01243_01342_01432_10243_10342_10432_20143
Counting sequence:
1, 1, 2, 6, 24, 113, 581, 3149, 17688, 102001, 600303, 3590921, 21768532, 133438243, 825696844, 5150735442, 32356470593, 204511706326, 1299656701871, 8299131182069, 53224431071103, 342671103498219, 2213972068163413, 14350163015085861, 93284901748124244, 608037623967390570, 3973026285497195222, 26019699731786911848, 170765455904355035040, 1122921736758291709193, 7397623439283332400981, 48817505031561978445909, 322665105173903932969897, 2135887434530690001822333, 14158441177626691512086291, 93978275090536216871715647, 624570877364819762382003846, 4155738591421682505671128894, 27682121234166383316172974775, 184590674644577123857192558221, 1232128301247363390522949370689, 8232205204373308791653617036225, 55051657091615808943755760430293, 368468076371578817141527931638093, 2468238991703214075625831845152531, 16546883572838235920493905147550215, 111012463805699756886816507992951441, 745314637907380593740292023985167725, 5007335496097423166238433100004882553, 33663590669102328508376759751871795161, 226458813004000215233814360306861745578, 1524340860213132968310989445121658687414, 10266648826535458276251573155661304464553, 69186178764083058272379252107165511691790, 466492668852950409396312007025163593576153, 3146998022390970263979340306269477096004739, 21240565998737195107267483763628211088234856, 143431951184993459557910585376643020364630823, 969010713391714684315446114512324661488658571, 6549484617881956681480664553837664754643641745, 44286863974594208613787545634040001617976708600, 299588882154067762800504138250045972998491557971, 2027465329734879720574181956360866106814201837052, 13726267739226722922272199494602902080877215563202, 92964546963175808882665527900357508999241409067279, 629858421739913239897432392319595927251715145652905, 4268981611062931897890652346269161291068766707450307, 28943875353416171675063115565875052616417848774526933, 196306928601081673773369989464365410076886753512504358, 1331854648657470105696311423835274780845384410458819499, 9038912325579591308216300031318066938060726503028480112, 61363443066354958823016600286893651243908015079674148754, 416709783087102823357769033424546290841478474057502949942, 2830639024350564728898945792994627218598073452265857846623, 19233513772747791249327457047554513008902571001372103195959, 130723238784744308979695787930774750443328743164115792050271, 888717630552636199250466952565921131301846471923182199895026, 6043500391703142059766994372437053014422474734334685801735046, 41107789789574928731976093563583321634295136481676793780389639, 279684035854616469283062344217061769774596987341145347959150981, 1903340458419225694847567659709764838442526799863226752549627719, 12955909493216289482798715334766989536866294902059152611169830309, 88210326122765450136016415725172117354896349637939848565613810629, 600715184104112448112373387192238541617394619093191329322115842097, 4091787796058501357536081056385716481827395373870347069742345705091, 27877295727430058265392234559936121825457994621451380969933699968893, 189967384371108325881504613204777851896815724453716422387538466901463, 1294780637900269649030481448930399092777816307872713397258789736427211, 8826734544296957980055668656754261561229047277932178065839306612977843, 60185058123529491188038630477323244229120508862668596763132628412627929, 410449896955257242270439461980029128340543282474774430646422911721749897, 2799707290638910253795274196775999713758735978129859693404615217634244073, 19100482533309832610539799454634802965949213453934825726599407003503346951, 130332751447819548230607648422293164996353365439011832220607233337061795911, 889485020549951540377328673171654101331772230326997423158509797934441136089, 6071527311532024095590297422500127090759179713371658136230780324925524490693, 41450516478581027987873161076523057368455294011876450497831037646868818878884, 283030414407011307461664908389599915388404137985572515608345320875648391512783, 1932884800943424879561877923427948761172573275953373084024707828775696105293506, 13202224624241163745693409953590838393620785003751211948619770700253943194592604, 90189331918881175829925895824296698086806206067377064077818830903281062674596079
Implicit equation for the generating function in Maple syntax:
(x-1)*F(x)^4+(-x+2)*F(x)^3+(-x-1)*F(x)^2+F(x)-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) F \! \left(x \right)^{4}+\left(-x +2\right) F \! \left(x \right)^{3}+\left(-x -1\right) F \! \left(x \right)^{2}+F \! \left(x \right)-1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 581
a(7) = 3149
a(8) = 17688
a(9) = 102001
a(10) = 600303
a(11) = 3590921
a(n+12) = 1600/8897*n*(n+1)*(2*n+1)/(n+10)/(n+12)/(n+11)*a(n)+40/8897*(n+1)*(1814*n^2+4123*n+2403)/(n+10)/(n+12)/(n+11)*a(n+1)-30/8897*(2178*n^3-12697*n^2-81881*n-96050)/(n+10)/(n+12)/(n+11)*a(n+2)+2/8897*(376384*n^3+3722439*n^2+12425549*n+13912914)/(n+10)/(n+12)/(n+11)*a(n+3)-12/8897*(532131*n^3+7201629*n^2+32240951*n+47807794)/(n+10)/(n+12)/(n+11)*a(n+4)+4/8897*(4749038*n^3+75272808*n^2+397041913*n+697149048)/(n+10)/(n+12)/(n+11)*a(n+5)-6/8897*(4978800*n^3+90328153*n^2+546634963*n+1103500758)/(n+10)/(n+12)/(n+11)*a(n+6)+1/8897*(28463783*n^3+583249173*n^2+3987133012*n+9093976596)/(n+10)/(n+12)/(n+11)*a(n+7)-1/8897*(17194963*n^3+393821559*n^2+3007073090*n+7655825904)/(n+10)/(n+12)/(n+11)*a(n+8)+2/8897*(3278329*n^3+83200071*n^2+703342100*n+1980771132)/(n+10)/(n+12)/(n+11)*a(n+9)-2/8897*(750095*n^2+13435303*n+60158832)/(n+12)/(n+11)*a(n+10)+1/8897*(182641*n+1732056)/(n+12)*a(n+11), n >= 12
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 581
a(7) = 3149
a(8) = 17688
a(9) = 102001
a(10) = 600303
a(11) = 3590921
a{\left(n + 12 \right)} = \frac{1600 n \left(n + 1\right) \left(2 n + 1\right) a{\left(n \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} + \frac{40 \left(n + 1\right) \left(1814 n^{2} + 4123 n + 2403\right) a{\left(n + 1 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} + \frac{\left(182641 n + 1732056\right) a{\left(n + 11 \right)}}{8897 \left(n + 12\right)} - \frac{2 \left(750095 n^{2} + 13435303 n + 60158832\right) a{\left(n + 10 \right)}}{8897 \left(n + 11\right) \left(n + 12\right)} - \frac{30 \left(2178 n^{3} - 12697 n^{2} - 81881 n - 96050\right) a{\left(n + 2 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} + \frac{2 \left(376384 n^{3} + 3722439 n^{2} + 12425549 n + 13912914\right) a{\left(n + 3 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} - \frac{12 \left(532131 n^{3} + 7201629 n^{2} + 32240951 n + 47807794\right) a{\left(n + 4 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} + \frac{2 \left(3278329 n^{3} + 83200071 n^{2} + 703342100 n + 1980771132\right) a{\left(n + 9 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} + \frac{4 \left(4749038 n^{3} + 75272808 n^{2} + 397041913 n + 697149048\right) a{\left(n + 5 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} - \frac{6 \left(4978800 n^{3} + 90328153 n^{2} + 546634963 n + 1103500758\right) a{\left(n + 6 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} - \frac{\left(17194963 n^{3} + 393821559 n^{2} + 3007073090 n + 7655825904\right) a{\left(n + 8 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)} + \frac{\left(28463783 n^{3} + 583249173 n^{2} + 3987133012 n + 9093976596\right) a{\left(n + 7 \right)}}{8897 \left(n + 10\right) \left(n + 11\right) \left(n + 12\right)}, \quad n \geq 12
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24559/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[18,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]+F[15,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[14,x]
F[12,x] = 1/F[14,x]*F[13,x]
F[13,x] = F[5,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[17,x]
F[17,x] = F[13,x]
F[18,x] = F[19,x]+F[31,x]
F[19,x] = F[20,x]+F[5,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[12,x]+F[22,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[14,x]*F[28,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[14,x]*F[28,x]
F[31,x] = F[32,x]
F[32,x] = F[14,x]*F[33,x]
F[33,x] = F[160,x]+F[34,x]
F[34,x] = F[154,x]+F[35,x]
F[35,x] = F[36,x]+F[48,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = F[38,x]+F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[14,x]*F[40,x]
F[40,x] = -F[46,x]+F[41,x]
F[41,x] = 1/F[14,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[44,x]+F[12,x]
F[44,x] = F[19,x]+F[45,x]
F[45,x] = F[0,x]+F[10,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[14,x]*F[28,x]
F[48,x] = -F[152,x]+F[49,x]
F[49,x] = F[146,x]+F[50,x]
F[50,x] = F[51,x]+F[53,x]
F[51,x] = F[52,x]
F[52,x] = F[14,x]*F[46,x]
F[53,x] = -F[144,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[56,x]
F[56,x] = F[134,x]+F[57,x]
F[57,x] = F[25,x]*F[58,x]
F[58,x] = 1/F[126,x]*F[59,x]
F[59,x] = -F[124,x]+F[60,x]
F[60,x] = 1/F[14,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = -F[67,x]+F[63,x]
F[63,x] = 1/F[14,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[2,x]+F[66,x]
F[66,x] = -F[0,x]+F[4,x]
F[67,x] = F[105,x]+F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[0,x]*F[2,x]
F[70,x] = F[71,x]
F[71,x] = F[14,x]*F[72,x]
F[72,x] = F[73,x]+F[79,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[2,x]+F[75,x]
F[75,x] = -F[2,x]+F[76,x]
F[76,x] = -F[0,x]+F[77,x]
F[77,x] = 1/F[14,x]*F[78,x]
F[78,x] = F[2,x]
F[79,x] = F[80,x]
F[80,x] = F[12,x]*F[14,x]*F[81,x]
F[81,x] = 1/F[14,x]/F[88,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[14,x]*F[85,x]
F[85,x] = F[75,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[2,x]*F[88,x]
F[88,x] = -1+(x^2-2*x)*F[88,x]^2+(2+x)*F[88,x]
F[89,x] = F[90,x]
F[90,x] = F[14,x]*F[91,x]
F[91,x] = F[101,x]+F[92,x]
F[92,x] = F[77,x]*F[93,x]
