02341_02431_03241_03421_04231_04321
Counting sequence:
1, 1, 2, 6, 24, 114, 600, 3372, 19824, 120426, 749976, 4762644, 30723792, 200778612, 1326360048, 8842981848, 59425117152, 402092408346, 2737156004376, 18732169337604, 128806616999184, 889479590046108, 6165939982059600, 42891532191557736, 299307319060137504, 2094684530280579204, 14698465904618271600, 103391859250744921032, 728921724455874437664, 5149722130698960310056, 36452793427943459541216, 258502230381854035397040, 1836252048586705964035008, 13064351285339412097452666, 93086856911367488874965784, 664194212869807647276675684, 4745398038984383168404384656, 33946006185024309584419138188, 243115989817433184083028079248, 1743090214757554905537513678792, 12510727228039899824443540005792, 89883165861304275497726457433068, 646376826183172836194296157755344, 4652483757356774570221586375075544, 33516379424491662872615797471726176, 241649128820923962435750703974420696, 1743625446363709768112039800174408992, 12590587146701777302368196690836722640, 90980758358285830188814991290082362944, 657886175476583519079435444907500602916, 4760332390677084581539663483009695394416, 34466527331862222321009111355303033993704, 249701196164851760773803778587492940113312, 1810073921029906072648056552378995252750232, 13128494645874546222193180072880140681328928, 95272456877355714342609853591191556566613008, 691743357403024365898560652397653035432617280, 5025041838744985930198913490786502026008913864, 36521087915854745438144359455987962173587937248, 265552112645559448851680853554026352702410113552, 1931749968200099720230997561300183368071609394752, 14058551723907651912165393734636130130689394847568, 102355813573075724181920262024018940996976042096064, 745522509073007171819006030616952269866027535330144, 5432248876291767535417303240917078903727163448878976, 39597139780188594027887721077937548406504234465920826, 288740758261776114113591863136074446498150993436396824, 2106238667249529533145237813129911396887982507996495652, 15369424291399086420224255180854306174116062386126061712, 112189877493227004366787381247069322374101025549117293548, 819202983092945268740956268198143438435477004733131278608, 5983662108096416715710643097119543226662604624951321514376, 43719618601413050434332076859839028433379696143458071186080, 319532974296699297658710470196447473692600968728108158485852, 2336046138209812933413279553857712698504403276606980913997328, 17083235073803093254657140104076787602754800342071165042006328, 124962145807890569452204984929148398043340726099667127219579872, 914330713946740475830977448781342411234561461256800363560575736, 6691778650190852452520229915907829747595406073683194154981715616, 48988068201702302028116506075656270284077180496372752740777400464, 358712678169587444454001061676846928264036056472802730078070211904, 2627290461054707576155659785771971746278985898400466333060858171660, 19247387378294848589695694969232071469321676318063976988177134457552, 141037727877177986557302915461969645785597561035837241696815163517304, 1033704031504405972128420222783734291349718956308257939157913296227296, 7577957582865503261430847647947457941146201206998083018267317411076296, 55564949917890717879737463479480435966152406924771892378338499640428384, 407511909616078816324505626662909519496028933493284135880140422982002992, 2989291069022834817912299550670398676444328526237735552906831188971334592, 21932220119253805641420220181801439175804835258736322686503175442662301368, 160946493884649536759913742492476295262545344585276908430924414391656987168, 1181307834098128307364496589571181291252244681070397898602126448169407400432, 8672123553482013528939449678852902731914189344531729930015792780477279551936, 63674694171543957799243486756545228676305151945433813232924749538230884359216, 467611953272222067082021832488215724812540463011033639910701411408743943142464, 3434630390883003500018846030445714607692604971489648782097174846920792298070944, 25231814037645356813978029435976117261295301350381020100226828064192998609269888, 185391342781785546347503953440334779327891653869728144258659718473701793892975460, 1362389936155974260282858570726688157899610208749783903669389047028573227393276016, 10013431841380955319656278717282408589325512782493229375657935217204610712941616424, 73609283846396475084679593013345762091317673234189918121253980559198224613893361824
Generating function in Maple syntax:
-2*x^2+2*x+1-x*(4*x^2-8*x+1)^(1/2)
Generating function in latex syntax:
-2 x^{2}+2 x +1-x \sqrt{4 x^{2}-8 x +1}
Generating function in sympy syntax:
-2*x**2 - x*sqrt(4*x**2 - 8*x + 1) + 2*x + 1
Implicit equation for the generating function in Maple syntax:
F(x)^2+(4*x^2-4*x-2)*F(x)-x^2+4*x+1 = 0
Implicit equation for the generating function in latex syntax:
F \! \left(x \right)^{2}+\left(4 x^{2}-4 x -2\right) F \! \left(x \right)-x^{2}+4 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(n+2) = -4*(n-2)/(1+n)*a(n)+4*(2*n-1)/(1+n)*a(1+n), n >= 3
Recurrence in latex format:
a{\left(0 \right)} = 1
a{\left(1 \right)} = 1
a{\left(2 \right)} = 2
