01324_01342_01432_04132_10324_10342_10432_14032_40132_41032
Counting sequence:
1, 1, 2, 6, 24, 110, 540, 2758, 14448, 77022, 415860, 2267078, 12452616, 68814798, 382168332, 2131181190, 11926192608, 66939251646, 376688820708, 2124542494342, 12006377078520, 67971210660654, 385409625059580, 2188442069645126, 12442365010054224, 70823083773243550, 403558158870752340, 2301748449902225478, 13140012140411446248, 75074007837858496142, 429252183272935308780, 2456068986419787174150, 14062169043699659573184, 80561679305123803131774, 461797710883272708458436, 2648539086822876131514630, 15197707001049164988588504, 87247666294882232571188718, 501096964738856630395438044, 2879194861405325192112891846, 16549760148463390209688937520, 95164404039866968681172802654, 547407926939895625347033875508, 3149876568473117566605935932614, 18130703479683106615964757108936, 104392122148688127017169666508110, 601238121820773686211067797140172, 3463739293794634153072283608143750, 19959900462006096346344676605940128, 115048503955200826031786522747349822, 663297375427680115468458771568251300, 3825038839904955184406472000506992518, 22062744248151975589542520192279488696, 127284470057710991760156647488993542318, 734479776556149628499432483504633526972, 4239057860008728736101278986275359554630, 24470377348813468592274176985217842151440, 141283268406334337705057057002139520897054, 815861874698682796054936006510206665334804, 4712112341910215630528263085276686072520006, 27219812081631011741187640027402975410016680, 157261579640014052571575983202101502049336334, 908711095252826346706332584277827966082419628, 5251610328223632446653606815083209999758586374, 30354320343707495548303553714683243826802335616, 175472022805508253819835167905641357158337199870, 1014501497577250575330957948376128088393395478404, 5866149458038211268296651697879987409520344392198, 33924030292995346847458904513640247813130181137304, 196206772465688375475262391146250415838986454510446, 1134935547347174325627271482977140595328862102197660, 6565647285209006547126357904053149701797962513470662, 37986702840001784026942710561860860827185377410359280, 219802168317744827438484632176206519903646675105098718, 1271971398474726575765010813496589132599435401768812532, 7361502340141197283674237292956512387201682976306282950, 42608680499811957854938964824828959852301767212063186568, 246644295257451810689956873957368992199827052780826575566, 1427855659913313125052060471572664893158835615480530536588, 8266786297940842239401878713588174326632673678957119520902, 47866013195484749899595901358760028234863976483129284784480, 277175572771031633972245280821547265972821817482137891228350, 1605161933426738586355450973426266995338116933469047460098404, 9296469212488551632802903531202198902365986500393286486825094, 53845773871620436838745000038537948680990556421479602014429816, 311902435685717446465916431937525114265357179169678970709456430, 1806835635389814330562332187410705185291751049749610973879506044, 10467680979455266085826630434417018508292884228568748654436340038, 60647583207022098418755171328339137050481761247299232887296361424, 351404222925291162520521851437339906245628985361592681339675479966, 2036245803381361701121854120455434392209332004511436543026631844820, 11800013216036928280761775028642334894260086986225618683829296874054, 68385368346627467879899389095608792910227624077068529267892986367848, 396343422049437983297784764235536451310495995520469868501373330733454, 2297244761412859648136599064752589607866706246076382142267941744863596, 13315866712387272657550641359788819335763951617560717734280961122575110, 77189386002997673280912262605707470625596082221883625474521645225232192, 447477447970574951795508394122390256810979924681900358222067406704602750, 2594236690896820096906787869191807763721826027254355670971359385064195908, 15040850593602508164375898627790251235693107376780176039362877097072007942, 87208545881506095261277811762483228737162764664557562435295226474129888600
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24721/
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[30,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[7,x]
F[7,x] = F[30,x]*F[8,x]
F[8,x] = F[23,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[30,x]*F[64,x]
F[12,x] = F[13,x]+F[4,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[30,x]*F[49,x]
F[15,x] = 1/F[30,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[73,x]+F[18,x]
F[18,x] = 1/F[30,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[30,x]
F[22,x] = F[10,x]+F[23,x]
F[23,x] = F[24,x]+F[39,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[30,x]*F[37,x]
F[26,x] = 1/F[5,x]*F[27,x]
F[27,x] = -F[31,x]+F[28,x]
F[28,x] = 1/F[30,x]*F[29,x]
F[29,x] = F[6,x]
F[30,x] = x
F[31,x] = -F[36,x]+F[32,x]
F[32,x] = 1/F[30,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[35,x]+F[6,x]
F[35,x] = (1+F[35,x])*x+F[35,x]^2
F[36,x] = F[26,x]*F[35,x]
F[37,x] = 1/F[30,x]*F[38,x]
