01243_01342_02143_02341_03142_03241_12340_13240
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3040, 16933, 97295, 572976, 3441666, 21009275, 129977901, 813245131, 5137337689, 32721463808, 209906542720, 1354945397044, 8794067685648, 57352470832517, 375641241706441, 2469745286680947, 16293562950272407, 107824036034083509, 715518462297203579, 4760124590000189530, 31740101880231545492, 212081554241088003663, 1419790228767502419045, 9521446634550338947952, 63955425665270254998940, 430221651888297286112177, 2897996822005629943384489, 19545627406744800710644727, 131979667707747458581954481, 892141220599339049101291089, 6036652508843127393325874399, 40885053930497938419314826107, 277147711122117192286579108185, 1880231025173489157714314250426, 12765602872575817806903976666596, 86732236998927859891337301278622, 589670617972667072880819787933984, 4011532492036610825165596861483802, 27306534185974705189926670873778516, 185978657647258266717680371162641883, 1267318734550869301003742514187478273, 8640160680497937166540342087952407991, 58933053537306685700482615483668559403, 402148111990198413630811492776186995552, 2745318140117245453879144527487744496208, 18748614984725999339650774186690905725295, 128087436886684493466049954137862313381509, 875379327440114282709938854164813744965611, 5984537213981382922451342313695722076497863, 40926257366234724309747137029386337076729001, 279965020583995576790636849816639722933882957, 1915708127709688936490804054578748549173189916, 13112112956498471578234495440171818485154390470, 89769355828533144672030733654410134066656574458, 614738313383056636892628039609427837093664595404, 4210698797696061528341317861729983744476090010689, 28847957280112569693180215816272334322187702135445, 197682624195746289774990222548235160712400543371146, 1354909450406380985254459371381946244586241749906530, 9288304153466361396588788339633393823359745783056600, 63685890647207127054767941408211354074281355384886656, 436744187552370830952494085758735806429254575361511589, 2995606804490533168024419600665032975360364797155117183, 20550059767662402931081170804163199407440984368947820625, 140996711486262449344416651256333373646525277299902523355, 967541619613552416685755999646078296923336726209849953312, 6640372117787400398702492907376419520280304399834754650084, 45580041763532367199112119828479244585537184067310901054810, 312906179232543740328070815357223504862774389035131605236586, 2148366547555846426061497331749065945085487270306386030802295, 14752147960249304906252984450855960238959881869530055479965287, 101310089200639245574191874152392667922364115433260184588085804, 695822904145317119933925212387409017256145553429987605042902374, 4779598833712238119842036346436457677802988342209762193339414170, 32834400109722978897271078574050432465687311160875455461170140084, 225584851657906912246246184277404739638337267015784041893986468184, 1550002363503603661389349516044558442573409089113617192806438724022, 10651108723095954208611278436104355765445701203345811785928564645970, 73197428690314741739771663382727275998972900248014812647586921743170, 503076429503373453622822293181430323554393301030992363610541344664723, 3457863956615854967214308401430773825141718848101308796547904026333901, 23769296860952999228721304586551640674800748087103377283177632384187953, 163402250506706845519078870989645746339168251769621253624947681941405313, 1123393279697304814041394086637674581290748142000508453648603772262880779, 7723898732362318787111448116811021248147089483061955833703337752242021413, 53109376615874448842022364958030524136734211649007798514871380230253689112, 365203294669655949777668870353495876127194762596841112877399491467719345598, 2511458644442718047602084615949471194962077119504428655159131923009659382715, 17272066003748977733511514219131133968838531140976772698588279974312436875307, 118792371362982601864292690606637110953932088449273733785050334353857060938386, 817067524199040835316923255393053482196151384726996123181358519201841217062844, 5620198372771477448728729264571779302887769185748539683269088379796430835748376, 38660622071254724694481487686566304081319464696747141021364283345538413343549898, 265955366701746242904517565767275828328469477816848189688704128148178001327946699
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25023/
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[10,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[71,x]
F[5,x] = F[10,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[48,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[10,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] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[24,x,k[0]]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[40,x,k[0]]+F[42,x,k[0],k[1]]+F[46,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[10,x]*F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[17,x,1,k[0],k[1]]
F[17,x,k[0],k[1],k[2]] = F[1,x]+F[18,x,k[0],k[1],k[2]]+F[20,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1]]+F[38,x,k[0],k[1],k[2]]+F[44,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[10,x]*F[19,x,k[0],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[17,x,k[0],k[1],k[2]]*k[0]-F[17,x,1,k[1],k[2]])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]*F[24,x,k[0]]
