03412_03421_30412_30421
Counting sequence:
1, 1, 2, 6, 24, 116, 632, 3716, 22980, 147200, 967544, 6486420, 44169636, 304620752, 2123140000, 14930424556, 105800427124, 754717657680, 5415106369608, 39053656201028, 282946536046948, 2058397550369520, 15030078168254768, 110115908648764636, 809218446978113396, 5963416850708492848, 44059446586885435960, 326294632426850561684, 2421755799627292047076, 18010729053994339474896, 134199547683228101567808, 1001692007366665200765260, 7489120309065068114352372, 56078405738284342639394960, 420521056688764669194828456, 3157691752265660565369686116, 23741465456510584553395115236, 178718661605969978605925744432, 1346877897821327372719525294160, 10161460459459062255699177677500, 76741328215492825092495736529908, 580129969866812003441871837866608, 4389583349632149775376796194116760, 33243290401595314966082464114607028, 251970368371918290785577158011337060, 1911362209610538223524169734912781584, 14510052805575098068153270546226221408, 110233324725572425375961899497315908652, 838032987466341350727384921126086372980, 6375303339030194468242344456530296317392, 48531101555954082319835529651040445570312, 369664502763195089347255899605885528605060, 2817429575225287417102667378392396909536868, 21485533353161903638677087737612137443805552, 163937216501415017598058793629773459890874224, 1251521880563522723451975189532223700027545756, 9559175170088860473134721940897792147327125108, 73049212738682960329146812013443637301057915056, 558491142636318786928981393542142209727859257592, 4271845573482886037500776250539758356824725152468, 32689369428420478697507223784517970345036741496292, 250255058291711532997829721762284980716542754285136, 1916630542977161030712602897918267683811586488500608, 14684777046345813491573782200984593267682353756367628, 112554844691444462713936887587182192257087197149628916, 863025531407100954190972476537252970219122999551326480, 6619736241520489124079311866955727594659169660416331112, 50793778833467076463502700652084709982659712025774106788, 389877864738321671838101399990862621622656384833730957796, 2993577288846585308924086062447326396557855063811357017520, 22992808807741039185230767396451120754741315601648547692176, 176656341524606662126429361678325543308442479919191327602300, 1357682601860417640297011761465520662482487880385010701608692, 10437474208486046572347510080454562985995954513322170383035632, 80263334268487957893576240125477026261065180648092650073476952, 617390892211602114574956617428509865668840735917725335443911668, 4750302163726171959742069232839983305134254142198593799847396452, 36559237859856086070842896125074496932596145225689914930942302608, 281439414440459523151309665175042216898665819191763541299715222944, 2167113775363462283952572770649280455799413718163704685501194776044, 16691091887240920848489804137084247276896525041618854775828815911796, 128585311184787414275665473837816600733428037560149424629330057783888, 990829627708403558272278680513892895051948379819475170412301871789000, 7636689790000452159750352501860758596352734630556207921296898510390724, 58871821663179260193751862692685890384786014809056616233752943678318436, 453945445311125317693168370592709803248245052061505869482096777605235696, 3500995081200514487588719945733748431838383742332291230506491010676747696, 27006533963556627941050264310707079988072985087667467766579055524706407516, 208369259459269335582043634080555397267993221004629190200485446063650633076, 1607992068633022497925047642412394596235382656107403885168260015430780733232, 12411311817933489281064718279034940817612831571146478276261222395599115327416, 95814919915445924470532841614497079234676768512581554070794954414072196464404, 739824084084282145275787555090928463168269925281216731596941147254732808973540, 5713495883672122501569253258244393303068303319254443227555030743748826833802960, 44131817918492026146826928971004505048328517647126614604923263200587481651383744, 340938880890342164110287104016371859728923083483204429360611511669821552894745804, 2634356102099380638296543575063951996544299478054094715941446613723998867542168308, 20358423156067735706682360340946067388355278100277439067578598510438446453369039248, 157356257533632700225845266198441142508241210321672429761025919081903572680044935208, 1216445587347919332483092306509911314240801650770860934070228971311814145043124822244, 9405215527704651408300135088026715871451772478336148259904918780911336105942899783396
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24521/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[28,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[28,x]*F[8,x]
F[8,x] = F[141,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[28,x]
F[12,x] = F[13,x]+F[139,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[28,x]
F[15,x] = -F[135,x]+F[16,x]
F[16,x] = 1/F[28,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = -F[94,x]+F[19,x]
F[19,x] = 1/F[28,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[28,x]
F[22,x] = F[23,x]+F[82,x]
F[23,x] = F[24,x]+F[63,x]
F[24,x] = F[25,x]*F[56,x]
F[25,x] = -F[29,x]+F[26,x]
F[26,x] = 1/F[28,x]*F[27,x]
F[27,x] = F[6,x]
F[28,x] = x
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[31,x]*F[36,x]
F[31,x] = 1/F[28,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[0,x]+F[34,x]
F[34,x] = 1/F[28,x]*F[35,x]
F[35,x] = F[2,x]
F[36,x] = F[37,x]+F[43,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[28,x]*F[40,x]
F[40,x] = F[37,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[28,x]*F[37,x]*F[40,x]
F[43,x] = F[44,x]
F[44,x] = F[28,x]*F[45,x]
F[45,x] = 1/F[28,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[37,x]+F[48,x]
F[48,x] = 1/F[0,x]*F[49,x]
F[49,x] = -F[59,x]+F[50,x]
F[50,x] = 1/F[28,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = (1+F[53,x])*x+F[53,x]^2
F[54,x] = -F[2,x]+F[55,x]
F[55,x] = -F[58,x]+F[56,x]
F[56,x] = 1/F[28,x]*F[57,x]
F[57,x] = F[2,x]
F[58,x] = 2+F[58,x]^2+(-2+x)*F[58,x]
F[59,x] = -F[62,x]+F[60,x]
F[60,x] = 1/F[28,x]*F[61,x]
F[61,x] = F[54,x]
F[62,x] = F[2,x]*F[48,x]
F[63,x] = F[64,x]
F[64,x] = F[28,x]*F[65,x]*F[68,x]
F[65,x] = 1/F[28,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[5,x]+F[25,x]
F[68,x] = 1/F[81,x]*F[69,x]
F[69,x] = -F[78,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[28,x]*F[72,x]
F[72,x] = 1/F[28,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[77,x]+F[75,x]
F[75,x] = 1/F[28,x]*F[76,x]
F[76,x] = F[6,x]
F[77,x] = F[4,x]*F[53,x]
F[78,x] = F[2,x]*F[79,x]
F[79,x] = 1/F[28,x]*F[80,x]
F[80,x] = F[55,x]
F[81,x] = -F[2,x]+F[33,x]
F[82,x] = F[83,x]
F[83,x] = F[28,x]*F[84,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[31,x]*F[36,x]*F[56,x]
F[87,x] = F[40,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[28,x]*F[31,x]*F[68,x]
F[90,x] = F[91,x]
F[91,x] = F[31,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[28,x]*F[45,x]*F[68,x]
F[94,x] = F[95,x]
F[95,x] = F[28,x]*F[96,x]
F[96,x] = F[133,x]+F[97,x]
F[97,x] = 1/F[28,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]+F[122,x]
F[100,x] = F[101,x]*F[58,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[28,x]
F[103,x] = F[104,x]+F[117,x]
