01243_01342_02143_10243_10342
Counting sequence:
1, 1, 2, 6, 24, 115, 615, 3526, 21188, 131670, 839113, 5453323, 36000929, 240739559, 1627198405, 11098994842, 76299076475, 528081362303, 3676757589239, 25734283792393, 180963914032314, 1277890689389355, 9058110971538301, 64427245226893806, 459680508454718816, 3289130057401180056, 23596230795073448659, 169688005505706775455, 1223001833601526072670, 8832828429515196099051, 63915468091014359983637, 463328364411528311143542, 3364320769245278453548070, 24467255531633998429837347, 178201157278795008528549291, 1299675727679133699313704971, 9491260238127584993850810208, 69397728492297898210612164852, 508007211970865552013944885716, 3722809766586441018173104934382, 27310104107855633720443270222710, 200541611665292444726557851946356, 1473985027495321235329051769255581, 10843497879207866698776425976105052, 79839021045017029934955448394648033, 588319807793845202319955255801746713, 4338587261682692709146003547700227252, 32018795148172105450307993413399689349, 236466464922463299556120345082043478572, 1747547848092425642091321395865884459286, 12923238496136149972607074053827241697377, 95627977897347693176197764469032815230127, 708042226063880129512058527464603391313296, 5245462532074760239876743344503058321110415, 38882064334440236514466501199307264334294707, 288367771782859051997389383685402514554047332, 2139771971664427179684082441999904282845392453, 15885598356729079518916723787594295063600568723, 117990582403774774264871803343758145359819589816, 876781881866752053096652254012013477793816515553, 6518225582883549134064770268540411481068087907328, 48479071400993939923111955503619408170976432142918, 360711590001347022720053875834265171398113179772737, 2684979125491451562256552639890299411077317406866149, 19993606468683183098718412649460747229964292830013648, 148937972326938906399050861962302288839809097521025210, 1109886875273732068857121850120181450540523872284881132, 8273820977973110238258561003894514536876970975926329540, 61699694242114296924302537164222506259639044022994402841, 460261831419701751443219686037655522132182280010627223389, 3434533297868337559420335803821997507784897305259453218711, 25637003826962348500117451250857898115172645826163591518082, 191425456375360549857563124006344593907585709376662523775795, 1429753874050417174997713889407867942105665219973387568735522, 10681899227099272075015152418487311661893944786149716529572331, 79828479297911614622185255564484713654567156575827044480232741, 596741360610116268161853873542539641913827632838528044563333358, 4462006288544755094486918039473165463768342557215972448918275373, 33372361775123032911723842496541071719808824465017081461209010769, 249662620899708080599341640656793612236002148149340912421417075974, 1868216170574356190218534006200428117243557844433856958034259617403, 13983151235624051541092957485522878816721434350751732511074082798905, 104685062559928767014060385374784051702808554567066637105637252780688, 783905328109717670706250069394439922639525327080789677137997834399525, 5871368614249807499240331694283925349970551527403317858990563363799540, 43985505693725352834583692116944341955542883005509208631741061982650323, 329588542802693227680173748237159661952789975263109031280643540489867390, 2470158034155395858202836266906793824713284814698320396665171096845451251, 18516777335115970622576120290094543640948967010902339261083083956809377826, 138832802063190210742941294961669238590671159362377852986066011934999213922, 1041124939523937049144731494447625890265048989566278028621909719588353690138, 7809006918025007401130381062769823275773193697117478864835377960230606734749, 58582667867334246590088481301269359547847936152148583369238873128861052756561, 439562978104434077420980125527010981526035835727830681827481013098798121023564, 3298754471988129495986029232815340134592710802565888474930230500982944511442285, 24760200365208140404075014086032546730583805388417282021141943284415651211300671, 185879716872572993462166148581289742268989668629995730562252868082105376000141859, 1395667583382027142823425276640596199303142877146460705100769992772584965856495200, 10480997731879470745590095118892578529342766088017478554613389002480896828197432676, 78721336700559031080952404417617314203334494119764731782947606146302739679979765250, 591357467110705617254184273511797818254522669579976683041000105166104074458760088804
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24742/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[5,x]+F[82,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[79,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[14,x,k[0]]+F[71,x,k[0]]+F[75,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[14,x,k[0]] = F[15,x,k[0]]*F[3,x]
F[15,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[16,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[17,x,k[0]]+F[71,x,k[0]]+F[74,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[3,x]
F[18,x,k[0]] = F[19,x,1,k[0]]
F[19,x,k[0],k[1]] = 1/(-1+k[0])*(F[20,x,k[0],k[1]]*k[0]-F[20,x,1,k[1]])
F[20,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[23,x,k[0],k[1]]+F[59,x,k[0],k[1]]+F[70,x,k[1],k[0]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[3,x]
F[22,x,k[0],k[1]] = 1/(-1+k[0])*(F[20,x,k[0],k[1]]*k[0]-F[20,x,1,k[1]])
F[23,x,k[0],k[1]] = F[24,x,k[0],k[1]]*F[3,x]
F[24,x,k[0],k[1]] = 1/(-1+k[0])*(F[25,x,k[0],k[1]]*k[0]-F[25,x,1,k[1]])
F[25,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[51,x,k[1],k[0]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]*F[3,x]
F[27,x,k[0],k[1]] = (F[16,x,k[0]]*k[0]-F[16,x,k[1]]*k[1])/(-k[1]+k[0])
F[28,x,k[0],k[1]] = F[29,x,k[0]]*F[30,x,k[0],k[1]]
F[29,x,k[0]] = k[0]*x
F[30,x,k[0],k[1]] = (F[31,x,k[0],1]*k[0]-F[31,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[31,x,k[0],k[1]] = F[32,x,k[0],k[0]*k[1]]
F[32,x,k[0],k[1]] = F[1,x]+F[26,x,k[0],k[1]]+F[28,x,k[0],k[1]]+F[33,x,k[0],k[1]]+F[62,x,k[1]]
F[33,x,k[0],k[1]] = F[3,x]*F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[35,x,1,k[0],k[1]]
F[35,x,k[0],k[1],k[2]] = F[1,x]+F[36,x,k[0],k[1],k[2]]+F[38,x,k[0],k[1],k[2]]+F[52,x,k[0],k[1],k[2]]+F[67,x,k[1],k[0],k[2]]+F[70,x,k[2],k[0]]
F[36,x,k[0],k[1],k[2]] = F[3,x]*F[37,x,k[0],k[1],k[2]]
F[37,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[35,x,k[0],k[1],k[2]]*k[0]-F[35,x,1,k[1],k[2]])
F[38,x,k[0],k[1],k[2]] = F[3,x]*F[39,x,k[0],k[1],k[2]]
F[39,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[40,x,k[0],k[1],k[2]]*k[0]-F[40,x,1,k[1],k[2]])
F[40,x,k[0],k[1],k[2]] = F[1,x]+F[36,x,k[0],k[1],k[2]]+F[41,x,k[0],k[1],k[2]]+F[43,x,k[0],k[1],k[2]]+F[47,x,k[1],k[0],k[2]]+F[51,x,k[2],k[0]]
F[41,x,k[0],k[1],k[2]] = F[3,x]*F[42,x,k[0],k[1],k[2]]
F[42,x,k[0],k[1],k[2]] = (F[27,x,k[0],k[2]]*k[0]-F[27,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[43,x,k[0],k[1],k[2]] = F[29,x,k[0]]*F[44,x,k[0],k[1],k[2]]
F[44,x,k[0],k[1],k[2]] = (F[45,x,k[0],1,k[2]]*k[0]-F[45,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[45,x,k[0],k[1],k[2]] = F[46,x,k[0],k[1],1,k[2]]
F[46,x,k[0],k[1],k[2],k[3]] = (F[31,x,k[0],k[1]*k[2]]*k[0]*k[1]-F[31,x,k[0],k[2]*k[3]/k[0]]*k[3])/(k[0]*k[1]-k[3])
F[47,x,k[0],k[1],k[2]] = F[29,x,k[0]]*F[48,x,k[1],k[0],k[2]]
F[48,x,k[0],k[1],k[2]] = (-F[49,x,1,k[1],k[2]]*k[1]+F[49,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[49,x,k[0],k[1],k[2]] = (F[50,x,k[0],k[1],1]*k[1]-F[50,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[50,x,k[0],k[1],k[2]] = F[32,x,k[0]*k[1],k[1]*k[2]]
F[51,x,k[0],k[1]] = F[29,x,k[0]]*F[32,x,k[1],k[0]]
F[52,x,k[0],k[1],k[2]] = F[29,x,k[0]]*F[53,x,k[0],k[1],k[2]]
F[53,x,k[0],k[1],k[2]] = (F[54,x,k[0],1,k[2]]*k[0]-F[54,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[54,x,k[0],k[1],k[2]] = F[55,x,k[0],k[0]*k[1],k[2]]
F[55,x,k[0],k[1],k[2]] = (F[56,x,k[0],k[1]]*k[1]-F[56,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[56,x,k[0],k[1]] = F[1,x]+F[33,x,k[0],k[1]]+F[57,x,k[0],k[1]]+F[59,x,k[0],k[1]]+F[62,x,k[1]]
F[57,x,k[0],k[1]] = F[3,x]*F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[40,x,1,k[0],k[1]]
F[59,x,k[0],k[1]] = F[29,x,k[0]]*F[60,x,k[0],k[1]]
F[60,x,k[0],k[1]] = (F[61,x,k[0],1]*k[0]-F[61,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[61,x,k[0],k[1]] = F[56,x,k[0],k[0]*k[1]]
F[62,x,k[0]] = F[29,x,k[0]]*F[63,x,k[0]]
F[63,x,k[0]] = F[1,x]+F[62,x,k[0]]+F[64,x,k[0]]+F[66,x,k[0]]
F[64,x,k[0]] = F[3,x]*F[65,x,k[0]]
F[65,x,k[0]] = F[20,x,1,k[0]]
F[66,x,k[0]] = F[16,x,k[0]]*F[3,x]
F[67,x,k[0],k[1],k[2]] = F[29,x,k[0]]*F[68,x,k[1],k[0],k[2]]
F[68,x,k[0],k[1],k[2]] = (-F[69,x,1,k[1],k[2]]*k[1]+F[69,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[69,x,k[0],k[1],k[2]] = F[55,x,k[0]*k[1],k[1],k[2]]
F[70,x,k[0],k[1]] = F[29,x,k[0]]*F[56,x,k[1],k[0]]
F[71,x,k[0]] = F[3,x]*F[72,x,k[0]]
F[72,x,k[0]] = 1/(-1+k[0])*(F[73,x,k[0]]*k[0]-F[73,x,1])
F[73,x,k[0]] = F[32,x,1,k[0]]
F[74,x,k[0]] = F[29,x,k[0]]*F[73,x,k[0]]
F[75,x,k[0]] = F[29,x,k[0]]*F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,1,k[0]]
F[77,x,k[0],k[1]] = (-F[78,x,1,k[1]]*k[1]+F[78,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[78,x,k[0],k[1]] = F[32,x,k[0]*k[1],k[1]]
F[79,x,k[0]] = F[29,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[81,x,1,k[0]]
F[81,x,k[0],k[1]] = F[56,x,k[0]*k[1],k[1]]
F[82,x] = F[3,x]*F[83,x]
F[83,x] = F[1,x]+F[84,x]+F[87,x]+F[88,x]
F[84,x] = F[3,x]*F[85,x]
F[85,x] = F[86,x,1]
F[86,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[87,x] = F[66,x,1]
F[88,x] = F[74,x,1]
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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{82}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{79}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{7}\! \left(x , y_{0}\right)+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}\right)+F_{14}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)+F_{75}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y_{0}\right) = -\frac{-F_{9}\! \left(x , y_{0}\right) y_{0}+F_{9}\! \left(x , 1\right)}{-1+y_{0}}
F_{14}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{15}\! \left(x , y_{0}\right) = -\frac{-F_{16}\! \left(x , y_{0}\right) y_{0}+F_{16}\! \left(x , 1\right)}{-1+y_{0}}
