01243_01342_01432_02143_10243_10342_10432
Counting sequence:
1, 1, 2, 6, 24, 113, 582, 3164, 17838, 103276, 610304, 3665958, 22316734, 137375886, 853661444, 5347781688, 33737151726, 214146508860, 1366687420552, 8764409343840, 56448444093538, 364981255686209, 2368199912713846, 15415480524323148, 100639006367616546, 658780634774681996, 4323025083927737160, 28433153591911085396, 187404336033096716644, 1237617222428427662668, 8188166338870878000232, 54266010900307109955696, 360215562471143967053838, 2394678573910802082163644, 15942004431929997799084024, 106270756242170127403071048, 709295215064356870370075888, 4739719992964637989320946388, 31707583639343607511270939896, 212340576692280322288099528048, 1423438642216633043014359037656, 9551216875932226698413275501160, 64146464459192789287464403109688, 431183472385999158440544975472326, 2900744321650583858397896592611646, 19529833614545368121859984778694934, 131587381395206028744167003445313332, 887242628740234599865646292615464088, 5986455462870132303862219101051661026, 40418843661040938827686886949441743604, 273069451076228427541088911922547099912, 1845977838588191894780819540999420054712, 12486296806268784257284563902131595278740, 84505484845267633597011815127303624283614, 572230537143829892386513835622099937776660, 3876889086715104692975398561560285080065320, 26279296423718252469591340248821777708048460, 178219137280749353123312607173119775770170312, 1209199139686440223388195548931155347293545072, 8207997844048742441608358770066769349009095368, 55739866723823360742968328305329869777174044136, 378684573071227967314675294955200965081796962136, 2573749709717780347364497588068070213321424369232, 17499527516320873632107833364034616903215136243936, 119028846552817105199197132216553521873125588283534, 809913887183588880044970311143989444967601800989788, 5512914429287299540298940275297116045557173813695416, 37538311431654376419005658846124730470616240564322280, 255690617112058127252262259278526236819051547650058752, 1742196453258250233505844071189481611943655474276463020, 11874562574845858878361370526207589657590811283426527368, 80960342780091881185885969790705241703793732530597965264, 552150546550947895101905031928025441592376802173623839656, 3766773524128759998858800606288646690559463178511862562768, 25704246616394548783851056901584062687989476454537751865536, 175452794521636805444069469572895544336729751925908677206776, 1197933048528733884819160115630426297246775631736407383609304, 8181229592991839932784570142583269402823899810242351926705752, 55887597869980982617905479811086376274870054661921628747426768, 381874183404231896351667447732220673111362846560910453984153952, 2609939370233998480599453661966614737982031293280526837013721752, 17841985265040676477569322928683792436015117694359544888885748032, 121998935942334598926097481043933310825503623612319378277103459664, 834385178965395018964686989331244783550276892746513643265875927080, 5707848567174049106777486418557223809937397492128639210163737444682, 39054525129298818216341075401122775858299137538738128382645486403713, 267276732195799998457262071819934992246823285772458030120620836819766, 1829530724125084706961931511439975860757867467086598058583231685152524, 12525786005458130324492700862030012651406518748358366907094032091689106, 85773874345902111337434502015793317967630072217116693965457903708442156, 587473017649541371372035519313109561165536771080298435018562865178783432, 4024406496174811816143498546812114978583181596991185196245080967681736068, 27573697101518976294585362233134563840771495429668680053567457819522683604, 188958173519338461616089708559070275483358296637494059709846981510226910204, 1295126598297995348671234906511232062366966662186482938081772603715061378568, 8878365302663110888141048777294631542063919761025075563443751941373305009456, 60873249358862532295182513823100792659461381688331730452937692791716272517858, 417437186018368594731538069587352872800489815345326340023425534485889267745252, 2863027330111513151298428707270835694227276748421942269587230367366881409233992, 19639396725975721857821366804772538492973895838018139868997194356725193171171000, 134740360550995301868025708129100728174909760034596231121909518396693080904699184
Implicit equation for the generating function in Maple syntax:
(3*x-2)*F(x)^4+(-6*x+4)*F(x)^3+2*x*F(x)^2-3*F(x)+1 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x -2\right) F \! \left(x \right)^{4}+\left(-6 x +4\right) F \! \left(x \right)^{3}+2 x F \! \left(x \right)^{2}-3 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) = 582
a(7) = 3164
a(8) = 17838
a(n+9) = 192/407*n*(n+1)*(2*n+1)/(n+9)/(n+8)/(n+7)*a(n)-16/407*(n+1)*(230*n^2+1174*n+1257)/(n+9)/(n+8)/(n+7)*a(n+1)-16/1221*(1231*n^3+6990*n^2+13499*n+8859)/(n+9)/(n+8)/(n+7)*a(n+2)+1/1221*(3617*n^3+98316*n^2+572425*n+929190)/(n+9)/(n+8)/(n+7)*a(n+3)+1/2442*(223387*n^3+2190678*n^2+6755264*n+6261150)/(n+9)/(n+8)/(n+7)*a(n+4)-1/3256*(418159*n^3+5275516*n^2+21635794*n+28540429)/(n+9)/(n+8)/(n+7)*a(n+5)+1/39072*(3441661*n^3+55226586*n^2+294989687*n+525100746)/(n+9)/(n+8)/(n+7)*a(n+6)-1/3256*(134687*n^2+1707842*n+5457366)/(n+8)/(n+9)*a(n+7)+3/3256*(12405*n+89393)/(n+9)*a(n+8), n >= 9
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 113
a(6) = 582
a(7) = 3164
a(8) = 17838
a{\left(n + 9 \right)} = \frac{192 n \left(n + 1\right) \left(2 n + 1\right) a{\left(n \right)}}{407 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} - \frac{16 \left(n + 1\right) \left(230 n^{2} + 1174 n + 1257\right) a{\left(n + 1 \right)}}{407 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{3 \left(12405 n + 89393\right) a{\left(n + 8 \right)}}{3256 \left(n + 9\right)} - \frac{\left(134687 n^{2} + 1707842 n + 5457366\right) a{\left(n + 7 \right)}}{3256 \left(n + 8\right) \left(n + 9\right)} - \frac{16 \left(1231 n^{3} + 6990 n^{2} + 13499 n + 8859\right) a{\left(n + 2 \right)}}{1221 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(3617 n^{3} + 98316 n^{2} + 572425 n + 929190\right) a{\left(n + 3 \right)}}{1221 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(223387 n^{3} + 2190678 n^{2} + 6755264 n + 6261150\right) a{\left(n + 4 \right)}}{2442 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} - \frac{\left(418159 n^{3} + 5275516 n^{2} + 21635794 n + 28540429\right) a{\left(n + 5 \right)}}{3256 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(3441661 n^{3} + 55226586 n^{2} + 294989687 n + 525100746\right) a{\left(n + 6 \right)}}{39072 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24678/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = F[156,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[20,x]
F[11,x] = F[12,x]+F[36,x]
F[12,x] = F[13,x]+F[14,x]
F[13,x] = F[0,x]*F[8,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[20,x]*F[25,x]
F[16,x] = F[17,x]+F[23,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = 1/F[20,x]*F[19,x]
F[19,x] = F[5,x]
F[20,x] = x
F[21,x] = F[22,x]
F[22,x] = F[16,x]*F[20,x]
F[23,x] = F[24,x]
F[24,x] = F[17,x]*F[20,x]
F[25,x] = F[0,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[20,x]*F[28,x]
F[28,x] = 1/F[18,x]/F[20,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[35,x]+F[31,x]
F[31,x] = 1/F[20,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[2,x]+F[34,x]
F[34,x] = -F[0,x]+F[4,x]
F[35,x] = F[2,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[20,x]*F[38,x]
F[38,x] = F[39,x]+F[51,x]
F[39,x] = F[28,x]*F[40,x]
F[40,x] = -F[50,x]+F[41,x]
F[41,x] = 1/F[20,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[44,x]+F[18,x]
F[44,x] = F[4,x]+F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[47,x]
F[47,x] = F[18,x]*F[20,x]
F[48,x] = F[49,x]
F[49,x] = F[20,x]*F[21,x]
F[50,x] = F[45,x]
F[51,x] = 1/F[20,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[14,x]+F[54,x]
F[54,x] = F[154,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[20,x]*F[57,x]
F[57,x] = -F[152,x]+F[58,x]
F[58,x] = 1/F[20,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[20,x]*F[61,x]
F[61,x] = F[150,x]+F[62,x]
F[62,x] = F[63,x]*F[65,x]
F[63,x] = F[18,x]+F[64,x]
F[64,x] = F[19,x]
F[65,x] = F[25,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[20,x]*F[68,x]*F[76,x]
F[68,x] = F[1,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[20,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[1,x]+F[20,x]
F[73,x] = F[69,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[20,x]*F[69,x]
F[76,x] = F[149,x]+F[77,x]
F[77,x] = F[25,x]+F[78,x]
F[78,x] = -F[140,x]+F[79,x]
F[79,x] = 1/F[20,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = -F[84,x]+F[82,x]
F[82,x] = 1/F[20,x]*F[83,x]
F[83,x] = F[33,x]
F[84,x] = F[122,x]+F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[0,x]*F[2,x]
F[87,x] = F[88,x]
F[88,x] = F[20,x]*F[89,x]
F[89,x] = F[90,x]+F[96,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[2,x]+F[92,x]
F[92,x] = -F[2,x]+F[93,x]
F[93,x] = -F[0,x]+F[94,x]
F[94,x] = 1/F[20,x]*F[95,x]
F[95,x] = F[2,x]
F[96,x] = F[97,x]
F[97,x] = F[18,x]*F[20,x]*F[98,x]
F[98,x] = 1/F[105,x]/F[20,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = -F[103,x]+F[101,x]
F[101,x] = 1/F[20,x]*F[102,x]
F[102,x] = F[92,x]
F[103,x] = F[104,x]+F[106,x]
F[104,x] = F[105,x]*F[2,x]
F[105,x] = 1+x^2*F[105,x]^3+(-x^2+x)*F[105,x]^2
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[20,x]