F[104,x] = F[105,x]+F[111,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[0,x]*F[4,x]
F[107,x] = F[108,x]*F[33,x]
F[108,x] = F[0,x]+F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[105,x]*F[28,x]
F[111,x] = F[112,x]+F[114,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[2,x]+F[6,x]
F[114,x] = F[108,x]*F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[28,x]*F[31,x]*F[38,x]
F[117,x] = F[108,x]*F[118,x]
F[118,x] = -F[121,x]+F[119,x]
F[119,x] = 1/F[28,x]*F[120,x]
F[120,x] = F[81,x]
F[121,x] = F[115,x]+F[33,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[28,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[101,x]*F[79,x]
F[126,x] = F[127,x]*F[68,x]
F[127,x] = -F[130,x]+F[128,x]
F[128,x] = 1/F[28,x]*F[129,x]
F[129,x] = F[101,x]
F[130,x] = F[101,x]+F[131,x]
F[131,x] = F[118,x]+F[132,x]
F[132,x] = F[121,x]+F[4,x]
F[133,x] = F[134,x]
F[134,x] = F[103,x]*F[28,x]*F[68,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[28,x]*F[68,x]
F[137,x] = 1/F[28,x]*F[138,x]
F[138,x] = F[9,x]
F[139,x] = F[140,x]
F[140,x] = F[28,x]*F[97,x]
F[141,x] = F[142,x]
F[142,x] = F[103,x]*F[28,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_{28}\! \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_{28}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{141}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{139}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{94}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{28}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{82}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{63}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{56}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = x
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{36}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{43}\! \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_{28}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right) F_{37}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{28}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{49}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{53}\! \left(x \right) x +F_{53} \left(x \right)^{2}+x
F_{54}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{2}\! \left(x \right)
F_{58}\! \left(x \right) = F_{58}\! \left(x \right) x +F_{58} \left(x \right)^{2}-2 F_{58}\! \left(x \right)+2
F_{59}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{54}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{48}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{28}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{25}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{81}\! \left(x \right)}
F_{69}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{28}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{6}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{55}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{33}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{28}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{56}\! \left(x \right)
F_{87}\! \left(x \right) = F_{40}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{68}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{31}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{28}\! \left(x \right) F_{45}\! \left(x \right) F_{68}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{28}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{133}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{122}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{58}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{117}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{111}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{33}\! \left(x \right)
F_{108}\! \left(x \right) = F_{0}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right) F_{28}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{114}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{114}\! \left(x \right) = F_{108}\! \left(x \right) F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{38}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = \frac{F_{120}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{120}\! \left(x \right) = F_{81}\! \left(x \right)
F_{121}\! \left(x \right) = F_{115}\! \left(x \right)+F_{33}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{28}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{101}\! \left(x \right) F_{79}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{101}\! \left(x \right)
F_{130}\! \left(x \right) = F_{101}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{118}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{121}\! \left(x \right)+F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \left(x \right) F_{68}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{28}\! \left(x \right) F_{68}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{9}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{28}\! \left(x \right) F_{97}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \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_28(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_28(x)*F_8(x))
Eq(F_8(x), F_141(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_28(x))
Eq(F_12(x), F_13(x) + F_139(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_28(x))
Eq(F_15(x), -F_135(x) + F_16(x))
Eq(F_16(x), F_17(x)/F_28(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_94(x))
Eq(F_19(x), F_20(x)/F_28(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_28(x))
Eq(F_22(x), F_23(x) + F_82(x))
Eq(F_23(x), F_24(x) + F_63(x))
Eq(F_24(x), F_25(x)*F_56(x))
Eq(F_25(x), F_26(x) - F_29(x))
Eq(F_26(x), F_27(x)/F_28(x))
Eq(F_27(x), F_6(x))
Eq(F_28(x), x)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_31(x)*F_36(x))
Eq(F_31(x), F_32(x)/F_28(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_0(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_28(x))
Eq(F_35(x), F_2(x))
Eq(F_36(x), F_37(x) + F_43(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_28(x)*F_40(x))
Eq(F_40(x), F_37(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_28(x)*F_37(x)*F_40(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_28(x)*F_45(x))
Eq(F_45(x), F_46(x)/F_28(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), -F_37(x) + F_48(x))
Eq(F_48(x), F_49(x)/F_0(x))
Eq(F_49(x), F_50(x) - F_59(x))
Eq(F_50(x), F_51(x)/F_28(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), (x - 3)*(F_53(x) + 1) + (F_53(x) + 1)**2 + F_53(x) + 2)
Eq(F_54(x), -F_2(x) + F_55(x))
Eq(F_55(x), F_56(x) - F_58(x))
Eq(F_56(x), F_57(x)/F_28(x))
Eq(F_57(x), F_2(x))
Eq(F_58(x), (x - 2)*F_58(x) + F_58(x)**2 + 2)
Eq(F_59(x), F_60(x) - F_62(x))
Eq(F_60(x), F_61(x)/F_28(x))
Eq(F_61(x), F_54(x))
Eq(F_62(x), F_2(x)*F_48(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_28(x)*F_65(x)*F_68(x))
Eq(F_65(x), F_66(x)/F_28(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_25(x) - F_5(x))
Eq(F_68(x), F_69(x)/F_81(x))
Eq(F_69(x), F_70(x) - F_78(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_28(x)*F_72(x))
Eq(F_72(x), F_73(x)/F_28(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x) - F_77(x))
Eq(F_75(x), F_76(x)/F_28(x))
Eq(F_76(x), F_6(x))
