02314_02341_02431_20314_20341_20431_23014_23041_23401_24031_24301
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2565, 12796, 64493, 327498, 1672550, 8579582, 44162889, 227951798, 1179198030, 6110928112, 31714900363, 164795231744, 857162810976, 4462201078202, 23245843132313, 121172902000916, 631963044384239, 3297404944197050, 17211590612979901, 89870211628171376, 469394397874084368, 2452288607865528072, 12814547638927387825, 66976339092519966830, 350119234217329938613, 1830536257033009911476, 9571962791202726424589, 50058454170770289851470, 261819457977822941699936, 1369523366081168316957226, 7164330416195581647663753, 37481461220370797528650752, 196105027104639160625402025, 1026098843043125865674786886, 5369269674004256728728521113, 28097285925291261264813656912, 147039665208978198588401676940, 769526700272684304501409553996, 4027450472474444808360246886853, 21079121211412687148323232161432, 110328871984723001569287869082650, 577482706762972890498058613062966, 3022739946154940176176815849848623, 15822443761191692936299778022702738, 82824034888753751861300457258153750, 433559210268513495985733691564316932, 2269597779260581291669926563120176309, 11881113287443376296106953568925220458, 62197439386923192616735217687837890503, 325607523878194329969537465119116388692, 1704599646207726365752320221415770848241, 8923925105946819920603434153564167111582, 46719110528322246554433348915058677962774, 244589575739609982328097865432067815125998, 1280517998855770600342385370637001317668481, 6704053378269864084212953116862275822263862, 35098856483726465739939258260357590029794526, 183760396415456651728871164897611517148707184, 962086368683478536683982558194661403326226691, 5037083592758147321360874530337503095546539072, 26372238362472680439243771084873641225184022312, 138075735099366824878788782989782840498663747178, 722919748851399713872708770271610655572877681065, 3784992277993345437463961991846212145985118208992, 19817183640842742767166093264631511650341448571417, 103757799581070656689190047203121809003117952722806, 543251984881185340550271549566220767513787241630297, 2844353153383385015236973650667043008338608040598864, 14892486852497242042096385651236490090313388135616052, 77974453763639040353602464024255310131528265225073436, 408261819605750104027645765500101530279375958432487901, 2137599861101456981427361121885978020594799498956703700, 11192193103982415760137940058036457793868213321585828388, 58601001141493290520131300823887209355166075547107700866, 306828617775609843317326061938442628645848039808485181491, 1606525458379297753215811915322833345952557700576311958562, 8411631124368076320895322592586420498215491401250019087026, 44042668816112205913435485284226618113169478377778507558304, 230604503236861220301508516442585787891259445059578247368621, 1207431880273446816850312249045720734198235062523566665028542, 6322053188663067407120642269991019300343647787865004099852567, 33102002071125659541562837883739698308558726217036728518888208, 173320904662354210061138678477885067391144558080093806859056905, 907503200352133368504471875345144039332383078128326288961615842, 4751665728229190755686293631329979683322608462015559063281908882, 24879638320979146649628291211223942720020838301473485299972728106, 130269480068796973725590228286336891283042784536092758848214470157, 682090034753733743981582749774676259812497061011204135863377453424, 3571421518354766560151457058886926431310189389045544192015108046927, 18699968486625369825429889083525285760603943500425393781315611456866, 97913138792049190575732118579317311781578921242791885978975836608341, 512674108177260759480266585598132414231838398941107914753345773896940, 2684368228385539595820456644611768704513755456351427033490201616713518, 14055395497254647048703993508049815922021196171945036719674769633918596
Generating function in Maple syntax:
((-10*x^4+38*x^3-48*x^2+19*x-2)*(5*x^2-6*x+1)^(1/2)+8*x^6-70*x^5+248*x^4-404*x^3+303*x^2-97*x+10)/(16*x^6-112*x^5+304*x^4-402*x^3+266*x^2-80*x+8)
Generating function in latex syntax:
\frac{\left(-10 x^{4}+38 x^{3}-48 x^{2}+19 x -2\right) \sqrt{5 x^{2}-6 x +1}+8 x^{6}-70 x^{5}+248 x^{4}-404 x^{3}+303 x^{2}-97 x +10}{16 x^{6}-112 x^{5}+304 x^{4}-402 x^{3}+266 x^{2}-80 x +8}
Generating function in sympy syntax:
(8*x**6 - 70*x**5 + 248*x**4 - 404*x**3 + 303*x**2 - 97*x + sqrt(5*x**2 - 6*x + 1)*(-10*x**4 + 38*x**3 - 48*x**2 + 19*x - 2) + 10)/(16*x**6 - 112*x**5 + 304*x**4 - 402*x**3 + 266*x**2 - 80*x + 8)
Implicit equation for the generating function in Maple syntax:
(4*x^2-6*x+1)*(x-1)^2*(-2+x)^2*(2*x-1)^2*F(x)^2-(x-1)*(2*x-1)*(8*x^6-70*x^5+248*x^4-404*x^3+303*x^2-97*x+10)*F(x)+4*x^8-48*x^7+218*x^6-580*x^5+875*x^4-733*x^3+330*x^2-73*x+6 = 0
Implicit equation for the generating function in latex syntax:
\left(4 x^{2}-6 x +1\right) \left(x -1\right)^{2} \left(-2+x \right)^{2} \left(2 x -1\right)^{2} F \! \left(x \right)^{2}-\left(x -1\right) \left(2 x -1\right) \left(8 x^{6}-70 x^{5}+248 x^{4}-404 x^{3}+303 x^{2}-97 x +10\right) F \! \left(x \right)+4 x^{8}-48 x^{7}+218 x^{6}-580 x^{5}+875 x^{4}-733 x^{3}+330 x^{2}-73 x +6 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 109
a(6) = 522
a(7) = 2565
a(8) = 12796
a(9) = 64493
a(10) = 327498
a(11) = 1672550
a(n+10) = -100*(n+1)/(n+10)*a(n)+20*(45*n+77)/(n+10)*a(n+1)-48*(72*n+179)/(n+10)*a(n+2)+1/2*(14757*n+48605)/(n+10)*a(n+3)-1/2*(19159*n+78991)/(n+10)*a(n+4)+3/2*(5203*n+25911)/(n+10)*a(n+5)-1/4*(16001*n+94079)/(n+10)*a(n+6)+5/2*(507*n+3464)/(n+10)*a(n+7)-3/4*(317*n+2485)/(n+10)*a(n+8)+1/2*(48*n+427)/(n+10)*a(n+9)+3/2/(n+10), n >= 12
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(4 \right)} = 24
a{\left(5 \right)} = 109
a{\left(6 \right)} = 522
a{\left(7 \right)} = 2565
a{\left(8 \right)} = 12796
a{\left(9 \right)} = 64493
a{\left(10 \right)} = 327498
a{\left(11 \right)} = 1672550
a{\left(n + 10 \right)} = - \frac{100 \left(n + 1\right) a{\left(n \right)}}{n + 10} + \frac{20 \left(45 n + 77\right) a{\left(n + 1 \right)}}{n + 10} + \frac{\left(48 n + 427\right) a{\left(n + 9 \right)}}{2 \left(n + 10\right)} - \frac{48 \left(72 n + 179\right) a{\left(n + 2 \right)}}{n + 10} - \frac{3 \left(317 n + 2485\right) a{\left(n + 8 \right)}}{4 \left(n + 10\right)} + \frac{5 \left(507 n + 3464\right) a{\left(n + 7 \right)}}{2 \left(n + 10\right)} + \frac{3 \left(5203 n + 25911\right) a{\left(n + 5 \right)}}{2 \left(n + 10\right)} + \frac{\left(14757 n + 48605\right) a{\left(n + 3 \right)}}{2 \left(n + 10\right)} - \frac{\left(16001 n + 94079\right) a{\left(n + 6 \right)}}{4 \left(n + 10\right)} - \frac{\left(19159 n + 78991\right) a{\left(n + 4 \right)}}{2 \left(n + 10\right)} + \frac{3}{2 \left(n + 10\right)}, \quad n \geq 12
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24650/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[21,x]*F[7,x]
F[7,x] = F[8,x]+F[84,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[21,x]*F[40,x]
