01243_01342_02143
Counting sequence:
1, 1, 2, 6, 24, 117, 652, 3990, 26161, 180874, 1304363, 9734618, 74749713, 587949192, 4720642702, 38582595201, 320285171194, 2695485674922, 22962873949422, 197762787536979, 1719953274654647, 15091603301319709, 133490230914329523, 1189470585981388380, 10670410272466501105, 96315669669289283724, 874366723973086692809, 7979702626390817108875, 73183235609983648682348, 674249767902932120574072, 6238520245762582211664070, 57952760260133996074746820, 540368290311200158737778213, 5056268372746187756964002904, 47468442162993789626356674658, 447025444171088400362008663522, 4222178412697421955150390378524, 39989759138303081541786614994383, 379756434508624648632745394849284, 3615320724799626382645713404772259, 34500029893932390768395128259503833, 329968640749380359976499332491872975, 3162711910801654439624548426820501466, 30376438795260190754755343463477844081, 292323547363920837377581003186664508525, 2818400020708407510465817293454822278616, 27221872912422314023001092221849285336585, 263376373846591291879187036352722822789213, 2552395969595434192075974577927057410921402, 24774368635646090627379211813996830402659676, 240831386582544285883169900036603582943238046, 2344519081804829204269624984690877326306177345, 22856008625106849099719655345847023077592666378, 223115663291411315058388200276554086868021644107, 2180826759346132144419108026009395671439005003334, 21342892887297138318809764270222226467090166911672, 209125542193829451164217741506640256507983237301568, 2051465607414536108123086967974675300465971135269131, 20146861605519348945682707828054850747925012209726609, 198070633013863697214493261054229935997208744277152689, 1949335746095441796251326904839741013418045173366821037, 19204021933667064229712527137377987107475080739821610856, 189374966558583940369224640907510496880735696223384328570, 1869236659387932158981430948785007571778610528650062460035, 18467346762616104196556791765823028874695082650256748627290, 182612690384549570277067274334942478814214297170697140468392, 1807307052762875448101503409230384857935939781961303563923071, 17901783285975709681425109145326022615162772860931751298787575, 177465252156311894941805039017939158939889130441647080213497522, 1760649198902656457023941856116599770720987725041224808422993303, 17480949871569854516411837852329143687564888461116883198500202377, 173692293321758049746413721847150168553146702866959309223261463752, 1727071934592662215680034995158970152920896685270329928556871986553, 17184862306014307127452088312819920965711730651435409877108153039707, 171111494731010212684815622614178711726420039493273117300977099572895, 1704911689963307981931746524597309180344906004731362398776744688358865, 16998341774704456651995999597049304993567653304120651033073355666997154, 169584391419931745020648467470137868826390651659618548717105550087578942, 1692905894926073585014501234206076302019733436281422616530881725013238089, 16909883393054880713022711816704341309327715499877804762796317789032719453, 169006245267103360131140946808349130560750399880244382370985033376136052642, 1690102210360254960002126243929310215537133966621444746682081665901807527865, 16910841630961436300901069931294445674082444727001913240391424448111171889728, 169298726124683781095963115490863184735318636119593002769963563694539802153558, 