01324_01342_01432_10324_10342_10432_13024_13042_13402_14032_14302
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2556, 12639, 62783, 312552, 1557651, 7766984, 38739716, 193254560, 964162462, 4810728095, 24005550686, 119799760214, 597926230722, 2984628984566, 14900029946193, 74394358619738, 371492496878452, 1855314483826184, 9267060815146287, 46293757532851579, 231290224321755892, 1155698834796053012, 5775405713700048657, 28864792721567707643, 144277996581297237466, 721232057541120336882, 3605709548507852981230, 18027887000319392488466, 90143602790249467451262, 450773833101738836939516, 2254311784395122828334512, 11274535488734962946127711, 56391121222101936742995167, 282064420231159108301891783, 1410943462090692627433402949, 7058183914085429803710831349, 35309926947714356140724313726, 176652461775663229361765125166, 883812685084093365671957904138, 4421983905866559750752435830608, 22125306357993183572542791966237, 110707116198630309637496934591069, 553955493488856700123378196803061, 2771956138394718695752702567131542, 13871042519377110157674336531472266, 69413238756868134154262497951555948, 347364329520483303987224160495798661, 1738349666010128324714581542088353144, 8699562697001185788626820853469396782, 43537699211543947534044232265530595639, 217891728185598610347584400277008621610, 1090492588405504005340668457861422980922, 5457715918750444612478038374837602120425, 27315234316886485101367087061576679648279, 136711272387983340701216821160318099959168, 684240436980005513260492988864604180269455, 3424662798946019354345345374695330674154122, 17140806139345988553216330847805512439270704, 85792380630185096610824667783191289875105100, 429407838544793644260051146261368041494396949, 2149288591248197961325909227876452377583579622, 10757782957749574726606802492868345257794422831, 53846053861877612580511787924246692755740051295, 269518039417866763683142511071978249652865951548, 1349038861426243793278635141928374056975233537438, 6752484096921818458982594413497082657203162670407, 33799089688383512036401118012542029273682521812850, 169179839554006731407704513113776873721717375267214, 846826117539699825742806730574951826896605205301296, 4238788792221310997964120765241260638964189286628768, 21217347356059478851029887315255627236233428118778435, 106204289285281993645808311076427555437218235169439282, 531611763972318917100489851740150972440585167411906185, 2661022611380649376728609885865115952550248862865425130, 13319990370824662311228830598414307142445246443122583894, 66674617791837317554939361496228750102051922301935613250, 333747757594737791726488713006836733917297668850099345539, 1670618555794268683906629188028666739172575607227683808830, 8362522480805728603111155126967413415092068645877514628017, 41859909342461794168065020335482028393160604803096165397426, 209536746071620139879014886330927861748907722396239999440924, 1048873172127972331912360743749803898985911385485150208254432, 5250329694562932700702656710875367788740529562806947630986110, 26281547964368082041723237286978035580158815232983889232990794, 131557625782419372855871996228737967229968884416719511164816823, 658539439933985519038643965471644573680934138168010755191977300, 3296462874150251023702702914707668889599463073287622618555015258, 16501186998445056151070482571784908072113935854059451846472226811, 82600513128583659645070155753936206929012678486944199373106821484, 413476501923481268931871788151370602645451414418636322994688777840, 2069757281403386123482019616527743670536794899845789998949310477595, 10360685073420843730505905313256310545649889329697137819929755109823, 51863039717938787362879119718056716052528039546318610623785633918746, 259613861296517749795354956225428652076441312775515514136355896207587
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24828/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[15,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -2+x^2+8*x+F[5,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[21,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]*F[2,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]^2*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[9,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]^2*F[15,x]*F[18,x]
F[21,x] = F[121,x]+F[22,x]
F[22,x] = -F[145,x]+F[23,x]
F[23,x] = -F[116,x]+F[24,x]
F[24,x] = -F[115,x]+F[25,x]
F[25,x] = 1/F[15,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[111,x]+F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = (x*F[29,x]^3+(2*x-1)*F[29,x]^2+(x^2-x+1)*F[29,x]+x^2)*(1+F[29,x])
F[30,x] = F[31,x]
F[31,x] = F[15,x]*F[32,x]
F[32,x] = F[33,x]+F[53,x]
F[33,x] = F[29,x]*F[34,x]
F[34,x] = F[0,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[15,x]*F[37,x]
F[37,x] = F[21,x]+F[38,x]
F[38,x] = F[10,x]+F[39,x]
F[39,x] = 1/F[0,x]*F[40,x]
F[40,x] = -F[49,x]+F[41,x]
F[41,x] = 1/F[15,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = (x^2+4*x-1)*F[44,x]^2+(4*x^2-5*x+2)*F[44,x]+4*x^2-x
F[45,x] = -F[2,x]+F[46,x]
F[46,x] = -F[5,x]+F[47,x]
F[47,x] = 1/F[15,x]*F[48,x]
F[48,x] = F[2,x]
F[49,x] = -F[52,x]+F[50,x]
F[50,x] = 1/F[15,x]*F[51,x]
F[51,x] = F[45,x]
F[52,x] = F[2,x]*F[39,x]
F[53,x] = F[54,x]*F[55,x]
F[54,x] = F[0,x]+F[28,x]
F[55,x] = -F[108,x]+F[56,x]
F[56,x] = -F[34,x]+F[57,x]
F[57,x] = F[105,x]+F[58,x]
F[58,x] = -F[103,x]+F[59,x]
F[59,x] = 1/F[15,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]+F[94,x]
F[62,x] = F[15,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[15,x]*F[65,x]
F[65,x] = F[66,x]+F[83,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[15,x]*F[68,x]
F[68,x] = 1+x*F[68,x]^4+F[68,x]^2*(x^2-2*x+3)+F[68,x]^3*(-1-x)+(-2+2*x)*F[68,x]
F[69,x] = F[70,x]
F[70,x] = F[15,x]*F[68,x]*F[71,x]
F[71,x] = F[72,x]+F[82,x]
F[72,x] = F[73,x]*F[80,x]
F[73,x] = F[12,x]+F[74,x]
F[74,x] = F[29,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[15,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[12,x]*F[74,x]
F[79,x] = F[68,x]*F[74,x]
F[80,x] = F[81,x]
F[81,x] = F[15,x]*F[18,x]
F[82,x] = F[12,x]*F[66,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[12,x]*F[15,x]
F[85,x] = F[86,x]
F[86,x] = F[15,x]*F[87,x]
F[87,x] = F[74,x]+F[88,x]
F[88,x] = F[55,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[15,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[55,x]*F[73,x]
F[93,x] = F[68,x]*F[88,x]
F[94,x] = F[95,x]
F[95,x] = F[15,x]*F[73,x]*F[96,x]
F[96,x] = F[62,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[15,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[12,x]*F[96,x]
F[101,x] = F[102,x]
F[102,x] = F[12,x]*F[68,x]*F[80,x]
F[103,x] = 1/F[15,x]*F[104,x]
F[104,x] = F[94,x]
F[105,x] = F[106,x]+F[108,x]
F[106,x] = F[107,x]+F[2,x]
F[107,x] = -F[29,x]+F[35,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[15,x]
F[110,x] = -F[12,x]+F[39,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[15,x]
F[113,x] = F[114,x]
F[114,x] = F[15,x]*F[54,x]*F[73,x]
F[115,x] = F[113,x]
F[116,x] = F[117,x]+F[121,x]
F[117,x] = F[118,x]+F[80,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[15,x]*F[18,x]
F[120,x] = F[2,x]+F[28,x]
F[121,x] = F[111,x]+F[122,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[15,x]
F[124,x] = F[125,x]+F[139,x]
F[125,x] = F[126,x]+F[137,x]
F[126,x] = F[12,x]*F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[117,x]*F[129,x]*F[15,x]
F[129,x] = 1/F[0,x]*F[130,x]
F[130,x] = -F[133,x]+F[131,x]
F[131,x] = 1/F[15,x]*F[132,x]
F[132,x] = F[35,x]
F[133,x] = -F[136,x]+F[134,x]
F[134,x] = 1/F[15,x]*F[135,x]
F[135,x] = F[107,x]
F[136,x] = F[129,x]*F[2,x]
F[137,x] = F[138,x]
F[138,x] = F[15,x]*F[18,x]*F[54,x]*F[68,x]*F[74,x]
F[139,x] = F[140,x]
F[140,x] = F[12,x]*F[141,x]
F[141,x] = F[121,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[129,x]*F[144,x]*F[15,x]
F[144,x] = F[116,x]
F[145,x] = F[0,x]*F[12,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x^{2} F_{5} \left(x \right)^{2}+2 x^{2} F_{5}\! \left(x \right)+4 x F_{5} \left(x \right)^{2}+x^{2}-13 x F_{5}\! \left(x \right)-F_{5} \left(x \right)^{2}+8 x +4 F_{5}\! \left(x \right)-2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{121}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{111}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = x F_{29} \left(x \right)^{4}+x^{2} F_{29} \left(x \right)^{2}+3 x F_{29} \left(x \right)^{3}+2 x^{2} F_{29}\! \left(x \right)+x F_{29} \left(x \right)^{2}-F_{29} \left(x \right)^{3}+x^{2}-F_{29}\! \left(x \right) x +F_{29}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{15}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{53}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{0}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{40}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = x^{2} F_{44} \left(x \right)^{2}+4 x^{2} F_{44}\! \left(x \right)+4 x F_{44} \left(x \right)^{2}+4 x^{2}-5 x F_{44}\! \left(x \right)-F_{44} \left(x \right)^{2}-x +2 F_{44}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{45}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right) F_{39}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{0}\! \left(x \right)+F_{28}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{105}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{94}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{83}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = x F_{68} \left(x \right)^{4}+x^{2} F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3} x -2 x F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3}+2 F_{68}\! \left(x \right) x +3 F_{68} \left(x \right)^{2}-2 F_{68}\! \left(x \right)+1