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0],k[1]] = F[24,x,k[1]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (-F[27,x,1,k[1]]*k[1]+F[27,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[27,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[40,x,k[0]]+F[42,x,k[0],k[1]]+F[43,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[10,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[31,x,1,k[0],k[1]]
F[31,x,k[0],k[1],k[2]] = F[1,x]+F[25,x,k[0],k[1]]+F[32,x,k[0],k[1],k[2]]+F[34,x,k[0],k[1],k[2]]+F[38,x,k[0],k[1],k[2]]+F[39,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[10,x]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[31,x,k[0],k[1],k[2]]*k[0]-F[31,x,1,k[1],k[2]])
F[34,x,k[0],k[1],k[2]] = F[24,x,k[0]]*F[35,x,k[0],k[1],k[2]]
F[35,x,k[0],k[1],k[2]] = (F[36,x,k[0],k[1]]*k[1]-F[36,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[36,x,k[0],k[1]] = (F[37,x,k[0],1]*k[0]-F[37,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[37,x,k[0],k[1]] = F[28,x,k[0],k[0]*k[1]]
F[38,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[31,x,k[0],k[1],k[2]]
F[39,x,k[0],k[1],k[2]] = F[10,x]*F[31,x,k[0],k[1],k[2]]
F[40,x,k[0]] = F[24,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[27,x,1,k[0]]
F[42,x,k[0],k[1]] = F[24,x,k[1]]*F[28,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[10,x]*F[28,x,k[0],k[1]]
F[44,x,k[0],k[1],k[2]] = F[10,x]*F[45,x,k[0],k[1],k[2]]
F[45,x,k[0],k[1],k[2]] = (F[31,x,k[0],k[1],k[2]]*k[2]-F[31,x,k[0],k[1],1])/(-1+k[2])
F[46,x,k[0],k[1]] = F[10,x]*F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[48,x,k[0]] = F[10,x]*F[49,x,k[0]]
F[49,x,k[0]] = (F[50,x,k[0]]*k[0]-F[50,x,1])/(-1+k[0])
F[50,x,k[0]] = F[1,x]+F[40,x,k[0]]+F[51,x,k[0]]+F[69,x,k[0]]
F[51,x,k[0]] = F[10,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]+F[62,x,k[0]]+F[65,x,k[0]]+F[67,x,k[0]]
F[53,x,k[0]] = F[10,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,1,k[0]]
F[55,x,k[0],k[1]] = 1/(-1+k[0])*(F[56,x,k[0],k[1]]*k[0]-F[56,x,1,k[1]])
F[56,x,k[0],k[1]] = F[1,x]+F[25,x,k[0],k[1]]+F[57,x,k[0],k[1]]+F[59,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[10,x]*F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = 1/(-1+k[0])*(F[56,x,k[0],k[1]]*k[0]-F[56,x,1,k[1]])
F[59,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[24,x,k[0]]
F[60,x,k[0],k[1]] = F[10,x]*F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[31,x,k[0],k[1],1]
F[62,x,k[0]] = F[10,x]*F[63,x,k[0]]
F[63,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[64,x,k[0]] = F[14,x,1,k[0]]
F[65,x,k[0]] = F[24,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[26,x,1,k[0]]
F[67,x,k[0]] = F[10,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[30,x,k[0],1]
F[69,x,k[0]] = F[70,x,k[0],1]
F[70,x,k[0],k[1]] = F[42,x,k[0]*k[1],k[1]]
F[71,x] = F[10,x]*F[72,x]
F[72,x] = F[50,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{71}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \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_{11}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , 1, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , 1, y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{22}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{23}\! \left(x , y_{0}, 1\right) y_{0}-F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{27}\! \left(x , 1, y_{1}\right) y_{1}-F_{27}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , 1, y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{31}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{36}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{36}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{36}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{37}\! \left(x , y_{0}, 1\right) y_{0}-F_{37}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{27}\! \left(x , 1, y_{0}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{31}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{48}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = -\frac{-F_{50}\! \left(x , y_{0}\right) y_{0}+F_{50}\! \left(x , 1\right)}{-1+y_{0}}
F_{50}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{55}\! \left(x , 1, y_{0}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{25}\! \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_{60}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{59}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}, 1\right)
F_{62}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{64}\! \left(x , y_{0}\right)+F_{64}\! \left(x , 1\right)}{-1+y_{0}}
F_{64}\! \left(x , y_{0}\right) = F_{14}\! \left(x , 1, y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{26}\! \left(x , 1, y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}, 1\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}, 1\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{71}\! \left(x \right) = F_{10}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{50}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_71(x))
Eq(F_5(x), F_10(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_11(x, k_0) + F_48(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_10(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), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_24(x, k_0))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_40(x, k_0) + F_42(x, k_0, k_1) + F_46(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_10(x)*F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_17(x, 1, k_0, k_1))