1695792696040150204833994437370292474439996438877568332728118996897805377918767, 16994837560313714463184149385599293701188517181684862742005228415860895859990440, 170404569731694236091655414082804130987586880364695116239307734686433472002853162, 1709465626156711460225036706287404186811515799928630981946186003819013210239926383, 17157323928168221197019812123173221332427808910782390110961366140079372493539286503, 172283649557656825464716303336017730308580448421029610046097611625090893893033824654, 1730769993958185789350457066299921513868019478471617385232919975683220572818136384207, 17395264303405437862557058627342638448657540265362866650776061060571537303868224229076, 174910075920781420974239993520947459975793052745995690054740194201894360324284227968376, 1759489283363942068653627344352111894298881768843511686710367529297252666611429874217450, 17706895965144114676839336066691316693135676047135507177858793639436601036762001262996354, 178270053167953546936018347353065294310566906767729285642697152589423922338830056965185125, 1795522114959265753946516041102128350678552025786391229168405102105999764934530159536973296, 18091555242191700147579472082758216761940394785584196740617177411231747220763029162056548001, 182360305231149822391332356110428561613180607005929456053533786157852626599918608501931899243, 1838868074484795441989511907413087869654780039710968637818353900491266771252618381370682296752, 18549550196708787086606943770747176165034302445405800087710275285262760423438489456654787374478
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://permpal.com/tree/25385/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,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,1,k[0]]
F[11,x,k[0],k[1]] = F[12,x,k[0]*k[1],k[1]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[48,x,k[0],k[1]]+F[68,x,k[1],k[0]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[22,x,k[1],k[0],k[2]]+F[66,x,k[2],k[0],k[1]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[3,x]
F[17,x,k[0],k[1],k[2]] = 1/(-1+k[0])*(F[15,x,k[0],k[1],k[2]]*k[0]-F[15,x,1,k[1],k[2]])
F[18,x,k[0],k[1],k[2]] = F[19,x,k[0],k[1],k[2]]*F[9,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],k[1]]*k[1]-F[20,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[20,x,k[0],k[1]] = (F[21,x,k[0],1]*k[0]-F[21,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[12,x,k[0],k[0]*k[1]]
F[22,x,k[0],k[1],k[2]] = F[23,x,k[1],k[0],k[2]]*F[9,x,k[0]]
F[23,x,k[0],k[1],k[2]] = (-F[24,x,1,k[1],k[2]]*k[1]+F[24,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[24,x,k[0],k[1],k[2]] = F[25,x,k[0]*k[1],k[1],k[2]]
F[25,x,k[0],k[1],k[2]] = F[1,x]+F[26,x,k[0],k[1],k[2]]+F[57,x,k[0],k[1],k[2]]+F[59,x,k[1],k[0],k[2]]+F[65,x,k[2],k[0],k[1]]
F[26,x,k[0],k[1],k[2]] = F[27,x,k[0],k[1],k[2]]*F[3,x]
F[27,x,k[0],k[1],k[2]] = F[28,x,1,k[0],k[1],k[2]]
F[28,x,k[0],k[1],k[2],k[3]] = F[1,x]+F[29,x,k[0],k[1],k[2],k[3]]+F[31,x,k[0],k[1],k[2],k[3]]+F[36,x,k[1],k[0],k[2],k[3]]+F[40,x,k[2],k[0],k[1],k[3]]+F[56,x,k[3],k[0],k[1],k[2]]
F[29,x,k[0],k[1],k[2],k[3]] = F[3,x]*F[30,x,k[0],k[1],k[2],k[3]]
F[30,x,k[0],k[1],k[2],k[3]] = 1/(-1+k[0])*(F[28,x,k[0],k[1],k[2],k[3]]*k[0]-F[28,x,1,k[1],k[2],k[3]])
F[31,x,k[0],k[1],k[2],k[3]] = F[32,x,k[0],k[1],k[2],k[3]]*F[9,x,k[0]]