Eq(F_77(x), F_4(x)*F_53(x))
Eq(F_78(x), F_2(x)*F_79(x))
Eq(F_79(x), F_80(x)/F_28(x))
Eq(F_80(x), F_55(x))
Eq(F_81(x), -F_2(x) + F_33(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_28(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_31(x)*F_36(x)*F_56(x))
Eq(F_87(x), F_40(x)*F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_28(x)*F_31(x)*F_68(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_31(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_28(x)*F_45(x)*F_68(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_28(x)*F_96(x))
Eq(F_96(x), F_133(x) + F_97(x))
Eq(F_97(x), F_98(x)/F_28(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x) + F_122(x))
Eq(F_100(x), F_101(x)*F_58(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_28(x))
Eq(F_103(x), F_104(x) + F_117(x))
Eq(F_104(x), F_105(x) + F_111(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_0(x)*F_4(x))
Eq(F_107(x), F_108(x)*F_33(x))
Eq(F_108(x), F_0(x) + F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_105(x)*F_28(x))
Eq(F_111(x), F_112(x) + F_114(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_2(x) + F_6(x))
Eq(F_114(x), F_108(x)*F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_28(x)*F_31(x)*F_38(x))
Eq(F_117(x), F_108(x)*F_118(x))
Eq(F_118(x), F_119(x) - F_121(x))
Eq(F_119(x), F_120(x)/F_28(x))
Eq(F_120(x), F_81(x))
Eq(F_121(x), F_115(x) + F_33(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_28(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_101(x)*F_79(x))
Eq(F_126(x), F_127(x)*F_68(x))
Eq(F_127(x), F_128(x) - F_130(x))
Eq(F_128(x), F_129(x)/F_28(x))
Eq(F_129(x), F_101(x))
Eq(F_130(x), F_101(x) + F_131(x))
Eq(F_131(x), F_118(x) + F_132(x))
Eq(F_132(x), F_121(x) + F_4(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_103(x)*F_28(x)*F_68(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_28(x)*F_68(x))
Eq(F_137(x), F_138(x)/F_28(x))
Eq(F_138(x), F_9(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_28(x)*F_97(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_103(x)*F_28(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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], 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[[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [5, 4], [5, 4], [5, 4], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 4], [5, 4], [5, 4], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 4], [3, 0], [5, 4], [5, 0], [5, 4]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 4], [5, 0], [5, 4], [5, 0], [5, 4]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[5, 4], [5, 0], [5, 4], [5, 0], [5, 4]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 4], [3, 0], [5, 4], [5, 4], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 4], [5, 0], [5, 4], [5, 4], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[5, 4], [5, 0], [5, 4], [5, 4], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[4, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[3, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "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": "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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24642/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[28,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[28,x]*F[8,x]
F[8,x] = F[141,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[28,x]
F[12,x] = F[13,x]+F[139,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[28,x]
F[15,x] = -F[135,x]+F[16,x]
F[16,x] = 1/F[28,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = -F[94,x]+F[19,x]
F[19,x] = 1/F[28,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[28,x]
F[22,x] = F[23,x]+F[82,x]
F[23,x] = F[24,x]+F[63,x]
F[24,x] = F[25,x]*F[56,x]
F[25,x] = -F[29,x]+F[26,x]
F[26,x] = 1/F[28,x]*F[27,x]
F[27,x] = F[6,x]
F[28,x] = x
F[29,x] = F[30,x]
F[30,x] = F[28,x]*F[31,x]*F[36,x]
F[31,x] = 1/F[28,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = -F[0,x]+F[34,x]
F[34,x] = 1/F[28,x]*F[35,x]
F[35,x] = F[2,x]
F[36,x] = F[37,x]+F[43,x]
F[37,x] = F[1,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[28,x]*F[40,x]
F[40,x] = F[37,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[28,x]*F[37,x]*F[40,x]
F[43,x] = F[44,x]
F[44,x] = F[28,x]*F[45,x]
F[45,x] = 1/F[28,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = -F[37,x]+F[48,x]
F[48,x] = 1/F[0,x]*F[49,x]
F[49,x] = -F[59,x]+F[50,x]
F[50,x] = 1/F[28,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = (1+F[53,x])*x+F[53,x]^2
F[54,x] = -F[2,x]+F[55,x]
F[55,x] = -F[58,x]+F[56,x]
F[56,x] = 1/F[28,x]*F[57,x]
F[57,x] = F[2,x]
F[58,x] = 2+F[58,x]^2+(-2+x)*F[58,x]
F[59,x] = -F[62,x]+F[60,x]
F[60,x] = 1/F[28,x]*F[61,x]
F[61,x] = F[54,x]
F[62,x] = F[2,x]*F[48,x]
F[63,x] = F[64,x]
F[64,x] = F[28,x]*F[65,x]*F[68,x]
F[65,x] = 1/F[28,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[5,x]+F[25,x]
F[68,x] = 1/F[81,x]*F[69,x]
F[69,x] = -F[78,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[28,x]*F[72,x]
F[72,x] = 1/F[28,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[77,x]+F[75,x]
F[75,x] = 1/F[28,x]*F[76,x]
F[76,x] = F[6,x]
F[77,x] = F[4,x]*F[53,x]
F[78,x] = F[2,x]*F[79,x]
F[79,x] = 1/F[28,x]*F[80,x]
F[80,x] = F[55,x]
F[81,x] = -F[2,x]+F[33,x]
F[82,x] = F[83,x]
F[83,x] = F[28,x]*F[84,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[31,x]*F[36,x]*F[56,x]
F[87,x] = F[40,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[28,x]*F[31,x]*F[68,x]
F[90,x] = F[91,x]
F[91,x] = F[31,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[28,x]*F[45,x]*F[68,x]
F[94,x] = F[95,x]
F[95,x] = F[28,x]*F[96,x]
F[96,x] = F[133,x]+F[97,x]
F[97,x] = 1/F[28,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]+F[122,x]
F[100,x] = F[101,x]*F[58,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[28,x]
F[103,x] = F[104,x]+F[117,x]
F[104,x] = F[105,x]+F[111,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[0,x]*F[4,x]
F[107,x] = F[108,x]*F[33,x]
F[108,x] = F[0,x]+F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[105,x]*F[28,x]
F[111,x] = F[112,x]+F[114,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[2,x]+F[6,x]
F[114,x] = F[108,x]*F[115,x]
F[115,x] = F[116,x]
F[116,x] = F[28,x]*F[31,x]*F[38,x]
F[117,x] = F[108,x]*F[118,x]
F[118,x] = -F[121,x]+F[119,x]
F[119,x] = 1/F[28,x]*F[120,x]
F[120,x] = F[81,x]
F[121,x] = F[115,x]+F[33,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[28,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[101,x]*F[79,x]
F[126,x] = F[127,x]*F[68,x]
F[127,x] = -F[130,x]+F[128,x]
F[128,x] = 1/F[28,x]*F[129,x]
F[129,x] = F[101,x]
F[130,x] = F[101,x]+F[131,x]
F[131,x] = F[118,x]+F[132,x]
F[132,x] = F[121,x]+F[4,x]
F[133,x] = F[134,x]
F[134,x] = F[103,x]*F[28,x]*F[68,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[28,x]*F[68,x]
F[137,x] = 1/F[28,x]*F[138,x]
F[138,x] = F[9,x]
F[139,x] = F[140,x]
F[140,x] = F[28,x]*F[97,x]
F[141,x] = F[142,x]