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right) F_{68}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{82}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right) F_{80}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{15}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{68}\! \left(x \right) F_{74}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{74}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{55}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \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_{55}\! \left(x \right) F_{73}\! \left(x \right)
F_{93}\! \left(x \right) = F_{68}\! \left(x \right) F_{88}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{15}\! \left(x \right) F_{73}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{62}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{15}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right) F_{80}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{94}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{108}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{2}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{15}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{15}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{15}\! \left(x \right) F_{54}\! \left(x \right) F_{73}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{80}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{120}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{121}\! \left(x \right) = F_{111}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{15}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{139}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{137}\! \left(x \right)
F_{126}\! \left(x \right) = F_{12}\! \left(x \right) F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{117}\! \left(x \right) F_{129}\! \left(x \right) F_{15}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{130}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{35}\! \left(x \right)
F_{133}\! \left(x \right) = -F_{136}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = \frac{F_{135}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{135}\! \left(x \right) = F_{107}\! \left(x \right)
F_{136}\! \left(x \right) = F_{129}\! \left(x \right) F_{2}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{54}\! \left(x \right) F_{68}\! \left(x \right) F_{74}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{121}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{129}\! \left(x \right) F_{144}\! \left(x \right) F_{15}\! \left(x \right)
F_{144}\! \left(x \right) = F_{116}\! \left(x \right)
F_{145}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_5(x)**2 + (2*x**2 - 13*x + 4)*F_5(x) - 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_21(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x)*F_2(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)**2*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_9(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)**2*F_15(x)*F_18(x))
Eq(F_21(x), F_121(x) + F_22(x))
Eq(F_22(x), -F_145(x) + F_23(x))
Eq(F_23(x), -F_116(x) + F_24(x))
Eq(F_24(x), -F_115(x) + F_25(x))
Eq(F_25(x), F_26(x)/F_15(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_111(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), x*(F_29(x) + 1)**4 + (-x - 1)*(F_29(x) + 1)**3 + (2*x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2*(x**2 - 2*x + 3) + F_29(x) + 1)
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_15(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_53(x))
Eq(F_33(x), F_29(x)*F_34(x))
Eq(F_34(x), F_0(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_15(x)*F_37(x))
Eq(F_37(x), F_21(x) + F_38(x))
Eq(F_38(x), F_10(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_0(x))
Eq(F_40(x), F_41(x) - F_49(x))
Eq(F_41(x), F_42(x)/F_15(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), x**2 + 8*x + (F_44(x) + 1)**2*(x**2 + 4*x - 1) + (F_44(x) + 1)*(2*x**2 - 13*x + 3) + F_44(x) - 2)
Eq(F_45(x), -F_2(x) + F_46(x))
Eq(F_46(x), F_47(x) - F_5(x))
Eq(F_47(x), F_48(x)/F_15(x))
Eq(F_48(x), F_2(x))
Eq(F_49(x), F_50(x) - F_52(x))
Eq(F_50(x), F_51(x)/F_15(x))
Eq(F_51(x), F_45(x))
Eq(F_52(x), F_2(x)*F_39(x))
Eq(F_53(x), F_54(x)*F_55(x))
Eq(F_54(x), F_0(x) + F_28(x))
Eq(F_55(x), -F_108(x) + F_56(x))
Eq(F_56(x), -F_34(x) + F_57(x))
Eq(F_57(x), F_105(x) + F_58(x))
Eq(F_58(x), -F_103(x) + F_59(x))
Eq(F_59(x), F_60(x)/F_15(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x) + F_94(x))
Eq(F_62(x), F_15(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_15(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_83(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_15(x)*F_68(x))
Eq(F_68(x), x*F_68(x)**4 + (-x - 1)*F_68(x)**3 + (2*x - 2)*F_68(x) + (x**2 - 2*x + 3)*F_68(x)**2 + 1)
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_15(x)*F_68(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_82(x))
Eq(F_72(x), F_73(x)*F_80(x))
Eq(F_73(x), F_12(x) + F_74(x))
Eq(F_74(x), F_29(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_15(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_12(x)*F_74(x))
Eq(F_79(x), F_68(x)*F_74(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_15(x)*F_18(x))
Eq(F_82(x), F_12(x)*F_66(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_12(x)*F_15(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_15(x)*F_87(x))
Eq(F_87(x), F_74(x) + F_88(x))
Eq(F_88(x), F_55(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_15(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_55(x)*F_73(x))
Eq(F_93(x), F_68(x)*F_88(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_15(x)*F_73(x)*F_96(x))
Eq(F_96(x), F_62(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_15(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_12(x)*F_96(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_12(x)*F_68(x)*F_80(x))
Eq(F_103(x), F_104(x)/F_15(x))
Eq(F_104(x), F_94(x))
Eq(F_105(x), F_106(x) + F_108(x))
Eq(F_106(x), F_107(x) + F_2(x))
Eq(F_107(x), -F_29(x) + F_35(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_15(x))
Eq(F_110(x), -F_12(x) + F_39(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_15(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_15(x)*F_54(x)*F_73(x))
Eq(F_115(x), F_113(x))
Eq(F_116(x), F_117(x) + F_121(x))
Eq(F_117(x), F_118(x) + F_80(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_15(x)*F_18(x))
Eq(F_120(x), F_2(x) + F_28(x))
Eq(F_121(x), F_111(x) + F_122(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_15(x))
Eq(F_124(x), F_125(x) + F_139(x))
Eq(F_125(x), F_126(x) + F_137(x))
Eq(F_126(x), F_12(x)*F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_117(x)*F_129(x)*F_15(x))
Eq(F_129(x), F_130(x)/F_0(x))
Eq(F_130(x), F_131(x) - F_133(x))
Eq(F_131(x), F_132(x)/F_15(x))
Eq(F_132(x), F_35(x))
Eq(F_133(x), F_134(x) - F_136(x))
Eq(F_134(x), F_135(x)/F_15(x))
Eq(F_135(x), F_107(x))
Eq(F_136(x), F_129(x)*F_2(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_15(x)*F_18(x)*F_54(x)*F_68(x)*F_74(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_12(x)*F_141(x))
Eq(F_141(x), F_121(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_129(x)*F_144(x)*F_15(x))
Eq(F_144(x), F_116(x))
Eq(F_145(x), F_0(x)*F_12(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25001/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (x^2+4*x-1)*F[6,x]^2+(4*x^2-5*x+2)*F[6,x]+4*x^2-x
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[21,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]*F[2,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]^2*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[9,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]^2*F[15,x]*F[18,x]
F[21,x] = F[22,x]+F[63,x]
F[22,x] = F[23,x]+F[31,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = (x*F[24,x]^3+(2*x-1)*F[24,x]^2+(x^2-x+1)*F[24,x]+x^2)*(1+F[24,x])
F[25,x] = F[26,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[12,x]*F[23,x]
F[29,x] = F[23,x]*F[30,x]
F[30,x] = 1+x*F[30,x]^4+F[30,x]^2*(x^2-2*x+3)+F[30,x]^3*(-1-x)+(-2+2*x)*F[30,x]
F[31,x] = -F[11,x]+F[32,x]
F[32,x] = -F[126,x]+F[33,x]
F[33,x] = -F[75,x]+F[34,x]
F[34,x] = -F[193,x]+F[35,x]
F[35,x] = 1/F[15,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]+F[64,x]
F[38,x] = F[24,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[15,x]*F[41,x]
F[41,x] = F[42,x]+F[97,x]
F[42,x] = F[24,x]*F[43,x]
F[43,x] = F[0,x]+F[44,x]
F[44,x] = F[24,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[15,x]*F[47,x]
F[47,x] = F[32,x]+F[48,x]
F[48,x] = F[49,x]+F[63,x]
F[49,x] = F[16,x]+F[50,x]
F[50,x] = -F[12,x]+F[51,x]
F[51,x] = 1/F[0,x]*F[52,x]
F[52,x] = -F[58,x]+F[53,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = -F[0,x]+F[56,x]
F[56,x] = 1/F[15,x]*F[57,x]
F[57,x] = F[2,x]
F[58,x] = -F[62,x]+F[59,x]
F[59,x] = 1/F[15,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = -F[6,x]+F[55,x]
F[62,x] = F[2,x]*F[51,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[24,x]*F[66,x]
F[66,x] = F[0,x]+F[38,x]
F[67,x] = F[68,x]
F[68,x] = F[15,x]*F[69,x]
F[69,x] = F[70,x]+F[90,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[63,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[15,x]*F[74,x]*F[82,x]
F[74,x] = F[75,x]
F[75,x] = F[63,x]+F[76,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[78,x]
