02341_03241_03421_20341_23041_30241_30421_32041
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3020, 16564, 92954, 531132, 3079790, 18078026, 107217242, 641519234, 3867799656, 23474907166, 143311673610, 879443921520, 5421772061080, 33564144888250, 208562284628972, 1300381674640620, 8132983307580286, 51010392951630424, 320772359492007404, 2021976949049396902, 12773736923541372144, 80863457314244057284, 512881025739569831192, 3258777608441393768072, 20740340372818272246796, 132206931238016601372412, 843972148394783465546308, 5395101658200803125480208, 34532987700582097758713286, 221309460955024788469480016, 1419933534455137440516556190, 9120349715472582646852872490, 58641587945935895779807592728, 377422595152974778598476754162, 2431402689497444800231227063244, 15677366618544011824065973203784, 101171537074432922122696320534332, 653424832971746073906701685087720, 4223467543854422651713905662120748, 27318959337654417841332848566665892, 176834413716932586099590683138606870, 1145418302964281357061773841159049184, 7424103183362430944276144604599824758, 48149858753538406325294693735380224250, 312468641491292192068405799010537539004, 2028935101480138628138632059370601655890, 13181676081838857887790100319219195787732, 85685015776470953959677798378889493703700, 557265799790495550679926056475582346048752, 3626061129589535213518924139758859667461664, 23605622489121896115601841126986970954259966, 153743293481086422884419213841267870648751212, 1001775581135566120191702962400171377154546002, 6530279010103936809701757181407679986766985070, 42586690049907354781581437910783023257174561782, 277837594896330308671910633319310379317300662074, 1813332776614959990567459447830662648635469898612, 11839355360533611871610140345049899163406392364114, 77328139163676709447496305772587293947613198495284, 505244004833674130917225865684720060877152930035244, 3302282715676681380392816270632751486250194602018216, 21590981201764472171886157809049433942910474411504888, 141211907262129599363016229904701637446251108759173524, 923861818701439704942319893045667388133136477789507204, 6046103830951304519463227981683119665071202506127895390, 39579777573102012867708827597241343829634889189265159288, 259177144768295761680240965055553833452582121096417986648, 1697626867003843368578078611292979274647379446559488589866, 11122609399313624971993927638994257215057185948927720447744, 72893178950994993700286009241981739346412941264502749117264, 477837058360337769260796562826232575232756477420228903753424, 3133160119202083058392397684649738544236970694579924872230272, 20549079797618420692423919614972272426614690447251617747073088, 134805155711692310174593348880967567096978214872656443698075924, 884549965030553541456463900440095114306143559968394369318091942, 5805471324548554293258003651376668734772689787480862215398666976, 38110920695942656696921539055662182969777329799027425963516392526, 250239532509254307948178112626908231106210717881851489852120405070, 1643443149724661433768031368485526315814428397210486254366710657774, 10795520309965426445334510600350674929157030385631013632787494650518, 70928457715354401972813451531687008389043128242733999014846782242484, 466104704888315205614687687706199249740607866332214955659074601532786, 3063589310907645398627347958823468017434537651407581224888111799800176, 20140016143713453737291142055005290713495283598026373600641628283854260, 132424846026091444308770324156906492059664396374877481635728986333405428, 870878914427982991716409177570031999152222652678456618272707057137557164, 5728263817294426088356677198938626756688841294207851802530565367143193788, 37684567775871673664302364639453999121936259103509001843665202973417453864, 247957793968110226614855742223416079320665880552611507789407955815277230850, 1631789537991790910735732430584965087928864228900820310088601248278286925224, 10740418028173834206160485169301225688186547412695647743559195459798351072316, 70704561995207007084818286705348418284053037712530953280118738613175473686230, 465523375622858658631784683627113191286004224977313616182612983453975233139696, 3065504751826051358105918437599243950071544641800030988166046114605529055630068
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24441/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = 1/F[4,x]*F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[4,x]
F[11,x] = F[12,x]+F[18,x]
F[12,x] = F[13,x]+F[5,x]
F[13,x] = -F[139,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[4,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]+F[41,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[26,x]*F[4,x]
F[21,x] = 1/F[4,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[4,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[27,x]*F[4,x]
F[30,x] = F[31,x]
F[31,x] = F[27,x]*F[32,x]*F[4,x]
F[32,x] = 1/F[37,x]/F[4,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[26,x]*F[37,x]
F[37,x] = 1/F[4,x]*F[38,x]
F[38,x] = F[2,x]
F[39,x] = F[40,x]
F[40,x] = F[26,x]*F[35,x]*F[4,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[91,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = 1/F[4,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]+F[83,x]
F[49,x] = -F[82,x]+F[50,x]
F[50,x] = 1/F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]+F[71,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[2,x]*F[24,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[69,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[0,x]*F[24,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[2,x]+F[53,x]
F[65,x] = F[66,x]
F[66,x] = F[2,x]^2*F[0,x]
F[67,x] = F[68,x]
F[68,x] = F[0,x]*F[2,x]*F[23,x]
F[69,x] = F[70,x]
F[70,x] = F[0,x]*F[4,x]*F[59,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]*F[78,x]
F[73,x] = 1/F[4,x]*F[74,x]
F[74,x] = F[75,x]
F[75,x] = -F[2,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[21,x]*F[4,x]
F[78,x] = F[2,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[0,x]*F[4,x]*F[81,x]
F[81,x] = F[0,x]+F[79,x]
F[82,x] = F[76,x]*F[81,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[49,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[81,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[81,x]*F[85,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[85,x]*F[86,x]
F[91,x] = -F[126,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[120,x]+F[95,x]
F[95,x] = 1/F[4,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = -F[114,x]+F[98,x]
F[98,x] = 1/F[4,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[8,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[112,x]
F[105,x] = F[106,x]+F[111,x]
F[106,x] = 1/F[4,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]+F[13,x]
F[109,x] = F[110,x]
F[110,x] = F[13,x]*F[4,x]*F[85,x]
F[111,x] = F[13,x]*F[85,x]
F[112,x] = F[113,x]*F[85,x]
F[113,x] = -F[12,x]+F[8,x]
F[114,x] = F[115,x]+F[118,x]
F[115,x] = F[116,x]+F[19,x]
F[116,x] = F[0,x]*F[117,x]
F[117,x] = -1+(x^2-2*x)*F[117,x]^2+(2+x)*F[117,x]
F[118,x] = F[119,x]
F[119,x] = F[115,x]*F[32,x]*F[4,x]
F[120,x] = 1/F[4,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = -F[125,x]+F[123,x]
F[123,x] = F[124,x]
F[124,x] = F[21,x]*F[4,x]*F[86,x]
F[125,x] = F[20,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = 1/F[4,x]*F[129,x]
F[129,x] = F[130,x]
F[130,x] = -F[135,x]+F[131,x]
F[131,x] = 1/F[4,x]*F[132,x]
F[132,x] = F[133,x]
F[133,x] = -F[134,x]+F[6,x]
F[134,x] = (x*F[134,x]+x-1)*(x*F[134,x]+x-2*F[134,x])
F[135,x] = F[136,x]*F[2,x]
F[136,x] = F[117,x]+F[137,x]
F[137,x] = F[138,x]
F[138,x] = F[117,x]*F[32,x]*F[4,x]
F[139,x] = F[140,x]