F_{16}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}\right)+F_{17}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)+F_{74}\! \left(x , y_{0}\right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , 1, y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{20}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{20}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{59}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{1}, y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{22}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{20}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{20}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{25}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{25}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{1}, y_{0}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = F_{27}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{16}\! \left(x , y_{0}\right) y_{0}-F_{16}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}\right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}\right) = y_{0} x
F_{30}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{31}\! \left(x , y_{0}, 1\right) y_{0}-F_{31}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{1}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{34}\! \left(x , y_{0}, y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , 1, y_{0}, y_{1}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{67}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{70}\! \left(x , y_{2}, y_{0}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{35}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{40}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{47}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{51}\! \left(x , y_{2}, y_{0}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{27}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{27}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}\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}, 1, y_{2}\right) y_{0}-F_{45}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{46}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{31}\! \left(x , y_{0}, y_{1} y_{2}\right) y_{0} y_{1}-F_{31}\! \left(x , y_{0}, \frac{y_{2} y_{3}}{y_{0}}\right) y_{3}}{y_{0} y_{1}-y_{3}}
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}\right) F_{48}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{49}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{49}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{50}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{50}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{32}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)
F_{51}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{1}, y_{0}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}\right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{54}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{54}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{55}\! \left(x , y_{0}, 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}, y_{1}\right) y_{1}-F_{56}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)+F_{59}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = F_{40}\! \left(x , 1, y_{0}, y_{1}\right)
F_{59}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}\right) F_{60}\! \left(x , y_{0}, y_{1}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{61}\! \left(x , y_{0}, 1\right) y_{0}-F_{61}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{56}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{62}\! \left(x , y_{0}\right) = F_{29}\! \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_{62}\! \left(x , y_{0}\right)+F_{64}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{20}\! \left(x , 1, y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}\right) F_{68}\! \left(x , y_{1}, y_{0}, y_{2}\right)
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{69}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{69}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{55}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{29}\! \left(x , y_{0}\right) F_{56}\! \left(x , y_{1}, y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{72}\! \left(x , y_{0}\right)
F_{72}\! \left(x , y_{0}\right) = -\frac{-F_{73}\! \left(x , y_{0}\right) y_{0}+F_{73}\! \left(x , 1\right)}{-1+y_{0}}
F_{73}\! \left(x , y_{0}\right) = F_{32}\! \left(x , 1, y_{0}\right)
F_{74}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right) F_{73}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right) F_{76}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{77}\! \left(x , 1, y_{0}\right)
F_{77}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{78}\! \left(x , 1, y_{1}\right) y_{1}-F_{78}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{78}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{79}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right) F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{81}\! \left(x , 1, y_{0}\right)
F_{81}\! \left(x , y_{0}, y_{1}\right) = F_{56}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{82}\! \left(x \right) = F_{3}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{1}\! \left(x \right)+F_{84}\! \left(x \right)+F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{84}\! \left(x \right) = F_{3}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x , 1\right)
F_{86}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{7}\! \left(x , y_{0}\right)+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{87}\! \left(x \right) = F_{66}\! \left(x , 1\right)
F_{88}\! \left(x \right) = F_{74}\! \left(x , 1\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_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_5(x) + F_82(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_79(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), F_1(x) + F_12(x, k_0) + F_14(x, k_0) + F_71(x, k_0) + F_75(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_15(x, k_0)*F_3(x))
Eq(F_15(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_16(x, k_0), F_1(x) + F_14(x, k_0) + F_17(x, k_0) + F_71(x, k_0) + F_74(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_3(x))
Eq(F_18(x, k_0), F_19(x, 1, k_0))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0, k_1) + F_20(x, 1, k_1))/(1 - k_0))
Eq(F_20(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_23(x, k_0, k_1) + F_59(x, k_0, k_1) + F_70(x, k_1, k_0))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_3(x))
Eq(F_22(x, k_0, k_1), (k_0*F_20(x, k_0, k_1) - F_20(x, 1, k_1))/(k_0 - 1))
Eq(F_23(x, k_0, k_1), F_24(x, k_0, k_1)*F_3(x))
Eq(F_24(x, k_0, k_1), (k_0*F_25(x, k_0, k_1) - F_25(x, 1, k_1))/(k_0 - 1))
Eq(F_25(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_26(x, k_0, k_1) + F_28(x, k_0, k_1) + F_51(x, k_1, k_0))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1)*F_3(x))
Eq(F_27(x, k_0, k_1), (-k_0*F_16(x, k_0) + k_1*F_16(x, k_1))/(-k_0 + k_1))
Eq(F_28(x, k_0, k_1), F_29(x, k_0)*F_30(x, k_0, k_1))
Eq(F_29(x, k_0), k_0*x)
Eq(F_30(x, k_0, k_1), (-k_0*F_31(x, k_0, 1) + k_1*F_31(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_0*k_1))
Eq(F_32(x, k_0, k_1), F_1(x) + F_26(x, k_0, k_1) + F_28(x, k_0, k_1) + F_33(x, k_0, k_1) + F_62(x, k_1))
Eq(F_33(x, k_0, k_1), F_3(x)*F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_35(x, 1, k_0, k_1))
Eq(F_35(x, k_0, k_1, k_2), F_1(x) + F_36(x, k_0, k_1, k_2) + F_38(x, k_0, k_1, k_2) + F_52(x, k_0, k_1, k_2) + F_67(x, k_1, k_0, k_2) + F_70(x, k_2, k_0))
Eq(F_36(x, k_0, k_1, k_2), F_3(x)*F_37(x, k_0, k_1, k_2))
Eq(F_37(x, k_0, k_1, k_2), (k_0*F_35(x, k_0, k_1, k_2) - F_35(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_38(x, k_0, k_1, k_2), F_3(x)*F_39(x, k_0, k_1, k_2))
Eq(F_39(x, k_0, k_1, k_2), (k_0*F_40(x, k_0, k_1, k_2) - F_40(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_40(x, k_0, k_1, k_2), F_1(x) + F_36(x, k_0, k_1, k_2) + F_41(x, k_0, k_1, k_2) + F_43(x, k_0, k_1, k_2) + F_47(x, k_1, k_0, k_2) + F_51(x, k_2, k_0))
Eq(F_41(x, k_0, k_1, k_2), F_3(x)*F_42(x, k_0, k_1, k_2))
Eq(F_42(x, k_0, k_1, k_2), (-k_0*F_27(x, k_0, k_2) + k_1*F_27(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_43(x, k_0, k_1, k_2), F_29(x, k_0)*F_44(x, k_0, k_1, k_2))
Eq(F_44(x, k_0, k_1, k_2), (-k_0*F_45(x, k_0, 1, k_2) + k_1*F_45(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_45(x, k_0, k_1, k_2), F_46(x, k_0, k_1, 1, k_2))
Eq(F_46(x, k_0, k_1, k_2, k_3), (-k_0*k_1*k_2*F_31(x, k_0, k_1*k_2) + k_2*k_3*F_31(x, k_0, k_2*k_3/k_0))/(-k_0*k_1*k_2 + k_2*k_3))
Eq(F_47(x, k_0, k_1, k_2), F_29(x, k_0)*F_48(x, k_1, k_0, k_2))
Eq(F_48(x, k_0, k_1, k_2), (-k_0*F_49(x, k_0/k_1, k_1, k_2) + k_1*F_49(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_49(x, k_0, k_1, k_2), (-k_1*F_50(x, k_0, k_1, 1) + k_2*F_50(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_50(x, k_0, k_1, k_2), F_32(x, k_0*k_1, k_1*k_2))
Eq(F_51(x, k_0, k_1), F_29(x, k_0)*F_32(x, k_1, k_0))
Eq(F_52(x, k_0, k_1, k_2), F_29(x, k_0)*F_53(x, k_0, k_1, k_2))
Eq(F_53(x, k_0, k_1, k_2), (-k_0*F_54(x, k_0, 1, k_2) + k_1*F_54(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_54(x, k_0, k_1, k_2), F_55(x, k_0, k_0*k_1, k_2))
Eq(F_55(x, k_0, k_1, k_2), (-k_1*F_56(x, k_0, k_1) + k_2*F_56(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_56(x, k_0, k_1), F_1(x) + F_33(x, k_0, k_1) + F_57(x, k_0, k_1) + F_59(x, k_0, k_1) + F_62(x, k_1))
Eq(F_57(x, k_0, k_1), F_3(x)*F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_40(x, 1, k_0, k_1))
Eq(F_59(x, k_0, k_1), F_29(x, k_0)*F_60(x, k_0, k_1))
Eq(F_60(x, k_0, k_1), (-k_0*F_61(x, k_0, 1) + k_1*F_61(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_61(x, k_0, k_1), F_56(x, k_0, k_0*k_1))
Eq(F_62(x, k_0), F_29(x, k_0)*F_63(x, k_0))
Eq(F_63(x, k_0), F_1(x) + F_62(x, k_0) + F_64(x, k_0) + F_66(x, k_0))
Eq(F_64(x, k_0), F_3(x)*F_65(x, k_0))
Eq(F_65(x, k_0), F_20(x, 1, k_0))
Eq(F_66(x, k_0), F_16(x, k_0)*F_3(x))
Eq(F_67(x, k_0, k_1, k_2), F_29(x, k_0)*F_68(x, k_1, k_0, k_2))
Eq(F_68(x, k_0, k_1, k_2), (-k_0*F_69(x, k_0/k_1, k_1, k_2) + k_1*F_69(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_69(x, k_0, k_1, k_2), F_55(x, k_0*k_1, k_1, k_2))
Eq(F_70(x, k_0, k_1), F_29(x, k_0)*F_56(x, k_1, k_0))
Eq(F_71(x, k_0), F_3(x)*F_72(x, k_0))
Eq(F_72(x, k_0), (k_0*F_73(x, k_0) - F_73(x, 1))/(k_0 - 1))