F[78,x] = F[15,x]*F[18,x]
F[79,x] = F[80,x]
F[80,x] = F[15,x]*F[18,x]*F[81,x]
F[81,x] = F[2,x]+F[38,x]
F[82,x] = 1/F[0,x]*F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[15,x]*F[85,x]
F[85,x] = F[44,x]
F[86,x] = -F[89,x]+F[87,x]
F[87,x] = 1/F[15,x]*F[88,x]
F[88,x] = F[45,x]
F[89,x] = F[2,x]*F[82,x]
F[90,x] = F[91,x]
F[91,x] = F[92,x]+F[95,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[15,x]*F[76,x]*F[82,x]
F[95,x] = F[96,x]
F[96,x] = F[15,x]*F[18,x]*F[23,x]*F[30,x]*F[66,x]
F[97,x] = F[66,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[15,x]
F[100,x] = 1/F[15,x]*F[101,x]
F[101,x] = F[102,x]
F[102,x] = 1/F[182,x]*F[103,x]
F[103,x] = -F[189,x]+F[104,x]
F[104,x] = 1/F[15,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]+F[169,x]
F[107,x] = -F[168,x]+F[108,x]
F[108,x] = F[109,x]+F[30,x]
F[109,x] = -F[156,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[15,x]
F[112,x] = F[113,x]+F[129,x]
F[113,x] = 1/F[15,x]*F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[15,x]
F[116,x] = 1/F[15,x]*F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]+F[121,x]
F[119,x] = F[120,x]+F[6,x]
F[120,x] = F[15,x]*F[24,x]
F[121,x] = F[122,x]*F[15,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[15,x]
F[124,x] = F[125,x]+F[29,x]
F[125,x] = F[12,x]*F[126,x]
F[126,x] = F[127,x]+F[30,x]
F[127,x] = F[128,x]
F[128,x] = F[124,x]*F[15,x]
F[129,x] = F[130,x]
F[130,x] = -F[165,x]+F[131,x]
F[131,x] = 1/F[15,x]*F[132,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]+F[156,x]
F[134,x] = F[135,x]+F[15,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[15,x]
F[137,x] = F[138,x]+F[145,x]
F[138,x] = F[139,x]+F[140,x]
F[139,x] = F[15,x]*F[30,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]*F[15,x]*F[30,x]
F[142,x] = F[143,x]+F[144,x]
F[143,x] = F[126,x]*F[77,x]
F[144,x] = F[12,x]*F[138,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[12,x]*F[15,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[15,x]
F[149,x] = F[150,x]+F[23,x]
F[150,x] = F[151,x]+F[98,x]
F[151,x] = F[152,x]
F[152,x] = F[12,x]*F[15,x]*F[153,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[126,x]*F[98,x]
F[155,x] = F[150,x]*F[30,x]
F[156,x] = F[157,x]
F[157,x] = F[126,x]*F[15,x]*F[158,x]
F[158,x] = F[134,x]+F[159,x]
F[159,x] = F[160,x]
F[160,x] = F[15,x]*F[161,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[12,x]*F[158,x]
F[163,x] = F[164,x]
F[164,x] = F[12,x]*F[30,x]*F[77,x]
F[165,x] = F[166,x]+F[30,x]
F[166,x] = F[167,x]
F[167,x] = F[12,x]*F[126,x]*F[15,x]*F[30,x]
F[168,x] = -2+x^2+8*x+F[168,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[168,x]
F[169,x] = F[170,x]
F[170,x] = F[15,x]*F[171,x]
F[171,x] = F[172,x]+F[188,x]
F[172,x] = F[173,x]*F[174,x]
F[173,x] = F[122,x]+F[30,x]
F[174,x] = F[175,x]+F[187,x]
F[175,x] = F[176,x]
F[176,x] = F[15,x]*F[177,x]
F[177,x] = F[178,x]+F[179,x]
F[178,x] = F[1,x]+F[15,x]
F[179,x] = F[180,x]+F[183,x]
F[180,x] = F[181,x]
F[181,x] = F[15,x]*F[182,x]
F[182,x] = F[1,x]+F[180,x]
F[183,x] = F[184,x]+F[185,x]+F[187,x]
F[184,x] = 0
F[185,x] = F[15,x]*F[186,x]
F[186,x] = F[15,x]+F[183,x]
F[187,x] = F[15,x]*F[180,x]
F[188,x] = F[102,x]*F[180,x]
F[189,x] = F[173,x]*F[190,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[1,x]+F[175,x]
F[192,x] = F[15,x]*F[182,x]
F[193,x] = F[194,x]
F[194,x] = F[126,x]*F[15,x]*F[66,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}+4 x^{2} F_{6}\! \left(x \right)+4 x F_{6} \left(x \right)^{2}+4 x^{2}-5 x F_{6}\! \left(x \right)-F_{6} \left(x \right)^{2}-x +2 F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{63}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = x F_{24} \left(x \right)^{4}+x^{2} F_{24} \left(x \right)^{2}+3 x F_{24} \left(x \right)^{3}+2 x^{2} F_{24}\! \left(x \right)+x F_{24} \left(x \right)^{2}-F_{24} \left(x \right)^{3}+x^{2}-F_{24}\! \left(x \right) x +F_{24}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = x F_{30} \left(x \right)^{4}+x^{2} F_{30} \left(x \right)^{2}-F_{30} \left(x \right)^{3} x -2 x F_{30} \left(x \right)^{2}-F_{30} \left(x \right)^{3}+2 F_{30}\! \left(x \right) x +3 F_{30} \left(x \right)^{2}-2 F_{30}\! \left(x \right)+1
F_{31}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{193}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{64}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{97}\! \left(x \right)
F_{42}\! \left(x \right) = F_{24}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{0}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{24}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{63}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{52}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{2}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{55}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{51}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{90}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right) F_{82}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{63}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{44}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{45}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2}\! \left(x \right) F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{15}\! \left(x \right) F_{76}\! \left(x \right) F_{82}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{30}\! \left(x \right) F_{66}\! \left(x \right)
F_{97}\! \left(x \right) = F_{66}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{15}\! \left(x \right)
F_{100}\! \left(x \right) = \frac{F_{101}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{182}\! \left(x \right)}
F_{103}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{169}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{168}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{30}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{156}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{15}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{129}\! \left(x \right)
F_{113}\! \left(x \right) = \frac{F_{114}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{15}\! \left(x \right)
F_{116}\! \left(x \right) = \frac{F_{117}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{121}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{6}\! \left(x \right)
F_{120}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{15}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{15}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{29}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{30}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{124}\! \left(x \right) F_{15}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{156}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{15}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{15}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{145}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{140}\! \left(x \right)
F_{139}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{15}\! \left(x \right) F_{30}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{143}\! \left(x \right) = F_{126}\! \left(x \right) F_{77}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{138}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{15}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{23}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{98}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{126}\! \left(x \right) F_{98}\! \left(x \right)
F_{155}\! \left(x \right) = F_{150}\! \left(x \right) F_{30}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{134}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{15}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{12}\! \left(x \right) F_{158}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{77}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{30}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{30}\! \left(x \right)
F_{168}\! \left(x \right) = x^{2} F_{168} \left(x \right)^{2}+2 x^{2} F_{168}\! \left(x \right)+4 x F_{168} \left(x \right)^{2}+x^{2}-13 x F_{168}\! \left(x \right)-F_{168} \left(x \right)^{2}+8 x +4 F_{168}\! \left(x \right)-2
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{15}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{188}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{122}\! \left(x \right)+F_{30}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{187}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{15}\! \left(x \right) F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{179}\! \left(x \right)
F_{178}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{183}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{15}\! \left(x \right) F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{185}\! \left(x \right)+F_{187}\! \left(x \right)
F_{184}\! \left(x \right) = 0
F_{185}\! \left(x \right) = F_{15}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{15}\! \left(x \right)+F_{183}\! \left(x \right)
F_{187}\! \left(x \right) = F_{15}\! \left(x \right) F_{180}\! \left(x \right)
F_{188}\! \left(x \right) = F_{102}\! \left(x \right) F_{180}\! \left(x \right)
F_{189}\! \left(x \right) = F_{173}\! \left(x \right) F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{1}\! \left(x \right)+F_{175}\! \left(x \right)
