02341_02431_03241_20341_20431_23041_23401_24031_24301_30241_32041_32401
Counting sequence:
1, 1, 2, 6, 24, 108, 517, 2575, 13200, 69180, 368993, 1996473, 10930943, 60449347, 337157867, 1894433853, 10713290104, 60929751936, 348274343213, 1999705051617, 11528295478127, 66703688809983, 387234852276218, 2254822308106572, 13165972883718071, 77072454501521947, 452236065372443323, 2659345492475584463, 15669672848134127315, 92503851701100523455, 547040757421063411710, 3240336659356540962330, 19223233034030596666088, 114205741230327731159560, 679418903428127892373605, 4047078861285623042768073, 24136209497887122915261499, 144109085020003067087257959, 861355330952983669027705268, 5153684721550463695022156070, 30865656034614727740683794999, 185026798668619753041332167395, 1110135511249544358513885681462, 6666251923747561586520275922214, 40062234500081491003780447044128, 240946601031561667912199277765168, 1450187359677675710497981867261750, 8734368685357375157543047554182476, 52641746397229568909496756628930655, 317474227513694856106574475728187207, 1915820663651850140587816503908640047, 11568015443539311179829693422002007743, 69889276391433421300440400111331829795, 422474519404652496582431752048820697151, 2555170753783994761253813561236672434305, 15461812046497209866518480656640980100681, 93608218500615013331244776643946232863491, 566987118372354587162456568096857345690323, 3435823996113529213507288816449865501537970, 20829573398332519943873291741090052015297110, 126332525415143931305897783480110035935141292, 766530107291187895766534715899700537324451112, 4652824718288880926848598765642628911503002981, 28253488385383688238875798117055100258510835783, 171628776425807035401095061155500623141834667432, 1042955454562519374377348451934358840302854412872, 6340072801346530596587458861513199763920336291077, 38554136841744584831156530709768185140199471210265, 234526328370802760153900811158451104766799996875619, 1427091834819118401590274903089925258384596235985639, 8686562148769670600894510629113600724884922743864836, 52890271964679495368245811157514109779216288325768742, 322130505817594465096812928007138438246295930880842803, 1962513133951823339531055116571949463170462845063075279, 11959542685191807102857142474613928432345716363703302032, 72901189551469332770382595869623719337984982998493773384, 444497765222947293642014949293074050154270807451158059878, 2710918620370291862544069514312503905514253027031057441922, 16537598092974602565535439101635812804183099765710180159834, 100910108082696282980466185008671034118632644810058560101764, 615886281653686085534197147206567452691660298795532025635903, 3759823394604006014295978506735030139686416661329119911475975, 22957941540569099647517216049400947582165130433562772281806578, 140215055580439998911299637175401101021208408520881468249361758, 856545145078107647284504487831081932920112257569641805149230616, 5233564231516740025799428810546976141247884037954396166458228272, 31984120515461695754729340624727252376524284182822300876701926785, 195505400139880216747149755807581681651244566590891450626769767343, 1195277099927946168108668050825862009211411552825190590751169763432, 7309068148067477851163625422843274258797544295871968203498123138852, 44703047676366465672032127651932808740765308724239807624947029750558, 273458963502398876083739182410867894019733427662563645733584310990434, 1673113340986513747664053949630925317863205279935029653359017058751874, 10238469578536133334311037643678722575997781306512710668288801705750026, 62664211371445778644711134093066943195832879598688921694174175670265869, 383598928608107788385569469453118639126133003833738541390333403068529277, 2348588529779459445227959358640616387111909450205754149702379087510953135, 14381584784657272773434112462113754448081647160079472005228781985891763631, 88079609355300071266675241024221378330589504424443018197538109924375321287, 539524838933619035873084807731869720701615643840430593498347270394812809847, 3305320569537996839329870052556833562333486231682075733976816290443497768607
Implicit equation for the generating function in Maple syntax:
x*(x-1)*(x^3-4*x+4)*F(x)^3+x*(x-2)*(x^2+2*x-4)*F(x)^2+(2*x^3+2*x^2-9*x+1)*F(x)+x^2+4*x-1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right) \left(x^{3}-4 x +4\right) F \! \left(x \right)^{3}+x \left(x -2\right) \left(x^{2}+2 x -4\right) F \! \left(x \right)^{2}+\left(2 x^{3}+2 x^{2}-9 x +1\right) F \! \left(x \right)+x^{2}+4 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 517
a(7) = 2575
a(8) = 13200
a(9) = 69180
a(10) = 368993
a(11) = 1996473
a(12) = 10930943
a(13) = 60449347