F[32,x,k[0],k[1],k[2],k[3]] = (F[33,x,k[0],1,k[2],k[3]]*k[0]-F[33,x,k[0],k[1]/k[0],k[2],k[3]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1],k[2],k[3]] = (F[34,x,k[0],k[1],k[3]]*k[0]*k[1]-F[34,x,k[0],k[2]/k[0],k[3]]*k[2])/(k[0]*k[1]-k[2])
F[34,x,k[0],k[1],k[2]] = F[35,x,1,k[0],k[1],k[2]]
F[35,x,k[0],k[1],k[2],k[3]] = F[25,x,k[0]*k[1],k[1]*k[2],k[3]]
F[36,x,k[0],k[1],k[2],k[3]] = F[37,x,k[1],k[0],k[2],k[3]]*F[9,x,k[0]]
F[37,x,k[0],k[1],k[2],k[3]] = (-F[38,x,1,k[1],k[2],k[3]]*k[1]+F[38,x,k[0]/k[1],k[1],k[2],k[3]]*k[0])/(-k[1]+k[0])
F[38,x,k[0],k[1],k[2],k[3]] = F[39,x,k[0]*k[1],k[1],k[2],k[3]]
F[39,x,k[0],k[1],k[2],k[3]] = (F[25,x,k[0],k[1],k[2]]*k[2]-F[25,x,k[0],k[1],k[3]]*k[3])/(-k[3]+k[2])
F[40,x,k[0],k[1],k[2],k[3]] = F[41,x,k[1],k[2],k[0],k[3]]*F[9,x,k[0]]
F[41,x,k[0],k[1],k[2],k[3]] = (F[42,x,k[0],k[1],k[2],1]*k[2]-F[42,x,k[0],k[1],k[2],k[3]/k[2]]*k[3])/(-k[3]+k[2])
F[42,x,k[0],k[1],k[2],k[3]] = F[43,x,k[0],k[1],k[2],k[2]*k[3]]
F[43,x,k[0],k[1],k[2],k[3]] = F[44,x,k[0],k[1],k[3]]+F[51,x,k[0],k[1],k[2],k[3]]
F[44,x,k[0],k[1],k[2]] = (F[45,x,k[0],k[2]]*k[0]-F[45,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[45,x,k[0],k[1]] = F[1,x]+F[46,x,k[0],k[1]]+F[48,x,k[0],k[1]]+F[50,x,k[1],k[0]]
F[46,x,k[0],k[1]] = F[3,x]*F[47,x,k[0],k[1]]
F[47,x,k[0],k[1]] = 1/(-1+k[0])*(F[45,x,k[0],k[1]]*k[0]-F[45,x,1,k[1]])
F[48,x,k[0],k[1]] = F[49,x,k[0],k[1]]*F[9,x,k[0]]
F[49,x,k[0],k[1]] = F[24,x,1,k[0],k[1]]
F[50,x,k[0],k[1]] = F[45,x,k[1],k[0]]*F[9,x,k[0]]
F[51,x,k[0],k[1],k[2],k[3]] = F[52,x,k[0],k[1],k[2],k[3]]
F[52,x,k[0],k[1],k[2],k[3]] = F[53,x,k[0],k[1],k[2],k[3]]*F[9,x,k[2]]
F[54,x,k[0],k[1],k[2],k[3]] = F[53,x,k[0],k[1],k[2],k[3]]*F[9,x,k[3]]
F[54,x,k[0],k[1],k[2],k[3]] = F[55,x,k[0],k[1],k[2],k[3]]
F[28,x,k[0],k[1],k[2],k[3]] = F[15,x,k[0],k[1],k[2]]+F[55,x,k[0],k[1],k[2],k[3]]
F[56,x,k[0],k[1],k[2],k[3]] = F[43,x,k[1],k[2],k[3],k[0]]*F[9,x,k[0]]
F[57,x,k[0],k[1],k[2]] = F[58,x,k[0],k[1],k[2]]*F[9,x,k[0]]
F[58,x,k[0],k[1],k[2]] = (F[49,x,k[0],k[1]]*k[1]-F[49,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[59,x,k[0],k[1],k[2]] = F[60,x,k[1],k[0],k[2]]*F[9,x,k[0]]
F[60,x,k[0],k[1],k[2]] = (F[61,x,k[0],k[1],1]*k[1]-F[61,x,k[0],k[1],k[2]/k[1]]*k[2])/(-k[2]+k[1])
F[61,x,k[0],k[1],k[2]] = F[62,x,k[0],k[1],k[1]*k[2]]
F[62,x,k[0],k[1],k[2]] = F[1,x]+F[50,x,k[2],k[0]]+F[57,x,k[0],k[1],k[2]]+F[59,x,k[1],k[0],k[2]]+F[63,x,k[0],k[1],k[2]]
F[63,x,k[0],k[1],k[2]] = F[3,x]*F[64,x,k[0],k[1],k[2]]
F[64,x,k[0],k[1],k[2]] = F[43,x,1,k[0],k[1],k[2]]
F[65,x,k[0],k[1],k[2]] = F[62,x,k[1],k[2],k[0]]*F[9,x,k[0]]
F[66,x,k[0],k[1],k[2]] = F[67,x,k[0],1,k[1],k[2]]
F[67,x,k[0],k[1],k[2],k[3]] = F[56,x,k[0]*k[1],k[2],k[3],k[0]]
F[68,x,k[0],k[1]] = F[69,x,k[1],k[0]]*F[9,x,k[0]]
F[69,x,k[0],k[1]] = F[61,x,k[0],k[1],1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x , 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 , 1, y_{0}\right)
F_{11}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{12}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{1}, y_{0}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{66}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{-F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{20}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{20}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{21}\! \left(x , y_{0}, 1\right) y_{0}-F_{21}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{21}\! \left(x , y_{0}, y_{1}\right) = F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{23}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{24}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{24}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{25}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{65}\! \left(x , y_{2}, y_{0}, y_{1}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{28}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{36}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right)+F_{40}\! \left(x , y_{2}, y_{0}, y_{1}, y_{3}\right)+F_{56}\! \left(x , y_{3}, y_{0}, y_{1}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{3}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = -\frac{-F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)}{-1+y_{0}}
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{9}\! \left(x , y_{0}\right)
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{33}\! \left(x , y_{0}, 1, y_{2}, y_{3}\right) y_{0}-F_{33}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}, y_{3}\right) y_{1}}{-y_{1}+y_{0}}
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{34}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{0} y_{1}-F_{34}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}, y_{3}\right) y_{2}}{y_{0} y_{1}-y_{2}}
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{35}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{25}\! \left(x , y_{0} y_{1}, y_{1} y_{2}, y_{3}\right)
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{37}\! \left(x , y_{1}, y_{0}, y_{2}, y_{3}\right) F_{9}\! \left(x , y_{0}\right)
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = -\frac{F_{38}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right) y_{1}-F_{38}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}, y_{3}\right) y_{0}}{-y_{1}+y_{0}}
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{39}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}, y_{3}\right)
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}-F_{25}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{3}}{-y_{3}+y_{2}}
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{41}\! \left(x , y_{1}, y_{2}, y_{0}, y_{3}\right) F_{9}\! \left(x , y_{0}\right)
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = \frac{F_{42}\! \left(x , y_{0}, y_{1}, y_{2}, 1\right) y_{2}-F_{42}\! \left(x , y_{0}, y_{1}, y_{2}, \frac{y_{3}}{y_{2}}\right) y_{3}}{-y_{3}+y_{2}}
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{43}\! \left(x , y_{0}, y_{1}, y_{2}, y_{2} y_{3}\right)
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{44}\! \left(x , y_{0}, y_{1}, y_{3}\right)+F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{45}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{45}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)+F_{50}\! \left(x , y_{1}, y_{0}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{3}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)
F_{47}\! \left(x , y_{0}, y_{1}\right) = -\frac{-F_{45}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{45}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{48}\! \left(x , y_{0}, y_{1}\right) = F_{49}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}, y_{1}\right) = F_{24}\! \left(x , 1, y_{0}, y_{1}\right)