Eq(F_17(x, k_0, k_1, k_2), F_1(x) + F_18(x, k_0, k_1, k_2) + F_20(x, k_0, k_1, k_2) + F_25(x, k_0, k_1) + F_38(x, k_0, k_1, k_2) + F_44(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_10(x)*F_19(x, k_0, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), (k_0*F_17(x, k_0, k_1, k_2) - F_17(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2)*F_24(x, k_0))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0, k_1), F_24(x, k_1)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_0*F_27(x, k_0/k_1, k_1) + k_1*F_27(x, 1, k_1))/(-k_0 + k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_40(x, k_0) + F_42(x, k_0, k_1) + F_43(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_10(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, 1, k_0, k_1))
Eq(F_31(x, k_0, k_1, k_2), F_1(x) + F_25(x, k_0, k_1) + F_32(x, k_0, k_1, k_2) + F_34(x, k_0, k_1, k_2) + F_38(x, k_0, k_1, k_2) + F_39(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_10(x)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), (k_0*F_31(x, k_0, k_1, k_2) - F_31(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_34(x, k_0, k_1, k_2), F_24(x, k_0)*F_35(x, k_0, k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2), (-k_1*F_36(x, k_0, k_1) + k_2*F_36(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_36(x, k_0, k_1), (-k_0*F_37(x, k_0, 1) + k_1*F_37(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1), F_28(x, k_0, k_0*k_1))
Eq(F_38(x, k_0, k_1, k_2), F_24(x, k_2)*F_31(x, k_0, k_1, k_2))
Eq(F_39(x, k_0, k_1, k_2), F_10(x)*F_31(x, k_0, k_1, k_2))
Eq(F_40(x, k_0), F_24(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_27(x, 1, k_0))
Eq(F_42(x, k_0, k_1), F_24(x, k_1)*F_28(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_10(x)*F_28(x, k_0, k_1))
Eq(F_44(x, k_0, k_1, k_2), F_10(x)*F_45(x, k_0, k_1, k_2))
Eq(F_45(x, k_0, k_1, k_2), (-k_2*F_31(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_46(x, k_0, k_1), F_10(x)*F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_48(x, k_0), F_10(x)*F_49(x, k_0))
Eq(F_49(x, k_0), (-k_0*F_50(x, k_0) + F_50(x, 1))/(1 - k_0))
Eq(F_50(x, k_0), F_1(x) + F_40(x, k_0) + F_51(x, k_0) + F_69(x, k_0))
Eq(F_51(x, k_0), F_10(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0) + F_62(x, k_0) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_53(x, k_0), F_10(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, 1, k_0))
Eq(F_55(x, k_0, k_1), (-k_0*F_56(x, k_0, k_1) + F_56(x, 1, k_1))/(1 - k_0))
Eq(F_56(x, k_0, k_1), F_1(x) + F_25(x, k_0, k_1) + F_57(x, k_0, k_1) + F_59(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_10(x)*F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), (k_0*F_56(x, k_0, k_1) - F_56(x, 1, k_1))/(k_0 - 1))
Eq(F_59(x, k_0, k_1), F_22(x, k_0, k_1)*F_24(x, k_0))
Eq(F_60(x, k_0, k_1), F_10(x)*F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_31(x, k_0, k_1, 1))
Eq(F_62(x, k_0), F_10(x)*F_63(x, k_0))
Eq(F_63(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_14(x, 1, k_0))
Eq(F_65(x, k_0), F_24(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_26(x, 1, k_0))
Eq(F_67(x, k_0), F_10(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_30(x, k_0, 1))
Eq(F_69(x, k_0), F_70(x, k_0, 1))
Eq(F_70(x, k_0, k_1), F_42(x, k_0*k_1, k_1))
Eq(F_71(x), F_10(x)*F_72(x))
Eq(F_72(x), F_50(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "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], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": 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], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]]}], "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": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"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": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": 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2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25160/
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[10,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[71,x]
F[5,x] = F[10,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[48,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[10,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] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[24,x,k[0]]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[40,x,k[0]]+F[42,x,k[0],k[1]]+F[46,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[10,x]*F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[17,x,1,k[0],k[1]]
F[17,x,k[0],k[1],k[2]] = F[1,x]+F[18,x,k[0],k[1],k[2]]+F[20,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1]]+F[38,x,k[0],k[1],k[2]]+F[44,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[10,x]*F[19,x,k[0],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[17,x,k[0],k[1],k[2]]*k[0]-F[17,x,1,k[1],k[2]])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]*F[24,x,k[0]]
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0],k[1]] = F[24,x,k[1]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (-F[27,x,1,k[1]]*k[1]+F[27,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[27,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[40,x,k[0]]+F[42,x,k[0],k[1]]+F[43,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[10,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[31,x,1,k[0],k[1]]
