03214_03241_04213_04231_13204_13240_14203_14230_30214_30241_31204_31240_40213_40231_41203_41230_021435_021453_031425_031452_201435_201453_254103_254130_301425_301452_354102_354120_524103_524130_534102_534120
Counting sequence:
1, 1, 2, 6, 24, 104, 448, 1888, 7808, 31872, 129024, 519680, 2086912, 8366080, 33505280, 134111232, 536641536, 2146992128, 8588886016, 34357510144, 137434234880, 549745852416, 2199002284032, 8796048982016, 35184279814144, 140737295417344, 562949550768128, 2251798974824448, 9007197509910528, 36028793395085312, 144115180559663104, 576460736734167040, 2305842977001439232, 9223371970282782720, 36893488009980149760, 147573952306208571392, 590295809774590099456, 2361183240232231763968, 9444732963265389264896, 37778931857871920431104, 151115727441383286374400, 604462909785874110611456, 2417851639185277884301312, 9671406556826873444171776, 38685626227483415637131264, 154742504910294302362435584, 618970019641916081263607808, 2475880078569177253054251008, 9903520314279805236960821248, 39614081257125554134819274752, 158456325028515164388205789184, 633825300114087116200633958400, 2535301200456402507998064279552, 10141204801825720370183127695360, 40564819207303106660713879306240, 162259276829212886010017509015552, 649037107316852480788792529125376, 2596148429267411832681412121591808, 10384593717069651221835726534475776, 41538374868278612813678250309976064, 166153499473114467395614065735761920, 664613997892457902440719144238186496, 2658455991569831676632323844149870592, 10633823966279326842574032920207425536, 42535295865117307646997292786472976384, 170141183460469231150614865394033229824, 680564733841876925746157594146125119488, 2722258935367507705308920129871903981568, 10889035741470030825958047002357261139968, 43556142965880123313424494927758011400192, 174224571863520493273177741452869332107264, 696898287454081973132260785105510607093760, 2787593149816327892609323370630826397007872, 11150372599265311570600215126182308347904000, 44601490397061246282731426158530108556574720, 178405961588244985131596280674687923846643712, 713623846352979940527745164245818153208119296, 2854495385411919762113738519009268485637275648, 11417981541647679048460545357952791602482118656, 45671926166590716193853515111370053558441345024, 182687704666362864775437030036052892188084797440, 730750818665451459101794663788266731975565377536, 2923003274661805836407272951366996868977888591872, 11692013098647223345629282815747486587321157943296, 46768052394588893382517518119252223030620537749504, 187072209578355573530070855860940002402187360600064, 748288838313422294120285009554435344002226656903168, 2993155353253689176481143249124718272463994647216128, 11972621413014756705924579495684079338102421809266688, 47890485652059026823698331135849234759575108040261632, 191561942608236107294793351159107783673976342492217344, 766247770432944429179173458486822843609947328080773120, 3064991081731777716716693942886014831553253503446024192, 12259964326927110866866775991897386319010702945828208640, 49039857307708443467467104413247959418779710746997555200, 196159429230833773869868418554212186274875683114552655872, 784637716923335095479473676039096482927582497109721481216, 3138550867693340381917894707840495488623621686538679615488, 12554203470773361527671578838809429230835334479947849793536, 50216813883093446110686315370291067801051562062564749737984, 200867255532373784442745261511587885609683753886179875880960
Generating function in Maple syntax:
(3*x-1)*(2*x^2-4*x+1)/(4*x-1)/(2*x-1)^2
Generating function in latex syntax:
\frac{\left(3 x -1\right) \left(2 x^{2}-4 x +1\right)}{\left(4 x -1\right) \left(2 x -1\right)^{2}}
Generating function in sympy syntax:
(3*x - 1)*(2*x**2 - 4*x + 1)/((2*x - 1)**2*(4*x - 1))
Implicit equation for the generating function in Maple syntax:
(4*x-1)*(2*x-1)^2*F(x)-(3*x-1)*(2*x^2-4*x+1) = 0
Implicit equation for the generating function in latex syntax:
\left(4 x -1\right) \left(2 x -1\right)^{2} F \! \left(x \right)-\left(3 x -1\right) \left(2 x^{2}-4 x +1\right) = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/8*4^n-1/4*2^n*n+2^(-1+n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{4^{n}}{8}-\frac{2^{n} n}{4}+2^{-1+n} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = 16*a(n)-20*a(n+1)+8*a(n+2), n >= 4
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(n +3\right) = 16 a \! \left(n \right)-20 a \! \left(n +1\right)+8 a \! \left(n +2\right), \quad n \geq 4
Specification 1
Strategy pack name: col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24341/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[109,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[106,x]+F[108,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[104,x,k[0]]+F[12,x,k[0]]
F[10,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[11,x] = x
