01342_01432_04132_10342_10432_14032_40132_41032
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3024, 16600, 93008, 528632, 3036016, 17572504, 102318256, 598547640, 3514448784, 20697555288, 122193434256, 722870024568, 4283626417712, 25420652476696, 151040171643632, 898365403478840, 5348177958053200, 31863910803613144, 189971863888481232, 1133286919217296888, 6764252546801191664, 40392674250900726680, 241304556987475797808, 1442078674261088894392, 8620965459242992376080, 51552719499645670469208, 308363556187027745995536, 1844925997351610277865080, 11040514128223244647741872, 66082315332681015545971224, 395602452858134015816904048, 2368664245230016163201287224, 14184453998834111909135410896, 84953401919612475669843221208, 508865463553505098270332359760, 3048419639120795432530261060344, 18263838744751984221148237695600, 109433748233891951807135352386712, 655766290852357203038419393631664, 3929909229677349335413404998102712, 23553142323911958397797050606771856, 141171045908466019691883604775291736, 846195281443214390393745178475284368, 5072495907584836676143846757313307512, 30408645418131385101355569033294974256, 182303492723355215113858607886127061784, 1092984177330474244850809376310892613616, 6553182839997611945350372280107409661240, 39292430290819285187942984218969756913744, 235603896792641746644069869433142840696792, 1412771389199118808824608205966302545134800, 8471808233740453634181739799956122632974328, 50803564462877744243798187420413990218961392, 304666851830522603623852289945652898768639384, 1827125404106187418035816394588331595629349936, 10957787518356363319009818885466190907713155000, 65718562305105932645369180322825950790201379856, 394151548346267801568845770011979849599700695128, 2364001857242062353838178497044297008731942861840, 14178856783954684034569254135758517129834057920632, 85043850633735642443151606677631618893361776814256, 510096591765192347793484568597225600571930119881752, 3059632562116368706716604461020498509571804507044464, 18352407564040475912906823623647881111086915398551096, 110083780391274563376581340049873379220439265792451024, 660328087321539134260921645196844856377175732773860568, 3960974093435121164326047252963805973149229441701010768, 23760178697855615355864045370589433286625605870322681080, 142528779633083221046919586896356297085073741887412494704, 854988566971519191593963917794935079161142083928533239448, 5128881393158126721665195991626252332221304651025552345776, 30767298187348313536912183601243677376962558664287067111608, 184569605758701753519752665609402847304260420197559135117712, 1107222508145840127243819847625598462938048095345415949858136, 6642220909326942954586042383586679320820573035421290767472784, 39846962158559701663172848892630157707110245472892474900663672, 239045419902874890968339318370587686683834765146280496807693360, 1434064783090131127747700904982965619996062821823843650940632344, 8603201306347830684277691957517485245410459945055045462625791216, 51612419190060572162710999121785450492248208835185467642356645688, 309635693212729945019710652548791500309304339557489660160848534352, 1857592097896450889533454144717424557032837434379133365921767152088, 11144282105031524926952848647532006962419563654180591316911601868240, 66858422176483784611114768334722176920167916867559057510090560760312, 401108918109734422215396370061714106610716252739036482009807355214064, 2406415260265587071910807396569854189159776102871956042054240785303448, 14437127288849578616927488240499986270398055885671481768057999043072304, 86614949956928542305349145083707964597519928355209313523747328841589176, 519644937969720693789264729678148512784351680031994282646887295985655568, 3117613156870598473446554221570652262800110930416843865366027456851542616, 18704209162970334779934534260061686559529733518529960322809373469278543120, 112216830434241572631500237399408730259886268911255906348948021517720844920, 673252685609707100454254897800555228839407623744519745517649516080253417392, 4039239182814913386304312081265634400956794326536522830221403536049067689496
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24406/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[113,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = (x^2+4*x-1)*F[11,x]^2+(4*x^2-5*x+2)*F[11,x]+4*x^2-x
F[12,x] = F[13,x]*F[2,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = F[17,x]+F[77,x]
F[17,x] = F[18,x]+F[43,x]
F[18,x] = F[19,x]*F[42,x]
F[19,x] = -F[32,x]+F[20,x]
F[20,x] = -F[29,x]+F[21,x]
F[21,x] = 1/F[13,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]+F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[13,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = -2+x^2+8*x+F[28,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[28,x]
F[29,x] = -F[32,x]+F[30,x]
F[30,x] = 1/F[13,x]*F[31,x]
F[31,x] = F[24,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]^2*F[2,x]
F[34,x] = F[1,x]+F[35,x]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[13,x]*F[37,x]
F[40,x] = F[41,x]
F[41,x] = F[13,x]*F[34,x]*F[36,x]*F[37,x]
F[42,x] = (1+F[42,x])*x+F[42,x]^2
F[43,x] = F[44,x]
F[44,x] = F[13,x]*F[45,x]
F[45,x] = F[46,x]+F[60,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[42,x]+F[43,x]
F[48,x] = F[49,x]
F[49,x] = F[13,x]*F[50,x]
F[50,x] = F[51,x]+F[74,x]
F[51,x] = 1/F[13,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[2,x]*F[42,x]
F[55,x] = F[56,x]
F[56,x] = F[13,x]*F[57,x]*F[59,x]
F[57,x] = 1/F[13,x]*F[58,x]
F[58,x] = F[6,x]
F[59,x] = F[42,x]+F[60,x]
F[60,x] = -F[73,x]+F[61,x]
F[61,x] = 1/F[28,x]*F[62,x]
F[62,x] = -F[68,x]+F[63,x]
F[63,x] = 1/F[13,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[28,x]+F[66,x]
F[66,x] = 1/F[13,x]*F[67,x]
F[67,x] = F[2,x]
F[68,x] = -F[72,x]+F[69,x]
F[69,x] = 1/F[13,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = -F[42,x]+F[65,x]
F[72,x] = F[11,x]*F[61,x]
F[73,x] = 2+F[73,x]^2+(-2+x)*F[73,x]
F[74,x] = F[60,x]*F[75,x]
F[75,x] = 1/F[13,x]*F[76,x]
F[76,x] = F[2,x]
F[77,x] = F[78,x]+F[97,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[42,x]+F[80,x]
F[80,x] = -F[2,x]+F[81,x]
F[81,x] = -F[73,x]+F[75,x]
F[82,x] = -F[47,x]+F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[13,x]*F[85,x]
F[85,x] = F[80,x]
F[86,x] = F[87,x]
F[87,x] = F[13,x]*F[88,x]
F[88,x] = 1/F[13,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = -F[93,x]+F[91,x]
F[91,x] = 1/F[13,x]*F[92,x]
F[92,x] = F[80,x]
F[93,x] = -F[96,x]+F[94,x]
F[94,x] = 1/F[13,x]*F[95,x]
F[95,x] = F[79,x]
F[96,x] = F[46,x]+F[75,x]
F[97,x] = F[11,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[13,x]
F[100,x] = 1/F[112,x]/F[13,x]*F[101,x]
F[101,x] = F[102,x]
F[102,x] = -F[81,x]+F[103,x]
F[103,x] = -F[111,x]+F[104,x]
F[104,x] = -F[107,x]+F[105,x]
F[105,x] = 1/F[13,x]*F[106,x]
F[106,x] = F[5,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[5,x]*F[73,x]
F[109,x] = F[110,x]
F[110,x] = F[55,x]+F[6,x]
F[111,x] = F[0,x]*F[73,x]
F[112,x] = F[11,x]+F[25,x]
F[113,x] = F[114,x]+F[120,x]
F[114,x] = F[115,x]+F[25,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[13,x]*F[25,x]
F[117,x] = F[118,x]+F[61,x]
F[118,x] = F[119,x]
F[119,x] = F[100,x]*F[13,x]
F[120,x] = F[110,x]+F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[112,x]*F[123,x]*F[13,x]
F[123,x] = -F[137,x]+F[124,x]
F[124,x] = 1/F[13,x]*F[125,x]
F[125,x] = F[126,x]
F[126,x] = F[117,x]*F[127,x]*F[13,x]
F[127,x] = -F[134,x]+F[128,x]
F[128,x] = -F[131,x]+F[129,x]
F[129,x] = 1/F[13,x]*F[130,x]
F[130,x] = F[79,x]
F[131,x] = -F[134,x]+F[132,x]
F[132,x] = 1/F[13,x]*F[133,x]
