02341_03142_03241_04132_04231_12340_13240_14230

Counting sequence:
1, 1, 2, 6, 24, 112, 562, 2920, 15468, 83013, 450036, 2460313, 13546668, 75047600, 417966986, 2338559651, 13137362636, 74065406788, 418888571234, 2375818703553, 13509448281356, 76995811160413, 439756108433736, 2516482915442732, 14425979316484796, 82833492200575271, 476346594352119990, 2743150027311582649, 15817705032186863652, 91320261446673083638, 527821010015022974318, 3054016674576372317875, 17688602972429586313776, 102548133358953436503978, 595046601189340406543892, 3455747814245165950092157, 20085448409485819249156852, 116829246990918181682394913, 680041930391926404244202806, 3961125735404818155220964768, 23087997139882991630932404600, 134655925437955856839848992345, 785821761450828801739818901066, 4588498910539656488230241553397, 26807393804327486385047571138308, 156698920407246389527804172910100, 916422116130518201536525638576964, 5362095445699944789054240456361171, 31388802224928175712611228636530168, 183826645159070339600210517879220005, 1077031563260804934520863082134101114, 6312883904770959341961132646076232074, 37016905434230328859744224487327445056, 217139702081000276617589631061938062681, 1274205282758422461446026708656931409918, 7479888415439821391953601912831504290899, 43923930217383359458831698451887060432976, 258019594300643162533609002114972442643882, 1516159584707412175325632281598148250402060, 8911963862143578044690985639855179151665455, 52400320867695173077408374875433590007519252, 308192780076572645383612534541157414547625825, 1813155714650880996400719968277371427900758518, 10670092756585184502239715166876141158501653646, 62808471079558598192244470299219622933762311248, 369812703388138589188120803044858345145012419240, 2177989563882977858868435927736190887180953355062, 12830307195743265614606555025902629498276295084524, 75600150968978810025710364056308888950102664757600, 445563695407341229855820723945335438486831163025296, 2626610965212931177576996671195216953844986005641064, 15487379280596451716461235923785651667331071541557614, 91338494449355809045977013669799868853747899962633884, 538791955130837246282248040219362882871366283297843420, 3178903863705102812498467593837530593705762101552145594, 18759467679398694815650134339101152092063746185702104560, 110725671360233061846606290950223889858166664251627148008, 653670338750066523538770798463950372108530026233960097594, 3859667607834172745874884090419119771042246834360682148642, 22793960868382029407793071765537272989661012903109347669042, 134637681211049090064011165393748378274490997314681981301964, 795405537645587507360076507025493320036173344686780747633968, 4699850577355682332354531048111005579995151878634777613562104, 27774822698734057862534014046655470335233293016510604056237356, 164168092215131259128435822791161592189895565041203065732318824, 970498524293419510869193586733085686551538479225560264338297700, 5738101040659914416966011559766965574972898759082210390913760454, 33931827321890855332086523935598344211928041671884841182460919618, 200683033753413731255335471946326626884585118715442920630043682664, 1187072030241070768006756718832500131710978506339522028068705034100, 7022717317612661682657037274704631630246179345695262732306316183782, 41552172876661124376439486811521514851209901746556318047146676106734, 245890360411665239017038637415823468002080220441862525288610300343120, 1455282455727842594253103638770477440658979291050815594946234510580812, 8614100992578699774904158069474682937064599485216870468361697393515664, 50995092511193882221566509547877878787810913116105545721455755434123016, 301926675803158666094392032509709294237900419398909077383207919081100300, 1787838201813191816519952890584687809131226068036183645808758692313571910, 10587844298437763157222889635160063612523057040347102680643164318865231346, 62710244556638698046110690369278197036739347512995378233483794956205561540, 371466877867450723871649478770571583888734397887940909172026956929193490120

Generating function in Maple syntax:
(-(2*x-1)^(5/2)*x*(x^4-10*x^3+13*x^2-6*x+1)*(-1+6*x)^(1/2)+70*x^8-640*x^7+1868*x^6-2603*x^5+2020*x^4-923*x^3+246*x^2-35*x+2)/(214*x^8-1268*x^7+2924*x^6-3520*x^5+2470*x^4-1048*x^3+264*x^2-36*x+2)

Generating function in latex syntax:
\frac{-\left(2 x -1\right)^{\frac{5}{2}} x \left(x^{4}-10 x^{3}+13 x^{2}-6 x +1\right) \sqrt{-1+6 x}+70 x^{8}-640 x^{7}+1868 x^{6}-2603 x^{5}+2020 x^{4}-923 x^{3}+246 x^{2}-35 x +2}{214 x^{8}-1268 x^{7}+2924 x^{6}-3520 x^{5}+2470 x^{4}-1048 x^{3}+264 x^{2}-36 x +2}