Eq(F_73(x, k_0), F_32(x, 1, k_0))
Eq(F_74(x, k_0), F_29(x, k_0)*F_73(x, k_0))
Eq(F_75(x, k_0), F_29(x, k_0)*F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, 1, k_0))
Eq(F_77(x, k_0, k_1), (-k_0*F_78(x, k_0/k_1, k_1) + k_1*F_78(x, 1, k_1))/(-k_0 + k_1))
Eq(F_78(x, k_0, k_1), F_32(x, k_0*k_1, k_1))
Eq(F_79(x, k_0), F_29(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_81(x, 1, k_0))
Eq(F_81(x, k_0, k_1), F_56(x, k_0*k_1, k_1))
Eq(F_82(x), F_3(x)*F_83(x))
Eq(F_83(x), F_1(x) + F_84(x) + F_87(x) + F_88(x))
Eq(F_84(x), F_3(x)*F_85(x))
Eq(F_85(x), F_86(x, 1))
Eq(F_86(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
Eq(F_87(x), F_66(x, 1))
Eq(F_88(x), F_74(x, 1))
Pack JSON:
{"name": "col_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
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0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 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, 1], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 3], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 3], [0, 3], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 3]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": 2, "col_idx": null, "tracked": true}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24773/
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[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[183,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = -F[0,x]+F[12,x]
F[12,x] = 1/F[4,x]*F[13,x]
F[13,x] = F[2,x]
F[14,x] = F[15,x,1]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]+F[180,x,k[0]]
F[18,x,k[0]] = F[179,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[79,x,k[0]]
F[21,x,k[0]] = F[147,x,k[0]]+F[22,x,k[0]]
F[22,x,k[0]] = F[143,x,k[0]]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[63,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[5,x]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]*F[79,x,k[0]]
F[21,x,k[0]] = F[27,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,1,k[0]]
F[31,x,k[0],k[1]] = F[30,x,k[0],k[1]]*F[79,x,k[0]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[34,x,k[0],k[1]]*F[79,x,k[1]]
F[34,x,k[0],k[1]] = F[35,x,k[0],k[1],1]
F[35,x,k[0],k[1],k[2]] = (F[36,x,k[0],k[1],k[2]]*k[2]-F[36,x,k[0],k[1],1])/(-1+k[2])
F[36,x,k[0],k[1],k[2]] = F[37,x,k[0],k[1]*k[2]]+F[83,x,k[0],k[1],k[2]]
F[38,x,k[0],k[1]] = F[142,x,k[0],k[1]]+F[37,x,k[0],k[1]]
F[39,x,k[0],k[1]] = 1/(-1+k[1])*(F[38,x,k[0],k[1]]*k[1]-F[38,x,k[0],1])
F[40,x,k[0],k[1]] = F[39,x,k[0],k[1]]*F[4,x]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = F[42,x,k[0],k[1]]
F[42,x,k[0],k[1]] = F[43,x,k[0],k[1]]*F[79,x,k[0]]
F[43,x,k[0],k[1]] = F[138,x,k[0],k[1]]+F[44,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[45,x,k[1],k[0]]
F[45,x,k[0],k[1]] = F[136,x,k[0],k[1]]+F[46,x,k[0]]
F[47,x,k[0]] = F[135,x,k[0]]+F[46,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[49,x,k[0]] = F[132,x,k[0]]+F[48,x,k[0]]
F[50,x,k[0]] = F[130,x,k[0]]+F[49,x,k[0]]
F[50,x,k[0]] = F[128,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[23,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,1,k[0]]
F[53,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[54,x,k[1]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[56,x,k[0]]+F[92,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = F[58,x,k[0]]*F[79,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[61,x,k[0]] = F[4,x]*F[60,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[63,x,k[0]] = F[10,x]+F[62,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[88,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[21,x,k[0]]*F[4,x]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]*F[79,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0],1]
F[72,x,k[0],k[1]] = (F[73,x,k[0],k[1]]*k[1]-F[73,x,k[0],1])/(-1+k[1])
F[74,x,k[0],k[1]] = F[4,x]*F[73,x,k[0],k[1]]
F[74,x,k[0],k[1]] = F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = F[76,x,k[0]*k[1]]+F[82,x,k[0],k[1]]
F[77,x,k[0]] = F[76,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[77,x,k[0]]*F[79,x,k[0]]
F[78,x,k[0]] = F[15,x,k[0]]
F[79,x,k[0]] = k[0]*x
F[80,x,k[0]] = F[81,x,1,k[0]]
F[81,x,k[0],k[1]] = -k[0]*(F[32,x,1,k[1]]-F[32,x,k[0],k[1]])/(-1+k[0])
F[82,x,k[0],k[1]] = F[83,x,1,k[0],k[1]]
F[83,x,k[0],k[1],k[2]] = -k[0]*(F[84,x,1,k[1],k[2]]-F[84,x,k[0],k[1],k[2]])/(-1+k[0])
F[84,x,k[0],k[1],k[2]] = F[85,x,k[0],k[1],k[1]*k[2]]
F[85,x,k[0],k[1],k[2]] = F[86,x,k[0],k[1],k[2]]
F[86,x,k[0],k[1],k[2]] = F[79,x,k[1]]*F[87,x,k[0],k[1],k[2]]
F[87,x,k[0],k[1],k[2]] = (F[36,x,k[0],k[1],1]*k[1]-F[36,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[4,x]*F[90,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[91,x,k[0]]*k[0]-F[91,x,1])
F[91,x,k[0]] = F[75,x,1,k[0]]
F[93,x,k[0]] = F[92,x,k[0]]+F[98,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[95,x,k[0]] = F[4,x]*F[94,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[97,x,k[0]] = F[4,x]*F[96,x,k[0]]
F[97,x,k[0]] = F[88,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[73,x,1,k[0]]
F[100,x,k[0],k[1]] = F[101,x,k[1],k[0]]
F[101,x,k[0],k[1]] = F[102,x,k[0],k[1]]*F[79,x,k[1]]
F[102,x,k[0],k[1]] = F[103,x,k[1],k[0]]
F[103,x,k[0],k[1]] = (F[104,x,k[0],1]*k[0]-F[104,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[104,x,k[0],k[1]] = F[105,x,1,k[0],k[1]]
F[105,x,k[0],k[1],k[2]] = F[106,x,k[0],k[1],k[1]*k[2]]
F[106,x,k[0],k[1],k[2]] = k[0]*F[107,x,k[2],k[2]]
F[107,x,k[0],k[1]] = F[108,x,k[1],k[0]]
F[108,x,k[0],k[1]] = F[109,x,k[0]]+F[113,x,k[0],k[1]]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[4,x]
F[111,x,k[0]] = F[112,x,k[0]]+F[27,x,k[0]]
F[112,x,k[0]] = F[96,x,k[0]]
F[113,x,k[0],k[1]] = F[114,x,k[0],1,k[1]]
F[114,x,k[0],k[1],k[2]] = (F[115,x,k[0],k[1],k[2]]*k[1]-F[115,x,k[0],1,k[2]])/(-1+k[1])
F[115,x,k[0],k[1],k[2]] = F[116,x,k[0],k[1],k[2]]
F[116,x,k[0],k[1],k[2]] = F[117,x,k[0],k[1],k[2]]*F[4,x]
F[117,x,k[0],k[1],k[2]] = F[118,x,k[0],k[2]]+F[126,x,k[0],k[1],k[2]]
F[119,x,k[0],k[1]] = F[118,x,k[0],k[1]]+F[123,x,k[0],k[1]]
F[120,x,k[0],k[1]] = F[119,x,k[0],k[1]]+F[56,x,k[0]]
F[120,x,k[0],k[1]] = F[121,x,k[1],k[0]]
F[122,x,k[0],k[1]] = F[121,x,k[0],k[1]]*F[4,x]
F[122,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[123,x,k[0],k[1]] = -k[1]*(F[124,x,k[0],1]-F[124,x,k[0],k[1]])/(-1+k[1])
F[124,x,k[0],k[1]] = F[125,x,k[1],k[0]]
F[125,x,k[0],k[1]] = F[85,x,1,k[0],k[1]]
F[126,x,k[0],k[1],k[2]] = -k[2]*(F[127,x,k[0],k[1],1]-F[127,x,k[0],k[1],k[2]])/(-1+k[2])
F[127,x,k[0],k[1],k[2]] = F[85,x,k[1],k[2],k[0]]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = F[4,x]*F[94,x,k[0]]
F[130,x,k[0]] = F[131,x,1,k[0]]
F[131,x,k[0],k[1]] = (F[53,x,k[0],k[1]]*k[0]-F[53,x,1,k[1]])/(-1+k[0])
F[132,x,k[0]] = F[133,x,1,k[0]]
F[133,x,k[0],k[1]] = (F[134,x,k[0],k[1]]*k[0]-F[134,x,1,k[1]])/(-1+k[0])
F[134,x,k[0],k[1]] = F[125,x,k[0],k[1]]+F[64,x,k[1]]
F[135,x,k[0]] = F[24,x,k[0]]
F[136,x,k[0],k[1]] = F[137,x,k[0],k[1],1]
F[137,x,k[0],k[1],k[2]] = (F[127,x,k[0],k[1],k[2]]-F[127,x,k[0],k[1],1])/(-1+k[2])
F[138,x,k[0],k[1]] = F[139,x,k[0],1,k[1]]
F[139,x,k[0],k[1],k[2]] = (F[140,x,k[0],k[1],k[2]]-F[140,x,k[0],1,k[2]])/(-1+k[1])
F[140,x,k[0],k[1],k[2]] = k[0]*F[141,x,k[0],k[1],k[2]]
F[141,x,k[0],k[1],k[2]] = F[115,x,k[2],k[0],k[1]]
F[142,x,k[0],k[1]] = -k[0]*(F[41,x,1,k[1]]-F[41,x,k[0],k[1]])/(-1+k[0])
F[69,x,k[0]] = F[143,x,k[0]]+F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,1,k[0]]
F[145,x,k[0],k[1]] = -k[1]*(F[146,x,1,k[1]]-F[146,x,k[0]/k[1],k[1]])/(-k[1]+k[0])
F[146,x,k[0],k[1]] = F[100,x,k[0]*k[1],k[1]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[4,x]
F[150,x,k[0]] = F[149,x,k[0]]*F[79,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = -k[0]*(F[152,x,1]-F[152,x,k[0]])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]+F[62,x,k[0]]
F[154,x,k[0],k[1]] = F[153,x,k[1]]+F[175,x,k[0],k[1]]
F[155,x,k[0],k[1]] = F[154,x,k[0],k[1]]*F[4,x]
F[155,x,k[0],k[1]] = F[156,x,k[0],k[1]]
F[156,x,k[0],k[1]] = F[157,x,k[1]]+F[173,x,k[0],k[1]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[79,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]+F[172,x,k[0]]
F[161,x,k[0]] = F[160,x,k[0]]+F[171,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[4,x]
F[163,x,k[0]] = F[164,x,k[0]]+F[27,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[168,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[4,x]
F[167,x,k[0]] = 1/(-1+k[0])*(F[163,x,k[0]]*k[0]-F[163,x,1])
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[170,x,1,k[0]]
F[170,x,k[0],k[1]] = -k[0]*(F[125,x,1,k[1]]-F[125,x,k[0],k[1]])/(-1+k[0])
F[171,x,k[0]] = F[100,x,1,k[0]]
F[172,x,k[0]] = F[146,x,1,k[0]]
F[173,x,k[0],k[1]] = F[174,x,k[0],k[1]]
F[174,x,k[0],k[1]] = F[175,x,k[0],k[1]]*F[4,x]
F[175,x,k[0],k[1]] = -k[1]*(F[176,x,k[0],1]-F[176,x,k[0],k[1]])/(-1+k[1])
F[176,x,k[0],k[1]] = F[177,x,k[0],k[1]]
F[177,x,k[0],k[1]] = F[178,x,k[0],k[1]]*F[79,x,k[1]]
F[178,x,k[0],k[1]] = F[36,x,k[0],k[1],1]
F[179,x,k[0]] = F[175,x,1,k[0]]
F[180,x,k[0]] = -k[0]*(F[181,x,1]-F[181,x,k[0]])/(-1+k[0])
F[181,x,k[0]] = F[182,x,1,k[0]]
F[182,x,k[0],k[1]] = k[0]*F[156,x,k[0],k[1]]
F[183,x] = F[152,x,1]
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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{183}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{2}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)+F_{180}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{179}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{143}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right)+F_{5}\! \left(x \right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , 1, y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{1}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{0}, y_{1}, 1\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{36}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{37}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{142}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{38}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{38}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{43}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{138}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{45}\! \left(x , y_{1}, y_{0}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{136}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{135}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{132}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{130}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{128}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{53}\! \left(x , 1, y_{0}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{54}\! \left(x , y_{1}\right)