F[133,x] = F[80,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[2,x]*F[37,x]
F[136,x] = F[13,x]*F[40,x]
F[137,x] = 1/F[13,x]*F[138,x]
F[138,x] = F[60,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_{13}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{113}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}+4 x^{2} F_{11}\! \left(x \right)+4 x F_{11} \left(x \right)^{2}+4 x^{2}-5 x F_{11}\! \left(x \right)-F_{11} \left(x \right)^{2}-x +2 F_{11}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{77}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{42}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = x^{2} F_{28} \left(x \right)^{2}+2 x^{2} F_{28}\! \left(x \right)+4 x F_{28} \left(x \right)^{2}+x^{2}-13 x F_{28}\! \left(x \right)-F_{28} \left(x \right)^{2}+8 x +4 F_{28}\! \left(x \right)-2
F_{29}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right) F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{42}\! \left(x \right) x +F_{42} \left(x \right)^{2}+x
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{60}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{74}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{13}\! \left(x \right) F_{57}\! \left(x \right) F_{59}\! \left(x \right)
F_{57}\! \left(x \right) = \frac{F_{58}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{58}\! \left(x \right) = F_{6}\! \left(x \right)
F_{59}\! \left(x \right) = F_{42}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{62}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{65}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{73}\! \left(x \right) = F_{73}\! \left(x \right) x +F_{73} \left(x \right)^{2}-2 F_{73}\! \left(x \right)+2
F_{74}\! \left(x \right) = F_{60}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{97}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{42}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{80}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{13}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{80}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{79}\! \left(x \right)
F_{96}\! \left(x \right) = F_{46}\! \left(x \right)+F_{75}\! \left(x \right)
F_{97}\! \left(x \right) = F_{11}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{13}\! \left(x \right)
F_{100}\! \left(x \right) = \frac{F_{101}\! \left(x \right)}{F_{112}\! \left(x \right) F_{13}\! \left(x \right)}
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{5}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{5}\! \left(x \right) F_{73}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{55}\! \left(x \right)+F_{6}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{73}\! \left(x \right)
F_{112}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{120}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{25}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{100}\! \left(x \right) F_{13}\! \left(x \right)
F_{120}\! \left(x \right) = F_{110}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{112}\! \left(x \right) F_{123}\! \left(x \right) F_{13}\! \left(x \right)
F_{123}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = \frac{F_{125}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{117}\! \left(x \right) F_{127}\! \left(x \right) F_{13}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{131}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{130}\! \left(x \right) = F_{79}\! \left(x \right)
F_{131}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = \frac{F_{133}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{133}\! \left(x \right) = F_{80}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{136}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{60}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_113(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x**2 + 8*x + (F_11(x) + 1)**2*(x**2 + 4*x - 1) + (F_11(x) + 1)*(2*x**2 - 13*x + 3) + F_11(x) - 2)
Eq(F_12(x), F_13(x)*F_2(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_77(x))
Eq(F_17(x), F_18(x) + F_43(x))
Eq(F_18(x), F_19(x)*F_42(x))
Eq(F_19(x), F_20(x) - F_32(x))
Eq(F_20(x), F_21(x) - F_29(x))
Eq(F_21(x), F_22(x)/F_13(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x) + F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_13(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_28(x)**2 + (2*x**2 - 13*x + 4)*F_28(x) - 2)
Eq(F_29(x), F_30(x) - F_32(x))
Eq(F_30(x), F_31(x)/F_13(x))
Eq(F_31(x), F_24(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_2(x)*F_34(x)**2)
Eq(F_34(x), F_1(x) + F_35(x))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_13(x)*F_37(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_13(x)*F_34(x)*F_36(x)*F_37(x))
Eq(F_42(x), (x - 3)*(F_42(x) + 1) + (F_42(x) + 1)**2 + F_42(x) + 2)
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_13(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_60(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_42(x) + F_43(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_13(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_74(x))
Eq(F_51(x), F_52(x)/F_13(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_2(x)*F_42(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_13(x)*F_57(x)*F_59(x))
Eq(F_57(x), F_58(x)/F_13(x))
Eq(F_58(x), F_6(x))
Eq(F_59(x), F_42(x) + F_60(x))
Eq(F_60(x), F_61(x) - F_73(x))
Eq(F_61(x), F_62(x)/F_28(x))
Eq(F_62(x), F_63(x) - F_68(x))
Eq(F_63(x), F_64(x)/F_13(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_28(x) + F_66(x))
Eq(F_66(x), F_67(x)/F_13(x))
Eq(F_67(x), F_2(x))
Eq(F_68(x), F_69(x) - F_72(x))
Eq(F_69(x), F_70(x)/F_13(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), -F_42(x) + F_65(x))
Eq(F_72(x), F_11(x)*F_61(x))
Eq(F_73(x), (x - 2)*F_73(x) + F_73(x)**2 + 2)
Eq(F_74(x), F_60(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_13(x))
Eq(F_76(x), F_2(x))
Eq(F_77(x), F_78(x) + F_97(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_42(x) + F_80(x))
Eq(F_80(x), -F_2(x) + F_81(x))
Eq(F_81(x), -F_73(x) + F_75(x))
Eq(F_82(x), -F_47(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_13(x))
Eq(F_85(x), F_80(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_13(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_13(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_91(x) - F_93(x))
Eq(F_91(x), F_92(x)/F_13(x))
Eq(F_92(x), F_80(x))
Eq(F_93(x), F_94(x) - F_96(x))
Eq(F_94(x), F_95(x)/F_13(x))
Eq(F_95(x), F_79(x))
Eq(F_96(x), F_46(x) + F_75(x))
Eq(F_97(x), F_11(x)*F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_13(x))
Eq(F_100(x), F_101(x)/(F_112(x)*F_13(x)))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x) - F_81(x))
Eq(F_103(x), F_104(x) - F_111(x))
Eq(F_104(x), F_105(x) - F_107(x))
Eq(F_105(x), F_106(x)/F_13(x))
Eq(F_106(x), F_5(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_5(x)*F_73(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_55(x) + F_6(x))
Eq(F_111(x), F_0(x)*F_73(x))
Eq(F_112(x), F_11(x) + F_25(x))
Eq(F_113(x), F_114(x) + F_120(x))
Eq(F_114(x), F_115(x) + F_25(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_13(x)*F_25(x))
Eq(F_117(x), F_118(x) + F_61(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_100(x)*F_13(x))
Eq(F_120(x), F_110(x) + F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_112(x)*F_123(x)*F_13(x))
Eq(F_123(x), F_124(x) - F_137(x))
Eq(F_124(x), F_125(x)/F_13(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_117(x)*F_127(x)*F_13(x))
Eq(F_127(x), F_128(x) - F_134(x))
Eq(F_128(x), F_129(x) - F_131(x))
Eq(F_129(x), F_130(x)/F_13(x))