F[31,x,k[0],k[1],k[2]] = F[1,x]+F[25,x,k[0],k[1]]+F[32,x,k[0],k[1],k[2]]+F[34,x,k[0],k[1],k[2]]+F[38,x,k[0],k[1],k[2]]+F[39,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[10,x]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[31,x,k[0],k[1],k[2]]*k[0]-F[31,x,1,k[1],k[2]])
F[34,x,k[0],k[1],k[2]] = F[24,x,k[0]]*F[35,x,k[0],k[1],k[2]]
F[35,x,k[0],k[1],k[2]] = (F[36,x,k[0],k[1]]*k[1]-F[36,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[36,x,k[0],k[1]] = (F[37,x,k[0],1]*k[0]-F[37,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[37,x,k[0],k[1]] = F[28,x,k[0],k[0]*k[1]]
F[38,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[31,x,k[0],k[1],k[2]]
F[39,x,k[0],k[1],k[2]] = F[10,x]*F[31,x,k[0],k[1],k[2]]
F[40,x,k[0]] = F[24,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[27,x,1,k[0]]
F[42,x,k[0],k[1]] = F[24,x,k[1]]*F[28,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[10,x]*F[28,x,k[0],k[1]]
F[44,x,k[0],k[1],k[2]] = F[10,x]*F[45,x,k[0],k[1],k[2]]
F[45,x,k[0],k[1],k[2]] = (F[31,x,k[0],k[1],k[2]]*k[2]-F[31,x,k[0],k[1],1])/(-1+k[2])
F[46,x,k[0],k[1]] = F[10,x]*F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[48,x,k[0]] = F[10,x]*F[49,x,k[0]]
F[49,x,k[0]] = (F[50,x,k[0]]*k[0]-F[50,x,1])/(-1+k[0])
F[50,x,k[0]] = F[1,x]+F[40,x,k[0]]+F[51,x,k[0]]+F[69,x,k[0]]
F[51,x,k[0]] = F[10,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]+F[62,x,k[0]]+F[65,x,k[0]]+F[67,x,k[0]]
F[53,x,k[0]] = F[10,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,1,k[0]]
F[55,x,k[0],k[1]] = 1/(-1+k[0])*(F[56,x,k[0],k[1]]*k[0]-F[56,x,1,k[1]])
F[56,x,k[0],k[1]] = F[1,x]+F[25,x,k[0],k[1]]+F[57,x,k[0],k[1]]+F[59,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[10,x]*F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = 1/(-1+k[0])*(F[56,x,k[0],k[1]]*k[0]-F[56,x,1,k[1]])
F[59,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[24,x,k[0]]
F[60,x,k[0],k[1]] = F[10,x]*F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[31,x,k[0],k[1],1]
F[62,x,k[0]] = F[10,x]*F[63,x,k[0]]
F[63,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[64,x,k[0]] = F[14,x,1,k[0]]
F[65,x,k[0]] = F[24,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[26,x,1,k[0]]
F[67,x,k[0]] = F[10,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[30,x,k[0],1]
F[69,x,k[0]] = F[70,x,k[0],1]
F[70,x,k[0],k[1]] = F[42,x,k[0]*k[1],k[1]]
F[71,x] = F[10,x]*F[72,x]
F[72,x] = F[50,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{71}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \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_{11}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , 1, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , 1, y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{22}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{23}\! \left(x , y_{0}, 1\right) y_{0}-F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{27}\! \left(x , 1, y_{1}\right) y_{1}-F_{27}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , 1, y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{31}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{36}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{36}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{36}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{37}\! \left(x , y_{0}, 1\right) y_{0}-F_{37}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{27}\! \left(x , 1, y_{0}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{31}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{48}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = -\frac{-F_{50}\! \left(x , y_{0}\right) y_{0}+F_{50}\! \left(x , 1\right)}{-1+y_{0}}
F_{50}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{55}\! \left(x , 1, y_{0}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{25}\! \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_{60}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{59}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}, 1\right)
F_{62}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{64}\! \left(x , y_{0}\right)+F_{64}\! \left(x , 1\right)}{-1+y_{0}}
F_{64}\! \left(x , y_{0}\right) = F_{14}\! \left(x , 1, y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{26}\! \left(x , 1, y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}, 1\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}, 1\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{71}\! \left(x \right) = F_{10}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{50}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_71(x))
Eq(F_5(x), F_10(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_11(x, k_0) + F_48(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_10(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), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_24(x, k_0))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_40(x, k_0) + F_42(x, k_0, k_1) + F_46(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_10(x)*F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_17(x, 1, k_0, k_1))