F[12,x,k[0]] = F[13,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[74,x,k[0]]+F[93,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[33,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[20,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[21,x,k[0]]+F[24,x,k[0]]
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[19,x,k[0]]*F[21,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[28,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]+F[32,x,k[0]]
F[29,x] = 0
F[30,x,k[0]] = F[19,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[22,x,k[0]]+F[28,x,k[0]]
F[32,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[33,x,k[0]] = F[34,x]+F[48,x,k[0]]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[11,x]*F[37,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]
F[42,x] = F[11,x]*F[43,x]
F[43,x] = F[1,x]+F[41,x]
F[44,x] = F[29,x]+F[45,x]+F[47,x]
F[45,x] = F[11,x]*F[46,x]
F[46,x] = F[38,x]+F[44,x]
F[47,x] = F[11,x]*F[40,x]
F[48,x,k[0]] = F[29,x]+F[49,x,k[0]]+F[64,x,k[0]]
F[49,x,k[0]] = F[11,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[54,x,k[0]]
F[51,x,k[0]] = F[22,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[11,x]*F[51,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[60,x,k[0]]
F[55,x,k[0]] = F[29,x]+F[56,x,k[0]]+F[58,x,k[0]]
F[56,x,k[0]] = F[11,x]*F[57,x,k[0]]
F[57,x,k[0]] = F[22,x,k[0]]+F[55,x,k[0]]
F[58,x,k[0]] = F[19,x,k[0]]*F[59,x,k[0]]
F[59,x,k[0]] = F[41,x]+F[55,x,k[0]]
F[60,x,k[0]] = 2*F[29,x]+F[61,x,k[0]]+F[63,x,k[0]]
F[61,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[52,x,k[0]]+F[60,x,k[0]]
F[63,x,k[0]] = F[11,x]*F[54,x,k[0]]
F[64,x,k[0]] = F[19,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]+F[70,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[19,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[41,x]+F[67,x,k[0]]
F[70,x,k[0]] = 2*F[29,x]+F[71,x,k[0]]+F[73,x,k[0]]
F[71,x,k[0]] = F[19,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[55,x,k[0]]+F[70,x,k[0]]
F[73,x,k[0]] = F[19,x,k[0]]*F[66,x,k[0]]
F[74,x,k[0]] = F[19,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[81,x,k[0]]
F[76,x,k[0]] = F[37,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[22,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[19,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[38,x]+F[78,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[87,x,k[0]]
F[82,x,k[0]] = F[25,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[29,x]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[19,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[38,x]+F[83,x,k[0]]
F[86,x,k[0]] = F[11,x]*F[82,x,k[0]]
F[87,x,k[0]] = F[28,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = 2*F[29,x]+F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[19,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[78,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = F[19,x,k[0]]*F[92,x,k[0]]
F[92,x,k[0]] = F[83,x,k[0]]+F[88,x,k[0]]
F[93,x,k[0]] = F[11,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[36,x]+F[95,x,k[0]]
F[95,x,k[0]] = F[82,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[100,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[11,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[25,x,k[0]]+F[97,x,k[0]]
F[100,x,k[0]] = 2*F[29,x]+F[101,x,k[0]]+F[103,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[11,x]
F[102,x,k[0]] = F[100,x,k[0]]+F[83,x,k[0]]
F[103,x,k[0]] = F[11,x]*F[96,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[11,x]
F[105,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[106,x] = F[107,x]
F[107,x] = F[13,x,1]
F[108,x] = F[11,x]*F[7,x]
F[109,x] = F[11,x]*F[5,x]
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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{109}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{106}\! \left(x \right)+F_{108}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \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) = \frac{F_{9}\! \left(x , y\right) y -F_{9}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \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_{74}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{29}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{56}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{37}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{105}\! \left(x , y\right) = \frac{F_{9}\! \left(x , y\right) y -F_{9}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{108}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{109}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_109(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_106(x) + F_108(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_104(x, k_0) + F_12(x, k_0))
Eq(F_10(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(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) + F_74(x, k_0) + F_93(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_33(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_20(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_21(x, k_0) + F_24(x, k_0))