F[11,x] = 1/F[39,x]*F[12,x]
F[12,x] = -F[23,x]+F[13,x]
F[13,x] = 1/F[21,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = (x*F[16,x]+x-1)*(x*F[16,x]+x-2*F[16,x])
F[17,x] = -F[2,x]+F[18,x]
F[18,x] = -F[22,x]+F[19,x]
F[19,x] = 1/F[21,x]*F[20,x]
F[20,x] = F[2,x]
F[21,x] = x
F[22,x] = -1+(x^2-2*x)*F[22,x]^2+(2+x)*F[22,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[21,x]*F[25,x]
F[25,x] = F[17,x]
F[26,x] = F[11,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[21,x]*F[29,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[1,x]+F[21,x]
F[31,x] = F[27,x]+F[32,x]
F[32,x] = F[33,x]+F[34,x]+F[38,x]
F[33,x] = 0
F[34,x] = F[21,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[21,x]
F[37,x] = F[32,x]
F[38,x] = F[21,x]*F[27,x]
F[39,x] = F[1,x]+F[27,x]
F[40,x] = 1/F[21,x]/F[22,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[21,x]*F[22,x]*F[43,x]*F[46,x]
F[43,x] = F[1,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[21,x]*F[43,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[43,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[21,x]*F[40,x]
F[50,x] = F[51,x]
F[51,x] = F[21,x]*F[52,x]
F[52,x] = F[53,x]+F[82,x]
F[53,x] = 1/F[21,x]/F[79,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = -F[58,x]+F[56,x]
F[56,x] = 1/F[21,x]*F[57,x]
F[57,x] = F[5,x]
F[58,x] = -F[59,x]+F[7,x]
F[59,x] = F[60,x]+F[9,x]
F[60,x] = F[61,x]
F[61,x] = F[21,x]*F[46,x]*F[62,x]
F[62,x] = 1/F[21,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[11,x]*F[21,x]*F[66,x]
F[66,x] = F[67,x]+F[71,x]
F[67,x] = F[21,x]+F[68,x]
F[68,x] = F[33,x]+F[69,x]+F[70,x]
F[69,x] = F[21,x]*F[67,x]
F[70,x] = F[21,x]*F[44,x]
F[71,x] = F[72,x]
F[72,x] = F[21,x]*F[73,x]
F[73,x] = F[74,x]+F[78,x]
F[74,x] = F[66,x]*F[75,x]
F[75,x] = F[43,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[75,x]^2*F[21,x]
F[78,x] = F[66,x]*F[75,x]
F[79,x] = F[22,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[21,x]*F[75,x]*F[79,x]
F[82,x] = F[83,x]
F[83,x] = F[50,x]*F[75,x]
F[84,x] = F[85,x]
F[85,x] = F[21,x]*F[46,x]*F[86,x]
F[86,x] = 1/F[21,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[64,x]+F[89,x]
F[89,x] = F[21,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[21,x]*F[92,x]
F[92,x] = F[88,x]+F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[21,x]*F[22,x]
F[95,x] = F[96,x]
F[96,x] = F[21,x]*F[75,x]*F[92,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{21}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{84}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right) F_{40}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = x^{2} F_{16} \left(x \right)^{2}+2 x^{2} F_{16}\! \left(x \right)-2 x F_{16} \left(x \right)^{2}+x^{2}-3 x F_{16}\! \left(x \right)-x +2 F_{16}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = x^{2} F_{22} \left(x \right)^{2}-2 x F_{22} \left(x \right)^{2}+F_{22}\! \left(x \right) x +2 F_{22}\! \left(x \right)-1
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{17}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{21}\! \left(x \right)
F_{37}\! \left(x \right) = F_{32}\! \left(x \right)
F_{38}\! \left(x \right) = F_{21}\! \left(x \right) F_{27}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{21}\! \left(x \right) F_{22}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{21}\! \left(x \right) F_{22}\! \left(x \right) F_{43}\! \left(x \right) F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{21}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{21}\! \left(x \right) F_{40}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{82}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{21}\! \left(x \right) F_{79}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{5}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{7}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{9}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{21}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{33}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{21}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{21}\! \left(x \right) F_{44}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{21}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{66}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{43}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{21}\! \left(x \right)
F_{78}\! \left(x \right) = F_{66}\! \left(x \right) F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = F_{22}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{21}\! \left(x \right) F_{75}\! \left(x \right) F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{50}\! \left(x \right) F_{75}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{64}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{21}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{21}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{88}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{21}\! \left(x \right) F_{22}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right) F_{75}\! \left(x \right) F_{92}\! \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_3(x))
Eq(F_3(x), F_21(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_21(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_84(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_21(x)*F_40(x))
Eq(F_11(x), F_12(x)/F_39(x))
Eq(F_12(x), F_13(x) - F_23(x))
Eq(F_13(x), F_14(x)/F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), x*(x - 2)*(F_16(x) + 1)**2 + (x + 1)*(F_16(x) + 1) + F_16(x) - 1)
Eq(F_17(x), F_18(x) - F_2(x))
Eq(F_18(x), F_19(x) - F_22(x))
Eq(F_19(x), F_20(x)/F_21(x))
Eq(F_20(x), F_2(x))
Eq(F_21(x), x)
Eq(F_22(x), x*(x - 2)*F_22(x)**2 + (x + 2)*F_22(x) - 1)
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_21(x))
Eq(F_25(x), F_17(x))
Eq(F_26(x), F_11(x)*F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_21(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_1(x) + F_21(x))
Eq(F_31(x), F_27(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_38(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_21(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_21(x))
Eq(F_37(x), F_32(x))
Eq(F_38(x), F_21(x)*F_27(x))
Eq(F_39(x), F_1(x) + F_27(x))
Eq(F_40(x), F_41(x)/(F_21(x)*F_22(x)))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_21(x)*F_22(x)*F_43(x)*F_46(x))
Eq(F_43(x), F_1(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_21(x)*F_43(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_43(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_21(x)*F_40(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_21(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_82(x))
Eq(F_53(x), F_54(x)/(F_21(x)*F_79(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x) - F_58(x))
Eq(F_56(x), F_57(x)/F_21(x))
Eq(F_57(x), F_5(x))
Eq(F_58(x), -F_59(x) + F_7(x))
Eq(F_59(x), F_60(x) + F_9(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_21(x)*F_46(x)*F_62(x))