F[93,x] = F[2,x]+F[94,x]
F[94,x] = -F[100,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[14,x]*F[97,x]
F[97,x] = F[83,x]+F[98,x]
F[98,x] = F[86,x]+F[99,x]
F[99,x] = F[0,x]+F[95,x]
F[100,x] = (x*F[100,x]+x-1)*(x*F[100,x]+x-2*F[100,x])
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[14,x]*F[81,x]
F[103,x] = 1/F[14,x]*F[104,x]
F[104,x] = F[93,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[14,x]
F[107,x] = F[108,x]+F[112,x]
F[108,x] = F[109,x]*F[58,x]
F[109,x] = 1/F[14,x]*F[110,x]
F[110,x] = F[111,x]
F[111,x] = -F[100,x]+F[10,x]
F[112,x] = F[113,x]+F[121,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[117,x]*F[14,x]
F[115,x] = F[100,x]+F[116,x]
F[116,x] = F[111,x]+F[2,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[28,x]*F[58,x]
F[119,x] = F[120,x]
F[120,x] = F[14,x]*F[28,x]*F[81,x]
F[121,x] = F[122,x]
F[122,x] = F[117,x]*F[123,x]*F[14,x]
F[123,x] = F[19,x]+F[43,x]
F[124,x] = F[125,x]
F[125,x] = F[117,x]*F[14,x]
F[126,x] = 1/F[0,x]*F[127,x]
F[127,x] = -F[130,x]+F[128,x]
F[128,x] = 1/F[14,x]*F[129,x]
F[129,x] = F[95,x]
F[130,x] = -F[133,x]+F[131,x]
F[131,x] = 1/F[14,x]*F[132,x]
F[132,x] = F[94,x]
F[133,x] = F[126,x]*F[2,x]
F[134,x] = F[135,x]
F[135,x] = -F[143,x]+F[136,x]
F[136,x] = 1/F[14,x]*F[137,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[14,x]*F[28,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[12,x]*F[28,x]*F[58,x]
F[141,x] = F[142,x]
F[142,x] = F[117,x]*F[12,x]*F[14,x]
F[143,x] = F[24,x]*F[58,x]
F[144,x] = F[145,x]
F[145,x] = F[14,x]*F[24,x]
F[146,x] = F[147,x]
F[147,x] = -F[51,x]+F[148,x]
F[148,x] = F[149,x]
F[149,x] = F[14,x]*F[150,x]
F[150,x] = F[151,x]
F[151,x] = F[12,x]*F[14,x]*F[28,x]*F[58,x]
F[152,x] = F[153,x]
F[153,x] = F[134,x]*F[14,x]
F[154,x] = F[155,x]
F[155,x] = F[14,x]*F[156,x]
F[156,x] = F[157,x]+F[158,x]
F[157,x] = F[117,x]*F[40,x]
F[158,x] = 1/F[14,x]*F[159,x]
F[159,x] = F[153,x]
F[160,x] = F[51,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_{14}\! \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_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{18}\! \left(x \right)+F_{8}\! \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_{15}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{160}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{154}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{48}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{12}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{152}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{146}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{144}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{134}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{25}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{126}\! \left(x \right)}
F_{59}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{105}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{79}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = \frac{F_{78}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{78}\! \left(x \right) = F_{2}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{14}\! \left(x \right) F_{88}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{75}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{2}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = x^{2} F_{88} \left(x \right)^{2}-2 x F_{88} \left(x \right)^{2}+F_{88}\! \left(x \right) x +2 F_{88}\! \left(x \right)-1
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{14}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{101}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{77}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{2}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{14}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{83}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{86}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right)+F_{95}\! \left(x \right)
F_{100}\! \left(x \right) = x^{2} F_{100} \left(x \right)^{2}+2 x^{2} F_{100}\! \left(x \right)-2 x F_{100} \left(x \right)^{2}+x^{2}-3 x F_{100}\! \left(x \right)-x +2 F_{100}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{14}\! \left(x \right) F_{81}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{93}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{14}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{58}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{10}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{121}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{115}\! \left(x \right) = F_{100}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{111}\! \left(x \right)+F_{2}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{28}\! \left(x \right) F_{58}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right) F_{81}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{117}\! \left(x \right) F_{123}\! \left(x \right) F_{14}\! \left(x \right)
F_{123}\! \left(x \right) = F_{19}\! \left(x \right)+F_{43}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{126}\! \left(x \right) = \frac{F_{127}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{127}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{95}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{94}\! \left(x \right)
F_{133}\! \left(x \right) = F_{126}\! \left(x \right) F_{2}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right) F_{58}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{143}\! \left(x \right) = F_{24}\! \left(x \right) F_{58}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{14}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right) F_{58}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{134}\! \left(x \right) F_{14}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{14}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{158}\! \left(x \right)
F_{157}\! \left(x \right) = F_{117}\! \left(x \right) F_{40}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{153}\! \left(x \right)
F_{160}\! \left(x \right) = F_{51}\! \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_14(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_14(x)*F_7(x))
Eq(F_7(x), F_18(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_15(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_14(x))
Eq(F_12(x), F_13(x)/F_14(x))
Eq(F_13(x), F_5(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_17(x))
Eq(F_17(x), F_13(x))
Eq(F_18(x), F_19(x) + F_31(x))
Eq(F_19(x), F_20(x) + F_5(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_12(x) + F_22(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_14(x)*F_28(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_14(x)*F_28(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_14(x)*F_33(x))
Eq(F_33(x), F_160(x) + F_34(x))
Eq(F_34(x), F_154(x) + F_35(x))
Eq(F_35(x), F_36(x) + F_48(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_14(x)*F_40(x))
Eq(F_40(x), F_41(x) - F_46(x))
Eq(F_41(x), F_42(x)/F_14(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x) - F_44(x))
Eq(F_44(x), F_19(x) + F_45(x))
Eq(F_45(x), F_0(x) + F_10(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_14(x)*F_28(x))
Eq(F_48(x), -F_152(x) + F_49(x))
Eq(F_49(x), F_146(x) + F_50(x))
Eq(F_50(x), F_51(x) + F_53(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_14(x)*F_46(x))
Eq(F_53(x), -F_144(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_56(x))
Eq(F_56(x), F_134(x) + F_57(x))
Eq(F_57(x), F_25(x)*F_58(x))
Eq(F_58(x), F_59(x)/F_126(x))
Eq(F_59(x), -F_124(x) + F_60(x))
Eq(F_60(x), F_61(x)/F_14(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) - F_67(x))
Eq(F_63(x), F_64(x)/F_14(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_2(x) + F_66(x))
Eq(F_66(x), -F_0(x) + F_4(x))
Eq(F_67(x), F_105(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_0(x)*F_2(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_14(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_79(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_2(x) + F_75(x))
Eq(F_75(x), -F_2(x) + F_76(x))
Eq(F_76(x), -F_0(x) + F_77(x))
Eq(F_77(x), F_78(x)/F_14(x))
Eq(F_78(x), F_2(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_12(x)*F_14(x)*F_81(x))
Eq(F_81(x), F_82(x)/(F_14(x)*F_88(x)))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_14(x))
Eq(F_85(x), F_75(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_2(x)*F_88(x))
Eq(F_88(x), x*(x - 2)*F_88(x)**2 + (x + 2)*F_88(x) - 1)
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_14(x)*F_91(x))
Eq(F_91(x), F_101(x) + F_92(x))
Eq(F_92(x), F_77(x)*F_93(x))
Eq(F_93(x), F_2(x) + F_94(x))
Eq(F_94(x), -F_100(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_14(x)*F_97(x))
Eq(F_97(x), F_83(x) + F_98(x))
Eq(F_98(x), F_86(x) + F_99(x))
Eq(F_99(x), F_0(x) + F_95(x))
Eq(F_100(x), x*(x - 2)*(F_100(x) + 1)**2 + (x + 1)*(F_100(x) + 1) + F_100(x) - 1)
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_14(x)*F_81(x))
Eq(F_103(x), F_104(x)/F_14(x))
Eq(F_104(x), F_93(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_14(x))
Eq(F_107(x), F_108(x) + F_112(x))
Eq(F_108(x), F_109(x)*F_58(x))
Eq(F_109(x), F_110(x)/F_14(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_10(x) - F_100(x))
Eq(F_112(x), F_113(x) + F_121(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_117(x)*F_14(x))
Eq(F_115(x), F_100(x) + F_116(x))
Eq(F_116(x), F_111(x) + F_2(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_28(x)*F_58(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_14(x)*F_28(x)*F_81(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_117(x)*F_123(x)*F_14(x))
Eq(F_123(x), F_19(x) + F_43(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_117(x)*F_14(x))
Eq(F_126(x), F_127(x)/F_0(x))
Eq(F_127(x), F_128(x) - F_130(x))