F_{192}\! \left(x \right) = F_{15}\! \left(x \right) F_{182}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{66}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x**2 + 8*x + (F_6(x) + 1)**2*(x**2 + 4*x - 1) + (F_6(x) + 1)*(2*x**2 - 13*x + 3) + F_6(x) - 2)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_21(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x)*F_2(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)**2*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_9(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)**2*F_15(x)*F_18(x))
Eq(F_21(x), F_22(x) + F_63(x))
Eq(F_22(x), F_23(x) + F_31(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), x*(F_24(x) + 1)**4 + (-x - 1)*(F_24(x) + 1)**3 + (2*x - 3)*(F_24(x) + 1) + (F_24(x) + 1)**2*(x**2 - 2*x + 3) + F_24(x) + 1)
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_12(x)*F_23(x))
Eq(F_29(x), F_23(x)*F_30(x))
Eq(F_30(x), x*F_30(x)**4 + (-x - 1)*F_30(x)**3 + (2*x - 2)*F_30(x) + (x**2 - 2*x + 3)*F_30(x)**2 + 1)
Eq(F_31(x), -F_11(x) + F_32(x))
Eq(F_32(x), -F_126(x) + F_33(x))
Eq(F_33(x), F_34(x) - F_75(x))
Eq(F_34(x), -F_193(x) + F_35(x))
Eq(F_35(x), F_36(x)/F_15(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x) + F_64(x))
Eq(F_38(x), F_24(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_15(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_97(x))
Eq(F_42(x), F_24(x)*F_43(x))
Eq(F_43(x), F_0(x) + F_44(x))
Eq(F_44(x), F_24(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_15(x)*F_47(x))
Eq(F_47(x), F_32(x) + F_48(x))
Eq(F_48(x), F_49(x) + F_63(x))
Eq(F_49(x), F_16(x) + F_50(x))
Eq(F_50(x), -F_12(x) + F_51(x))
Eq(F_51(x), F_52(x)/F_0(x))
Eq(F_52(x), F_53(x) - F_58(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), -F_0(x) + F_56(x))
Eq(F_56(x), F_57(x)/F_15(x))
Eq(F_57(x), F_2(x))
Eq(F_58(x), F_59(x) - F_62(x))
Eq(F_59(x), F_60(x)/F_15(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_55(x) - F_6(x))
Eq(F_62(x), F_2(x)*F_51(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_24(x)*F_66(x))
Eq(F_66(x), F_0(x) + F_38(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_15(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_90(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_63(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_15(x)*F_74(x)*F_82(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_63(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_15(x)*F_18(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_15(x)*F_18(x)*F_81(x))
Eq(F_81(x), F_2(x) + F_38(x))
Eq(F_82(x), F_83(x)/F_0(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_15(x))
Eq(F_85(x), F_44(x))
Eq(F_86(x), F_87(x) - F_89(x))
Eq(F_87(x), F_88(x)/F_15(x))
Eq(F_88(x), F_45(x))
Eq(F_89(x), F_2(x)*F_82(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_92(x) + F_95(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_15(x)*F_76(x)*F_82(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_15(x)*F_18(x)*F_23(x)*F_30(x)*F_66(x))
Eq(F_97(x), F_66(x)*F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_15(x))
Eq(F_100(x), F_101(x)/F_15(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)/F_182(x))
Eq(F_103(x), F_104(x) - F_189(x))
Eq(F_104(x), F_105(x)/F_15(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) + F_169(x))
Eq(F_107(x), F_108(x) - F_168(x))
Eq(F_108(x), F_109(x) + F_30(x))
Eq(F_109(x), F_110(x) - F_156(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_15(x))
Eq(F_112(x), F_113(x) + F_129(x))
Eq(F_113(x), F_114(x)/F_15(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_15(x))
Eq(F_116(x), F_117(x)/F_15(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x) + F_121(x))
Eq(F_119(x), F_120(x) + F_6(x))
Eq(F_120(x), F_15(x)*F_24(x))
Eq(F_121(x), F_122(x)*F_15(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_15(x))
Eq(F_124(x), F_125(x) + F_29(x))
Eq(F_125(x), F_12(x)*F_126(x))
Eq(F_126(x), F_127(x) + F_30(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_124(x)*F_15(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x) - F_165(x))
Eq(F_131(x), F_132(x)/F_15(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x) + F_156(x))
Eq(F_134(x), F_135(x) + F_15(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_15(x))
Eq(F_137(x), F_138(x) + F_145(x))
Eq(F_138(x), F_139(x) + F_140(x))
Eq(F_139(x), F_15(x)*F_30(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x)*F_15(x)*F_30(x))
Eq(F_142(x), F_143(x) + F_144(x))
Eq(F_143(x), F_126(x)*F_77(x))
Eq(F_144(x), F_12(x)*F_138(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_12(x)*F_15(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_15(x))
Eq(F_149(x), F_150(x) + F_23(x))
Eq(F_150(x), F_151(x) + F_98(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_12(x)*F_15(x)*F_153(x))
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_126(x)*F_98(x))
Eq(F_155(x), F_150(x)*F_30(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_126(x)*F_15(x)*F_158(x))
Eq(F_158(x), F_134(x) + F_159(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_15(x)*F_161(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_12(x)*F_158(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_12(x)*F_30(x)*F_77(x))
Eq(F_165(x), F_166(x) + F_30(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_12(x)*F_126(x)*F_15(x)*F_30(x))
Eq(F_168(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_168(x)**2 + (2*x**2 - 13*x + 4)*F_168(x) - 2)
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_15(x)*F_171(x))
Eq(F_171(x), F_172(x) + F_188(x))
Eq(F_172(x), F_173(x)*F_174(x))
Eq(F_173(x), F_122(x) + F_30(x))
Eq(F_174(x), F_175(x) + F_187(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_15(x)*F_177(x))
Eq(F_177(x), F_178(x) + F_179(x))
Eq(F_178(x), F_1(x) + F_15(x))
Eq(F_179(x), F_180(x) + F_183(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_15(x)*F_182(x))
Eq(F_182(x), F_1(x) + F_180(x))
Eq(F_183(x), F_184(x) + F_185(x) + F_187(x))
Eq(F_184(x), 0)
Eq(F_185(x), F_15(x)*F_186(x))
Eq(F_186(x), F_15(x) + F_183(x))
Eq(F_187(x), F_15(x)*F_180(x))
Eq(F_188(x), F_102(x)*F_180(x))
Eq(F_189(x), F_173(x)*F_190(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_1(x) + F_175(x))
Eq(F_192(x), F_15(x)*F_182(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_126(x)*F_15(x)*F_66(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 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{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25014/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[15,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = -2+x^2+8*x+F[5,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[21,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]*F[2,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]^2*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[9,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]^2*F[15,x]*F[18,x]
F[21,x] = F[121,x]+F[22,x]
F[22,x] = -F[145,x]+F[23,x]
F[23,x] = -F[116,x]+F[24,x]
F[24,x] = -F[115,x]+F[25,x]
F[25,x] = 1/F[15,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[111,x]+F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = (1+F[29,x])*(x*F[29,x]^3+(2*x-1)*F[29,x]^2+(x^2-x+1)*F[29,x]+x^2)
F[30,x] = F[31,x]
F[31,x] = F[15,x]*F[32,x]
F[32,x] = F[33,x]+F[53,x]
F[33,x] = F[29,x]*F[34,x]
F[34,x] = F[0,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[15,x]*F[37,x]
F[37,x] = F[21,x]+F[38,x]
F[38,x] = F[10,x]+F[39,x]
F[39,x] = 1/F[0,x]*F[40,x]
F[40,x] = -F[49,x]+F[41,x]
F[41,x] = 1/F[15,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = (x^2+4*x-1)*F[44,x]^2+(4*x^2-5*x+2)*F[44,x]+4*x^2-x
F[45,x] = -F[2,x]+F[46,x]
F[46,x] = -F[5,x]+F[47,x]
F[47,x] = 1/F[15,x]*F[48,x]
F[48,x] = F[2,x]
F[49,x] = -F[52,x]+F[50,x]
F[50,x] = 1/F[15,x]*F[51,x]
F[51,x] = F[45,x]
F[52,x] = F[2,x]*F[39,x]
F[53,x] = F[54,x]*F[55,x]
F[54,x] = F[0,x]+F[28,x]
F[55,x] = -F[108,x]+F[56,x]
F[56,x] = -F[34,x]+F[57,x]
F[57,x] = F[105,x]+F[58,x]
F[58,x] = -F[103,x]+F[59,x]
F[59,x] = 1/F[15,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]+F[94,x]
F[62,x] = F[15,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[15,x]*F[65,x]
F[65,x] = F[66,x]+F[83,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[15,x]*F[68,x]
F[68,x] = 1+x*F[68,x]^4+F[68,x]^2*(x^2-2*x+3)+F[68,x]^3*(-1-x)+(-2+2*x)*F[68,x]
F[69,x] = F[70,x]
F[70,x] = F[15,x]*F[68,x]*F[71,x]
F[71,x] = F[72,x]+F[82,x]
F[72,x] = F[73,x]*F[80,x]
F[73,x] = F[12,x]+F[74,x]
F[74,x] = F[29,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[15,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[12,x]*F[74,x]
F[79,x] = F[68,x]*F[74,x]
F[80,x] = F[81,x]
F[81,x] = F[15,x]*F[18,x]
F[82,x] = F[12,x]*F[66,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[12,x]*F[15,x]
F[85,x] = F[86,x]
F[86,x] = F[15,x]*F[87,x]
F[87,x] = F[74,x]+F[88,x]
F[88,x] = F[55,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]*F[15,x]*F[91,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[55,x]*F[73,x]
F[93,x] = F[68,x]*F[88,x]
F[94,x] = F[95,x]
F[95,x] = F[15,x]*F[73,x]*F[96,x]
F[96,x] = F[62,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[15,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[12,x]*F[96,x]
F[101,x] = F[102,x]
F[102,x] = F[12,x]*F[68,x]*F[80,x]
F[103,x] = 1/F[15,x]*F[104,x]
F[104,x] = F[94,x]
F[105,x] = F[106,x]+F[108,x]
F[106,x] = F[107,x]+F[2,x]
F[107,x] = -F[29,x]+F[35,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[15,x]
F[110,x] = -F[12,x]+F[39,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[15,x]
F[113,x] = F[114,x]
F[114,x] = F[15,x]*F[54,x]*F[73,x]
F[115,x] = F[113,x]
F[116,x] = F[117,x]+F[121,x]
F[117,x] = F[118,x]+F[80,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[15,x]*F[18,x]