Eq(F_62(x), F_63(x)/F_21(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_11(x)*F_21(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_71(x))
Eq(F_67(x), F_21(x) + F_68(x))
Eq(F_68(x), F_33(x) + F_69(x) + F_70(x))
Eq(F_69(x), F_21(x)*F_67(x))
Eq(F_70(x), F_21(x)*F_44(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_21(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_78(x))
Eq(F_74(x), F_66(x)*F_75(x))
Eq(F_75(x), F_43(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_21(x)*F_75(x)**2)
Eq(F_78(x), F_66(x)*F_75(x))
Eq(F_79(x), F_22(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_21(x)*F_75(x)*F_79(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_50(x)*F_75(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_21(x)*F_46(x)*F_86(x))
Eq(F_86(x), F_87(x)/F_21(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_64(x) + F_89(x))
Eq(F_89(x), F_21(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_21(x)*F_92(x))
Eq(F_92(x), F_88(x) + F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_21(x)*F_22(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_21(x)*F_75(x)*F_92(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 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, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 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"pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 5], [0, 5]]}, {"patt": [1, 0], "pos": [[0, 5], [2, 4]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[2, 4]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24948/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[21,x]*F[7,x]
F[7,x] = F[8,x]+F[84,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[21,x]*F[40,x]
F[11,x] = 1/F[39,x]*F[12,x]
F[12,x] = -F[23,x]+F[13,x]
F[13,x] = 1/F[21,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = (x*F[16,x]+x-2*F[16,x])*(x*F[16,x]+x-1)
F[17,x] = -F[2,x]+F[18,x]
F[18,x] = -F[22,x]+F[19,x]
F[19,x] = 1/F[21,x]*F[20,x]
F[20,x] = F[2,x]
F[21,x] = x
F[22,x] = -1+(x^2-2*x)*F[22,x]^2+(2+x)*F[22,x]
F[23,x] = -F[26,x]+F[24,x]
F[24,x] = 1/F[21,x]*F[25,x]
F[25,x] = F[17,x]
F[26,x] = F[11,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[21,x]*F[29,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[1,x]+F[21,x]
F[31,x] = F[27,x]+F[32,x]
F[32,x] = F[33,x]+F[34,x]+F[38,x]
F[33,x] = 0
F[34,x] = F[21,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[21,x]
F[37,x] = F[32,x]
F[38,x] = F[21,x]*F[27,x]
F[39,x] = F[1,x]+F[27,x]
F[40,x] = 1/F[21,x]/F[22,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[21,x]*F[22,x]*F[43,x]*F[46,x]
F[43,x] = F[1,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[21,x]*F[43,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[43,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[21,x]*F[40,x]
F[50,x] = F[51,x]
F[51,x] = F[21,x]*F[52,x]
F[52,x] = F[53,x]+F[82,x]
F[53,x] = 1/F[21,x]/F[79,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = -F[58,x]+F[56,x]
F[56,x] = 1/F[21,x]*F[57,x]
F[57,x] = F[5,x]
F[58,x] = -F[59,x]+F[7,x]
F[59,x] = F[60,x]+F[9,x]
F[60,x] = F[61,x]
F[61,x] = F[21,x]*F[46,x]*F[62,x]
F[62,x] = 1/F[21,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[11,x]*F[21,x]*F[66,x]
F[66,x] = F[67,x]+F[71,x]
F[67,x] = F[21,x]+F[68,x]
F[68,x] = F[33,x]+F[69,x]+F[70,x]
F[69,x] = F[21,x]*F[67,x]
F[70,x] = F[21,x]*F[44,x]
F[71,x] = F[72,x]
F[72,x] = F[21,x]*F[73,x]
F[73,x] = F[74,x]+F[78,x]
F[74,x] = F[66,x]*F[75,x]
F[75,x] = F[43,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[75,x]^2*F[21,x]
F[78,x] = F[66,x]*F[75,x]
F[79,x] = F[22,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[21,x]*F[75,x]*F[79,x]
F[82,x] = F[83,x]
F[83,x] = F[50,x]*F[75,x]
F[84,x] = F[85,x]
F[85,x] = F[21,x]*F[46,x]*F[86,x]
F[86,x] = 1/F[21,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[64,x]+F[89,x]
F[89,x] = F[21,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[21,x]*F[92,x]
F[92,x] = F[88,x]+F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[21,x]*F[22,x]
F[95,x] = F[96,x]
F[96,x] = F[21,x]*F[75,x]*F[92,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{21}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{84}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right) F_{40}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{39}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = x^{2} F_{16} \left(x \right)^{2}+2 x^{2} F_{16}\! \left(x \right)-2 x F_{16} \left(x \right)^{2}+x^{2}-3 x F_{16}\! \left(x \right)-x +2 F_{16}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = x^{2} F_{22} \left(x \right)^{2}-2 x F_{22} \left(x \right)^{2}+F_{22}\! \left(x \right) x +2 F_{22}\! \left(x \right)-1
F_{23}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{17}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{21}\! \left(x \right)
F_{37}\! \left(x \right) = F_{32}\! \left(x \right)
F_{38}\! \left(x \right) = F_{21}\! \left(x \right) F_{27}\! \left(x \right)
F_{39}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{21}\! \left(x \right) F_{22}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{21}\! \left(x \right) F_{22}\! \left(x \right) F_{43}\! \left(x \right) F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{21}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{21}\! \left(x \right) F_{40}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{82}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{21}\! \left(x \right) F_{79}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{5}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{7}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{9}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{21}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{21}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{33}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{21}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{21}\! \left(x \right) F_{44}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{21}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{78}\! \left(x \right)
F_{74}\! \left(x \right) = F_{66}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{43}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{75} \left(x \right)^{2} F_{21}\! \left(x \right)
F_{78}\! \left(x \right) = F_{66}\! \left(x \right) F_{75}\! \left(x \right)
F_{79}\! \left(x \right) = F_{22}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{21}\! \left(x \right) F_{75}\! \left(x \right) F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{50}\! \left(x \right) F_{75}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{64}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{21}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{21}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{88}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{21}\! \left(x \right) F_{22}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right) F_{75}\! \left(x \right) F_{92}\! \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_3(x))