F[38,x] = F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[30,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[30,x]*F[43,x]*F[64,x]
F[43,x] = 1/F[30,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = -F[46,x]+F[32,x]
F[46,x] = -F[47,x]+F[28,x]
F[47,x] = F[48,x]+F[54,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[1,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[49,x]^2*F[30,x]
F[52,x] = F[53,x]
F[53,x] = F[49,x]^2*F[30,x]*F[48,x]
F[54,x] = -F[62,x]+F[55,x]
F[55,x] = 1/F[30,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[61,x]+F[58,x]
F[58,x] = -F[0,x]+F[59,x]
F[59,x] = 1/F[30,x]*F[60,x]
F[60,x] = F[2,x]
F[61,x] = (-1+4*x)*F[61,x]^2+F[61,x]+x^2
F[62,x] = F[63,x]
F[63,x] = F[15,x]*F[30,x]*F[49,x]
F[64,x] = 1/F[0,x]*F[65,x]
F[65,x] = -F[69,x]+F[66,x]
F[66,x] = 1/F[30,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[20,x]+F[35,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[30,x]*F[71,x]
F[71,x] = F[20,x]
F[72,x] = F[2,x]*F[64,x]
F[73,x] = F[74,x]+F[91,x]
F[74,x] = F[75,x]+F[84,x]
F[75,x] = -F[82,x]+F[76,x]
F[76,x] = -F[77,x]+F[18,x]
F[77,x] = -F[80,x]+F[78,x]
F[78,x] = 1/F[30,x]*F[79,x]
F[79,x] = F[57,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = -F[49,x]+F[26,x]
F[82,x] = F[83,x]
F[83,x] = F[30,x]*F[54,x]
F[84,x] = F[85,x]
F[85,x] = F[30,x]*F[86,x]
F[86,x] = F[87,x]+F[90,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[48,x]*F[81,x]
F[89,x] = F[49,x]*F[82,x]
F[90,x] = F[49,x]*F[77,x]
F[91,x] = F[92,x]
F[92,x] = F[26,x]*F[30,x]*F[93,x]
F[93,x] = 1/F[30,x]*F[94,x]
F[94,x] = F[82,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_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{23}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{64}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{49}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{37}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{35}\! \left(x \right) x +F_{35} \left(x \right)^{2}+x
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{35}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{30}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{30}\! \left(x \right) F_{43}\! \left(x \right) F_{64}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{28}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{54}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49} \left(x \right)^{2} F_{30}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49} \left(x \right)^{2} F_{30}\! \left(x \right) F_{48}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)
F_{61}\! \left(x \right) = 4 x F_{61} \left(x \right)^{2}+x^{2}-F_{61} \left(x \right)^{2}+F_{61}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{49}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{65}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{20}\! \left(x \right)
F_{72}\! \left(x \right) = F_{2}\! \left(x \right) F_{64}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{91}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{84}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{18}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{57}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{26}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{30}\! \left(x \right) F_{54}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{30}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{48}\! \left(x \right) F_{81}\! \left(x \right)
F_{89}\! \left(x \right) = F_{49}\! \left(x \right) F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{49}\! \left(x \right) F_{77}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{82}\! \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_30(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_30(x)*F_8(x))
Eq(F_8(x), F_23(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_30(x)*F_64(x))
Eq(F_12(x), F_13(x) + F_4(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_30(x)*F_49(x))
Eq(F_15(x), F_16(x)/F_30(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) - F_73(x))
Eq(F_18(x), F_19(x)/F_30(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_30(x))
Eq(F_22(x), F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_39(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_30(x)*F_37(x))
Eq(F_26(x), F_27(x)/F_5(x))
Eq(F_27(x), F_28(x) - F_31(x))
Eq(F_28(x), F_29(x)/F_30(x))
Eq(F_29(x), F_6(x))
Eq(F_30(x), x)
Eq(F_31(x), F_32(x) - F_36(x))
Eq(F_32(x), F_33(x)/F_30(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), -F_35(x) + F_6(x))
Eq(F_35(x), (x - 3)*(F_35(x) + 1) + (F_35(x) + 1)**2 + F_35(x) + 2)
Eq(F_36(x), F_26(x)*F_35(x))
Eq(F_37(x), F_38(x)/F_30(x))
Eq(F_38(x), F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_30(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_30(x)*F_43(x)*F_64(x))
Eq(F_43(x), F_44(x)/F_30(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_32(x) - F_46(x))
Eq(F_46(x), F_28(x) - F_47(x))