Eq(F_130(x), F_79(x))
Eq(F_131(x), F_132(x) - F_134(x))
Eq(F_132(x), F_133(x)/F_13(x))
Eq(F_133(x), F_80(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_2(x)*F_37(x))
Eq(F_136(x), F_13(x)*F_40(x))
Eq(F_137(x), F_138(x)/F_13(x))
Eq(F_138(x), F_60(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, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 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, 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, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 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, 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, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 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": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[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, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 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": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], 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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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], 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"ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24762/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[16,x]*F[8,x]
F[8,x] = F[11,x]+F[9,x]
F[9,x] = F[10,x]*F[4,x]
F[10,x] = (1+F[10,x])*x+F[10,x]^2
F[11,x] = F[12,x]+F[32,x]
F[12,x] = F[13,x]+F[18,x]
F[13,x] = -F[17,x]+F[14,x]
F[14,x] = 1/F[16,x]*F[15,x]
F[15,x] = F[2,x]
F[16,x] = x
F[17,x] = 2+F[17,x]^2+(-2+x)*F[17,x]
F[18,x] = F[19,x]
F[19,x] = F[16,x]*F[20,x]*F[26,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = (x^2+4*x-1)*F[21,x]^2+(4*x^2-5*x+2)*F[21,x]+4*x^2-x
F[22,x] = -F[25,x]+F[23,x]
F[23,x] = 1/F[16,x]*F[24,x]
F[24,x] = F[2,x]
F[25,x] = -2+x^2+8*x+F[25,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[25,x]
F[26,x] = F[27,x,1]
F[27,x,k[0]] = (F[28,x,k[0]]*k[0]-F[28,x,1])/(-1+k[0])
F[29,x,k[0]] = F[28,x,k[0]]*F[31,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]
F[30,x,k[0]] = x*(1+F[30,x,k[0]])*k[0]+F[30,x,k[0]]^2
F[31,x,k[0]] = k[0]*x
F[32,x] = F[33,x]
F[33,x] = F[16,x]*F[34,x]*F[36,x]
F[34,x] = 1/F[16,x]*F[35,x]
F[35,x] = F[6,x]
F[36,x] = F[28,x,1]
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_{16}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \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_{11}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{10}\! \left(x \right) x +F_{10} \left(x \right)^{2}+x
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{32}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{17}\! \left(x \right) x +F_{17} \left(x \right)^{2}-2 F_{17}\! \left(x \right)+2
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = x^{2} F_{21} \left(x \right)^{2}+4 x^{2} F_{21}\! \left(x \right)+4 x F_{21} \left(x \right)^{2}+4 x^{2}-5 x F_{21}\! \left(x \right)-F_{21} \left(x \right)^{2}-x +2 F_{21}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{25}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{2}\! \left(x \right)
F_{25}\! \left(x \right) = x^{2} F_{25} \left(x \right)^{2}+2 x^{2} F_{25}\! \left(x \right)+4 x F_{25} \left(x \right)^{2}+x^{2}-13 x F_{25}\! \left(x \right)-F_{25} \left(x \right)^{2}+8 x +4 F_{25}\! \left(x \right)-2
F_{26}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{27}\! \left(x , y\right) = -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = x F_{30}\! \left(x , y\right) y +y x +F_{30}\! \left(x , y\right)^{2}
F_{31}\! \left(x , y\right) = y x
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{16}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{6}\! \left(x \right)
F_{36}\! \left(x \right) = F_{28}\! \left(x , 1\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_16(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_16(x)*F_8(x))
Eq(F_8(x), F_11(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_4(x))
Eq(F_10(x), (x - 3)*(F_10(x) + 1) + (F_10(x) + 1)**2 + F_10(x) + 2)
Eq(F_11(x), F_12(x) + F_32(x))
Eq(F_12(x), F_13(x) + F_18(x))
Eq(F_13(x), F_14(x) - F_17(x))
Eq(F_14(x), F_15(x)/F_16(x))
Eq(F_15(x), F_2(x))
Eq(F_16(x), x)
Eq(F_17(x), (x - 2)*F_17(x) + F_17(x)**2 + 2)
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_16(x)*F_20(x)*F_26(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), x**2 + 8*x + (F_21(x) + 1)**2*(x**2 + 4*x - 1) + (F_21(x) + 1)*(2*x**2 - 13*x + 3) + F_21(x) - 2)
Eq(F_22(x), F_23(x) - F_25(x))
Eq(F_23(x), F_24(x)/F_16(x))
Eq(F_24(x), F_2(x))
Eq(F_25(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_25(x)**2 + (2*x**2 - 13*x + 4)*F_25(x) - 2)
Eq(F_26(x), F_27(x, 1))
Eq(F_27(x, k_0), (-k_0*F_28(x, k_0) + F_28(x, 1))/(1 - k_0))
Eq(F_29(x, k_0), F_28(x, k_0)*F_31(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0))
Eq(F_30(x, k_0), (k_0*x - 3)*(F_30(x, k_0) + 1) + (F_30(x, k_0) + 1)**2 + F_30(x, k_0) + 2)
Eq(F_31(x, k_0), k_0*x)
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_16(x)*F_34(x)*F_36(x))
Eq(F_34(x), F_35(x)/F_16(x))
Eq(F_35(x), F_6(x))
Eq(F_36(x), F_28(x, 1))
Pack JSON:
{"name": "point_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "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, 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, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 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, 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, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 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": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[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, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 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": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[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, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 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], "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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 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[1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25534/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[115,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = (x^2+4*x-1)*F[11,x]^2+(4*x^2-5*x+2)*F[11,x]+4*x^2-x
F[12,x] = F[13,x]*F[2,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = F[17,x]+F[77,x]
F[17,x] = F[18,x]+F[41,x]
F[18,x] = F[19,x]*F[40,x]
F[19,x] = -F[30,x]+F[20,x]
F[20,x] = -F[26,x]+F[21,x]
F[21,x] = 1/F[13,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[13,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = -F[30,x]+F[27,x]
F[27,x] = 1/F[13,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = -F[11,x]+F[23,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]^2*F[2,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[13,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[13,x]*F[35,x]
F[38,x] = F[39,x]
F[39,x] = F[13,x]*F[32,x]*F[34,x]*F[35,x]
F[40,x] = (1+F[40,x])*x+F[40,x]^2
F[41,x] = F[42,x]
F[42,x] = F[13,x]*F[43,x]
F[43,x] = F[44,x]+F[58,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[40,x]+F[41,x]
F[46,x] = F[47,x]
F[47,x] = F[13,x]*F[48,x]
F[48,x] = F[49,x]+F[74,x]
F[49,x] = 1/F[13,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[2,x]*F[40,x]
F[53,x] = F[54,x]
F[54,x] = F[13,x]*F[55,x]*F[57,x]
F[55,x] = 1/F[13,x]*F[56,x]
F[56,x] = F[6,x]