a(n+14) = 115/16*(n+2)*(n+1)/(2*n+29)/(n+14)*a(n)-1/32*(1423*n+4282)*(n+2)/(2*n+29)/(n+14)*a(n+1)+1/32*(3760*n^2+31869*n+61220)/(2*n+29)/(n+14)*a(n+2)-1/32*(4079*n^2+74955*n+225772)/(2*n+29)/(n+14)*a(n+3)-1/16*(3394*n^2-25695*n-193075)/(2*n+29)/(n+14)*a(n+4)+3/16*(6812*n^2+43254*n+30927)/(2*n+29)/(n+14)*a(n+5)-1/16*(48206*n^2+505551*n+1258654)/(2*n+29)/(n+14)*a(n+6)+1/8*(35837*n^2+475692*n+1561051)/(2*n+29)/(n+14)*a(n+7)-1/8*(36497*n^2+570276*n+2219602)/(2*n+29)/(n+14)*a(n+8)+1/2*(6542*n^2+116811*n+520669)/(2*n+29)/(n+14)*a(n+9)-1/4*(6698*n^2+134763*n+677467)/(2*n+29)/(n+14)*a(n+10)+1/4*(2476*n^2+55623*n+312290)/(2*n+29)/(n+14)*a(n+11)-(164*n^2+4062*n+25141)/(2*n+29)/(n+14)*a(n+12)+(28*n^2+750*n+5021)/(2*n+29)/(n+14)*a(n+13), n >= 14
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 517
a(7) = 2575
a(8) = 13200
a(9) = 69180
a(10) = 368993
a(11) = 1996473
a(12) = 10930943
a(13) = 60449347
a{\left(n + 14 \right)} = \frac{115 \left(n + 1\right) \left(n + 2\right) a{\left(n \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(n + 2\right) \left(1423 n + 4282\right) a{\left(n + 1 \right)}}{32 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(28 n^{2} + 750 n + 5021\right) a{\left(n + 13 \right)}}{\left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(164 n^{2} + 4062 n + 25141\right) a{\left(n + 12 \right)}}{\left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(2476 n^{2} + 55623 n + 312290\right) a{\left(n + 11 \right)}}{4 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(3394 n^{2} - 25695 n - 193075\right) a{\left(n + 4 \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(3760 n^{2} + 31869 n + 61220\right) a{\left(n + 2 \right)}}{32 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(4079 n^{2} + 74955 n + 225772\right) a{\left(n + 3 \right)}}{32 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(6542 n^{2} + 116811 n + 520669\right) a{\left(n + 9 \right)}}{2 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(6698 n^{2} + 134763 n + 677467\right) a{\left(n + 10 \right)}}{4 \left(n + 14\right) \left(2 n + 29\right)} + \frac{3 \left(6812 n^{2} + 43254 n + 30927\right) a{\left(n + 5 \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)} + \frac{\left(35837 n^{2} + 475692 n + 1561051\right) a{\left(n + 7 \right)}}{8 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(36497 n^{2} + 570276 n + 2219602\right) a{\left(n + 8 \right)}}{8 \left(n + 14\right) \left(2 n + 29\right)} - \frac{\left(48206 n^{2} + 505551 n + 1258654\right) a{\left(n + 6 \right)}}{16 \left(n + 14\right) \left(2 n + 29\right)}, \quad n \geq 14
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24889/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[56,x]+F[9,x]
F[9,x] = F[10,x]+F[51,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[20,x]
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[13,x]*F[15,x]*F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]*F[4,x]
F[22,x] = F[13,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[13,x]*F[25,x]*F[4,x]
F[25,x] = 1/F[4,x]/F[5,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[48,x]+F[28,x]
F[28,x] = 1/F[4,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = -F[0,x]+F[33,x]
F[33,x] = 1/F[4,x]*F[34,x]
F[34,x] = F[2,x]
F[35,x] = -F[47,x]+F[36,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,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[46,x]
F[41,x] = F[16,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[45,x]+F[5,x]
F[45,x] = 1+(F[45,x]^3-F[45,x]^2+F[45,x])*x
F[46,x] = F[18,x]*F[33,x]
F[47,x] = F[38,x]+F[44,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[32,x]
F[51,x] = F[52,x]
F[52,x] = F[33,x]*F[4,x]*F[53,x]
F[53,x] = F[14,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[25,x]*F[4,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[53,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{56}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{51}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{4}\! \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_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{4}\! \left(x \right) F_{5}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{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_{46}\! \left(x \right)
F_{41}\! \left(x \right) = F_{16}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = x F_{45} \left(x \right)^{3}-x F_{45} \left(x \right)^{2}+x F_{45}\! \left(x \right)+1
F_{46}\! \left(x \right) = F_{18}\! \left(x \right) F_{33}\! \left(x \right)
F_{47}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{32}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{14}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_56(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_51(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_20(x))
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_13(x)*F_15(x)*F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x)*F_4(x))
Eq(F_22(x), F_13(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_13(x)*F_25(x)*F_4(x))