Eq(F_47(x), F_48(x) + F_54(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_1(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_30(x)*F_49(x)**2)
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_30(x)*F_48(x)*F_49(x)**2)
Eq(F_54(x), F_55(x) - F_62(x))
Eq(F_55(x), F_56(x)/F_30(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_61(x))
Eq(F_58(x), -F_0(x) + F_59(x))
Eq(F_59(x), F_60(x)/F_30(x))
Eq(F_60(x), F_2(x))
Eq(F_61(x), x**2 + 4*x + (2 - 8*x)*(F_61(x) + 1) + (4*x - 1)*(F_61(x) + 1)**2 + F_61(x) - 1)
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_15(x)*F_30(x)*F_49(x))
Eq(F_64(x), F_65(x)/F_0(x))
Eq(F_65(x), F_66(x) - F_69(x))
Eq(F_66(x), F_67(x)/F_30(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_20(x) + F_35(x))
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_30(x))
Eq(F_71(x), F_20(x))
Eq(F_72(x), F_2(x)*F_64(x))
Eq(F_73(x), F_74(x) + F_91(x))
Eq(F_74(x), F_75(x) + F_84(x))
Eq(F_75(x), F_76(x) - F_82(x))
Eq(F_76(x), F_18(x) - F_77(x))
Eq(F_77(x), F_78(x) - F_80(x))
Eq(F_78(x), F_79(x)/F_30(x))
Eq(F_79(x), F_57(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_26(x) - F_49(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_30(x)*F_54(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_30(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_90(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_48(x)*F_81(x))
Eq(F_89(x), F_49(x)*F_82(x))
Eq(F_90(x), F_49(x)*F_77(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_26(x)*F_30(x)*F_93(x))
Eq(F_93(x), F_94(x)/F_30(x))
Eq(F_94(x), F_82(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, 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0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 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0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 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"ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 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2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [3, 0], [3, 1], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [3, 0], [3, 3], [3, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 1], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[2, 2]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"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": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 3], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [2, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 0], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 0], [2, 3], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 1], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 1], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionInferralStrategy", "gps": [{"patt": [0], "pos": [[1, 0]]}]}}]}, {"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], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24760/
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[7,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[6,x,k[0]] = x*F[6,x,k[0]]*k[0]+F[6,x,k[0]]^2-2*F[6,x,k[0]]+2
F[7,x] = 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_{7}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{6}\! \left(x , y\right) = x F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , y\right)^{2}-2 F_{6}\! \left(x , y\right)+2
F_{7}\! \left(x \right) = x
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_7(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_6(x, k_0), (k_0*x - 2)*F_6(x, k_0) + F_6(x, k_0)**2 + 2)
Eq(F_7(x), 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, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false, "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 1, "own_col": true, "own_row": true, "include_empty": false}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.fusion.fusion", "rule_class": "FusionRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[0, 0]]}]}]}], "strategy": {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionStrategy", "row_idx": null, "col_idx": 0, "tracked": true}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24770/
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[30,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[7,x]
F[7,x] = F[30,x]*F[8,x]
F[8,x] = F[23,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[30,x]*F[60,x]
F[12,x] = F[13,x]+F[4,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[30,x]*F[45,x]
F[15,x] = 1/F[30,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[69,x]+F[18,x]
F[18,x] = 1/F[30,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[30,x]
F[22,x] = F[10,x]+F[23,x]
F[23,x] = F[24,x]+F[39,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[30,x]*F[37,x]
F[26,x] = 1/F[5,x]*F[27,x]
F[27,x] = -F[31,x]+F[28,x]
F[28,x] = 1/F[30,x]*F[29,x]
F[29,x] = F[6,x]
F[30,x] = x
F[31,x] = -F[36,x]+F[32,x]
F[32,x] = 1/F[30,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[35,x]+F[6,x]