F[140,x] = F[4,x]*F[73,x]*F[86,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = \frac{F_{9}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{18}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{5}\! \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_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{41}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{37}\! \left(x \right) F_{4}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{26}\! \left(x \right) F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{91}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{83}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{71}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{69}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{0}\! \left(x \right) F_{24}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{2}\! \left(x \right)+F_{53}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right) F_{78}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{0}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{76}\! \left(x \right) F_{81}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right) F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right) F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{120}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{8}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{112}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{111}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{13}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{111}\! \left(x \right) = F_{13}\! \left(x \right) F_{85}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{85}\! \left(x \right)
F_{113}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{118}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{19}\! \left(x \right)
F_{116}\! \left(x \right) = F_{0}\! \left(x \right) F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = x^{2} F_{117} \left(x \right)^{2}-2 x F_{117} \left(x \right)^{2}+F_{117}\! \left(x \right) x +2 F_{117}\! \left(x \right)-1
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = -F_{125}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{125}\! \left(x \right) = F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{6}\! \left(x \right)
F_{134}\! \left(x \right) = x^{2} F_{134} \left(x \right)^{2}+2 x^{2} F_{134}\! \left(x \right)-2 x F_{134} \left(x \right)^{2}+x^{2}-3 x F_{134}\! \left(x \right)-x +2 F_{134}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{2}\! \left(x \right)
F_{136}\! \left(x \right) = F_{117}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{117}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right) F_{86}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x)/F_4(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_4(x))
Eq(F_11(x), F_12(x) + F_18(x))
Eq(F_12(x), F_13(x) + F_5(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_4(x))
Eq(F_16(x), F_17(x)/F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) + F_41(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_26(x)*F_4(x))
Eq(F_21(x), F_22(x)/F_4(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_4(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_27(x)*F_4(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_27(x)*F_32(x)*F_4(x))
Eq(F_32(x), F_33(x)/(F_37(x)*F_4(x)))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_26(x)*F_37(x))
Eq(F_37(x), F_38(x)/F_4(x))
Eq(F_38(x), F_2(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_26(x)*F_35(x)*F_4(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_91(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x)/F_4(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) + F_83(x))
Eq(F_49(x), F_50(x) - F_82(x))
Eq(F_50(x), F_51(x)/F_4(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x) + F_71(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_2(x)*F_24(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_69(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_0(x)*F_24(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_2(x) + F_53(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_0(x)*F_2(x)**2)
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_0(x)*F_2(x)*F_23(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_0(x)*F_4(x)*F_59(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x)*F_78(x))
Eq(F_73(x), F_74(x)/F_4(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), -F_2(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_21(x)*F_4(x))
Eq(F_78(x), F_2(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_0(x)*F_4(x)*F_81(x))
Eq(F_81(x), F_0(x) + F_79(x))
Eq(F_82(x), F_76(x)*F_81(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_49(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_81(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_81(x)*F_85(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_85(x)*F_86(x))
Eq(F_91(x), -F_126(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_120(x) + F_95(x))
Eq(F_95(x), F_96(x)/F_4(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), -F_114(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_4(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_8(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_112(x))
Eq(F_105(x), F_106(x) + F_111(x))
Eq(F_106(x), F_107(x)/F_4(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x) + F_13(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_13(x)*F_4(x)*F_85(x))
Eq(F_111(x), F_13(x)*F_85(x))
Eq(F_112(x), F_113(x)*F_85(x))
Eq(F_113(x), -F_12(x) + F_8(x))
Eq(F_114(x), F_115(x) + F_118(x))
Eq(F_115(x), F_116(x) + F_19(x))
Eq(F_116(x), F_0(x)*F_117(x))
Eq(F_117(x), x*(x - 2)*F_117(x)**2 + (x + 2)*F_117(x) - 1)
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_115(x)*F_32(x)*F_4(x))
Eq(F_120(x), F_121(x)/F_4(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x) - F_125(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_21(x)*F_4(x)*F_86(x))
Eq(F_125(x), F_20(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x)/F_4(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x) - F_135(x))
Eq(F_131(x), F_132(x)/F_4(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), -F_134(x) + F_6(x))
Eq(F_134(x), x*(x - 2)*(F_134(x) + 1)**2 + (x + 1)*(F_134(x) + 1) + F_134(x) - 1)
Eq(F_135(x), F_136(x)*F_2(x))
Eq(F_136(x), F_117(x) + F_137(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_117(x)*F_32(x)*F_4(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_4(x)*F_73(x)*F_86(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "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]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], 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{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24631/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x]+F[7,x]
F[6,x] = -1+(x^2-2*x)*F[6,x]^2+(2+x)*F[6,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[33,x]
F[10,x] = F[11,x]+F[29,x]
F[11,x] = F[12,x]+F[6,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]*F[6,x]
F[14,x] = 1/F[19,x]/F[4,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[27,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = 1/F[4,x]*F[20,x]
F[20,x] = F[2,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[4,x]
F[25,x] = F[26,x]
F[26,x] = F[14,x]*F[22,x]*F[4,x]
F[27,x] = F[28,x]
F[28,x] = F[17,x]*F[21,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = 1/F[4,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[147,x]+F[36,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[144,x]+F[39,x]
F[39,x] = F[40,x]+F[5,x]
F[40,x] = -F[87,x]+F[41,x]
F[41,x] = F[42,x]+F[49,x]
F[42,x] = F[43,x]
F[43,x] = F[21,x]*F[4,x]*F[44,x]
F[44,x] = 1/F[4,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[0,x]+F[47,x]
F[47,x] = 1/F[4,x]*F[48,x]
F[48,x] = F[2,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[105,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = 1/F[4,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[103,x]+F[57,x]
F[57,x] = -F[102,x]+F[58,x]
F[58,x] = 1/F[4,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[2,x]*F[44,x]
F[63,x] = F[101,x]+F[64,x]
F[64,x] = F[100,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[98,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[0,x]*F[5,x]
F[70,x] = F[71,x]+F[77,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[65,x]+F[69,x]
F[75,x] = F[76,x]
F[76,x] = F[2,x]^2*F[0,x]
F[77,x] = F[78,x]
F[78,x] = F[0,x]*F[2,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = (x*F[80,x]+x-2*F[80,x])*(x*F[80,x]+x-1)
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[38,x]+F[84,x]
F[84,x] = F[85,x]+F[87,x]
F[85,x] = -F[5,x]+F[86,x]
F[86,x] = -F[41,x]+F[44,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[83,x]*F[89,x]
F[89,x] = F[90,x]+F[93,x]
F[90,x] = F[0,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[0,x]*F[4,x]*F[90,x]