F[120,x] = F[2,x]+F[28,x]
F[121,x] = F[111,x]+F[122,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[15,x]
F[124,x] = F[125,x]+F[139,x]
F[125,x] = F[126,x]+F[137,x]
F[126,x] = F[12,x]*F[127,x]
F[127,x] = F[128,x]
F[128,x] = F[117,x]*F[129,x]*F[15,x]
F[129,x] = 1/F[0,x]*F[130,x]
F[130,x] = -F[133,x]+F[131,x]
F[131,x] = 1/F[15,x]*F[132,x]
F[132,x] = F[35,x]
F[133,x] = -F[136,x]+F[134,x]
F[134,x] = 1/F[15,x]*F[135,x]
F[135,x] = F[107,x]
F[136,x] = F[129,x]*F[2,x]
F[137,x] = F[138,x]
F[138,x] = F[15,x]*F[18,x]*F[54,x]*F[68,x]*F[74,x]
F[139,x] = F[140,x]
F[140,x] = F[12,x]*F[141,x]
F[141,x] = F[121,x]+F[142,x]
F[142,x] = F[143,x]
F[143,x] = F[129,x]*F[144,x]*F[15,x]
F[144,x] = F[116,x]
F[145,x] = F[0,x]*F[12,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x^{2} F_{5} \left(x \right)^{2}+2 x^{2} F_{5}\! \left(x \right)+4 x F_{5} \left(x \right)^{2}+x^{2}-13 x F_{5}\! \left(x \right)-F_{5} \left(x \right)^{2}+8 x +4 F_{5}\! \left(x \right)-2
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{121}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{145}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{116}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{115}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{111}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = x F_{29} \left(x \right)^{4}+x^{2} F_{29} \left(x \right)^{2}+3 x F_{29} \left(x \right)^{3}+2 x^{2} F_{29}\! \left(x \right)+x F_{29} \left(x \right)^{2}-F_{29} \left(x \right)^{3}+x^{2}-F_{29}\! \left(x \right) x +F_{29}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{15}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{53}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{0}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{15}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{40}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = x^{2} F_{44} \left(x \right)^{2}+4 x^{2} F_{44}\! \left(x \right)+4 x F_{44} \left(x \right)^{2}+4 x^{2}-5 x F_{44}\! \left(x \right)-F_{44} \left(x \right)^{2}-x +2 F_{44}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{52}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = \frac{F_{51}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{51}\! \left(x \right) = F_{45}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right) F_{39}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{0}\! \left(x \right)+F_{28}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{105}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{103}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{94}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{83}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = x F_{68} \left(x \right)^{4}+x^{2} F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3} x -2 x F_{68} \left(x \right)^{2}-F_{68} \left(x \right)^{3}+2 F_{68}\! \left(x \right) x +3 F_{68} \left(x \right)^{2}-2 F_{68}\! \left(x \right)+1
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{15}\! \left(x \right) F_{68}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{82}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right) F_{80}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{29}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{15}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{68}\! \left(x \right) F_{74}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{74}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{55}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \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_{55}\! \left(x \right) F_{73}\! \left(x \right)
F_{93}\! \left(x \right) = F_{68}\! \left(x \right) F_{88}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{15}\! \left(x \right) F_{73}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{62}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{15}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right) F_{80}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{94}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{108}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{2}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{15}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{15}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{15}\! \left(x \right) F_{54}\! \left(x \right) F_{73}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{121}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{80}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{120}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{121}\! \left(x \right) = F_{111}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{15}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{139}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{137}\! \left(x \right)
F_{126}\! \left(x \right) = F_{12}\! \left(x \right) F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{117}\! \left(x \right) F_{129}\! \left(x \right) F_{15}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{130}\! \left(x \right) = -F_{133}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{35}\! \left(x \right)
F_{133}\! \left(x \right) = -F_{136}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = \frac{F_{135}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{135}\! \left(x \right) = F_{107}\! \left(x \right)
F_{136}\! \left(x \right) = F_{129}\! \left(x \right) F_{2}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{54}\! \left(x \right) F_{68}\! \left(x \right) F_{74}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{121}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{129}\! \left(x \right) F_{144}\! \left(x \right) F_{15}\! \left(x \right)
F_{144}\! \left(x \right) = F_{116}\! \left(x \right)
F_{145}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_5(x)**2 + (2*x**2 - 13*x + 4)*F_5(x) - 2)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_21(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x)*F_2(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)**2*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_9(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)**2*F_15(x)*F_18(x))
Eq(F_21(x), F_121(x) + F_22(x))
Eq(F_22(x), -F_145(x) + F_23(x))
Eq(F_23(x), -F_116(x) + F_24(x))
Eq(F_24(x), -F_115(x) + F_25(x))
Eq(F_25(x), F_26(x)/F_15(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_111(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), x*(F_29(x) + 1)**4 + (-x - 1)*(F_29(x) + 1)**3 + (2*x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2*(x**2 - 2*x + 3) + F_29(x) + 1)
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_15(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_53(x))
Eq(F_33(x), F_29(x)*F_34(x))
Eq(F_34(x), F_0(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_15(x)*F_37(x))
Eq(F_37(x), F_21(x) + F_38(x))
Eq(F_38(x), F_10(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_0(x))
Eq(F_40(x), F_41(x) - F_49(x))
Eq(F_41(x), F_42(x)/F_15(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), x**2 + 8*x + (F_44(x) + 1)**2*(x**2 + 4*x - 1) + (F_44(x) + 1)*(2*x**2 - 13*x + 3) + F_44(x) - 2)
Eq(F_45(x), -F_2(x) + F_46(x))
Eq(F_46(x), F_47(x) - F_5(x))
Eq(F_47(x), F_48(x)/F_15(x))
Eq(F_48(x), F_2(x))
Eq(F_49(x), F_50(x) - F_52(x))
Eq(F_50(x), F_51(x)/F_15(x))
Eq(F_51(x), F_45(x))
Eq(F_52(x), F_2(x)*F_39(x))
Eq(F_53(x), F_54(x)*F_55(x))
Eq(F_54(x), F_0(x) + F_28(x))
Eq(F_55(x), -F_108(x) + F_56(x))
Eq(F_56(x), -F_34(x) + F_57(x))
Eq(F_57(x), F_105(x) + F_58(x))
Eq(F_58(x), -F_103(x) + F_59(x))
Eq(F_59(x), F_60(x)/F_15(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x) + F_94(x))
Eq(F_62(x), F_15(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_15(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_83(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_15(x)*F_68(x))
Eq(F_68(x), x*F_68(x)**4 + (-x - 1)*F_68(x)**3 + (2*x - 2)*F_68(x) + (x**2 - 2*x + 3)*F_68(x)**2 + 1)
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_15(x)*F_68(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_82(x))
Eq(F_72(x), F_73(x)*F_80(x))
Eq(F_73(x), F_12(x) + F_74(x))
Eq(F_74(x), F_29(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_15(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_12(x)*F_74(x))
Eq(F_79(x), F_68(x)*F_74(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_15(x)*F_18(x))
Eq(F_82(x), F_12(x)*F_66(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_12(x)*F_15(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_15(x)*F_87(x))
Eq(F_87(x), F_74(x) + F_88(x))
Eq(F_88(x), F_55(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x)*F_15(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_55(x)*F_73(x))
Eq(F_93(x), F_68(x)*F_88(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_15(x)*F_73(x)*F_96(x))
Eq(F_96(x), F_62(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_15(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_12(x)*F_96(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_12(x)*F_68(x)*F_80(x))
Eq(F_103(x), F_104(x)/F_15(x))
Eq(F_104(x), F_94(x))
Eq(F_105(x), F_106(x) + F_108(x))
Eq(F_106(x), F_107(x) + F_2(x))
Eq(F_107(x), -F_29(x) + F_35(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_15(x))
Eq(F_110(x), -F_12(x) + F_39(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_15(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_15(x)*F_54(x)*F_73(x))
Eq(F_115(x), F_113(x))
Eq(F_116(x), F_117(x) + F_121(x))