Eq(F_128(x), F_129(x)/F_14(x))
Eq(F_129(x), F_95(x))
Eq(F_130(x), F_131(x) - F_133(x))
Eq(F_131(x), F_132(x)/F_14(x))
Eq(F_132(x), F_94(x))
Eq(F_133(x), F_126(x)*F_2(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x) - F_143(x))
Eq(F_136(x), F_137(x)/F_14(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_14(x)*F_28(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_12(x)*F_28(x)*F_58(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_117(x)*F_12(x)*F_14(x))
Eq(F_143(x), F_24(x)*F_58(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_14(x)*F_24(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x) - F_51(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_14(x)*F_150(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_12(x)*F_14(x)*F_28(x)*F_58(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_134(x)*F_14(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_14(x)*F_156(x))
Eq(F_156(x), F_157(x) + F_158(x))
Eq(F_157(x), F_117(x)*F_40(x))
Eq(F_158(x), F_159(x)/F_14(x))
Eq(F_159(x), F_153(x))
Eq(F_160(x), F_51(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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "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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"pos": [[0, 3], [0, 2], [0, 3], [0, 3], [1, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 3], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 1], [0, 3], [0, 3], [1, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 2], [0, 3], [0, 3], [1, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 3], [3, 3]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 0], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [2, 3], [2, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 3], [2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [3, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [2, 3], [2, 3], [3, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 3], [2, 3], [2, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [2, 3], [2, 3], [3, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 3], [3, 0], [3, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [3, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24639/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = F[45,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]+F[42,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = (x*F[11,x]+x-1)*(x*F[11,x]+x-2*F[11,x])
F[12,x] = -F[2,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[16,x]
F[15,x] = x
F[16,x] = 1/F[15,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = -F[26,x]+F[19,x]
F[19,x] = F[0,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]
F[22,x] = F[23,x]+F[37,x]
F[23,x] = F[19,x]+F[24,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[2,x]*F[26,x]
F[26,x] = -1+(x^2-2*x)*F[26,x]^2+(2+x)*F[26,x]
F[27,x] = F[28,x]
F[28,x] = F[15,x]*F[29,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[18,x]*F[31,x]
F[31,x] = 1/F[15,x]*F[32,x]
F[32,x] = F[2,x]
F[33,x] = F[34,x]
F[34,x] = F[15,x]*F[16,x]*F[35,x]
F[35,x] = 1/F[15,x]/F[26,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[24,x]+F[38,x]
F[38,x] = 1/F[15,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[2,x]+F[41,x]
F[41,x] = -F[0,x]+F[31,x]
F[42,x] = F[43,x]
F[43,x] = F[15,x]*F[44,x]
F[44,x] = F[10,x]
F[45,x] = F[46,x]+F[62,x]
F[46,x] = F[47,x]+F[5,x]
F[47,x] = F[48,x]
F[48,x] = F[15,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[15,x]*F[51,x]
F[51,x] = F[52,x]+F[57,x]
F[52,x] = F[53,x]+F[55,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[5,x]
F[55,x] = F[56,x]
F[56,x] = F[15,x]*F[51,x]
F[57,x] = F[58,x]
F[58,x] = F[15,x]*F[53,x]*F[59,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[15,x]*F[59,x]
F[62,x] = F[63,x]
F[63,x] = F[15,x]*F[64,x]
F[64,x] = F[159,x]+F[65,x]
F[65,x] = F[153,x]+F[66,x]
F[66,x] = F[67,x]+F[79,x]
F[67,x] = F[2,x]*F[68,x]
F[68,x] = F[4,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[15,x]*F[71,x]
F[71,x] = -F[77,x]+F[72,x]
F[72,x] = 1/F[15,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[75,x]+F[53,x]
F[75,x] = F[46,x]+F[76,x]
F[76,x] = F[13,x]+F[26,x]
F[77,x] = F[78,x]
F[78,x] = F[15,x]*F[53,x]*F[59,x]
F[79,x] = -F[151,x]+F[80,x]
F[80,x] = F[145,x]+F[81,x]
F[81,x] = F[82,x]+F[84,x]
F[82,x] = F[83,x]
F[83,x] = F[15,x]*F[77,x]
F[84,x] = -F[144,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[15,x]*F[87,x]
F[87,x] = F[134,x]+F[88,x]
F[88,x] = F[52,x]*F[89,x]
F[89,x] = 1/F[125,x]*F[90,x]
F[90,x] = -F[123,x]+F[91,x]
F[91,x] = 1/F[15,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = -F[97,x]+F[94,x]
F[94,x] = 1/F[15,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[2,x]+F[5,x]
F[97,x] = F[106,x]+F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[0,x]*F[2,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[15,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[4,x]*F[41,x]
F[104,x] = F[105,x]
F[105,x] = F[15,x]*F[35,x]*F[53,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[15,x]
F[108,x] = F[109,x]+F[112,x]
F[109,x] = F[110,x]*F[89,x]
F[110,x] = 1/F[15,x]*F[111,x]
F[111,x] = F[12,x]
F[112,x] = F[113,x]+F[120,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[116,x]*F[15,x]
F[115,x] = F[11,x]+F[13,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[59,x]*F[89,x]
F[118,x] = F[119,x]
F[119,x] = F[15,x]*F[35,x]*F[59,x]
F[120,x] = F[121,x]
F[121,x] = F[116,x]*F[122,x]*F[15,x]
F[122,x] = F[46,x]+F[74,x]
F[123,x] = F[124,x]
F[124,x] = F[116,x]*F[15,x]
F[125,x] = 1/F[0,x]*F[126,x]
F[126,x] = -F[129,x]+F[127,x]
F[127,x] = 1/F[15,x]*F[128,x]
F[128,x] = F[20,x]
F[129,x] = -F[133,x]+F[130,x]
F[130,x] = 1/F[15,x]*F[131,x]
F[131,x] = F[132,x]
F[132,x] = -F[2,x]+F[18,x]
F[133,x] = F[125,x]*F[2,x]
F[134,x] = F[135,x]
F[135,x] = -F[143,x]+F[136,x]
F[136,x] = 1/F[15,x]*F[137,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[15,x]*F[59,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[53,x]*F[59,x]*F[89,x]
F[141,x] = F[142,x]
F[142,x] = F[116,x]*F[15,x]*F[53,x]
F[143,x] = F[51,x]*F[89,x]
F[144,x] = F[50,x]
F[145,x] = F[146,x]
F[146,x] = -F[82,x]+F[147,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[15,x]
F[149,x] = F[150,x]
F[150,x] = F[15,x]*F[53,x]*F[59,x]*F[89,x]
F[151,x] = F[152,x]
F[152,x] = F[134,x]*F[15,x]
F[153,x] = F[154,x]
F[154,x] = F[15,x]*F[155,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[116,x]*F[71,x]
F[157,x] = 1/F[15,x]*F[158,x]
F[158,x] = F[152,x]
F[159,x] = F[82,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_{15}\! \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_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{45}\! \left(x \right)+F_{8}\! \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_{42}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}+2 x^{2} F_{11}\! \left(x \right)-2 x F_{11} \left(x \right)^{2}+x^{2}-3 x F_{11}\! \left(x \right)-x +2 F_{11}\! \left(x \right)
F_{12}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{37}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = x^{2} F_{26} \left(x \right)^{2}-2 x F_{26} \left(x \right)^{2}+F_{26}\! \left(x \right) x +2 F_{26}\! \left(x \right)-1
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{18}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{15}\! \left(x \right) F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{15}\! \left(x \right) F_{26}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{31}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{62}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{15}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{15}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{5}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right) F_{51}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{159}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{153}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{79}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{53}\! \left(x \right)
F_{75}\! \left(x \right) = F_{46}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{13}\! \left(x \right)+F_{26}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{59}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{151}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{145}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{15}\! \left(x \right) F_{77}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{144}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{134}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{52}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{125}\! \left(x \right)}
F_{90}\! \left(x \right) = -F_{123}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{97}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{97}\! \left(x \right) = F_{106}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{15}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{15}\! \left(x \right) F_{35}\! \left(x \right) F_{53}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{15}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{112}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{89}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{120}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{116}\! \left(x \right) F_{15}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right)+F_{13}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{59}\! \left(x \right) F_{89}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{15}\! \left(x \right) F_{35}\! \left(x \right) F_{59}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{116}\! \left(x \right) F_{122}\! \left(x \right) F_{15}\! \left(x \right)
F_{122}\! \left(x \right) = F_{46}\! \left(x \right)+F_{74}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{116}\! \left(x \right) F_{15}\! \left(x \right)