F[57,x] = F[40,x]+F[58,x]
F[58,x] = -F[68,x]+F[59,x]
F[59,x] = 1/F[73,x]*F[60,x]
F[60,x] = -F[69,x]+F[61,x]
F[61,x] = 1/F[13,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[40,x]+F[64,x]
F[64,x] = -F[11,x]+F[65,x]
F[65,x] = -F[68,x]+F[66,x]
F[66,x] = 1/F[13,x]*F[67,x]
F[67,x] = F[2,x]
F[68,x] = 2+F[68,x]^2+(-2+x)*F[68,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[13,x]*F[71,x]
F[71,x] = F[64,x]
F[72,x] = F[11,x]*F[59,x]
F[73,x] = -2+x^2+8*x+F[73,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[73,x]
F[74,x] = F[58,x]*F[75,x]
F[75,x] = 1/F[13,x]*F[76,x]
F[76,x] = F[2,x]
F[77,x] = F[78,x]+F[96,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = -F[0,x]+F[75,x]
F[80,x] = -F[45,x]+F[81,x]
F[81,x] = -F[85,x]+F[82,x]
F[82,x] = 1/F[13,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[40,x]+F[79,x]
F[85,x] = F[86,x]
F[86,x] = F[13,x]*F[87,x]
F[87,x] = 1/F[13,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[92,x]+F[90,x]
F[90,x] = 1/F[13,x]*F[91,x]
F[91,x] = F[84,x]
F[92,x] = -F[95,x]+F[93,x]
F[93,x] = 1/F[13,x]*F[94,x]
F[94,x] = F[79,x]
F[95,x] = F[44,x]+F[75,x]
F[96,x] = F[11,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[13,x]*F[99,x]
F[99,x] = 1/F[113,x]/F[13,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = -F[112,x]+F[102,x]
F[102,x] = -F[111,x]+F[103,x]
F[103,x] = -F[106,x]+F[104,x]
F[104,x] = 1/F[13,x]*F[105,x]
F[105,x] = F[5,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[5,x]*F[68,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[56,x]
F[110,x] = F[54,x]
F[111,x] = F[0,x]*F[68,x]
F[112,x] = F[2,x]+F[84,x]
F[113,x] = F[11,x]+F[114,x]
F[114,x] = F[2,x]+F[29,x]
F[115,x] = F[116,x]+F[122,x]
F[116,x] = F[114,x]+F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[114,x]*F[119,x]*F[13,x]
F[119,x] = F[120,x]+F[59,x]
F[120,x] = F[121,x]
F[121,x] = F[13,x]*F[99,x]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[108,x]
F[124,x] = F[125,x]
F[125,x] = F[113,x]*F[126,x]*F[13,x]
F[126,x] = -F[140,x]+F[127,x]
F[127,x] = 1/F[13,x]*F[128,x]
F[128,x] = F[129,x]
F[129,x] = F[119,x]*F[13,x]*F[130,x]
F[130,x] = -F[137,x]+F[131,x]
F[131,x] = -F[134,x]+F[132,x]
F[132,x] = 1/F[13,x]*F[133,x]
F[133,x] = F[79,x]
F[134,x] = -F[137,x]+F[135,x]
F[135,x] = 1/F[13,x]*F[136,x]
F[136,x] = F[84,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[2,x]*F[35,x]
F[139,x] = F[13,x]*F[38,x]
F[140,x] = 1/F[13,x]*F[141,x]
F[141,x] = F[58,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_{13}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{115}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}+4 x^{2} F_{11}\! \left(x \right)+4 x F_{11} \left(x \right)^{2}+4 x^{2}-5 x F_{11}\! \left(x \right)-F_{11} \left(x \right)^{2}-x +2 F_{11}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{77}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{41}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{40}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right) F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{40}\! \left(x \right) x +F_{40} \left(x \right)^{2}+x
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{13}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{58}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{74}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right) F_{40}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right) F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{6}\! \left(x \right)
F_{57}\! \left(x \right) = F_{40}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{73}\! \left(x \right)}
F_{60}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{40}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)
F_{68}\! \left(x \right) = F_{68}\! \left(x \right) x +F_{68} \left(x \right)^{2}-2 F_{68}\! \left(x \right)+2
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = x^{2} F_{73} \left(x \right)^{2}+2 x^{2} F_{73}\! \left(x \right)+4 x F_{73} \left(x \right)^{2}+x^{2}-13 x F_{73}\! \left(x \right)-F_{73} \left(x \right)^{2}+8 x +4 F_{73}\! \left(x \right)-2
F_{74}\! \left(x \right) = F_{58}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{96}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{79}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{13}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{84}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{79}\! \left(x \right)
F_{95}\! \left(x \right) = F_{44}\! \left(x \right)+F_{75}\! \left(x \right)
F_{96}\! \left(x \right) = F_{11}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{113}\! \left(x \right) F_{13}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{106}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{5}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{56}\! \left(x \right)
F_{110}\! \left(x \right) = F_{54}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{68}\! \left(x \right)
F_{112}\! \left(x \right) = F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{113}\! \left(x \right) = F_{11}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{122}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{114}\! \left(x \right) F_{119}\! \left(x \right) F_{13}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{59}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{13}\! \left(x \right) F_{99}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{108}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{113}\! \left(x \right) F_{126}\! \left(x \right) F_{13}\! \left(x \right)
F_{126}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = \frac{F_{128}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{119}\! \left(x \right) F_{13}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = \frac{F_{133}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{133}\! \left(x \right) = F_{79}\! \left(x \right)
F_{134}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = \frac{F_{136}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{136}\! \left(x \right) = F_{84}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{139}\! \left(x \right) = F_{13}\! \left(x \right) F_{38}\! \left(x \right)
F_{140}\! \left(x \right) = \frac{F_{141}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{141}\! \left(x \right) = F_{58}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_115(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x**2 + 8*x + (F_11(x) + 1)**2*(x**2 + 4*x - 1) + (F_11(x) + 1)*(2*x**2 - 13*x + 3) + F_11(x) - 2)
Eq(F_12(x), F_13(x)*F_2(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_77(x))
Eq(F_17(x), F_18(x) + F_41(x))
Eq(F_18(x), F_19(x)*F_40(x))
Eq(F_19(x), F_20(x) - F_30(x))
Eq(F_20(x), F_21(x) - F_26(x))
Eq(F_21(x), F_22(x)/F_13(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_13(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), F_27(x) - F_30(x))
Eq(F_27(x), F_28(x)/F_13(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), -F_11(x) + F_23(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_2(x)*F_32(x)**2)
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_13(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_13(x)*F_35(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_13(x)*F_32(x)*F_34(x)*F_35(x))
Eq(F_40(x), (x - 3)*(F_40(x) + 1) + (F_40(x) + 1)**2 + F_40(x) + 2)
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_13(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_58(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_40(x) + F_41(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_74(x))