F[142,x] = F[103,x]*F[28,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_{28}\! \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_{28}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{141}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{139}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{28}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{94}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{28}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{82}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{63}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{56}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = x
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{36}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{43}\! \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_{28}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{28}\! \left(x \right) F_{37}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{28}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = \frac{F_{49}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{49}\! \left(x \right) = -F_{59}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{53}\! \left(x \right) x +F_{53} \left(x \right)^{2}+x
F_{54}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{2}\! \left(x \right)
F_{58}\! \left(x \right) = F_{58}\! \left(x \right) x +F_{58} \left(x \right)^{2}-2 F_{58}\! \left(x \right)+2
F_{59}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{54}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{48}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{28}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{25}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{81}\! \left(x \right)}
F_{69}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{28}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{6}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{55}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{33}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{28}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{56}\! \left(x \right)
F_{87}\! \left(x \right) = F_{40}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{68}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{31}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{28}\! \left(x \right) F_{45}\! \left(x \right) F_{68}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{28}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{133}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{122}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{58}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{117}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{111}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{33}\! \left(x \right)
F_{108}\! \left(x \right) = F_{0}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right) F_{28}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{114}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{114}\! \left(x \right) = F_{108}\! \left(x \right) F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{38}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = \frac{F_{120}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{120}\! \left(x \right) = F_{81}\! \left(x \right)
F_{121}\! \left(x \right) = F_{115}\! \left(x \right)+F_{33}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{28}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{101}\! \left(x \right) F_{79}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{101}\! \left(x \right)
F_{130}\! \left(x \right) = F_{101}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{118}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{121}\! \left(x \right)+F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \left(x \right) F_{68}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{28}\! \left(x \right) F_{68}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{9}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{28}\! \left(x \right) F_{97}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{103}\! \left(x \right) F_{28}\! \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_28(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_28(x)*F_8(x))
Eq(F_8(x), F_141(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_28(x))
Eq(F_12(x), F_13(x) + F_139(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_28(x))
Eq(F_15(x), -F_135(x) + F_16(x))
Eq(F_16(x), F_17(x)/F_28(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) - F_94(x))
Eq(F_19(x), F_20(x)/F_28(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_28(x))
Eq(F_22(x), F_23(x) + F_82(x))
Eq(F_23(x), F_24(x) + F_63(x))
Eq(F_24(x), F_25(x)*F_56(x))
Eq(F_25(x), F_26(x) - F_29(x))
Eq(F_26(x), F_27(x)/F_28(x))
Eq(F_27(x), F_6(x))
Eq(F_28(x), x)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_28(x)*F_31(x)*F_36(x))
Eq(F_31(x), F_32(x)/F_28(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), -F_0(x) + F_34(x))
Eq(F_34(x), F_35(x)/F_28(x))
Eq(F_35(x), F_2(x))
Eq(F_36(x), F_37(x) + F_43(x))
Eq(F_37(x), F_1(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_28(x)*F_40(x))
Eq(F_40(x), F_37(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_28(x)*F_37(x)*F_40(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_28(x)*F_45(x))
Eq(F_45(x), F_46(x)/F_28(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), -F_37(x) + F_48(x))
Eq(F_48(x), F_49(x)/F_0(x))
Eq(F_49(x), F_50(x) - F_59(x))
Eq(F_50(x), F_51(x)/F_28(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), (x - 3)*(F_53(x) + 1) + (F_53(x) + 1)**2 + F_53(x) + 2)
Eq(F_54(x), -F_2(x) + F_55(x))
Eq(F_55(x), F_56(x) - F_58(x))
Eq(F_56(x), F_57(x)/F_28(x))
Eq(F_57(x), F_2(x))
Eq(F_58(x), (x - 2)*F_58(x) + F_58(x)**2 + 2)
Eq(F_59(x), F_60(x) - F_62(x))
Eq(F_60(x), F_61(x)/F_28(x))
Eq(F_61(x), F_54(x))
Eq(F_62(x), F_2(x)*F_48(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_28(x)*F_65(x)*F_68(x))
Eq(F_65(x), F_66(x)/F_28(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_25(x) - F_5(x))
Eq(F_68(x), F_69(x)/F_81(x))
Eq(F_69(x), F_70(x) - F_78(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_28(x)*F_72(x))
Eq(F_72(x), F_73(x)/F_28(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x) - F_77(x))
Eq(F_75(x), F_76(x)/F_28(x))
Eq(F_76(x), F_6(x))
Eq(F_77(x), F_4(x)*F_53(x))
Eq(F_78(x), F_2(x)*F_79(x))
Eq(F_79(x), F_80(x)/F_28(x))
Eq(F_80(x), F_55(x))
Eq(F_81(x), -F_2(x) + F_33(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_28(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_31(x)*F_36(x)*F_56(x))
Eq(F_87(x), F_40(x)*F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_28(x)*F_31(x)*F_68(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_31(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_28(x)*F_45(x)*F_68(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_28(x)*F_96(x))
Eq(F_96(x), F_133(x) + F_97(x))
Eq(F_97(x), F_98(x)/F_28(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x) + F_122(x))
Eq(F_100(x), F_101(x)*F_58(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_28(x))
Eq(F_103(x), F_104(x) + F_117(x))
Eq(F_104(x), F_105(x) + F_111(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_0(x)*F_4(x))
Eq(F_107(x), F_108(x)*F_33(x))
Eq(F_108(x), F_0(x) + F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_105(x)*F_28(x))