F[35,x] = (1+F[35,x])*x+F[35,x]^2
F[36,x] = F[26,x]*F[35,x]
F[37,x] = 1/F[30,x]*F[38,x]
F[38,x] = F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[30,x]*F[41,x]*F[60,x]
F[41,x] = -F[42,x]+F[32,x]
F[42,x] = -F[43,x]+F[28,x]
F[43,x] = F[44,x]+F[50,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[45,x]^2*F[30,x]
F[48,x] = F[49,x]
F[49,x] = F[45,x]^2*F[30,x]*F[44,x]
F[50,x] = -F[58,x]+F[51,x]
F[51,x] = 1/F[30,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[2,x]+F[54,x]
F[54,x] = -F[57,x]+F[55,x]
F[55,x] = 1/F[30,x]*F[56,x]
F[56,x] = F[2,x]
F[57,x] = -1+x^2+4*x+F[57,x]^2*(-1+4*x)+(3-8*x)*F[57,x]
F[58,x] = F[59,x]
F[59,x] = F[15,x]*F[30,x]*F[45,x]
F[60,x] = 1/F[0,x]*F[61,x]
F[61,x] = -F[65,x]+F[62,x]
F[62,x] = 1/F[30,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[20,x]+F[35,x]
F[65,x] = -F[68,x]+F[66,x]
F[66,x] = 1/F[30,x]*F[67,x]
F[67,x] = F[20,x]
F[68,x] = F[2,x]*F[60,x]
F[69,x] = F[70,x]+F[87,x]
F[70,x] = F[71,x]+F[80,x]
F[71,x] = -F[78,x]+F[72,x]
F[72,x] = -F[73,x]+F[18,x]
F[73,x] = -F[76,x]+F[74,x]
F[74,x] = 1/F[30,x]*F[75,x]
F[75,x] = F[53,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = -F[45,x]+F[26,x]
F[78,x] = F[79,x]
F[79,x] = F[30,x]*F[50,x]
F[80,x] = F[81,x]
F[81,x] = F[30,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[44,x]*F[77,x]
F[85,x] = F[45,x]*F[78,x]
F[86,x] = F[45,x]*F[73,x]
F[87,x] = F[88,x]
F[88,x] = F[26,x]*F[30,x]*F[89,x]
F[89,x] = 1/F[30,x]*F[90,x]
F[90,x] = F[78,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_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{23}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{60}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{45}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{37}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{35}\! \left(x \right) x +F_{35} \left(x \right)^{2}+x
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{35}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{30}\! \left(x \right) F_{41}\! \left(x \right) F_{60}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{32}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{28}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{50}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{45} \left(x \right)^{2} F_{30}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45} \left(x \right)^{2} F_{30}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{2}\! \left(x \right)
F_{57}\! \left(x \right) = 4 F_{57} \left(x \right)^{2} x +x^{2}-8 F_{57}\! \left(x \right) x -F_{57} \left(x \right)^{2}+4 x +3 F_{57}\! \left(x \right)-1
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{45}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{61}\! \left(x \right) = -F_{65}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{20}\! \left(x \right)
F_{68}\! \left(x \right) = F_{2}\! \left(x \right) F_{60}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{87}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{80}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{18}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{53}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{26}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{30}\! \left(x \right) F_{50}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{30}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{44}\! \left(x \right) F_{77}\! \left(x \right)
F_{85}\! \left(x \right) = F_{45}\! \left(x \right) F_{78}\! \left(x \right)
F_{86}\! \left(x \right) = F_{45}\! \left(x \right) F_{73}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{90}\! \left(x \right) = F_{78}\! \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_30(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_30(x)*F_8(x))
Eq(F_8(x), F_23(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_30(x)*F_60(x))
Eq(F_12(x), F_13(x) + F_4(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_30(x)*F_45(x))
Eq(F_15(x), F_16(x)/F_30(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) - F_69(x))
Eq(F_18(x), F_19(x)/F_30(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_30(x))
Eq(F_22(x), F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_39(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_30(x)*F_37(x))
Eq(F_26(x), F_27(x)/F_5(x))
Eq(F_27(x), F_28(x) - F_31(x))
Eq(F_28(x), F_29(x)/F_30(x))
Eq(F_29(x), F_6(x))
Eq(F_30(x), x)
Eq(F_31(x), F_32(x) - F_36(x))
Eq(F_32(x), F_33(x)/F_30(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), -F_35(x) + F_6(x))
Eq(F_35(x), (x - 3)*(F_35(x) + 1) + (F_35(x) + 1)**2 + F_35(x) + 2)
Eq(F_36(x), F_26(x)*F_35(x))
Eq(F_37(x), F_38(x)/F_30(x))
Eq(F_38(x), F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_30(x)*F_41(x)*F_60(x))
Eq(F_41(x), F_32(x) - F_42(x))
Eq(F_42(x), F_28(x) - F_43(x))
Eq(F_43(x), F_44(x) + F_50(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_30(x)*F_45(x)**2)
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_30(x)*F_44(x)*F_45(x)**2)