Eq(F_49(x), F_50(x)/F_13(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_2(x)*F_40(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_13(x)*F_55(x)*F_57(x))
Eq(F_55(x), F_56(x)/F_13(x))
Eq(F_56(x), F_6(x))
Eq(F_57(x), F_40(x) + F_58(x))
Eq(F_58(x), F_59(x) - F_68(x))
Eq(F_59(x), F_60(x)/F_73(x))
Eq(F_60(x), F_61(x) - F_69(x))
Eq(F_61(x), F_62(x)/F_13(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_40(x) + F_64(x))
Eq(F_64(x), -F_11(x) + F_65(x))
Eq(F_65(x), F_66(x) - F_68(x))
Eq(F_66(x), F_67(x)/F_13(x))
Eq(F_67(x), F_2(x))
Eq(F_68(x), (x - 2)*F_68(x) + F_68(x)**2 + 2)
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_13(x))
Eq(F_71(x), F_64(x))
Eq(F_72(x), F_11(x)*F_59(x))
Eq(F_73(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_73(x)**2 + (2*x**2 - 13*x + 4)*F_73(x) - 2)
Eq(F_74(x), F_58(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_13(x))
Eq(F_76(x), F_2(x))
Eq(F_77(x), F_78(x) + F_96(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), -F_0(x) + F_75(x))
Eq(F_80(x), -F_45(x) + F_81(x))
Eq(F_81(x), F_82(x) - F_85(x))
Eq(F_82(x), F_83(x)/F_13(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), -F_40(x) + F_79(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_13(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_13(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_90(x) - F_92(x))
Eq(F_90(x), F_91(x)/F_13(x))
Eq(F_91(x), F_84(x))
Eq(F_92(x), F_93(x) - F_95(x))
Eq(F_93(x), F_94(x)/F_13(x))
Eq(F_94(x), F_79(x))
Eq(F_95(x), F_44(x) + F_75(x))
Eq(F_96(x), F_11(x)*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_13(x)*F_99(x))
Eq(F_99(x), F_100(x)/(F_113(x)*F_13(x)))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x) - F_112(x))
Eq(F_102(x), F_103(x) - F_111(x))
Eq(F_103(x), F_104(x) - F_106(x))
Eq(F_104(x), F_105(x)/F_13(x))
Eq(F_105(x), F_5(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_5(x)*F_68(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_56(x))
Eq(F_110(x), F_54(x))
Eq(F_111(x), F_0(x)*F_68(x))
Eq(F_112(x), F_2(x) + F_84(x))
Eq(F_113(x), F_11(x) + F_114(x))
Eq(F_114(x), F_2(x) + F_29(x))
Eq(F_115(x), F_116(x) + F_122(x))
Eq(F_116(x), F_114(x) + F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_114(x)*F_119(x)*F_13(x))
Eq(F_119(x), F_120(x) + F_59(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_13(x)*F_99(x))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_108(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_113(x)*F_126(x)*F_13(x))
Eq(F_126(x), F_127(x) - F_140(x))
Eq(F_127(x), F_128(x)/F_13(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_119(x)*F_13(x)*F_130(x))
Eq(F_130(x), F_131(x) - F_137(x))
Eq(F_131(x), F_132(x) - F_134(x))
Eq(F_132(x), F_133(x)/F_13(x))
Eq(F_133(x), F_79(x))
Eq(F_134(x), F_135(x) - F_137(x))
Eq(F_135(x), F_136(x)/F_13(x))
Eq(F_136(x), F_84(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_2(x)*F_35(x))
Eq(F_139(x), F_13(x)*F_38(x))
Eq(F_140(x), F_141(x)/F_13(x))
Eq(F_141(x), F_58(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, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 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, 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, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 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, 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, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 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": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[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, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 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": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[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, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 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], "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], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"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": []}, 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{"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 4], [3, 4]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 4], [3, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 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": [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, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25905/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[115,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = (x^2+4*x-1)*F[11,x]^2+(4*x^2-5*x+2)*F[11,x]+4*x^2-x
F[12,x] = F[13,x]*F[2,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = F[17,x]+F[77,x]
F[17,x] = F[18,x]+F[41,x]
F[18,x] = F[19,x]*F[40,x]
F[19,x] = -F[30,x]+F[20,x]
F[20,x] = -F[26,x]+F[21,x]
F[21,x] = 1/F[13,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[13,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = -F[30,x]+F[27,x]
F[27,x] = 1/F[13,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = -F[11,x]+F[23,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]^2*F[2,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[13,x]*F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[1,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[13,x]*F[35,x]
F[38,x] = F[39,x]
F[39,x] = F[13,x]*F[32,x]*F[34,x]*F[35,x]
F[40,x] = (1+F[40,x])*x+F[40,x]^2
F[41,x] = F[42,x]
F[42,x] = F[13,x]*F[43,x]
F[43,x] = F[44,x]+F[58,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[40,x]+F[41,x]
F[46,x] = F[47,x]
F[47,x] = F[13,x]*F[48,x]
F[48,x] = F[49,x]+F[74,x]
F[49,x] = 1/F[13,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[2,x]*F[40,x]
F[53,x] = F[54,x]
F[54,x] = F[13,x]*F[55,x]*F[57,x]
F[55,x] = 1/F[13,x]*F[56,x]
F[56,x] = F[6,x]
F[57,x] = F[40,x]+F[58,x]
F[58,x] = -F[68,x]+F[59,x]
F[59,x] = 1/F[73,x]*F[60,x]
F[60,x] = -F[69,x]+F[61,x]
F[61,x] = 1/F[13,x]*F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[40,x]+F[64,x]
F[64,x] = -F[11,x]+F[65,x]
F[65,x] = -F[68,x]+F[66,x]
F[66,x] = 1/F[13,x]*F[67,x]
F[67,x] = F[2,x]
F[68,x] = 2+F[68,x]^2+(-2+x)*F[68,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[13,x]*F[71,x]
F[71,x] = F[64,x]
F[72,x] = F[11,x]*F[59,x]
F[73,x] = -2+x^2+8*x+F[73,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[73,x]
F[74,x] = F[58,x]*F[75,x]
F[75,x] = 1/F[13,x]*F[76,x]
F[76,x] = F[2,x]
F[77,x] = F[78,x]+F[96,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = -F[0,x]+F[75,x]
F[80,x] = -F[45,x]+F[81,x]
F[81,x] = -F[85,x]+F[82,x]
F[82,x] = 1/F[13,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = -F[40,x]+F[79,x]
F[85,x] = F[86,x]
F[86,x] = F[13,x]*F[87,x]
F[87,x] = 1/F[13,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = -F[92,x]+F[90,x]
F[90,x] = 1/F[13,x]*F[91,x]
F[91,x] = F[84,x]
F[92,x] = -F[95,x]+F[93,x]
F[93,x] = 1/F[13,x]*F[94,x]
F[94,x] = F[79,x]
F[95,x] = F[44,x]+F[75,x]
F[96,x] = F[11,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[13,x]*F[99,x]
F[99,x] = 1/F[113,x]/F[13,x]*F[100,x]
F[100,x] = F[101,x]
F[101,x] = -F[112,x]+F[102,x]
F[102,x] = -F[111,x]+F[103,x]
F[103,x] = -F[106,x]+F[104,x]
F[104,x] = 1/F[13,x]*F[105,x]
F[105,x] = F[5,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[5,x]*F[68,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[56,x]
F[110,x] = F[54,x]
F[111,x] = F[0,x]*F[68,x]
F[112,x] = F[2,x]+F[84,x]
F[113,x] = F[11,x]+F[114,x]
F[114,x] = F[2,x]+F[29,x]
F[115,x] = F[116,x]+F[122,x]
F[116,x] = F[114,x]+F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[114,x]*F[119,x]*F[13,x]