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_19(x, k_0)*F_21(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_28(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_19(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0) + F_32(x, k_0))
Eq(F_29(x), 0)
Eq(F_30(x, k_0), F_19(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_22(x, k_0) + F_28(x, k_0))
Eq(F_32(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_33(x, k_0), F_34(x) + F_48(x, k_0))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_11(x)*F_37(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_11(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_41(x))
Eq(F_44(x), F_29(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_11(x)*F_46(x))
Eq(F_46(x), F_38(x) + F_44(x))
Eq(F_47(x), F_11(x)*F_40(x))
Eq(F_48(x, k_0), F_29(x) + F_49(x, k_0) + F_64(x, k_0))
Eq(F_49(x, k_0), F_11(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_54(x, k_0))
Eq(F_51(x, k_0), F_22(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_11(x)*F_51(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_60(x, k_0))
Eq(F_55(x, k_0), F_29(x) + F_56(x, k_0) + F_58(x, k_0))
Eq(F_56(x, k_0), F_11(x)*F_57(x, k_0))
Eq(F_57(x, k_0), F_22(x, k_0) + F_55(x, k_0))
Eq(F_58(x, k_0), F_19(x, k_0)*F_59(x, k_0))
Eq(F_59(x, k_0), F_41(x) + F_55(x, k_0))
Eq(F_60(x, k_0), 2*F_29(x) + F_61(x, k_0) + F_63(x, k_0))
Eq(F_61(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_52(x, k_0) + F_60(x, k_0))
Eq(F_63(x, k_0), F_11(x)*F_54(x, k_0))
Eq(F_64(x, k_0), F_19(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0) + F_70(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_19(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_41(x) + F_67(x, k_0))
Eq(F_70(x, k_0), 2*F_29(x) + F_71(x, k_0) + F_73(x, k_0))
Eq(F_71(x, k_0), F_19(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_55(x, k_0) + F_70(x, k_0))
Eq(F_73(x, k_0), F_19(x, k_0)*F_66(x, k_0))
Eq(F_74(x, k_0), F_19(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_81(x, k_0))
Eq(F_76(x, k_0), F_37(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_22(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_19(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_38(x) + F_78(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_87(x, k_0))
Eq(F_82(x, k_0), F_25(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_29(x) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_19(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_38(x) + F_83(x, k_0))
Eq(F_86(x, k_0), F_11(x)*F_82(x, k_0))
Eq(F_87(x, k_0), F_28(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), 2*F_29(x) + F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_19(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_78(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), F_19(x, k_0)*F_92(x, k_0))
Eq(F_92(x, k_0), F_83(x, k_0) + F_88(x, k_0))
Eq(F_93(x, k_0), F_11(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_36(x) + F_95(x, k_0))
Eq(F_95(x, k_0), F_82(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_100(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_11(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_25(x, k_0) + F_97(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0) + 2*F_29(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_11(x))
Eq(F_102(x, k_0), F_100(x, k_0) + F_83(x, k_0))
Eq(F_103(x, k_0), F_11(x)*F_96(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_11(x))
Eq(F_105(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_13(x, 1))
Eq(F_108(x), F_11(x)*F_7(x))
Eq(F_109(x), F_11(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1, 4], "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, 2, 1, 3], "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, 3, 2, 0, 4], "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, 0, 3], "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]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 5, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 5, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], 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2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24342/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[27,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[24,x]+F[26,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[22,x,k[0]]
F[10,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[20,x,k[0]]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0],1]*k[0]-F[15,x,k[0],1/k[0]])
F[15,x,k[0],k[1]] = (F[16,x,1,k[0],k[1]]*k[0]-F[16,x,1/k[0],k[0],k[1]])/(-1+k[0])
F[16,x,k[0],k[1],k[2]] = F[17,x,k[0]*k[1]]+F[18,x,k[1]*k[2]]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[21,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = 2*F[19,x,k[0]]+F[1,x]
F[22,x,k[0]] = F[11,x]*F[23,x,k[0]]
F[23,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[24,x] = F[25,x]
F[25,x] = F[13,x,1]
F[26,x] = F[11,x]*F[7,x]