Eq(F_50(x), F_51(x) - F_58(x))
Eq(F_51(x), F_52(x)/F_30(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), -F_2(x) + F_54(x))
Eq(F_54(x), F_55(x) - F_57(x))
Eq(F_55(x), F_56(x)/F_30(x))
Eq(F_56(x), F_2(x))
Eq(F_57(x), x**2 + 4*x + (3 - 8*x)*F_57(x) + (4*x - 1)*F_57(x)**2 - 1)
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_15(x)*F_30(x)*F_45(x))
Eq(F_60(x), F_61(x)/F_0(x))
Eq(F_61(x), F_62(x) - F_65(x))
Eq(F_62(x), F_63(x)/F_30(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_20(x) + F_35(x))
Eq(F_65(x), F_66(x) - F_68(x))
Eq(F_66(x), F_67(x)/F_30(x))
Eq(F_67(x), F_20(x))
Eq(F_68(x), F_2(x)*F_60(x))
Eq(F_69(x), F_70(x) + F_87(x))
Eq(F_70(x), F_71(x) + F_80(x))
Eq(F_71(x), F_72(x) - F_78(x))
Eq(F_72(x), F_18(x) - F_73(x))
Eq(F_73(x), F_74(x) - F_76(x))
Eq(F_74(x), F_75(x)/F_30(x))
Eq(F_75(x), F_53(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_26(x) - F_45(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_30(x)*F_50(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_30(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_44(x)*F_77(x))
Eq(F_85(x), F_45(x)*F_78(x))
Eq(F_86(x), F_45(x)*F_73(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_26(x)*F_30(x)*F_89(x))
Eq(F_89(x), F_90(x)/F_30(x))
Eq(F_90(x), F_78(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": 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{"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], 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[1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 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, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[4, 2], [4, 2], [4, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 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": "EquivalencePathRule", "rules": [{"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": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24844/
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[30,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[7,x]
F[7,x] = F[30,x]*F[8,x]
F[8,x] = F[23,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[30,x]*F[60,x]
F[12,x] = F[13,x]+F[4,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[30,x]*F[45,x]
F[15,x] = 1/F[30,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[69,x]+F[18,x]
F[18,x] = 1/F[30,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[30,x]
F[22,x] = F[10,x]+F[23,x]
F[23,x] = F[24,x]+F[39,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[30,x]*F[37,x]
F[26,x] = 1/F[5,x]*F[27,x]
F[27,x] = -F[31,x]+F[28,x]
F[28,x] = 1/F[30,x]*F[29,x]
F[29,x] = F[6,x]
F[30,x] = x
F[31,x] = -F[36,x]+F[32,x]
F[32,x] = 1/F[30,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[35,x]+F[6,x]
F[35,x] = (1+F[35,x])*x+F[35,x]^2
F[36,x] = F[26,x]*F[35,x]
F[37,x] = 1/F[30,x]*F[38,x]
F[38,x] = F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[30,x]*F[41,x]*F[60,x]
F[41,x] = -F[42,x]+F[32,x]
F[42,x] = -F[43,x]+F[28,x]
F[43,x] = F[44,x]+F[50,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[1,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[45,x]^2*F[30,x]
F[48,x] = F[49,x]
F[49,x] = F[45,x]^2*F[30,x]*F[44,x]
F[50,x] = -F[58,x]+F[51,x]
F[51,x] = 1/F[30,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = -F[2,x]+F[54,x]
F[54,x] = -F[57,x]+F[55,x]
F[55,x] = 1/F[30,x]*F[56,x]
F[56,x] = F[2,x]
F[57,x] = -1+x^2+4*x+F[57,x]^2*(-1+4*x)+(3-8*x)*F[57,x]
F[58,x] = F[59,x]
F[59,x] = F[15,x]*F[30,x]*F[45,x]
F[60,x] = 1/F[0,x]*F[61,x]
F[61,x] = -F[65,x]+F[62,x]
F[62,x] = 1/F[30,x]*F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[20,x]+F[35,x]
F[65,x] = -F[68,x]+F[66,x]
F[66,x] = 1/F[30,x]*F[67,x]
F[67,x] = F[20,x]
F[68,x] = F[2,x]*F[60,x]
F[69,x] = F[70,x]+F[87,x]
F[70,x] = F[71,x]+F[80,x]
F[71,x] = -F[78,x]+F[72,x]
F[72,x] = -F[73,x]+F[18,x]
F[73,x] = -F[76,x]+F[74,x]
F[74,x] = 1/F[30,x]*F[75,x]
F[75,x] = F[53,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = -F[45,x]+F[26,x]
F[78,x] = F[79,x]
F[79,x] = F[30,x]*F[50,x]
F[80,x] = F[81,x]
F[81,x] = F[30,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[44,x]*F[77,x]
F[85,x] = F[45,x]*F[78,x]
F[86,x] = F[45,x]*F[73,x]
F[87,x] = F[88,x]
F[88,x] = F[26,x]*F[30,x]*F[89,x]
F[89,x] = 1/F[30,x]*F[90,x]
F[90,x] = F[78,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_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{23}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{60}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{45}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{37}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{35}\! \left(x \right) x +F_{35} \left(x \right)^{2}+x