Eq(F_25(x), F_26(x)/(F_4(x)*F_5(x)))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x) - F_48(x))
Eq(F_28(x), F_29(x)/F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), -F_0(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_4(x))
Eq(F_34(x), F_2(x))
Eq(F_35(x), F_36(x) - F_47(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_46(x))
Eq(F_41(x), F_16(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), -F_45(x) + F_5(x))
Eq(F_45(x), x*F_45(x)**3 - x*F_45(x)**2 + x*F_45(x) + 1)
Eq(F_46(x), F_18(x)*F_33(x))
Eq(F_47(x), F_38(x) + F_44(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_32(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_33(x)*F_4(x)*F_53(x))
Eq(F_53(x), F_14(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_25(x)*F_4(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_53(x)*F_8(x))
Pack JSON:
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Specification JSON:
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[1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24907/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[21,x]+F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]*F[13,x]
F[12,x] = x*(1+F[12,x])*(F[12,x]^2+F[12,x]+1)
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[13,x]*F[17,x]
F[17,x] = -F[20,x]+F[18,x]
F[18,x] = 1/F[4,x]*F[19,x]
F[19,x] = F[12,x]
F[20,x] = 1+(F[20,x]^3-F[20,x]^2+F[20,x])*x
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[73,x]
F[24,x] = F[13,x]*F[25,x]
F[25,x] = 1/F[4,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[18,x]+F[28,x]
F[28,x] = F[29,x]+F[5,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = 1/F[13,x]/F[4,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[70,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]*F[68,x]
F[36,x] = -F[34,x]+F[37,x]
F[37,x] = -F[49,x]+F[38,x]
F[38,x] = 1/F[4,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[0,x]+F[41,x]
F[41,x] = F[0,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = 1/F[4,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = -F[0,x]+F[47,x]
F[47,x] = 1/F[4,x]*F[48,x]
F[48,x] = F[2,x]
F[49,x] = F[50,x]
F[50,x] = F[38,x]*F[4,x]*F[51,x]
F[51,x] = 1/F[4,x]/F[56,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]+F[66,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]*F[59,x]
F[56,x] = F[37,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[44,x]*F[51,x]
F[59,x] = F[13,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[13,x]*F[59,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[51,x]*F[62,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[54,x]*F[68,x]
F[68,x] = 1/F[13,x]/F[4,x]*F[69,x]
F[69,x] = F[60,x]
F[70,x] = -F[71,x]+F[49,x]
F[71,x] = F[72,x]
F[72,x] = F[13,x]*F[4,x]*F[8,x]
F[73,x] = F[47,x]*F[60,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{21}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x F_{12} \left(x \right)^{3}+2 x F_{12} \left(x \right)^{2}+2 F_{12}\! \left(x \right) x +x
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{12}\! \left(x \right)
F_{20}\! \left(x \right) = x F_{20} \left(x \right)^{3}-x F_{20} \left(x \right)^{2}+x F_{20}\! \left(x \right)+1
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{73}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{5}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{13}\! \left(x \right) F_{4}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{70}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{0}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = \frac{F_{45}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{4}\! \left(x \right) F_{56}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{66}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right) F_{59}\! \left(x \right)
F_{56}\! \left(x \right) = F_{37}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right) F_{51}\! \left(x \right)
F_{59}\! \left(x \right) = F_{13}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right) F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = \frac{F_{69}\! \left(x \right)}{F_{13}\! \left(x \right) F_{4}\! \left(x \right)}
F_{69}\! \left(x \right) = F_{60}\! \left(x \right)
F_{70}\! \left(x \right) = -F_{71}\! \left(x \right)+F_{49}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{73}\! \left(x \right) = F_{47}\! \left(x \right) F_{60}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_21(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x)*F_13(x))
Eq(F_12(x), x*(F_12(x) + 1)**3 - x*(F_12(x) + 1)**2 + (x - 1)*(F_12(x) + 1) + F_12(x) + 1)
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_13(x)*F_17(x))
Eq(F_17(x), F_18(x) - F_20(x))
Eq(F_18(x), F_19(x)/F_4(x))
Eq(F_19(x), F_12(x))
Eq(F_20(x), x*F_20(x)**3 - x*F_20(x)**2 + x*F_20(x) + 1)
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_73(x))
