01342_03142_03412_30142_30412
Counting sequence:
1, 1, 2, 6, 24, 115, 614, 3510, 21028, 130399, 830534, 5404457, 35793794, 240595875, 1637718193, 11269560680, 78286178109, 548375220884, 3869676982547, 27487289762158, 196407677193804, 1410931239561839, 10184979906091800, 73847523933018068, 537614784498951932, 3928472941411445308, 28805011748218937444, 211881303573556514719, 1563140977575104567524, 11563668397447553134821, 85764015323595143158856, 637608973576957884371583, 4750925775729944629659259, 35474578536124066352427636, 265410049158566253510099417, 1989432534325316622922578323, 14938519878162493295595765781, 112359780650493478763393581021, 846449240307343620117644204713, 6386198379836678472204144944617, 48250601161932580729458932622387, 365049434561341756908521507151228, 2765420774602676266126386157561872, 20975159927157216982429032008543538, 159279387226789113812675749799510311, 1210880963522092001028173812659872742, 9215305485101996739788025386962608312, 70204446289803630573628120697697079514, 535361983660737883504216246674703669806, 4086401547233530465786019026654794666031, 31219703641892212120693536833367032172496, 238723584548325485593167836210546515887957, 1826947952371394307551313860004337679665409, 13992896669820793051581808732948290769454831, 107257273630679668260568635349694137326473985, 822756517825898498591674766292332884891078869, 6315820739638729216027803777106466414127588309, 48516692744743263932340143172838627353997038884, 372945287632797038472199450444410946848734973625, 2868677604616626094874694958732325334367199622229, 22079624370870145243633895673772384714563846497229, 170045848609768755240020052363358330211010660921623, 1310377207134758412827910288155237169144086236644063, 10103561797203808242963551733089380650158602487877615, 77945825293676181408672976232882122090692150760168754, 601650204783460711301941613776622583132985891293915924, 4646448509062121159722562569852347497247064465458079305, 35901893335975742534612042164712488849162069075336681817, 277540487929057257468795516123856655789972918072630205379, 2146554898624956315538175076161672923647007012237377335127, 16609572636316963357291795303330078654193837458411304000343, 128579021611847718448651777565251492556475293499151079761782, 995798813272858603993740102214699808881086729283973725218082, 7715387979802739330771880196371614850030556069887655153653961, 59803096517467324107712785575868397908948354270768002130462257, 463729329366670019130358191168919998905492228074526015149699123, 3597293647057761699714578575246066105743417261511339471770269860, 27916005172300866477299012777456255884210960404077907301319804898, 216716755688207625697449344862041037161605660579849783075825583710, 1683020863121268584929760693454448975890138578803111111059479307852, 13074960833170374482766343718894289779872399620064763803022793176762, 101611163644434062265452476354965731420766787849713049270869738397375, 789930650054132315159417619115781312343254848674689486719950535940598, 6142986042627580742200937069196663401703030894179936064470705998210065, 47786998183627826406969249625692969107210636501665775731036138085966231, 371857362657001383233528260471246345113879404701666944029956015840768433, 2894518291318192593070364759492241696934266834955056248607661876281869271, 22537537671974416980268319400867117544706056000852195829817690209689061874, 175535097217885024086578989415503109708056877322604970979534495458252116348, 1367558676758004950835520263266568078048922662393747590264159643194290013778, 10657362808362752444021609628422519322544988741194147910326659864285828519476, 83075443297350740656363016595279685732902655144591077296003928587463245883075, 647757073736658244764762261756230167642219930783775347524539863797147183719164, 5052028229455374220317441459538549429922459874079347021848803872029251866174705, 39412237022283491394032774873356492002980339946415787871393747527635997997987317, 307542965186921406022648867353025528900723203688396590235370872391870897489241615, 2400422317734796400749331915006710695034201490249866969252928206889970394887101565, 18740211335950451046782132227586384264016040944986705997855122400742602623502708625, 146340377438125986898360741783586034659233508555987092830028251584165945778161807975, 1143022207619980286590676838826864863738884993326212866898282903407710974951117072511, 8929846431452853724353260907856727502812411709169802418317965146129340011912527649499