F_{54}\! \left(x , y_{0}\right) = F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{56}\! \left(x , y_{0}\right)+F_{92}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{60}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{62}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right)+F_{62}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{64}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{64}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{69}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{71}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{72}\! \left(x , y_{0}, 1\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{73}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{73}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{4}\! \left(x \right) F_{73}\! \left(x , y_{0}, y_{1}\right)
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{75}\! \left(x , y_{0}, y_{1}\right)
F_{75}\! \left(x , y_{0}, y_{1}\right) = F_{76}\! \left(x , y_{0} y_{1}\right)+F_{82}\! \left(x , y_{0}, y_{1}\right)
F_{77}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)+F_{80}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{77}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = y_{0} x
F_{80}\! \left(x , y_{0}\right) = F_{81}\! \left(x , 1, y_{0}\right)
F_{81}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{32}\! \left(x , 1, y_{1}\right)-F_{32}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{82}\! \left(x , y_{0}, y_{1}\right) = F_{83}\! \left(x , 1, y_{0}, y_{1}\right)
F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{84}\! \left(x , 1, y_{1}, y_{2}\right)-F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{85}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{85}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{86}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{86}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{79}\! \left(x , y_{1}\right) F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{36}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-y_{2} F_{36}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{88}\! \left(x , y_{0}\right) = F_{89}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = -\frac{-F_{91}\! \left(x , y_{0}\right) y_{0}+F_{91}\! \left(x , 1\right)}{-1+y_{0}}
F_{91}\! \left(x , y_{0}\right) = F_{75}\! \left(x , 1, y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{92}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{94}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{96}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{96}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{88}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{73}\! \left(x , 1, y_{0}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = F_{101}\! \left(x , y_{1}, y_{0}\right)
F_{101}\! \left(x , y_{0}, y_{1}\right) = F_{102}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{1}\right)
F_{102}\! \left(x , y_{0}, y_{1}\right) = F_{103}\! \left(x , y_{1}, y_{0}\right)
F_{103}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{104}\! \left(x , y_{0}, 1\right) y_{0}-F_{104}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{104}\! \left(x , y_{0}, y_{1}\right) = F_{105}\! \left(x , 1, y_{0}, y_{1}\right)
F_{105}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{106}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{106}\! \left(x , y_{0}, y_{1}, y_{2}\right) = y_{0} F_{107}\! \left(x , y_{2}, y_{2}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(x , y_{1}, y_{0}\right)
F_{108}\! \left(x , y_{0}, y_{1}\right) = F_{109}\! \left(x , y_{0}\right)+F_{113}\! \left(x , y_{0}, y_{1}\right)
F_{109}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{96}\! \left(x , y_{0}\right)
F_{113}\! \left(x , y_{0}, y_{1}\right) = F_{114}\! \left(x , y_{0}, 1, y_{1}\right)
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{115}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{117}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)
F_{117}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{118}\! \left(x , y_{0}, y_{2}\right)+F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{118}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{119}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{1}, y_{0}\right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{123}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{124}\! \left(x , y_{0}, 1\right)-F_{124}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{124}\! \left(x , y_{0}, y_{1}\right) = F_{125}\! \left(x , y_{1}, y_{0}\right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{85}\! \left(x , 1, y_{0}, y_{1}\right)
F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} \left(F_{127}\! \left(x , y_{0}, y_{1}, 1\right)-F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{2}}
F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{85}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{128}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right)
F_{129}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{94}\! \left(x , y_{0}\right)
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , 1, y_{0}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{53}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{53}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{132}\! \left(x , y_{0}\right) = F_{133}\! \left(x , 1, y_{0}\right)
F_{133}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{134}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{134}\! \left(x , y_{0}, y_{1}\right) = F_{125}\! \left(x , y_{0}, y_{1}\right)+F_{64}\! \left(x , y_{1}\right)
F_{135}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{137}\! \left(x , y_{0}, y_{1}, 1\right)
F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{127}\! \left(x , y_{0}, y_{1}, 1\right)-F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right)}{-1+y_{2}}
F_{138}\! \left(x , y_{0}, y_{1}\right) = F_{139}\! \left(x , y_{0}, 1, y_{1}\right)
F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{140}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) = y_{0} F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{115}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{142}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{41}\! \left(x , 1, y_{1}\right)-F_{41}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{69}\! \left(x , y_{0}\right) = F_{143}\! \left(x , y_{0}\right)+F_{144}\! \left(x , y_{0}\right)
F_{144}\! \left(x , y_{0}\right) = F_{145}\! \left(x , 1, y_{0}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{146}\! \left(x , 1, y_{1}\right)-F_{146}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}
F_{146}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{147}\! \left(x , y_{0}\right) = F_{148}\! \left(x , y_{0}\right)
F_{148}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{150}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{150}\! \left(x , y_{0}\right) = F_{151}\! \left(x , y_{0}\right)
F_{151}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{152}\! \left(x , 1\right)-F_{152}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{152}\! \left(x , y_{0}\right) = F_{153}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)
F_{154}\! \left(x , y_{0}, y_{1}\right) = F_{153}\! \left(x , y_{1}\right)+F_{175}\! \left(x , y_{0}, y_{1}\right)
F_{155}\! \left(x , y_{0}, y_{1}\right) = F_{154}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{155}\! \left(x , y_{0}, y_{1}\right) = F_{156}\! \left(x , y_{0}, y_{1}\right)
F_{156}\! \left(x , y_{0}, y_{1}\right) = F_{157}\! \left(x , y_{1}\right)+F_{173}\! \left(x , y_{0}, y_{1}\right)
F_{157}\! \left(x , y_{0}\right) = F_{158}\! \left(x , y_{0}\right)
F_{158}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{159}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right)+F_{172}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right)+F_{171}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}\right) = F_{162}\! \left(x , y_{0}\right)
F_{162}\! \left(x , y_{0}\right) = F_{163}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{163}\! \left(x , y_{0}\right) = F_{164}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{164}\! \left(x , y_{0}\right) = F_{165}\! \left(x , y_{0}\right)+F_{168}\! \left(x , y_{0}\right)
F_{165}\! \left(x , y_{0}\right) = F_{166}\! \left(x , y_{0}\right)
F_{166}\! \left(x , y_{0}\right) = F_{167}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{167}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{163}\! \left(x , y_{0}\right)+F_{163}\! \left(x , 1\right)}{-1+y_{0}}
F_{168}\! \left(x , y_{0}\right) = F_{169}\! \left(x , y_{0}\right)
F_{169}\! \left(x , y_{0}\right) = F_{170}\! \left(x , 1, y_{0}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{125}\! \left(x , 1, y_{1}\right)-F_{125}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{171}\! \left(x , y_{0}\right) = F_{100}\! \left(x , 1, y_{0}\right)
F_{172}\! \left(x , y_{0}\right) = F_{146}\! \left(x , 1, y_{0}\right)
F_{173}\! \left(x , y_{0}, y_{1}\right) = F_{174}\! \left(x , y_{0}, y_{1}\right)
F_{174}\! \left(x , y_{0}, y_{1}\right) = F_{175}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{176}\! \left(x , y_{0}, 1\right)-F_{176}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{177}\! \left(x , y_{0}, y_{1}\right)
F_{177}\! \left(x , y_{0}, y_{1}\right) = F_{178}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{1}\right)
F_{178}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{1}, 1\right)
F_{179}\! \left(x , y_{0}\right) = F_{175}\! \left(x , 1, y_{0}\right)
F_{180}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{181}\! \left(x , 1\right)-F_{181}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{181}\! \left(x , y_{0}\right) = F_{182}\! \left(x , 1, y_{0}\right)
F_{182}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{156}\! \left(x , y_{0}, y_{1}\right)