Eq(F_17(x, k_0, k_1, k_2), F_1(x) + F_18(x, k_0, k_1, k_2) + F_20(x, k_0, k_1, k_2) + F_25(x, k_0, k_1) + F_38(x, k_0, k_1, k_2) + F_44(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_10(x)*F_19(x, k_0, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), (k_0*F_17(x, k_0, k_1, k_2) - F_17(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2)*F_24(x, k_0))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0, k_1), F_24(x, k_1)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_0*F_27(x, k_0/k_1, k_1) + k_1*F_27(x, 1, k_1))/(-k_0 + k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_40(x, k_0) + F_42(x, k_0, k_1) + F_43(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_10(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, 1, k_0, k_1))
Eq(F_31(x, k_0, k_1, k_2), F_1(x) + F_25(x, k_0, k_1) + F_32(x, k_0, k_1, k_2) + F_34(x, k_0, k_1, k_2) + F_38(x, k_0, k_1, k_2) + F_39(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_10(x)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), (k_0*F_31(x, k_0, k_1, k_2) - F_31(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_34(x, k_0, k_1, k_2), F_24(x, k_0)*F_35(x, k_0, k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2), (-k_1*F_36(x, k_0, k_1) + k_2*F_36(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_36(x, k_0, k_1), (-k_0*F_37(x, k_0, 1) + k_1*F_37(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1), F_28(x, k_0, k_0*k_1))
Eq(F_38(x, k_0, k_1, k_2), F_24(x, k_2)*F_31(x, k_0, k_1, k_2))
Eq(F_39(x, k_0, k_1, k_2), F_10(x)*F_31(x, k_0, k_1, k_2))
Eq(F_40(x, k_0), F_24(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_27(x, 1, k_0))
Eq(F_42(x, k_0, k_1), F_24(x, k_1)*F_28(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_10(x)*F_28(x, k_0, k_1))
Eq(F_44(x, k_0, k_1, k_2), F_10(x)*F_45(x, k_0, k_1, k_2))
Eq(F_45(x, k_0, k_1, k_2), (-k_2*F_31(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_46(x, k_0, k_1), F_10(x)*F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_48(x, k_0), F_10(x)*F_49(x, k_0))
Eq(F_49(x, k_0), (-k_0*F_50(x, k_0) + F_50(x, 1))/(1 - k_0))
Eq(F_50(x, k_0), F_1(x) + F_40(x, k_0) + F_51(x, k_0) + F_69(x, k_0))
Eq(F_51(x, k_0), F_10(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0) + F_62(x, k_0) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_53(x, k_0), F_10(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, 1, k_0))
Eq(F_55(x, k_0, k_1), (-k_0*F_56(x, k_0, k_1) + F_56(x, 1, k_1))/(1 - k_0))
Eq(F_56(x, k_0, k_1), F_1(x) + F_25(x, k_0, k_1) + F_57(x, k_0, k_1) + F_59(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_10(x)*F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), (k_0*F_56(x, k_0, k_1) - F_56(x, 1, k_1))/(k_0 - 1))
Eq(F_59(x, k_0, k_1), F_22(x, k_0, k_1)*F_24(x, k_0))
Eq(F_60(x, k_0, k_1), F_10(x)*F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_31(x, k_0, k_1, 1))
Eq(F_62(x, k_0), F_10(x)*F_63(x, k_0))
Eq(F_63(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_14(x, 1, k_0))
Eq(F_65(x, k_0), F_24(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_26(x, 1, k_0))
Eq(F_67(x, k_0), F_10(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_30(x, k_0, 1))
Eq(F_69(x, k_0), F_70(x, k_0, 1))
Eq(F_70(x, k_0, k_1), F_42(x, k_0*k_1, k_1))
Eq(F_71(x), F_10(x)*F_72(x))
Eq(F_72(x), F_50(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "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], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": 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], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]]}], "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": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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, 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2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [2, 0], [4, 0], [4, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25347/
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[10,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[71,x]
F[5,x] = F[10,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[48,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[10,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] = x
F[11,x,k[0]] = F[12,x,k[0]]*F[24,x,k[0]]
F[12,x,k[0]] = F[13,x,1,k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0]*k[1],k[1]]
F[14,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[40,x,k[0]]+F[42,x,k[0],k[1]]+F[46,x,k[0],k[1]]
F[15,x,k[0],k[1]] = F[10,x]*F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[17,x,1,k[0],k[1]]
F[17,x,k[0],k[1],k[2]] = F[1,x]+F[18,x,k[0],k[1],k[2]]+F[20,x,k[0],k[1],k[2]]+F[25,x,k[0],k[1]]+F[38,x,k[0],k[1],k[2]]+F[44,x,k[0],k[1],k[2]]
F[18,x,k[0],k[1],k[2]] = F[10,x]*F[19,x,k[0],k[1],k[2]]
F[19,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[17,x,k[0],k[1],k[2]]*k[0]-F[17,x,1,k[1],k[2]])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]*F[24,x,k[0]]
F[21,x,k[0],k[1],k[2]] = (F[22,x,k[0],k[1]]*k[1]-F[22,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0],k[1]] = F[24,x,k[1]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (-F[27,x,1,k[1]]*k[1]+F[27,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[27,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[28,x,k[0],k[1]] = F[1,x]+F[29,x,k[0],k[1]]+F[40,x,k[0]]+F[42,x,k[0],k[1]]+F[43,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[10,x]*F[30,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[31,x,1,k[0],k[1]]
F[31,x,k[0],k[1],k[2]] = F[1,x]+F[25,x,k[0],k[1]]+F[32,x,k[0],k[1],k[2]]+F[34,x,k[0],k[1],k[2]]+F[38,x,k[0],k[1],k[2]]+F[39,x,k[0],k[1],k[2]]