F[93,x] = F[94,x]
F[94,x] = F[4,x]*F[90,x]*F[95,x]
F[95,x] = F[89,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[89,x]*F[95,x]
F[98,x] = F[99,x]
F[99,x] = F[0,x]*F[4,x]*F[67,x]
F[100,x] = F[85,x]*F[91,x]
F[101,x] = F[41,x]*F[91,x]
F[102,x] = F[46,x]*F[90,x]
F[103,x] = F[104,x]
F[104,x] = F[4,x]*F[57,x]*F[95,x]
F[105,x] = -F[135,x]+F[106,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[129,x]
F[109,x] = 1/F[4,x]*F[110,x]
F[110,x] = F[111,x]
F[111,x] = -F[124,x]+F[112,x]
F[112,x] = F[113,x]+F[44,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[123,x]
F[116,x] = F[117,x]+F[122,x]
F[117,x] = 1/F[4,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = -F[33,x]+F[120,x]
F[120,x] = 1/F[4,x]*F[121,x]
F[121,x] = F[81,x]
F[122,x] = F[85,x]*F[95,x]
F[123,x] = F[41,x]*F[95,x]
F[124,x] = F[125,x]+F[127,x]
F[125,x] = F[126,x]+F[42,x]
F[126,x] = F[0,x]*F[6,x]
F[127,x] = F[128,x]
F[128,x] = F[125,x]*F[14,x]*F[4,x]
F[129,x] = 1/F[4,x]*F[130,x]
F[130,x] = F[131,x]
F[131,x] = -F[134,x]+F[132,x]
F[132,x] = F[133,x]
F[133,x] = F[4,x]*F[44,x]*F[89,x]
F[134,x] = F[43,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = 1/F[4,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[143,x]+F[140,x]
F[140,x] = F[141,x]+F[29,x]
F[141,x] = F[142,x]
F[142,x] = F[117,x]*F[4,x]
F[143,x] = F[11,x]*F[2,x]
F[144,x] = F[145,x]+F[6,x]
F[145,x] = F[146,x]
F[146,x] = F[144,x]*F[21,x]*F[4,x]
F[147,x] = F[148,x]
F[148,x] = F[36,x]*F[4,x]*F[95,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}-2 x F_{6} \left(x \right)^{2}+F_{6}\! \left(x \right) x +2 F_{6}\! \left(x \right)-1
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{33}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{19}\! \left(x \right) F_{4}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{17}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{147}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{144}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{105}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{103}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{102}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{63}\! \left(x \right) = F_{101}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{100}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{98}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = x^{2} F_{80} \left(x \right)^{2}+2 x^{2} F_{80}\! \left(x \right)-2 x F_{80} \left(x \right)^{2}+x^{2}-3 x F_{80}\! \left(x \right)-x +2 F_{80}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{38}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{89}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right) F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{100}\! \left(x \right) = F_{85}\! \left(x \right) F_{91}\! \left(x \right)
F_{101}\! \left(x \right) = F_{41}\! \left(x \right) F_{91}\! \left(x \right)
F_{102}\! \left(x \right) = F_{46}\! \left(x \right) F_{90}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right) F_{95}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{129}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{44}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{123}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{122}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{81}\! \left(x \right)
F_{122}\! \left(x \right) = F_{85}\! \left(x \right) F_{95}\! \left(x \right)
F_{123}\! \left(x \right) = F_{41}\! \left(x \right) F_{95}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{42}\! \left(x \right)
F_{126}\! \left(x \right) = F_{0}\! \left(x \right) F_{6}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{125}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right) F_{89}\! \left(x \right)
F_{134}\! \left(x \right) = F_{43}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{29}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{6}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{144}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right) F_{95}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x*(x - 2)*F_6(x)**2 + (x + 2)*F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_33(x))
Eq(F_10(x), F_11(x) + F_29(x))
Eq(F_11(x), F_12(x) + F_6(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x)*F_6(x))
Eq(F_14(x), F_15(x)/(F_19(x)*F_4(x)))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_27(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x)/F_4(x))
Eq(F_20(x), F_2(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_4(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_14(x)*F_22(x)*F_4(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_17(x)*F_21(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x)/F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_147(x) + F_36(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), -F_144(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_5(x))
Eq(F_40(x), F_41(x) - F_87(x))
Eq(F_41(x), F_42(x) + F_49(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_21(x)*F_4(x)*F_44(x))
Eq(F_44(x), F_45(x)/F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), -F_0(x) + F_47(x))
Eq(F_47(x), F_48(x)/F_4(x))
Eq(F_48(x), F_2(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_105(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_4(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_103(x) + F_57(x))
Eq(F_57(x), -F_102(x) + F_58(x))
Eq(F_58(x), F_59(x)/F_4(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_2(x)*F_44(x))
Eq(F_63(x), F_101(x) + F_64(x))
Eq(F_64(x), F_100(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_98(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_0(x)*F_5(x))
Eq(F_70(x), F_71(x) + F_77(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_65(x) + F_69(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_0(x)*F_2(x)**2)
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_0(x)*F_2(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), x*(x - 2)*(F_80(x) + 1)**2 + (x + 1)*(F_80(x) + 1) + F_80(x) - 1)
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_38(x) + F_84(x))
Eq(F_84(x), F_85(x) + F_87(x))
Eq(F_85(x), -F_5(x) + F_86(x))
Eq(F_86(x), -F_41(x) + F_44(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_83(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_93(x))
Eq(F_90(x), F_0(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_0(x)*F_4(x)*F_90(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_4(x)*F_90(x)*F_95(x))
Eq(F_95(x), F_89(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_89(x)*F_95(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_0(x)*F_4(x)*F_67(x))
Eq(F_100(x), F_85(x)*F_91(x))
Eq(F_101(x), F_41(x)*F_91(x))
Eq(F_102(x), F_46(x)*F_90(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_4(x)*F_57(x)*F_95(x))
Eq(F_105(x), F_106(x) - F_135(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_129(x))
Eq(F_109(x), F_110(x)/F_4(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x) - F_124(x))
Eq(F_112(x), F_113(x) + F_44(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_123(x))
Eq(F_116(x), F_117(x) + F_122(x))
Eq(F_117(x), F_118(x)/F_4(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x) - F_33(x))
Eq(F_120(x), F_121(x)/F_4(x))
Eq(F_121(x), F_81(x))
Eq(F_122(x), F_85(x)*F_95(x))
Eq(F_123(x), F_41(x)*F_95(x))
Eq(F_124(x), F_125(x) + F_127(x))
Eq(F_125(x), F_126(x) + F_42(x))
Eq(F_126(x), F_0(x)*F_6(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_125(x)*F_14(x)*F_4(x))
Eq(F_129(x), F_130(x)/F_4(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x) - F_134(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_4(x)*F_44(x)*F_89(x))
Eq(F_134(x), F_43(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x)/F_4(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x) - F_143(x))
Eq(F_140(x), F_141(x) + F_29(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_117(x)*F_4(x))
Eq(F_143(x), F_11(x)*F_2(x))