F_{183}\! \left(x \right) = F_{152}\! \left(x , 1\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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_183(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), -F_0(x) + F_12(x))
Eq(F_12(x), F_13(x)/F_4(x))
Eq(F_13(x), F_2(x))
Eq(F_14(x), F_15(x, 1))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0) + F_180(x, k_0))
Eq(F_18(x, k_0), F_179(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_79(x, k_0))
Eq(F_21(x, k_0), F_147(x, k_0) + F_22(x, k_0))
Eq(F_22(x, k_0), F_143(x, k_0) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_63(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_5(x))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0)*F_79(x, k_0))
Eq(F_21(x, k_0), F_27(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, 1, k_0))
Eq(F_31(x, k_0, k_1), F_30(x, k_0, k_1)*F_79(x, k_0))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_34(x, k_0, k_1)*F_79(x, k_1))
Eq(F_34(x, k_0, k_1), F_35(x, k_0, k_1, 1))
Eq(F_35(x, k_0, k_1, k_2), (-k_2*F_36(x, k_0, k_1, k_2) + F_36(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_36(x, k_0, k_1, k_2), F_37(x, k_0, k_1*k_2) + F_83(x, k_0, k_1, k_2))
Eq(F_38(x, k_0, k_1), F_142(x, k_0, k_1) + F_37(x, k_0, k_1))
Eq(F_39(x, k_0, k_1), (k_1*F_38(x, k_0, k_1) - F_38(x, k_0, 1))/(k_1 - 1))
Eq(F_40(x, k_0, k_1), F_39(x, k_0, k_1)*F_4(x))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, k_0, k_1))
Eq(F_42(x, k_0, k_1), F_43(x, k_0, k_1)*F_79(x, k_0))
Eq(F_43(x, k_0, k_1), F_138(x, k_0, k_1) + F_44(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_45(x, k_1, k_0))
Eq(F_45(x, k_0, k_1), F_136(x, k_0, k_1) + F_46(x, k_0))
Eq(F_47(x, k_0), F_135(x, k_0) + F_46(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_49(x, k_0), F_132(x, k_0) + F_48(x, k_0))
Eq(F_50(x, k_0), F_130(x, k_0) + F_49(x, k_0))
Eq(F_50(x, k_0), F_128(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_23(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, 1, k_0))
Eq(F_53(x, k_0, k_1), F_100(x, k_0, k_1) + F_54(x, k_1))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_56(x, k_0) + F_92(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), F_58(x, k_0)*F_79(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_61(x, k_0), F_4(x)*F_60(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_63(x, k_0), F_10(x) + F_62(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_88(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_21(x, k_0)*F_4(x))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0)*F_79(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0, 1))
Eq(F_72(x, k_0, k_1), (-k_1*F_73(x, k_0, k_1) + F_73(x, k_0, 1))/(1 - k_1))
Eq(F_74(x, k_0, k_1), F_4(x)*F_73(x, k_0, k_1))
Eq(F_74(x, k_0, k_1), F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), F_76(x, k_0*k_1) + F_82(x, k_0, k_1))
Eq(F_77(x, k_0), F_76(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_77(x, k_0)*F_79(x, k_0))
Eq(F_78(x, k_0), F_15(x, k_0))
Eq(F_79(x, k_0), k_0*x)
Eq(F_80(x, k_0), F_81(x, 1, k_0))
Eq(F_81(x, k_0, k_1), -F_32(x, 1, k_1) + (-k_0*F_32(x, k_0, k_1) + F_32(x, 1, k_1))/(1 - k_0))
Eq(F_82(x, k_0, k_1), F_83(x, 1, k_0, k_1))
Eq(F_83(x, k_0, k_1, k_2), -F_84(x, 1, k_1, k_2) + (-k_0*F_84(x, k_0, k_1, k_2) + F_84(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_84(x, k_0, k_1, k_2), F_85(x, k_0, k_1, k_1*k_2))
Eq(F_85(x, k_0, k_1, k_2), F_86(x, k_0, k_1, k_2))
Eq(F_86(x, k_0, k_1, k_2), F_79(x, k_1)*F_87(x, k_0, k_1, k_2))
Eq(F_87(x, k_0, k_1, k_2), (-k_1*F_36(x, k_0, k_1, 1) + k_2*F_36(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_4(x)*F_90(x, k_0))
Eq(F_90(x, k_0), (k_0*F_91(x, k_0) - F_91(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), F_75(x, 1, k_0))
Eq(F_93(x, k_0), F_92(x, k_0) + F_98(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_95(x, k_0), F_4(x)*F_94(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_97(x, k_0), F_4(x)*F_96(x, k_0))
Eq(F_97(x, k_0), F_88(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_73(x, 1, k_0))
Eq(F_100(x, k_0, k_1), F_101(x, k_1, k_0))
Eq(F_101(x, k_0, k_1), F_102(x, k_0, k_1)*F_79(x, k_1))
Eq(F_102(x, k_0, k_1), F_103(x, k_1, k_0))
Eq(F_103(x, k_0, k_1), (-k_0*F_104(x, k_0, 1) + k_1*F_104(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_104(x, k_0, k_1), F_105(x, 1, k_0, k_1))
Eq(F_105(x, k_0, k_1, k_2), F_106(x, k_0, k_1, k_1*k_2))
Eq(F_106(x, k_0, k_1, k_2), k_0*F_107(x, k_2, k_2))
Eq(F_107(x, k_0, k_1), F_108(x, k_1, k_0))
Eq(F_108(x, k_0, k_1), F_109(x, k_0) + F_113(x, k_0, k_1))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_4(x))
Eq(F_111(x, k_0), F_112(x, k_0) + F_27(x, k_0))
Eq(F_112(x, k_0), F_96(x, k_0))
Eq(F_113(x, k_0, k_1), F_114(x, k_0, 1, k_1))
Eq(F_114(x, k_0, k_1, k_2), (-k_1*F_115(x, k_0, k_1, k_2) + F_115(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_115(x, k_0, k_1, k_2), F_116(x, k_0, k_1, k_2))
Eq(F_116(x, k_0, k_1, k_2), F_117(x, k_0, k_1, k_2)*F_4(x))
Eq(F_117(x, k_0, k_1, k_2), F_118(x, k_0, k_2) + F_126(x, k_0, k_1, k_2))
Eq(F_119(x, k_0, k_1), F_118(x, k_0, k_1) + F_123(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), F_119(x, k_0, k_1) + F_56(x, k_0))
Eq(F_120(x, k_0, k_1), F_121(x, k_1, k_0))
Eq(F_122(x, k_0, k_1), F_121(x, k_0, k_1)*F_4(x))
Eq(F_122(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_123(x, k_0, k_1), -F_124(x, k_0, 1) + (k_1*F_124(x, k_0, k_1) - F_124(x, k_0, 1))/(k_1 - 1))
Eq(F_124(x, k_0, k_1), F_125(x, k_1, k_0))
Eq(F_125(x, k_0, k_1), F_85(x, 1, k_0, k_1))
Eq(F_126(x, k_0, k_1, k_2), -F_127(x, k_0, k_1, 1) + (k_2*F_127(x, k_0, k_1, k_2) - F_127(x, k_0, k_1, 1))/(k_2 - 1))
Eq(F_127(x, k_0, k_1, k_2), F_85(x, k_1, k_2, k_0))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), F_4(x)*F_94(x, k_0))
Eq(F_130(x, k_0), F_131(x, 1, k_0))
Eq(F_131(x, k_0, k_1), (-k_0*F_53(x, k_0, k_1) + F_53(x, 1, k_1))/(1 - k_0))
Eq(F_132(x, k_0), F_133(x, 1, k_0))
Eq(F_133(x, k_0, k_1), (-k_0*F_134(x, k_0, k_1) + F_134(x, 1, k_1))/(1 - k_0))
Eq(F_134(x, k_0, k_1), F_125(x, k_0, k_1) + F_64(x, k_1))
Eq(F_135(x, k_0), F_24(x, k_0))
Eq(F_136(x, k_0, k_1), F_137(x, k_0, k_1, 1))
Eq(F_137(x, k_0, k_1, k_2), -F_127(x, k_0, k_1, k_2) + (-k_2*F_127(x, k_0, k_1, k_2) + F_127(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_138(x, k_0, k_1), F_139(x, k_0, 1, k_1))
Eq(F_139(x, k_0, k_1, k_2), -F_140(x, k_0, k_1, k_2) + (-k_1*F_140(x, k_0, k_1, k_2) + F_140(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_140(x, k_0, k_1, k_2), k_0*F_141(x, k_0, k_1, k_2))
Eq(F_141(x, k_0, k_1, k_2), F_115(x, k_2, k_0, k_1))
Eq(F_142(x, k_0, k_1), -F_41(x, 1, k_1) + (-k_0*F_41(x, k_0, k_1) + F_41(x, 1, k_1))/(1 - k_0))
Eq(F_69(x, k_0), F_143(x, k_0) + F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, 1, k_0))
Eq(F_145(x, k_0, k_1), -F_146(x, k_0/k_1, k_1) + (-k_0*F_146(x, k_0/k_1, k_1) + k_1*F_146(x, 1, k_1))/(-k_0 + k_1))
Eq(F_146(x, k_0, k_1), F_100(x, k_0*k_1, k_1))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_4(x))
Eq(F_150(x, k_0), F_149(x, k_0)*F_79(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), -F_152(x, 1) + (k_0*F_152(x, k_0) - F_152(x, 1))/(k_0 - 1))
Eq(F_152(x, k_0), F_153(x, k_0) + F_62(x, k_0))
Eq(F_154(x, k_0, k_1), F_153(x, k_1) + F_175(x, k_0, k_1))
Eq(F_155(x, k_0, k_1), F_154(x, k_0, k_1)*F_4(x))
Eq(F_155(x, k_0, k_1), F_156(x, k_0, k_1))
Eq(F_156(x, k_0, k_1), F_157(x, k_1) + F_173(x, k_0, k_1))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_79(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0) + F_172(x, k_0))
Eq(F_161(x, k_0), F_160(x, k_0) + F_171(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0)*F_4(x))
Eq(F_163(x, k_0), F_164(x, k_0) + F_27(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_168(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_4(x))
Eq(F_167(x, k_0), (k_0*F_163(x, k_0) - F_163(x, 1))/(k_0 - 1))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_170(x, 1, k_0))
Eq(F_170(x, k_0, k_1), -F_125(x, 1, k_1) + (-k_0*F_125(x, k_0, k_1) + F_125(x, 1, k_1))/(1 - k_0))
Eq(F_171(x, k_0), F_100(x, 1, k_0))
Eq(F_172(x, k_0), F_146(x, 1, k_0))
Eq(F_173(x, k_0, k_1), F_174(x, k_0, k_1))
Eq(F_174(x, k_0, k_1), F_175(x, k_0, k_1)*F_4(x))
Eq(F_175(x, k_0, k_1), -F_176(x, k_0, 1) + (k_1*F_176(x, k_0, k_1) - F_176(x, k_0, 1))/(k_1 - 1))
Eq(F_176(x, k_0, k_1), F_177(x, k_0, k_1))
Eq(F_177(x, k_0, k_1), F_178(x, k_0, k_1)*F_79(x, k_1))
Eq(F_178(x, k_0, k_1), F_36(x, k_0, k_1, 1))
Eq(F_179(x, k_0), F_175(x, 1, k_0))
Eq(F_180(x, k_0), -F_181(x, 1) + (k_0*F_181(x, k_0) - F_181(x, 1))/(k_0 - 1))
Eq(F_181(x, k_0), F_182(x, 1, k_0))
Eq(F_182(x, k_0, k_1), k_0*F_156(x, k_0, k_1))
Eq(F_183(x), F_152(x, 1))
Pack JSON:
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Specification JSON:
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"pos": [[1, 0], [3, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 1], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 1], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 1], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[3, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[3, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 2], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 2], [2, 2], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[2, 2]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25947/
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[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[183,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[14,x]
F[11,x] = -F[0,x]+F[12,x]
F[12,x] = 1/F[4,x]*F[13,x]
F[13,x] = F[2,x]
F[14,x] = F[15,x,1]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[4,x]
F[17,x,k[0]] = F[18,x,k[0]]+F[180,x,k[0]]
F[18,x,k[0]] = F[179,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[79,x,k[0]]
F[21,x,k[0]] = F[147,x,k[0]]+F[22,x,k[0]]
F[22,x,k[0]] = F[143,x,k[0]]+F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]+F[63,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[5,x]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]*F[79,x,k[0]]
F[21,x,k[0]] = F[27,x,k[0]]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,1,k[0]]
F[31,x,k[0],k[1]] = F[30,x,k[0],k[1]]*F[79,x,k[0]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[34,x,k[0],k[1]]*F[79,x,k[1]]