F[32,x,k[0],k[1],k[2]] = F[10,x]*F[33,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[31,x,k[0],k[1],k[2]]*k[0]-F[31,x,1,k[1],k[2]])
F[34,x,k[0],k[1],k[2]] = F[24,x,k[0]]*F[35,x,k[0],k[1],k[2]]
F[35,x,k[0],k[1],k[2]] = (F[36,x,k[0],k[1]]*k[1]-F[36,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[36,x,k[0],k[1]] = (F[37,x,k[0],1]*k[0]-F[37,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[37,x,k[0],k[1]] = F[28,x,k[0],k[0]*k[1]]
F[38,x,k[0],k[1],k[2]] = F[24,x,k[2]]*F[31,x,k[0],k[1],k[2]]
F[39,x,k[0],k[1],k[2]] = F[10,x]*F[31,x,k[0],k[1],k[2]]
F[40,x,k[0]] = F[24,x,k[0]]*F[41,x,k[0]]
F[41,x,k[0]] = F[27,x,1,k[0]]
F[42,x,k[0],k[1]] = F[24,x,k[1]]*F[28,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[10,x]*F[28,x,k[0],k[1]]
F[44,x,k[0],k[1],k[2]] = F[10,x]*F[45,x,k[0],k[1],k[2]]
F[45,x,k[0],k[1],k[2]] = (F[31,x,k[0],k[1],k[2]]*k[2]-F[31,x,k[0],k[1],1])/(-1+k[2])
F[46,x,k[0],k[1]] = F[10,x]*F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = (F[28,x,k[0],k[1]]*k[1]-F[28,x,k[0],1])/(-1+k[1])
F[48,x,k[0]] = F[10,x]*F[49,x,k[0]]
F[49,x,k[0]] = (F[50,x,k[0]]*k[0]-F[50,x,1])/(-1+k[0])
F[50,x,k[0]] = F[1,x]+F[40,x,k[0]]+F[51,x,k[0]]+F[69,x,k[0]]
F[51,x,k[0]] = F[10,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[1,x]+F[53,x,k[0]]+F[62,x,k[0]]+F[65,x,k[0]]+F[67,x,k[0]]
F[53,x,k[0]] = F[10,x]*F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,1,k[0]]
F[55,x,k[0],k[1]] = 1/(-1+k[0])*(F[56,x,k[0],k[1]]*k[0]-F[56,x,1,k[1]])
F[56,x,k[0],k[1]] = F[1,x]+F[25,x,k[0],k[1]]+F[57,x,k[0],k[1]]+F[59,x,k[0],k[1]]+F[60,x,k[0],k[1]]
F[57,x,k[0],k[1]] = F[10,x]*F[58,x,k[0],k[1]]
F[58,x,k[0],k[1]] = 1/(-1+k[0])*(F[56,x,k[0],k[1]]*k[0]-F[56,x,1,k[1]])
F[59,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[24,x,k[0]]
F[60,x,k[0],k[1]] = F[10,x]*F[61,x,k[0],k[1]]
F[61,x,k[0],k[1]] = F[31,x,k[0],k[1],1]
F[62,x,k[0]] = F[10,x]*F[63,x,k[0]]
F[63,x,k[0]] = 1/(-1+k[0])*(F[64,x,k[0]]*k[0]-F[64,x,1])
F[64,x,k[0]] = F[14,x,1,k[0]]
F[65,x,k[0]] = F[24,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[26,x,1,k[0]]
F[67,x,k[0]] = F[10,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[30,x,k[0],1]
F[69,x,k[0]] = F[70,x,k[0],1]
F[70,x,k[0],k[1]] = F[42,x,k[0]*k[1],k[1]]
F[71,x] = F[10,x]*F[72,x]
F[72,x] = F[50,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{71}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \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_{11}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}
F_{10}\! \left(x \right) = x
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , 1, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}\right) = F_{17}\! \left(x , 1, y_{0}, y_{1}\right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{0}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{22}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{22}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{23}\! \left(x , y_{0}, 1\right) y_{0}-F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{24}\! \left(x , y_{0}\right) = y_{0} x
F_{25}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{27}\! \left(x , 1, y_{1}\right) y_{1}-F_{27}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}
F_{27}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{28}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{29}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , 1, y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{31}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{36}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{36}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{36}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{37}\! \left(x , y_{0}, 1\right) y_{0}-F_{37}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{37}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{24}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{40}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}\right) = F_{27}\! \left(x , 1, y_{0}\right)
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{28}\! \left(x , y_{0}, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{10}\! \left(x \right) F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{31}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{48}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = -\frac{-F_{50}\! \left(x , y_{0}\right) y_{0}+F_{50}\! \left(x , 1\right)}{-1+y_{0}}
F_{50}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{55}\! \left(x , 1, y_{0}\right)
F_{55}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{56}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{25}\! \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_{60}\! \left(x , y_{0}, y_{1}\right)
F_{57}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}\right)
F_{58}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{59}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x \right) F_{61}\! \left(x , y_{0}, y_{1}\right)
F_{61}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}, 1\right)
F_{62}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{64}\! \left(x , y_{0}\right)+F_{64}\! \left(x , 1\right)}{-1+y_{0}}
F_{64}\! \left(x , y_{0}\right) = F_{14}\! \left(x , 1, y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}\right) = F_{26}\! \left(x , 1, y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{30}\! \left(x , y_{0}, 1\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}, 1\right)