Eq(F_3(x), F_21(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_21(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_84(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_21(x)*F_40(x))
Eq(F_11(x), F_12(x)/F_39(x))
Eq(F_12(x), F_13(x) - F_23(x))
Eq(F_13(x), F_14(x)/F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), x*(x - 2)*(F_16(x) + 1)**2 + (x + 1)*(F_16(x) + 1) + F_16(x) - 1)
Eq(F_17(x), F_18(x) - F_2(x))
Eq(F_18(x), F_19(x) - F_22(x))
Eq(F_19(x), F_20(x)/F_21(x))
Eq(F_20(x), F_2(x))
Eq(F_21(x), x)
Eq(F_22(x), x*(x - 2)*F_22(x)**2 + (x + 2)*F_22(x) - 1)
Eq(F_23(x), F_24(x) - F_26(x))
Eq(F_24(x), F_25(x)/F_21(x))
Eq(F_25(x), F_17(x))
Eq(F_26(x), F_11(x)*F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_21(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_1(x) + F_21(x))
Eq(F_31(x), F_27(x) + F_32(x))
Eq(F_32(x), F_33(x) + F_34(x) + F_38(x))
Eq(F_33(x), 0)
Eq(F_34(x), F_21(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_21(x))
Eq(F_37(x), F_32(x))
Eq(F_38(x), F_21(x)*F_27(x))
Eq(F_39(x), F_1(x) + F_27(x))
Eq(F_40(x), F_41(x)/(F_21(x)*F_22(x)))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_21(x)*F_22(x)*F_43(x)*F_46(x))
Eq(F_43(x), F_1(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_21(x)*F_43(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_43(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_21(x)*F_40(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_21(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_82(x))
Eq(F_53(x), F_54(x)/(F_21(x)*F_79(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x) - F_58(x))
Eq(F_56(x), F_57(x)/F_21(x))
Eq(F_57(x), F_5(x))
Eq(F_58(x), -F_59(x) + F_7(x))
Eq(F_59(x), F_60(x) + F_9(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_21(x)*F_46(x)*F_62(x))
Eq(F_62(x), F_63(x)/F_21(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_11(x)*F_21(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_71(x))
Eq(F_67(x), F_21(x) + F_68(x))
Eq(F_68(x), F_33(x) + F_69(x) + F_70(x))
Eq(F_69(x), F_21(x)*F_67(x))
Eq(F_70(x), F_21(x)*F_44(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_21(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_78(x))
Eq(F_74(x), F_66(x)*F_75(x))
Eq(F_75(x), F_43(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_21(x)*F_75(x)**2)
Eq(F_78(x), F_66(x)*F_75(x))
Eq(F_79(x), F_22(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_21(x)*F_75(x)*F_79(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_50(x)*F_75(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_21(x)*F_46(x)*F_86(x))
Eq(F_86(x), F_87(x)/F_21(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_64(x) + F_89(x))
Eq(F_89(x), F_21(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_21(x)*F_92(x))
Eq(F_92(x), F_88(x) + F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_21(x)*F_22(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_21(x)*F_75(x)*F_92(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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"rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24961/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[8,x]+F[83,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]*F[38,x]
F[11,x] = 1/F[37,x]*F[12,x]
F[12,x] = -F[19,x]+F[13,x]
F[13,x] = 1/F[18,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = -F[0,x]+F[16,x]
F[16,x] = 1/F[18,x]*F[17,x]
F[17,x] = F[2,x]
F[18,x] = x
F[19,x] = -F[24,x]+F[20,x]
F[20,x] = 1/F[18,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = -F[23,x]+F[15,x]
F[23,x] = (x*F[23,x]+x-2*F[23,x])*(x*F[23,x]+x-1)
F[24,x] = F[11,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[18,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[1,x]+F[18,x]
F[29,x] = F[25,x]+F[30,x]
F[30,x] = F[31,x]+F[32,x]+F[36,x]
F[31,x] = 0
F[32,x] = F[18,x]*F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[18,x]
F[35,x] = F[30,x]
F[36,x] = F[18,x]*F[25,x]
F[37,x] = F[1,x]+F[25,x]
F[38,x] = 1/F[18,x]/F[41,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[18,x]*F[41,x]*F[42,x]*F[45,x]
F[41,x] = -1+(x^2-2*x)*F[41,x]^2+(2+x)*F[41,x]
F[42,x] = F[1,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[18,x]*F[42,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[42,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[18,x]*F[38,x]
F[49,x] = F[50,x]
F[50,x] = F[18,x]*F[51,x]
F[51,x] = F[52,x]+F[81,x]
F[52,x] = 1/F[18,x]/F[78,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[57,x]+F[55,x]
F[55,x] = 1/F[18,x]*F[56,x]
F[56,x] = F[5,x]
F[57,x] = -F[58,x]+F[7,x]
F[58,x] = F[59,x]+F[9,x]
F[59,x] = F[60,x]
F[60,x] = F[18,x]*F[45,x]*F[61,x]
F[61,x] = 1/F[18,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[18,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[18,x]+F[67,x]
F[67,x] = F[31,x]+F[68,x]+F[69,x]
F[68,x] = F[18,x]*F[66,x]
F[69,x] = F[18,x]*F[43,x]
F[70,x] = F[71,x]
F[71,x] = F[18,x]*F[72,x]
F[72,x] = F[73,x]+F[77,x]
F[73,x] = F[65,x]*F[74,x]
F[74,x] = F[42,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[74,x]^2*F[18,x]
F[77,x] = F[65,x]*F[74,x]
F[78,x] = F[41,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[74,x]*F[78,x]
F[81,x] = F[82,x]
F[82,x] = F[49,x]*F[74,x]
F[83,x] = F[84,x]
F[84,x] = F[18,x]*F[45,x]*F[85,x]
F[85,x] = 1/F[18,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[63,x]+F[88,x]
F[88,x] = F[18,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[18,x]*F[91,x]
F[91,x] = F[87,x]+F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[18,x]*F[41,x]
F[94,x] = F[95,x]
F[95,x] = F[18,x]*F[74,x]*F[91,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{83}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{37}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{19}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{15}\! \left(x \right)
F_{23}\! \left(x \right) = x^{2} F_{23} \left(x \right)^{2}+2 x^{2} F_{23}\! \left(x \right)-2 x F_{23} \left(x \right)^{2}+x^{2}-3 x F_{23}\! \left(x \right)-x +2 F_{23}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{18}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right)
F_{35}\! \left(x \right) = F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right) F_{25}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{18}\! \left(x \right) F_{41}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right) F_{41}\! \left(x \right) F_{42}\! \left(x \right) F_{45}\! \left(x \right)
F_{41}\! \left(x \right) = x^{2} F_{41} \left(x \right)^{2}-2 x F_{41} \left(x \right)^{2}+F_{41}\! \left(x \right) x +2 F_{41}\! \left(x \right)-1
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{81}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{18}\! \left(x \right) F_{78}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{5}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{7}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{9}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{31}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{65}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{42}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{74} \left(x \right)^{2} F_{18}\! \left(x \right)