Eq(F_117(x), F_118(x) + F_80(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_15(x)*F_18(x))
Eq(F_120(x), F_2(x) + F_28(x))
Eq(F_121(x), F_111(x) + F_122(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_15(x))
Eq(F_124(x), F_125(x) + F_139(x))
Eq(F_125(x), F_126(x) + F_137(x))
Eq(F_126(x), F_12(x)*F_127(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_117(x)*F_129(x)*F_15(x))
Eq(F_129(x), F_130(x)/F_0(x))
Eq(F_130(x), F_131(x) - F_133(x))
Eq(F_131(x), F_132(x)/F_15(x))
Eq(F_132(x), F_35(x))
Eq(F_133(x), F_134(x) - F_136(x))
Eq(F_134(x), F_135(x)/F_15(x))
Eq(F_135(x), F_107(x))
Eq(F_136(x), F_129(x)*F_2(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_15(x)*F_18(x)*F_54(x)*F_68(x)*F_74(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_12(x)*F_141(x))
Eq(F_141(x), F_121(x) + F_142(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_129(x)*F_144(x)*F_15(x))
Eq(F_144(x), F_116(x))
Eq(F_145(x), F_0(x)*F_12(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25109/
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[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = 1/F[19,x]*F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = (x*F[10,x]^3+(2*x-1)*F[10,x]^2+(x^2-x+1)*F[10,x]+x^2)*(1+F[10,x])
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[14,x]+F[20,x]
F[14,x] = F[15,x]*F[2,x]
F[15,x] = 1/F[0,x]*F[16,x]
F[16,x] = -F[20,x]+F[17,x]
F[17,x] = 1/F[19,x]*F[18,x]
F[18,x] = F[9,x]
F[19,x] = x
F[20,x] = F[21,x]+F[29,x]
F[21,x] = F[22,x]
F[22,x] = F[19,x]*F[23,x]*F[7,x]
F[23,x] = F[24,x,1]
F[24,x,k[0]] = (F[25,x,k[0]]*k[0]-F[25,x,1])/(-1+k[0])
F[25,x,k[0]] = F[1,x]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[25,x,k[0]]^2*F[28,x,k[0]]
F[28,x,k[0]] = k[0]*x
F[29,x] = F[30,x]
F[30,x] = F[19,x]*F[31,x]*F[66,x]
F[31,x] = -F[65,x]+F[32,x]
F[32,x] = F[33,x]+F[4,x]
F[33,x] = F[34,x]
F[34,x] = F[19,x]*F[35,x]
F[35,x] = F[36,x]+F[63,x]
F[36,x] = -F[57,x]+F[37,x]
F[37,x] = 1/F[19,x]*F[38,x]
F[38,x] = F[39,x]
F[39,x] = -F[4,x]+F[40,x]
F[40,x] = -F[41,x]+F[17,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[0,x]*F[43,x]
F[43,x] = -F[44,x]+F[15,x]
F[44,x] = 1+x*F[44,x]^4+F[44,x]^2*(x^2-2*x+3)+F[44,x]^3*(-1-x)+(-2+2*x)*F[44,x]
F[45,x] = F[46,x]
F[46,x] = F[19,x]*F[47,x]
F[47,x] = F[48,x,1]
F[48,x,k[0]] = (F[49,x,k[0]]*k[0]-F[49,x,1])/(-1+k[0])
F[50,x,k[0]] = F[49,x,k[0]]+F[55,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[52,x,k[0]]
F[51,x,k[0]] = F[26,x,k[0]]*F[7,x]
F[52,x,k[0]] = F[31,x]*F[53,x,k[0]]
F[54,x,k[0]] = F[25,x,k[0]]+F[53,x,k[0]]
F[54,x,k[0]] = F[15,k[0]*x]
F[55,x,k[0]] = F[31,x]*F[56,x,k[0]]
F[56,x,k[0]] = (1+F[56,x,k[0]])*(x*F[56,x,k[0]]^3*k[0]+(2*x*k[0]-1)*F[56,x,k[0]]^2+(x^2*k[0]^2-x*k[0]+1)*F[56,x,k[0]]+x^2*k[0]^2)
F[57,x] = F[58,x]
F[58,x] = F[15,x]*F[59,x]
F[59,x] = 1/F[15,x]/F[19,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[10,x]*F[19,x]*F[31,x]
F[63,x] = F[64,x]
F[64,x] = F[15,x]*F[59,x]
F[65,x] = F[5,x]+F[61,x]
F[66,x] = F[67,x,1]
F[67,x,k[0]] = (F[53,x,k[0]]*k[0]-F[53,x,1])/(-1+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_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = \frac{F_{8}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = x F_{10} \left(x \right)^{4}+x^{2} F_{10} \left(x \right)^{2}+3 x F_{10} \left(x \right)^{3}+2 x^{2} F_{10}\! \left(x \right)+x F_{10} \left(x \right)^{2}-F_{10} \left(x \right)^{3}+x^{2}-F_{10}\! \left(x \right) x +F_{10}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{20}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{9}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{29}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{23}\! \left(x \right) F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x , 1\right)
F_{24}\! \left(x , y\right) = -\frac{-F_{25}\! \left(x , y\right) y +F_{25}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{25}\! \left(x , y\right)^{2} F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = y x
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \left(x \right) F_{31}\! \left(x \right) F_{66}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{65}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{63}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{17}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{0}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{15}\! \left(x \right)
F_{44}\! \left(x \right) = x F_{44} \left(x \right)^{4}+x^{2} F_{44} \left(x \right)^{2}-F_{44} \left(x \right)^{3} x -2 x F_{44} \left(x \right)^{2}-F_{44} \left(x \right)^{3}+2 F_{44}\! \left(x \right) x +3 F_{44} \left(x \right)^{2}-2 F_{44}\! \left(x \right)+1
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = -\frac{-F_{49}\! \left(x , y\right) y +F_{49}\! \left(x , 1\right)}{-1+y}
F_{50}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{52}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{15}\! \left(y x \right)
F_{55}\! \left(x , y\right) = F_{31}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = x^{2} F_{56}\! \left(x , y\right)^{2} y^{2}+x F_{56}\! \left(x , y\right)^{4} y +2 x^{2} F_{56}\! \left(x , y\right) y^{2}+3 x F_{56}\! \left(x , y\right)^{3} y +x^{2} y^{2}+x F_{56}\! \left(x , y\right)^{2} y -x F_{56}\! \left(x , y\right) y -F_{56}\! \left(x , y\right)^{3}+F_{56}\! \left(x , y\right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right) F_{19}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{10}\! \left(x \right) F_{19}\! \left(x \right) F_{31}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right) F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{5}\! \left(x \right)+F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x , 1\right)
F_{67}\! \left(x , y\right) = -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}
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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_19(x)*F_7(x))
Eq(F_7(x), F_8(x)/F_19(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), x*(F_10(x) + 1)**4 + (-x - 1)*(F_10(x) + 1)**3 + (2*x - 3)*(F_10(x) + 1) + (F_10(x) + 1)**2*(x**2 - 2*x + 3) + F_10(x) + 1)
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_19(x))
Eq(F_13(x), F_14(x) + F_20(x))
Eq(F_14(x), F_15(x)*F_2(x))
Eq(F_15(x), F_16(x)/F_0(x))
Eq(F_16(x), F_17(x) - F_20(x))
Eq(F_17(x), F_18(x)/F_19(x))
Eq(F_18(x), F_9(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x) + F_29(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_19(x)*F_23(x)*F_7(x))
Eq(F_23(x), F_24(x, 1))
Eq(F_24(x, k_0), (-k_0*F_25(x, k_0) + F_25(x, 1))/(1 - k_0))
Eq(F_25(x, k_0), F_1(x) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_25(x, k_0)**2*F_28(x, k_0))
Eq(F_28(x, k_0), k_0*x)
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_19(x)*F_31(x)*F_66(x))
Eq(F_31(x), F_32(x) - F_65(x))
Eq(F_32(x), F_33(x) + F_4(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_19(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_63(x))
Eq(F_36(x), F_37(x) - F_57(x))
Eq(F_37(x), F_38(x)/F_19(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), -F_4(x) + F_40(x))
Eq(F_40(x), F_17(x) - F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_0(x)*F_43(x))
Eq(F_43(x), F_15(x) - F_44(x))
Eq(F_44(x), x*F_44(x)**4 + (-x - 1)*F_44(x)**3 + (2*x - 2)*F_44(x) + (x**2 - 2*x + 3)*F_44(x)**2 + 1)
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_19(x)*F_47(x))
Eq(F_47(x), F_48(x, 1))
Eq(F_48(x, k_0), (-k_0*F_49(x, k_0) + F_49(x, 1))/(1 - k_0))
Eq(F_50(x, k_0), F_49(x, k_0) + F_55(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_52(x, k_0))
Eq(F_51(x, k_0), F_26(x, k_0)*F_7(x))
Eq(F_52(x, k_0), F_31(x)*F_53(x, k_0))
Eq(F_54(x, k_0), F_25(x, k_0) + F_53(x, k_0))
Eq(F_54(x, k_0), F_15(k_0*x))
Eq(F_55(x, k_0), F_31(x)*F_56(x, k_0))
Eq(F_56(x, k_0), k_0*x*(F_56(x, k_0) + 1)**4 + (-k_0*x - 1)*(F_56(x, k_0) + 1)**3 + (2*k_0*x - 3)*(F_56(x, k_0) + 1) + (F_56(x, k_0) + 1)**2*(k_0**2*x**2 - 2*k_0*x + 3) + F_56(x, k_0) + 1)
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_15(x)*F_59(x))
Eq(F_59(x), F_60(x)/(F_15(x)*F_19(x)))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_10(x)*F_19(x)*F_31(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_15(x)*F_59(x))
Eq(F_65(x), F_5(x) + F_61(x))
Eq(F_66(x), F_67(x, 1))
Eq(F_67(x, k_0), (-k_0*F_53(x, k_0) + F_53(x, 1))/(1 - 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:
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[[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", 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1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [3, 1], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [3, 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[0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [1, 0], "pos": [[1, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 0], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 2], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 2, "tracked": true}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25418/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[15,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]+F[7,x]
F[6,x] = (x^2+4*x-1)*F[6,x]^2+(4*x^2-5*x+2)*F[6,x]+4*x^2-x
F[7,x] = F[8,x]
F[8,x] = F[15,x]*F[9,x]
F[9,x] = F[10,x]+F[21,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]*F[2,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x]
F[14,x] = F[12,x]^2*F[15,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]*F[9,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]^2*F[15,x]*F[18,x]