a{\left(n + 2 \right)} = - \frac{4 \left(n - 2\right) a{\left(n \right)}}{n + 1} + \frac{4 \left(2 n - 1\right) a{\left(n + 1 \right)}}{n + 1}, \quad n \geq 3
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24460/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[109,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[20,x]
F[13,x] = F[14,x]+F[29,x]
F[14,x] = F[15,x]*F[21,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[20,x]
F[17,x] = 1/F[20,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[2,x]+F[6,x]
F[20,x] = x
F[21,x] = F[0,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[20,x]*F[24,x]
F[24,x] = 1/F[20,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[0,x]+F[27,x]
F[27,x] = 1/F[20,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x] = F[30,x]
F[30,x] = F[20,x]*F[31,x]
F[31,x] = F[104,x]+F[32,x]
F[32,x] = 1/F[20,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[19,x]*F[24,x]
F[36,x] = F[37,x]
F[37,x] = F[20,x]*F[38,x]*F[71,x]
F[38,x] = F[39,x]
F[39,x] = F[20,x]*F[40,x]
F[40,x] = F[101,x]+F[41,x]
F[41,x] = F[42,x]+F[98,x]
F[42,x] = F[43,x]+F[90,x]
F[43,x] = F[27,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[20,x]*F[4,x]*F[46,x]
F[46,x] = F[27,x]+F[47,x]
F[47,x] = 1/F[20,x]/F[70,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[20,x]*F[51,x]
F[51,x] = -F[67,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[20,x]*F[54,x]
F[54,x] = 1/F[20,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[57,x]+F[62,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[20,x]*F[59,x]
F[59,x] = F[6,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[2,x]*F[21,x]
F[62,x] = F[63,x]
F[63,x] = F[20,x]*F[64,x]
F[64,x] = F[65,x]+F[73,x]
F[65,x] = F[34,x]+F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[2,x]*F[24,x]
F[68,x] = F[69,x]
F[69,x] = F[20,x]*F[70,x]*F[71,x]
F[70,x] = F[19,x]+F[2,x]
F[71,x] = 1/F[20,x]*F[72,x]
F[72,x] = F[47,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[2,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[20,x]*F[71,x]
F[78,x] = F[79,x]
F[79,x] = F[20,x]*F[71,x]*F[80,x]
F[80,x] = F[19,x]+F[81,x]
F[81,x] = F[5,x]+F[82,x]
F[82,x] = -F[5,x]+F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[20,x]*F[85,x]
F[85,x] = F[6,x]
F[86,x] = F[87,x]
F[87,x] = F[20,x]*F[88,x]
F[88,x] = 1/F[20,x]*F[89,x]
F[89,x] = F[38,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[0,x]*F[19,x]
F[92,x] = F[93,x]
F[93,x] = F[20,x]*F[94,x]
F[94,x] = F[34,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[78,x]+F[97,x]
F[97,x] = F[0,x]*F[76,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[20,x]*F[46,x]
F[100,x] = F[38,x]+F[4,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[20,x]*F[46,x]
F[103,x] = F[4,x]+F[81,x]
F[104,x] = F[105,x]
F[105,x] = -F[108,x]+F[106,x]
F[106,x] = 1/F[20,x]*F[107,x]
F[107,x] = F[78,x]
F[108,x] = F[17,x]*F[76,x]
F[109,x] = -F[134,x]+F[110,x]
F[110,x] = -F[132,x]+F[111,x]
F[111,x] = 1/F[20,x]*F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]+F[120,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[20,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[0,x]*F[21,x]
F[118,x] = F[119,x]
F[119,x] = F[20,x]*F[24,x]*F[4,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[2,x]*F[20,x]
F[122,x] = F[0,x]+F[123,x]
F[123,x] = F[124,x]+F[2,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]*F[20,x]
F[126,x] = F[127,x]+F[44,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[123,x]
F[129,x] = F[130,x]+F[49,x]
F[130,x] = F[131,x]
F[131,x] = F[20,x]*F[47,x]
F[132,x] = F[133,x]
F[133,x] = F[122,x]*F[20,x]*F[27,x]
F[134,x] = F[128,x]+F[135,x]
F[135,x] = F[0,x]^2
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_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{109}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{0}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{20}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{104}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right) F_{24}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right) F_{38}\! \left(x \right) F_{71}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{20}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{101}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{98}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{90}\! \left(x \right)
F_{43}\! \left(x \right) = F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{27}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{20}\! \left(x \right) F_{70}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{6}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{21}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{34}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right) F_{70}\! \left(x \right) F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{47}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{2}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{5}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{6}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{38}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{20}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{34}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{78}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{0}\! \left(x \right) F_{76}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{100}\! \left(x \right) = F_{38}\! \left(x \right)+F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{103}\! \left(x \right) = F_{4}\! \left(x \right)+F_{81}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{78}\! \left(x \right)