Specification 1
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/24525/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[22,x,k[0]]
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[46,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[8,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[22,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],1,k[2]]*k[0]-F[20,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[21,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[21,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = (-F[28,x,k[0],1,k[2]]*k[2]+F[28,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[28,x,k[0],k[1],k[2]] = F[29,x,k[0],k[1]*k[2],k[2]]
F[29,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[2]]+F[30,x,k[0],k[2]]+F[32,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]
F[30,x,k[0],k[1]] = F[22,x,k[0]]*F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = (F[11,x,k[0],1]*k[0]-F[11,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[32,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[29,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = (F[35,x,k[0],k[2]]*k[0]-F[35,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[35,x,k[0],k[1]] = (-F[36,x,1,k[1]]*k[1]+F[36,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[36,x,k[0],k[1]] = F[1,x]+F[37,x,k[1]]+F[44,x,k[0],k[1]]+F[45,x,k[0],k[1]]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = F[39,x,1,k[0]]
F[39,x,k[0],k[1]] = F[1,x]+F[30,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]*F[8,x]
F[41,x,k[0],k[1]] = 1/(-1+k[0])*(F[39,x,k[0],k[1]]*k[0]-F[39,x,1,k[1]])
F[42,x,k[0],k[1]] = F[22,x,k[1]]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[28,x,k[0],1,k[1]]
F[44,x,k[0],k[1]] = F[22,x,k[1]]*F[36,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[46,x,k[0]*k[1],k[1]]
F[46,x,k[0],k[1]] = F[22,x,k[1]]*F[35,x,k[0],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
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_{46}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{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_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \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_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{12}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{25}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{28}\! \left(x , y_{0}, 1, y_{2}\right) y_{2}-F_{28}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right) y_{1}}{-y_{2}+y_{1}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{11}\! \left(x , y_{0}, 1\right) y_{0}-F_{11}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{35}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{35}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{35}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{36}\! \left(x , 1, y_{1}\right) y_{1}-y_{0} F_{36}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , 1, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, 1, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_22(x, k_0))
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_46(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_8(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_22(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, 1, k_2) + k_1*F_20(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_12(x, k_0, k_1) + k_2*F_12(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1, k_2), F_22(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_21(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_22(x, k_2)*F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), (-k_1*F_28(x, k_0, k_1/k_2, k_2) + k_2*F_28(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_28(x, k_0, k_1, k_2), F_29(x, k_0, k_1*k_2, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_2) + F_30(x, k_0, k_2) + F_32(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2))
Eq(F_30(x, k_0, k_1), F_22(x, k_0)*F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), (-k_0*F_11(x, k_0, 1) + k_1*F_11(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1, k_2), F_22(x, k_1)*F_29(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_22(x, k_2)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (-k_0*F_35(x, k_0, k_2) + k_1*F_35(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_35(x, k_0, k_1), (-k_0*F_36(x, k_0/k_1, k_1) + k_1*F_36(x, 1, k_1))/(-k_0 + k_1))