F[21,x] = F[22,x]+F[63,x]
F[22,x] = F[23,x]+F[31,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = (x*F[24,x]^3+(2*x-1)*F[24,x]^2+(x^2-x+1)*F[24,x]+x^2)*(1+F[24,x])
F[25,x] = F[26,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[12,x]*F[23,x]
F[29,x] = F[23,x]*F[30,x]
F[30,x] = 1+x*F[30,x]^4+F[30,x]^2*(x^2-2*x+3)+F[30,x]^3*(-1-x)+(-2+2*x)*F[30,x]
F[31,x] = -F[11,x]+F[32,x]
F[32,x] = -F[126,x]+F[33,x]
F[33,x] = -F[75,x]+F[34,x]
F[34,x] = -F[193,x]+F[35,x]
F[35,x] = 1/F[15,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]+F[64,x]
F[38,x] = F[24,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[15,x]*F[41,x]
F[41,x] = F[42,x]+F[97,x]
F[42,x] = F[24,x]*F[43,x]
F[43,x] = F[0,x]+F[44,x]
F[44,x] = F[24,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[15,x]*F[47,x]
F[47,x] = F[32,x]+F[48,x]
F[48,x] = F[49,x]+F[63,x]
F[49,x] = F[16,x]+F[50,x]
F[50,x] = -F[12,x]+F[51,x]
F[51,x] = 1/F[0,x]*F[52,x]
F[52,x] = -F[58,x]+F[53,x]
F[53,x] = 1/F[15,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = -F[0,x]+F[56,x]
F[56,x] = 1/F[15,x]*F[57,x]
F[57,x] = F[2,x]
F[58,x] = -F[62,x]+F[59,x]
F[59,x] = 1/F[15,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = -F[6,x]+F[55,x]
F[62,x] = F[2,x]*F[51,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[65,x]
F[65,x] = F[15,x]*F[24,x]*F[66,x]
F[66,x] = F[0,x]+F[38,x]
F[67,x] = F[68,x]
F[68,x] = F[15,x]*F[69,x]
F[69,x] = F[70,x]+F[90,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[63,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[15,x]*F[74,x]*F[82,x]
F[74,x] = F[75,x]
F[75,x] = F[63,x]+F[76,x]
F[76,x] = F[77,x]+F[79,x]
F[77,x] = F[78,x]
F[78,x] = F[15,x]*F[18,x]
F[79,x] = F[80,x]
F[80,x] = F[15,x]*F[18,x]*F[81,x]
F[81,x] = F[2,x]+F[38,x]
F[82,x] = 1/F[0,x]*F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[15,x]*F[85,x]
F[85,x] = F[44,x]
F[86,x] = -F[89,x]+F[87,x]
F[87,x] = 1/F[15,x]*F[88,x]
F[88,x] = F[45,x]
F[89,x] = F[2,x]*F[82,x]
F[90,x] = F[91,x]
F[91,x] = F[92,x]+F[95,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[15,x]*F[76,x]*F[82,x]
F[95,x] = F[96,x]
F[96,x] = F[15,x]*F[18,x]*F[23,x]*F[30,x]*F[66,x]
F[97,x] = F[66,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[15,x]
F[100,x] = 1/F[15,x]*F[101,x]
F[101,x] = F[102,x]
F[102,x] = 1/F[182,x]*F[103,x]
F[103,x] = -F[189,x]+F[104,x]
F[104,x] = 1/F[15,x]*F[105,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]+F[169,x]
F[107,x] = -F[168,x]+F[108,x]
F[108,x] = F[109,x]+F[30,x]
F[109,x] = -F[156,x]+F[110,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[15,x]
F[112,x] = F[113,x]+F[129,x]
F[113,x] = 1/F[15,x]*F[114,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[15,x]
F[116,x] = 1/F[15,x]*F[117,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]+F[121,x]
F[119,x] = F[120,x]+F[6,x]
F[120,x] = F[15,x]*F[24,x]
F[121,x] = F[122,x]*F[15,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[15,x]
F[124,x] = F[125,x]+F[29,x]
F[125,x] = F[12,x]*F[126,x]
F[126,x] = F[127,x]+F[30,x]
F[127,x] = F[128,x]
F[128,x] = F[124,x]*F[15,x]
F[129,x] = F[130,x]
F[130,x] = -F[165,x]+F[131,x]
F[131,x] = 1/F[15,x]*F[132,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]+F[156,x]
F[134,x] = F[135,x]+F[15,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[15,x]
F[137,x] = F[138,x]+F[145,x]
F[138,x] = F[139,x]+F[140,x]
F[139,x] = F[15,x]*F[30,x]
F[140,x] = F[141,x]
F[141,x] = F[142,x]*F[15,x]*F[30,x]
F[142,x] = F[143,x]+F[144,x]
F[143,x] = F[126,x]*F[77,x]
F[144,x] = F[12,x]*F[138,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[12,x]*F[15,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[15,x]
F[149,x] = F[150,x]+F[23,x]
F[150,x] = F[151,x]+F[98,x]
F[151,x] = F[152,x]
F[152,x] = F[12,x]*F[15,x]*F[153,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[126,x]*F[98,x]
F[155,x] = F[150,x]*F[30,x]
F[156,x] = F[157,x]
F[157,x] = F[126,x]*F[15,x]*F[158,x]
F[158,x] = F[134,x]+F[159,x]
F[159,x] = F[160,x]
F[160,x] = F[15,x]*F[161,x]
F[161,x] = F[162,x]+F[163,x]
F[162,x] = F[12,x]*F[158,x]
F[163,x] = F[164,x]
F[164,x] = F[12,x]*F[30,x]*F[77,x]
F[165,x] = F[166,x]+F[30,x]
F[166,x] = F[167,x]
F[167,x] = F[12,x]*F[126,x]*F[15,x]*F[30,x]
F[168,x] = -2+x^2+8*x+F[168,x]^2*(x^2+4*x-1)+(2*x^2-13*x+4)*F[168,x]
F[169,x] = F[170,x]
F[170,x] = F[15,x]*F[171,x]
F[171,x] = F[172,x]+F[188,x]
F[172,x] = F[173,x]*F[174,x]
F[173,x] = F[122,x]+F[30,x]
F[174,x] = F[175,x]+F[187,x]
F[175,x] = F[176,x]
F[176,x] = F[15,x]*F[177,x]
F[177,x] = F[178,x]+F[179,x]
F[178,x] = F[1,x]+F[15,x]
F[179,x] = F[180,x]+F[183,x]
F[180,x] = F[181,x]
F[181,x] = F[15,x]*F[182,x]
F[182,x] = F[1,x]+F[180,x]
F[183,x] = F[184,x]+F[185,x]+F[187,x]
F[184,x] = 0
F[185,x] = F[15,x]*F[186,x]
F[186,x] = F[15,x]+F[183,x]
F[187,x] = F[15,x]*F[180,x]
F[188,x] = F[102,x]*F[180,x]
F[189,x] = F[173,x]*F[190,x]
F[190,x] = F[191,x]+F[192,x]
F[191,x] = F[1,x]+F[175,x]
F[192,x] = F[15,x]*F[182,x]
F[193,x] = F[194,x]
F[194,x] = F[126,x]*F[15,x]*F[66,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)+F_{7}\! \left(x \right)
F_{6}\! \left(x \right) = x^{2} F_{6} \left(x \right)^{2}+4 x^{2} F_{6}\! \left(x \right)+4 x F_{6} \left(x \right)^{2}+4 x^{2}-5 x F_{6}\! \left(x \right)-F_{6} \left(x \right)^{2}-x +2 F_{6}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{63}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = x F_{24} \left(x \right)^{4}+x^{2} F_{24} \left(x \right)^{2}+3 x F_{24} \left(x \right)^{3}+2 x^{2} F_{24}\! \left(x \right)+x F_{24} \left(x \right)^{2}-F_{24} \left(x \right)^{3}+x^{2}-F_{24}\! \left(x \right) x +F_{24}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{29}\! \left(x \right) = F_{23}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = x F_{30} \left(x \right)^{4}+x^{2} F_{30} \left(x \right)^{2}-F_{30} \left(x \right)^{3} x -2 x F_{30} \left(x \right)^{2}-F_{30} \left(x \right)^{3}+2 F_{30}\! \left(x \right) x +3 F_{30} \left(x \right)^{2}-2 F_{30}\! \left(x \right)+1
F_{31}\! \left(x \right) = -F_{11}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{75}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{193}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{64}\! \left(x \right)
F_{38}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{97}\! \left(x \right)
F_{42}\! \left(x \right) = F_{24}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{0}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{24}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{63}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{52}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = \frac{F_{57}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{57}\! \left(x \right) = F_{2}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{6}\! \left(x \right)+F_{55}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right) F_{51}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{0}\! \left(x \right)+F_{38}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{90}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{74}\! \left(x \right) F_{82}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{63}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{82}\! \left(x \right) = \frac{F_{83}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{44}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = \frac{F_{88}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{88}\! \left(x \right) = F_{45}\! \left(x \right)
F_{89}\! \left(x \right) = F_{2}\! \left(x \right) F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{15}\! \left(x \right) F_{76}\! \left(x \right) F_{82}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right) F_{23}\! \left(x \right) F_{30}\! \left(x \right) F_{66}\! \left(x \right)
F_{97}\! \left(x \right) = F_{66}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{15}\! \left(x \right)
F_{100}\! \left(x \right) = \frac{F_{101}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{182}\! \left(x \right)}
F_{103}\! \left(x \right) = -F_{189}\! \left(x \right)+F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = \frac{F_{105}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{169}\! \left(x \right)
F_{107}\! \left(x \right) = -F_{168}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{30}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{156}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{15}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{129}\! \left(x \right)
F_{113}\! \left(x \right) = \frac{F_{114}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{15}\! \left(x \right)
F_{116}\! \left(x \right) = \frac{F_{117}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{121}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{6}\! \left(x \right)
F_{120}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{15}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{15}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{29}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{30}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{124}\! \left(x \right) F_{15}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = \frac{F_{132}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{156}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{15}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{15}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{145}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{140}\! \left(x \right)