Eq(F_144(x), F_145(x) + F_6(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_144(x)*F_21(x)*F_4(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_36(x)*F_4(x)*F_95(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "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]]}, {"patt": [3, 2, 0, 4, 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", 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[2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[3, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24851/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = 1/F[4,x]*F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[4,x]
F[11,x] = F[12,x]+F[18,x]
F[12,x] = F[13,x]+F[5,x]
F[13,x] = -F[139,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = 1/F[4,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]+F[41,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[26,x]*F[4,x]
F[21,x] = 1/F[4,x]*F[22,x]
F[22,x] = F[23,x]
F[23,x] = -F[0,x]+F[24,x]
F[24,x] = 1/F[4,x]*F[25,x]
F[25,x] = F[2,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[27,x]*F[4,x]
F[30,x] = F[31,x]
F[31,x] = F[27,x]*F[32,x]*F[4,x]
F[32,x] = 1/F[37,x]/F[4,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[26,x]*F[37,x]
F[37,x] = 1/F[4,x]*F[38,x]
F[38,x] = F[2,x]
F[39,x] = F[40,x]
F[40,x] = F[26,x]*F[35,x]*F[4,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[91,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = 1/F[4,x]*F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]+F[83,x]
F[49,x] = -F[82,x]+F[50,x]
F[50,x] = 1/F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]+F[71,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[2,x]*F[24,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[69,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[0,x]*F[24,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[2,x]+F[53,x]
F[65,x] = F[66,x]
F[66,x] = F[2,x]^2*F[0,x]
F[67,x] = F[68,x]
F[68,x] = F[0,x]*F[2,x]*F[23,x]
F[69,x] = F[70,x]
F[70,x] = F[0,x]*F[4,x]*F[59,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]*F[78,x]
F[73,x] = 1/F[4,x]*F[74,x]
F[74,x] = F[75,x]
F[75,x] = -F[2,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[21,x]*F[4,x]
F[78,x] = F[2,x]+F[79,x]
F[79,x] = F[80,x]
F[80,x] = F[0,x]*F[4,x]*F[81,x]
F[81,x] = F[0,x]+F[79,x]
F[82,x] = F[76,x]*F[81,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[49,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[81,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[81,x]*F[85,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[85,x]*F[86,x]
F[91,x] = -F[126,x]+F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[120,x]+F[95,x]
F[95,x] = 1/F[4,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = -F[114,x]+F[98,x]
F[98,x] = 1/F[4,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[8,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[112,x]
F[105,x] = F[106,x]+F[111,x]
F[106,x] = 1/F[4,x]*F[107,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]+F[13,x]
F[109,x] = F[110,x]
F[110,x] = F[13,x]*F[4,x]*F[85,x]
F[111,x] = F[13,x]*F[85,x]
F[112,x] = F[113,x]*F[85,x]
F[113,x] = -F[12,x]+F[8,x]
F[114,x] = F[115,x]+F[118,x]
F[115,x] = F[116,x]+F[19,x]
F[116,x] = F[0,x]*F[117,x]
F[117,x] = -1+(x^2-2*x)*F[117,x]^2+(2+x)*F[117,x]
F[118,x] = F[119,x]
F[119,x] = F[115,x]*F[32,x]*F[4,x]
F[120,x] = 1/F[4,x]*F[121,x]
F[121,x] = F[122,x]
F[122,x] = -F[125,x]+F[123,x]
F[123,x] = F[124,x]
F[124,x] = F[21,x]*F[4,x]*F[86,x]
F[125,x] = F[20,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = 1/F[4,x]*F[129,x]
F[129,x] = F[130,x]
F[130,x] = -F[135,x]+F[131,x]
F[131,x] = 1/F[4,x]*F[132,x]
F[132,x] = F[133,x]
F[133,x] = -F[134,x]+F[6,x]
F[134,x] = (x*F[134,x]+x-1)*(x*F[134,x]+x-2*F[134,x])
F[135,x] = F[136,x]*F[2,x]
F[136,x] = F[117,x]+F[137,x]
F[137,x] = F[138,x]
F[138,x] = F[117,x]*F[32,x]*F[4,x]
F[139,x] = F[140,x]
F[140,x] = F[4,x]*F[73,x]*F[86,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = \frac{F_{9}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{18}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{5}\! \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_{4}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{41}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = \frac{F_{22}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{2}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{27}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{37}\! \left(x \right) F_{4}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{26}\! \left(x \right) F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{91}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = \frac{F_{47}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{83}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{71}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{69}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{0}\! \left(x \right) F_{24}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{2}\! \left(x \right)+F_{53}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{23}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right) F_{78}\! \left(x \right)
F_{73}\! \left(x \right) = \frac{F_{74}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{0}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{76}\! \left(x \right) F_{81}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{81}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right) F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right) F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{120}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = \frac{F_{96}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{114}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = \frac{F_{99}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{8}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{112}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{111}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{13}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{111}\! \left(x \right) = F_{13}\! \left(x \right) F_{85}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{85}\! \left(x \right)
F_{113}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{118}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{19}\! \left(x \right)
F_{116}\! \left(x \right) = F_{0}\! \left(x \right) F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = x^{2} F_{117} \left(x \right)^{2}-2 x F_{117} \left(x \right)^{2}+F_{117}\! \left(x \right) x +2 F_{117}\! \left(x \right)-1
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{115}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = -F_{125}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{125}\! \left(x \right) = F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = \frac{F_{129}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{6}\! \left(x \right)
F_{134}\! \left(x \right) = x^{2} F_{134} \left(x \right)^{2}+2 x^{2} F_{134}\! \left(x \right)-2 x F_{134} \left(x \right)^{2}+x^{2}-3 x F_{134}\! \left(x \right)-x +2 F_{134}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{2}\! \left(x \right)
F_{136}\! \left(x \right) = F_{117}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{117}\! \left(x \right) F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right) F_{86}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x)/F_4(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_4(x))
Eq(F_11(x), F_12(x) + F_18(x))
Eq(F_12(x), F_13(x) + F_5(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_4(x))
Eq(F_16(x), F_17(x)/F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) + F_41(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_26(x)*F_4(x))
Eq(F_21(x), F_22(x)/F_4(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), -F_0(x) + F_24(x))
Eq(F_24(x), F_25(x)/F_4(x))
Eq(F_25(x), F_2(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_27(x)*F_4(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_27(x)*F_32(x)*F_4(x))
Eq(F_32(x), F_33(x)/(F_37(x)*F_4(x)))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_26(x)*F_37(x))
Eq(F_37(x), F_38(x)/F_4(x))
Eq(F_38(x), F_2(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_26(x)*F_35(x)*F_4(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_91(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x)/F_4(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x) + F_83(x))
Eq(F_49(x), F_50(x) - F_82(x))