F_{125}\! \left(x \right) = \frac{F_{126}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{126}\! \left(x \right) = -F_{129}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = \frac{F_{128}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{128}\! \left(x \right) = F_{20}\! \left(x \right)
F_{129}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{18}\! \left(x \right)
F_{133}\! \left(x \right) = F_{125}\! \left(x \right) F_{2}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{53}\! \left(x \right) F_{59}\! \left(x \right) F_{89}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{116}\! \left(x \right) F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{143}\! \left(x \right) = F_{51}\! \left(x \right) F_{89}\! \left(x \right)
F_{144}\! \left(x \right) = F_{50}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{15}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{59}\! \left(x \right) F_{89}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{134}\! \left(x \right) F_{15}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{15}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{116}\! \left(x \right) F_{71}\! \left(x \right)
F_{157}\! \left(x \right) = \frac{F_{158}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{158}\! \left(x \right) = F_{152}\! \left(x \right)
F_{159}\! \left(x \right) = F_{82}\! \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_15(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_15(x)*F_7(x))
Eq(F_7(x), F_45(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_42(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x*(x - 2)*(F_11(x) + 1)**2 + (x + 1)*(F_11(x) + 1) + F_11(x) - 1)
Eq(F_12(x), F_13(x) - F_2(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_16(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x)/F_15(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_26(x))
Eq(F_19(x), F_0(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_37(x))
Eq(F_23(x), F_19(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_2(x)*F_26(x))
Eq(F_26(x), x*(x - 2)*F_26(x)**2 + (x + 2)*F_26(x) - 1)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_15(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_18(x)*F_31(x))
Eq(F_31(x), F_32(x)/F_15(x))
Eq(F_32(x), F_2(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_15(x)*F_16(x)*F_35(x))
Eq(F_35(x), F_36(x)/(F_15(x)*F_26(x)))
Eq(F_36(x), F_37(x))
Eq(F_37(x), -F_24(x) + F_38(x))
Eq(F_38(x), F_39(x)/F_15(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), -F_2(x) + F_41(x))
Eq(F_41(x), -F_0(x) + F_31(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_15(x)*F_44(x))
Eq(F_44(x), F_10(x))
Eq(F_45(x), F_46(x) + F_62(x))
Eq(F_46(x), F_47(x) + F_5(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_15(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_15(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_57(x))
Eq(F_52(x), F_53(x) + F_55(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_5(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_15(x)*F_51(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_15(x)*F_53(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_15(x)*F_59(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_15(x)*F_64(x))
Eq(F_64(x), F_159(x) + F_65(x))
Eq(F_65(x), F_153(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_79(x))
Eq(F_67(x), F_2(x)*F_68(x))
Eq(F_68(x), F_4(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_15(x)*F_71(x))
Eq(F_71(x), F_72(x) - F_77(x))
Eq(F_72(x), F_73(x)/F_15(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_53(x) - F_75(x))
Eq(F_75(x), F_46(x) + F_76(x))
Eq(F_76(x), F_13(x) + F_26(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_15(x)*F_53(x)*F_59(x))
Eq(F_79(x), -F_151(x) + F_80(x))
Eq(F_80(x), F_145(x) + F_81(x))
Eq(F_81(x), F_82(x) + F_84(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_15(x)*F_77(x))
Eq(F_84(x), -F_144(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_15(x)*F_87(x))
Eq(F_87(x), F_134(x) + F_88(x))
Eq(F_88(x), F_52(x)*F_89(x))
Eq(F_89(x), F_90(x)/F_125(x))
Eq(F_90(x), -F_123(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_15(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_94(x) - F_97(x))
Eq(F_94(x), F_95(x)/F_15(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), -F_2(x) + F_5(x))
Eq(F_97(x), F_106(x) + F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_0(x)*F_2(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_15(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_4(x)*F_41(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_15(x)*F_35(x)*F_53(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_15(x))
Eq(F_108(x), F_109(x) + F_112(x))
Eq(F_109(x), F_110(x)*F_89(x))
Eq(F_110(x), F_111(x)/F_15(x))
Eq(F_111(x), F_12(x))
Eq(F_112(x), F_113(x) + F_120(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_116(x)*F_15(x))
Eq(F_115(x), F_11(x) + F_13(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_59(x)*F_89(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_15(x)*F_35(x)*F_59(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_116(x)*F_122(x)*F_15(x))
Eq(F_122(x), F_46(x) + F_74(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_116(x)*F_15(x))
Eq(F_125(x), F_126(x)/F_0(x))
Eq(F_126(x), F_127(x) - F_129(x))
Eq(F_127(x), F_128(x)/F_15(x))
Eq(F_128(x), F_20(x))
Eq(F_129(x), F_130(x) - F_133(x))
Eq(F_130(x), F_131(x)/F_15(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_18(x) - F_2(x))
Eq(F_133(x), F_125(x)*F_2(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x) - F_143(x))
Eq(F_136(x), F_137(x)/F_15(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_15(x)*F_59(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_53(x)*F_59(x)*F_89(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_116(x)*F_15(x)*F_53(x))
Eq(F_143(x), F_51(x)*F_89(x))
Eq(F_144(x), F_50(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_147(x) - F_82(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_15(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_15(x)*F_53(x)*F_59(x)*F_89(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_134(x)*F_15(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_15(x)*F_155(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_116(x)*F_71(x))
Eq(F_157(x), F_158(x)/F_15(x))
Eq(F_158(x), F_152(x))
Eq(F_159(x), F_82(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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"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, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "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, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 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{"patt": [1, 0, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [2, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [2, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [5, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [2, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [5, 5]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [5, 0], [5, 2], [5, 2], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 2], [5, 2], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [0, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 4], [2, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 5], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 5], [0, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 5], [2, 3], [2, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 3], [0, 4], [0, 4], [2, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 3], [0, 5], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 3], [0, 5], [0, 4], [2, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 5], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 5], [0, 4], [2, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 5], [2, 4], [2, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [2, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [2, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [5, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [2, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [5, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [5, 0], [5, 2], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 2], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 2], [5, 2], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 5], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 5], [5, 2], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [5, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [5, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24801/
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[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[15,x]*F[7,x]
F[7,x] = F[45,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]+F[42,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = (x*F[11,x]+x-2*F[11,x])*(x*F[11,x]+x-1)
F[12,x] = -F[2,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[16,x]
F[15,x] = x
F[16,x] = 1/F[15,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = -F[26,x]+F[19,x]
F[19,x] = F[0,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[15,x]*F[22,x]
F[22,x] = F[23,x]+F[37,x]
F[23,x] = F[19,x]+F[24,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[2,x]*F[26,x]
F[26,x] = -1+F[26,x]^2*(x^2-2*x)+(2+x)*F[26,x]
F[27,x] = F[28,x]
F[28,x] = F[15,x]*F[29,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[18,x]*F[31,x]
F[31,x] = 1/F[15,x]*F[32,x]
F[32,x] = F[2,x]
F[33,x] = F[34,x]
F[34,x] = F[15,x]*F[16,x]*F[35,x]
F[35,x] = 1/F[15,x]/F[26,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[24,x]+F[38,x]