Eq(F_36(x, k_0, k_1), F_1(x) + F_37(x, k_1) + F_44(x, k_0, k_1) + F_45(x, k_0, k_1))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), F_39(x, 1, k_0))
Eq(F_39(x, k_0, k_1), F_1(x) + F_30(x, k_0, k_1) + F_40(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1)*F_8(x))
Eq(F_41(x, k_0, k_1), (k_0*F_39(x, k_0, k_1) - F_39(x, 1, k_1))/(k_0 - 1))
Eq(F_42(x, k_0, k_1), F_22(x, k_1)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_28(x, k_0, 1, k_1))
Eq(F_44(x, k_0, k_1), F_22(x, k_1)*F_36(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_46(x, k_0*k_1, k_1))
Eq(F_46(x, k_0, k_1), F_22(x, k_1)*F_35(x, k_0, k_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, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"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, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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, 3, 4, 2], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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, 3, 4, 2], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "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, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 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, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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, 3, 1, 4, 2], "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], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 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", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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, 3, 1, 4, 2], "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], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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, 3, 1, 4, 2], "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], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 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"tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[3, 0]]}], "indices": [0, 0, 0, 0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}, {"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, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [4, 1], [4, 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{"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [1, 1], [2, 1], [4, 1]], [[3, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 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, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25404/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[22,x,k[0]]
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[46,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[8,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[22,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],1,k[2]]*k[0]-F[20,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[21,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[21,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = (-F[28,x,k[0],1,k[2]]*k[2]+F[28,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[28,x,k[0],k[1],k[2]] = F[29,x,k[0],k[1]*k[2],k[2]]
F[29,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[2]]+F[30,x,k[0],k[2]]+F[32,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]
F[30,x,k[0],k[1]] = F[22,x,k[0]]*F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = (F[11,x,k[0],1]*k[0]-F[11,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[32,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[29,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = (F[35,x,k[0],k[2]]*k[0]-F[35,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[35,x,k[0],k[1]] = (-F[36,x,1,k[1]]*k[1]+F[36,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[36,x,k[0],k[1]] = F[1,x]+F[37,x,k[1]]+F[44,x,k[0],k[1]]+F[45,x,k[0],k[1]]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = F[39,x,1,k[0]]
F[39,x,k[0],k[1]] = F[1,x]+F[30,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]*F[8,x]
F[41,x,k[0],k[1]] = 1/(-1+k[0])*(F[39,x,k[0],k[1]]*k[0]-F[39,x,1,k[1]])
F[42,x,k[0],k[1]] = F[22,x,k[1]]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[28,x,k[0],1,k[1]]
F[44,x,k[0],k[1]] = F[22,x,k[1]]*F[36,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[46,x,k[0]*k[1],k[1]]
F[46,x,k[0],k[1]] = F[22,x,k[1]]*F[35,x,k[0],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