F_{50}\! \left(x , y_{0}, y_{1}\right) = F_{45}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{52}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{53}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{9}\! \left(x , y_{2}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{53}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) F_{9}\! \left(x , y_{3}\right)
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{55}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{43}\! \left(x , y_{1}, y_{2}, y_{3}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{49}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{49}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{60}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{61}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{61}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{62}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)
F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{50}\! \left(x , y_{2}, y_{0}\right)+F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{3}\! \left(x \right) F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{43}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{62}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{67}\! \left(x , y_{0}, 1, y_{1}, y_{2}\right)
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) = F_{56}\! \left(x , y_{0} y_{1}, y_{2}, y_{3}, y_{0}\right)
F_{68}\! \left(x , y_{0}, y_{1}\right) = F_{69}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}, y_{1}\right) = F_{61}\! \left(x , y_{0}, y_{1}, 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(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, 1, k_0))
Eq(F_11(x, k_0, k_1), F_12(x, k_0*k_1, k_1))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_48(x, k_0, k_1) + F_68(x, k_1, k_0))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_22(x, k_1, k_0, k_2) + F_66(x, k_2, k_0, k_1))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_3(x))
Eq(F_17(x, k_0, k_1, k_2), (k_0*F_15(x, k_0, k_1, k_2) - F_15(x, 1, k_1, k_2))/(k_0 - 1))
Eq(F_18(x, k_0, k_1, k_2), F_19(x, k_0, k_1, k_2)*F_9(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_1*F_20(x, k_0, k_1) + k_2*F_20(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_20(x, k_0, k_1), (-k_0*F_21(x, k_0, 1) + k_1*F_21(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_12(x, k_0, k_0*k_1))
Eq(F_22(x, k_0, k_1, k_2), F_23(x, k_1, k_0, k_2)*F_9(x, k_0))
Eq(F_23(x, k_0, k_1, k_2), (-k_0*F_24(x, k_0/k_1, k_1, k_2) + k_1*F_24(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_24(x, k_0, k_1, k_2), F_25(x, k_0*k_1, k_1, k_2))
Eq(F_25(x, k_0, k_1, k_2), F_1(x) + F_26(x, k_0, k_1, k_2) + F_57(x, k_0, k_1, k_2) + F_59(x, k_1, k_0, k_2) + F_65(x, k_2, k_0, k_1))
Eq(F_26(x, k_0, k_1, k_2), F_27(x, k_0, k_1, k_2)*F_3(x))
Eq(F_27(x, k_0, k_1, k_2), F_28(x, 1, k_0, k_1, k_2))
Eq(F_28(x, k_0, k_1, k_2, k_3), F_1(x) + F_29(x, k_0, k_1, k_2, k_3) + F_31(x, k_0, k_1, k_2, k_3) + F_36(x, k_1, k_0, k_2, k_3) + F_40(x, k_2, k_0, k_1, k_3) + F_56(x, k_3, k_0, k_1, k_2))
Eq(F_29(x, k_0, k_1, k_2, k_3), F_3(x)*F_30(x, k_0, k_1, k_2, k_3))
Eq(F_30(x, k_0, k_1, k_2, k_3), (k_0*F_28(x, k_0, k_1, k_2, k_3) - F_28(x, 1, k_1, k_2, k_3))/(k_0 - 1))
Eq(F_31(x, k_0, k_1, k_2, k_3), F_32(x, k_0, k_1, k_2, k_3)*F_9(x, k_0))