F[119,x] = F[120,x]+F[59,x]
F[120,x] = F[121,x]
F[121,x] = F[13,x]*F[99,x]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[108,x]
F[124,x] = F[125,x]
F[125,x] = F[113,x]*F[126,x]*F[13,x]
F[126,x] = -F[140,x]+F[127,x]
F[127,x] = 1/F[13,x]*F[128,x]
F[128,x] = F[129,x]
F[129,x] = F[119,x]*F[13,x]*F[130,x]
F[130,x] = -F[137,x]+F[131,x]
F[131,x] = -F[134,x]+F[132,x]
F[132,x] = 1/F[13,x]*F[133,x]
F[133,x] = F[79,x]
F[134,x] = -F[137,x]+F[135,x]
F[135,x] = 1/F[13,x]*F[136,x]
F[136,x] = F[84,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[2,x]*F[35,x]
F[139,x] = F[13,x]*F[38,x]
F[140,x] = 1/F[13,x]*F[141,x]
F[141,x] = F[58,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_{13}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{115}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}+4 x^{2} F_{11}\! \left(x \right)+4 x F_{11} \left(x \right)^{2}+4 x^{2}-5 x F_{11}\! \left(x \right)-F_{11} \left(x \right)^{2}-x +2 F_{11}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{77}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{41}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{40}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{13}\! \left(x \right) F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right) F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{40}\! \left(x \right) x +F_{40} \left(x \right)^{2}+x
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{13}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{58}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{74}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right) F_{40}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right) F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{6}\! \left(x \right)
F_{57}\! \left(x \right) = F_{40}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{73}\! \left(x \right)}
F_{60}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{40}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)
F_{68}\! \left(x \right) = F_{68}\! \left(x \right) x +F_{68} \left(x \right)^{2}-2 F_{68}\! \left(x \right)+2
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{59}\! \left(x \right)
F_{73}\! \left(x \right) = x^{2} F_{73} \left(x \right)^{2}+2 x^{2} F_{73}\! \left(x \right)+4 x F_{73} \left(x \right)^{2}+x^{2}-13 x F_{73}\! \left(x \right)-F_{73} \left(x \right)^{2}+8 x +4 F_{73}\! \left(x \right)-2
F_{74}\! \left(x \right) = F_{58}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{96}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{85}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{79}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{13}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{84}\! \left(x \right)
F_{92}\! \left(x \right) = -F_{95}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{79}\! \left(x \right)
F_{95}\! \left(x \right) = F_{44}\! \left(x \right)+F_{75}\! \left(x \right)
F_{96}\! \left(x \right) = F_{11}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = \frac{F_{100}\! \left(x \right)}{F_{113}\! \left(x \right) F_{13}\! \left(x \right)}
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{112}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{106}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{5}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{5}\! \left(x \right) F_{68}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{56}\! \left(x \right)
F_{110}\! \left(x \right) = F_{54}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{68}\! \left(x \right)
F_{112}\! \left(x \right) = F_{2}\! \left(x \right)+F_{84}\! \left(x \right)
F_{113}\! \left(x \right) = F_{11}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{122}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{114}\! \left(x \right) F_{119}\! \left(x \right) F_{13}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{59}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{13}\! \left(x \right) F_{99}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{108}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{113}\! \left(x \right) F_{126}\! \left(x \right) F_{13}\! \left(x \right)
F_{126}\! \left(x \right) = -F_{140}\! \left(x \right)+F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = \frac{F_{128}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{119}\! \left(x \right) F_{13}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = \frac{F_{133}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{133}\! \left(x \right) = F_{79}\! \left(x \right)
F_{134}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = \frac{F_{136}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{136}\! \left(x \right) = F_{84}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{139}\! \left(x \right) = F_{13}\! \left(x \right) F_{38}\! \left(x \right)
F_{140}\! \left(x \right) = \frac{F_{141}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{141}\! \left(x \right) = F_{58}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_115(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x**2 + 8*x + (F_11(x) + 1)**2*(x**2 + 4*x - 1) + (F_11(x) + 1)*(2*x**2 - 13*x + 3) + F_11(x) - 2)
Eq(F_12(x), F_13(x)*F_2(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_77(x))
Eq(F_17(x), F_18(x) + F_41(x))
Eq(F_18(x), F_19(x)*F_40(x))
Eq(F_19(x), F_20(x) - F_30(x))
Eq(F_20(x), F_21(x) - F_26(x))
Eq(F_21(x), F_22(x)/F_13(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_13(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), F_27(x) - F_30(x))
Eq(F_27(x), F_28(x)/F_13(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), -F_11(x) + F_23(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_2(x)*F_32(x)**2)
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_13(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_1(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_13(x)*F_35(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_13(x)*F_32(x)*F_34(x)*F_35(x))
Eq(F_40(x), (x - 3)*(F_40(x) + 1) + (F_40(x) + 1)**2 + F_40(x) + 2)
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_13(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_58(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_40(x) + F_41(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_13(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_74(x))
Eq(F_49(x), F_50(x)/F_13(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_2(x)*F_40(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_13(x)*F_55(x)*F_57(x))
Eq(F_55(x), F_56(x)/F_13(x))
Eq(F_56(x), F_6(x))
Eq(F_57(x), F_40(x) + F_58(x))
Eq(F_58(x), F_59(x) - F_68(x))
Eq(F_59(x), F_60(x)/F_73(x))
Eq(F_60(x), F_61(x) - F_69(x))
Eq(F_61(x), F_62(x)/F_13(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_40(x) + F_64(x))
Eq(F_64(x), -F_11(x) + F_65(x))
Eq(F_65(x), F_66(x) - F_68(x))
Eq(F_66(x), F_67(x)/F_13(x))
Eq(F_67(x), F_2(x))
Eq(F_68(x), (x - 2)*F_68(x) + F_68(x)**2 + 2)
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_13(x))
Eq(F_71(x), F_64(x))
Eq(F_72(x), F_11(x)*F_59(x))
Eq(F_73(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_73(x)**2 + (2*x**2 - 13*x + 4)*F_73(x) - 2)
Eq(F_74(x), F_58(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_13(x))
Eq(F_76(x), F_2(x))
Eq(F_77(x), F_78(x) + F_96(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), -F_0(x) + F_75(x))
Eq(F_80(x), -F_45(x) + F_81(x))
Eq(F_81(x), F_82(x) - F_85(x))
Eq(F_82(x), F_83(x)/F_13(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), -F_40(x) + F_79(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_13(x)*F_87(x))