F_{70}\! \left(x , y_{0}, y_{1}\right) = F_{42}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{71}\! \left(x \right) = F_{10}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{50}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_71(x))
Eq(F_5(x), F_10(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_11(x, k_0) + F_48(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_10(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), x)
Eq(F_11(x, k_0), F_12(x, k_0)*F_24(x, k_0))
Eq(F_12(x, k_0), F_13(x, 1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0*k_1, k_1))
Eq(F_14(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_40(x, k_0) + F_42(x, k_0, k_1) + F_46(x, k_0, k_1))
Eq(F_15(x, k_0, k_1), F_10(x)*F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_17(x, 1, k_0, k_1))
Eq(F_17(x, k_0, k_1, k_2), F_1(x) + F_18(x, k_0, k_1, k_2) + F_20(x, k_0, k_1, k_2) + F_25(x, k_0, k_1) + F_38(x, k_0, k_1, k_2) + F_44(x, k_0, k_1, k_2))
Eq(F_18(x, k_0, k_1, k_2), F_10(x)*F_19(x, k_0, k_1, k_2))
Eq(F_19(x, k_0, k_1, k_2), (k_0*F_17(x, k_0, k_1, k_2) - F_17(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2)*F_24(x, k_0))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_22(x, k_0, k_1) + k_2*F_22(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0, k_1), F_24(x, k_1)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_0*F_27(x, k_0/k_1, k_1) + k_1*F_27(x, 1, k_1))/(-k_0 + k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_28(x, k_0, k_1), F_1(x) + F_29(x, k_0, k_1) + F_40(x, k_0) + F_42(x, k_0, k_1) + F_43(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_10(x)*F_30(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, 1, k_0, k_1))
Eq(F_31(x, k_0, k_1, k_2), F_1(x) + F_25(x, k_0, k_1) + F_32(x, k_0, k_1, k_2) + F_34(x, k_0, k_1, k_2) + F_38(x, k_0, k_1, k_2) + F_39(x, k_0, k_1, k_2))
Eq(F_32(x, k_0, k_1, k_2), F_10(x)*F_33(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), (k_0*F_31(x, k_0, k_1, k_2) - F_31(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_34(x, k_0, k_1, k_2), F_24(x, k_0)*F_35(x, k_0, k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2), (-k_1*F_36(x, k_0, k_1) + k_2*F_36(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_36(x, k_0, k_1), (-k_0*F_37(x, k_0, 1) + k_1*F_37(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_37(x, k_0, k_1), F_28(x, k_0, k_0*k_1))
Eq(F_38(x, k_0, k_1, k_2), F_24(x, k_2)*F_31(x, k_0, k_1, k_2))
Eq(F_39(x, k_0, k_1, k_2), F_10(x)*F_31(x, k_0, k_1, k_2))
Eq(F_40(x, k_0), F_24(x, k_0)*F_41(x, k_0))
Eq(F_41(x, k_0), F_27(x, 1, k_0))
Eq(F_42(x, k_0, k_1), F_24(x, k_1)*F_28(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_10(x)*F_28(x, k_0, k_1))
Eq(F_44(x, k_0, k_1, k_2), F_10(x)*F_45(x, k_0, k_1, k_2))
Eq(F_45(x, k_0, k_1, k_2), (-k_2*F_31(x, k_0, k_1, k_2) + F_31(x, k_0, k_1, 1))/(1 - k_2))
Eq(F_46(x, k_0, k_1), F_10(x)*F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (-k_1*F_28(x, k_0, k_1) + F_28(x, k_0, 1))/(1 - k_1))
Eq(F_48(x, k_0), F_10(x)*F_49(x, k_0))
Eq(F_49(x, k_0), (-k_0*F_50(x, k_0) + F_50(x, 1))/(1 - k_0))
Eq(F_50(x, k_0), F_1(x) + F_40(x, k_0) + F_51(x, k_0) + F_69(x, k_0))
Eq(F_51(x, k_0), F_10(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_1(x) + F_53(x, k_0) + F_62(x, k_0) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_53(x, k_0), F_10(x)*F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, 1, k_0))
Eq(F_55(x, k_0, k_1), (-k_0*F_56(x, k_0, k_1) + F_56(x, 1, k_1))/(1 - k_0))
Eq(F_56(x, k_0, k_1), F_1(x) + F_25(x, k_0, k_1) + F_57(x, k_0, k_1) + F_59(x, k_0, k_1) + F_60(x, k_0, k_1))
Eq(F_57(x, k_0, k_1), F_10(x)*F_58(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), (k_0*F_56(x, k_0, k_1) - F_56(x, 1, k_1))/(k_0 - 1))
Eq(F_59(x, k_0, k_1), F_22(x, k_0, k_1)*F_24(x, k_0))
Eq(F_60(x, k_0, k_1), F_10(x)*F_61(x, k_0, k_1))
Eq(F_61(x, k_0, k_1), F_31(x, k_0, k_1, 1))
Eq(F_62(x, k_0), F_10(x)*F_63(x, k_0))
Eq(F_63(x, k_0), (k_0*F_64(x, k_0) - F_64(x, 1))/(k_0 - 1))
Eq(F_64(x, k_0), F_14(x, 1, k_0))
Eq(F_65(x, k_0), F_24(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_26(x, 1, k_0))
Eq(F_67(x, k_0), F_10(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_30(x, k_0, 1))
Eq(F_69(x, k_0), F_70(x, k_0, 1))
Eq(F_70(x, k_0, k_1), F_42(x, k_0*k_1, k_1))
Eq(F_71(x), F_10(x)*F_72(x))
Eq(F_72(x), F_50(x, 1))
Pack JSON:
{"name": "point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "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], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": 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], [0, 2, 3, 4, 1], [0, 3, 1, 4, 2], [0, 3, 2, 4, 1], [1, 2, 3, 4, 0], [1, 3, 2, 4, 0]]}], "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": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"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": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", 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0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [1, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 1, "tracked": true}}]}
Specification 4
Strategy pack name: all_the_strategies_2_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25601/
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,1]
F[4,x,k[0]] = F[5,x]*F[6,x,k[0]]
F[5,x] = x