F[38,x] = 1/F[15,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[2,x]+F[41,x]
F[41,x] = -F[0,x]+F[31,x]
F[42,x] = F[43,x]
F[43,x] = F[15,x]*F[44,x]
F[44,x] = F[10,x]
F[45,x] = F[46,x]+F[62,x]
F[46,x] = F[47,x]+F[5,x]
F[47,x] = F[48,x]
F[48,x] = F[15,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[15,x]*F[51,x]
F[51,x] = F[52,x]+F[57,x]
F[52,x] = F[53,x]+F[55,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[5,x]
F[55,x] = F[56,x]
F[56,x] = F[15,x]*F[51,x]
F[57,x] = F[58,x]
F[58,x] = F[15,x]*F[53,x]*F[59,x]
F[59,x] = F[1,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[15,x]*F[59,x]
F[62,x] = F[63,x]
F[63,x] = F[15,x]*F[64,x]
F[64,x] = F[159,x]+F[65,x]
F[65,x] = F[153,x]+F[66,x]
F[66,x] = F[67,x]+F[79,x]
F[67,x] = F[2,x]*F[68,x]
F[68,x] = F[4,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[15,x]*F[71,x]
F[71,x] = -F[77,x]+F[72,x]
F[72,x] = 1/F[15,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[75,x]+F[53,x]
F[75,x] = F[46,x]+F[76,x]
F[76,x] = F[13,x]+F[26,x]
F[77,x] = F[78,x]
F[78,x] = F[15,x]*F[53,x]*F[59,x]
F[79,x] = -F[151,x]+F[80,x]
F[80,x] = F[145,x]+F[81,x]
F[81,x] = F[82,x]+F[84,x]
F[82,x] = F[83,x]
F[83,x] = F[15,x]*F[77,x]
F[84,x] = -F[144,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[15,x]*F[87,x]
F[87,x] = F[134,x]+F[88,x]
F[88,x] = F[52,x]*F[89,x]
F[89,x] = 1/F[125,x]*F[90,x]
F[90,x] = -F[123,x]+F[91,x]
F[91,x] = 1/F[15,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = -F[97,x]+F[94,x]
F[94,x] = 1/F[15,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = -F[2,x]+F[5,x]
F[97,x] = F[106,x]+F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[0,x]*F[2,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[15,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[4,x]*F[41,x]
F[104,x] = F[105,x]
F[105,x] = F[15,x]*F[35,x]*F[53,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[15,x]
F[108,x] = F[109,x]+F[112,x]
F[109,x] = F[110,x]*F[89,x]
F[110,x] = 1/F[15,x]*F[111,x]
F[111,x] = F[12,x]
F[112,x] = F[113,x]+F[120,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[116,x]*F[15,x]
F[115,x] = F[11,x]+F[13,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[59,x]*F[89,x]
F[118,x] = F[119,x]
F[119,x] = F[15,x]*F[35,x]*F[59,x]
F[120,x] = F[121,x]
F[121,x] = F[116,x]*F[122,x]*F[15,x]
F[122,x] = F[46,x]+F[74,x]
F[123,x] = F[124,x]
F[124,x] = F[116,x]*F[15,x]
F[125,x] = 1/F[0,x]*F[126,x]
F[126,x] = -F[129,x]+F[127,x]
F[127,x] = 1/F[15,x]*F[128,x]
F[128,x] = F[20,x]
F[129,x] = -F[133,x]+F[130,x]
F[130,x] = 1/F[15,x]*F[131,x]
F[131,x] = F[132,x]
F[132,x] = -F[2,x]+F[18,x]
F[133,x] = F[125,x]*F[2,x]
F[134,x] = F[135,x]
F[135,x] = -F[143,x]+F[136,x]
F[136,x] = 1/F[15,x]*F[137,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[15,x]*F[59,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[53,x]*F[59,x]*F[89,x]
F[141,x] = F[142,x]
F[142,x] = F[116,x]*F[15,x]*F[53,x]
F[143,x] = F[51,x]*F[89,x]
F[144,x] = F[50,x]
F[145,x] = F[146,x]
F[146,x] = -F[82,x]+F[147,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[15,x]
F[149,x] = F[150,x]
F[150,x] = F[15,x]*F[53,x]*F[59,x]*F[89,x]
F[151,x] = F[152,x]
F[152,x] = F[134,x]*F[15,x]
F[153,x] = F[154,x]
F[154,x] = F[15,x]*F[155,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[116,x]*F[71,x]
F[157,x] = 1/F[15,x]*F[158,x]
F[158,x] = F[152,x]
F[159,x] = F[82,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_{15}\! \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_{15}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{45}\! \left(x \right)+F_{8}\! \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_{42}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}+2 x^{2} F_{11}\! \left(x \right)-2 x F_{11} \left(x \right)^{2}+x^{2}-3 x F_{11}\! \left(x \right)-x +2 F_{11}\! \left(x \right)
F_{12}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{0}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{37}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = x^{2} F_{26} \left(x \right)^{2}-2 x F_{26} \left(x \right)^{2}+F_{26}\! \left(x \right) x +2 F_{26}\! \left(x \right)-1
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{18}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{15}\! \left(x \right) F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{15}\! \left(x \right) F_{26}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{31}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{62}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{5}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{15}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{15}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{5}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right) F_{51}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{1}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{159}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{153}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{79}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{53}\! \left(x \right)
F_{75}\! \left(x \right) = F_{46}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{13}\! \left(x \right)+F_{26}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{59}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{151}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{145}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{15}\! \left(x \right) F_{77}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{144}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{134}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{52}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{125}\! \left(x \right)}
F_{90}\! \left(x \right) = -F_{123}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{97}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{97}\! \left(x \right) = F_{106}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{15}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{15}\! \left(x \right) F_{35}\! \left(x \right) F_{53}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{15}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{112}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{89}\! \left(x \right)
F_{110}\! \left(x \right) = \frac{F_{111}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{111}\! \left(x \right) = F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{120}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{116}\! \left(x \right) F_{15}\! \left(x \right)
F_{115}\! \left(x \right) = F_{11}\! \left(x \right)+F_{13}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{59}\! \left(x \right) F_{89}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{15}\! \left(x \right) F_{35}\! \left(x \right) F_{59}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{116}\! \left(x \right) F_{122}\! \left(x \right) F_{15}\! \left(x \right)
F_{122}\! \left(x \right) = F_{46}\! \left(x \right)+F_{74}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{116}\! \left(x \right) F_{15}\! \left(x \right)
F_{125}\! \left(x \right) = \frac{F_{126}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{126}\! \left(x \right) = -F_{129}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = \frac{F_{128}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{128}\! \left(x \right) = F_{20}\! \left(x \right)
F_{129}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = \frac{F_{131}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{18}\! \left(x \right)
F_{133}\! \left(x \right) = F_{125}\! \left(x \right) F_{2}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{53}\! \left(x \right) F_{59}\! \left(x \right) F_{89}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{116}\! \left(x \right) F_{15}\! \left(x \right) F_{53}\! \left(x \right)
F_{143}\! \left(x \right) = F_{51}\! \left(x \right) F_{89}\! \left(x \right)
F_{144}\! \left(x \right) = F_{50}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{15}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{15}\! \left(x \right) F_{53}\! \left(x \right) F_{59}\! \left(x \right) F_{89}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{134}\! \left(x \right) F_{15}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{15}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{116}\! \left(x \right) F_{71}\! \left(x \right)
F_{157}\! \left(x \right) = \frac{F_{158}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{158}\! \left(x \right) = F_{152}\! \left(x \right)
F_{159}\! \left(x \right) = F_{82}\! \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_15(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_15(x)*F_7(x))
Eq(F_7(x), F_45(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_42(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x*(x - 2)*(F_11(x) + 1)**2 + (x + 1)*(F_11(x) + 1) + F_11(x) - 1)
Eq(F_12(x), F_13(x) - F_2(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_16(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x)/F_15(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_26(x))
Eq(F_19(x), F_0(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_37(x))
Eq(F_23(x), F_19(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_2(x)*F_26(x))
Eq(F_26(x), x*(x - 2)*F_26(x)**2 + (x + 2)*F_26(x) - 1)
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_15(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_18(x)*F_31(x))
Eq(F_31(x), F_32(x)/F_15(x))
Eq(F_32(x), F_2(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_15(x)*F_16(x)*F_35(x))
Eq(F_35(x), F_36(x)/(F_15(x)*F_26(x)))
Eq(F_36(x), F_37(x))
Eq(F_37(x), -F_24(x) + F_38(x))
Eq(F_38(x), F_39(x)/F_15(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), -F_2(x) + F_41(x))