Eq(F_87(x), F_88(x)/F_13(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_90(x) - F_92(x))
Eq(F_90(x), F_91(x)/F_13(x))
Eq(F_91(x), F_84(x))
Eq(F_92(x), F_93(x) - F_95(x))
Eq(F_93(x), F_94(x)/F_13(x))
Eq(F_94(x), F_79(x))
Eq(F_95(x), F_44(x) + F_75(x))
Eq(F_96(x), F_11(x)*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_13(x)*F_99(x))
Eq(F_99(x), F_100(x)/(F_113(x)*F_13(x)))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x) - F_112(x))
Eq(F_102(x), F_103(x) - F_111(x))
Eq(F_103(x), F_104(x) - F_106(x))
Eq(F_104(x), F_105(x)/F_13(x))
Eq(F_105(x), F_5(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_5(x)*F_68(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_56(x))
Eq(F_110(x), F_54(x))
Eq(F_111(x), F_0(x)*F_68(x))
Eq(F_112(x), F_2(x) + F_84(x))
Eq(F_113(x), F_11(x) + F_114(x))
Eq(F_114(x), F_2(x) + F_29(x))
Eq(F_115(x), F_116(x) + F_122(x))
Eq(F_116(x), F_114(x) + F_117(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_114(x)*F_119(x)*F_13(x))
Eq(F_119(x), F_120(x) + F_59(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_13(x)*F_99(x))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_108(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_113(x)*F_126(x)*F_13(x))
Eq(F_126(x), F_127(x) - F_140(x))
Eq(F_127(x), F_128(x)/F_13(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_119(x)*F_13(x)*F_130(x))
Eq(F_130(x), F_131(x) - F_137(x))
Eq(F_131(x), F_132(x) - F_134(x))
Eq(F_132(x), F_133(x)/F_13(x))
Eq(F_133(x), F_79(x))
Eq(F_134(x), F_135(x) - F_137(x))
Eq(F_135(x), F_136(x)/F_13(x))
Eq(F_136(x), F_84(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_2(x)*F_35(x))
Eq(F_139(x), F_13(x)*F_38(x))
Eq(F_140(x), F_141(x)/F_13(x))
Eq(F_141(x), F_58(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, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 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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[[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 3, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 2], [3, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 2], [3, 2]]}, {"patt": [0, 1], "pos": [[3, 3], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 4], [3, 4]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 4], [3, 4]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 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": [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, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25911/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[113,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]+F[12,x]
F[11,x] = (x^2+4*x-1)*F[11,x]^2+(4*x^2-5*x+2)*F[11,x]+4*x^2-x
F[12,x] = F[13,x]*F[2,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = F[17,x]+F[77,x]
F[17,x] = F[18,x]+F[43,x]
F[18,x] = F[19,x]*F[42,x]
F[19,x] = -F[32,x]+F[20,x]
F[20,x] = -F[29,x]+F[21,x]
F[21,x] = 1/F[13,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]+F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[28,x]+F[26,x]
F[26,x] = 1/F[13,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = -2+x^2+8*x+F[28,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[28,x]
F[29,x] = -F[32,x]+F[30,x]
F[30,x] = 1/F[13,x]*F[31,x]
F[31,x] = F[24,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]^2*F[2,x]
F[34,x] = F[1,x]+F[35,x]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[13,x]*F[37,x]
F[40,x] = F[41,x]
F[41,x] = F[13,x]*F[34,x]*F[36,x]*F[37,x]
F[42,x] = (1+F[42,x])*x+F[42,x]^2
F[43,x] = F[44,x]
F[44,x] = F[13,x]*F[45,x]
F[45,x] = F[46,x]+F[60,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[42,x]+F[43,x]
F[48,x] = F[49,x]
F[49,x] = F[13,x]*F[50,x]
F[50,x] = F[51,x]+F[74,x]
F[51,x] = 1/F[13,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[2,x]*F[42,x]
F[55,x] = F[56,x]
F[56,x] = F[13,x]*F[57,x]*F[59,x]
F[57,x] = 1/F[13,x]*F[58,x]
F[58,x] = F[6,x]
F[59,x] = F[42,x]+F[60,x]
F[60,x] = -F[73,x]+F[61,x]
F[61,x] = 1/F[28,x]*F[62,x]
F[62,x] = -F[68,x]+F[63,x]
F[63,x] = 1/F[13,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = -F[28,x]+F[66,x]
F[66,x] = 1/F[13,x]*F[67,x]
F[67,x] = F[2,x]
F[68,x] = -F[72,x]+F[69,x]
F[69,x] = 1/F[13,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = -F[42,x]+F[65,x]
F[72,x] = F[11,x]*F[61,x]
F[73,x] = 2+F[73,x]^2+(-2+x)*F[73,x]
F[74,x] = F[60,x]*F[75,x]
F[75,x] = 1/F[13,x]*F[76,x]
F[76,x] = F[2,x]
F[77,x] = F[78,x]+F[97,x]
F[78,x] = F[79,x]+F[82,x]
F[79,x] = F[42,x]+F[80,x]
F[80,x] = -F[2,x]+F[81,x]
F[81,x] = -F[73,x]+F[75,x]
F[82,x] = -F[47,x]+F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[13,x]*F[85,x]
F[85,x] = F[80,x]
F[86,x] = F[87,x]
F[87,x] = F[13,x]*F[88,x]
F[88,x] = 1/F[13,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = -F[93,x]+F[91,x]
F[91,x] = 1/F[13,x]*F[92,x]
F[92,x] = F[80,x]
F[93,x] = -F[96,x]+F[94,x]
F[94,x] = 1/F[13,x]*F[95,x]
F[95,x] = F[79,x]
F[96,x] = F[46,x]+F[75,x]
F[97,x] = F[11,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[13,x]
F[100,x] = 1/F[112,x]/F[13,x]*F[101,x]
F[101,x] = F[102,x]
F[102,x] = -F[81,x]+F[103,x]
F[103,x] = -F[111,x]+F[104,x]
F[104,x] = -F[107,x]+F[105,x]
F[105,x] = 1/F[13,x]*F[106,x]
F[106,x] = F[5,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[5,x]*F[73,x]
F[109,x] = F[110,x]
F[110,x] = F[55,x]+F[6,x]
F[111,x] = F[0,x]*F[73,x]
F[112,x] = F[11,x]+F[25,x]
F[113,x] = F[114,x]+F[120,x]
F[114,x] = F[115,x]+F[25,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[13,x]*F[25,x]
F[117,x] = F[118,x]+F[61,x]
F[118,x] = F[119,x]
F[119,x] = F[100,x]*F[13,x]
F[120,x] = F[110,x]+F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[112,x]*F[123,x]*F[13,x]
F[123,x] = -F[137,x]+F[124,x]
F[124,x] = 1/F[13,x]*F[125,x]
F[125,x] = F[126,x]
F[126,x] = F[117,x]*F[127,x]*F[13,x]
F[127,x] = -F[134,x]+F[128,x]
F[128,x] = -F[131,x]+F[129,x]
F[129,x] = 1/F[13,x]*F[130,x]
F[130,x] = F[79,x]
F[131,x] = -F[134,x]+F[132,x]
F[132,x] = 1/F[13,x]*F[133,x]
F[133,x] = F[80,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[2,x]*F[37,x]
F[136,x] = F[13,x]*F[40,x]
F[137,x] = 1/F[13,x]*F[138,x]
F[138,x] = F[60,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_{13}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{113}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x^{2} F_{11} \left(x \right)^{2}+4 x^{2} F_{11}\! \left(x \right)+4 x F_{11} \left(x \right)^{2}+4 x^{2}-5 x F_{11}\! \left(x \right)-F_{11} \left(x \right)^{2}-x +2 F_{11}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{77}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{42}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = x^{2} F_{28} \left(x \right)^{2}+2 x^{2} F_{28}\! \left(x \right)+4 x F_{28} \left(x \right)^{2}+x^{2}-13 x F_{28}\! \left(x \right)-F_{28} \left(x \right)^{2}+8 x +4 F_{28}\! \left(x \right)-2
F_{29}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34} \left(x \right)^{2} F_{2}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{1}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{37}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{13}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right) F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{42}\! \left(x \right) x +F_{42} \left(x \right)^{2}+x
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{60}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{74}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{13}\! \left(x \right) F_{57}\! \left(x \right) F_{59}\! \left(x \right)