Eq(F_24(x), F_13(x)*F_25(x))
Eq(F_25(x), F_26(x)/F_4(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), -F_18(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_5(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x)/(F_13(x)*F_4(x)))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_70(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x)*F_68(x))
Eq(F_36(x), -F_34(x) + F_37(x))
Eq(F_37(x), F_38(x) - F_49(x))
Eq(F_38(x), F_39(x)/F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), -F_0(x) + F_41(x))
Eq(F_41(x), F_0(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x)/F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), -F_0(x) + F_47(x))
Eq(F_47(x), F_48(x)/F_4(x))
Eq(F_48(x), F_2(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_38(x)*F_4(x)*F_51(x))
Eq(F_51(x), F_52(x)/(F_4(x)*F_56(x)))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x) + F_66(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x)*F_59(x))
Eq(F_56(x), F_37(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_44(x)*F_51(x))
Eq(F_59(x), F_13(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_13(x)*F_59(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_51(x)*F_62(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_54(x)*F_68(x))
Eq(F_68(x), F_69(x)/(F_13(x)*F_4(x)))
Eq(F_69(x), F_60(x))
Eq(F_70(x), F_49(x) - F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_13(x)*F_4(x)*F_8(x))
Eq(F_73(x), F_47(x)*F_60(x))
Pack JSON:
{"name": "point_placements_tracked_fusion", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 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"comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 4], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[2, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 4], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[0, 5]]}, {"patt": [0], "pos": [[0, 6]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[1, 6]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0], "pos": [[2, 5]]}, {"patt": [0], "pos": [[2, 6]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[3, 5]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 5], [1, 5]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 5], [1, 5]]}, {"patt": [1, 0], "pos": [[3, 6], [3, 4]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [0, 3], [2, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 0], "pos": [[0, 3], [0, 3], [2, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 4], [3, 4], [3, 4], [3, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[3, 6], [3, 6], [3, 6], [3, 6]]}], "requirements": [[{"patt": [0], "pos": [[1, 5]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25142/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[53,x]+F[9,x]
F[9,x] = F[10,x]+F[51,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[15,x]*F[4,x]
F[13,x] = 1/F[4,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[21,x]*F[4,x]
F[21,x] = F[15,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[15,x]*F[24,x]*F[4,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[21,x]*F[27,x]*F[4,x]
F[27,x] = 1/F[4,x]/F[5,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = -F[48,x]+F[30,x]
F[30,x] = 1/F[4,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = -F[0,x]+F[13,x]
F[35,x] = -F[47,x]+F[36,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,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[46,x]
F[41,x] = F[17,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[45,x]+F[5,x]
F[45,x] = 1+(F[45,x]^3-F[45,x]^2+F[45,x])*x
F[46,x] = F[13,x]*F[19,x]
F[47,x] = F[38,x]+F[44,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[34,x]
F[51,x] = F[52,x]
F[52,x] = F[10,x]*F[21,x]*F[4,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]*F[8,x]
F[55,x] = F[15,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[15,x]*F[27,x]*F[4,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{53}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{51}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{4}\! \left(x \right) F_{5}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{31}\! \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_{35}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{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_{46}\! \left(x \right)
F_{41}\! \left(x \right) = F_{17}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = x F_{45} \left(x \right)^{3}-x F_{45} \left(x \right)^{2}+x F_{45}\! \left(x \right)+1
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{47}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{34}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{10}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_53(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_51(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_15(x)*F_4(x))