Eq(F_111(x), F_112(x) + F_114(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_2(x) + F_6(x))
Eq(F_114(x), F_108(x)*F_115(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_28(x)*F_31(x)*F_38(x))
Eq(F_117(x), F_108(x)*F_118(x))
Eq(F_118(x), F_119(x) - F_121(x))
Eq(F_119(x), F_120(x)/F_28(x))
Eq(F_120(x), F_81(x))
Eq(F_121(x), F_115(x) + F_33(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_28(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_101(x)*F_79(x))
Eq(F_126(x), F_127(x)*F_68(x))
Eq(F_127(x), F_128(x) - F_130(x))
Eq(F_128(x), F_129(x)/F_28(x))
Eq(F_129(x), F_101(x))
Eq(F_130(x), F_101(x) + F_131(x))
Eq(F_131(x), F_118(x) + F_132(x))
Eq(F_132(x), F_121(x) + F_4(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_103(x)*F_28(x)*F_68(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_28(x)*F_68(x))
Eq(F_137(x), F_138(x)/F_28(x))
Eq(F_138(x), F_9(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_28(x)*F_97(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_103(x)*F_28(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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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], [0, 2]], [[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, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [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": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": 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{"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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24866/
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[29,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[29,x]*F[8,x]
F[8,x] = F[141,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[2,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[29,x]
F[13,x] = F[139,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[29,x]
F[16,x] = -F[135,x]+F[17,x]
F[17,x] = 1/F[29,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[94,x]+F[20,x]
F[20,x] = 1/F[29,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[29,x]
F[23,x] = F[24,x]+F[82,x]
F[24,x] = F[25,x]+F[63,x]
F[25,x] = F[26,x]*F[55,x]
F[26,x] = -F[30,x]+F[27,x]
F[27,x] = 1/F[29,x]*F[28,x]
F[28,x] = F[6,x]
F[29,x] = x
F[30,x] = F[31,x]
F[31,x] = F[29,x]*F[32,x]*F[39,x]
F[32,x] = 1/F[29,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = -F[2,x]+F[36,x]
F[36,x] = -F[0,x]+F[37,x]
F[37,x] = 1/F[29,x]*F[38,x]
F[38,x] = F[2,x]
F[39,x] = F[40,x]+F[45,x]
F[40,x] = F[1,x]+F[41,x]
F[41,x] = F[29,x]*F[42,x]
F[42,x] = F[40,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[29,x]*F[40,x]*F[42,x]
F[45,x] = F[46,x]
F[46,x] = F[29,x]*F[47,x]
F[47,x] = 1/F[29,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = -F[40,x]+F[50,x]
F[50,x] = 1/F[0,x]*F[51,x]
F[51,x] = -F[57,x]+F[52,x]
F[52,x] = 1/F[29,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[0,x]+F[55,x]
F[55,x] = 1/F[29,x]*F[56,x]
F[56,x] = F[2,x]
F[57,x] = -F[62,x]+F[58,x]
F[58,x] = 1/F[29,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[61,x]+F[54,x]
F[61,x] = (1+F[61,x])*x+F[61,x]^2
F[62,x] = F[2,x]*F[50,x]
F[63,x] = F[64,x]
F[64,x] = F[29,x]*F[65,x]*F[68,x]
F[65,x] = 1/F[29,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[10,x]+F[26,x]
F[68,x] = 1/F[35,x]*F[69,x]
F[69,x] = -F[78,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[29,x]*F[72,x]
F[72,x] = 1/F[29,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[77,x]+F[75,x]
F[75,x] = 1/F[29,x]*F[76,x]
F[76,x] = F[6,x]
F[77,x] = F[4,x]*F[61,x]
F[78,x] = F[2,x]*F[79,x]
F[79,x] = 1/F[29,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[2,x]+F[60,x]
F[82,x] = F[83,x]
F[83,x] = F[29,x]*F[84,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[32,x]*F[39,x]*F[55,x]
F[87,x] = F[42,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[29,x]*F[32,x]*F[68,x]
F[90,x] = F[91,x]
F[91,x] = F[32,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[29,x]*F[47,x]*F[68,x]
F[94,x] = F[95,x]
F[95,x] = F[29,x]*F[96,x]
F[96,x] = F[133,x]+F[97,x]
F[97,x] = 1/F[29,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]+F[122,x]
F[100,x] = F[101,x]*F[121,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[29,x]
F[103,x] = F[104,x]+F[117,x]
F[104,x] = F[105,x]+F[111,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[0,x]*F[4,x]
F[107,x] = F[108,x]*F[34,x]
F[108,x] = F[0,x]+F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[105,x]*F[29,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[4,x]*F[5,x]
F[113,x] = F[108,x]*F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[29,x]*F[40,x]
F[116,x] = F[114,x]+F[34,x]
F[117,x] = F[108,x]*F[118,x]
F[118,x] = -F[116,x]+F[119,x]
F[119,x] = 1/F[29,x]*F[120,x]
F[120,x] = F[35,x]
F[121,x] = 2+F[121,x]^2+(-2+x)*F[121,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[29,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[101,x]*F[79,x]
F[126,x] = F[127,x]*F[68,x]
F[127,x] = -F[130,x]+F[128,x]
F[128,x] = 1/F[29,x]*F[129,x]
F[129,x] = F[101,x]
F[130,x] = F[101,x]+F[131,x]
F[131,x] = F[118,x]+F[132,x]
F[132,x] = F[116,x]+F[4,x]
F[133,x] = F[134,x]
F[134,x] = F[103,x]*F[29,x]*F[68,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[29,x]*F[68,x]
F[137,x] = 1/F[29,x]*F[138,x]
F[138,x] = F[9,x]
F[139,x] = F[140,x]
F[140,x] = F[29,x]*F[97,x]
F[141,x] = F[142,x]
F[142,x] = F[103,x]*F[29,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_{29}\! \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_{29}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{141}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{13}\! \left(x \right) = F_{139}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{29}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{94}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{82}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{63}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{55}\! \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_{29}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = x
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right) F_{32}\! \left(x \right) F_{39}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{45}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{29}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{29}\! \left(x \right) F_{40}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{29}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{51}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{2}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{61}\! \left(x \right) x +F_{61} \left(x \right)^{2}+x
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{50}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{29}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{35}\! \left(x \right)}
F_{69}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{29}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{6}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{2}\! \left(x \right)+F_{60}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{29}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{32}\! \left(x \right) F_{39}\! \left(x \right) F_{55}\! \left(x \right)