Eq(F_50(x), F_51(x)/F_4(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x) + F_71(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_2(x)*F_24(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_69(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_0(x)*F_24(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_2(x) + F_53(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_0(x)*F_2(x)**2)
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_0(x)*F_2(x)*F_23(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_0(x)*F_4(x)*F_59(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x)*F_78(x))
Eq(F_73(x), F_74(x)/F_4(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), -F_2(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_21(x)*F_4(x))
Eq(F_78(x), F_2(x) + F_79(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_0(x)*F_4(x)*F_81(x))
Eq(F_81(x), F_0(x) + F_79(x))
Eq(F_82(x), F_76(x)*F_81(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_49(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_81(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_81(x)*F_85(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_85(x)*F_86(x))
Eq(F_91(x), -F_126(x) + F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_120(x) + F_95(x))
Eq(F_95(x), F_96(x)/F_4(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), -F_114(x) + F_98(x))
Eq(F_98(x), F_99(x)/F_4(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_8(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_112(x))
Eq(F_105(x), F_106(x) + F_111(x))
Eq(F_106(x), F_107(x)/F_4(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x) + F_13(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_13(x)*F_4(x)*F_85(x))
Eq(F_111(x), F_13(x)*F_85(x))
Eq(F_112(x), F_113(x)*F_85(x))
Eq(F_113(x), -F_12(x) + F_8(x))
Eq(F_114(x), F_115(x) + F_118(x))
Eq(F_115(x), F_116(x) + F_19(x))
Eq(F_116(x), F_0(x)*F_117(x))
Eq(F_117(x), x*(x - 2)*F_117(x)**2 + (x + 2)*F_117(x) - 1)
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_115(x)*F_32(x)*F_4(x))
Eq(F_120(x), F_121(x)/F_4(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x) - F_125(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_21(x)*F_4(x)*F_86(x))
Eq(F_125(x), F_20(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x)/F_4(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x) - F_135(x))
Eq(F_131(x), F_132(x)/F_4(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), -F_134(x) + F_6(x))
Eq(F_134(x), x*(x - 2)*(F_134(x) + 1)**2 + (x + 1)*(F_134(x) + 1) + F_134(x) - 1)
Eq(F_135(x), F_136(x)*F_2(x))
Eq(F_136(x), F_117(x) + F_137(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_117(x)*F_32(x)*F_4(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_4(x)*F_73(x)*F_86(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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{"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}], [{"patt": [0], "pos": [[3, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25078/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[6,x]+F[7,x]
F[6,x] = -1+(x^2-2*x)*F[6,x]^2+(2+x)*F[6,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[33,x]
F[10,x] = F[11,x]+F[29,x]
F[11,x] = F[12,x]+F[6,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]*F[6,x]
F[14,x] = 1/F[19,x]/F[4,x]*F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[27,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = 1/F[4,x]*F[20,x]
F[20,x] = F[2,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[4,x]
F[25,x] = F[26,x]
F[26,x] = F[14,x]*F[22,x]*F[4,x]
F[27,x] = F[28,x]
F[28,x] = F[17,x]*F[21,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = 1/F[4,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[147,x]+F[36,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,x] = F[38,x]
F[38,x] = -F[144,x]+F[39,x]
F[39,x] = F[40,x]+F[5,x]
F[40,x] = -F[87,x]+F[41,x]
F[41,x] = F[42,x]+F[49,x]
F[42,x] = F[43,x]
F[43,x] = F[21,x]*F[4,x]*F[44,x]
F[44,x] = 1/F[4,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[0,x]+F[47,x]
F[47,x] = 1/F[4,x]*F[48,x]
F[48,x] = F[2,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[105,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = 1/F[4,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[103,x]+F[57,x]
F[57,x] = -F[102,x]+F[58,x]
F[58,x] = 1/F[4,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[2,x]*F[44,x]
F[63,x] = F[101,x]+F[64,x]
F[64,x] = F[100,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[98,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[0,x]*F[5,x]
F[70,x] = F[71,x]+F[77,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[65,x]+F[69,x]
F[75,x] = F[76,x]
F[76,x] = F[2,x]^2*F[0,x]
F[77,x] = F[78,x]
F[78,x] = F[0,x]*F[2,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = (x*F[80,x]+x-1)*(x*F[80,x]+x-2*F[80,x])
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[38,x]+F[84,x]
F[84,x] = F[85,x]+F[87,x]
F[85,x] = -F[5,x]+F[86,x]
F[86,x] = -F[41,x]+F[44,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[83,x]*F[89,x]
F[89,x] = F[90,x]+F[93,x]
F[90,x] = F[0,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[0,x]*F[4,x]*F[90,x]
F[93,x] = F[94,x]
F[94,x] = F[4,x]*F[90,x]*F[95,x]
F[95,x] = F[89,x]+F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[89,x]*F[95,x]
F[98,x] = F[99,x]
F[99,x] = F[0,x]*F[4,x]*F[67,x]
F[100,x] = F[85,x]*F[91,x]
F[101,x] = F[41,x]*F[91,x]
F[102,x] = F[46,x]*F[90,x]
F[103,x] = F[104,x]
F[104,x] = F[4,x]*F[57,x]*F[95,x]
F[105,x] = -F[135,x]+F[106,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[129,x]
F[109,x] = 1/F[4,x]*F[110,x]
F[110,x] = F[111,x]
F[111,x] = -F[124,x]+F[112,x]
F[112,x] = F[113,x]+F[44,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]+F[123,x]
F[116,x] = F[117,x]+F[122,x]
F[117,x] = 1/F[4,x]*F[118,x]
F[118,x] = F[119,x]
F[119,x] = -F[33,x]+F[120,x]
F[120,x] = 1/F[4,x]*F[121,x]
F[121,x] = F[81,x]
F[122,x] = F[85,x]*F[95,x]
F[123,x] = F[41,x]*F[95,x]
F[124,x] = F[125,x]+F[127,x]
F[125,x] = F[126,x]+F[42,x]
F[126,x] = F[0,x]*F[6,x]
F[127,x] = F[128,x]
F[128,x] = F[125,x]*F[14,x]*F[4,x]
F[129,x] = 1/F[4,x]*F[130,x]
F[130,x] = F[131,x]
F[131,x] = -F[134,x]+F[132,x]
F[132,x] = F[133,x]
F[133,x] = F[4,x]*F[44,x]*F[89,x]
F[134,x] = F[43,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = 1/F[4,x]*F[138,x]
F[138,x] = F[139,x]
F[139,x] = -F[143,x]+F[140,x]
F[140,x] = F[141,x]+F[29,x]
F[141,x] = F[142,x]
F[142,x] = F[117,x]*F[4,x]
F[143,x] = F[11,x]*F[2,x]
F[144,x] = F[145,x]+F[6,x]
F[145,x] = F[146,x]
F[146,x] = F[144,x]*F[21,x]*F[4,x]
F[147,x] = F[148,x]
F[148,x] = F[36,x]*F[4,x]*F[95,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}-2 x F_{6} \left(x \right)^{2}+F_{6}\! \left(x \right) x +2 F_{6}\! \left(x \right)-1
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{33}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{29}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right) F_{6}\! \left(x \right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{19}\! \left(x \right) F_{4}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{17}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{147}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{144}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{5}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{87}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{105}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{103}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{102}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{44}\! \left(x \right)
F_{63}\! \left(x \right) = F_{101}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{100}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{98}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{65}\! \left(x \right)+F_{69}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = x^{2} F_{80} \left(x \right)^{2}+2 x^{2} F_{80}\! \left(x \right)-2 x F_{80} \left(x \right)^{2}+x^{2}-3 x F_{80}\! \left(x \right)-x +2 F_{80}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{38}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{87}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{0}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{89}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right) F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{100}\! \left(x \right) = F_{85}\! \left(x \right) F_{91}\! \left(x \right)