F[27,x] = F[11,x]*F[5,x]
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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x , 1\right)
F_{8}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{9}\! \left(x , y_{0}\right)+F_{9}\! \left(x , 1\right)}{-1+y_{0}}
F_{9}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{12}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)
F_{10}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = \frac{y_{0} F_{15}\! \left(x , y_{0}, 1\right)-F_{15}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{-1+y_{0}}
F_{15}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{16}\! \left(x , 1, y_{0}, y_{1}\right)-F_{16}\! \left(x , \frac{1}{y_{0}}, y_{0}, y_{1}\right)}{-1+y_{0}}
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) = F_{17}\! \left(x , y_{0} y_{1}\right)+F_{18}\! \left(x , y_{1} y_{2}\right)
F_{17}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}\right)
F_{18}\! \left(x , y_{0}\right) = F_{19}\! \left(x , y_{0}\right)
F_{19}\! \left(x , y_{0}\right) = F_{20}\! \left(x , y_{0}\right) F_{21}\! \left(x , y_{0}\right)
F_{20}\! \left(x , y_{0}\right) = y_{0} x
F_{21}\! \left(x , y_{0}\right) = 2 F_{19}\! \left(x , y_{0}\right)+F_{1}\! \left(x \right)
F_{22}\! \left(x , y_{0}\right) = F_{11}\! \left(x \right) F_{23}\! \left(x , y_{0}\right)
F_{23}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{9}\! \left(x , y_{0}\right)+F_{9}\! \left(x , 1\right)}{-1+y_{0}}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_27(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_24(x) + F_26(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_22(x, k_0))
Eq(F_10(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_20(x, k_0))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0, 1) - F_15(x, k_0, 1/k_0))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), (-k_0*F_16(x, 1, k_0, k_1) + F_16(x, 1/k_0, k_0, k_1))/(1 - k_0))
Eq(F_16(x, k_0, k_1, k_2), F_17(x, k_0*k_1) + F_18(x, k_1*k_2))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_21(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_1(x) + 2*F_19(x, k_0))
Eq(F_22(x, k_0), F_11(x)*F_23(x, k_0))
Eq(F_23(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_13(x, 1))
Eq(F_26(x), F_11(x)*F_7(x))
Eq(F_27(x), F_11(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1, 4], "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, 2, 1, 3], "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, 3, 2, 0, 4], "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, 0, 3], "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]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], 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3], [0, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 3], [0, 4]]}, {"patt": [2, 0, 1], "pos": [[0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}]}
Specification 3
Strategy pack name: col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24343/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[28,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[25,x]+F[27,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[23,x,k[0]]
F[10,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[21,x,k[0]]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0],1]*k[0]-F[15,x,k[0],1/k[0]])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[0]*k[1]]
F[16,x,k[0],k[1]] = (F[17,x,k[0],k[1]]*k[0]-F[17,x,1,k[1]])/(-1+k[0])
F[17,x,k[0],k[1]] = F[18,x,k[0]]+F[19,x,k[1]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = 2*F[20,x,k[0]]+F[1,x]
F[23,x,k[0]] = F[11,x]*F[24,x,k[0]]
F[24,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[25,x] = F[26,x]
F[26,x] = F[13,x,1]
F[27,x] = F[11,x]*F[7,x]
F[28,x] = F[11,x]*F[5,x]
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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \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) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = \frac{y F_{15}\! \left(x , y , 1\right)-F_{15}\! \left(x , y , \frac{1}{y}\right)}{-1+y}
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , y z \right)
F_{16}\! \left(x , y , z\right) = -\frac{-y F_{17}\! \left(x , y , z\right)+F_{17}\! \left(x , 1, z\right)}{-1+y}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y\right)+F_{19}\! \left(x , z\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = 2 F_{20}\! \left(x , y\right)+F_{1}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_28(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_25(x) + F_27(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_23(x, k_0))
Eq(F_10(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_21(x, k_0))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0, 1) - F_15(x, k_0, 1/k_0))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_0*k_1))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0, k_1) + F_17(x, 1, k_1))/(1 - k_0))