F[108,x] = F[109,x]+F[118,x]
F[109,x] = F[110,x]*F[94,x]
F[110,x] = F[111,x]+F[2,x]
F[111,x] = -F[117,x]+F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[20,x]
F[114,x] = F[100,x]+F[115,x]
F[115,x] = F[103,x]+F[116,x]
F[116,x] = F[0,x]+F[112,x]
F[117,x] = x*(1+F[117,x])^2*(x*F[117,x]+1)
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[20,x]*F[98,x]
F[120,x] = 1/F[20,x]*F[121,x]
F[121,x] = F[110,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[20,x]
F[124,x] = F[125,x]+F[129,x]
F[125,x] = F[126,x]*F[25,x]
F[126,x] = 1/F[20,x]*F[127,x]
F[127,x] = F[128,x]
F[128,x] = -F[117,x]+F[46,x]
F[129,x] = F[130,x]+F[136,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[134,x]*F[20,x]
F[132,x] = F[117,x]+F[133,x]
F[133,x] = F[128,x]+F[2,x]
F[134,x] = 1/F[20,x]*F[135,x]
F[135,x] = F[78,x]
F[136,x] = F[137,x]
F[137,x] = F[134,x]*F[138,x]*F[20,x]
F[138,x] = F[139,x]+F[43,x]
F[139,x] = F[48,x]+F[5,x]
F[140,x] = F[141,x]*F[25,x]
F[141,x] = 1/F[0,x]*F[142,x]
F[142,x] = -F[145,x]+F[143,x]
F[143,x] = 1/F[20,x]*F[144,x]
F[144,x] = F[112,x]
F[145,x] = -F[148,x]+F[146,x]
F[146,x] = 1/F[20,x]*F[147,x]
F[147,x] = F[111,x]
F[148,x] = F[141,x]*F[2,x]
F[149,x] = F[20,x]*F[25,x]
F[150,x] = F[151,x]
F[151,x] = F[134,x]*F[18,x]*F[20,x]
F[152,x] = F[153,x]
F[153,x] = F[23,x]*F[25,x]
F[154,x] = F[155,x]
F[155,x] = F[20,x]*F[23,x]*F[25,x]
F[156,x] = F[157,x]
F[157,x] = F[16,x]*F[20,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_{20}\! \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_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{156}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{36}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{25}\! \left(x \right) = F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right) F_{20}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{39}\! \left(x \right) = F_{28}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{18}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right) F_{21}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{154}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{20}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{152}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{20}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{150}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{18}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{19}\! \left(x \right)
F_{65}\! \left(x \right) = F_{25}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right) F_{68}\! \left(x \right) F_{76}\! \left(x \right)
F_{68}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{20}\! \left(x \right) F_{69}\! \left(x \right)
F_{76}\! \left(x \right) = F_{149}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{25}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{33}\! \left(x \right)
F_{84}\! \left(x \right) = F_{122}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{96}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{2}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{2}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{105}\! \left(x \right) F_{20}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{92}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{2}\! \left(x \right)
F_{105}\! \left(x \right) = x^{2} F_{105} \left(x \right)^{3}-x^{2} F_{105} \left(x \right)^{2}+x F_{105} \left(x \right)^{2}+1
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{20}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{118}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{94}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{2}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{20}\! \left(x \right)
F_{114}\! \left(x \right) = F_{100}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{103}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{0}\! \left(x \right)+F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = x^{2} F_{117} \left(x \right)^{3}+2 x^{2} F_{117} \left(x \right)^{2}+x^{2} F_{117}\! \left(x \right)+x F_{117} \left(x \right)^{2}+2 x F_{117}\! \left(x \right)+x
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{110}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{20}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{129}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{25}\! \left(x \right)
F_{126}\! \left(x \right) = \frac{F_{127}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{46}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{136}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{134}\! \left(x \right) F_{20}\! \left(x \right)
F_{132}\! \left(x \right) = F_{117}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{128}\! \left(x \right)+F_{2}\! \left(x \right)
F_{134}\! \left(x \right) = \frac{F_{135}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{135}\! \left(x \right) = F_{78}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{134}\! \left(x \right) F_{138}\! \left(x \right) F_{20}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{43}\! \left(x \right)
F_{139}\! \left(x \right) = F_{48}\! \left(x \right)+F_{5}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{25}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{142}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{144}\! \left(x \right) = F_{112}\! \left(x \right)
F_{145}\! \left(x \right) = -F_{148}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = \frac{F_{147}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{147}\! \left(x \right) = F_{111}\! \left(x \right)
F_{148}\! \left(x \right) = F_{141}\! \left(x \right) F_{2}\! \left(x \right)
F_{149}\! \left(x \right) = F_{20}\! \left(x \right) F_{25}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{134}\! \left(x \right) F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \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_20(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_20(x)*F_7(x))
Eq(F_7(x), F_156(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_20(x))
Eq(F_11(x), F_12(x) + F_36(x))
Eq(F_12(x), F_13(x) + F_14(x))
Eq(F_13(x), F_0(x)*F_8(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_20(x)*F_25(x))
Eq(F_16(x), F_17(x) + F_23(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x)/F_20(x))
Eq(F_19(x), F_5(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_16(x)*F_20(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_17(x)*F_20(x))
Eq(F_25(x), F_0(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_20(x)*F_28(x))
Eq(F_28(x), F_29(x)/(F_18(x)*F_20(x)))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_35(x))
Eq(F_31(x), F_32(x)/F_20(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_2(x) + F_34(x))
Eq(F_34(x), -F_0(x) + F_4(x))
Eq(F_35(x), F_2(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_20(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_51(x))
Eq(F_39(x), F_28(x)*F_40(x))
Eq(F_40(x), F_41(x) - F_50(x))
Eq(F_41(x), F_42(x)/F_20(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_18(x) - F_44(x))
Eq(F_44(x), F_4(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_18(x)*F_20(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_20(x)*F_21(x))
Eq(F_50(x), F_45(x))
Eq(F_51(x), F_52(x)/F_20(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), -F_14(x) + F_54(x))
Eq(F_54(x), F_154(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_20(x)*F_57(x))
Eq(F_57(x), -F_152(x) + F_58(x))
Eq(F_58(x), F_59(x)/F_20(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_20(x)*F_61(x))
Eq(F_61(x), F_150(x) + F_62(x))
Eq(F_62(x), F_63(x)*F_65(x))
Eq(F_63(x), F_18(x) + F_64(x))
Eq(F_64(x), F_19(x))
Eq(F_65(x), F_25(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_20(x)*F_68(x)*F_76(x))
Eq(F_68(x), F_1(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_20(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_1(x) + F_20(x))
Eq(F_73(x), F_69(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_20(x)*F_69(x))
Eq(F_76(x), F_149(x) + F_77(x))
Eq(F_77(x), F_25(x) + F_78(x))
Eq(F_78(x), -F_140(x) + F_79(x))
Eq(F_79(x), F_80(x)/F_20(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_82(x) - F_84(x))
Eq(F_82(x), F_83(x)/F_20(x))
Eq(F_83(x), F_33(x))
Eq(F_84(x), F_122(x) + F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_0(x)*F_2(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_20(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_96(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_2(x) + F_92(x))
Eq(F_92(x), -F_2(x) + F_93(x))
Eq(F_93(x), -F_0(x) + F_94(x))
Eq(F_94(x), F_95(x)/F_20(x))
Eq(F_95(x), F_2(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_18(x)*F_20(x)*F_98(x))
Eq(F_98(x), F_99(x)/(F_105(x)*F_20(x)))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x) - F_103(x))
Eq(F_101(x), F_102(x)/F_20(x))
Eq(F_102(x), F_92(x))
Eq(F_103(x), F_104(x) + F_106(x))
Eq(F_104(x), F_105(x)*F_2(x))
Eq(F_105(x), x**2*F_105(x)**3 - x*(x - 1)*F_105(x)**2 + 1)
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_20(x))
Eq(F_108(x), F_109(x) + F_118(x))
Eq(F_109(x), F_110(x)*F_94(x))
Eq(F_110(x), F_111(x) + F_2(x))
Eq(F_111(x), F_112(x) - F_117(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_20(x))
Eq(F_114(x), F_100(x) + F_115(x))
Eq(F_115(x), F_103(x) + F_116(x))
Eq(F_116(x), F_0(x) + F_112(x))
Eq(F_117(x), x**2*(F_117(x) + 1)**3 - x*(x - 1)*(F_117(x) + 1)**2)