F[34,x,k[0],k[1]] = F[35,x,k[0],k[1],1]
F[35,x,k[0],k[1],k[2]] = (F[36,x,k[0],k[1],k[2]]*k[2]-F[36,x,k[0],k[1],1])/(-1+k[2])
F[36,x,k[0],k[1],k[2]] = F[37,x,k[0],k[1]*k[2]]+F[83,x,k[0],k[1],k[2]]
F[38,x,k[0],k[1]] = F[142,x,k[0],k[1]]+F[37,x,k[0],k[1]]
F[39,x,k[0],k[1]] = 1/(-1+k[1])*(F[38,x,k[0],k[1]]*k[1]-F[38,x,k[0],1])
F[40,x,k[0],k[1]] = F[39,x,k[0],k[1]]*F[4,x]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]
F[41,x,k[0],k[1]] = F[42,x,k[0],k[1]]
F[42,x,k[0],k[1]] = F[43,x,k[0],k[1]]*F[79,x,k[0]]
F[43,x,k[0],k[1]] = F[138,x,k[0],k[1]]+F[44,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[45,x,k[1],k[0]]
F[45,x,k[0],k[1]] = F[136,x,k[0],k[1]]+F[46,x,k[0]]
F[47,x,k[0]] = F[135,x,k[0]]+F[46,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[49,x,k[0]] = F[132,x,k[0]]+F[48,x,k[0]]
F[50,x,k[0]] = F[130,x,k[0]]+F[49,x,k[0]]
F[50,x,k[0]] = F[128,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[23,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,1,k[0]]
F[53,x,k[0],k[1]] = F[100,x,k[0],k[1]]+F[54,x,k[1]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[4,x]*F[56,x,k[0]]
F[57,x,k[0]] = F[56,x,k[0]]+F[92,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[59,x,k[0]] = F[58,x,k[0]]*F[79,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[61,x,k[0]] = F[4,x]*F[60,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[63,x,k[0]] = F[10,x]+F[62,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[88,x,k[0]]
F[65,x,k[0]] = F[64,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[66,x,k[0]]
F[66,x,k[0]] = F[21,x,k[0]]*F[4,x]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[4,x]*F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]*F[79,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0],1]
F[72,x,k[0],k[1]] = (F[73,x,k[0],k[1]]*k[1]-F[73,x,k[0],1])/(-1+k[1])
F[74,x,k[0],k[1]] = F[4,x]*F[73,x,k[0],k[1]]
F[74,x,k[0],k[1]] = F[75,x,k[0],k[1]]
F[75,x,k[0],k[1]] = F[76,x,k[0]*k[1]]+F[82,x,k[0],k[1]]
F[77,x,k[0]] = F[76,x,k[0]]+F[80,x,k[0]]
F[78,x,k[0]] = F[77,x,k[0]]*F[79,x,k[0]]
F[78,x,k[0]] = F[15,x,k[0]]
F[79,x,k[0]] = k[0]*x
F[80,x,k[0]] = F[81,x,1,k[0]]
F[81,x,k[0],k[1]] = -k[0]*(F[32,x,1,k[1]]-F[32,x,k[0],k[1]])/(-1+k[0])
F[82,x,k[0],k[1]] = F[83,x,1,k[0],k[1]]
F[83,x,k[0],k[1],k[2]] = -k[0]*(F[84,x,1,k[1],k[2]]-F[84,x,k[0],k[1],k[2]])/(-1+k[0])
F[84,x,k[0],k[1],k[2]] = F[85,x,k[0],k[1],k[1]*k[2]]
F[85,x,k[0],k[1],k[2]] = F[86,x,k[0],k[1],k[2]]
F[86,x,k[0],k[1],k[2]] = F[79,x,k[1]]*F[87,x,k[0],k[1],k[2]]
F[87,x,k[0],k[1],k[2]] = (F[36,x,k[0],k[1],1]*k[1]-F[36,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[4,x]*F[90,x,k[0]]
F[90,x,k[0]] = 1/(-1+k[0])*(F[91,x,k[0]]*k[0]-F[91,x,1])
F[91,x,k[0]] = F[75,x,1,k[0]]
F[93,x,k[0]] = F[92,x,k[0]]+F[98,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]
F[95,x,k[0]] = F[4,x]*F[94,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[97,x,k[0]] = F[4,x]*F[96,x,k[0]]
F[97,x,k[0]] = F[88,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[73,x,1,k[0]]
F[100,x,k[0],k[1]] = F[101,x,k[1],k[0]]
F[101,x,k[0],k[1]] = F[102,x,k[0],k[1]]*F[79,x,k[1]]
F[102,x,k[0],k[1]] = F[103,x,k[1],k[0]]
F[103,x,k[0],k[1]] = (F[104,x,k[0],1]*k[0]-F[104,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[104,x,k[0],k[1]] = F[105,x,1,k[0],k[1]]
F[105,x,k[0],k[1],k[2]] = F[106,x,k[0],k[1],k[1]*k[2]]
F[106,x,k[0],k[1],k[2]] = k[0]*F[107,x,k[2],k[2]]
F[107,x,k[0],k[1]] = F[108,x,k[1],k[0]]
F[108,x,k[0],k[1]] = F[109,x,k[0]]+F[113,x,k[0],k[1]]
F[109,x,k[0]] = F[110,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]*F[4,x]
F[111,x,k[0]] = F[112,x,k[0]]+F[27,x,k[0]]
F[112,x,k[0]] = F[96,x,k[0]]
F[113,x,k[0],k[1]] = F[114,x,k[0],1,k[1]]
F[114,x,k[0],k[1],k[2]] = (F[115,x,k[0],k[1],k[2]]*k[1]-F[115,x,k[0],1,k[2]])/(-1+k[1])
F[115,x,k[0],k[1],k[2]] = F[116,x,k[0],k[1],k[2]]
F[116,x,k[0],k[1],k[2]] = F[117,x,k[0],k[1],k[2]]*F[4,x]
F[117,x,k[0],k[1],k[2]] = F[118,x,k[0],k[2]]+F[126,x,k[0],k[1],k[2]]
F[119,x,k[0],k[1]] = F[118,x,k[0],k[1]]+F[123,x,k[0],k[1]]
F[120,x,k[0],k[1]] = F[119,x,k[0],k[1]]+F[56,x,k[0]]
F[120,x,k[0],k[1]] = F[121,x,k[1],k[0]]
F[122,x,k[0],k[1]] = F[121,x,k[0],k[1]]*F[4,x]
F[122,x,k[0],k[1]] = F[53,x,k[0],k[1]]
F[123,x,k[0],k[1]] = -k[1]*(F[124,x,k[0],1]-F[124,x,k[0],k[1]])/(-1+k[1])
F[124,x,k[0],k[1]] = F[125,x,k[1],k[0]]
F[125,x,k[0],k[1]] = F[85,x,1,k[0],k[1]]
F[126,x,k[0],k[1],k[2]] = -k[2]*(F[127,x,k[0],k[1],1]-F[127,x,k[0],k[1],k[2]])/(-1+k[2])
F[127,x,k[0],k[1],k[2]] = F[85,x,k[1],k[2],k[0]]
F[128,x,k[0]] = F[129,x,k[0]]
F[129,x,k[0]] = F[4,x]*F[94,x,k[0]]
F[130,x,k[0]] = F[131,x,1,k[0]]
F[131,x,k[0],k[1]] = (F[53,x,k[0],k[1]]*k[0]-F[53,x,1,k[1]])/(-1+k[0])
F[132,x,k[0]] = F[133,x,1,k[0]]
F[133,x,k[0],k[1]] = (F[134,x,k[0],k[1]]*k[0]-F[134,x,1,k[1]])/(-1+k[0])
F[134,x,k[0],k[1]] = F[125,x,k[0],k[1]]+F[64,x,k[1]]
F[135,x,k[0]] = F[24,x,k[0]]
F[136,x,k[0],k[1]] = F[137,x,k[0],k[1],1]
F[137,x,k[0],k[1],k[2]] = (F[127,x,k[0],k[1],k[2]]-F[127,x,k[0],k[1],1])/(-1+k[2])
F[138,x,k[0],k[1]] = F[139,x,k[0],1,k[1]]
F[139,x,k[0],k[1],k[2]] = (F[140,x,k[0],k[1],k[2]]-F[140,x,k[0],1,k[2]])/(-1+k[1])
F[140,x,k[0],k[1],k[2]] = k[0]*F[141,x,k[0],k[1],k[2]]
F[141,x,k[0],k[1],k[2]] = F[115,x,k[2],k[0],k[1]]
F[142,x,k[0],k[1]] = -k[0]*(F[41,x,1,k[1]]-F[41,x,k[0],k[1]])/(-1+k[0])
F[69,x,k[0]] = F[143,x,k[0]]+F[144,x,k[0]]
F[144,x,k[0]] = F[145,x,1,k[0]]
F[145,x,k[0],k[1]] = -k[1]*(F[146,x,1,k[1]]-F[146,x,k[0]/k[1],k[1]])/(-k[1]+k[0])
F[146,x,k[0],k[1]] = F[100,x,k[0]*k[1],k[1]]
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[4,x]
F[150,x,k[0]] = F[149,x,k[0]]*F[79,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = -k[0]*(F[152,x,1]-F[152,x,k[0]])/(-1+k[0])
F[152,x,k[0]] = F[153,x,k[0]]+F[62,x,k[0]]
F[154,x,k[0],k[1]] = F[153,x,k[1]]+F[175,x,k[0],k[1]]
F[155,x,k[0],k[1]] = F[154,x,k[0],k[1]]*F[4,x]
F[155,x,k[0],k[1]] = F[156,x,k[0],k[1]]
F[156,x,k[0],k[1]] = F[157,x,k[1]]+F[173,x,k[0],k[1]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[79,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]+F[172,x,k[0]]
F[161,x,k[0]] = F[160,x,k[0]]+F[171,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]*F[4,x]
F[163,x,k[0]] = F[164,x,k[0]]+F[27,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[168,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]
F[166,x,k[0]] = F[167,x,k[0]]*F[4,x]
F[167,x,k[0]] = 1/(-1+k[0])*(F[163,x,k[0]]*k[0]-F[163,x,1])
F[168,x,k[0]] = F[169,x,k[0]]
F[169,x,k[0]] = F[170,x,1,k[0]]
F[170,x,k[0],k[1]] = -k[0]*(F[125,x,1,k[1]]-F[125,x,k[0],k[1]])/(-1+k[0])
F[171,x,k[0]] = F[100,x,1,k[0]]
F[172,x,k[0]] = F[146,x,1,k[0]]
F[173,x,k[0],k[1]] = F[174,x,k[0],k[1]]
F[174,x,k[0],k[1]] = F[175,x,k[0],k[1]]*F[4,x]
F[175,x,k[0],k[1]] = -k[1]*(F[176,x,k[0],1]-F[176,x,k[0],k[1]])/(-1+k[1])
F[176,x,k[0],k[1]] = F[177,x,k[0],k[1]]
F[177,x,k[0],k[1]] = F[178,x,k[0],k[1]]*F[79,x,k[1]]
F[178,x,k[0],k[1]] = F[36,x,k[0],k[1],1]
F[179,x,k[0]] = F[175,x,1,k[0]]
F[180,x,k[0]] = -k[0]*(F[181,x,1]-F[181,x,k[0]])/(-1+k[0])
F[181,x,k[0]] = F[182,x,1,k[0]]
F[182,x,k[0],k[1]] = k[0]*F[156,x,k[0],k[1]]
F[183,x] = F[152,x,1]
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_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{183}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{2}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{15}\! \left(x , y_{0}\right) = F_{16}\! \left(x , y_{0}\right)
F_{16}\! \left(x , y_{0}\right) = F_{17}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{17}\! \left(x , y_{0}\right) = F_{18}\! \left(x , y_{0}\right)+F_{180}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{179}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)
F_{22}\! \left(x , y_{0}\right) = F_{143}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}\right)
F_{24}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right)+F_{5}\! \left(x \right)
F_{25}\! \left(x , y_{0}\right) = F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{30}\! \left(x , 1, y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{30}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{0}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{32}\! \left(x , y_{0}, y_{1}\right)
F_{32}\! \left(x , y_{0}, y_{1}\right) = F_{33}\! \left(x , y_{0}, y_{1}\right)
F_{33}\! \left(x , y_{0}, y_{1}\right) = F_{34}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{1}\right)
F_{34}\! \left(x , y_{0}, y_{1}\right) = F_{35}\! \left(x , y_{0}, y_{1}, 1\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{36}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{37}\! \left(x , y_{0}, y_{1} y_{2}\right)+F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{38}\! \left(x , y_{0}, y_{1}\right) = F_{142}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{38}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{38}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{39}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{43}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{138}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{45}\! \left(x , y_{1}, y_{0}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{136}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{135}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{132}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{130}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{128}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right)+F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{53}\! \left(x , 1, y_{0}\right)
F_{53}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{54}\! \left(x , y_{1}\right)
F_{54}\! \left(x , y_{0}\right) = F_{55}\! \left(x , y_{0}\right)
F_{55}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{56}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{56}\! \left(x , y_{0}\right)+F_{92}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{58}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{59}\! \left(x , y_{0}\right) = F_{60}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{60}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{62}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right)+F_{62}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{64}\! \left(x , y_{0}\right)+F_{88}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{64}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{21}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{67}\! \left(x , y_{0}\right) = F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{69}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{71}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{71}\! \left(x , y_{0}\right) = F_{72}\! \left(x , y_{0}, 1\right)