Eq(F_17(x, k_0, k_1), F_18(x, k_0) + F_19(x, k_1))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_1(x) + 2*F_20(x, k_0))
Eq(F_23(x, k_0), F_11(x)*F_24(x, k_0))
Eq(F_24(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_13(x, 1))
Eq(F_27(x), F_11(x)*F_7(x))
Eq(F_28(x), F_11(x)*F_5(x))
Pack JSON:
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Specification JSON:
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"gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 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"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 4
Strategy pack name: col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24362/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[109,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[106,x]+F[108,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[104,x,k[0]]+F[12,x,k[0]]
F[10,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[11,x] = x
F[12,x,k[0]] = F[13,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[74,x,k[0]]+F[93,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[33,x,k[0]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[20,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0]] = F[21,x,k[0]]+F[24,x,k[0]]
F[21,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[23,x,k[0]] = F[19,x,k[0]]*F[21,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]+F[28,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[19,x,k[0]]*F[27,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[25,x,k[0]]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]+F[32,x,k[0]]
F[29,x] = 0
F[30,x,k[0]] = F[19,x,k[0]]*F[31,x,k[0]]
F[31,x,k[0]] = F[22,x,k[0]]+F[28,x,k[0]]
F[32,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[33,x,k[0]] = F[34,x]+F[48,x,k[0]]
F[34,x] = F[35,x]
F[35,x] = F[11,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[11,x]*F[37,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[42,x]
F[42,x] = F[11,x]*F[43,x]
F[43,x] = F[1,x]+F[41,x]
F[44,x] = F[29,x]+F[45,x]+F[47,x]
F[45,x] = F[11,x]*F[46,x]
F[46,x] = F[38,x]+F[44,x]
F[47,x] = F[11,x]*F[40,x]
F[48,x,k[0]] = F[29,x]+F[49,x,k[0]]+F[64,x,k[0]]
F[49,x,k[0]] = F[11,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[54,x,k[0]]
F[51,x,k[0]] = F[22,x,k[0]]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[11,x]*F[51,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[60,x,k[0]]
F[55,x,k[0]] = F[29,x]+F[56,x,k[0]]+F[58,x,k[0]]
F[56,x,k[0]] = F[11,x]*F[57,x,k[0]]
F[57,x,k[0]] = F[22,x,k[0]]+F[55,x,k[0]]
F[58,x,k[0]] = F[19,x,k[0]]*F[59,x,k[0]]
F[59,x,k[0]] = F[41,x]+F[55,x,k[0]]
F[60,x,k[0]] = 2*F[29,x]+F[61,x,k[0]]+F[63,x,k[0]]
F[61,x,k[0]] = F[11,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[52,x,k[0]]+F[60,x,k[0]]
F[63,x,k[0]] = F[11,x]*F[54,x,k[0]]
F[64,x,k[0]] = F[19,x,k[0]]*F[65,x,k[0]]
F[65,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]+F[70,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[68,x,k[0]] = F[19,x,k[0]]*F[69,x,k[0]]
F[69,x,k[0]] = F[41,x]+F[67,x,k[0]]
F[70,x,k[0]] = 2*F[29,x]+F[71,x,k[0]]+F[73,x,k[0]]
F[71,x,k[0]] = F[19,x,k[0]]*F[72,x,k[0]]
F[72,x,k[0]] = F[55,x,k[0]]+F[70,x,k[0]]
F[73,x,k[0]] = F[19,x,k[0]]*F[66,x,k[0]]
F[74,x,k[0]] = F[19,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]+F[81,x,k[0]]
F[76,x,k[0]] = F[37,x]+F[77,x,k[0]]
F[77,x,k[0]] = F[22,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[19,x,k[0]]*F[80,x,k[0]]
F[80,x,k[0]] = F[38,x]+F[78,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[87,x,k[0]]
F[82,x,k[0]] = F[25,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[29,x]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[19,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[38,x]+F[83,x,k[0]]
F[86,x,k[0]] = F[11,x]*F[82,x,k[0]]
F[87,x,k[0]] = F[28,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = 2*F[29,x]+F[89,x,k[0]]+F[91,x,k[0]]
F[89,x,k[0]] = F[19,x,k[0]]*F[90,x,k[0]]
F[90,x,k[0]] = F[78,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = F[19,x,k[0]]*F[92,x,k[0]]
F[92,x,k[0]] = F[83,x,k[0]]+F[88,x,k[0]]
F[93,x,k[0]] = F[11,x]*F[94,x,k[0]]
F[94,x,k[0]] = F[36,x]+F[95,x,k[0]]
F[95,x,k[0]] = F[82,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = F[100,x,k[0]]+F[97,x,k[0]]
F[97,x,k[0]] = F[98,x,k[0]]
F[98,x,k[0]] = F[11,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[25,x,k[0]]+F[97,x,k[0]]
F[100,x,k[0]] = 2*F[29,x]+F[101,x,k[0]]+F[103,x,k[0]]
F[101,x,k[0]] = F[102,x,k[0]]*F[11,x]
F[102,x,k[0]] = F[100,x,k[0]]+F[83,x,k[0]]
F[103,x,k[0]] = F[11,x]*F[96,x,k[0]]
F[104,x,k[0]] = F[105,x,k[0]]*F[11,x]
F[105,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[106,x] = F[107,x]
F[107,x] = F[13,x,1]
F[108,x] = F[11,x]*F[7,x]
F[109,x] = F[11,x]*F[5,x]