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_{46}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{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_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \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_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{12}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{25}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{28}\! \left(x , y_{0}, 1, y_{2}\right) y_{2}-F_{28}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right) y_{1}}{-y_{2}+y_{1}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{11}\! \left(x , y_{0}, 1\right) y_{0}-F_{11}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{35}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{35}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{35}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{36}\! \left(x , 1, y_{1}\right) y_{1}-y_{0} F_{36}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , 1, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, 1, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_22(x, k_0))
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_46(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_8(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_22(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, 1, k_2) + k_1*F_20(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_12(x, k_0, k_1) + k_2*F_12(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1, k_2), F_22(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_21(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_22(x, k_2)*F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), (-k_1*F_28(x, k_0, k_1/k_2, k_2) + k_2*F_28(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_28(x, k_0, k_1, k_2), F_29(x, k_0, k_1*k_2, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_2) + F_30(x, k_0, k_2) + F_32(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2))
Eq(F_30(x, k_0, k_1), F_22(x, k_0)*F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), (-k_0*F_11(x, k_0, 1) + k_1*F_11(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1, k_2), F_22(x, k_1)*F_29(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_22(x, k_2)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (-k_0*F_35(x, k_0, k_2) + k_1*F_35(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_35(x, k_0, k_1), (-k_0*F_36(x, k_0/k_1, k_1) + k_1*F_36(x, 1, k_1))/(-k_0 + k_1))
Eq(F_36(x, k_0, k_1), F_1(x) + F_37(x, k_1) + F_44(x, k_0, k_1) + F_45(x, k_0, k_1))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), F_39(x, 1, k_0))
Eq(F_39(x, k_0, k_1), F_1(x) + F_30(x, k_0, k_1) + F_40(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1)*F_8(x))
Eq(F_41(x, k_0, k_1), (k_0*F_39(x, k_0, k_1) - F_39(x, 1, k_1))/(k_0 - 1))
Eq(F_42(x, k_0, k_1), F_22(x, k_1)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_28(x, k_0, 1, k_1))
Eq(F_44(x, k_0, k_1), F_22(x, k_1)*F_36(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_46(x, k_0*k_1, k_1))
Eq(F_46(x, k_0, k_1), F_22(x, k_1)*F_35(x, k_0, k_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, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"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, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
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"tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[3, 0]]}], "indices": [0, 0, 0, 0], "direction": 3, "own_col": true, "own_row": true, "include_empty": true}}, {"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, 0]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [1, 1], [4, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [4, 1], [4, 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{"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[1, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}]}, {"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 0]]}]}]}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [1, 1], [2, 1], [4, 1]], [[3, 0]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "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, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 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, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_req_corrob_symmetries