F_{108}\! \left(x \right) = F_{17}\! \left(x \right) F_{76}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{132}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = \frac{F_{112}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{120}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{20}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{0}\! \left(x \right) F_{21}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{20}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{122}\! \left(x \right) = F_{0}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{2}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{44}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{123}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{49}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{122}\! \left(x \right) F_{20}\! \left(x \right) F_{27}\! \left(x \right)
F_{134}\! \left(x \right) = F_{128}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{0} \left(x \right)^{2}
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_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_109(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_20(x))
Eq(F_13(x), F_14(x) + F_29(x))
Eq(F_14(x), F_15(x)*F_21(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_20(x))
Eq(F_17(x), F_18(x)/F_20(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_2(x) + F_6(x))
Eq(F_20(x), x)
Eq(F_21(x), F_0(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_20(x)*F_24(x))
Eq(F_24(x), F_25(x)/F_20(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_0(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_20(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_20(x)*F_31(x))
Eq(F_31(x), F_104(x) + F_32(x))
Eq(F_32(x), F_33(x)/F_20(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_19(x)*F_24(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_20(x)*F_38(x)*F_71(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_20(x)*F_40(x))
Eq(F_40(x), F_101(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_98(x))
Eq(F_42(x), F_43(x) + F_90(x))
Eq(F_43(x), F_27(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_20(x)*F_4(x)*F_46(x))
Eq(F_46(x), F_27(x) + F_47(x))
Eq(F_47(x), F_48(x)/(F_20(x)*F_70(x)))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_20(x)*F_51(x))
Eq(F_51(x), F_52(x) - F_67(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_20(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_20(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x) + F_62(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_20(x))
Eq(F_59(x), F_6(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_2(x)*F_21(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_20(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_73(x))
Eq(F_65(x), F_34(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_2(x)*F_24(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_20(x)*F_70(x)*F_71(x))
Eq(F_70(x), F_19(x) + F_2(x))
Eq(F_71(x), F_72(x)/F_20(x))
Eq(F_72(x), F_47(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_2(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_20(x)*F_71(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_20(x)*F_71(x)*F_80(x))
Eq(F_80(x), F_19(x) + F_81(x))
Eq(F_81(x), F_5(x) + F_82(x))
Eq(F_82(x), -F_5(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_20(x))
Eq(F_85(x), F_6(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_20(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_20(x))
Eq(F_89(x), F_38(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_0(x)*F_19(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_20(x)*F_94(x))
Eq(F_94(x), F_34(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_78(x) + F_97(x))
Eq(F_97(x), F_0(x)*F_76(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_20(x)*F_46(x))
Eq(F_100(x), F_38(x) + F_4(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_20(x)*F_46(x))
Eq(F_103(x), F_4(x) + F_81(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) - F_108(x))
Eq(F_106(x), F_107(x)/F_20(x))
Eq(F_107(x), F_78(x))
Eq(F_108(x), F_17(x)*F_76(x))
Eq(F_109(x), F_110(x) - F_134(x))
Eq(F_110(x), F_111(x) - F_132(x))
Eq(F_111(x), F_112(x)/F_20(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x) + F_120(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_20(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_0(x)*F_21(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_20(x)*F_24(x)*F_4(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_2(x)*F_20(x))
Eq(F_122(x), F_0(x) + F_123(x))
Eq(F_123(x), F_124(x) + F_2(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x)*F_20(x))