F_{101}\! \left(x \right) = F_{41}\! \left(x \right) F_{91}\! \left(x \right)
F_{102}\! \left(x \right) = F_{46}\! \left(x \right) F_{90}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right) F_{95}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{135}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{129}\! \left(x \right)
F_{109}\! \left(x \right) = \frac{F_{110}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = -F_{124}\! \left(x \right)+F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{44}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{123}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{122}\! \left(x \right)
F_{117}\! \left(x \right) = \frac{F_{118}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = -F_{33}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = \frac{F_{121}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{121}\! \left(x \right) = F_{81}\! \left(x \right)
F_{122}\! \left(x \right) = F_{85}\! \left(x \right) F_{95}\! \left(x \right)
F_{123}\! \left(x \right) = F_{41}\! \left(x \right) F_{95}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{127}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{42}\! \left(x \right)
F_{126}\! \left(x \right) = F_{0}\! \left(x \right) F_{6}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{125}\! \left(x \right) F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right) F_{89}\! \left(x \right)
F_{134}\! \left(x \right) = F_{43}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = \frac{F_{138}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = -F_{143}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{29}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{6}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{144}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right) F_{95}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x*(x - 2)*F_6(x)**2 + (x + 2)*F_6(x) - 1)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_33(x))
Eq(F_10(x), F_11(x) + F_29(x))
Eq(F_11(x), F_12(x) + F_6(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x)*F_6(x))
Eq(F_14(x), F_15(x)/(F_19(x)*F_4(x)))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_27(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x)/F_4(x))
Eq(F_20(x), F_2(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_4(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_14(x)*F_22(x)*F_4(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_17(x)*F_21(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x)/F_4(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_147(x) + F_36(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), -F_144(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_5(x))
Eq(F_40(x), F_41(x) - F_87(x))
Eq(F_41(x), F_42(x) + F_49(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_21(x)*F_4(x)*F_44(x))
Eq(F_44(x), F_45(x)/F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), -F_0(x) + F_47(x))
Eq(F_47(x), F_48(x)/F_4(x))
Eq(F_48(x), F_2(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_105(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_4(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_103(x) + F_57(x))
Eq(F_57(x), -F_102(x) + F_58(x))
Eq(F_58(x), F_59(x)/F_4(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_2(x)*F_44(x))
Eq(F_63(x), F_101(x) + F_64(x))
Eq(F_64(x), F_100(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_98(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_0(x)*F_5(x))
Eq(F_70(x), F_71(x) + F_77(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_65(x) + F_69(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_0(x)*F_2(x)**2)
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_0(x)*F_2(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), x*(x - 2)*(F_80(x) + 1)**2 + (x + 1)*(F_80(x) + 1) + F_80(x) - 1)
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_38(x) + F_84(x))
Eq(F_84(x), F_85(x) + F_87(x))
Eq(F_85(x), -F_5(x) + F_86(x))
Eq(F_86(x), -F_41(x) + F_44(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_83(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_93(x))
Eq(F_90(x), F_0(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_0(x)*F_4(x)*F_90(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_4(x)*F_90(x)*F_95(x))
Eq(F_95(x), F_89(x) + F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_89(x)*F_95(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_0(x)*F_4(x)*F_67(x))
Eq(F_100(x), F_85(x)*F_91(x))
Eq(F_101(x), F_41(x)*F_91(x))
Eq(F_102(x), F_46(x)*F_90(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_4(x)*F_57(x)*F_95(x))
Eq(F_105(x), F_106(x) - F_135(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_129(x))
Eq(F_109(x), F_110(x)/F_4(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x) - F_124(x))
Eq(F_112(x), F_113(x) + F_44(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_123(x))
Eq(F_116(x), F_117(x) + F_122(x))
Eq(F_117(x), F_118(x)/F_4(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x) - F_33(x))
Eq(F_120(x), F_121(x)/F_4(x))
Eq(F_121(x), F_81(x))
Eq(F_122(x), F_85(x)*F_95(x))
Eq(F_123(x), F_41(x)*F_95(x))
Eq(F_124(x), F_125(x) + F_127(x))
Eq(F_125(x), F_126(x) + F_42(x))
Eq(F_126(x), F_0(x)*F_6(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_125(x)*F_14(x)*F_4(x))
Eq(F_129(x), F_130(x)/F_4(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x) - F_134(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_4(x)*F_44(x)*F_89(x))
Eq(F_134(x), F_43(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x)/F_4(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x) - F_143(x))
Eq(F_140(x), F_141(x) + F_29(x))
Eq(F_141(x), F_142(x))
Eq(F_142(x), F_117(x)*F_4(x))
Eq(F_143(x), F_11(x)*F_2(x))
Eq(F_144(x), F_145(x) + F_6(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_144(x)*F_21(x)*F_4(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_36(x)*F_4(x)*F_95(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "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]]}, {"patt": [3, 2, 0, 4, 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": [[2, 1]]}, {"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, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 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[2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [2, 3, 1, 0], "pos": [[4, 6], [4, 6], [4, 6], [4, 6]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}], [{"patt": [0], "pos": [[3, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 2, 3, 4, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [2, 0, 3, 4, 1], [2, 3, 0, 4, 1], [3, 0, 2, 4, 1], [3, 0, 4, 2, 1], [3, 2, 0, 4, 1]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25250/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[146,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]+F[123,x,k[0]]
F[11,x,k[0]] = F[0,x]+F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[20,x,k[0]]
F[14,x,k[0]] = F[118,x,k[0]]+F[15,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]+F[21,x,k[0]]
F[16,x,k[0]] = F[0,x]*F[17,x,k[0]]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[17,x,k[0]]*F[20,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[17,x,k[0]]*F[23,x,k[0]]*F[4,x]
F[23,x,k[0]] = F[24,x,k[0]]+F[28,x,k[0]]
F[24,x,k[0]] = F[0,x]*F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,k[0]]+F[5,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[20,x,k[0]]*F[23,x,k[0]]
F[28,x,k[0]] = F[115,x,k[0]]+F[29,x,k[0]]
F[29,x,k[0]] = F[109,x,k[0]]+F[30,x,k[0]]
F[30,x,k[0]] = F[17,x,k[0]]*F[31,x]
F[31,x] = -F[108,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = 1/F[4,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[104,x]+F[37,x]
F[37,x] = F[102,x]+F[38,x]
F[38,x] = F[39,x]+F[86,x]
F[39,x] = F[0,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[0,x]*F[4,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[52,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = (x*F[46,x]+x-2*F[46,x])*(x*F[46,x]+x-1)
F[47,x] = -F[2,x]+F[48,x]
F[48,x] = -F[51,x]+F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[2,x]