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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{109}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{106}\! \left(x \right)+F_{108}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \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) = \frac{F_{9}\! \left(x , y\right) y -F_{9}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \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_{74}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{24}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{29}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{56}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{41}\! \left(x \right)+F_{67}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{37}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{38}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{82}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{89}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)
F_{101}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{102}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{105}\! \left(x , y\right) = \frac{F_{9}\! \left(x , y\right) y -F_{9}\! \left(x , 1\right)}{-1+y}
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{108}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{109}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_109(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_106(x) + F_108(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_104(x, k_0) + F_12(x, k_0))
Eq(F_10(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(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) + F_74(x, k_0) + F_93(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_33(x, k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_20(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0), F_21(x, k_0) + F_24(x, k_0))
Eq(F_21(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_23(x, k_0), F_19(x, k_0)*F_21(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0) + F_28(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_19(x, k_0)*F_27(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_25(x, k_0))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0) + F_32(x, k_0))
Eq(F_29(x), 0)
Eq(F_30(x, k_0), F_19(x, k_0)*F_31(x, k_0))
Eq(F_31(x, k_0), F_22(x, k_0) + F_28(x, k_0))
Eq(F_32(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_33(x, k_0), F_34(x) + F_48(x, k_0))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_11(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_11(x)*F_37(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_11(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_41(x))
Eq(F_44(x), F_29(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_11(x)*F_46(x))
Eq(F_46(x), F_38(x) + F_44(x))
Eq(F_47(x), F_11(x)*F_40(x))
Eq(F_48(x, k_0), F_29(x) + F_49(x, k_0) + F_64(x, k_0))
Eq(F_49(x, k_0), F_11(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_54(x, k_0))
Eq(F_51(x, k_0), F_22(x, k_0) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_11(x)*F_51(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_60(x, k_0))
Eq(F_55(x, k_0), F_29(x) + F_56(x, k_0) + F_58(x, k_0))
Eq(F_56(x, k_0), F_11(x)*F_57(x, k_0))
Eq(F_57(x, k_0), F_22(x, k_0) + F_55(x, k_0))
Eq(F_58(x, k_0), F_19(x, k_0)*F_59(x, k_0))
Eq(F_59(x, k_0), F_41(x) + F_55(x, k_0))
Eq(F_60(x, k_0), 2*F_29(x) + F_61(x, k_0) + F_63(x, k_0))
Eq(F_61(x, k_0), F_11(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_52(x, k_0) + F_60(x, k_0))
Eq(F_63(x, k_0), F_11(x)*F_54(x, k_0))
Eq(F_64(x, k_0), F_19(x, k_0)*F_65(x, k_0))
Eq(F_65(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0) + F_70(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_68(x, k_0), F_19(x, k_0)*F_69(x, k_0))
Eq(F_69(x, k_0), F_41(x) + F_67(x, k_0))
Eq(F_70(x, k_0), 2*F_29(x) + F_71(x, k_0) + F_73(x, k_0))
Eq(F_71(x, k_0), F_19(x, k_0)*F_72(x, k_0))
Eq(F_72(x, k_0), F_55(x, k_0) + F_70(x, k_0))
Eq(F_73(x, k_0), F_19(x, k_0)*F_66(x, k_0))
Eq(F_74(x, k_0), F_19(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0) + F_81(x, k_0))
Eq(F_76(x, k_0), F_37(x) + F_77(x, k_0))
Eq(F_77(x, k_0), F_22(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_19(x, k_0)*F_80(x, k_0))
Eq(F_80(x, k_0), F_38(x) + F_78(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_87(x, k_0))
Eq(F_82(x, k_0), F_25(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_29(x) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_19(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_38(x) + F_83(x, k_0))
Eq(F_86(x, k_0), F_11(x)*F_82(x, k_0))
Eq(F_87(x, k_0), F_28(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), 2*F_29(x) + F_89(x, k_0) + F_91(x, k_0))
Eq(F_89(x, k_0), F_19(x, k_0)*F_90(x, k_0))
Eq(F_90(x, k_0), F_78(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), F_19(x, k_0)*F_92(x, k_0))
Eq(F_92(x, k_0), F_83(x, k_0) + F_88(x, k_0))
Eq(F_93(x, k_0), F_11(x)*F_94(x, k_0))
Eq(F_94(x, k_0), F_36(x) + F_95(x, k_0))
Eq(F_95(x, k_0), F_82(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), F_100(x, k_0) + F_97(x, k_0))
Eq(F_97(x, k_0), F_98(x, k_0))
Eq(F_98(x, k_0), F_11(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_25(x, k_0) + F_97(x, k_0))