Eq(F_32(x, k_0, k_1, k_2, k_3), (-k_0*F_33(x, k_0, 1, k_2, k_3) + k_1*F_33(x, k_0, k_1/k_0, k_2, k_3))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1, k_2, k_3), (-k_0*k_1*F_34(x, k_0, k_1, k_3) + k_2*F_34(x, k_0, k_2/k_0, k_3))/(-k_0*k_1 + k_2))
Eq(F_34(x, k_0, k_1, k_2), F_35(x, 1, k_0, k_1, k_2))
Eq(F_35(x, k_0, k_1, k_2, k_3), F_25(x, k_0*k_1, k_1*k_2, k_3))
Eq(F_36(x, k_0, k_1, k_2, k_3), F_37(x, k_1, k_0, k_2, k_3)*F_9(x, k_0))
Eq(F_37(x, k_0, k_1, k_2, k_3), (-k_0*F_38(x, k_0/k_1, k_1, k_2, k_3) + k_1*F_38(x, 1, k_1, k_2, k_3))/(-k_0 + k_1))
Eq(F_38(x, k_0, k_1, k_2, k_3), F_39(x, k_0*k_1, k_1, k_2, k_3))
Eq(F_39(x, k_0, k_1, k_2, k_3), (-k_2*F_25(x, k_0, k_1, k_2) + k_3*F_25(x, k_0, k_1, k_3))/(-k_2 + k_3))
Eq(F_40(x, k_0, k_1, k_2, k_3), F_41(x, k_1, k_2, k_0, k_3)*F_9(x, k_0))
Eq(F_41(x, k_0, k_1, k_2, k_3), (-k_2*F_42(x, k_0, k_1, k_2, 1) + k_3*F_42(x, k_0, k_1, k_2, k_3/k_2))/(-k_2 + k_3))
Eq(F_42(x, k_0, k_1, k_2, k_3), F_43(x, k_0, k_1, k_2, k_2*k_3))
Eq(F_43(x, k_0, k_1, k_2, k_3), F_44(x, k_0, k_1, k_3) + F_51(x, k_0, k_1, k_2, k_3))
Eq(F_44(x, k_0, k_1, k_2), (-k_0*F_45(x, k_0, k_2) + k_1*F_45(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_45(x, k_0, k_1), F_1(x) + F_46(x, k_0, k_1) + F_48(x, k_0, k_1) + F_50(x, k_1, k_0))
Eq(F_46(x, k_0, k_1), F_3(x)*F_47(x, k_0, k_1))
Eq(F_47(x, k_0, k_1), (k_0*F_45(x, k_0, k_1) - F_45(x, 1, k_1))/(k_0 - 1))
Eq(F_48(x, k_0, k_1), F_49(x, k_0, k_1)*F_9(x, k_0))
Eq(F_49(x, k_0, k_1), F_24(x, 1, k_0, k_1))
Eq(F_50(x, k_0, k_1), F_45(x, k_1, k_0)*F_9(x, k_0))
Eq(F_51(x, k_0, k_1, k_2, k_3), F_52(x, k_0, k_1, k_2, k_3))
Eq(F_52(x, k_0, k_1, k_2, k_3), F_53(x, k_0, k_1, k_2, k_3)*F_9(x, k_2))
Eq(F_54(x, k_0, k_1, k_2, k_3), F_53(x, k_0, k_1, k_2, k_3)*F_9(x, k_3))
Eq(F_54(x, k_0, k_1, k_2, k_3), F_55(x, k_0, k_1, k_2, k_3))
Eq(F_28(x, k_0, k_1, k_2, k_3), F_15(x, k_0, k_1, k_2) + F_55(x, k_0, k_1, k_2, k_3))
Eq(F_56(x, k_0, k_1, k_2, k_3), F_43(x, k_1, k_2, k_3, k_0)*F_9(x, k_0))
Eq(F_57(x, k_0, k_1, k_2), F_58(x, k_0, k_1, k_2)*F_9(x, k_0))
Eq(F_58(x, k_0, k_1, k_2), (-k_1*F_49(x, k_0, k_1) + k_2*F_49(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_59(x, k_0, k_1, k_2), F_60(x, k_1, k_0, k_2)*F_9(x, k_0))
Eq(F_60(x, k_0, k_1, k_2), (-k_1*F_61(x, k_0, k_1, 1) + k_2*F_61(x, k_0, k_1, k_2/k_1))/(-k_1 + k_2))
Eq(F_61(x, k_0, k_1, k_2), F_62(x, k_0, k_1, k_1*k_2))
Eq(F_62(x, k_0, k_1, k_2), F_1(x) + F_50(x, k_2, k_0) + F_57(x, k_0, k_1, k_2) + F_59(x, k_1, k_0, k_2) + F_63(x, k_0, k_1, k_2))
Eq(F_63(x, k_0, k_1, k_2), F_3(x)*F_64(x, k_0, k_1, k_2))
Eq(F_64(x, k_0, k_1, k_2), F_43(x, 1, k_0, k_1, k_2))
Eq(F_65(x, k_0, k_1, k_2), F_62(x, k_1, k_2, k_0)*F_9(x, k_0))
Eq(F_66(x, k_0, k_1, k_2), F_67(x, k_0, 1, k_1, k_2))
Eq(F_67(x, k_0, k_1, k_2, k_3), F_56(x, k_0*k_1, k_2, k_3, k_0))
Eq(F_68(x, k_0, k_1), F_69(x, k_1, k_0)*F_9(x, k_0))
Eq(F_69(x, k_0, k_1), F_61(x, k_0, k_1, 1))
Pack JSON:
{"name": "row_and_col_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3]], "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]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 2, 1, 4, 3]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 4], [0, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 4], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 4], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 4], [0, 3]]}, 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