Eq(F_41(x), -F_0(x) + F_31(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_15(x)*F_44(x))
Eq(F_44(x), F_10(x))
Eq(F_45(x), F_46(x) + F_62(x))
Eq(F_46(x), F_47(x) + F_5(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_15(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_15(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_57(x))
Eq(F_52(x), F_53(x) + F_55(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_5(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_15(x)*F_51(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_15(x)*F_53(x)*F_59(x))
Eq(F_59(x), F_1(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_15(x)*F_59(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_15(x)*F_64(x))
Eq(F_64(x), F_159(x) + F_65(x))
Eq(F_65(x), F_153(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_79(x))
Eq(F_67(x), F_2(x)*F_68(x))
Eq(F_68(x), F_4(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_15(x)*F_71(x))
Eq(F_71(x), F_72(x) - F_77(x))
Eq(F_72(x), F_73(x)/F_15(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_53(x) - F_75(x))
Eq(F_75(x), F_46(x) + F_76(x))
Eq(F_76(x), F_13(x) + F_26(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_15(x)*F_53(x)*F_59(x))
Eq(F_79(x), -F_151(x) + F_80(x))
Eq(F_80(x), F_145(x) + F_81(x))
Eq(F_81(x), F_82(x) + F_84(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_15(x)*F_77(x))
Eq(F_84(x), -F_144(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_15(x)*F_87(x))
Eq(F_87(x), F_134(x) + F_88(x))
Eq(F_88(x), F_52(x)*F_89(x))
Eq(F_89(x), F_90(x)/F_125(x))
Eq(F_90(x), -F_123(x) + F_91(x))
Eq(F_91(x), F_92(x)/F_15(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_94(x) - F_97(x))
Eq(F_94(x), F_95(x)/F_15(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), -F_2(x) + F_5(x))
Eq(F_97(x), F_106(x) + F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_0(x)*F_2(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_15(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_4(x)*F_41(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_15(x)*F_35(x)*F_53(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_15(x))
Eq(F_108(x), F_109(x) + F_112(x))
Eq(F_109(x), F_110(x)*F_89(x))
Eq(F_110(x), F_111(x)/F_15(x))
Eq(F_111(x), F_12(x))
Eq(F_112(x), F_113(x) + F_120(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_116(x)*F_15(x))
Eq(F_115(x), F_11(x) + F_13(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_59(x)*F_89(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_15(x)*F_35(x)*F_59(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_116(x)*F_122(x)*F_15(x))
Eq(F_122(x), F_46(x) + F_74(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_116(x)*F_15(x))
Eq(F_125(x), F_126(x)/F_0(x))
Eq(F_126(x), F_127(x) - F_129(x))
Eq(F_127(x), F_128(x)/F_15(x))
Eq(F_128(x), F_20(x))
Eq(F_129(x), F_130(x) - F_133(x))
Eq(F_130(x), F_131(x)/F_15(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_18(x) - F_2(x))
Eq(F_133(x), F_125(x)*F_2(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x) - F_143(x))
Eq(F_136(x), F_137(x)/F_15(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_15(x)*F_59(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_53(x)*F_59(x)*F_89(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_116(x)*F_15(x)*F_53(x))
Eq(F_143(x), F_51(x)*F_89(x))
Eq(F_144(x), F_50(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_147(x) - F_82(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_15(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_15(x)*F_53(x)*F_59(x)*F_89(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_134(x)*F_15(x))
Eq(F_153(x), F_154(x))
Eq(F_154(x), F_15(x)*F_155(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_116(x)*F_71(x))
Eq(F_157(x), F_158(x)/F_15(x))
Eq(F_158(x), F_152(x))
Eq(F_159(x), F_82(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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"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, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "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, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], 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5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [5, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [2, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [5, 5]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [5, 0], [5, 2], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 2], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 2], [5, 2], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 5], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 5], [5, 2], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 3], [0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 3], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 4], [0, 4], [0, 4], [2, 4], [2, 4]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 3], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 4], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [0, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [0, 5], [5, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [2, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 5], [0, 5], [0, 5], [2, 5], [5, 5]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 2], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25316/
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[28,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[91,x]
F[5,x] = F[28,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[4,x]+F[8,x,k[0]]
F[8,x,k[0]] = F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]*F[52,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[43,x,k[0]]+F[87,x,k[0]]+F[90,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[14,x,k[0]] = F[13,x,k[0]]+F[86,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]+F[6,x]
F[15,x,k[0]] = F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[52,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]+F[85,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[84,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]+F[69,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]+F[57,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]+F[29,x,k[0]]
F[25,x,k[0]] = F[24,x,k[0]]*F[28,x]
F[25,x,k[0]] = F[26,x,k[0]]
F[27,x,k[0]] = F[26,x,k[0]]+F[7,x,k[0]]
F[27,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[28,x] = x
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[33,x,k[0]]+F[35,x,k[0]]+F[56,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[11,x,k[0]]*F[28,x]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[28,x]*F[30,x,k[0]]
F[35,x,k[0]] = F[36,x,k[0]]
F[36,x,k[0]] = F[28,x]*F[37,x,k[0]]
F[37,x,k[0]] = F[35,x,k[0]]+F[38,x,k[0]]+F[55,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[28,x]*F[40,x,k[0]]
F[40,x,k[0]] = F[12,x,k[0]]+F[41,x,k[0]]+F[43,x,k[0]]+F[53,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[18,x,k[0]]*F[28,x]
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[28,x]*F[45,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]
F[47,x,k[0]] = F[28,x]*F[46,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = (F[49,x,k[0]]-F[49,x,1])/(-1+k[0])
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]*F[52,x,k[0]]
F[51,x,k[0]] = F[40,x,k[0]]
F[52,x,k[0]] = k[0]*x
F[53,x,k[0]] = F[40,x,k[0]]*F[54,x,k[0]]
F[54,x,k[0]] = k[0]*x
F[55,x,k[0]] = F[28,x]*F[37,x,k[0]]
F[56,x,k[0]] = F[28,x]*F[30,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[11,x,k[0]] = F[58,x,k[0]]+F[59,x,k[0]]
F[59,x,k[0]] = F[12,x,k[0]]+F[41,x,k[0]]+F[60,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]
F[61,x,k[0]] = F[28,x]*F[62,x,k[0]]
F[62,x,k[0]] = F[37,x,k[0]]+F[63,x,k[0]]
F[64,x,k[0]] = F[63,x,k[0]]+F[67,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[46,x,k[0]] = F[65,x,k[0]]+F[66,x,k[0]]
F[66,x,k[0]] = F[37,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]
F[40,x,k[0]] = F[59,x,k[0]]+F[68,x,k[0]]
F[70,x,k[0]] = F[59,x,k[0]]+F[69,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[74,x,k[0]]+F[76,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[13,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[31,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]
F[75,x,k[0]] = F[19,x,k[0]]*F[28,x]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[28,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[62,x,k[0]]+F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = F[28,x]*F[40,x,k[0]]*F[81,x]
F[81,x] = F[1,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[28,x]*F[81,x]
F[84,x,k[0]] = F[30,x,k[0]]
F[85,x,k[0]] = F[69,x,k[0]]
F[86,x,k[0]] = F[26,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]
F[88,x,k[0]] = F[28,x]*F[89,x,k[0]]
F[89,x,k[0]] = F[24,x,k[0]]
F[90,x,k[0]] = F[11,x,k[0]]*F[54,x,k[0]]
F[91,x] = F[28,x]*F[92,x]
F[92,x] = F[93,x,1]
F[93,x,k[0]] = F[4,x]+F[49,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{91}\! \left(x \right)
F_{5}\! \left(x \right) = F_{28}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{87}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{6}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{28}\! \left(x \right) = x
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = -\frac{-F_{49}\! \left(x , y\right)+F_{49}\! \left(x , 1\right)}{-1+y}
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = y x
F_{53}\! \left(x , y\right) = F_{40}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = y x
F_{55}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{30}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{13}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{28}\! \left(x \right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{40}\! \left(x , y\right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{1}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{28}\! \left(x \right) F_{81}\! \left(x \right)