F_{57}\! \left(x \right) = \frac{F_{58}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{58}\! \left(x \right) = F_{6}\! \left(x \right)
F_{59}\! \left(x \right) = F_{42}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = \frac{F_{62}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{62}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = \frac{F_{64}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{28}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{65}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{61}\! \left(x \right)
F_{73}\! \left(x \right) = F_{73}\! \left(x \right) x +F_{73} \left(x \right)^{2}-2 F_{73}\! \left(x \right)+2
F_{74}\! \left(x \right) = F_{60}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{97}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{82}\! \left(x \right)
F_{79}\! \left(x \right) = F_{42}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{80}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{13}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = -F_{93}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = \frac{F_{92}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{92}\! \left(x \right) = F_{80}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{79}\! \left(x \right)
F_{96}\! \left(x \right) = F_{46}\! \left(x \right)+F_{75}\! \left(x \right)
F_{97}\! \left(x \right) = F_{11}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{13}\! \left(x \right)
F_{100}\! \left(x \right) = \frac{F_{101}\! \left(x \right)}{F_{112}\! \left(x \right) F_{13}\! \left(x \right)}
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{81}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = -F_{111}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{5}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{5}\! \left(x \right) F_{73}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{55}\! \left(x \right)+F_{6}\! \left(x \right)
F_{111}\! \left(x \right) = F_{0}\! \left(x \right) F_{73}\! \left(x \right)
F_{112}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{120}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{25}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{61}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{100}\! \left(x \right) F_{13}\! \left(x \right)
F_{120}\! \left(x \right) = F_{110}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{112}\! \left(x \right) F_{123}\! \left(x \right) F_{13}\! \left(x \right)
F_{123}\! \left(x \right) = -F_{137}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = \frac{F_{125}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{117}\! \left(x \right) F_{127}\! \left(x \right) F_{13}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = -F_{131}\! \left(x \right)+F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{130}\! \left(x \right) = F_{79}\! \left(x \right)
F_{131}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = \frac{F_{133}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{133}\! \left(x \right) = F_{80}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{2}\! \left(x \right) F_{37}\! \left(x \right)
F_{136}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{13}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{60}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_113(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x) + F_12(x))
Eq(F_11(x), x**2 + 8*x + (F_11(x) + 1)**2*(x**2 + 4*x - 1) + (F_11(x) + 1)*(2*x**2 - 13*x + 3) + F_11(x) - 2)
Eq(F_12(x), F_13(x)*F_2(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_77(x))
Eq(F_17(x), F_18(x) + F_43(x))
Eq(F_18(x), F_19(x)*F_42(x))
Eq(F_19(x), F_20(x) - F_32(x))
Eq(F_20(x), F_21(x) - F_29(x))
Eq(F_21(x), F_22(x)/F_13(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x) + F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), F_26(x) - F_28(x))
Eq(F_26(x), F_27(x)/F_13(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_28(x)**2 + (2*x**2 - 13*x + 4)*F_28(x) - 2)
Eq(F_29(x), F_30(x) - F_32(x))
Eq(F_30(x), F_31(x)/F_13(x))
Eq(F_31(x), F_24(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_2(x)*F_34(x)**2)
Eq(F_34(x), F_1(x) + F_35(x))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_13(x)*F_37(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_13(x)*F_34(x)*F_36(x)*F_37(x))
Eq(F_42(x), (x - 3)*(F_42(x) + 1) + (F_42(x) + 1)**2 + F_42(x) + 2)
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_13(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_60(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_42(x) + F_43(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_13(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_74(x))
Eq(F_51(x), F_52(x)/F_13(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_2(x)*F_42(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_13(x)*F_57(x)*F_59(x))
Eq(F_57(x), F_58(x)/F_13(x))
Eq(F_58(x), F_6(x))
Eq(F_59(x), F_42(x) + F_60(x))
Eq(F_60(x), F_61(x) - F_73(x))
Eq(F_61(x), F_62(x)/F_28(x))
Eq(F_62(x), F_63(x) - F_68(x))
Eq(F_63(x), F_64(x)/F_13(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), -F_28(x) + F_66(x))
Eq(F_66(x), F_67(x)/F_13(x))
Eq(F_67(x), F_2(x))
Eq(F_68(x), F_69(x) - F_72(x))
Eq(F_69(x), F_70(x)/F_13(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), -F_42(x) + F_65(x))
Eq(F_72(x), F_11(x)*F_61(x))
Eq(F_73(x), (x - 2)*F_73(x) + F_73(x)**2 + 2)
Eq(F_74(x), F_60(x)*F_75(x))
Eq(F_75(x), F_76(x)/F_13(x))
Eq(F_76(x), F_2(x))
Eq(F_77(x), F_78(x) + F_97(x))
Eq(F_78(x), F_79(x) + F_82(x))
Eq(F_79(x), F_42(x) + F_80(x))
Eq(F_80(x), -F_2(x) + F_81(x))
Eq(F_81(x), -F_73(x) + F_75(x))
Eq(F_82(x), -F_47(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_13(x))
Eq(F_85(x), F_80(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_13(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_13(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_91(x) - F_93(x))
Eq(F_91(x), F_92(x)/F_13(x))
Eq(F_92(x), F_80(x))
Eq(F_93(x), F_94(x) - F_96(x))
Eq(F_94(x), F_95(x)/F_13(x))
Eq(F_95(x), F_79(x))
Eq(F_96(x), F_46(x) + F_75(x))
Eq(F_97(x), F_11(x)*F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_13(x))
Eq(F_100(x), F_101(x)/(F_112(x)*F_13(x)))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x) - F_81(x))
Eq(F_103(x), F_104(x) - F_111(x))
Eq(F_104(x), F_105(x) - F_107(x))
Eq(F_105(x), F_106(x)/F_13(x))
Eq(F_106(x), F_5(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_5(x)*F_73(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_55(x) + F_6(x))
Eq(F_111(x), F_0(x)*F_73(x))
Eq(F_112(x), F_11(x) + F_25(x))
Eq(F_113(x), F_114(x) + F_120(x))
Eq(F_114(x), F_115(x) + F_25(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_13(x)*F_25(x))
Eq(F_117(x), F_118(x) + F_61(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_100(x)*F_13(x))
Eq(F_120(x), F_110(x) + F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_112(x)*F_123(x)*F_13(x))
Eq(F_123(x), F_124(x) - F_137(x))
Eq(F_124(x), F_125(x)/F_13(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_117(x)*F_127(x)*F_13(x))
Eq(F_127(x), F_128(x) - F_134(x))
Eq(F_128(x), F_129(x) - F_131(x))
Eq(F_129(x), F_130(x)/F_13(x))
Eq(F_130(x), F_79(x))
Eq(F_131(x), F_132(x) - F_134(x))
Eq(F_132(x), F_133(x)/F_13(x))
Eq(F_133(x), F_80(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_2(x)*F_37(x))
Eq(F_136(x), F_13(x)*F_40(x))
Eq(F_137(x), F_138(x)/F_13(x))
Eq(F_138(x), F_60(x))
Pack JSON:
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Specification JSON:
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