Eq(F_13(x), F_14(x)/F_4(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_21(x)*F_4(x))
Eq(F_21(x), F_15(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_15(x)*F_24(x)*F_4(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_21(x)*F_27(x)*F_4(x))
Eq(F_27(x), F_28(x)/(F_4(x)*F_5(x)))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x) - F_48(x))
Eq(F_30(x), F_31(x)/F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), -F_0(x) + F_13(x))
Eq(F_35(x), F_36(x) - F_47(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_46(x))
Eq(F_41(x), F_17(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), -F_45(x) + F_5(x))
Eq(F_45(x), x*F_45(x)**3 - x*F_45(x)**2 + x*F_45(x) + 1)
Eq(F_46(x), F_13(x)*F_19(x))
Eq(F_47(x), F_38(x) + F_44(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_34(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_10(x)*F_21(x)*F_4(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x)*F_8(x))
Eq(F_55(x), F_15(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_15(x)*F_27(x)*F_4(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 2], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], 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"ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25635/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[56,x]+F[9,x]
F[9,x] = F[10,x]+F[51,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[0,x]*F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[20,x]
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[1,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[13,x]*F[15,x]*F[4,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]*F[4,x]
F[22,x] = F[13,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[13,x]*F[25,x]*F[4,x]
F[25,x] = 1/F[4,x]/F[5,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[48,x]+F[28,x]
F[28,x] = 1/F[4,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = -F[0,x]+F[33,x]
F[33,x] = 1/F[4,x]*F[34,x]
F[34,x] = F[2,x]
F[35,x] = -F[47,x]+F[36,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,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[46,x]
F[41,x] = F[16,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[45,x]+F[5,x]
F[45,x] = 1+(F[45,x]^3-F[45,x]^2+F[45,x])*x
F[46,x] = F[18,x]*F[33,x]
F[47,x] = F[38,x]+F[44,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[32,x]
F[51,x] = F[52,x]
F[52,x] = F[33,x]*F[4,x]*F[53,x]
F[53,x] = F[14,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[25,x]*F[4,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[53,x]*F[8,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{56}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{51}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{4}\! \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_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{4}\! \left(x \right) F_{5}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{2}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{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_{46}\! \left(x \right)
F_{41}\! \left(x \right) = F_{16}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = x F_{45} \left(x \right)^{3}-x F_{45} \left(x \right)^{2}+x F_{45}\! \left(x \right)+1
F_{46}\! \left(x \right) = F_{18}\! \left(x \right) F_{33}\! \left(x \right)
F_{47}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{32}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{14}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right) F_{8}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_56(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_51(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_0(x)*F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_20(x))
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_1(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_13(x)*F_15(x)*F_4(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x)*F_4(x))
Eq(F_22(x), F_13(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_13(x)*F_25(x)*F_4(x))
Eq(F_25(x), F_26(x)/(F_4(x)*F_5(x)))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x) - F_48(x))
Eq(F_28(x), F_29(x)/F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), -F_0(x) + F_33(x))
Eq(F_33(x), F_34(x)/F_4(x))
Eq(F_34(x), F_2(x))
Eq(F_35(x), F_36(x) - F_47(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_46(x))
Eq(F_41(x), F_16(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), -F_45(x) + F_5(x))
Eq(F_45(x), x*F_45(x)**3 - x*F_45(x)**2 + x*F_45(x) + 1)
Eq(F_46(x), F_18(x)*F_33(x))
Eq(F_47(x), F_38(x) + F_44(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_32(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_33(x)*F_4(x)*F_53(x))