Tree: http://www.permpal.com/tree/25915/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[9,x,k[0]]
F[6,x,k[0]] = F[7,x,k[0]]*F[8,x]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x] = x
F[9,x,k[0]] = F[10,x,k[0]]*F[22,x,k[0]]
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[46,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[8,x]
F[14,x,k[0],k[1]] = F[15,x,1,k[0],k[1]]
F[15,x,k[0],k[1],k[2]] = F[1,x]+F[16,x,k[0],k[1],k[2]]+F[18,x,k[0],k[1],k[2]]+F[23,x,k[0],k[1],k[2]]+F[26,x,k[0],k[1],k[2]]
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0],k[1],k[2]]*F[8,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[22,x,k[0]]
F[19,x,k[0],k[1],k[2]] = (F[20,x,k[0],1,k[2]]*k[0]-F[20,x,k[0],k[1]/k[0],k[2]]*k[1])/(-k[1]+k[0])
F[20,x,k[0],k[1],k[2]] = F[21,x,k[0],k[0]*k[1],k[2]]
F[21,x,k[0],k[1],k[2]] = (F[12,x,k[0],k[1]]*k[1]-F[12,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[22,x,k[0]] = k[0]*x
F[23,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[24,x,k[0],k[1],k[2]]
F[24,x,k[0],k[1],k[2]] = (-F[25,x,1,k[1],k[2]]*k[1]+F[25,x,k[0]/k[1],k[1],k[2]]*k[0])/(-k[1]+k[0])
F[25,x,k[0],k[1],k[2]] = F[21,x,k[0]*k[1],k[1],k[2]]
F[26,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[27,x,k[0],k[1],k[2]]
F[27,x,k[0],k[1],k[2]] = (-F[28,x,k[0],1,k[2]]*k[2]+F[28,x,k[0],k[1]/k[2],k[2]]*k[1])/(-k[2]+k[1])
F[28,x,k[0],k[1],k[2]] = F[29,x,k[0],k[1]*k[2],k[2]]
F[29,x,k[0],k[1],k[2]] = F[1,x]+F[13,x,k[0],k[2]]+F[30,x,k[0],k[2]]+F[32,x,k[0],k[1],k[2]]+F[33,x,k[0],k[1],k[2]]
F[30,x,k[0],k[1]] = F[22,x,k[0]]*F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = (F[11,x,k[0],1]*k[0]-F[11,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[32,x,k[0],k[1],k[2]] = F[22,x,k[1]]*F[29,x,k[0],k[1],k[2]]
F[33,x,k[0],k[1],k[2]] = F[22,x,k[2]]*F[34,x,k[0],k[1],k[2]]
F[34,x,k[0],k[1],k[2]] = (F[35,x,k[0],k[2]]*k[0]-F[35,x,k[1],k[2]]*k[1])/(-k[1]+k[0])
F[35,x,k[0],k[1]] = (-F[36,x,1,k[1]]*k[1]+F[36,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[36,x,k[0],k[1]] = F[1,x]+F[37,x,k[1]]+F[44,x,k[0],k[1]]+F[45,x,k[0],k[1]]
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = F[39,x,1,k[0]]
F[39,x,k[0],k[1]] = F[1,x]+F[30,x,k[0],k[1]]+F[40,x,k[0],k[1]]+F[42,x,k[0],k[1]]
F[40,x,k[0],k[1]] = F[41,x,k[0],k[1]]*F[8,x]
F[41,x,k[0],k[1]] = 1/(-1+k[0])*(F[39,x,k[0],k[1]]*k[0]-F[39,x,1,k[1]])
F[42,x,k[0],k[1]] = F[22,x,k[1]]*F[43,x,k[0],k[1]]
F[43,x,k[0],k[1]] = F[28,x,k[0],1,k[1]]
F[44,x,k[0],k[1]] = F[22,x,k[1]]*F[36,x,k[0],k[1]]
F[45,x,k[0],k[1]] = F[46,x,k[0]*k[1],k[1]]
F[46,x,k[0],k[1]] = F[22,x,k[1]]*F[35,x,k[0],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)
F_{6}\! \left(x , y_{0}\right) = F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{7}\! \left(x , y_{0}\right) = -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}
F_{8}\! \left(x \right) = x
F_{9}\! \left(x , y_{0}\right) = F_{10}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)
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_{46}\! \left(x , y_{0}, y_{1}\right)
F_{13}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{14}\! \left(x , y_{0}, y_{1}\right) = F_{15}\! \left(x , 1, y_{0}, y_{1}\right)
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{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_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{8}\! \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_{22}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{20}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{20}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{12}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}
F_{22}\! \left(x , y_{0}\right) = y_{0} x
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{25}\! \left(x , 1, y_{1}, y_{2}\right) y_{1}-F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right) y_{0}}{-y_{1}+y_{0}}
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{21}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) = -\frac{F_{28}\! \left(x , y_{0}, 1, y_{2}\right) y_{2}-F_{28}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right) y_{1}}{-y_{2}+y_{1}}
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{29}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{2}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{30}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}, y_{1}\right)