F_{139}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{15}\! \left(x \right) F_{30}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{144}\! \left(x \right)
F_{143}\! \left(x \right) = F_{126}\! \left(x \right) F_{77}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{138}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{15}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{23}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{98}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{12}\! \left(x \right) F_{15}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{126}\! \left(x \right) F_{98}\! \left(x \right)
F_{155}\! \left(x \right) = F_{150}\! \left(x \right) F_{30}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{134}\! \left(x \right)+F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{15}\! \left(x \right) F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{163}\! \left(x \right)
F_{162}\! \left(x \right) = F_{12}\! \left(x \right) F_{158}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{77}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{30}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{30}\! \left(x \right)
F_{168}\! \left(x \right) = x^{2} F_{168} \left(x \right)^{2}+2 x^{2} F_{168}\! \left(x \right)+4 x F_{168} \left(x \right)^{2}+x^{2}-13 x F_{168}\! \left(x \right)-F_{168} \left(x \right)^{2}+8 x +4 F_{168}\! \left(x \right)-2
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)
F_{170}\! \left(x \right) = F_{15}\! \left(x \right) F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{188}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{122}\! \left(x \right)+F_{30}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{187}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{15}\! \left(x \right) F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{179}\! \left(x \right)
F_{178}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{183}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{15}\! \left(x \right) F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{1}\! \left(x \right)+F_{180}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{185}\! \left(x \right)+F_{187}\! \left(x \right)
F_{184}\! \left(x \right) = 0
F_{185}\! \left(x \right) = F_{15}\! \left(x \right) F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{15}\! \left(x \right)+F_{183}\! \left(x \right)
F_{187}\! \left(x \right) = F_{15}\! \left(x \right) F_{180}\! \left(x \right)
F_{188}\! \left(x \right) = F_{102}\! \left(x \right) F_{180}\! \left(x \right)
F_{189}\! \left(x \right) = F_{173}\! \left(x \right) F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{192}\! \left(x \right)
F_{191}\! \left(x \right) = F_{1}\! \left(x \right)+F_{175}\! \left(x \right)
F_{192}\! \left(x \right) = F_{15}\! \left(x \right) F_{182}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{126}\! \left(x \right) F_{15}\! \left(x \right) F_{66}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_15(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x) + F_7(x))
Eq(F_6(x), x**2 + 8*x + (F_6(x) + 1)**2*(x**2 + 4*x - 1) + (F_6(x) + 1)*(2*x**2 - 13*x + 3) + F_6(x) - 2)
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_15(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_21(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x)*F_2(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_12(x)**2*F_15(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x)*F_9(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)**2*F_15(x)*F_18(x))
Eq(F_21(x), F_22(x) + F_63(x))
Eq(F_22(x), F_23(x) + F_31(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), x*(F_24(x) + 1)**4 + (-x - 1)*(F_24(x) + 1)**3 + (2*x - 3)*(F_24(x) + 1) + (F_24(x) + 1)**2*(x**2 - 2*x + 3) + F_24(x) + 1)
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_12(x)*F_23(x))
Eq(F_29(x), F_23(x)*F_30(x))
Eq(F_30(x), x*F_30(x)**4 + (-x - 1)*F_30(x)**3 + (2*x - 2)*F_30(x) + (x**2 - 2*x + 3)*F_30(x)**2 + 1)
Eq(F_31(x), -F_11(x) + F_32(x))
Eq(F_32(x), -F_126(x) + F_33(x))
Eq(F_33(x), F_34(x) - F_75(x))
Eq(F_34(x), -F_193(x) + F_35(x))
Eq(F_35(x), F_36(x)/F_15(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x) + F_64(x))
Eq(F_38(x), F_24(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_15(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_97(x))
Eq(F_42(x), F_24(x)*F_43(x))
Eq(F_43(x), F_0(x) + F_44(x))
Eq(F_44(x), F_24(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_15(x)*F_47(x))
Eq(F_47(x), F_32(x) + F_48(x))
Eq(F_48(x), F_49(x) + F_63(x))
Eq(F_49(x), F_16(x) + F_50(x))
Eq(F_50(x), -F_12(x) + F_51(x))
Eq(F_51(x), F_52(x)/F_0(x))
Eq(F_52(x), F_53(x) - F_58(x))
Eq(F_53(x), F_54(x)/F_15(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), -F_0(x) + F_56(x))
Eq(F_56(x), F_57(x)/F_15(x))
Eq(F_57(x), F_2(x))
Eq(F_58(x), F_59(x) - F_62(x))
Eq(F_59(x), F_60(x)/F_15(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_55(x) - F_6(x))
Eq(F_62(x), F_2(x)*F_51(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_15(x)*F_24(x)*F_66(x))
Eq(F_66(x), F_0(x) + F_38(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_15(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_90(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_63(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_15(x)*F_74(x)*F_82(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_63(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_79(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_15(x)*F_18(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_15(x)*F_18(x)*F_81(x))
Eq(F_81(x), F_2(x) + F_38(x))
Eq(F_82(x), F_83(x)/F_0(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_15(x))
Eq(F_85(x), F_44(x))
Eq(F_86(x), F_87(x) - F_89(x))
Eq(F_87(x), F_88(x)/F_15(x))
Eq(F_88(x), F_45(x))
Eq(F_89(x), F_2(x)*F_82(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_92(x) + F_95(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_15(x)*F_76(x)*F_82(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_15(x)*F_18(x)*F_23(x)*F_30(x)*F_66(x))
Eq(F_97(x), F_66(x)*F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_15(x))
Eq(F_100(x), F_101(x)/F_15(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)/F_182(x))
Eq(F_103(x), F_104(x) - F_189(x))
Eq(F_104(x), F_105(x)/F_15(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x) + F_169(x))
Eq(F_107(x), F_108(x) - F_168(x))
Eq(F_108(x), F_109(x) + F_30(x))
Eq(F_109(x), F_110(x) - F_156(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_15(x))
Eq(F_112(x), F_113(x) + F_129(x))
Eq(F_113(x), F_114(x)/F_15(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_15(x))
Eq(F_116(x), F_117(x)/F_15(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x) + F_121(x))
Eq(F_119(x), F_120(x) + F_6(x))
Eq(F_120(x), F_15(x)*F_24(x))
Eq(F_121(x), F_122(x)*F_15(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_15(x))
Eq(F_124(x), F_125(x) + F_29(x))
Eq(F_125(x), F_12(x)*F_126(x))
Eq(F_126(x), F_127(x) + F_30(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_124(x)*F_15(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_131(x) - F_165(x))
Eq(F_131(x), F_132(x)/F_15(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x) + F_156(x))
Eq(F_134(x), F_135(x) + F_15(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_15(x))
Eq(F_137(x), F_138(x) + F_145(x))
Eq(F_138(x), F_139(x) + F_140(x))
Eq(F_139(x), F_15(x)*F_30(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_142(x)*F_15(x)*F_30(x))
Eq(F_142(x), F_143(x) + F_144(x))
Eq(F_143(x), F_126(x)*F_77(x))
Eq(F_144(x), F_12(x)*F_138(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_12(x)*F_15(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_15(x))
Eq(F_149(x), F_150(x) + F_23(x))
Eq(F_150(x), F_151(x) + F_98(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_12(x)*F_15(x)*F_153(x))
Eq(F_153(x), F_154(x) + F_155(x))
Eq(F_154(x), F_126(x)*F_98(x))
Eq(F_155(x), F_150(x)*F_30(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_126(x)*F_15(x)*F_158(x))
Eq(F_158(x), F_134(x) + F_159(x))
Eq(F_159(x), F_160(x))
Eq(F_160(x), F_15(x)*F_161(x))
Eq(F_161(x), F_162(x) + F_163(x))
Eq(F_162(x), F_12(x)*F_158(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_12(x)*F_30(x)*F_77(x))
Eq(F_165(x), F_166(x) + F_30(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_12(x)*F_126(x)*F_15(x)*F_30(x))
Eq(F_168(x), x**2 + 8*x + (x**2 + 4*x - 1)*F_168(x)**2 + (2*x**2 - 13*x + 4)*F_168(x) - 2)
Eq(F_169(x), F_170(x))
Eq(F_170(x), F_15(x)*F_171(x))
Eq(F_171(x), F_172(x) + F_188(x))
Eq(F_172(x), F_173(x)*F_174(x))
Eq(F_173(x), F_122(x) + F_30(x))
Eq(F_174(x), F_175(x) + F_187(x))
Eq(F_175(x), F_176(x))
Eq(F_176(x), F_15(x)*F_177(x))
Eq(F_177(x), F_178(x) + F_179(x))
Eq(F_178(x), F_1(x) + F_15(x))
Eq(F_179(x), F_180(x) + F_183(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_15(x)*F_182(x))
Eq(F_182(x), F_1(x) + F_180(x))
Eq(F_183(x), F_184(x) + F_185(x) + F_187(x))
Eq(F_184(x), 0)
Eq(F_185(x), F_15(x)*F_186(x))
Eq(F_186(x), F_15(x) + F_183(x))
Eq(F_187(x), F_15(x)*F_180(x))
Eq(F_188(x), F_102(x)*F_180(x))
Eq(F_189(x), F_173(x)*F_190(x))
Eq(F_190(x), F_191(x) + F_192(x))
Eq(F_191(x), F_1(x) + F_175(x))
Eq(F_192(x), F_15(x)*F_182(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_126(x)*F_15(x)*F_66(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 2, 4], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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