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_20(x)*F_98(x))
Eq(F_120(x), F_121(x)/F_20(x))
Eq(F_121(x), F_110(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_20(x))
Eq(F_124(x), F_125(x) + F_129(x))
Eq(F_125(x), F_126(x)*F_25(x))
Eq(F_126(x), F_127(x)/F_20(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), -F_117(x) + F_46(x))
Eq(F_129(x), F_130(x) + F_136(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_134(x)*F_20(x))
Eq(F_132(x), F_117(x) + F_133(x))
Eq(F_133(x), F_128(x) + F_2(x))
Eq(F_134(x), F_135(x)/F_20(x))
Eq(F_135(x), F_78(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_134(x)*F_138(x)*F_20(x))
Eq(F_138(x), F_139(x) + F_43(x))
Eq(F_139(x), F_48(x) + F_5(x))
Eq(F_140(x), F_141(x)*F_25(x))
Eq(F_141(x), F_142(x)/F_0(x))
Eq(F_142(x), F_143(x) - F_145(x))
Eq(F_143(x), F_144(x)/F_20(x))
Eq(F_144(x), F_112(x))
Eq(F_145(x), F_146(x) - F_148(x))
Eq(F_146(x), F_147(x)/F_20(x))
Eq(F_147(x), F_111(x))
Eq(F_148(x), F_141(x)*F_2(x))
Eq(F_149(x), F_20(x)*F_25(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_134(x)*F_18(x)*F_20(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_23(x)*F_25(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_20(x)*F_23(x)*F_25(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_16(x)*F_20(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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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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"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]]}, {"patt": [1, 0, 3, 2], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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]]}, {"patt": [1, 0, 3, 2], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24700/
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[16,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[14,x]
F[11,x] = F[12,x]+F[15,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[13,x]
F[16,x] = F[17,x]
F[17,x] = F[14,x]*F[18,x]
F[18,x] = F[164,x]+F[19,x]
F[19,x] = F[133,x]+F[20,x]
F[20,x] = F[21,x]+F[75,x]
F[21,x] = F[0,x]*F[22,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = F[24,x]
F[24,x] = F[14,x]*F[25,x]
F[25,x] = -F[70,x]+F[26,x]
F[26,x] = 1/F[14,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[29,x]+F[12,x]
F[29,x] = F[30,x]+F[59,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = 1+x^2*F[31,x]^3+(-x^2+x)*F[31,x]^2
F[32,x] = F[33,x]
F[33,x] = F[14,x]*F[34,x]
F[34,x] = 1/F[14,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[31,x]+F[37,x]
F[37,x] = F[0,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[14,x]*F[40,x]
F[40,x] = F[41,x]+F[54,x]
F[41,x] = F[37,x]+F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[2,x]*F[31,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[36,x]*F[48,x]
F[48,x] = 1/F[14,x]*F[49,x]
F[49,x] = F[2,x]
F[50,x] = F[51,x]
F[51,x] = F[14,x]*F[34,x]*F[52,x]
F[52,x] = 1/F[14,x]/F[31,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[42,x]+F[55,x]
F[55,x] = 1/F[14,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[2,x]+F[58,x]
F[58,x] = -F[0,x]+F[48,x]
F[59,x] = F[5,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[14,x]*F[64,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = F[12,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[64,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[65,x]
F[70,x] = F[71,x]
F[71,x] = F[60,x]+F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = x*(1+F[73,x])^2*(x*F[73,x]+1)
F[74,x] = -F[2,x]+F[32,x]
F[75,x] = F[76,x]
F[76,x] = F[14,x]*F[64,x]*F[77,x]
F[77,x] = F[0,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[80,x]
F[80,x] = 1/F[14,x]/F[85,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]+F[94,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[77,x]*F[85,x]
F[85,x] = 1/F[0,x]*F[86,x]
F[86,x] = -F[89,x]+F[87,x]
F[87,x] = 1/F[14,x]*F[88,x]
F[88,x] = F[38,x]
F[89,x] = -F[93,x]+F[90,x]
F[90,x] = 1/F[14,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = -F[2,x]+F[36,x]
F[93,x] = F[2,x]*F[85,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[98,x]
F[98,x] = F[14,x]*F[52,x]*F[85,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[14,x]*F[85,x]
F[101,x] = 1/F[14,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = -F[132,x]+F[104,x]
F[104,x] = 1/F[14,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = -F[110,x]+F[107,x]
F[107,x] = 1/F[14,x]*F[108,x]
F[108,x] = F[109,x]
F[109,x] = -F[2,x]+F[5,x]
F[110,x] = F[111,x]+F[119,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[0,x]*F[2,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[14,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[4,x]*F[58,x]
F[117,x] = F[118,x]
F[118,x] = F[12,x]*F[14,x]*F[52,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[14,x]
F[121,x] = F[122,x]+F[125,x]
F[122,x] = F[123,x]*F[77,x]
F[123,x] = 1/F[14,x]*F[124,x]
F[124,x] = F[74,x]
F[125,x] = F[126,x]+F[129,x]
F[126,x] = F[127,x]
F[127,x] = F[101,x]*F[128,x]*F[14,x]
F[128,x] = F[32,x]+F[73,x]
F[129,x] = F[130,x]
F[130,x] = F[101,x]*F[131,x]*F[14,x]
F[131,x] = F[28,x]+F[59,x]
F[132,x] = F[77,x]*F[85,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[14,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[25,x]*F[80,x]
F[137,x] = 1/F[14,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[14,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = -F[163,x]+F[142,x]
F[142,x] = 1/F[14,x]*F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[14,x]*F[145,x]
F[145,x] = F[146,x]+F[161,x]
F[146,x] = F[11,x]*F[147,x]
F[147,x] = F[148,x]+F[77,x]
F[148,x] = F[149,x]
F[149,x] = F[14,x]*F[150,x]*F[158,x]
F[150,x] = F[1,x]+F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[14,x]*F[153,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[1,x]+F[14,x]
F[155,x] = F[151,x]+F[156,x]
F[156,x] = F[157,x]
F[157,x] = F[14,x]*F[151,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[103,x]+F[77,x]
F[160,x] = F[14,x]*F[77,x]
F[161,x] = F[162,x]
F[162,x] = F[101,x]*F[12,x]*F[14,x]
F[163,x] = F[64,x]*F[77,x]
F[164,x] = F[165,x]
F[165,x] = F[14,x]*F[154,x]*F[64,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_{16}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \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_{13}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{164}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{133}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{75}\! \left(x \right)
F_{21}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{70}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{12}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{59}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = x^{2} F_{31} \left(x \right)^{3}-x^{2} F_{31} \left(x \right)^{2}+x F_{31} \left(x \right)^{2}+1
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \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_{41}\! \left(x \right)+F_{54}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right) F_{31}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{36}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{14}\! \left(x \right) F_{31}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{60}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = x^{2} F_{73} \left(x \right)^{3}+2 x^{2} F_{73} \left(x \right)^{2}+x^{2} F_{73}\! \left(x \right)+x F_{73} \left(x \right)^{2}+2 x F_{73}\! \left(x \right)+x
F_{74}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{14}\! \left(x \right) F_{85}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{94}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{86}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{38}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{36}\! \left(x \right)
F_{93}\! \left(x \right) = F_{2}\! \left(x \right) F_{85}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{85}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{14}\! \left(x \right) F_{85}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{132}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{110}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{119}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{14}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{14}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{125}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{77}\! \left(x \right)
F_{123}\! \left(x \right) = \frac{F_{124}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{124}\! \left(x \right) = F_{74}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{129}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{101}\! \left(x \right) F_{128}\! \left(x \right) F_{14}\! \left(x \right)
F_{128}\! \left(x \right) = F_{32}\! \left(x \right)+F_{73}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{101}\! \left(x \right) F_{131}\! \left(x \right) F_{14}\! \left(x \right)
F_{131}\! \left(x \right) = F_{28}\! \left(x \right)+F_{59}\! \left(x \right)
F_{132}\! \left(x \right) = F_{77}\! \left(x \right) F_{85}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{14}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{25}\! \left(x \right) F_{80}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{14}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{163}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = \frac{F_{143}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{14}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{161}\! \left(x \right)