Eq(F_126(x), F_127(x) + F_44(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_123(x))
Eq(F_129(x), F_130(x) + F_49(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_20(x)*F_47(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_122(x)*F_20(x)*F_27(x))
Eq(F_134(x), F_128(x) + F_135(x))
Eq(F_135(x), F_0(x)**2)
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [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, 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{"patt": [0, 3, 2, 1], "pos": [[2, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [3, 2], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [3, 4], [3, 1], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 2, 1, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 2], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 4], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 2], [3, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 4], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 4], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 1], [3, 2], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 1], [3, 4], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 4], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 4], [3, 1], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24655/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[20,x]*F[8,x]
F[8,x] = F[109,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[20,x]
F[13,x] = F[14,x]+F[29,x]
F[14,x] = F[15,x]*F[21,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[20,x]
F[17,x] = 1/F[20,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[2,x]+F[6,x]
F[20,x] = x
F[21,x] = F[0,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[20,x]*F[24,x]
F[24,x] = 1/F[20,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[0,x]+F[27,x]
F[27,x] = 1/F[20,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x] = F[30,x]
F[30,x] = F[20,x]*F[31,x]
F[31,x] = F[104,x]+F[32,x]
F[32,x] = 1/F[20,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[19,x]*F[24,x]
F[36,x] = F[37,x]
F[37,x] = F[20,x]*F[38,x]*F[71,x]
F[38,x] = F[39,x]
F[39,x] = F[20,x]*F[40,x]
F[40,x] = F[101,x]+F[41,x]
F[41,x] = F[42,x]+F[98,x]
F[42,x] = F[43,x]+F[90,x]
F[43,x] = F[27,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[20,x]*F[4,x]*F[46,x]
F[46,x] = F[27,x]+F[47,x]
F[47,x] = 1/F[20,x]/F[70,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[20,x]*F[51,x]
F[51,x] = -F[67,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[20,x]*F[54,x]
F[54,x] = 1/F[20,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[57,x]+F[62,x]
F[57,x] = -F[60,x]+F[58,x]
F[58,x] = 1/F[20,x]*F[59,x]
F[59,x] = F[6,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[2,x]*F[21,x]
F[62,x] = F[63,x]
F[63,x] = F[20,x]*F[64,x]
F[64,x] = F[65,x]+F[73,x]
F[65,x] = F[34,x]+F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[2,x]*F[24,x]
F[68,x] = F[69,x]
F[69,x] = F[20,x]*F[70,x]*F[71,x]
F[70,x] = F[19,x]+F[2,x]
F[71,x] = 1/F[20,x]*F[72,x]
F[72,x] = F[47,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[2,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[20,x]*F[71,x]
F[78,x] = F[79,x]
F[79,x] = F[20,x]*F[71,x]*F[80,x]
F[80,x] = F[19,x]+F[81,x]
F[81,x] = F[5,x]+F[82,x]
F[82,x] = -F[5,x]+F[83,x]
F[83,x] = -F[86,x]+F[84,x]
F[84,x] = 1/F[20,x]*F[85,x]
F[85,x] = F[6,x]
F[86,x] = F[87,x]
F[87,x] = F[20,x]*F[88,x]
F[88,x] = 1/F[20,x]*F[89,x]
F[89,x] = F[38,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[0,x]*F[19,x]
F[92,x] = F[93,x]
F[93,x] = F[20,x]*F[94,x]
F[94,x] = F[34,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[78,x]+F[97,x]
F[97,x] = F[0,x]*F[76,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[20,x]*F[46,x]
F[100,x] = F[38,x]+F[4,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[20,x]*F[46,x]
F[103,x] = F[4,x]+F[81,x]
F[104,x] = F[105,x]
F[105,x] = -F[108,x]+F[106,x]
F[106,x] = 1/F[20,x]*F[107,x]
F[107,x] = F[78,x]
F[108,x] = F[17,x]*F[76,x]
F[109,x] = -F[134,x]+F[110,x]
F[110,x] = -F[132,x]+F[111,x]
F[111,x] = 1/F[20,x]*F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]+F[120,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[20,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[0,x]*F[21,x]
F[118,x] = F[119,x]
F[119,x] = F[20,x]*F[24,x]*F[4,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[2,x]*F[20,x]
F[122,x] = F[0,x]+F[123,x]
F[123,x] = F[124,x]+F[2,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]*F[20,x]
F[126,x] = F[127,x]+F[44,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[123,x]
F[129,x] = F[130,x]+F[49,x]
F[130,x] = F[131,x]
F[131,x] = F[20,x]*F[47,x]
F[132,x] = F[133,x]
F[133,x] = F[122,x]*F[20,x]*F[27,x]
F[134,x] = F[128,x]+F[135,x]
F[135,x] = F[0,x]^2