F_{84}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{28}\! \left(x \right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{24}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{91}\! \left(x \right) = F_{28}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x , 1\right)
F_{93}\! \left(x , y\right) = F_{4}\! \left(x \right)+F_{49}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_28(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_91(x))
Eq(F_5(x), F_28(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_4(x) + F_8(x, k_0))
Eq(F_8(x, k_0), F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0)*F_52(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_43(x, k_0) + F_87(x, k_0) + F_90(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_14(x, k_0), F_13(x, k_0) + F_86(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0) + F_6(x))
Eq(F_15(x, k_0), F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_52(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0) + F_85(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_84(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0) + F_69(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0) + F_57(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0) + F_29(x, k_0))
Eq(F_25(x, k_0), F_24(x, k_0)*F_28(x))
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_27(x, k_0), F_26(x, k_0) + F_7(x, k_0))
Eq(F_27(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_28(x), x)
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_33(x, k_0) + F_35(x, k_0) + F_56(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_11(x, k_0)*F_28(x))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_28(x)*F_30(x, k_0))
Eq(F_35(x, k_0), F_36(x, k_0))
Eq(F_36(x, k_0), F_28(x)*F_37(x, k_0))
Eq(F_37(x, k_0), F_35(x, k_0) + F_38(x, k_0) + F_55(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_28(x)*F_40(x, k_0))
Eq(F_40(x, k_0), F_12(x, k_0) + F_41(x, k_0) + F_43(x, k_0) + F_53(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_18(x, k_0)*F_28(x))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_28(x)*F_45(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0))
Eq(F_47(x, k_0), F_28(x)*F_46(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), -F_49(x, k_0) + (k_0*F_49(x, k_0) - F_49(x, 1))/(k_0 - 1))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0)*F_52(x, k_0))
Eq(F_51(x, k_0), F_40(x, k_0))
Eq(F_52(x, k_0), k_0*x)
Eq(F_53(x, k_0), F_40(x, k_0)*F_54(x, k_0))
Eq(F_54(x, k_0), k_0*x)
Eq(F_55(x, k_0), F_28(x)*F_37(x, k_0))
Eq(F_56(x, k_0), F_28(x)*F_30(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_11(x, k_0), F_58(x, k_0) + F_59(x, k_0))
Eq(F_59(x, k_0), F_12(x, k_0) + F_41(x, k_0) + F_60(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0))
Eq(F_61(x, k_0), F_28(x)*F_62(x, k_0))
Eq(F_62(x, k_0), F_37(x, k_0) + F_63(x, k_0))
Eq(F_64(x, k_0), F_63(x, k_0) + F_67(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_46(x, k_0), F_65(x, k_0) + F_66(x, k_0))
Eq(F_66(x, k_0), F_37(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0))
Eq(F_40(x, k_0), F_59(x, k_0) + F_68(x, k_0))
Eq(F_70(x, k_0), F_59(x, k_0) + F_69(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_74(x, k_0) + F_76(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_13(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_31(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0))
Eq(F_75(x, k_0), F_19(x, k_0)*F_28(x))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_28(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_62(x, k_0) + F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), F_28(x)*F_40(x, k_0)*F_81(x))
Eq(F_81(x), F_1(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_28(x)*F_81(x))
Eq(F_84(x, k_0), F_30(x, k_0))
Eq(F_85(x, k_0), F_69(x, k_0))
Eq(F_86(x, k_0), F_26(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0))
Eq(F_88(x, k_0), F_28(x)*F_89(x, k_0))
Eq(F_89(x, k_0), F_24(x, k_0))
Eq(F_90(x, k_0), F_11(x, k_0)*F_54(x, k_0))
Eq(F_91(x), F_28(x)*F_92(x))
Eq(F_92(x), F_93(x, 1))
Eq(F_93(x, k_0), F_4(x) + F_49(x, k_0))
Pack JSON:
{"name": "point_and_row_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": true, "place_col": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": 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[0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2], [4, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 0], [0, 2], [1, 2], [4, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 0], [0, 2], [2, 2], [4, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [4, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [2, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [1, 2], [4, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [2, 2], [4, 2]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[2, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "SumComponentAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25559/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[18,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]+F[15,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[14,x]
F[12,x] = 1/F[14,x]*F[13,x]
F[13,x] = F[5,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[17,x]
F[17,x] = F[13,x]
F[18,x] = F[19,x]+F[31,x]
F[19,x] = F[20,x]+F[5,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[12,x]+F[22,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[14,x]*F[28,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[14,x]*F[28,x]
F[31,x] = F[32,x]
F[32,x] = F[14,x]*F[33,x]
F[33,x] = F[160,x]+F[34,x]
F[34,x] = F[154,x]+F[35,x]
F[35,x] = F[36,x]+F[48,x]
F[36,x] = F[2,x]*F[37,x]
F[37,x] = F[38,x]+F[4,x]
F[38,x] = F[39,x]
F[39,x] = F[14,x]*F[40,x]
F[40,x] = -F[46,x]+F[41,x]
F[41,x] = 1/F[14,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[44,x]+F[12,x]
F[44,x] = F[19,x]+F[45,x]
F[45,x] = F[0,x]+F[10,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[14,x]*F[28,x]
F[48,x] = -F[152,x]+F[49,x]
F[49,x] = F[146,x]+F[50,x]
F[50,x] = F[51,x]+F[53,x]
F[51,x] = F[52,x]
F[52,x] = F[14,x]*F[46,x]
F[53,x] = -F[144,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[56,x]
F[56,x] = F[134,x]+F[57,x]
F[57,x] = F[25,x]*F[58,x]
F[58,x] = 1/F[126,x]*F[59,x]
F[59,x] = -F[124,x]+F[60,x]
F[60,x] = 1/F[14,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = -F[67,x]+F[63,x]
F[63,x] = 1/F[14,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[2,x]+F[66,x]
F[66,x] = -F[0,x]+F[4,x]
F[67,x] = F[105,x]+F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[0,x]*F[2,x]
F[70,x] = F[71,x]
F[71,x] = F[14,x]*F[72,x]
F[72,x] = F[73,x]+F[79,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[2,x]+F[75,x]
F[75,x] = -F[2,x]+F[76,x]
F[76,x] = -F[0,x]+F[77,x]
F[77,x] = 1/F[14,x]*F[78,x]
F[78,x] = F[2,x]
F[79,x] = F[80,x]
F[80,x] = F[12,x]*F[14,x]*F[81,x]
F[81,x] = 1/F[14,x]/F[88,x]*F[82,x]
F[82,x] = F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[14,x]*F[85,x]
F[85,x] = F[75,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[2,x]*F[88,x]
F[88,x] = -1+(x^2-2*x)*F[88,x]^2+(2+x)*F[88,x]
F[89,x] = F[90,x]
F[90,x] = F[14,x]*F[91,x]
F[91,x] = F[101,x]+F[92,x]
F[92,x] = F[77,x]*F[93,x]
F[93,x] = F[2,x]+F[94,x]
F[94,x] = -F[100,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[14,x]*F[97,x]
F[97,x] = F[83,x]+F[98,x]
F[98,x] = F[86,x]+F[99,x]
F[99,x] = F[0,x]+F[95,x]
F[100,x] = (x*F[100,x]+x-2*F[100,x])*(x*F[100,x]+x-1)
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[14,x]*F[81,x]
F[103,x] = 1/F[14,x]*F[104,x]
F[104,x] = F[93,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[14,x]
F[107,x] = F[108,x]+F[112,x]
F[108,x] = F[109,x]*F[58,x]
F[109,x] = 1/F[14,x]*F[110,x]
F[110,x] = F[111,x]
F[111,x] = -F[100,x]+F[10,x]
F[112,x] = F[113,x]+F[121,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[117,x]*F[14,x]
F[115,x] = F[100,x]+F[116,x]
F[116,x] = F[111,x]+F[2,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[28,x]*F[58,x]
F[119,x] = F[120,x]
F[120,x] = F[14,x]*F[28,x]*F[81,x]
F[121,x] = F[122,x]
F[122,x] = F[117,x]*F[123,x]*F[14,x]
F[123,x] = F[19,x]+F[43,x]
F[124,x] = F[125,x]
F[125,x] = F[117,x]*F[14,x]
F[126,x] = 1/F[0,x]*F[127,x]
F[127,x] = -F[130,x]+F[128,x]
F[128,x] = 1/F[14,x]*F[129,x]
F[129,x] = F[95,x]
F[130,x] = -F[133,x]+F[131,x]
F[131,x] = 1/F[14,x]*F[132,x]
F[132,x] = F[94,x]
F[133,x] = F[126,x]*F[2,x]
F[134,x] = F[135,x]
F[135,x] = -F[143,x]+F[136,x]
F[136,x] = 1/F[14,x]*F[137,x]
F[137,x] = F[138,x]
F[138,x] = F[139,x]*F[14,x]*F[28,x]
F[139,x] = F[140,x]+F[141,x]
F[140,x] = F[12,x]*F[28,x]*F[58,x]
F[141,x] = F[142,x]
F[142,x] = F[117,x]*F[12,x]*F[14,x]
F[143,x] = F[24,x]*F[58,x]
F[144,x] = F[145,x]
F[145,x] = F[14,x]*F[24,x]
F[146,x] = F[147,x]
F[147,x] = -F[51,x]+F[148,x]
F[148,x] = F[149,x]
F[149,x] = F[14,x]*F[150,x]
F[150,x] = F[151,x]
F[151,x] = F[12,x]*F[14,x]*F[28,x]*F[58,x]
F[152,x] = F[153,x]
F[153,x] = F[134,x]*F[14,x]
F[154,x] = F[155,x]
F[155,x] = F[14,x]*F[156,x]
F[156,x] = F[157,x]+F[158,x]
F[157,x] = F[117,x]*F[40,x]
F[158,x] = 1/F[14,x]*F[159,x]
F[159,x] = F[153,x]