Generating function in sympy syntax:
(70*x**8 - 640*x**7 + 1868*x**6 - 2603*x**5 + 2020*x**4 - 923*x**3 + 246*x**2 - x*(2*x - 1)**(5/2)*sqrt(6*x - 1)*(x**4 - 10*x**3 + 13*x**2 - 6*x + 1) - 35*x + 2)/(214*x**8 - 1268*x**7 + 2924*x**6 - 3520*x**5 + 2470*x**4 - 1048*x**3 + 264*x**2 - 36*x + 2)

Implicit equation for the generating function in Maple syntax:
(107*x^8-634*x^7+1462*x^6-1760*x^5+1235*x^4-524*x^3+132*x^2-18*x+1)*F(x)^2+(-70*x^8+640*x^7-1868*x^6+2603*x^5-2020*x^4+923*x^3-246*x^2+35*x-2)*F(x)+11*x^8-134*x^7+542*x^6-915*x^5+804*x^4-401*x^3+114*x^2-17*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(107 x^{8}-634 x^{7}+1462 x^{6}-1760 x^{5}+1235 x^{4}-524 x^{3}+132 x^{2}-18 x +1\right) F \! \left(x \right)^{2}+\left(-70 x^{8}+640 x^{7}-1868 x^{6}+2603 x^{5}-2020 x^{4}+923 x^{3}-246 x^{2}+35 x -2\right) F \! \left(x \right)+11 x^{8}-134 x^{7}+542 x^{6}-915 x^{5}+804 x^{4}-401 x^{3}+114 x^{2}-17 x +1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 562
a(7) = 2920
a(8) = 15468
a(9) = 83013
a(10) = 450036
a(11) = 2460313
a(12) = 13546668
a(13) = 75047600
a(n+14) = -1284*n/(13+n)*a(n)+4*(97+8*n)/(13+n)*a(13+n)+8*(3531+2663*n)/(13+n)*a(n+1)-43*(6453+2885*n)/(13+n)*a(n+2)+4*(292491+94604*n)/(13+n)*a(n+3)-3*(939291+237443*n)/(13+n)*a(n+4)+4*(1090187+225300*n)/(13+n)*a(n+5)-12*(384664+67035*n)/(13+n)*a(n+6)+4*(865421+130148*n)/(13+n)*a(n+7)-(1871721+247321*n)/(13+n)*a(n+8)+4*(183049+21562*n)/(13+n)*a(n+9)-4*(51265+5448*n)/(13+n)*a(n+10)+4*(9995+968*n)/(13+n)*a(n+11)-(5133+457*n)/(13+n)*a(n+12), n >= 14

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 562
a(7) = 2920
a(8) = 15468
a(9) = 83013
a(10) = 450036
a(11) = 2460313
a(12) = 13546668
a(13) = 75047600
a{\left(n + 14 \right)} = - \frac{1284 n a{\left(n \right)}}{n + 13} + \frac{4 \left(8 n + 97\right) a{\left(n + 13 \right)}}{n + 13} - \frac{\left(457 n + 5133\right) a{\left(n + 12 \right)}}{n + 13} + \frac{4 \left(968 n + 9995\right) a{\left(n + 11 \right)}}{n + 13} + \frac{8 \left(2663 n + 3531\right) a{\left(n + 1 \right)}}{n + 13} - \frac{43 \left(2885 n + 6453\right) a{\left(n + 2 \right)}}{n + 13} - \frac{4 \left(5448 n + 51265\right) a{\left(n + 10 \right)}}{n + 13} + \frac{4 \left(21562 n + 183049\right) a{\left(n + 9 \right)}}{n + 13} - \frac{12 \left(67035 n + 384664\right) a{\left(n + 6 \right)}}{n + 13} + \frac{4 \left(94604 n + 292491\right) a{\left(n + 3 \right)}}{n + 13} + \frac{4 \left(130148 n + 865421\right) a{\left(n + 7 \right)}}{n + 13} + \frac{4 \left(225300 n + 1090187\right) a{\left(n + 5 \right)}}{n + 13} - \frac{3 \left(237443 n + 939291\right) a{\left(n + 4 \right)}}{n + 13} - \frac{\left(247321 n + 1871721\right) a{\left(n + 8 \right)}}{n + 13}, \quad n \geq 14

Specification 1
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25064/
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[41,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[41,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[27,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[18,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[19,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x]+F[22,x,k[0]]+F[26,x,k[0]]
F[21,x] = 0
F[22,x,k[0]] = F[18,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = F[20,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[14,x,k[0]]*F[18,x,k[0]]
F[26,x,k[0]] = F[18,x,k[0]]*F[19,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[42,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[35,x,k[0]]
F[29,x,k[0]] = F[2,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[14,x,k[0]]*F[18,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[29,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[10,x,k[0]]*F[2,x]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[41,x]
F[37,x,k[0]] = F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[4,x]
F[39,x,k[0]] = (F[11,x,k[0]]-F[11,x,1])/(-1+k[0])
F[40,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[41,x] = x
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[41,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[55,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[39,x,k[0]]*F[47,x]
F[47,x] = F[4,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[2,x]*F[50,x]*F[52,x]
F[50,x] = F[1,x]+F[51,x]
F[51,x] = F[41,x]*F[50,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[50,x]*F[52,x]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[41,x]*F[57,x,k[0]]