F_{77}\! \left(x \right) = F_{65}\! \left(x \right) F_{74}\! \left(x \right)
F_{78}\! \left(x \right) = F_{41}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{74}\! \left(x \right) F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{49}\! \left(x \right) F_{74}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{63}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{18}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{18}\! \left(x \right) F_{41}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{18}\! \left(x \right) F_{74}\! \left(x \right) F_{91}\! \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_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_83(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x)*F_38(x))
Eq(F_11(x), F_12(x)/F_37(x))
Eq(F_12(x), F_13(x) - F_19(x))
Eq(F_13(x), F_14(x)/F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), -F_0(x) + F_16(x))
Eq(F_16(x), F_17(x)/F_18(x))
Eq(F_17(x), F_2(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x) - F_24(x))
Eq(F_20(x), F_21(x)/F_18(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_15(x) - F_23(x))
Eq(F_23(x), x*(x - 2)*(F_23(x) + 1)**2 + (x + 1)*(F_23(x) + 1) + F_23(x) - 1)
Eq(F_24(x), F_11(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_18(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_1(x) + F_18(x))
Eq(F_29(x), F_25(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_36(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_18(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_18(x))
Eq(F_35(x), F_30(x))
Eq(F_36(x), F_18(x)*F_25(x))
Eq(F_37(x), F_1(x) + F_25(x))
Eq(F_38(x), F_39(x)/(F_18(x)*F_41(x)))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_18(x)*F_41(x)*F_42(x)*F_45(x))
Eq(F_41(x), x*(x - 2)*F_41(x)**2 + (x + 2)*F_41(x) - 1)
Eq(F_42(x), F_1(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_18(x)*F_42(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_42(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_18(x)*F_38(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_18(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_81(x))
Eq(F_52(x), F_53(x)/(F_18(x)*F_78(x)))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x) - F_57(x))
Eq(F_55(x), F_56(x)/F_18(x))
Eq(F_56(x), F_5(x))
Eq(F_57(x), -F_58(x) + F_7(x))
Eq(F_58(x), F_59(x) + F_9(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_18(x)*F_45(x)*F_61(x))
Eq(F_61(x), F_62(x)/F_18(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_18(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_18(x) + F_67(x))
Eq(F_67(x), F_31(x) + F_68(x) + F_69(x))
Eq(F_68(x), F_18(x)*F_66(x))
Eq(F_69(x), F_18(x)*F_43(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_18(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_77(x))
Eq(F_73(x), F_65(x)*F_74(x))
Eq(F_74(x), F_42(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_18(x)*F_74(x)**2)
Eq(F_77(x), F_65(x)*F_74(x))
Eq(F_78(x), F_41(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_74(x)*F_78(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_49(x)*F_74(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_18(x)*F_45(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_18(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_63(x) + F_88(x))
Eq(F_88(x), F_18(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_18(x)*F_91(x))
Eq(F_91(x), F_87(x) + F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_18(x)*F_41(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_18(x)*F_74(x)*F_91(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 5]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 4]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0, 1], "pos": [[0, 5], [0, 5]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 4], [2, 4]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 5], [0, 5]]}, {"patt": [1, 0], "pos": [[0, 5], [2, 4]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 4], [2, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[2, 4]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25137/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[18,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[18,x]*F[7,x]
F[7,x] = F[8,x]+F[83,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[18,x]*F[38,x]
F[11,x] = 1/F[37,x]*F[12,x]
F[12,x] = -F[19,x]+F[13,x]
F[13,x] = 1/F[18,x]*F[14,x]
F[14,x] = F[15,x]
F[15,x] = -F[0,x]+F[16,x]
F[16,x] = 1/F[18,x]*F[17,x]
F[17,x] = F[2,x]
F[18,x] = x
F[19,x] = -F[24,x]+F[20,x]
F[20,x] = 1/F[18,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = -F[23,x]+F[15,x]
F[23,x] = (x*F[23,x]+x-1)*(x*F[23,x]+x-2*F[23,x])
F[24,x] = F[11,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[18,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[1,x]+F[18,x]
F[29,x] = F[25,x]+F[30,x]
F[30,x] = F[31,x]+F[32,x]+F[36,x]
F[31,x] = 0
F[32,x] = F[18,x]*F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[18,x]
F[35,x] = F[30,x]
F[36,x] = F[18,x]*F[25,x]
F[37,x] = F[1,x]+F[25,x]
F[38,x] = 1/F[18,x]/F[41,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[18,x]*F[41,x]*F[42,x]*F[45,x]
F[41,x] = -1+F[41,x]^2*(x^2-2*x)+(2+x)*F[41,x]
F[42,x] = F[1,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[18,x]*F[42,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[42,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[18,x]*F[38,x]
F[49,x] = F[50,x]
F[50,x] = F[18,x]*F[51,x]
F[51,x] = F[52,x]+F[81,x]
F[52,x] = 1/F[18,x]/F[78,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[57,x]+F[55,x]
F[55,x] = 1/F[18,x]*F[56,x]
F[56,x] = F[5,x]
F[57,x] = -F[58,x]+F[7,x]
F[58,x] = F[59,x]+F[9,x]
F[59,x] = F[60,x]
F[60,x] = F[18,x]*F[45,x]*F[61,x]
F[61,x] = 1/F[18,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[11,x]*F[18,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[18,x]+F[67,x]
F[67,x] = F[31,x]+F[68,x]+F[69,x]
F[68,x] = F[18,x]*F[66,x]
F[69,x] = F[18,x]*F[43,x]
F[70,x] = F[71,x]
F[71,x] = F[18,x]*F[72,x]
F[72,x] = F[73,x]+F[77,x]
F[73,x] = F[65,x]*F[74,x]
F[74,x] = F[42,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[74,x]^2*F[18,x]
F[77,x] = F[65,x]*F[74,x]
F[78,x] = F[41,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[18,x]*F[74,x]*F[78,x]
F[81,x] = F[82,x]
F[82,x] = F[49,x]*F[74,x]
F[83,x] = F[84,x]
F[84,x] = F[18,x]*F[45,x]*F[85,x]
F[85,x] = 1/F[18,x]*F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[63,x]+F[88,x]
F[88,x] = F[18,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[18,x]*F[91,x]
F[91,x] = F[87,x]+F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[18,x]*F[41,x]
F[94,x] = F[95,x]