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{35}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{30}\! \left(x \right) F_{41}\! \left(x \right) F_{60}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{32}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{28}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{50}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{1}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{45} \left(x \right)^{2} F_{30}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45} \left(x \right)^{2} F_{30}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = -F_{58}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{57}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{2}\! \left(x \right)
F_{57}\! \left(x \right) = 4 F_{57} \left(x \right)^{2} x +x^{2}-8 F_{57}\! \left(x \right) x -F_{57} \left(x \right)^{2}+4 x +3 F_{57}\! \left(x \right)-1
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{45}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{61}\! \left(x \right) = -F_{65}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = \frac{F_{63}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{68}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{20}\! \left(x \right)
F_{68}\! \left(x \right) = F_{2}\! \left(x \right) F_{60}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{87}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{80}\! \left(x \right)
F_{71}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{18}\! \left(x \right)
F_{73}\! \left(x \right) = -F_{76}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = \frac{F_{75}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{75}\! \left(x \right) = F_{53}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{26}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{30}\! \left(x \right) F_{50}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{30}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{44}\! \left(x \right) F_{77}\! \left(x \right)
F_{85}\! \left(x \right) = F_{45}\! \left(x \right) F_{78}\! \left(x \right)
F_{86}\! \left(x \right) = F_{45}\! \left(x \right) F_{73}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{90}\! \left(x \right) = F_{78}\! \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_30(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_30(x)*F_8(x))
Eq(F_8(x), F_23(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_30(x)*F_60(x))
Eq(F_12(x), F_13(x) + F_4(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_30(x)*F_45(x))
Eq(F_15(x), F_16(x)/F_30(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) - F_69(x))
Eq(F_18(x), F_19(x)/F_30(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_30(x))
Eq(F_22(x), F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_39(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_30(x)*F_37(x))
Eq(F_26(x), F_27(x)/F_5(x))
Eq(F_27(x), F_28(x) - F_31(x))
Eq(F_28(x), F_29(x)/F_30(x))
Eq(F_29(x), F_6(x))
Eq(F_30(x), x)
Eq(F_31(x), F_32(x) - F_36(x))
Eq(F_32(x), F_33(x)/F_30(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), -F_35(x) + F_6(x))
Eq(F_35(x), (x - 3)*(F_35(x) + 1) + (F_35(x) + 1)**2 + F_35(x) + 2)
Eq(F_36(x), F_26(x)*F_35(x))
Eq(F_37(x), F_38(x)/F_30(x))
Eq(F_38(x), F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_30(x)*F_41(x)*F_60(x))
Eq(F_41(x), F_32(x) - F_42(x))
Eq(F_42(x), F_28(x) - F_43(x))
Eq(F_43(x), F_44(x) + F_50(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_1(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_30(x)*F_45(x)**2)
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_30(x)*F_44(x)*F_45(x)**2)
Eq(F_50(x), F_51(x) - F_58(x))
Eq(F_51(x), F_52(x)/F_30(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), -F_2(x) + F_54(x))
Eq(F_54(x), F_55(x) - F_57(x))
Eq(F_55(x), F_56(x)/F_30(x))
Eq(F_56(x), F_2(x))
Eq(F_57(x), x**2 + 4*x + (3 - 8*x)*F_57(x) + (4*x - 1)*F_57(x)**2 - 1)
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_15(x)*F_30(x)*F_45(x))
Eq(F_60(x), F_61(x)/F_0(x))
Eq(F_61(x), F_62(x) - F_65(x))
Eq(F_62(x), F_63(x)/F_30(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_20(x) + F_35(x))
Eq(F_65(x), F_66(x) - F_68(x))
Eq(F_66(x), F_67(x)/F_30(x))
Eq(F_67(x), F_20(x))
Eq(F_68(x), F_2(x)*F_60(x))
Eq(F_69(x), F_70(x) + F_87(x))
Eq(F_70(x), F_71(x) + F_80(x))
Eq(F_71(x), F_72(x) - F_78(x))
Eq(F_72(x), F_18(x) - F_73(x))
Eq(F_73(x), F_74(x) - F_76(x))
Eq(F_74(x), F_75(x)/F_30(x))
Eq(F_75(x), F_53(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_26(x) - F_45(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_30(x)*F_50(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_30(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_44(x)*F_77(x))
Eq(F_85(x), F_45(x)*F_78(x))
Eq(F_86(x), F_45(x)*F_73(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_26(x)*F_30(x)*F_89(x))
Eq(F_89(x), F_90(x)/F_30(x))