F_{146}\! \left(x \right) = F_{11}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{77}\! \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_{158}\! \left(x \right)
F_{150}\! \left(x \right) = F_{1}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{14}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{155}\! \left(x \right) = F_{151}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{14}\! \left(x \right) F_{151}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{103}\! \left(x \right)+F_{77}\! \left(x \right)
F_{160}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{163}\! \left(x \right) = F_{64}\! \left(x \right) F_{77}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{14}\! \left(x \right) F_{154}\! \left(x \right) F_{64}\! \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_16(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_14(x))
Eq(F_11(x), F_12(x) + F_15(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_13(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)*F_18(x))
Eq(F_18(x), F_164(x) + F_19(x))
Eq(F_19(x), F_133(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_75(x))
Eq(F_21(x), F_0(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_14(x)*F_25(x))
Eq(F_25(x), F_26(x) - F_70(x))
Eq(F_26(x), F_27(x)/F_14(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x) - F_29(x))
Eq(F_29(x), F_30(x) + F_59(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), x**2*F_31(x)**3 - x*(x - 1)*F_31(x)**2 + 1)
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_14(x)*F_34(x))
Eq(F_34(x), F_35(x)/F_14(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), -F_31(x) + F_37(x))
Eq(F_37(x), F_0(x) + F_38(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_54(x))
Eq(F_41(x), F_37(x) + F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_2(x)*F_31(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_36(x)*F_48(x))
Eq(F_48(x), F_49(x)/F_14(x))
Eq(F_49(x), F_2(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_14(x)*F_34(x)*F_52(x))
Eq(F_52(x), F_53(x)/(F_14(x)*F_31(x)))
Eq(F_53(x), F_54(x))
Eq(F_54(x), -F_42(x) + F_55(x))
Eq(F_55(x), F_56(x)/F_14(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), -F_2(x) + F_58(x))
Eq(F_58(x), -F_0(x) + F_48(x))
Eq(F_59(x), F_5(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_14(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), F_12(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_64(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_65(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_60(x) + F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), x**2*(F_73(x) + 1)**3 - x*(x - 1)*(F_73(x) + 1)**2)
Eq(F_74(x), -F_2(x) + F_32(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_14(x)*F_64(x)*F_77(x))
Eq(F_77(x), F_0(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_80(x))
Eq(F_80(x), F_81(x)/(F_14(x)*F_85(x)))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x) + F_94(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_77(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_0(x))
Eq(F_86(x), F_87(x) - F_89(x))
Eq(F_87(x), F_88(x)/F_14(x))
Eq(F_88(x), F_38(x))
Eq(F_89(x), F_90(x) - F_93(x))
Eq(F_90(x), F_91(x)/F_14(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), -F_2(x) + F_36(x))
Eq(F_93(x), F_2(x)*F_85(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_14(x)*F_52(x)*F_85(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_14(x)*F_85(x))
Eq(F_101(x), F_102(x)/F_14(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x) - F_132(x))
Eq(F_104(x), F_105(x)/F_14(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) - F_110(x))
Eq(F_107(x), F_108(x)/F_14(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), -F_2(x) + F_5(x))
Eq(F_110(x), F_111(x) + F_119(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_0(x)*F_2(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_14(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_4(x)*F_58(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_12(x)*F_14(x)*F_52(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_14(x))
Eq(F_121(x), F_122(x) + F_125(x))
Eq(F_122(x), F_123(x)*F_77(x))
Eq(F_123(x), F_124(x)/F_14(x))
Eq(F_124(x), F_74(x))
Eq(F_125(x), F_126(x) + F_129(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_101(x)*F_128(x)*F_14(x))
Eq(F_128(x), F_32(x) + F_73(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_101(x)*F_131(x)*F_14(x))
Eq(F_131(x), F_28(x) + F_59(x))
Eq(F_132(x), F_77(x)*F_85(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_14(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_25(x)*F_80(x))
Eq(F_137(x), F_138(x)/F_14(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_14(x)*F_140(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x) - F_163(x))
Eq(F_142(x), F_143(x)/F_14(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_14(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_161(x))
Eq(F_146(x), F_11(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_77(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_14(x)*F_150(x)*F_158(x))
Eq(F_150(x), F_1(x) + F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_14(x)*F_153(x))
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_1(x) + F_14(x))
Eq(F_155(x), F_151(x) + F_156(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_14(x)*F_151(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_103(x) + F_77(x))
Eq(F_160(x), F_14(x)*F_77(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_101(x)*F_12(x)*F_14(x))
Eq(F_163(x), F_64(x)*F_77(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_14(x)*F_154(x)*F_64(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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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": [0, 2, 1, 4, 3], "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]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 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": [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": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "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]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 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": [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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"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]]}, {"patt": [1, 0, 3, 2], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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]]}, {"patt": [1, 0, 3, 2], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25002/
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[12,x]*F[4,x]
F[4,x] = F[1,x]+F[5,x]+F[79,x]
F[5,x] = F[12,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[10,x,k[0]]+F[13,x,k[0]]+F[76,x,k[0]]+F[9,x]
F[9,x] = 0
F[10,x,k[0]] = F[11,x,k[0]]*F[12,x]
F[11,x,k[0]] = -k[0]*(F[8,x,1]-F[8,x,k[0]])/(-1+k[0])
F[12,x] = x
F[13,x,k[0]] = F[12,x]*F[14,x,k[0]]
F[14,x,k[0]] = -k[0]*(F[15,x,1]-F[15,x,k[0]])/(-1+k[0])
F[15,x,k[0]] = F[10,x,k[0]]+F[16,x,k[0]]+F[73,x,k[0]]+F[9,x]
F[16,x,k[0]] = F[12,x]*F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[24,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]+F[26,x,k[0]]
F[21,x,k[0]] = F[20,x,k[0]]+F[42,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]+F[25,x,k[0]]
F[23,x,k[0]] = F[22,x,k[0]]*F[24,x,k[0]]
F[23,x,k[0]] = F[14,x,k[0]]
F[24,x,k[0]] = k[0]*x
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]+F[31,x,k[0]]+F[41,x,k[0]]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[12,x]*F[29,x,k[0]]
F[30,x,k[0]] = F[24,x,k[0]]*F[29,x,k[0]]
F[30,x,k[0]] = F[15,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[33,x,k[0]] = F[31,x,k[0]]+F[34,x,k[0]]+F[38,x,k[0]]+F[40,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[12,x]*F[36,x,k[0]]
F[37,x,k[0]] = F[24,x,k[0]]*F[36,x,k[0]]
F[37,x,k[0]] = F[8,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]
F[39,x,k[0]] = F[12,x]*F[26,x,k[0]]
F[40,x,k[0]] = F[12,x]*F[33,x,k[0]]
F[41,x,k[0]] = F[12,x]*F[26,x,k[0]]
F[42,x,k[0]] = k[0]*F[43,x,k[0]]
F[43,x,k[0]] = F[27,x,k[0]]+F[44,x,k[0]]
F[44,x,k[0]] = F[45,x,k[0]]
F[45,x,k[0]] = F[12,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[48,x,k[0]] = F[47,x,k[0]]+F[63,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[57,x,k[0]]+F[69,x,k[0]]
F[49,x,k[0]] = F[34,x,k[0]]+F[50,x,k[0]]
F[51,x,k[0]] = F[50,x,k[0]]+F[54,x,k[0]]
F[51,x,k[0]] = F[17,x,k[0]]+F[52,x]
F[52,x] = F[53,x,1]
F[53,x,k[0]] = F[15,x,k[0]]+F[4,x]
F[54,x,k[0]] = F[55,x,k[0]]
F[56,x,k[0]] = F[53,x,k[0]]+F[55,x,k[0]]
F[56,x,k[0]] = 1/(-1+k[0])*(F[53,x,k[0]]*k[0]-F[53,x,1])
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[12,x]*F[59,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]+F[68,x,k[0]]
F[61,x,k[0]] = F[12,x]*F[60,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[63,x,k[0]] = F[50,x,k[0]]+F[62,x,k[0]]+F[66,x,k[0]]
F[64,x,k[0]] = F[42,x,k[0]]+F[63,x,k[0]]
F[65,x,k[0]] = F[24,x,k[0]]*F[64,x,k[0]]
F[65,x,k[0]] = F[15,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[12,x]*F[19,x,k[0]]
F[68,x,k[0]] = F[46,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[12,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[19,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = F[43,x,k[0]]