Eq(F_100(x, k_0), F_101(x, k_0) + F_103(x, k_0) + 2*F_29(x))
Eq(F_101(x, k_0), F_102(x, k_0)*F_11(x))
Eq(F_102(x, k_0), F_100(x, k_0) + F_83(x, k_0))
Eq(F_103(x, k_0), F_11(x)*F_96(x, k_0))
Eq(F_104(x, k_0), F_105(x, k_0)*F_11(x))
Eq(F_105(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_13(x, 1))
Eq(F_108(x), F_11(x)*F_7(x))
Eq(F_109(x), F_11(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1, 4], "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, 2, 1, 3], "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, 3, 2, 0, 4], "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, 0, 3], "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]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 5, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 5, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "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": [1, 4, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [4, 2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [4, 2, 3, 1, 0], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [4, 2, 3, 1, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1, 4], "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, 2, 1, 3], "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, 3, 2, 0, 4], "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, 0, 3], "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]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 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[[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/24363/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[28,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[25,x]+F[27,x]+F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[8,x,1]
F[8,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[23,x,k[0]]
F[10,x,k[0]] = F[11,x]*F[8,x,k[0]]
F[11,x] = x
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[21,x,k[0]]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0],1]*k[0]-F[15,x,k[0],1/k[0]])
F[15,x,k[0],k[1]] = F[16,x,k[0],k[0]*k[1]]
F[16,x,k[0],k[1]] = (F[17,x,k[0],k[1]]*k[0]-F[17,x,1,k[1]])/(-1+k[0])
F[17,x,k[0],k[1]] = F[18,x,k[0]]+F[19,x,k[1]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = 2*F[20,x,k[0]]+F[1,x]
F[23,x,k[0]] = F[11,x]*F[24,x,k[0]]
F[24,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[25,x] = F[26,x]
F[26,x] = F[13,x,1]
F[27,x] = F[11,x]*F[7,x]
F[28,x] = F[11,x]*F[5,x]
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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{11}\! \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) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = \frac{y F_{15}\! \left(x , y , 1\right)-F_{15}\! \left(x , y , \frac{1}{y}\right)}{-1+y}
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , y z \right)
F_{16}\! \left(x , y , z\right) = -\frac{-y F_{17}\! \left(x , y , z\right)+F_{17}\! \left(x , 1, z\right)}{-1+y}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y\right)+F_{19}\! \left(x , z\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = 2 F_{20}\! \left(x , y\right)+F_{1}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_28(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_25(x) + F_27(x) + F_6(x))
Eq(F_6(x), F_11(x)*F_7(x))
Eq(F_7(x), F_8(x, 1))
Eq(F_8(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_23(x, k_0))
Eq(F_10(x, k_0), F_11(x)*F_8(x, k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_21(x, k_0))
Eq(F_14(x, k_0), (k_0*F_15(x, k_0, 1) - F_15(x, k_0, 1/k_0))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_0*k_1))
Eq(F_16(x, k_0, k_1), (-k_0*F_17(x, k_0, k_1) + F_17(x, 1, k_1))/(1 - k_0))
Eq(F_17(x, k_0, k_1), F_18(x, k_0) + F_19(x, k_1))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_1(x) + 2*F_20(x, k_0))
Eq(F_23(x, k_0), F_11(x)*F_24(x, k_0))
Eq(F_24(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_13(x, 1))
Eq(F_27(x), F_11(x)*F_7(x))
Eq(F_28(x), F_11(x)*F_5(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1, 4], "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, 2, 1, 3], "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, 3, 2, 0, 4], "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, 0, 3], "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]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 5, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 5, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 5, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2, 5], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 5, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 5, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 2, 4, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 3, 4, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [5, 3, 4, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 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