F_{87}\! \left(x \right) = F_{42}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{29}\! \left(x \right) F_{32}\! \left(x \right) F_{68}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{32}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{29}\! \left(x \right) F_{47}\! \left(x \right) F_{68}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{29}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{133}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{122}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{121}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{29}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{117}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{111}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{34}\! \left(x \right)
F_{108}\! \left(x \right) = F_{0}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right) F_{29}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right) F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{29}\! \left(x \right) F_{40}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{34}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = \frac{F_{120}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{120}\! \left(x \right) = F_{35}\! \left(x \right)
F_{121}\! \left(x \right) = F_{121}\! \left(x \right) x +F_{121} \left(x \right)^{2}-2 F_{121}\! \left(x \right)+2
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{29}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{101}\! \left(x \right) F_{79}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{101}\! \left(x \right)
F_{130}\! \left(x \right) = F_{101}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{118}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{116}\! \left(x \right)+F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{103}\! \left(x \right) F_{29}\! \left(x \right) F_{68}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{29}\! \left(x \right) F_{68}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{9}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{29}\! \left(x \right) F_{97}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{103}\! \left(x \right) F_{29}\! \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_29(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_29(x)*F_8(x))
Eq(F_8(x), F_141(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_2(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_29(x))
Eq(F_13(x), F_139(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_29(x))
Eq(F_16(x), -F_135(x) + F_17(x))
Eq(F_17(x), F_18(x)/F_29(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x) - F_94(x))
Eq(F_20(x), F_21(x)/F_29(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_29(x))
Eq(F_23(x), F_24(x) + F_82(x))
Eq(F_24(x), F_25(x) + F_63(x))
Eq(F_25(x), F_26(x)*F_55(x))
Eq(F_26(x), F_27(x) - F_30(x))
Eq(F_27(x), F_28(x)/F_29(x))
Eq(F_28(x), F_6(x))
Eq(F_29(x), x)
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_29(x)*F_32(x)*F_39(x))
Eq(F_32(x), F_33(x)/F_29(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), -F_2(x) + F_36(x))
Eq(F_36(x), -F_0(x) + F_37(x))
Eq(F_37(x), F_38(x)/F_29(x))
Eq(F_38(x), F_2(x))
Eq(F_39(x), F_40(x) + F_45(x))
Eq(F_40(x), F_1(x) + F_41(x))
Eq(F_41(x), F_29(x)*F_42(x))
Eq(F_42(x), F_40(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_29(x)*F_40(x)*F_42(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_29(x)*F_47(x))
Eq(F_47(x), F_48(x)/F_29(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), -F_40(x) + F_50(x))
Eq(F_50(x), F_51(x)/F_0(x))
Eq(F_51(x), F_52(x) - F_57(x))
Eq(F_52(x), F_53(x)/F_29(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), -F_0(x) + F_55(x))
Eq(F_55(x), F_56(x)/F_29(x))
Eq(F_56(x), F_2(x))
Eq(F_57(x), F_58(x) - F_62(x))
Eq(F_58(x), F_59(x)/F_29(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_54(x) - F_61(x))
Eq(F_61(x), (x - 3)*(F_61(x) + 1) + (F_61(x) + 1)**2 + F_61(x) + 2)
Eq(F_62(x), F_2(x)*F_50(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_29(x)*F_65(x)*F_68(x))
Eq(F_65(x), F_66(x)/F_29(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), -F_10(x) + F_26(x))
Eq(F_68(x), F_69(x)/F_35(x))
Eq(F_69(x), F_70(x) - F_78(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_29(x)*F_72(x))
Eq(F_72(x), F_73(x)/F_29(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x) - F_77(x))
Eq(F_75(x), F_76(x)/F_29(x))
Eq(F_76(x), F_6(x))
Eq(F_77(x), F_4(x)*F_61(x))
Eq(F_78(x), F_2(x)*F_79(x))
Eq(F_79(x), F_80(x)/F_29(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_2(x) + F_60(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_29(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_32(x)*F_39(x)*F_55(x))
Eq(F_87(x), F_42(x)*F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_29(x)*F_32(x)*F_68(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_32(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_29(x)*F_47(x)*F_68(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_29(x)*F_96(x))
Eq(F_96(x), F_133(x) + F_97(x))
Eq(F_97(x), F_98(x)/F_29(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x) + F_122(x))
Eq(F_100(x), F_101(x)*F_121(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_29(x))
Eq(F_103(x), F_104(x) + F_117(x))
Eq(F_104(x), F_105(x) + F_111(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_0(x)*F_4(x))
Eq(F_107(x), F_108(x)*F_34(x))
Eq(F_108(x), F_0(x) + F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_105(x)*F_29(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_4(x)*F_5(x))
Eq(F_113(x), F_108(x)*F_114(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_29(x)*F_40(x))
Eq(F_116(x), F_114(x) + F_34(x))
Eq(F_117(x), F_108(x)*F_118(x))
Eq(F_118(x), -F_116(x) + F_119(x))
Eq(F_119(x), F_120(x)/F_29(x))
Eq(F_120(x), F_35(x))
Eq(F_121(x), (x - 2)*F_121(x) + F_121(x)**2 + 2)
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_29(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_101(x)*F_79(x))
Eq(F_126(x), F_127(x)*F_68(x))
Eq(F_127(x), F_128(x) - F_130(x))
Eq(F_128(x), F_129(x)/F_29(x))
Eq(F_129(x), F_101(x))
Eq(F_130(x), F_101(x) + F_131(x))
Eq(F_131(x), F_118(x) + F_132(x))
Eq(F_132(x), F_116(x) + F_4(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_103(x)*F_29(x)*F_68(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_29(x)*F_68(x))
Eq(F_137(x), F_138(x)/F_29(x))
Eq(F_138(x), F_9(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_29(x)*F_97(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_103(x)*F_29(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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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], [0, 2]], [[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, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], 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[3, 0], [3, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[3, 0], [5, 4], [5, 4], [5, 0], [5, 4]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[5, 0], [5, 4], [5, 4], [5, 0], [5, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [5, 4], [5, 4], [5, 4], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 4], [5, 4], [5, 4], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 4], [3, 0], [5, 4], [5, 0], [5, 4]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[3, 4], [5, 0], [5, 4], [5, 0], [5, 4]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[5, 4], [5, 0], [5, 4], [5, 0], [5, 4]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 3], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [2, 3], [2, 3]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 4], [3, 0], [5, 4], [5, 4], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[3, 4], [5, 0], [5, 4], [5, 4], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[5, 4], [5, 0], [5, 4], [5, 4], [5, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}], [{"patt": [0], "pos": [[4, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[3, 1]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25501/