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_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{20}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{109}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{0}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{20}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{20}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{104}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right) F_{24}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right) F_{38}\! \left(x \right) F_{71}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{20}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{101}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{98}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{90}\! \left(x \right)
F_{43}\! \left(x \right) = F_{27}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{27}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = \frac{F_{48}\! \left(x \right)}{F_{20}\! \left(x \right) F_{70}\! \left(x \right)}
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{67}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{60}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = \frac{F_{59}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{59}\! \left(x \right) = F_{6}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right) F_{21}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{34}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right) F_{70}\! \left(x \right) F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{71}\! \left(x \right) = \frac{F_{72}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{72}\! \left(x \right) = F_{47}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{2}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{20}\! \left(x \right) F_{71}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{5}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = -F_{5}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = \frac{F_{85}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{85}\! \left(x \right) = F_{6}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{38}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{19}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{20}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{34}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{78}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{0}\! \left(x \right) F_{76}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{100}\! \left(x \right) = F_{38}\! \left(x \right)+F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{20}\! \left(x \right) F_{46}\! \left(x \right)
F_{103}\! \left(x \right) = F_{4}\! \left(x \right)+F_{81}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = -F_{108}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{78}\! \left(x \right)
F_{108}\! \left(x \right) = F_{17}\! \left(x \right) F_{76}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{134}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{132}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = \frac{F_{112}\! \left(x \right)}{F_{20}\! \left(x \right)}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{120}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{20}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{0}\! \left(x \right) F_{21}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{20}\! \left(x \right) F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{122}\! \left(x \right) = F_{0}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{2}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{20}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{44}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{123}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{49}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{20}\! \left(x \right) F_{47}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{122}\! \left(x \right) F_{20}\! \left(x \right) F_{27}\! \left(x \right)
F_{134}\! \left(x \right) = F_{128}\! \left(x \right)+F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{0} \left(x \right)^{2}
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_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_20(x)*F_8(x))
Eq(F_8(x), F_109(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_20(x))
Eq(F_13(x), F_14(x) + F_29(x))
Eq(F_14(x), F_15(x)*F_21(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_20(x))
Eq(F_17(x), F_18(x)/F_20(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_2(x) + F_6(x))
Eq(F_20(x), x)
Eq(F_21(x), F_0(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_20(x)*F_24(x))
Eq(F_24(x), F_25(x)/F_20(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_0(x) + F_27(x))
Eq(F_27(x), F_28(x)/F_20(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_20(x)*F_31(x))
Eq(F_31(x), F_104(x) + F_32(x))
Eq(F_32(x), F_33(x)/F_20(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_19(x)*F_24(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_20(x)*F_38(x)*F_71(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_20(x)*F_40(x))
Eq(F_40(x), F_101(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_98(x))
Eq(F_42(x), F_43(x) + F_90(x))
Eq(F_43(x), F_27(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_20(x)*F_4(x)*F_46(x))
Eq(F_46(x), F_27(x) + F_47(x))