F_{72}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{73}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{73}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{4}\! \left(x \right) F_{73}\! \left(x , y_{0}, y_{1}\right)
F_{74}\! \left(x , y_{0}, y_{1}\right) = F_{75}\! \left(x , y_{0}, y_{1}\right)
F_{75}\! \left(x , y_{0}, y_{1}\right) = F_{76}\! \left(x , y_{0} y_{1}\right)+F_{82}\! \left(x , y_{0}, y_{1}\right)
F_{77}\! \left(x , y_{0}\right) = F_{76}\! \left(x , y_{0}\right)+F_{80}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{77}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{15}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = y_{0} x
F_{80}\! \left(x , y_{0}\right) = F_{81}\! \left(x , 1, y_{0}\right)
F_{81}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{32}\! \left(x , 1, y_{1}\right)-F_{32}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{82}\! \left(x , y_{0}, y_{1}\right) = F_{83}\! \left(x , 1, y_{0}, y_{1}\right)
F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{0} \left(F_{84}\! \left(x , 1, y_{1}, y_{2}\right)-F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{0}}
F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{85}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{85}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{86}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{86}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{79}\! \left(x , y_{1}\right) F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{36}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-y_{2} F_{36}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{88}\! \left(x , y_{0}\right) = F_{89}\! \left(x , y_{0}\right)
F_{89}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{90}\! \left(x , y_{0}\right)
F_{90}\! \left(x , y_{0}\right) = -\frac{-F_{91}\! \left(x , y_{0}\right) y_{0}+F_{91}\! \left(x , 1\right)}{-1+y_{0}}
F_{91}\! \left(x , y_{0}\right) = F_{75}\! \left(x , 1, y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{92}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{94}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{94}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{96}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{96}\! \left(x , y_{0}\right)
F_{97}\! \left(x , y_{0}\right) = F_{88}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{73}\! \left(x , 1, y_{0}\right)
F_{100}\! \left(x , y_{0}, y_{1}\right) = F_{101}\! \left(x , y_{1}, y_{0}\right)
F_{101}\! \left(x , y_{0}, y_{1}\right) = F_{102}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{1}\right)
F_{102}\! \left(x , y_{0}, y_{1}\right) = F_{103}\! \left(x , y_{1}, y_{0}\right)
F_{103}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{104}\! \left(x , y_{0}, 1\right) y_{0}-F_{104}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{104}\! \left(x , y_{0}, y_{1}\right) = F_{105}\! \left(x , 1, y_{0}, y_{1}\right)
F_{105}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{106}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{106}\! \left(x , y_{0}, y_{1}, y_{2}\right) = y_{0} F_{107}\! \left(x , y_{2}, y_{2}\right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(x , y_{1}, y_{0}\right)
F_{108}\! \left(x , y_{0}, y_{1}\right) = F_{109}\! \left(x , y_{0}\right)+F_{113}\! \left(x , y_{0}, y_{1}\right)
F_{109}\! \left(x , y_{0}\right) = F_{110}\! \left(x , y_{0}\right)
F_{110}\! \left(x , y_{0}\right) = F_{111}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{111}\! \left(x , y_{0}\right) = F_{112}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{112}\! \left(x , y_{0}\right) = F_{96}\! \left(x , y_{0}\right)
F_{113}\! \left(x , y_{0}, y_{1}\right) = F_{114}\! \left(x , y_{0}, 1, y_{1}\right)
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{115}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{117}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{4}\! \left(x \right)
F_{117}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{118}\! \left(x , y_{0}, y_{2}\right)+F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{119}\! \left(x , y_{0}, y_{1}\right) = F_{118}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{119}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}\right)
F_{120}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{1}, y_{0}\right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = F_{121}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{122}\! \left(x , y_{0}, y_{1}\right) = F_{53}\! \left(x , y_{0}, y_{1}\right)
F_{123}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{124}\! \left(x , y_{0}, 1\right)-F_{124}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{124}\! \left(x , y_{0}, y_{1}\right) = F_{125}\! \left(x , y_{1}, y_{0}\right)
F_{125}\! \left(x , y_{0}, y_{1}\right) = F_{85}\! \left(x , 1, y_{0}, y_{1}\right)
F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{y_{2} \left(F_{127}\! \left(x , y_{0}, y_{1}, 1\right)-F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right)\right)}{-1+y_{2}}
F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{85}\! \left(x , y_{1}, y_{2}, y_{0}\right)
F_{128}\! \left(x , y_{0}\right) = F_{129}\! \left(x , y_{0}\right)
F_{129}\! \left(x , y_{0}\right) = F_{4}\! \left(x \right) F_{94}\! \left(x , y_{0}\right)
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , 1, y_{0}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{53}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{53}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{132}\! \left(x , y_{0}\right) = F_{133}\! \left(x , 1, y_{0}\right)
F_{133}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{134}\! \left(x , y_{0}, y_{1}\right)+F_{134}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{134}\! \left(x , y_{0}, y_{1}\right) = F_{125}\! \left(x , y_{0}, y_{1}\right)+F_{64}\! \left(x , y_{1}\right)
F_{135}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)
F_{136}\! \left(x , y_{0}, y_{1}\right) = F_{137}\! \left(x , y_{0}, y_{1}, 1\right)
F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{127}\! \left(x , y_{0}, y_{1}, 1\right)-F_{127}\! \left(x , y_{0}, y_{1}, y_{2}\right)}{-1+y_{2}}
F_{138}\! \left(x , y_{0}, y_{1}\right) = F_{139}\! \left(x , y_{0}, 1, y_{1}\right)
F_{139}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{140}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}
F_{140}\! \left(x , y_{0}, y_{1}, y_{2}\right) = y_{0} F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{141}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{115}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{142}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{41}\! \left(x , 1, y_{1}\right)-F_{41}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{69}\! \left(x , y_{0}\right) = F_{143}\! \left(x , y_{0}\right)+F_{144}\! \left(x , y_{0}\right)
F_{144}\! \left(x , y_{0}\right) = F_{145}\! \left(x , 1, y_{0}\right)
F_{145}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{146}\! \left(x , 1, y_{1}\right)-F_{146}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}
F_{146}\! \left(x , y_{0}, y_{1}\right) = F_{100}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{147}\! \left(x , y_{0}\right) = F_{148}\! \left(x , y_{0}\right)
F_{148}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{150}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{150}\! \left(x , y_{0}\right) = F_{151}\! \left(x , y_{0}\right)
F_{151}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{152}\! \left(x , 1\right)-F_{152}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{152}\! \left(x , y_{0}\right) = F_{153}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)
F_{154}\! \left(x , y_{0}, y_{1}\right) = F_{153}\! \left(x , y_{1}\right)+F_{175}\! \left(x , y_{0}, y_{1}\right)
F_{155}\! \left(x , y_{0}, y_{1}\right) = F_{154}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{155}\! \left(x , y_{0}, y_{1}\right) = F_{156}\! \left(x , y_{0}, y_{1}\right)
F_{156}\! \left(x , y_{0}, y_{1}\right) = F_{157}\! \left(x , y_{1}\right)+F_{173}\! \left(x , y_{0}, y_{1}\right)
F_{157}\! \left(x , y_{0}\right) = F_{158}\! \left(x , y_{0}\right)
F_{158}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)
F_{159}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right)+F_{172}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}\right) = F_{160}\! \left(x , y_{0}\right)+F_{171}\! \left(x , y_{0}\right)
F_{161}\! \left(x , y_{0}\right) = F_{162}\! \left(x , y_{0}\right)
F_{162}\! \left(x , y_{0}\right) = F_{163}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{163}\! \left(x , y_{0}\right) = F_{164}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)
F_{164}\! \left(x , y_{0}\right) = F_{165}\! \left(x , y_{0}\right)+F_{168}\! \left(x , y_{0}\right)
F_{165}\! \left(x , y_{0}\right) = F_{166}\! \left(x , y_{0}\right)
F_{166}\! \left(x , y_{0}\right) = F_{167}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)
F_{167}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{163}\! \left(x , y_{0}\right)+F_{163}\! \left(x , 1\right)}{-1+y_{0}}
F_{168}\! \left(x , y_{0}\right) = F_{169}\! \left(x , y_{0}\right)
F_{169}\! \left(x , y_{0}\right) = F_{170}\! \left(x , 1, y_{0}\right)
F_{170}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{0} \left(F_{125}\! \left(x , 1, y_{1}\right)-F_{125}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}
F_{171}\! \left(x , y_{0}\right) = F_{100}\! \left(x , 1, y_{0}\right)
F_{172}\! \left(x , y_{0}\right) = F_{146}\! \left(x , 1, y_{0}\right)
F_{173}\! \left(x , y_{0}, y_{1}\right) = F_{174}\! \left(x , y_{0}, y_{1}\right)
F_{174}\! \left(x , y_{0}, y_{1}\right) = F_{175}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)
F_{175}\! \left(x , y_{0}, y_{1}\right) = -\frac{y_{1} \left(F_{176}\! \left(x , y_{0}, 1\right)-F_{176}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{1}}