F[57,x,k[0]] = 1/(-1+k[0])*(F[58,x,k[0]]*k[0]-F[58,x,1])
F[59,x,k[0]] = F[41,x]*F[58,x,k[0]]
F[59,x,k[0]] = F[27,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{39}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x \right) = x
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{2}\! \left(x \right) F_{50}\! \left(x \right) F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{41}\! \left(x \right) F_{50}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{50}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -\frac{-y F_{58}\! \left(x , y\right)+F_{58}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{27}\! \left(x , y\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_41(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_41(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_27(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_18(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_19(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x) + F_22(x, k_0) + F_26(x, k_0))
Eq(F_21(x), 0)
Eq(F_22(x, k_0), F_18(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), F_20(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_14(x, k_0)*F_18(x, k_0))
Eq(F_26(x, k_0), F_18(x, k_0)*F_19(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_42(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_35(x, k_0))
Eq(F_29(x, k_0), F_2(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_14(x, k_0)*F_18(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_29(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_10(x, k_0)*F_2(x))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_41(x))
Eq(F_37(x, k_0), F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_4(x))
Eq(F_39(x, k_0), -F_11(x, k_0) + (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_41(x), x)
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_41(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_55(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_39(x, k_0)*F_47(x))
Eq(F_47(x), F_4(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_2(x)*F_50(x)*F_52(x))
Eq(F_50(x), F_1(x) + F_51(x))
Eq(F_51(x), F_41(x)*F_50(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_50(x)*F_52(x))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_41(x)*F_57(x, k_0))
Eq(F_57(x, k_0), (k_0*F_58(x, k_0) - F_58(x, 1))/(k_0 - 1))
Eq(F_59(x, k_0), F_41(x)*F_58(x, k_0))
Eq(F_59(x, k_0), F_27(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.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.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "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": "FusableRowAndColumnPlacementFactory", "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": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0], "pos": [[4, 4]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[5, 2]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [2, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [2, 3]]}, {"patt": [0, 1], "pos": [[3, 4], [3, 4]]}, {"patt": [0, 1], "pos": [[4, 2], [4, 2]]}, {"patt": [1, 0], "pos": [[4, 2], [4, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [3, 3], [3, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [3, 3], [3, 4]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 3], [3, 4]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [3, 3], [3, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [5, 3], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [5, 4], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [5, 4], [5, 4]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [5, 3], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [5, 4], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [5, 4], [5, 4]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 4], [5, 4], [5, 4]]}, {"patt": [0, 2, 1], "pos": [[5, 4], [5, 4], [5, 4]]}, {"patt": [1, 2, 0], "pos": [[3, 4], [5, 4], [5, 3]]}, {"patt": [1, 2, 0], "pos": [[3, 4], [5, 4], [5, 4]]}, {"patt": [1, 2, 0], "pos": [[5, 4], [5, 4], [5, 3]]}, {"patt": [1, 2, 0], "pos": [[5, 4], [5, 4], [5, 4]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 3], [3, 3], [3, 3], [3, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [3, 3], [5, 4], [5, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [5, 3], [5, 4], [5, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [3, 3], [5, 4], [5, 