F[95,x] = F[18,x]*F[74,x]*F[91,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{18}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{83}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{37}\! \left(x \right)}
F_{12}\! \left(x \right) = -F_{19}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = x
F_{19}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{23}\! \left(x \right)+F_{15}\! \left(x \right)
F_{23}\! \left(x \right) = x^{2} F_{23} \left(x \right)^{2}+2 x^{2} F_{23}\! \left(x \right)-2 x F_{23} \left(x \right)^{2}+x^{2}-3 x F_{23}\! \left(x \right)-x +2 F_{23}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{18}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x \right) = F_{18}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right)
F_{35}\! \left(x \right) = F_{30}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right) F_{25}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{18}\! \left(x \right) F_{41}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right) F_{41}\! \left(x \right) F_{42}\! \left(x \right) F_{45}\! \left(x \right)
F_{41}\! \left(x \right) = x^{2} F_{41} \left(x \right)^{2}-2 x F_{41} \left(x \right)^{2}+F_{41}\! \left(x \right) x +2 F_{41}\! \left(x \right)-1
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{18}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{18}\! \left(x \right) F_{38}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{18}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{81}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{18}\! \left(x \right) F_{78}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{5}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{7}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{9}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{31}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{18}\! \left(x \right) F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right) F_{43}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{65}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{42}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{74} \left(x \right)^{2} F_{18}\! \left(x \right)
F_{77}\! \left(x \right) = F_{65}\! \left(x \right) F_{74}\! \left(x \right)
F_{78}\! \left(x \right) = F_{41}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{18}\! \left(x \right) F_{74}\! \left(x \right) F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{49}\! \left(x \right) F_{74}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{18}\! \left(x \right) F_{45}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{18}\! \left(x \right)}
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{63}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{18}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{87}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{18}\! \left(x \right) F_{41}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{18}\! \left(x \right) F_{74}\! \left(x \right) F_{91}\! \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_3(x))
Eq(F_3(x), F_18(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_18(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_83(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_18(x)*F_38(x))
Eq(F_11(x), F_12(x)/F_37(x))
Eq(F_12(x), F_13(x) - F_19(x))
Eq(F_13(x), F_14(x)/F_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), -F_0(x) + F_16(x))
Eq(F_16(x), F_17(x)/F_18(x))
Eq(F_17(x), F_2(x))
Eq(F_18(x), x)
Eq(F_19(x), F_20(x) - F_24(x))
Eq(F_20(x), F_21(x)/F_18(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_15(x) - F_23(x))
Eq(F_23(x), x*(x - 2)*(F_23(x) + 1)**2 + (x + 1)*(F_23(x) + 1) + F_23(x) - 1)
Eq(F_24(x), F_11(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_18(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_1(x) + F_18(x))
Eq(F_29(x), F_25(x) + F_30(x))
Eq(F_30(x), F_31(x) + F_32(x) + F_36(x))
Eq(F_31(x), 0)
Eq(F_32(x), F_18(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_18(x))
Eq(F_35(x), F_30(x))
Eq(F_36(x), F_18(x)*F_25(x))
Eq(F_37(x), F_1(x) + F_25(x))
Eq(F_38(x), F_39(x)/(F_18(x)*F_41(x)))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_18(x)*F_41(x)*F_42(x)*F_45(x))
Eq(F_41(x), x*(x - 2)*F_41(x)**2 + (x + 2)*F_41(x) - 1)
Eq(F_42(x), F_1(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_18(x)*F_42(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_42(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_18(x)*F_38(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_18(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_81(x))
Eq(F_52(x), F_53(x)/(F_18(x)*F_78(x)))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x) - F_57(x))
Eq(F_55(x), F_56(x)/F_18(x))
Eq(F_56(x), F_5(x))
Eq(F_57(x), -F_58(x) + F_7(x))
Eq(F_58(x), F_59(x) + F_9(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_18(x)*F_45(x)*F_61(x))
Eq(F_61(x), F_62(x)/F_18(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_11(x)*F_18(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_18(x) + F_67(x))
Eq(F_67(x), F_31(x) + F_68(x) + F_69(x))
Eq(F_68(x), F_18(x)*F_66(x))
Eq(F_69(x), F_18(x)*F_43(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_18(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_77(x))
Eq(F_73(x), F_65(x)*F_74(x))
Eq(F_74(x), F_42(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_18(x)*F_74(x)**2)
Eq(F_77(x), F_65(x)*F_74(x))
Eq(F_78(x), F_41(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_18(x)*F_74(x)*F_78(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_49(x)*F_74(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_18(x)*F_45(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_18(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_63(x) + F_88(x))
Eq(F_88(x), F_18(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_18(x)*F_91(x))
Eq(F_91(x), F_87(x) + F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_18(x)*F_41(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_18(x)*F_74(x)*F_91(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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1]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[2, 4]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 4], [1, 4]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 4], [1, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 4]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 1, 4], [0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [2, 0, 3, 1, 4], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 1, 4], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 5
Strategy pack name: point_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25669/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[8,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]+F[87,x]
F[6,x] = 0
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[1,x]+F[10,x]+F[23,x]+F[84,x]
F[10,x] = F[11,x]*F[8,x]
F[11,x] = F[1,x]+F[12,x]+F[23,x]+F[50,x]+F[82,x]
F[12,x] = F[13,x]*F[8,x]