F_{176}\! \left(x , y_{0}, y_{1}\right) = F_{177}\! \left(x , y_{0}, y_{1}\right)
F_{177}\! \left(x , y_{0}, y_{1}\right) = F_{178}\! \left(x , y_{0}, y_{1}\right) F_{79}\! \left(x , y_{1}\right)
F_{178}\! \left(x , y_{0}, y_{1}\right) = F_{36}\! \left(x , y_{0}, y_{1}, 1\right)
F_{179}\! \left(x , y_{0}\right) = F_{175}\! \left(x , 1, y_{0}\right)
F_{180}\! \left(x , y_{0}\right) = -\frac{y_{0} \left(F_{181}\! \left(x , 1\right)-F_{181}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}
F_{181}\! \left(x , y_{0}\right) = F_{182}\! \left(x , 1, y_{0}\right)
F_{182}\! \left(x , y_{0}, y_{1}\right) = y_{0} F_{156}\! \left(x , y_{0}, y_{1}\right)
F_{183}\! \left(x \right) = F_{152}\! \left(x , 1\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_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_183(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_14(x))
Eq(F_11(x), -F_0(x) + F_12(x))
Eq(F_12(x), F_13(x)/F_4(x))
Eq(F_13(x), F_2(x))
Eq(F_14(x), F_15(x, 1))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_4(x))
Eq(F_17(x, k_0), F_18(x, k_0) + F_180(x, k_0))
Eq(F_18(x, k_0), F_179(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_79(x, k_0))
Eq(F_21(x, k_0), F_147(x, k_0) + F_22(x, k_0))
Eq(F_22(x, k_0), F_143(x, k_0) + F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0) + F_63(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_5(x))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0)*F_79(x, k_0))
Eq(F_21(x, k_0), F_27(x, k_0) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, 1, k_0))
Eq(F_31(x, k_0, k_1), F_30(x, k_0, k_1)*F_79(x, k_0))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_34(x, k_0, k_1)*F_79(x, k_1))
Eq(F_34(x, k_0, k_1), F_35(x, k_0, k_1, 1))
Eq(F_35(x, k_0, k_1, k_2), (-k_2*F_36(x, k_0, k_1, k_2) + F_36(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_36(x, k_0, k_1, k_2), F_37(x, k_0, k_1*k_2) + F_83(x, k_0, k_1, k_2))
Eq(F_38(x, k_0, k_1), F_142(x, k_0, k_1) + F_37(x, k_0, k_1))
Eq(F_39(x, k_0, k_1), (k_1*F_38(x, k_0, k_1) - F_38(x, k_0, 1))/(k_1 - 1))
Eq(F_40(x, k_0, k_1), F_39(x, k_0, k_1)*F_4(x))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1))
Eq(F_41(x, k_0, k_1), F_42(x, k_0, k_1))
Eq(F_42(x, k_0, k_1), F_43(x, k_0, k_1)*F_79(x, k_0))
Eq(F_43(x, k_0, k_1), F_138(x, k_0, k_1) + F_44(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_45(x, k_1, k_0))
Eq(F_45(x, k_0, k_1), F_136(x, k_0, k_1) + F_46(x, k_0))
Eq(F_47(x, k_0), F_135(x, k_0) + F_46(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_49(x, k_0), F_132(x, k_0) + F_48(x, k_0))
Eq(F_50(x, k_0), F_130(x, k_0) + F_49(x, k_0))
Eq(F_50(x, k_0), F_128(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_23(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, 1, k_0))
Eq(F_53(x, k_0, k_1), F_100(x, k_0, k_1) + F_54(x, k_1))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_4(x)*F_56(x, k_0))
Eq(F_57(x, k_0), F_56(x, k_0) + F_92(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_59(x, k_0), F_58(x, k_0)*F_79(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_61(x, k_0), F_4(x)*F_60(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_63(x, k_0), F_10(x) + F_62(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_88(x, k_0))
Eq(F_65(x, k_0), F_64(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_66(x, k_0))
Eq(F_66(x, k_0), F_21(x, k_0)*F_4(x))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_4(x)*F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0)*F_79(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0, 1))
Eq(F_72(x, k_0, k_1), (-k_1*F_73(x, k_0, k_1) + F_73(x, k_0, 1))/(1 - k_1))
Eq(F_74(x, k_0, k_1), F_4(x)*F_73(x, k_0, k_1))
Eq(F_74(x, k_0, k_1), F_75(x, k_0, k_1))
Eq(F_75(x, k_0, k_1), F_76(x, k_0*k_1) + F_82(x, k_0, k_1))
Eq(F_77(x, k_0), F_76(x, k_0) + F_80(x, k_0))
Eq(F_78(x, k_0), F_77(x, k_0)*F_79(x, k_0))
Eq(F_78(x, k_0), F_15(x, k_0))
Eq(F_79(x, k_0), k_0*x)
Eq(F_80(x, k_0), F_81(x, 1, k_0))
Eq(F_81(x, k_0, k_1), -F_32(x, 1, k_1) + (-k_0*F_32(x, k_0, k_1) + F_32(x, 1, k_1))/(1 - k_0))
Eq(F_82(x, k_0, k_1), F_83(x, 1, k_0, k_1))
Eq(F_83(x, k_0, k_1, k_2), -F_84(x, 1, k_1, k_2) + (-k_0*F_84(x, k_0, k_1, k_2) + F_84(x, 1, k_1, k_2))/(1 - k_0))
Eq(F_84(x, k_0, k_1, k_2), F_85(x, k_0, k_1, k_1*k_2))
Eq(F_85(x, k_0, k_1, k_2), F_86(x, k_0, k_1, k_2))
Eq(F_86(x, k_0, k_1, k_2), F_79(x, k_1)*F_87(x, k_0, k_1, k_2))
Eq(F_87(x, k_0, k_1, k_2), (-k_1*F_36(x, k_0, k_1, 1) + k_2*F_36(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_4(x)*F_90(x, k_0))
Eq(F_90(x, k_0), (k_0*F_91(x, k_0) - F_91(x, 1))/(k_0 - 1))
Eq(F_91(x, k_0), F_75(x, 1, k_0))
Eq(F_93(x, k_0), F_92(x, k_0) + F_98(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0))
Eq(F_95(x, k_0), F_4(x)*F_94(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_97(x, k_0), F_4(x)*F_96(x, k_0))
Eq(F_97(x, k_0), F_88(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_73(x, 1, k_0))
Eq(F_100(x, k_0, k_1), F_101(x, k_1, k_0))
Eq(F_101(x, k_0, k_1), F_102(x, k_0, k_1)*F_79(x, k_1))
Eq(F_102(x, k_0, k_1), F_103(x, k_1, k_0))
Eq(F_103(x, k_0, k_1), (-k_0*F_104(x, k_0, 1) + k_1*F_104(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_104(x, k_0, k_1), F_105(x, 1, k_0, k_1))
Eq(F_105(x, k_0, k_1, k_2), F_106(x, k_0, k_1, k_1*k_2))
Eq(F_106(x, k_0, k_1, k_2), k_0*F_107(x, k_2, k_2))
Eq(F_107(x, k_0, k_1), F_108(x, k_1, k_0))
Eq(F_108(x, k_0, k_1), F_109(x, k_0) + F_113(x, k_0, k_1))
Eq(F_109(x, k_0), F_110(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0)*F_4(x))
Eq(F_111(x, k_0), F_112(x, k_0) + F_27(x, k_0))
Eq(F_112(x, k_0), F_96(x, k_0))
Eq(F_113(x, k_0, k_1), F_114(x, k_0, 1, k_1))
Eq(F_114(x, k_0, k_1, k_2), (-k_1*F_115(x, k_0, k_1, k_2) + F_115(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_115(x, k_0, k_1, k_2), F_116(x, k_0, k_1, k_2))
Eq(F_116(x, k_0, k_1, k_2), F_117(x, k_0, k_1, k_2)*F_4(x))
Eq(F_117(x, k_0, k_1, k_2), F_118(x, k_0, k_2) + F_126(x, k_0, k_1, k_2))
Eq(F_119(x, k_0, k_1), F_118(x, k_0, k_1) + F_123(x, k_0, k_1))
Eq(F_120(x, k_0, k_1), F_119(x, k_0, k_1) + F_56(x, k_0))
Eq(F_120(x, k_0, k_1), F_121(x, k_1, k_0))
Eq(F_122(x, k_0, k_1), F_121(x, k_0, k_1)*F_4(x))
Eq(F_122(x, k_0, k_1), F_53(x, k_0, k_1))
Eq(F_123(x, k_0, k_1), -F_124(x, k_0, 1) + (k_1*F_124(x, k_0, k_1) - F_124(x, k_0, 1))/(k_1 - 1))
Eq(F_124(x, k_0, k_1), F_125(x, k_1, k_0))
Eq(F_125(x, k_0, k_1), F_85(x, 1, k_0, k_1))
Eq(F_126(x, k_0, k_1, k_2), -F_127(x, k_0, k_1, 1) + (k_2*F_127(x, k_0, k_1, k_2) - F_127(x, k_0, k_1, 1))/(k_2 - 1))
Eq(F_127(x, k_0, k_1, k_2), F_85(x, k_1, k_2, k_0))
Eq(F_128(x, k_0), F_129(x, k_0))
Eq(F_129(x, k_0), F_4(x)*F_94(x, k_0))
Eq(F_130(x, k_0), F_131(x, 1, k_0))
Eq(F_131(x, k_0, k_1), (-k_0*F_53(x, k_0, k_1) + F_53(x, 1, k_1))/(1 - k_0))
Eq(F_132(x, k_0), F_133(x, 1, k_0))
Eq(F_133(x, k_0, k_1), (-k_0*F_134(x, k_0, k_1) + F_134(x, 1, k_1))/(1 - k_0))
Eq(F_134(x, k_0, k_1), F_125(x, k_0, k_1) + F_64(x, k_1))
Eq(F_135(x, k_0), F_24(x, k_0))
Eq(F_136(x, k_0, k_1), F_137(x, k_0, k_1, 1))
Eq(F_137(x, k_0, k_1, k_2), -F_127(x, k_0, k_1, k_2) + (-k_2*F_127(x, k_0, k_1, k_2) + F_127(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_138(x, k_0, k_1), F_139(x, k_0, 1, k_1))
Eq(F_139(x, k_0, k_1, k_2), -F_140(x, k_0, k_1, k_2) + (-k_1*F_140(x, k_0, k_1, k_2) + F_140(x, k_0, 1, k_2))/(1 - k_1))
Eq(F_140(x, k_0, k_1, k_2), k_0*F_141(x, k_0, k_1, k_2))
Eq(F_141(x, k_0, k_1, k_2), F_115(x, k_2, k_0, k_1))
Eq(F_142(x, k_0, k_1), -F_41(x, 1, k_1) + (-k_0*F_41(x, k_0, k_1) + F_41(x, 1, k_1))/(1 - k_0))
Eq(F_69(x, k_0), F_143(x, k_0) + F_144(x, k_0))
Eq(F_144(x, k_0), F_145(x, 1, k_0))
Eq(F_145(x, k_0, k_1), -F_146(x, k_0/k_1, k_1) + (-k_0*F_146(x, k_0/k_1, k_1) + k_1*F_146(x, 1, k_1))/(-k_0 + k_1))
Eq(F_146(x, k_0, k_1), F_100(x, k_0*k_1, k_1))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_4(x))
Eq(F_150(x, k_0), F_149(x, k_0)*F_79(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), -F_152(x, 1) + (k_0*F_152(x, k_0) - F_152(x, 1))/(k_0 - 1))
Eq(F_152(x, k_0), F_153(x, k_0) + F_62(x, k_0))
Eq(F_154(x, k_0, k_1), F_153(x, k_1) + F_175(x, k_0, k_1))
Eq(F_155(x, k_0, k_1), F_154(x, k_0, k_1)*F_4(x))
Eq(F_155(x, k_0, k_1), F_156(x, k_0, k_1))
Eq(F_156(x, k_0, k_1), F_157(x, k_1) + F_173(x, k_0, k_1))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_79(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0) + F_172(x, k_0))
Eq(F_161(x, k_0), F_160(x, k_0) + F_171(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0)*F_4(x))
Eq(F_163(x, k_0), F_164(x, k_0) + F_27(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_168(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0))
Eq(F_166(x, k_0), F_167(x, k_0)*F_4(x))
Eq(F_167(x, k_0), (k_0*F_163(x, k_0) - F_163(x, 1))/(k_0 - 1))
Eq(F_168(x, k_0), F_169(x, k_0))
Eq(F_169(x, k_0), F_170(x, 1, k_0))
Eq(F_170(x, k_0, k_1), -F_125(x, 1, k_1) + (-k_0*F_125(x, k_0, k_1) + F_125(x, 1, k_1))/(1 - k_0))
Eq(F_171(x, k_0), F_100(x, 1, k_0))
Eq(F_172(x, k_0), F_146(x, 1, k_0))
Eq(F_173(x, k_0, k_1), F_174(x, k_0, k_1))
Eq(F_174(x, k_0, k_1), F_175(x, k_0, k_1)*F_4(x))
Eq(F_175(x, k_0, k_1), -F_176(x, k_0, 1) + (k_1*F_176(x, k_0, k_1) - F_176(x, k_0, 1))/(k_1 - 1))
Eq(F_176(x, k_0, k_1), F_177(x, k_0, k_1))
Eq(F_177(x, k_0, k_1), F_178(x, k_0, k_1)*F_79(x, k_1))
Eq(F_178(x, k_0, k_1), F_36(x, k_0, k_1, 1))
Eq(F_179(x, k_0), F_175(x, 1, k_0))
Eq(F_180(x, k_0), -F_181(x, 1) + (k_0*F_181(x, k_0) - F_181(x, 1))/(k_0 - 1))
Eq(F_181(x, k_0), F_182(x, 1, k_0))
Eq(F_182(x, k_0, k_1), k_0*F_156(x, k_0, k_1))
Eq(F_183(x), F_152(x, 1))
Pack JSON:
{"name": "point_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, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2]], "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}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2]]}], "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, 1, 3, 4, 2], "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": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 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], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 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], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], 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