F[51,x] = -1+(x^2-2*x)*F[51,x]^2+(2+x)*F[51,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[76,x]
F[55,x] = F[56,x]+F[74,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[49,x]+F[52,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[57,x]*F[60,x]
F[60,x] = 1/F[4,x]/F[49,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[72,x]
F[64,x] = F[49,x]*F[65,x]
F[65,x] = F[66,x]+F[70,x]
F[66,x] = F[67,x]
F[67,x] = F[1,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[67,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[60,x]*F[66,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[63,x]*F[65,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[57,x]*F[65,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[65,x]*F[78,x]
F[78,x] = F[79,x]+F[81,x]
F[79,x] = 1/F[4,x]*F[80,x]
F[80,x] = F[2,x]
F[81,x] = -F[84,x]+F[82,x]
F[82,x] = 1/F[4,x]*F[83,x]
F[83,x] = F[47,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[60,x]*F[78,x]
F[86,x] = F[100,x]+F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[98,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[0,x]*F[5,x]
F[93,x] = F[32,x]+F[94,x]
F[94,x] = F[6,x]*F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[0,x]*F[4,x]*F[97,x]
F[97,x] = F[0,x]+F[95,x]
F[98,x] = F[99,x]
F[99,x] = F[2,x]^2*F[0,x]
F[100,x] = F[101,x]
F[101,x] = F[0,x]*F[2,x]*F[42,x]
F[102,x] = F[103,x]
F[103,x] = F[0,x]*F[37,x]*F[4,x]
F[104,x] = F[105,x]
F[105,x] = F[0,x]*F[106,x]
F[106,x] = F[107,x]
F[107,x] = F[4,x]*F[44,x]*F[97,x]
F[108,x] = F[2,x]*F[95,x]
F[109,x,k[0]] = F[110,x,k[0]]*F[95,x]
F[110,x,k[0]] = F[111,x,k[0]]
F[111,x,k[0]] = F[112,x,k[0]]*F[17,x,k[0]]*F[4,x]
F[112,x,k[0]] = F[113,x,k[0]]+F[79,x]
F[113,x,k[0]] = F[114,x,k[0]]
F[114,x,k[0]] = F[0,x]*F[112,x,k[0]]*F[20,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[95,x]
F[25,x,k[0]] = F[116,x,k[0]]+F[117,x,k[0]]
F[117,x,k[0]] = F[110,x,k[0]]+F[17,x,k[0]]
F[118,x,k[0]] = k[0]*F[119,x,k[0]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[0,x]*F[121,x,k[0]]*F[4,x]
F[122,x,k[0]] = F[121,x,k[0]]*F[20,x,k[0]]
F[122,x,k[0]] = F[12,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]+F[130,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[2,x]
F[125,x,k[0]] = F[1,x]+F[126,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]
F[127,x,k[0]] = F[128,x,k[0]]*F[20,x,k[0]]
F[128,x,k[0]] = F[129,x,k[0]]+F[17,x,k[0]]
F[129,x,k[0]] = F[126,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[4,x]
F[132,x,k[0]] = F[133,x,k[0]]+F[139,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]*F[2,x]
F[135,x,k[0]] = F[134,x,k[0]]*F[4,x]
F[135,x,k[0]] = F[136,x,k[0]]
F[137,x,k[0]] = F[130,x,k[0]]+F[136,x,k[0]]
F[10,x,k[0]] = F[137,x,k[0]]+F[138,x,k[0]]
F[138,x,k[0]] = F[0,x]*F[125,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]+F[142,x,k[0]]
F[141,x,k[0]] = F[125,x,k[0]]*F[93,x]
F[142,x,k[0]] = F[143,x,k[0]]*F[17,x,k[0]]
F[144,x,k[0]] = F[143,x,k[0]]+F[145,x,k[0]]
F[23,x,k[0]] = F[144,x,k[0]]+F[91,x]
F[145,x,k[0]] = F[0,x]*F[26,x,k[0]]
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[0,x]*F[148,x,k[0]]*F[4,x]
F[148,x,k[0]] = F[149,x,k[0]]+F[150,x,k[0]]
F[149,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[150,x,k[0]] = F[151,x,k[0]]
F[151,x,k[0]] = F[0,x]*F[152,x,k[0]]*F[20,x,k[0]]
F[153,x,k[0]] = F[0,x]*F[152,x,k[0]]*F[4,x]
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]+F[174,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[172,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[4,x]
F[160,x,k[0]] = F[159,x,k[0]]*F[20,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]
F[161,x,k[0]] = F[12,x,k[0]]+F[162,x,k[0]]
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[4,x]
F[164,x,k[0]] = F[150,x,k[0]]+F[165,x,k[0]]
F[165,x,k[0]] = -k[0]*(F[166,x,1]-F[166,x,k[0]])/(-1+k[0])
F[9,x,k[0]] = F[166,x,k[0]]+F[167,x]
F[167,x] = F[168,x]+F[169,x]
F[168,x] = F[0,x]+F[89,x]
F[169,x] = F[170,x]+F[6,x]
F[170,x] = F[171,x]
F[171,x] = F[2,x]*F[4,x]*F[8,x]
F[172,x,k[0]] = F[173,x,k[0]]
F[173,x,k[0]] = F[159,x,k[0]]*F[2,x]*F[4,x]
F[174,x,k[0]] = k[0]*F[175,x,k[0]]
F[175,x,k[0]] = F[176,x,k[0]]
F[176,x,k[0]] = F[0,x]*F[177,x,k[0]]*F[4,x]
F[177,x,k[0]] = F[178,x,k[0]]+F[180,x,k[0]]
F[178,x,k[0]] = F[179,x,k[0]]
F[179,x,k[0]] = F[117,x,k[0]]*F[159,x,k[0]]*F[4,x]
F[159,x,k[0]] = F[180,x,k[0]]+F[181,x,k[0]]
F[181,x,k[0]] = F[121,x,k[0]]+F[178,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{123}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{102}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{86}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{52}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = x^{2} F_{46} \left(x \right)^{2}+2 x^{2} F_{46}\! \left(x \right)-2 x F_{46} \left(x \right)^{2}+x^{2}-3 x F_{46}\! \left(x \right)-x +2 F_{46}\! \left(x \right)
F_{47}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{51}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{2}\! \left(x \right)
F_{51}\! \left(x \right) = x^{2} F_{51} \left(x \right)^{2}-2 x F_{51} \left(x \right)^{2}+F_{51}\! \left(x \right) x +2 F_{51}\! \left(x \right)-1
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{76}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{74}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{4}\! \left(x \right) F_{49}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{64}\! \left(x \right) = F_{49}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{1}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right) F_{66}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right) F_{65}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right) F_{65}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{2}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{84}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{83}\! \left(x \right) = F_{47}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right) F_{78}\! \left(x \right)
F_{86}\! \left(x \right) = F_{100}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{98}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{0}\! \left(x \right) F_{5}\! \left(x \right)
F_{93}\! \left(x \right) = F_{32}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{6}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{0}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{2} \left(x \right)^{2} F_{0}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{0}\! \left(x \right) F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{0}\! \left(x \right) F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right) F_{97}\! \left(x \right)
F_{108}\! \left(x \right) = F_{2}\! \left(x \right) F_{95}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right) F_{95}\! \left(x \right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{112}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{79}\! \left(x \right)
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{112}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{95}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = y F_{119}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x , y\right)
F_{120}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{121}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{122}\! \left(x , y\right) = F_{121}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{122}\! \left(x , y\right) = F_{12}\! \left(x , y\right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{128}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{129}\! \left(x , y\right)+F_{17}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = F_{126}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{139}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right) F_{2}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{134}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{138}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{125}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{93}\! \left(x \right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{91}\! \left(x \right)