F[13,x] = F[14,x,1]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[18,x,k[0]]+F[23,x]+F[76,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[8,x]
F[17,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[18,x,k[0]] = k[0]*F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[8,x]
F[20,x,k[0]] = 1/(-1+k[0])*(F[21,x,k[0]]*k[0]-F[21,x,1])
F[21,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[22,x,k[0]]+F[23,x]+F[75,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[8,x]
F[23,x] = F[24,x]*F[8,x]
F[24,x] = F[25,x]+F[60,x]
F[25,x] = F[1,x]+F[23,x]+F[26,x]+F[27,x]
F[26,x] = F[25,x]*F[8,x]
F[27,x] = F[28,x]*F[8,x]
F[28,x] = F[1,x]+F[29,x]+F[30,x]+F[56,x]+F[59,x]
F[29,x] = F[28,x]*F[8,x]
F[30,x] = F[31,x]*F[8,x]
F[31,x] = F[32,x,1]
F[32,x,k[0]] = F[1,x]+F[30,x]+F[33,x,k[0]]+F[34,x,k[0]]+F[37,x,k[0]]+F[55,x,k[0]]
F[33,x,k[0]] = F[32,x,k[0]]*F[8,x]
F[34,x,k[0]] = k[0]*F[35,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]*F[8,x]
F[36,x,k[0]] = 1/(-1+k[0])*(F[32,x,k[0]]*k[0]-F[32,x,1])
F[37,x,k[0]] = F[38,x,k[0]]*F[8,x]
F[38,x,k[0]] = F[39,x,k[0]]+F[54,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]+F[45,x,k[0]]
F[40,x,k[0]] = F[1,x]+F[23,x]+F[27,x]+F[41,x,k[0]]+F[42,x,k[0]]
F[41,x,k[0]] = F[40,x,k[0]]*F[8,x]
F[42,x,k[0]] = k[0]*F[43,x,k[0]]
F[43,x,k[0]] = F[44,x,k[0]]*F[8,x]
F[44,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[45,x,k[0]] = F[46,x]
F[46,x] = -F[53,x]+F[47,x]
F[47,x] = 1/F[8,x]*F[48,x]
F[48,x] = -F[1,x]-F[23,x]-F[49,x]-F[50,x]+F[24,x]
F[49,x] = F[22,x,1]
F[50,x] = F[51,x]*F[8,x]
F[51,x] = F[52,x,1]
F[52,x,k[0]] = 1/(-1+k[0])*(F[21,x,k[0]]*k[0]-F[21,x,1])
F[53,x] = F[40,x,1]
F[54,x,k[0]] = F[46,x]
F[55,x,k[0]] = F[40,x,k[0]]*F[8,x]
F[56,x] = F[57,x]*F[8,x]
F[57,x] = F[28,x]+F[58,x]
F[58,x] = F[46,x]
F[59,x] = F[25,x]*F[8,x]
F[60,x] = F[61,x]
F[61,x] = F[25,x]*F[62,x]*F[8,x]
F[62,x] = F[63,x,1]
F[63,x,k[0]] = F[1,x]+F[64,x,k[0]]+F[65,x,k[0]]+F[67,x,k[0]]+F[69,x,k[0]]
F[64,x,k[0]] = F[63,x,k[0]]*F[8,x]
F[65,x,k[0]] = F[66,x,k[0]]*F[8,x]
F[66,x,k[0]] = 1/(-1+k[0])*(F[63,x,k[0]]*k[0]-F[63,x,1])
F[67,x,k[0]] = F[63,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = k[0]*x
F[69,x,k[0]] = F[70,x,k[0]]*F[8,x]
F[70,x,k[0]] = F[1,x]+F[71,x,k[0]]+F[72,x,k[0]]+F[74,x,k[0]]
F[71,x,k[0]] = F[70,x,k[0]]*F[8,x]
F[72,x,k[0]] = F[73,x,k[0]]*F[8,x]
F[73,x,k[0]] = 1/(-1+k[0])*(F[70,x,k[0]]*k[0]-F[70,x,1])
F[74,x,k[0]] = F[68,x,k[0]]*F[70,x,k[0]]
F[75,x,k[0]] = F[39,x,k[0]]*F[8,x]
F[76,x,k[0]] = F[77,x,k[0]]*F[8,x]
F[77,x,k[0]] = F[78,x,k[0]]+F[81,x,k[0]]
F[78,x,k[0]] = F[1,x]+F[23,x]+F[27,x]+F[42,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[8,x]*F[80,x,k[0]]
F[80,x,k[0]] = 1/(-1+k[0])*(F[78,x,k[0]]*k[0]-F[78,x,1])
F[81,x,k[0]] = F[46,x]
F[82,x] = F[8,x]*F[83,x]
F[83,x] = F[77,x,1]
F[84,x] = F[8,x]*F[85,x]
F[85,x] = F[1,x]+F[30,x]+F[56,x]+F[59,x]+F[86,x]
F[86,x] = F[8,x]*F[83,x]
F[87,x] = F[8,x]*F[88,x]
F[88,x] = F[5,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[8,x]*F[91,x]
F[91,x] = F[107,x]+F[92,x]
F[92,x] = F[105,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = -F[95,x]+F[9,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = -1+(x^2-2*x)*F[96,x]^2+(2+x)*F[96,x]
F[97,x] = F[98,x]
F[98,x] = F[8,x]*F[95,x]*F[99,x]
F[99,x] = F[100,x]+F[103,x]
F[100,x] = F[1,x]+F[101,x]
F[101,x] = F[102,x]
F[102,x] = F[100,x]*F[8,x]
F[103,x] = F[104,x]
F[104,x] = F[99,x]^2*F[8,x]
F[105,x] = F[106,x]
F[106,x] = F[100,x]*F[8,x]*F[93,x]
F[107,x] = F[108,x]
F[108,x] = F[100,x]*F[109,x]*F[8,x]
F[109,x] = 1/F[8,x]*F[110,x]
F[110,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)+F_{87}\! \left(x \right)
F_{6}\! \left(x \right) = 0
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{23}\! \left(x \right)+F_{84}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)+F_{23}\! \left(x \right)+F_{50}\! \left(x \right)+F_{82}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{14}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{23}\! \left(x \right)+F_{76}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{17}\! \left(x , y\right) = -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x , y\right) = y F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x \right)+F_{75}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{60}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{8}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{29}\! \left(x \right) = F_{28}\! \left(x \right) F_{8}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x , 1\right)
F_{32}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{32}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{34}\! \left(x , y\right) = y F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{36}\! \left(x , y\right) = -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)+F_{45}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{27}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{42}\! \left(x , y\right) = y F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{44}\! \left(x , y\right) = -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}
F_{45}\! \left(x , y\right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{53}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{48}\! \left(x \right) = -F_{1}\! \left(x \right)-F_{23}\! \left(x \right)-F_{49}\! \left(x \right)-F_{50}\! \left(x \right)+F_{24}\! \left(x \right)
F_{49}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right) F_{8}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x , 1\right)
F_{52}\! \left(x , y\right) = -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}
F_{53}\! \left(x \right) = F_{40}\! \left(x , 1\right)
F_{54}\! \left(x , y\right) = F_{46}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right) F_{8}\! \left(x \right)
F_{57}\! \left(x \right) = F_{28}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{46}\! \left(x \right)
F_{59}\! \left(x \right) = F_{25}\! \left(x \right) F_{8}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{25}\! \left(x \right) F_{62}\! \left(x \right) F_{8}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x , 1\right)
F_{63}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{64}\! \left(x , y\right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{63}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{66}\! \left(x , y\right) = -\frac{-F_{63}\! \left(x , y\right) y +F_{63}\! \left(x , 1\right)}{-1+y}
F_{67}\! \left(x , y\right) = F_{63}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = y x
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{70}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{70}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{73}\! \left(x , y\right) = -\frac{-F_{70}\! \left(x , y\right) y +F_{70}\! \left(x , 1\right)}{-1+y}
F_{74}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{27}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{8}\! \left(x \right) F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}