F[73,x,k[0]] = F[24,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[50,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = k[0]*F[27,x,k[0]]
F[76,x,k[0]] = F[24,x,k[0]]*F[77,x,k[0]]
F[77,x,k[0]] = F[50,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = k[0]*F[34,x,k[0]]
F[79,x] = F[12,x]*F[52,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{79}\! \left(x \right)
F_{5}\! \left(x \right) = F_{12}\! \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_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = 0
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{y \left(F_{8}\! \left(x , 1\right)-F_{8}\! \left(x , y\right)\right)}{-1+y}
F_{12}\! \left(x \right) = x
F_{13}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = -\frac{y \left(F_{15}\! \left(x , 1\right)-F_{15}\! \left(x , y\right)\right)}{-1+y}
F_{15}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{73}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{24}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y x
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = y F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{27}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{34}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x , 1\right)
F_{53}\! \left(x , y\right) = F_{15}\! \left(x , y\right)+F_{4}\! \left(x \right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{60}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{19}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{43}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = y F_{27}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{50}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = y F_{34}\! \left(x , y\right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_1(x) + F_5(x) + F_79(x))
Eq(F_5(x), F_12(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_10(x, k_0) + F_13(x, k_0) + F_76(x, k_0) + F_9(x))
Eq(F_9(x), 0)
Eq(F_10(x, k_0), F_11(x, k_0)*F_12(x))
Eq(F_11(x, k_0), -F_8(x, 1) + (k_0*F_8(x, k_0) - F_8(x, 1))/(k_0 - 1))
Eq(F_12(x), x)
Eq(F_13(x, k_0), F_12(x)*F_14(x, k_0))
Eq(F_14(x, k_0), -F_15(x, 1) + (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_15(x, k_0), F_10(x, k_0) + F_16(x, k_0) + F_73(x, k_0) + F_9(x))
Eq(F_16(x, k_0), F_12(x)*F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_24(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0) + F_26(x, k_0))
Eq(F_21(x, k_0), F_20(x, k_0) + F_42(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0) + F_25(x, k_0))
Eq(F_23(x, k_0), F_22(x, k_0)*F_24(x, k_0))
Eq(F_23(x, k_0), F_14(x, k_0))
Eq(F_24(x, k_0), k_0*x)
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0) + F_31(x, k_0) + F_41(x, k_0))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_12(x)*F_29(x, k_0))
Eq(F_30(x, k_0), F_24(x, k_0)*F_29(x, k_0))
Eq(F_30(x, k_0), F_15(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_33(x, k_0), F_31(x, k_0) + F_34(x, k_0) + F_38(x, k_0) + F_40(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_12(x)*F_36(x, k_0))
Eq(F_37(x, k_0), F_24(x, k_0)*F_36(x, k_0))
Eq(F_37(x, k_0), F_8(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0))
Eq(F_39(x, k_0), F_12(x)*F_26(x, k_0))
Eq(F_40(x, k_0), F_12(x)*F_33(x, k_0))
Eq(F_41(x, k_0), F_12(x)*F_26(x, k_0))
Eq(F_42(x, k_0), k_0*F_43(x, k_0))
Eq(F_43(x, k_0), F_27(x, k_0) + F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x, k_0))
Eq(F_45(x, k_0), F_12(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_48(x, k_0), F_47(x, k_0) + F_63(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_57(x, k_0) + F_69(x, k_0))
Eq(F_49(x, k_0), F_34(x, k_0) + F_50(x, k_0))
Eq(F_51(x, k_0), F_50(x, k_0) + F_54(x, k_0))
Eq(F_51(x, k_0), F_17(x, k_0) + F_52(x))
Eq(F_52(x), F_53(x, 1))
Eq(F_53(x, k_0), F_15(x, k_0) + F_4(x))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_56(x, k_0), F_53(x, k_0) + F_55(x, k_0))
Eq(F_56(x, k_0), (k_0*F_53(x, k_0) - F_53(x, 1))/(k_0 - 1))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_12(x)*F_59(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0) + F_68(x, k_0))
Eq(F_61(x, k_0), F_12(x)*F_60(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_63(x, k_0), F_50(x, k_0) + F_62(x, k_0) + F_66(x, k_0))
Eq(F_64(x, k_0), F_42(x, k_0) + F_63(x, k_0))
Eq(F_65(x, k_0), F_24(x, k_0)*F_64(x, k_0))
Eq(F_65(x, k_0), F_15(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_12(x)*F_19(x, k_0))
Eq(F_68(x, k_0), F_46(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_12(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_19(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), F_43(x, k_0))
Eq(F_73(x, k_0), F_24(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_50(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), k_0*F_27(x, k_0))
Eq(F_76(x, k_0), F_24(x, k_0)*F_77(x, k_0))
Eq(F_77(x, k_0), F_50(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), k_0*F_34(x, k_0))
Eq(F_79(x), F_12(x)*F_52(x))
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:
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[0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [2, 1]]}, 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1], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 0], [1, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 0], [2, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 0], [0, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 0], [0, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 0], [0, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [2, 1], [4, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[4, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[4, 1]]}]}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25455/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[20,x]*F[7,x]
F[7,x] = F[156,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[20,x]
F[11,x] = F[12,x]+F[36,x]
F[12,x] = F[13,x]+F[14,x]
F[13,x] = F[0,x]*F[8,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[20,x]*F[25,x]
F[16,x] = F[17,x]+F[23,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = 1/F[20,x]*F[19,x]
F[19,x] = F[5,x]
F[20,x] = x
F[21,x] = F[22,x]
F[22,x] = F[16,x]*F[20,x]
F[23,x] = F[24,x]
F[24,x] = F[17,x]*F[20,x]
F[25,x] = F[0,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[20,x]*F[28,x]
F[28,x] = 1/F[18,x]/F[20,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[35,x]+F[31,x]
F[31,x] = 1/F[20,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[2,x]+F[34,x]
F[34,x] = -F[0,x]+F[4,x]
F[35,x] = F[2,x]*F[4,x]
F[36,x] = F[37,x]
F[37,x] = F[20,x]*F[38,x]
F[38,x] = F[39,x]+F[51,x]
F[39,x] = F[28,x]*F[40,x]
F[40,x] = -F[50,x]+F[41,x]
F[41,x] = 1/F[20,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = -F[44,x]+F[18,x]
F[44,x] = F[4,x]+F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[47,x]
F[47,x] = F[18,x]*F[20,x]
F[48,x] = F[49,x]
F[49,x] = F[20,x]*F[21,x]
F[50,x] = F[45,x]
F[51,x] = 1/F[20,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[14,x]+F[54,x]
F[54,x] = F[154,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[20,x]*F[57,x]
F[57,x] = -F[152,x]+F[58,x]
F[58,x] = 1/F[20,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[20,x]*F[61,x]
F[61,x] = F[150,x]+F[62,x]
F[62,x] = F[63,x]*F[65,x]
F[63,x] = F[18,x]+F[64,x]
F[64,x] = F[19,x]
F[65,x] = F[25,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[20,x]*F[68,x]*F[76,x]
F[68,x] = F[1,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[20,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[1,x]+F[20,x]
F[73,x] = F[69,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[20,x]*F[69,x]
F[76,x] = F[149,x]+F[77,x]
F[77,x] = F[25,x]+F[78,x]
F[78,x] = -F[140,x]+F[79,x]
F[79,x] = 1/F[20,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = -F[84,x]+F[82,x]
F[82,x] = 1/F[20,x]*F[83,x]
F[83,x] = F[33,x]
F[84,x] = F[122,x]+F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[0,x]*F[2,x]
F[87,x] = F[88,x]
F[88,x] = F[20,x]*F[89,x]
F[89,x] = F[90,x]+F[96,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[2,x]+F[92,x]
F[92,x] = -F[2,x]+F[93,x]
F[93,x] = -F[0,x]+F[94,x]
F[94,x] = 1/F[20,x]*F[95,x]
F[95,x] = F[2,x]
F[96,x] = F[97,x]
F[97,x] = F[18,x]*F[20,x]*F[98,x]
F[98,x] = 1/F[105,x]/F[20,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = -F[103,x]+F[101,x]
F[101,x] = 1/F[20,x]*F[102,x]
F[102,x] = F[92,x]
F[103,x] = F[104,x]+F[106,x]
F[104,x] = F[105,x]*F[2,x]
F[105,x] = 1+x^2*F[105,x]^3+(-x^2+x)*F[105,x]^2
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[20,x]
F[108,x] = F[109,x]+F[118,x]
F[109,x] = F[110,x]*F[94,x]
F[110,x] = F[111,x]+F[2,x]
F[111,x] = -F[117,x]+F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[20,x]
F[114,x] = F[100,x]+F[115,x]
F[115,x] = F[103,x]+F[116,x]
F[116,x] = F[0,x]+F[112,x]
F[117,x] = x*(1+F[117,x])^2*(x*F[117,x]+1)
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[20,x]*F[98,x]
F[120,x] = 1/F[20,x]*F[121,x]
F[121,x] = F[110,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[20,x]
F[124,x] = F[125,x]+F[129,x]
F[125,x] = F[126,x]*F[25,x]
F[126,x] = 1/F[20,x]*F[127,x]
F[127,x] = F[128,x]
F[128,x] = -F[117,x]+F[46,x]
F[129,x] = F[130,x]+F[136,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[134,x]*F[20,x]
F[132,x] = F[117,x]+F[133,x]