F_{145}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{26}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{148}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{150}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{152}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{152}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)+F_{174}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{172}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{160}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{162}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{164}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{165}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = -\frac{y \left(F_{166}\! \left(x , 1\right)-F_{166}\! \left(x , y\right)\right)}{-1+y}
F_{9}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{169}\! \left(x \right)
F_{168}\! \left(x \right) = F_{0}\! \left(x \right)+F_{89}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{6}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{172}\! \left(x , y\right) = F_{173}\! \left(x , y\right)
F_{173}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x , y\right) = y F_{175}\! \left(x , y\right)
F_{175}\! \left(x , y\right) = F_{176}\! \left(x , y\right)
F_{176}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{177}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{177}\! \left(x , y\right) = F_{178}\! \left(x , y\right)+F_{180}\! \left(x , y\right)
F_{178}\! \left(x , y\right) = F_{179}\! \left(x , y\right)
F_{179}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{159}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{180}\! \left(x , y\right)+F_{181}\! \left(x , y\right)
F_{181}\! \left(x , y\right) = F_{121}\! \left(x , y\right)+F_{178}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_146(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0) + F_123(x, k_0))
Eq(F_11(x, k_0), F_0(x) + F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_20(x, k_0))
Eq(F_14(x, k_0), F_118(x, k_0) + F_15(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0) + F_21(x, k_0))
Eq(F_16(x, k_0), F_0(x)*F_17(x, k_0))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_17(x, k_0)*F_20(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_17(x, k_0)*F_23(x, k_0)*F_4(x))
Eq(F_23(x, k_0), F_24(x, k_0) + F_28(x, k_0))
Eq(F_24(x, k_0), F_0(x)*F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, k_0) + F_5(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_20(x, k_0)*F_23(x, k_0))
Eq(F_28(x, k_0), F_115(x, k_0) + F_29(x, k_0))
Eq(F_29(x, k_0), F_109(x, k_0) + F_30(x, k_0))
Eq(F_30(x, k_0), F_17(x, k_0)*F_31(x))
Eq(F_31(x), -F_108(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x)/F_4(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), -F_104(x) + F_37(x))
Eq(F_37(x), F_102(x) + F_38(x))
Eq(F_38(x), F_39(x) + F_86(x))
Eq(F_39(x), F_0(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_0(x)*F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_52(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), x*(x - 2)*(F_46(x) + 1)**2 + (x + 1)*(F_46(x) + 1) + F_46(x) - 1)
Eq(F_47(x), -F_2(x) + F_48(x))
Eq(F_48(x), F_49(x) - F_51(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_2(x))
Eq(F_51(x), x*(x - 2)*F_51(x)**2 + (x + 2)*F_51(x) - 1)
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_76(x))
Eq(F_55(x), F_56(x) + F_74(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_49(x) + F_52(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_57(x)*F_60(x))
Eq(F_60(x), F_61(x)/(F_4(x)*F_49(x)))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_72(x))
Eq(F_64(x), F_49(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_70(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_1(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_67(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_60(x)*F_66(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_63(x)*F_65(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_57(x)*F_65(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_65(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_81(x))
Eq(F_79(x), F_80(x)/F_4(x))
Eq(F_80(x), F_2(x))
Eq(F_81(x), F_82(x) - F_84(x))
Eq(F_82(x), F_83(x)/F_4(x))
Eq(F_83(x), F_47(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_60(x)*F_78(x))
Eq(F_86(x), F_100(x) + F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_98(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_0(x)*F_5(x))
Eq(F_93(x), F_32(x) + F_94(x))
Eq(F_94(x), F_6(x)*F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_0(x)*F_4(x)*F_97(x))
Eq(F_97(x), F_0(x) + F_95(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_0(x)*F_2(x)**2)
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_0(x)*F_2(x)*F_42(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_0(x)*F_37(x)*F_4(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_0(x)*F_106(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_4(x)*F_44(x)*F_97(x))
Eq(F_108(x), F_2(x)*F_95(x))
Eq(F_109(x, k_0), F_110(x, k_0)*F_95(x))
Eq(F_110(x, k_0), F_111(x, k_0))
Eq(F_111(x, k_0), F_112(x, k_0)*F_17(x, k_0)*F_4(x))
Eq(F_112(x, k_0), F_113(x, k_0) + F_79(x))
Eq(F_113(x, k_0), F_114(x, k_0))
Eq(F_114(x, k_0), F_0(x)*F_112(x, k_0)*F_20(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0)*F_95(x))
Eq(F_25(x, k_0), F_116(x, k_0) + F_117(x, k_0))
Eq(F_117(x, k_0), F_110(x, k_0) + F_17(x, k_0))
Eq(F_118(x, k_0), k_0*F_119(x, k_0))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_0(x)*F_121(x, k_0)*F_4(x))
Eq(F_122(x, k_0), F_121(x, k_0)*F_20(x, k_0))
Eq(F_122(x, k_0), F_12(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0) + F_130(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_2(x))
Eq(F_125(x, k_0), F_1(x) + F_126(x, k_0))
Eq(F_126(x, k_0), F_127(x, k_0))
Eq(F_127(x, k_0), F_128(x, k_0)*F_20(x, k_0))
Eq(F_128(x, k_0), F_129(x, k_0) + F_17(x, k_0))
Eq(F_129(x, k_0), F_126(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_4(x))
Eq(F_132(x, k_0), F_133(x, k_0) + F_139(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0)*F_2(x))
Eq(F_135(x, k_0), F_134(x, k_0)*F_4(x))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_137(x, k_0), F_130(x, k_0) + F_136(x, k_0))
Eq(F_10(x, k_0), F_137(x, k_0) + F_138(x, k_0))
Eq(F_138(x, k_0), F_0(x)*F_125(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0) + F_142(x, k_0))
Eq(F_141(x, k_0), F_125(x, k_0)*F_93(x))
Eq(F_142(x, k_0), F_143(x, k_0)*F_17(x, k_0))
Eq(F_144(x, k_0), F_143(x, k_0) + F_145(x, k_0))
Eq(F_23(x, k_0), F_144(x, k_0) + F_91(x))
Eq(F_145(x, k_0), F_0(x)*F_26(x, k_0))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_0(x)*F_148(x, k_0)*F_4(x))
Eq(F_148(x, k_0), F_149(x, k_0) + F_150(x, k_0))
Eq(F_149(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_150(x, k_0), F_151(x, k_0))
Eq(F_151(x, k_0), F_0(x)*F_152(x, k_0)*F_20(x, k_0))
Eq(F_153(x, k_0), F_0(x)*F_152(x, k_0)*F_4(x))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0) + F_174(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_172(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_4(x))
Eq(F_160(x, k_0), F_159(x, k_0)*F_20(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0))
Eq(F_161(x, k_0), F_12(x, k_0) + F_162(x, k_0))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_4(x))
Eq(F_164(x, k_0), F_150(x, k_0) + F_165(x, k_0))
Eq(F_165(x, k_0), -F_166(x, 1) + (k_0*F_166(x, k_0) - F_166(x, 1))/(k_0 - 1))
Eq(F_9(x, k_0), F_166(x, k_0) + F_167(x))
Eq(F_167(x), F_168(x) + F_169(x))
Eq(F_168(x), F_0(x) + F_89(x))
Eq(F_169(x), F_170(x) + F_6(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_2(x)*F_4(x)*F_8(x))
Eq(F_172(x, k_0), F_173(x, k_0))
Eq(F_173(x, k_0), F_159(x, k_0)*F_2(x)*F_4(x))
Eq(F_174(x, k_0), k_0*F_175(x, k_0))
Eq(F_175(x, k_0), F_176(x, k_0))
Eq(F_176(x, k_0), F_0(x)*F_177(x, k_0)*F_4(x))
Eq(F_177(x, k_0), F_178(x, k_0) + F_180(x, k_0))
Eq(F_178(x, k_0), F_179(x, k_0))
Eq(F_179(x, k_0), F_117(x, k_0)*F_159(x, k_0)*F_4(x))
Eq(F_159(x, k_0), F_180(x, k_0) + F_181(x, k_0))
Eq(F_181(x, k_0), F_121(x, k_0) + F_178(x, k_0))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "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": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "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]]}, {"patt": [3, 2, 0, 4, 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", 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