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[29,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[29,x]*F[8,x]
F[8,x] = F[141,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[2,x]+F[6,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[29,x]
F[13,x] = F[139,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[29,x]
F[16,x] = -F[135,x]+F[17,x]
F[17,x] = 1/F[29,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[94,x]+F[20,x]
F[20,x] = 1/F[29,x]*F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[29,x]
F[23,x] = F[24,x]+F[82,x]
F[24,x] = F[25,x]+F[63,x]
F[25,x] = F[26,x]*F[55,x]
F[26,x] = -F[30,x]+F[27,x]
F[27,x] = 1/F[29,x]*F[28,x]
F[28,x] = F[6,x]
F[29,x] = x
F[30,x] = F[31,x]
F[31,x] = F[29,x]*F[32,x]*F[39,x]
F[32,x] = 1/F[29,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[2,x]+F[35,x]
F[35,x] = -F[2,x]+F[36,x]
F[36,x] = -F[0,x]+F[37,x]
F[37,x] = 1/F[29,x]*F[38,x]
F[38,x] = F[2,x]
F[39,x] = F[40,x]+F[45,x]
F[40,x] = F[1,x]+F[41,x]
F[41,x] = F[29,x]*F[42,x]
F[42,x] = F[40,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[29,x]*F[40,x]*F[42,x]
F[45,x] = F[46,x]
F[46,x] = F[29,x]*F[47,x]
F[47,x] = 1/F[29,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = -F[40,x]+F[50,x]
F[50,x] = 1/F[0,x]*F[51,x]
F[51,x] = -F[57,x]+F[52,x]
F[52,x] = 1/F[29,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[0,x]+F[55,x]
F[55,x] = 1/F[29,x]*F[56,x]
F[56,x] = F[2,x]
F[57,x] = -F[62,x]+F[58,x]
F[58,x] = 1/F[29,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = -F[61,x]+F[54,x]
F[61,x] = (1+F[61,x])*x+F[61,x]^2
F[62,x] = F[2,x]*F[50,x]
F[63,x] = F[64,x]
F[64,x] = F[29,x]*F[65,x]*F[68,x]
F[65,x] = 1/F[29,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = -F[10,x]+F[26,x]
F[68,x] = 1/F[35,x]*F[69,x]
F[69,x] = -F[78,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[29,x]*F[72,x]
F[72,x] = 1/F[29,x]*F[73,x]
F[73,x] = F[74,x]
F[74,x] = -F[77,x]+F[75,x]
F[75,x] = 1/F[29,x]*F[76,x]
F[76,x] = F[6,x]
F[77,x] = F[4,x]*F[61,x]
F[78,x] = F[2,x]*F[79,x]
F[79,x] = 1/F[29,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[2,x]+F[60,x]
F[82,x] = F[83,x]
F[83,x] = F[29,x]*F[84,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[32,x]*F[39,x]*F[55,x]
F[87,x] = F[42,x]*F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[29,x]*F[32,x]*F[68,x]
F[90,x] = F[91,x]
F[91,x] = F[32,x]*F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[29,x]*F[47,x]*F[68,x]
F[94,x] = F[95,x]
F[95,x] = F[29,x]*F[96,x]
F[96,x] = F[133,x]+F[97,x]
F[97,x] = 1/F[29,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]+F[122,x]
F[100,x] = F[101,x]*F[121,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[29,x]
F[103,x] = F[104,x]+F[117,x]
F[104,x] = F[105,x]+F[111,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[0,x]*F[4,x]
F[107,x] = F[108,x]*F[34,x]
F[108,x] = F[0,x]+F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[105,x]*F[29,x]
F[111,x] = F[112,x]+F[113,x]
F[112,x] = F[4,x]*F[5,x]
F[113,x] = F[108,x]*F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[29,x]*F[40,x]
F[116,x] = F[114,x]+F[34,x]
F[117,x] = F[108,x]*F[118,x]
F[118,x] = -F[116,x]+F[119,x]
F[119,x] = 1/F[29,x]*F[120,x]
F[120,x] = F[35,x]
F[121,x] = 2+F[121,x]^2+(-2+x)*F[121,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[29,x]
F[124,x] = F[125,x]+F[126,x]
F[125,x] = F[101,x]*F[79,x]
F[126,x] = F[127,x]*F[68,x]
F[127,x] = -F[130,x]+F[128,x]
F[128,x] = 1/F[29,x]*F[129,x]
F[129,x] = F[101,x]
F[130,x] = F[101,x]+F[131,x]
F[131,x] = F[118,x]+F[132,x]
F[132,x] = F[116,x]+F[4,x]
F[133,x] = F[134,x]
F[134,x] = F[103,x]*F[29,x]*F[68,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[29,x]*F[68,x]
F[137,x] = 1/F[29,x]*F[138,x]
F[138,x] = F[9,x]
F[139,x] = F[140,x]
F[140,x] = F[29,x]*F[97,x]
F[141,x] = F[142,x]
F[142,x] = F[103,x]*F[29,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_{29}\! \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_{29}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{141}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{13}\! \left(x \right) = F_{139}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{29}\! \left(x \right)
F_{16}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{94}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{82}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{63}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{55}\! \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_{29}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = x
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right) F_{32}\! \left(x \right) F_{39}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{45}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{29}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{29}\! \left(x \right) F_{40}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{29}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{51}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{2}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{61}\! \left(x \right) x +F_{61} \left(x \right)^{2}+x
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{50}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{29}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = \frac{F_{66}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = -F_{10}\! \left(x \right)+F_{26}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{35}\! \left(x \right)}
F_{69}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{29}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = \frac{F_{73}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{6}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{2}\! \left(x \right)+F_{60}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{29}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{32}\! \left(x \right) F_{39}\! \left(x \right) F_{55}\! \left(x \right)
F_{87}\! \left(x \right) = F_{42}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{29}\! \left(x \right) F_{32}\! \left(x \right) F_{68}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{32}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{29}\! \left(x \right) F_{47}\! \left(x \right) F_{68}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{29}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{133}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = \frac{F_{98}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{122}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{121}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{29}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{117}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{111}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{34}\! \left(x \right)