F[133,x] = F[128,x]+F[2,x]
F[134,x] = 1/F[20,x]*F[135,x]
F[135,x] = F[78,x]
F[136,x] = F[137,x]
F[137,x] = F[134,x]*F[138,x]*F[20,x]
F[138,x] = F[139,x]+F[43,x]
F[139,x] = F[48,x]+F[5,x]
F[140,x] = F[141,x]*F[25,x]
F[141,x] = 1/F[0,x]*F[142,x]
F[142,x] = -F[145,x]+F[143,x]
F[143,x] = 1/F[20,x]*F[144,x]
F[144,x] = F[112,x]
F[145,x] = -F[148,x]+F[146,x]
F[146,x] = 1/F[20,x]*F[147,x]
F[147,x] = F[111,x]
F[148,x] = F[141,x]*F[2,x]
F[149,x] = F[20,x]*F[25,x]
F[150,x] = F[151,x]
F[151,x] = F[134,x]*F[18,x]*F[20,x]
F[152,x] = F[153,x]
F[153,x] = F[23,x]*F[25,x]
F[154,x] = F[155,x]
F[155,x] = F[20,x]*F[23,x]*F[25,x]
F[156,x] = F[157,x]
F[157,x] = F[16,x]*F[20,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_{20}\! \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_{20}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{156}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{20}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{36}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)
F_{13}\! \left(x \right) = F_{0}\! \left(x \right) F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{5}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{25}\! \left(x \right) = F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{20}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right) F_{20}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{39}\! \left(x \right) = F_{28}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{18}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{20}\! \left(x \right) F_{21}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{14}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{154}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{20}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{152}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{20}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{150}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{18}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{19}\! \left(x \right)
F_{65}\! \left(x \right) = F_{25}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right) F_{68}\! \left(x \right) F_{76}\! \left(x \right)
F_{68}\! \left(x \right) = F_{1}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{20}\! \left(x \right) F_{69}\! \left(x \right)
F_{76}\! \left(x \right) = F_{149}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{25}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{33}\! \left(x \right)
F_{84}\! \left(x \right) = F_{122}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{20}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{96}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{2}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{2}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{105}\! \left(x \right) F_{20}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{92}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{2}\! \left(x \right)
F_{105}\! \left(x \right) = x^{2} F_{105} \left(x \right)^{3}-x^{2} F_{105} \left(x \right)^{2}+x F_{105} \left(x \right)^{2}+1
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{20}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{118}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{94}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{2}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{20}\! \left(x \right)
F_{114}\! \left(x \right) = F_{100}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{103}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{0}\! \left(x \right)+F_{112}\! \left(x \right)
F_{117}\! \left(x \right) = x^{2} F_{117} \left(x \right)^{3}+2 x^{2} F_{117} \left(x \right)^{2}+x^{2} F_{117}\! \left(x \right)+x F_{117} \left(x \right)^{2}+2 x F_{117}\! \left(x \right)+x
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{20}\! \left(x \right) F_{98}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{110}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{20}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{129}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{25}\! \left(x \right)
F_{126}\! \left(x \right) = \frac{F_{127}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{117}\! \left(x \right)+F_{46}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{136}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{134}\! \left(x \right) F_{20}\! \left(x \right)
F_{132}\! \left(x \right) = F_{117}\! \left(x \right)+F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{128}\! \left(x \right)+F_{2}\! \left(x \right)
F_{134}\! \left(x \right) = \frac{F_{135}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{135}\! \left(x \right) = F_{78}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{134}\! \left(x \right) F_{138}\! \left(x \right) F_{20}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{43}\! \left(x \right)
F_{139}\! \left(x \right) = F_{48}\! \left(x \right)+F_{5}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{25}\! \left(x \right)
F_{141}\! \left(x \right) = \frac{F_{142}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{142}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = \frac{F_{144}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{144}\! \left(x \right) = F_{112}\! \left(x \right)
F_{145}\! \left(x \right) = -F_{148}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = \frac{F_{147}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{147}\! \left(x \right) = F_{111}\! \left(x \right)
F_{148}\! \left(x \right) = F_{141}\! \left(x \right) F_{2}\! \left(x \right)
F_{149}\! \left(x \right) = F_{20}\! \left(x \right) F_{25}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{134}\! \left(x \right) F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \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_20(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_20(x)*F_7(x))
Eq(F_7(x), F_156(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_20(x))
Eq(F_11(x), F_12(x) + F_36(x))
Eq(F_12(x), F_13(x) + F_14(x))
Eq(F_13(x), F_0(x)*F_8(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_20(x)*F_25(x))
Eq(F_16(x), F_17(x) + F_23(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x)/F_20(x))
Eq(F_19(x), F_5(x))
Eq(F_20(x), x)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_16(x)*F_20(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_17(x)*F_20(x))
Eq(F_25(x), F_0(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_20(x)*F_28(x))
Eq(F_28(x), F_29(x)/(F_18(x)*F_20(x)))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_35(x))
Eq(F_31(x), F_32(x)/F_20(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_2(x) + F_34(x))
Eq(F_34(x), -F_0(x) + F_4(x))
Eq(F_35(x), F_2(x)*F_4(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_20(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_51(x))
Eq(F_39(x), F_28(x)*F_40(x))
Eq(F_40(x), F_41(x) - F_50(x))
Eq(F_41(x), F_42(x)/F_20(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_18(x) - F_44(x))
Eq(F_44(x), F_4(x) + F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_18(x)*F_20(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_20(x)*F_21(x))
Eq(F_50(x), F_45(x))
Eq(F_51(x), F_52(x)/F_20(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), -F_14(x) + F_54(x))
Eq(F_54(x), F_154(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_20(x)*F_57(x))
Eq(F_57(x), -F_152(x) + F_58(x))
Eq(F_58(x), F_59(x)/F_20(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_20(x)*F_61(x))
Eq(F_61(x), F_150(x) + F_62(x))
Eq(F_62(x), F_63(x)*F_65(x))
Eq(F_63(x), F_18(x) + F_64(x))
Eq(F_64(x), F_19(x))
Eq(F_65(x), F_25(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_20(x)*F_68(x)*F_76(x))
Eq(F_68(x), F_1(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_20(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_1(x) + F_20(x))
Eq(F_73(x), F_69(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_20(x)*F_69(x))
Eq(F_76(x), F_149(x) + F_77(x))
Eq(F_77(x), F_25(x) + F_78(x))
Eq(F_78(x), -F_140(x) + F_79(x))
Eq(F_79(x), F_80(x)/F_20(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_82(x) - F_84(x))
Eq(F_82(x), F_83(x)/F_20(x))
Eq(F_83(x), F_33(x))
Eq(F_84(x), F_122(x) + F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_0(x)*F_2(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_20(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_96(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_2(x) + F_92(x))
Eq(F_92(x), -F_2(x) + F_93(x))
Eq(F_93(x), -F_0(x) + F_94(x))
Eq(F_94(x), F_95(x)/F_20(x))
Eq(F_95(x), F_2(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_18(x)*F_20(x)*F_98(x))
Eq(F_98(x), F_99(x)/(F_105(x)*F_20(x)))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x) - F_103(x))
Eq(F_101(x), F_102(x)/F_20(x))
Eq(F_102(x), F_92(x))
Eq(F_103(x), F_104(x) + F_106(x))
Eq(F_104(x), F_105(x)*F_2(x))
Eq(F_105(x), x**2*F_105(x)**3 - x*(x - 1)*F_105(x)**2 + 1)
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_20(x))
Eq(F_108(x), F_109(x) + F_118(x))
Eq(F_109(x), F_110(x)*F_94(x))
Eq(F_110(x), F_111(x) + F_2(x))
Eq(F_111(x), F_112(x) - F_117(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_20(x))
Eq(F_114(x), F_100(x) + F_115(x))
Eq(F_115(x), F_103(x) + F_116(x))
Eq(F_116(x), F_0(x) + F_112(x))
Eq(F_117(x), x**2*(F_117(x) + 1)**3 - x*(x - 1)*(F_117(x) + 1)**2)