F_{81}\! \left(x , y\right) = F_{46}\! \left(x \right)
F_{82}\! \left(x \right) = F_{8}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{77}\! \left(x , 1\right)
F_{84}\! \left(x \right) = F_{8}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{56}\! \left(x \right)+F_{59}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{8}\! \left(x \right) F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{8}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{5}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{8}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{107}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{105}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{9}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = x^{2} F_{96} \left(x \right)^{2}-2 x F_{96} \left(x \right)^{2}+F_{96}\! \left(x \right) x +2 F_{96}\! \left(x \right)-1
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{8}\! \left(x \right) F_{95}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{103}\! \left(x \right)
F_{100}\! \left(x \right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right) F_{8}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{99} \left(x \right)^{2} F_{8}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{100}\! \left(x \right) F_{8}\! \left(x \right) F_{93}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{100}\! \left(x \right) F_{109}\! \left(x \right) F_{8}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{8}\! \left(x \right)}
F_{110}\! \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_3(x))
Eq(F_3(x), F_4(x)*F_8(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x) + F_87(x))
Eq(F_6(x), 0)
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_1(x) + F_10(x) + F_23(x) + F_84(x))
Eq(F_10(x), F_11(x)*F_8(x))
Eq(F_11(x), F_1(x) + F_12(x) + F_23(x) + F_50(x) + F_82(x))
Eq(F_12(x), F_13(x)*F_8(x))
Eq(F_13(x), F_14(x, 1))
Eq(F_14(x, k_0), (-k_0*F_15(x, k_0) + F_15(x, 1))/(1 - k_0))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_18(x, k_0) + F_23(x) + F_76(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_8(x))
Eq(F_17(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_18(x, k_0), k_0*F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_8(x))
Eq(F_20(x, k_0), (k_0*F_21(x, k_0) - F_21(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), F_1(x) + F_18(x, k_0) + F_22(x, k_0) + F_23(x) + F_75(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_8(x))
Eq(F_23(x), F_24(x)*F_8(x))
Eq(F_24(x), F_25(x) + F_60(x))
Eq(F_25(x), F_1(x) + F_23(x) + F_26(x) + F_27(x))
Eq(F_26(x), F_25(x)*F_8(x))
Eq(F_27(x), F_28(x)*F_8(x))
Eq(F_28(x), F_1(x) + F_29(x) + F_30(x) + F_56(x) + F_59(x))
Eq(F_29(x), F_28(x)*F_8(x))
Eq(F_30(x), F_31(x)*F_8(x))
Eq(F_31(x), F_32(x, 1))
Eq(F_32(x, k_0), F_1(x) + F_30(x) + F_33(x, k_0) + F_34(x, k_0) + F_37(x, k_0) + F_55(x, k_0))
Eq(F_33(x, k_0), F_32(x, k_0)*F_8(x))
Eq(F_34(x, k_0), k_0*F_35(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0)*F_8(x))
Eq(F_36(x, k_0), (k_0*F_32(x, k_0) - F_32(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_38(x, k_0)*F_8(x))
Eq(F_38(x, k_0), F_39(x, k_0) + F_54(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0) + F_45(x, k_0))
Eq(F_40(x, k_0), F_1(x) + F_23(x) + F_27(x) + F_41(x, k_0) + F_42(x, k_0))
Eq(F_41(x, k_0), F_40(x, k_0)*F_8(x))
Eq(F_42(x, k_0), k_0*F_43(x, k_0))
Eq(F_43(x, k_0), F_44(x, k_0)*F_8(x))
Eq(F_44(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_45(x, k_0), F_46(x))
Eq(F_46(x), F_47(x) - F_53(x))
Eq(F_47(x), F_48(x)/F_8(x))
Eq(F_48(x), -F_1(x) - F_23(x) + F_24(x) - F_49(x) - F_50(x))
Eq(F_49(x), F_22(x, 1))
Eq(F_50(x), F_51(x)*F_8(x))
Eq(F_51(x), F_52(x, 1))
Eq(F_52(x, k_0), (-k_0*F_21(x, k_0) + F_21(x, 1))/(1 - k_0))
Eq(F_53(x), F_40(x, 1))
Eq(F_54(x, k_0), F_46(x))
Eq(F_55(x, k_0), F_40(x, k_0)*F_8(x))
Eq(F_56(x), F_57(x)*F_8(x))
Eq(F_57(x), F_28(x) + F_58(x))
Eq(F_58(x), F_46(x))
Eq(F_59(x), F_25(x)*F_8(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_25(x)*F_62(x)*F_8(x))
Eq(F_62(x), F_63(x, 1))
Eq(F_63(x, k_0), F_1(x) + F_64(x, k_0) + F_65(x, k_0) + F_67(x, k_0) + F_69(x, k_0))
Eq(F_64(x, k_0), F_63(x, k_0)*F_8(x))
Eq(F_65(x, k_0), F_66(x, k_0)*F_8(x))
Eq(F_66(x, k_0), (k_0*F_63(x, k_0) - F_63(x, 1))/(k_0 - 1))
Eq(F_67(x, k_0), F_63(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), k_0*x)
Eq(F_69(x, k_0), F_70(x, k_0)*F_8(x))
Eq(F_70(x, k_0), F_1(x) + F_71(x, k_0) + F_72(x, k_0) + F_74(x, k_0))
Eq(F_71(x, k_0), F_70(x, k_0)*F_8(x))
Eq(F_72(x, k_0), F_73(x, k_0)*F_8(x))
Eq(F_73(x, k_0), (k_0*F_70(x, k_0) - F_70(x, 1))/(k_0 - 1))
Eq(F_74(x, k_0), F_68(x, k_0)*F_70(x, k_0))
Eq(F_75(x, k_0), F_39(x, k_0)*F_8(x))
Eq(F_76(x, k_0), F_77(x, k_0)*F_8(x))
Eq(F_77(x, k_0), F_78(x, k_0) + F_81(x, k_0))
Eq(F_78(x, k_0), F_1(x) + F_23(x) + F_27(x) + F_42(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_8(x)*F_80(x, k_0))
Eq(F_80(x, k_0), (k_0*F_78(x, k_0) - F_78(x, 1))/(k_0 - 1))
Eq(F_81(x, k_0), F_46(x))
Eq(F_82(x), F_8(x)*F_83(x))
Eq(F_83(x), F_77(x, 1))
Eq(F_84(x), F_8(x)*F_85(x))
Eq(F_85(x), F_1(x) + F_30(x) + F_56(x) + F_59(x) + F_86(x))
Eq(F_86(x), F_8(x)*F_83(x))
Eq(F_87(x), F_8(x)*F_88(x))
Eq(F_88(x), F_5(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_8(x)*F_91(x))
Eq(F_91(x), F_107(x) + F_92(x))
Eq(F_92(x), F_105(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_9(x) - F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), x*(x - 2)*F_96(x)**2 + (x + 2)*F_96(x) - 1)
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_8(x)*F_95(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_103(x))
Eq(F_100(x), F_1(x) + F_101(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_100(x)*F_8(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_8(x)*F_99(x)**2)
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_100(x)*F_8(x)*F_93(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_100(x)*F_109(x)*F_8(x))
Eq(F_109(x), F_110(x)/F_8(x))
Eq(F_110(x), F_5(x))
Pack JSON:
{"name": "point_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": false, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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"pos": [[0, 2], [0, 0], [0, 0], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", 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[1, 2, 3, 0], "pos": [[2, 2], [2, 3], [2, 3], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 3], [2, 3], [2, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 3], [2, 0], [2, 0], [2, 3]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[2, 3], [2, 0], [2, 3], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 3], [2, 3], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[2, 3], [2, 0], [2, 3], [2, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[2, 3], [2, 3], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], 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