F_{108}\! \left(x \right) = F_{0}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right) F_{29}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{113}\! \left(x \right)
F_{112}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{113}\! \left(x \right) = F_{108}\! \left(x \right) F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{29}\! \left(x \right) F_{40}\! \left(x \right)
F_{116}\! \left(x \right) = F_{114}\! \left(x \right)+F_{34}\! \left(x \right)
F_{117}\! \left(x \right) = F_{108}\! \left(x \right) F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = \frac{F_{120}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{120}\! \left(x \right) = F_{35}\! \left(x \right)
F_{121}\! \left(x \right) = F_{121}\! \left(x \right) x +F_{121} \left(x \right)^{2}-2 F_{121}\! \left(x \right)+2
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{29}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{126}\! \left(x \right)
F_{125}\! \left(x \right) = F_{101}\! \left(x \right) F_{79}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{68}\! \left(x \right)
F_{127}\! \left(x \right) = -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{101}\! \left(x \right)
F_{130}\! \left(x \right) = F_{101}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{118}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{116}\! \left(x \right)+F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{103}\! \left(x \right) F_{29}\! \left(x \right) F_{68}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{29}\! \left(x \right) F_{68}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{29}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{9}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{29}\! \left(x \right) F_{97}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{103}\! \left(x \right) F_{29}\! \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_29(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_29(x)*F_8(x))
Eq(F_8(x), F_141(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_2(x) + F_6(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_29(x))
Eq(F_13(x), F_139(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_29(x))
Eq(F_16(x), -F_135(x) + F_17(x))
Eq(F_17(x), F_18(x)/F_29(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x) - F_94(x))
Eq(F_20(x), F_21(x)/F_29(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_29(x))
Eq(F_23(x), F_24(x) + F_82(x))
Eq(F_24(x), F_25(x) + F_63(x))
Eq(F_25(x), F_26(x)*F_55(x))
Eq(F_26(x), F_27(x) - F_30(x))
Eq(F_27(x), F_28(x)/F_29(x))
Eq(F_28(x), F_6(x))
Eq(F_29(x), x)
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_29(x)*F_32(x)*F_39(x))
Eq(F_32(x), F_33(x)/F_29(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_2(x) + F_35(x))
Eq(F_35(x), -F_2(x) + F_36(x))
Eq(F_36(x), -F_0(x) + F_37(x))
Eq(F_37(x), F_38(x)/F_29(x))
Eq(F_38(x), F_2(x))
Eq(F_39(x), F_40(x) + F_45(x))
Eq(F_40(x), F_1(x) + F_41(x))
Eq(F_41(x), F_29(x)*F_42(x))
Eq(F_42(x), F_40(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_29(x)*F_40(x)*F_42(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_29(x)*F_47(x))
Eq(F_47(x), F_48(x)/F_29(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), -F_40(x) + F_50(x))
Eq(F_50(x), F_51(x)/F_0(x))
Eq(F_51(x), F_52(x) - F_57(x))
Eq(F_52(x), F_53(x)/F_29(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), -F_0(x) + F_55(x))
Eq(F_55(x), F_56(x)/F_29(x))
Eq(F_56(x), F_2(x))
Eq(F_57(x), F_58(x) - F_62(x))
Eq(F_58(x), F_59(x)/F_29(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_54(x) - F_61(x))
Eq(F_61(x), (x - 3)*(F_61(x) + 1) + (F_61(x) + 1)**2 + F_61(x) + 2)
Eq(F_62(x), F_2(x)*F_50(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_29(x)*F_65(x)*F_68(x))
Eq(F_65(x), F_66(x)/F_29(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), -F_10(x) + F_26(x))
Eq(F_68(x), F_69(x)/F_35(x))
Eq(F_69(x), F_70(x) - F_78(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_29(x)*F_72(x))
Eq(F_72(x), F_73(x)/F_29(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x) - F_77(x))
Eq(F_75(x), F_76(x)/F_29(x))
Eq(F_76(x), F_6(x))
Eq(F_77(x), F_4(x)*F_61(x))
Eq(F_78(x), F_2(x)*F_79(x))
Eq(F_79(x), F_80(x)/F_29(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_2(x) + F_60(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_29(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_32(x)*F_39(x)*F_55(x))
Eq(F_87(x), F_42(x)*F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_29(x)*F_32(x)*F_68(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_32(x)*F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_29(x)*F_47(x)*F_68(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_29(x)*F_96(x))
Eq(F_96(x), F_133(x) + F_97(x))
Eq(F_97(x), F_98(x)/F_29(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x) + F_122(x))
Eq(F_100(x), F_101(x)*F_121(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_29(x))
Eq(F_103(x), F_104(x) + F_117(x))
Eq(F_104(x), F_105(x) + F_111(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_0(x)*F_4(x))
Eq(F_107(x), F_108(x)*F_34(x))
Eq(F_108(x), F_0(x) + F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_105(x)*F_29(x))
Eq(F_111(x), F_112(x) + F_113(x))
Eq(F_112(x), F_4(x)*F_5(x))
Eq(F_113(x), F_108(x)*F_114(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_29(x)*F_40(x))
Eq(F_116(x), F_114(x) + F_34(x))
Eq(F_117(x), F_108(x)*F_118(x))
Eq(F_118(x), -F_116(x) + F_119(x))
Eq(F_119(x), F_120(x)/F_29(x))
Eq(F_120(x), F_35(x))
Eq(F_121(x), (x - 2)*F_121(x) + F_121(x)**2 + 2)
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_29(x))
Eq(F_124(x), F_125(x) + F_126(x))
Eq(F_125(x), F_101(x)*F_79(x))
Eq(F_126(x), F_127(x)*F_68(x))
Eq(F_127(x), F_128(x) - F_130(x))
Eq(F_128(x), F_129(x)/F_29(x))
Eq(F_129(x), F_101(x))
Eq(F_130(x), F_101(x) + F_131(x))
Eq(F_131(x), F_118(x) + F_132(x))
Eq(F_132(x), F_116(x) + F_4(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_103(x)*F_29(x)*F_68(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_29(x)*F_68(x))
Eq(F_137(x), F_138(x)/F_29(x))
Eq(F_138(x), F_9(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_29(x)*F_97(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_103(x)*F_29(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, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 3, 4, 1, 2], [0, 3, 4, 2, 1], [3, 0, 4, 1, 2], [3, 0, 4, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "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], [0, 2]], [[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, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [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": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}], "strategy": {"class_module": 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