4]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [5, 3], [5, 4], [5, 4]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 3], [3, 3], [3, 3], [3, 4]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 3], [3, 3], [3, 3], [3, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 3], [3, 4], [3, 3], [3, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 3], [3, 4], [3, 3], [3, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [1, 1], [1, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[5, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 1], [1, 1], [1, 1], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[5, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[5, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[5, 4], [5, 3], [5, 3], [5, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[5, 4], [5, 3], [5, 4], [5, 3]]}, {"patt": [3, 0, 2, 1], "pos": [[5, 4], [5, 3], [5, 4], [5, 4]]}, {"patt": [3, 1, 2, 0], "pos": [[5, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [3, 1, 2, 0], "pos": [[5, 4], [5, 3], [5, 3], [5, 3]]}, {"patt": [3, 1, 2, 0], "pos": [[5, 4], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 3], [3, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 3], [3, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 3], [3, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 3], [3, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 3], [3, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 3], [3, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 3], [3, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[3, 3], [3, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 3], [3, 3], [3, 3], [5, 3], [5, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 3], [3, 3], [3, 3], [5, 4], [5, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 3], [3, 3], [5, 3], [5, 3], [5, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 3], [3, 3], [5, 3], [5, 4], [5, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, 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[{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "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, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}]}], "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": true}}}]}, {"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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25210/
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[41,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[41,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = F[27,x,k[0]]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[4,x]
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[18,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]+F[19,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[15,x,k[0]]*F[18,x,k[0]]
F[18,x,k[0]] = k[0]*x
F[19,x,k[0]] = F[16,x,k[0]]+F[20,x,k[0]]
F[20,x,k[0]] = F[21,x]+F[22,x,k[0]]+F[26,x,k[0]]
F[21,x] = 0
F[22,x,k[0]] = F[18,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = F[20,x,k[0]]+F[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[14,x,k[0]]*F[18,x,k[0]]
F[26,x,k[0]] = F[18,x,k[0]]*F[19,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]+F[42,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[35,x,k[0]]
F[29,x,k[0]] = F[2,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[14,x,k[0]]*F[18,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = F[29,x,k[0]]+F[33,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]+F[35,x,k[0]]
F[34,x,k[0]] = F[10,x,k[0]]*F[2,x]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]*F[41,x]
F[37,x,k[0]] = F[38,x,k[0]]+F[40,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[4,x]
F[39,x,k[0]] = (F[11,x,k[0]]-F[11,x,1])/(-1+k[0])
F[40,x,k[0]] = 1/(-1+k[0])*(F[27,x,k[0]]*k[0]-F[27,x,1])
F[41,x] = x
F[42,x,k[0]] = F[43,x,k[0]]
F[43,x,k[0]] = F[41,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]+F[55,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[46,x,k[0]] = F[39,x,k[0]]*F[47,x]
F[47,x] = F[4,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[2,x]*F[50,x]*F[52,x]
F[50,x] = F[1,x]+F[51,x]
F[51,x] = F[41,x]*F[50,x]
F[52,x] = F[1,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[41,x]*F[50,x]*F[52,x]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[41,x]*F[57,x,k[0]]
F[57,x,k[0]] = 1/(-1+k[0])*(F[58,x,k[0]]*k[0]-F[58,x,1])
F[59,x,k[0]] = F[41,x]*F[58,x,k[0]]
