, k_0, k_1), F_1(x) + F_50(x, k_0, k_1) + F_85(x, k_0, k_1) + F_87(x, k_0, k_1))
Eq(F_85(x, k_0, k_1), F_7(x)*F_86(x, k_0, k_1))
Eq(F_86(x, k_0, k_1), (k_0*F_84(x, k_0, k_1) - F_84(x, 1, k_1))/(k_0 - 1))
Eq(F_87(x, k_0, k_1), F_36(x, k_0)*F_88(x, k_0, k_1))
Eq(F_88(x, k_0, k_1), F_1(x) + F_89(x, k_0, k_1) + F_92(x, k_0, k_1) + F_95(x, k_0, k_1) + F_98(x, k_0, k_1))
Eq(F_89(x, k_0, k_1), F_7(x)*F_90(x, k_0, k_1))
Eq(F_90(x, k_0, k_1), (-k_0*F_91(x, k_0, 1) + k_1*F_91(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_91(x, k_0, k_1), F_13(x, k_0, k_0*k_1))
Eq(F_92(x, k_0, k_1), F_36(x, k_0)*F_93(x, k_0, k_1))
Eq(F_93(x, k_0, k_1), (-k_0*F_94(x, k_0, 1) + k_1*F_94(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_94(x, k_0, k_1), F_20(x, k_0, k_0*k_1))
Eq(F_95(x, k_0, k_1), F_36(x, k_0)*F_96(x, k_0, k_1))
Eq(F_96(x, k_0, k_1), (-k_0*F_97(x, k_0, 1) + k_1*F_97(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_97(x, k_0, k_1), F_88(x, k_0, k_0*k_1))
Eq(F_98(x, k_0, k_1), F_36(x, k_1)*F_88(x, k_0, k_1))
Eq(F_99(x, k_0, k_1), F_100(x, k_0, k_1))
Eq(F_100(x, k_0, k_1), F_101(x, k_0*k_1, k_1))
Eq(F_101(x, k_0, k_1), F_102(x, k_0, k_1)*F_36(x, k_0))
Eq(F_102(x, k_0, k_1), F_103(x, k_0, k_1) + F_104(x, k_0, k_1))
Eq(F_103(x, k_0, k_1), F_57(x, k_0, 1, k_1))
Eq(F_104(x, k_0, k_1), F_105(x, k_0, k_1))
Eq(F_105(x, k_0, k_1), F_102(x, k_0, k_1)*F_36(x, k_0)*F_43(x, k_0))
Eq(F_107(x, k_0, k_1), F_106(x, k_0, k_0*k_1))
Eq(F_107(x, k_0, k_1), F_108(k_0*x, k_1))
Eq(F_108(x, k_0), F_109(x) + F_110(x, k_0))
Eq(F_109(x), x*F_109(x)**4 + (-x - 1)*F_109(x)**3 + (2*x - 2)*F_109(x) + (x**2 - 2*x + 3)*F_109(x)**2 + 1)
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_36(x, k_0))
Eq(F_112(x, k_0), F_113(x, k_0) + F_114(x, k_0))
Eq(F_113(x, k_0), F_108(x, k_0)*F_43(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0))
Eq(F_115(x, k_0), F_109(x)*F_116(x, k_0)*F_7(x))
Eq(F_117(x, k_0), F_116(x, k_0)*F_7(x))
Eq(F_117(x, k_0), F_118(x, k_0))
Eq(F_108(x, k_0), F_118(x, k_0) + F_43(x, k_0))
Eq(F_119(x, k_0, k_1, k_2, k_3), F_120(x, k_0, k_1, k_2, k_3))
Eq(F_120(x, k_0, k_1, k_2, k_3), F_106(x, k_1, k_2)*F_36(x, k_0)*F_62(x, k_3)*F_76(x, k_0, k_3))
Eq(F_121(x, k_0, k_1), F_122(x, k_0, k_1)*F_36(x, k_1))
Eq(F_122(x, k_0, k_1), F_123(x, k_0, 1, k_1))
Eq(F_123(x, k_0, k_1, k_2), F_31(x, k_0, k_1*k_2, k_2))
Pack JSON:
{"name": "row_and_col_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": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "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, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], 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