Eq(F_90(x), F_78(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": 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{"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], 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[1, 1]]}, {"patt": [0, 1], "pos": [[3, 0], [3, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 3]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 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, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [2, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[2, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[3, 3], [3, 3], [3, 3]]}, {"patt": [0, 2, 1], "pos": [[4, 0], [4, 2], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[4, 2], [4, 2], [4, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [3, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 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": "EquivalencePathRule", "rules": [{"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": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24952/
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[30,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 2+F[5,x]^2+(-2+x)*F[5,x]
F[6,x] = F[7,x]
F[7,x] = F[30,x]*F[8,x]
F[8,x] = F[23,x]+F[9,x]
F[9,x] = F[10,x]+F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[30,x]*F[64,x]
F[12,x] = F[13,x]+F[4,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[30,x]*F[49,x]
F[15,x] = 1/F[30,x]*F[16,x]
F[16,x] = F[17,x]
F[17,x] = -F[73,x]+F[18,x]
F[18,x] = 1/F[30,x]*F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[30,x]
F[22,x] = F[10,x]+F[23,x]
F[23,x] = F[24,x]+F[39,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[30,x]*F[37,x]
F[26,x] = 1/F[5,x]*F[27,x]
F[27,x] = -F[31,x]+F[28,x]
F[28,x] = 1/F[30,x]*F[29,x]
F[29,x] = F[6,x]
F[30,x] = x
F[31,x] = -F[36,x]+F[32,x]
F[32,x] = 1/F[30,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = -F[35,x]+F[6,x]
F[35,x] = (1+F[35,x])*x+F[35,x]^2
F[36,x] = F[26,x]*F[35,x]
F[37,x] = 1/F[30,x]*F[38,x]
F[38,x] = F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[30,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[30,x]*F[43,x]*F[64,x]
F[43,x] = 1/F[30,x]*F[44,x]
F[44,x] = F[45,x]
F[45,x] = -F[46,x]+F[32,x]
F[46,x] = -F[47,x]+F[28,x]
F[47,x] = F[48,x]+F[54,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[1,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[49,x]^2*F[30,x]
F[52,x] = F[53,x]
F[53,x] = F[49,x]^2*F[30,x]*F[48,x]
F[54,x] = -F[62,x]+F[55,x]
F[55,x] = 1/F[30,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = -F[61,x]+F[58,x]
F[58,x] = -F[0,x]+F[59,x]
F[59,x] = 1/F[30,x]*F[60,x]
F[60,x] = F[2,x]
F[61,x] = (-1+4*x)*F[61,x]^2+F[61,x]+x^2
F[62,x] = F[63,x]
F[63,x] = F[15,x]*F[30,x]*F[49,x]
F[64,x] = 1/F[0,x]*F[65,x]
F[65,x] = -F[69,x]+F[66,x]
F[66,x] = 1/F[30,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[20,x]+F[35,x]
F[69,x] = -F[72,x]+F[70,x]
F[70,x] = 1/F[30,x]*F[71,x]
F[71,x] = F[20,x]
F[72,x] = F[2,x]*F[64,x]
F[73,x] = F[74,x]+F[91,x]
F[74,x] = F[75,x]+F[84,x]
F[75,x] = -F[82,x]+F[76,x]
F[76,x] = -F[77,x]+F[18,x]
F[77,x] = -F[80,x]+F[78,x]
F[78,x] = 1/F[30,x]*F[79,x]
F[79,x] = F[57,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = -F[49,x]+F[26,x]
F[82,x] = F[83,x]
F[83,x] = F[30,x]*F[54,x]
F[84,x] = F[85,x]
F[85,x] = F[30,x]*F[86,x]
F[86,x] = F[87,x]+F[90,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[48,x]*F[81,x]
F[89,x] = F[49,x]*F[82,x]
F[90,x] = F[49,x]*F[77,x]
F[91,x] = F[92,x]
F[92,x] = F[26,x]*F[30,x]*F[93,x]
F[93,x] = 1/F[30,x]*F[94,x]
F[94,x] = F[82,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_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{30}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{23}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{64}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{49}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = \frac{F_{19}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{30}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{37}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{5}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{31}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x \right) = -F_{36}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{35}\! \left(x \right) x +F_{35} \left(x \right)^{2}+x
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{35}\! \left(x \right)
F_{37}\! \left(x \right) = \frac{F_{38}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{38}\! \left(x \right) = F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{30}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{30}\! \left(x \right) F_{43}\! \left(x \right) F_{64}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = -F_{46}\! \left(x \right)+F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{28}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{54}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49} \left(x \right)^{2} F_{30}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49} \left(x \right)^{2} F_{30}\! \left(x \right) F_{48}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = \frac{F_{56}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{61}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{2}\! \left(x \right)