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_20(x)*F_98(x))
Eq(F_120(x), F_121(x)/F_20(x))
Eq(F_121(x), F_110(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_20(x))
Eq(F_124(x), F_125(x) + F_129(x))
Eq(F_125(x), F_126(x)*F_25(x))
Eq(F_126(x), F_127(x)/F_20(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), -F_117(x) + F_46(x))
Eq(F_129(x), F_130(x) + F_136(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_134(x)*F_20(x))
Eq(F_132(x), F_117(x) + F_133(x))
Eq(F_133(x), F_128(x) + F_2(x))
Eq(F_134(x), F_135(x)/F_20(x))
Eq(F_135(x), F_78(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_134(x)*F_138(x)*F_20(x))
Eq(F_138(x), F_139(x) + F_43(x))
Eq(F_139(x), F_48(x) + F_5(x))
Eq(F_140(x), F_141(x)*F_25(x))
Eq(F_141(x), F_142(x)/F_0(x))
Eq(F_142(x), F_143(x) - F_145(x))
Eq(F_143(x), F_144(x)/F_20(x))
Eq(F_144(x), F_112(x))
Eq(F_145(x), F_146(x) - F_148(x))
Eq(F_146(x), F_147(x)/F_20(x))
Eq(F_147(x), F_111(x))
Eq(F_148(x), F_141(x)*F_2(x))
Eq(F_149(x), F_20(x)*F_25(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_134(x)*F_18(x)*F_20(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_23(x)*F_25(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_20(x)*F_23(x)*F_25(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_16(x)*F_20(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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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": [0, 2, 1, 4, 3], "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]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 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": [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": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "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]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 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": [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": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "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, 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[[1, 1], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[2, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [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": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "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": "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, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"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": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 0]]}], "indices": [0, 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]]}, {"patt": [1, 0, 3, 2], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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]]}, {"patt": [1, 0, 3, 2], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25688/
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[16,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[14,x]
F[11,x] = F[12,x]+F[15,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[13,x]
F[16,x] = F[17,x]
F[17,x] = F[14,x]*F[18,x]
F[18,x] = F[164,x]+F[19,x]
F[19,x] = F[133,x]+F[20,x]
F[20,x] = F[21,x]+F[75,x]
F[21,x] = F[0,x]*F[22,x]
F[22,x] = F[23,x]+F[4,x]
F[23,x] = F[24,x]
F[24,x] = F[14,x]*F[25,x]
F[25,x] = -F[70,x]+F[26,x]
F[26,x] = 1/F[14,x]*F[27,x]
F[27,x] = F[28,x]
F[28,x] = -F[29,x]+F[12,x]
F[29,x] = F[30,x]+F[59,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = 1+x^2*F[31,x]^3+(-x^2+x)*F[31,x]^2
F[32,x] = F[33,x]
F[33,x] = F[14,x]*F[34,x]
F[34,x] = 1/F[14,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[31,x]+F[37,x]
F[37,x] = F[0,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[14,x]*F[40,x]
F[40,x] = F[41,x]+F[54,x]
F[41,x] = F[37,x]+F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[2,x]*F[31,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[46,x]
F[46,x] = F[47,x]+F[50,x]
F[47,x] = F[36,x]*F[48,x]
F[48,x] = 1/F[14,x]*F[49,x]
F[49,x] = F[2,x]
F[50,x] = F[51,x]
F[51,x] = F[14,x]*F[34,x]*F[52,x]
F[52,x] = 1/F[14,x]/F[31,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[42,x]+F[55,x]
F[55,x] = 1/F[14,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[2,x]+F[58,x]
F[58,x] = -F[0,x]+F[48,x]
F[59,x] = F[5,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[14,x]*F[64,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = F[12,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[64,x]
F[68,x] = F[69,x]
F[69,x] = F[14,x]*F[65,x]
F[70,x] = F[71,x]
F[71,x] = F[60,x]+F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = x*(1+F[73,x])^2*(x*F[73,x]+1)
F[74,x] = -F[2,x]+F[32,x]
F[75,x] = F[76,x]
F[76,x] = F[14,x]*F[64,x]*F[77,x]
F[77,x] = F[0,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[14,x]*F[80,x]
F[80,x] = 1/F[14,x]/F[85,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]+F[94,x]
F[83,x] = F[84,x]
F[84,x] = F[14,x]*F[77,x]*F[85,x]
F[85,x] = 1/F[0,x]*F[86,x]
F[86,x] = -F[89,x]+F[87,x]
F[87,x] = 1/F[14,x]*F[88,x]
F[88,x] = F[38,x]
F[89,x] = -F[93,x]+F[90,x]
F[90,x] = 1/F[14,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = -F[2,x]+F[36,x]
F[93,x] = F[2,x]*F[85,x]
F[94,x] = F[95,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[97,x]+F[99,x]
F[97,x] = F[98,x]
F[98,x] = F[14,x]*F[52,x]*F[85,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[14,x]*F[85,x]
F[101,x] = 1/F[14,x]*F[102,x]
F[102,x] = F[103,x]
F[103,x] = -F[132,x]+F[104,x]
F[104,x] = 1/F[14,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = -F[110,x]+F[107,x]
F[107,x] = 1/F[14,x]*F[108,x]
F[108,x] = F[109,x]
F[109,x] = -F[2,x]+F[5,x]
F[110,x] = F[111,x]+F[119,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[0,x]*F[2,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[14,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[4,x]*F[58,x]
F[117,x] = F[118,x]
F[118,x] = F[12,x]*F[14,x]*F[52,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[14,x]
F[121,x] = F[122,x]+F[125,x]
F[122,x] = F[123,x]*F[77,x]
F[123,x] = 1/F[14,x]*F[124,x]
F[124,x] = F[74,x]
F[125,x] = F[126,x]+F[129,x]
F[126,x] = F[127,x]
F[127,x] = F[101,x]*F[128,x]*F[14,x]
F[128,x] = F[32,x]+F[73,x]
F[129,x] = F[130,x]
F[130,x] = F[101,x]*F[131,x]*F[14,x]
F[131,x] = F[28,x]+F[59,x]
F[132,x] = F[77,x]*F[85,x]
F[133,x] = F[134,x]
F[134,x] = F[135,x]*F[14,x]
F[135,x] = F[136,x]+F[137,x]
F[136,x] = F[25,x]*F[80,x]
F[137,x] = 1/F[14,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[14,x]*F[140,x]
F[140,x] = F[141,x]
F[141,x] = -F[163,x]+F[142,x]
F[142,x] = 1/F[14,x]*F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[14,x]*F[145,x]
F[145,x] = F[146,x]+F[161,x]
F[146,x] = F[11,x]*F[147,x]
F[147,x] = F[148,x]+F[77,x]
F[148,x] = F[149,x]
F[149,x] = F[14,x]*F[150,x]*F[158,x]
F[150,x] = F[1,x]+F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[14,x]*F[153,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[1,x]+F[14,x]
F[155,x] = F[151,x]+F[156,x]
F[156,x] = F[157,x]
F[157,x] = F[14,x]*F[151,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[103,x]+F[77,x]
F[160,x] = F[14,x]*F[77,x]
F[161,x] = F[162,x]
F[162,x] = F[101,x]*F[12,x]*F[14,x]
F[163,x] = F[64,x]*F[77,x]
F[164,x] = F[165,x]
F[165,x] = F[14,x]*F[154,x]*F[64,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_{16}\! \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_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \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_{13}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{164}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{133}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{75}\! \left(x \right)
F_{21}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{70}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{12}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{59}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = x^{2} F_{31} \left(x \right)^{3}-x^{2} F_{31} \left(x \right)^{2}+x F_{31} \left(x \right)^{2}+1
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \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_{41}\! \left(x \right)+F_{54}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right) F_{31}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{47}\! \left(x \right) = F_{36}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{14}\! \left(x \right) F_{31}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{48}\! \left(x \right)
F_{59}\! \left(x \right) = F_{5}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{60}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = x^{2} F_{73} \left(x \right)^{3}+2 x^{2} F_{73} \left(x \right)^{2}+x^{2} F_{73}\! \left(x \right)+x F_{73} \left(x \right)^{2}+2 x F_{73}\! \left(x \right)+x
F_{74}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{14}\! \left(x \right) F_{64}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{0}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{14}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{14}\! \left(x \right) F_{85}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{94}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = \frac{F_{86}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{86}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{38}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{36}\! \left(x \right)