F[160,x] = F[51,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_{14}\! \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_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{18}\! \left(x \right)+F_{8}\! \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_{15}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = \frac{F_{13}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{13}\! \left(x \right) = F_{5}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{160}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{154}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{48}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{12}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{0}\! \left(x \right)+F_{10}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{152}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{146}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{144}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{134}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{25}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{126}\! \left(x \right)}
F_{59}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{105}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{79}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = \frac{F_{78}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{78}\! \left(x \right) = F_{2}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = \frac{F_{82}\! \left(x \right)}{F_{14}\! \left(x \right) F_{88}\! \left(x \right)}
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{75}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{2}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = x^{2} F_{88} \left(x \right)^{2}-2 x F_{88} \left(x \right)^{2}+F_{88}\! \left(x \right) x +2 F_{88}\! \left(x \right)-1
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{14}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{101}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{77}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{2}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{14}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{83}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{86}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right)+F_{95}\! \left(x \right)
F_{100}\! \left(x \right) = x^{2} F_{100} \left(x \right)^{2}+2 x^{2} F_{100}\! \left(x \right)-2 x F_{100} \left(x \right)^{2}+x^{2}-3 x F_{100}\! \left(x \right)-x +2 F_{100}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{14}\! \left(x \right) F_{81}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{93}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{14}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{58}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{100}\! \left(x \right)+F_{10}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{121}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{115}\! \left(x \right) = F_{100}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{111}\! \left(x \right)+F_{2}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{28}\! \left(x \right) F_{58}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right) F_{81}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{117}\! \left(x \right) F_{123}\! \left(x \right) F_{14}\! \left(x \right)
F_{123}\! \left(x \right) = F_{19}\! \left(x \right)+F_{43}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{117}\! \left(x \right) F_{14}\! \left(x \right)
F_{126}\! \left(x \right) = \frac{F_{127}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{127}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{95}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{94}\! \left(x \right)
F_{133}\! \left(x \right) = F_{126}\! \left(x \right) F_{2}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = \frac{F_{137}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{141}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right) F_{58}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{117}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{143}\! \left(x \right) = F_{24}\! \left(x \right) F_{58}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{14}\! \left(x \right) F_{24}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{14}\! \left(x \right) F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{28}\! \left(x \right) F_{58}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{134}\! \left(x \right) F_{14}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{14}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{158}\! \left(x \right)
F_{157}\! \left(x \right) = F_{117}\! \left(x \right) F_{40}\! \left(x \right)
F_{158}\! \left(x \right) = \frac{F_{159}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{159}\! \left(x \right) = F_{153}\! \left(x \right)
F_{160}\! \left(x \right) = F_{51}\! \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_14(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_14(x)*F_7(x))
Eq(F_7(x), F_18(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_15(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_14(x))
Eq(F_12(x), F_13(x)/F_14(x))
Eq(F_13(x), F_5(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_17(x))
Eq(F_17(x), F_13(x))
Eq(F_18(x), F_19(x) + F_31(x))
Eq(F_19(x), F_20(x) + F_5(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_12(x) + F_22(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_14(x)*F_28(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_14(x)*F_28(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_14(x)*F_33(x))
Eq(F_33(x), F_160(x) + F_34(x))
Eq(F_34(x), F_154(x) + F_35(x))
Eq(F_35(x), F_36(x) + F_48(x))
Eq(F_36(x), F_2(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_4(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_14(x)*F_40(x))
Eq(F_40(x), F_41(x) - F_46(x))
Eq(F_41(x), F_42(x)/F_14(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x) - F_44(x))
Eq(F_44(x), F_19(x) + F_45(x))
Eq(F_45(x), F_0(x) + F_10(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_14(x)*F_28(x))
Eq(F_48(x), -F_152(x) + F_49(x))
Eq(F_49(x), F_146(x) + F_50(x))
Eq(F_50(x), F_51(x) + F_53(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_14(x)*F_46(x))
Eq(F_53(x), -F_144(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_56(x))
Eq(F_56(x), F_134(x) + F_57(x))
Eq(F_57(x), F_25(x)*F_58(x))
Eq(F_58(x), F_59(x)/F_126(x))
Eq(F_59(x), -F_124(x) + F_60(x))
Eq(F_60(x), F_61(x)/F_14(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) - F_67(x))
Eq(F_63(x), F_64(x)/F_14(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_2(x) + F_66(x))
Eq(F_66(x), -F_0(x) + F_4(x))
Eq(F_67(x), F_105(x) + F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_0(x)*F_2(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_14(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_79(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_2(x) + F_75(x))
Eq(F_75(x), -F_2(x) + F_76(x))
Eq(F_76(x), -F_0(x) + F_77(x))
Eq(F_77(x), F_78(x)/F_14(x))
Eq(F_78(x), F_2(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_12(x)*F_14(x)*F_81(x))
Eq(F_81(x), F_82(x)/(F_14(x)*F_88(x)))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_14(x))
Eq(F_85(x), F_75(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_2(x)*F_88(x))
Eq(F_88(x), x*(x - 2)*F_88(x)**2 + (x + 2)*F_88(x) - 1)
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_14(x)*F_91(x))
Eq(F_91(x), F_101(x) + F_92(x))
Eq(F_92(x), F_77(x)*F_93(x))
Eq(F_93(x), F_2(x) + F_94(x))
Eq(F_94(x), -F_100(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_14(x)*F_97(x))
Eq(F_97(x), F_83(x) + F_98(x))
Eq(F_98(x), F_86(x) + F_99(x))
Eq(F_99(x), F_0(x) + F_95(x))
Eq(F_100(x), x*(x - 2)*(F_100(x) + 1)**2 + (x + 1)*(F_100(x) + 1) + F_100(x) - 1)
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_14(x)*F_81(x))
Eq(F_103(x), F_104(x)/F_14(x))
Eq(F_104(x), F_93(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_14(x))
Eq(F_107(x), F_108(x) + F_112(x))
Eq(F_108(x), F_109(x)*F_58(x))
Eq(F_109(x), F_110(x)/F_14(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_10(x) - F_100(x))
Eq(F_112(x), F_113(x) + F_121(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_117(x)*F_14(x))
Eq(F_115(x), F_100(x) + F_116(x))
Eq(F_116(x), F_111(x) + F_2(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_28(x)*F_58(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_14(x)*F_28(x)*F_81(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_117(x)*F_123(x)*F_14(x))
Eq(F_123(x), F_19(x) + F_43(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_117(x)*F_14(x))
Eq(F_126(x), F_127(x)/F_0(x))
Eq(F_127(x), F_128(x) - F_130(x))
Eq(F_128(x), F_129(x)/F_14(x))
Eq(F_129(x), F_95(x))
Eq(F_130(x), F_131(x) - F_133(x))
Eq(F_131(x), F_132(x)/F_14(x))
Eq(F_132(x), F_94(x))
Eq(F_133(x), F_126(x)*F_2(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x) - F_143(x))
Eq(F_136(x), F_137(x)/F_14(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_139(x)*F_14(x)*F_28(x))
Eq(F_139(x), F_140(x) + F_141(x))
Eq(F_140(x), F_12(x)*F_28(x)*F_58(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_117(x)*F_12(x)*F_14(x))
Eq(F_143(x), F_24(x)*F_58(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_14(x)*F_24(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x) - F_51(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_14(x)*F_150(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_12(x)*F_14(x)*F_28(x)*F_58(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_134(x)*F_14(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_14(x)*F_156(x))
Eq(F_156(x), F_157(x) + F_158(x))
Eq(F_157(x), F_117(x)*F_40(x))
Eq(F_158(x), F_159(x)/F_14(x))
Eq(F_159(x), F_153(x))
Eq(F_160(x), F_51(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, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [2, 0, 1, 4, 3]], "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, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"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, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "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, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 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