F_{61}\! \left(x \right) = 4 x F_{61} \left(x \right)^{2}+x^{2}-F_{61} \left(x \right)^{2}+F_{61}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{49}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{65}\! \left(x \right) = -F_{69}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{35}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = \frac{F_{71}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{71}\! \left(x \right) = F_{20}\! \left(x \right)
F_{72}\! \left(x \right) = F_{2}\! \left(x \right) F_{64}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{91}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{84}\! \left(x \right)
F_{75}\! \left(x \right) = -F_{82}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = -F_{77}\! \left(x \right)+F_{18}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{80}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = \frac{F_{79}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{79}\! \left(x \right) = F_{57}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = -F_{49}\! \left(x \right)+F_{26}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{30}\! \left(x \right) F_{54}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{30}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{90}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{48}\! \left(x \right) F_{81}\! \left(x \right)
F_{89}\! \left(x \right) = F_{49}\! \left(x \right) F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{49}\! \left(x \right) F_{77}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{82}\! \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_30(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), (x - 2)*F_5(x) + F_5(x)**2 + 2)
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_30(x)*F_8(x))
Eq(F_8(x), F_23(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_30(x)*F_64(x))
Eq(F_12(x), F_13(x) + F_4(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_30(x)*F_49(x))
Eq(F_15(x), F_16(x)/F_30(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x) - F_73(x))
Eq(F_18(x), F_19(x)/F_30(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_30(x))
Eq(F_22(x), F_10(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_39(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_30(x)*F_37(x))
Eq(F_26(x), F_27(x)/F_5(x))
Eq(F_27(x), F_28(x) - F_31(x))
Eq(F_28(x), F_29(x)/F_30(x))
Eq(F_29(x), F_6(x))
Eq(F_30(x), x)
Eq(F_31(x), F_32(x) - F_36(x))
Eq(F_32(x), F_33(x)/F_30(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), -F_35(x) + F_6(x))
Eq(F_35(x), (x - 3)*(F_35(x) + 1) + (F_35(x) + 1)**2 + F_35(x) + 2)
Eq(F_36(x), F_26(x)*F_35(x))
Eq(F_37(x), F_38(x)/F_30(x))
Eq(F_38(x), F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_30(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_30(x)*F_43(x)*F_64(x))
Eq(F_43(x), F_44(x)/F_30(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_32(x) - F_46(x))
Eq(F_46(x), F_28(x) - F_47(x))
Eq(F_47(x), F_48(x) + F_54(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_1(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_30(x)*F_49(x)**2)
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_30(x)*F_48(x)*F_49(x)**2)
Eq(F_54(x), F_55(x) - F_62(x))
Eq(F_55(x), F_56(x)/F_30(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x) - F_61(x))
Eq(F_58(x), -F_0(x) + F_59(x))
Eq(F_59(x), F_60(x)/F_30(x))
Eq(F_60(x), F_2(x))
Eq(F_61(x), x**2 + 4*x + (2 - 8*x)*(F_61(x) + 1) + (4*x - 1)*(F_61(x) + 1)**2 + F_61(x) - 1)
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_15(x)*F_30(x)*F_49(x))
Eq(F_64(x), F_65(x)/F_0(x))
Eq(F_65(x), F_66(x) - F_69(x))
Eq(F_66(x), F_67(x)/F_30(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_20(x) + F_35(x))
Eq(F_69(x), F_70(x) - F_72(x))
Eq(F_70(x), F_71(x)/F_30(x))
Eq(F_71(x), F_20(x))
Eq(F_72(x), F_2(x)*F_64(x))
Eq(F_73(x), F_74(x) + F_91(x))
Eq(F_74(x), F_75(x) + F_84(x))
Eq(F_75(x), F_76(x) - F_82(x))
Eq(F_76(x), F_18(x) - F_77(x))
Eq(F_77(x), F_78(x) - F_80(x))
Eq(F_78(x), F_79(x)/F_30(x))
Eq(F_79(x), F_57(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_26(x) - F_49(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_30(x)*F_54(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_30(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_90(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_48(x)*F_81(x))
Eq(F_89(x), F_49(x)*F_82(x))
Eq(F_90(x), F_49(x)*F_77(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_26(x)*F_30(x)*F_93(x))
Eq(F_93(x), F_94(x)/F_30(x))
Eq(F_94(x), F_82(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 2, 4], [0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [0, 4, 1, 3, 2], [1, 0, 3, 2, 4], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 4, 0, 3, 2], [4, 0, 1, 3, 2], [4, 1, 0, 3, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, 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