F_{93}\! \left(x \right) = F_{2}\! \left(x \right) F_{85}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{85}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{14}\! \left(x \right) F_{85}\! \left(x \right)
F_{101}\! \left(x \right) = \frac{F_{102}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{132}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = -F_{110}\! \left(x \right)+F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = \frac{F_{108}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{119}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{14}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{14}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{125}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{77}\! \left(x \right)
F_{123}\! \left(x \right) = \frac{F_{124}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{124}\! \left(x \right) = F_{74}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{129}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{101}\! \left(x \right) F_{128}\! \left(x \right) F_{14}\! \left(x \right)
F_{128}\! \left(x \right) = F_{32}\! \left(x \right)+F_{73}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{101}\! \left(x \right) F_{131}\! \left(x \right) F_{14}\! \left(x \right)
F_{131}\! \left(x \right) = F_{28}\! \left(x \right)+F_{59}\! \left(x \right)
F_{132}\! \left(x \right) = F_{77}\! \left(x \right) F_{85}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{14}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{137}\! \left(x \right)
F_{136}\! \left(x \right) = F_{25}\! \left(x \right) F_{80}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{14}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = -F_{163}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = \frac{F_{143}\! \left(x \right)}{F_{14}\! \left(x \right)}
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{14}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{161}\! \left(x \right)
F_{146}\! \left(x \right) = F_{11}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{77}\! \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_{158}\! \left(x \right)
F_{150}\! \left(x \right) = F_{1}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{14}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{155}\! \left(x \right) = F_{151}\! \left(x \right)+F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{14}\! \left(x \right) F_{151}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{103}\! \left(x \right)+F_{77}\! \left(x \right)
F_{160}\! \left(x \right) = F_{14}\! \left(x \right) F_{77}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{163}\! \left(x \right) = F_{64}\! \left(x \right) F_{77}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{14}\! \left(x \right) F_{154}\! \left(x \right) F_{64}\! \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_16(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_14(x))
Eq(F_11(x), F_12(x) + F_15(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_13(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_14(x)*F_18(x))
Eq(F_18(x), F_164(x) + F_19(x))
Eq(F_19(x), F_133(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_75(x))
Eq(F_21(x), F_0(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_4(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_14(x)*F_25(x))
Eq(F_25(x), F_26(x) - F_70(x))
Eq(F_26(x), F_27(x)/F_14(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x) - F_29(x))
Eq(F_29(x), F_30(x) + F_59(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), x**2*F_31(x)**3 - x*(x - 1)*F_31(x)**2 + 1)
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_14(x)*F_34(x))
Eq(F_34(x), F_35(x)/F_14(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), -F_31(x) + F_37(x))
Eq(F_37(x), F_0(x) + F_38(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_54(x))
Eq(F_41(x), F_37(x) + F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_2(x)*F_31(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_50(x))
Eq(F_47(x), F_36(x)*F_48(x))
Eq(F_48(x), F_49(x)/F_14(x))
Eq(F_49(x), F_2(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_14(x)*F_34(x)*F_52(x))
Eq(F_52(x), F_53(x)/(F_14(x)*F_31(x)))
Eq(F_53(x), F_54(x))
Eq(F_54(x), -F_42(x) + F_55(x))
Eq(F_55(x), F_56(x)/F_14(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), -F_2(x) + F_58(x))
Eq(F_58(x), -F_0(x) + F_48(x))
Eq(F_59(x), F_5(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_14(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), F_12(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_64(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_14(x)*F_65(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_60(x) + F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), x**2*(F_73(x) + 1)**3 - x*(x - 1)*(F_73(x) + 1)**2)
Eq(F_74(x), -F_2(x) + F_32(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_14(x)*F_64(x)*F_77(x))
Eq(F_77(x), F_0(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_14(x)*F_80(x))
Eq(F_80(x), F_81(x)/(F_14(x)*F_85(x)))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x) + F_94(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_14(x)*F_77(x)*F_85(x))
Eq(F_85(x), F_86(x)/F_0(x))
Eq(F_86(x), F_87(x) - F_89(x))
Eq(F_87(x), F_88(x)/F_14(x))
Eq(F_88(x), F_38(x))
Eq(F_89(x), F_90(x) - F_93(x))
Eq(F_90(x), F_91(x)/F_14(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), -F_2(x) + F_36(x))
Eq(F_93(x), F_2(x)*F_85(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_97(x) + F_99(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_14(x)*F_52(x)*F_85(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_14(x)*F_85(x))
Eq(F_101(x), F_102(x)/F_14(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x) - F_132(x))
Eq(F_104(x), F_105(x)/F_14(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) - F_110(x))
Eq(F_107(x), F_108(x)/F_14(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), -F_2(x) + F_5(x))
Eq(F_110(x), F_111(x) + F_119(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_0(x)*F_2(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_14(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_4(x)*F_58(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_12(x)*F_14(x)*F_52(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_14(x))
Eq(F_121(x), F_122(x) + F_125(x))
Eq(F_122(x), F_123(x)*F_77(x))
Eq(F_123(x), F_124(x)/F_14(x))
Eq(F_124(x), F_74(x))
Eq(F_125(x), F_126(x) + F_129(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_101(x)*F_128(x)*F_14(x))
Eq(F_128(x), F_32(x) + F_73(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_101(x)*F_131(x)*F_14(x))
Eq(F_131(x), F_28(x) + F_59(x))
Eq(F_132(x), F_77(x)*F_85(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_135(x)*F_14(x))
Eq(F_135(x), F_136(x) + F_137(x))
Eq(F_136(x), F_25(x)*F_80(x))
Eq(F_137(x), F_138(x)/F_14(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_14(x)*F_140(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x) - F_163(x))
Eq(F_142(x), F_143(x)/F_14(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_14(x)*F_145(x))
Eq(F_145(x), F_146(x) + F_161(x))
Eq(F_146(x), F_11(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_77(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_14(x)*F_150(x)*F_158(x))
Eq(F_150(x), F_1(x) + F_151(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_14(x)*F_153(x))
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_1(x) + F_14(x))
Eq(F_155(x), F_151(x) + F_156(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_14(x)*F_151(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_103(x) + F_77(x))
Eq(F_160(x), F_14(x)*F_77(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_101(x)*F_12(x)*F_14(x))
Eq(F_163(x), F_64(x)*F_77(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_14(x)*F_154(x)*F_64(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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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], [0, 2, 1, 4, 3], [1, 0, 2, 4, 3], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2]], "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": [0, 2, 1, 4, 3], "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]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 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": [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": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 4, 3], "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]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 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": [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": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "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]]}], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 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": [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": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "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]]}], "requirements": [], "assumptions": []}, "children": [{"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": [0, 2, 1, 4, 3], "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]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 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