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[8,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,k[0],1]
F[11,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[30,x,k[0],k[1]]+F[32,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,1,k[0],k[1]]
F[14,x,k[0],k[1],k[2]] = F[15,x,k[0],k[1],k[2]]*F[5,x]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[17,x,k[0],k[1],k[2]]+F[20,x,k[1],k[0],k[2]]+F[28,x,k[2],k[0],k[1]]
F[16,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[14,x,k[0],k[1],k[2]]*k[0]-F[14,x,1,k[1],k[2]])
F[17,x,k[0],k[1],k[2]] = (F[18,x,k[0],1,k[2]]*k[0]-F[18,x,k[0],k[1]/k[0],k[2]]*k[1])/(k[0]-k[1])
F[18,x,k[0],k[1],k[2]] = (F[19,x,k[0],k[1]]*k[0]*k[1]-F[19,x,k[0],k[2]/k[0]]*k[2])/(k[0]*k[1]-k[2])
F[19,x,k[0],k[1]] = F[11,x,k[0],k[1]]*F[9,x,k[0]]
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[1],k[2]]
F[21,x,k[0],k[1],k[2]] = 1/(k[0]-k[1])*(F[22,x,k[0],1,k[2]]*k[0]-F[22,x,k[0],k[1]/k[0],k[2]]*k[1])
F[22,x,k[0],k[1],k[2]] = F[23,x,k[1],k[0]]*F[24,x,k[2]]*F[9,x,k[0]]
F[23,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[1,x]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[25,x,k[0]]*F[9,x,k[0]]
F[28,x,k[0],k[1],k[2]] = F[29,x,k[0],k[1],k[2]]
F[29,x,k[0],k[1],k[2]] = F[15,x,k[1],k[2],k[0]]*F[24,x,k[0]]*F[9,x,k[0]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[10,x,k[0]]*F[24,x,k[1]]*F[9,x,k[0]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[12,x,k[1],k[0]]*F[24,x,k[0]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y_{0}\right) = F_{5}\! \left(x \right) F_{6}\! \left(x , y_{0}\right)
F_{5}\! \left(x \right) = x
F_{6}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{4}\! \left(x , y_{0}\right) y_{0}+F_{4}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{9}\! \left(x , y_{0}\right) = y_{0} x
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}, 1\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , 1, y_{0}, y_{1}\right)
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{5}\! \left(x \right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{28}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{14}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{18}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{18}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{y_{0}-y_{1}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{19}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{19}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right) y_{2}}{y_{0} y_{1}-y_{2}}
F_{19}\! \left(x , y_{0}, y_{1}\right) = F_{11}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{0} F_{22}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{22}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{y_{0}-y_{1}}
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{1}, y_{0}\right) F_{24}\! \left(x , y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{24}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{27}\! \left(x , y_{0}\right)
F_{27}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{15}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = F_{10}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{0}\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_{12}\! \left(x , y_{1}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\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, 1))
Eq(F_4(x, k_0), F_5(x)*F_6(x, k_0))
Eq(F_5(x), x)
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_8(x, k_0))
Eq(F_7(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, k_0, 1))
Eq(F_11(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_30(x, k_0, k_1) + F_32(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, 1, k_0, k_1))
Eq(F_14(x, k_0, k_1, k_2), F_15(x, k_0, k_1, k_2)*F_5(x))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_17(x, k_0, k_1, k_2) + F_20(x, k_1, k_0, k_2) + F_28(x, k_2, k_0, k_1))
Eq(F_16(x, k_0, k_1, k_2), (k_0*F_14(x, k_0, k_1, k_2) - F_14(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_17(x, k_0, k_1, k_2), (-k_0*F_18(x, k_0, 1, k_2) + k_1*F_18(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_18(x, k_0, k_1, k_2), (-k_0*k_1*F_19(x, k_0, k_1) + k_2*F_19(x, k_0, k_2/k_0))/(-k_0*k_1 + k_2))
Eq(F_19(x, k_0, k_1), F_11(x, k_0, k_1)*F_9(x, k_0))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_1, k_2))
Eq(F_21(x, k_0, k_1, k_2), (k_0*F_22(x, k_0, 1, k_2) - k_1*F_22(x, k_0, k_1/k_0, k_2))/(k_0 - k_1))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_1, k_0)*F_24(x, k_2)*F_9(x, k_0))
Eq(F_23(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_1(x) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_25(x, k_0)*F_9(x, k_0))
Eq(F_28(x, k_0, k_1, k_2), F_29(x, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_15(x, k_1, k_2, k_0)*F_24(x, k_0)*F_9(x, k_0))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_10(x, k_0)*F_24(x, k_1)*F_9(x, k_0))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_12(x, k_1, k_0)*F_24(x, k_0)*F_9(x, k_0))
Pack JSON:
{"name": "all_the_strategies_2_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionFactory", "ignore_parent": false, "maxreqlen": 2, "extra_basis": [], "limited_insertion": true, "allow_factorable_insertions": true}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "AllPlacementsFactory", "ignore_parent": false}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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