Eq(F_53(x), F_14(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_25(x)*F_4(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_53(x)*F_8(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 4, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 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[1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 1]]}], "indices": [0], "direction": 2, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 3], [2, 3], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 4], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 4], [2, 4], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 4], [2, 4], [2, 4], [2, 4]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25882/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[53,x]+F[9,x]
F[9,x] = F[10,x]+F[51,x]
F[10,x] = F[0,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[15,x]*F[4,x]
F[13,x] = 1/F[4,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[16,x]*F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[16,x]*F[21,x]*F[4,x]
F[21,x] = F[15,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[15,x]*F[24,x]*F[4,x]
F[24,x] = F[21,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[21,x]*F[27,x]*F[4,x]
F[27,x] = 1/F[4,x]/F[5,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = -F[48,x]+F[30,x]
F[30,x] = 1/F[4,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = -F[0,x]+F[13,x]
F[35,x] = -F[47,x]+F[36,x]
F[36,x] = 1/F[4,x]*F[37,x]
F[37,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[46,x]
F[41,x] = F[17,x]*F[42,x]
F[42,x] = 1/F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = -F[45,x]+F[5,x]
F[45,x] = 1+(F[45,x]^3-F[45,x]^2+F[45,x])*x
F[46,x] = F[13,x]*F[19,x]
F[47,x] = F[38,x]+F[44,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[34,x]
F[51,x] = F[52,x]
F[52,x] = F[10,x]*F[21,x]*F[4,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]*F[8,x]
F[55,x] = F[15,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[15,x]*F[27,x]*F[4,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{53}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{51}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{4}\! \left(x \right) F_{5}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = -F_{48}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{31}\! \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_{35}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{35}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{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_{46}\! \left(x \right)
F_{41}\! \left(x \right) = F_{17}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{5}\! \left(x \right)
F_{45}\! \left(x \right) = x F_{45} \left(x \right)^{3}-x F_{45} \left(x \right)^{2}+x F_{45}\! \left(x \right)+1
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{47}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{34}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{10}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right) F_{4}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_53(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_51(x))
Eq(F_10(x), F_0(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_15(x)*F_4(x))
Eq(F_13(x), F_14(x)/F_4(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_16(x)*F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_16(x)*F_21(x)*F_4(x))
Eq(F_21(x), F_15(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_15(x)*F_24(x)*F_4(x))
Eq(F_24(x), F_21(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_21(x)*F_27(x)*F_4(x))
Eq(F_27(x), F_28(x)/(F_4(x)*F_5(x)))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x) - F_48(x))
Eq(F_30(x), F_31(x)/F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), -F_0(x) + F_13(x))
Eq(F_35(x), F_36(x) - F_47(x))
Eq(F_36(x), F_37(x)/F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_46(x))
Eq(F_41(x), F_17(x)*F_42(x))
Eq(F_42(x), F_43(x)/F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), -F_45(x) + F_5(x))
Eq(F_45(x), x*F_45(x)**3 - x*F_45(x)**2 + x*F_45(x) + 1)
Eq(F_46(x), F_13(x)*F_19(x))
Eq(F_47(x), F_38(x) + F_44(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_34(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_10(x)*F_21(x)*F_4(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x)*F_8(x))
Eq(F_55(x), F_15(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_15(x)*F_27(x)*F_4(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [2, 3, 0, 4, 1], [2, 3, 4, 0, 1], [2, 4, 0, 3, 1], [2, 4, 3, 0, 1], [3, 0, 2, 4, 1], [3, 2, 0, 4, 1], [3, 2, 4, 0, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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"requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 0], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 2], [0, 2], [0, 2], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 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