F_{31}\! \left(x , y_{0}, y_{1}\right) = \frac{F_{11}\! \left(x , y_{0}, 1\right) y_{0}-F_{11}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{1}\right) F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{22}\! \left(x , y_{2}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{F_{35}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{35}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}
F_{35}\! \left(x , y_{0}, y_{1}\right) = -\frac{F_{36}\! \left(x , 1, y_{1}\right) y_{1}-y_{0} F_{36}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}
F_{36}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)
F_{37}\! \left(x , y_{0}\right) = F_{38}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y_{0}\right) = F_{39}\! \left(x , 1, y_{0}\right)
F_{39}\! \left(x , y_{0}, y_{1}\right) = F_{1}\! \left(x \right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)
F_{40}\! \left(x , y_{0}, y_{1}\right) = F_{41}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)
F_{41}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{42}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)
F_{43}\! \left(x , y_{0}, y_{1}\right) = F_{28}\! \left(x , y_{0}, 1, y_{1}\right)
F_{44}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{36}\! \left(x , y_{0}, y_{1}\right)
F_{45}\! \left(x , y_{0}, y_{1}\right) = F_{46}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{46}\! \left(x , y_{0}, y_{1}\right) = F_{22}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}, y_{1}\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_9(x, k_0))
Eq(F_6(x, k_0), F_7(x, k_0)*F_8(x))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x), x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_22(x, k_0))
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_46(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_8(x))
Eq(F_14(x, k_0, k_1), F_15(x, 1, k_0, k_1))
Eq(F_15(x, k_0, k_1, k_2), F_1(x) + F_16(x, k_0, k_1, k_2) + F_18(x, k_0, k_1, k_2) + F_23(x, k_0, k_1, k_2) + F_26(x, k_0, k_1, k_2))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0, k_1, k_2)*F_8(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_22(x, k_0))
Eq(F_19(x, k_0, k_1, k_2), (-k_0*F_20(x, k_0, 1, k_2) + k_1*F_20(x, k_0, k_1/k_0, k_2))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1, k_2), F_21(x, k_0, k_0*k_1, k_2))
Eq(F_21(x, k_0, k_1, k_2), (-k_1*F_12(x, k_0, k_1) + k_2*F_12(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0, k_1, k_2), F_22(x, k_1)*F_24(x, k_0, k_1, k_2))
Eq(F_24(x, k_0, k_1, k_2), (-k_0*F_25(x, k_0/k_1, k_1, k_2) + k_1*F_25(x, 1, k_1, k_2))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1, k_2), F_21(x, k_0*k_1, k_1, k_2))
Eq(F_26(x, k_0, k_1, k_2), F_22(x, k_2)*F_27(x, k_0, k_1, k_2))
Eq(F_27(x, k_0, k_1, k_2), (-k_1*F_28(x, k_0, k_1/k_2, k_2) + k_2*F_28(x, k_0, 1, k_2))/(-k_1 + k_2))
Eq(F_28(x, k_0, k_1, k_2), F_29(x, k_0, k_1*k_2, k_2))
Eq(F_29(x, k_0, k_1, k_2), F_1(x) + F_13(x, k_0, k_2) + F_30(x, k_0, k_2) + F_32(x, k_0, k_1, k_2) + F_33(x, k_0, k_1, k_2))
Eq(F_30(x, k_0, k_1), F_22(x, k_0)*F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), (-k_0*F_11(x, k_0, 1) + k_1*F_11(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_32(x, k_0, k_1, k_2), F_22(x, k_1)*F_29(x, k_0, k_1, k_2))
Eq(F_33(x, k_0, k_1, k_2), F_22(x, k_2)*F_34(x, k_0, k_1, k_2))
Eq(F_34(x, k_0, k_1, k_2), (-k_0*F_35(x, k_0, k_2) + k_1*F_35(x, k_1, k_2))/(-k_0 + k_1))
Eq(F_35(x, k_0, k_1), (-k_0*F_36(x, k_0/k_1, k_1) + k_1*F_36(x, 1, k_1))/(-k_0 + k_1))
Eq(F_36(x, k_0, k_1), F_1(x) + F_37(x, k_1) + F_44(x, k_0, k_1) + F_45(x, k_0, k_1))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), F_39(x, 1, k_0))
Eq(F_39(x, k_0, k_1), F_1(x) + F_30(x, k_0, k_1) + F_40(x, k_0, k_1) + F_42(x, k_0, k_1))
Eq(F_40(x, k_0, k_1), F_41(x, k_0, k_1)*F_8(x))
Eq(F_41(x, k_0, k_1), (k_0*F_39(x, k_0, k_1) - F_39(x, 1, k_1))/(k_0 - 1))
Eq(F_42(x, k_0, k_1), F_22(x, k_1)*F_43(x, k_0, k_1))
Eq(F_43(x, k_0, k_1), F_28(x, k_0, 1, k_1))
Eq(F_44(x, k_0, k_1), F_22(x, k_1)*F_36(x, k_0, k_1))
Eq(F_45(x, k_0, k_1), F_46(x, k_0*k_1, k_1))
Eq(F_46(x, k_0, k_1), F_22(x, k_1)*F_35(x, k_0, k_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, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]], "symmetry": true}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"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, 3, 4, 2], [0, 3, 1, 4, 2], [0, 3, 4, 1, 2], [3, 0, 1, 4, 2], [3, 0, 4, 1, 2]]}], "iterative": false}
Specification JSON:
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