F[59,x,k[0]] = F[27,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{41}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{19}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y x
F_{19}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{18}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right) F_{41}\! \left(x \right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{39}\! \left(x , y\right) = -\frac{-F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}
F_{41}\! \left(x \right) = x
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{2}\! \left(x \right) F_{50}\! \left(x \right) F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{1}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{41}\! \left(x \right) F_{50}\! \left(x \right)
F_{52}\! \left(x \right) = F_{1}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right) F_{50}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = -\frac{-y F_{58}\! \left(x , y\right)+F_{58}\! \left(x , 1\right)}{-1+y}
F_{59}\! \left(x , y\right) = F_{41}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{27}\! \left(x , y\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_41(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_41(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), F_27(x, k_0) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_4(x))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_18(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0) + F_19(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_15(x, k_0)*F_18(x, k_0))
Eq(F_18(x, k_0), k_0*x)
Eq(F_19(x, k_0), F_16(x, k_0) + F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x) + F_22(x, k_0) + F_26(x, k_0))
Eq(F_21(x), 0)
Eq(F_22(x, k_0), F_18(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), F_20(x, k_0) + F_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_14(x, k_0)*F_18(x, k_0))
Eq(F_26(x, k_0), F_18(x, k_0)*F_19(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0) + F_42(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_35(x, k_0))
Eq(F_29(x, k_0), F_2(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_14(x, k_0)*F_18(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), F_29(x, k_0) + F_33(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0) + F_35(x, k_0))
Eq(F_34(x, k_0), F_10(x, k_0)*F_2(x))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0)*F_41(x))
Eq(F_37(x, k_0), F_38(x, k_0) + F_40(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_4(x))
Eq(F_39(x, k_0), -F_11(x, k_0) + (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), (k_0*F_27(x, k_0) - F_27(x, 1))/(k_0 - 1))
Eq(F_41(x), x)
Eq(F_42(x, k_0), F_43(x, k_0))
Eq(F_43(x, k_0), F_41(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0) + F_55(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_46(x, k_0), F_39(x, k_0)*F_47(x))
Eq(F_47(x), F_4(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_2(x)*F_50(x)*F_52(x))
Eq(F_50(x), F_1(x) + F_51(x))
Eq(F_51(x), F_41(x)*F_50(x))
Eq(F_52(x), F_1(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_41(x)*F_50(x)*F_52(x))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_41(x)*F_57(x, k_0))
Eq(F_57(x, k_0), (k_0*F_58(x, k_0) - F_58(x, 1))/(k_0 - 1))
Eq(F_59(x, k_0), F_41(x)*F_58(x, k_0))
Eq(F_59(x, k_0), F_27(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.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.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "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": "FusableRowAndColumnPlacementFactory", "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": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "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", 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{"patt": [0, 1, 2], "pos": [[0, 3], [3, 3], [3, 4]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [3, 3], [3, 4]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [3, 3], [3, 4]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 3], [3, 3], [3, 4]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [5, 3], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [5, 4], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [5, 4], [5, 4]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [5, 3], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [5, 4], [5, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [5, 4], [5, 4]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": 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