Eq(F_47(x), F_48(x)/(F_20(x)*F_70(x)))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_20(x)*F_51(x))
Eq(F_51(x), F_52(x) - F_67(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_20(x)*F_54(x))
Eq(F_54(x), F_55(x)/F_20(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_57(x) + F_62(x))
Eq(F_57(x), F_58(x) - F_60(x))
Eq(F_58(x), F_59(x)/F_20(x))
Eq(F_59(x), F_6(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_2(x)*F_21(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_20(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_73(x))
Eq(F_65(x), F_34(x) + F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_2(x)*F_24(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_20(x)*F_70(x)*F_71(x))
Eq(F_70(x), F_19(x) + F_2(x))
Eq(F_71(x), F_72(x)/F_20(x))
Eq(F_72(x), F_47(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_2(x)*F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_20(x)*F_71(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_20(x)*F_71(x)*F_80(x))
Eq(F_80(x), F_19(x) + F_81(x))
Eq(F_81(x), F_5(x) + F_82(x))
Eq(F_82(x), -F_5(x) + F_83(x))
Eq(F_83(x), F_84(x) - F_86(x))
Eq(F_84(x), F_85(x)/F_20(x))
Eq(F_85(x), F_6(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_20(x)*F_88(x))
Eq(F_88(x), F_89(x)/F_20(x))
Eq(F_89(x), F_38(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_0(x)*F_19(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_20(x)*F_94(x))
Eq(F_94(x), F_34(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_78(x) + F_97(x))
Eq(F_97(x), F_0(x)*F_76(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_20(x)*F_46(x))
Eq(F_100(x), F_38(x) + F_4(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_20(x)*F_46(x))
Eq(F_103(x), F_4(x) + F_81(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x) - F_108(x))
Eq(F_106(x), F_107(x)/F_20(x))
Eq(F_107(x), F_78(x))
Eq(F_108(x), F_17(x)*F_76(x))
Eq(F_109(x), F_110(x) - F_134(x))
Eq(F_110(x), F_111(x) - F_132(x))
Eq(F_111(x), F_112(x)/F_20(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x) + F_120(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_20(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_0(x)*F_21(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_20(x)*F_24(x)*F_4(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_2(x)*F_20(x))
Eq(F_122(x), F_0(x) + F_123(x))
Eq(F_123(x), F_124(x) + F_2(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x)*F_20(x))
Eq(F_126(x), F_127(x) + F_44(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_123(x))
Eq(F_129(x), F_130(x) + F_49(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_20(x)*F_47(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_122(x)*F_20(x)*F_27(x))
Eq(F_134(x), F_128(x) + F_135(x))
Eq(F_135(x), F_0(x)**2)
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [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]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 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]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [2, 0, 1], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [2, 1, 0], "pos": [[2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 2], 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"pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 4], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 4], [3, 1], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: partial_row_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25029/
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[13,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[0,x]+F[6,x,k[0]]
F[6,x,k[0]] = k[0]*F[7,x,k[0]]
F[7,x,k[0]] = F[14,x,k[0]]+F[15,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[8,x] = 0
F[10,x,k[0]] = F[14,x,k[0]]+F[8,x]+F[9,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[13,x]
F[12,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[13,x] = x
F[14,x,k[0]] = F[13,x]*F[5,x,k[0]]
F[15,x,k[0]] = k[0]*F[16,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]+F[18,x,k[0]]+F[8,x]
F[17,x,k[0]] = F[13,x]*F[7,x,k[0]]
F[18,x,k[0]] = k[0]*F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[13,x]*F[21,x,k[0]]
F[21,x,k[0]] = F[17,x,k[0]]+F[22,x,k[0]]+F[23,x,k[0]]+F[24,x,k[0]]+F[8,x]
F[9,x,k[0]] = F[22,x,k[0]]+F[23,x,k[0]]+F[8,x]
F[23,x,k[0]] = F[13,x]*F[7,x,k[0]]
F[24,x,k[0]] = k[0]*F[19,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = y F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{8}\! \left(x \right) = 0
F_{10}\! \left(x , y\right) = F_{14}\! \left(x , y\right)+F_{8}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x \right)
F_{12}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x \right) = x
F_{14}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{5}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y F_{16}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{17}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = y F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{9}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{8}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = y F_{19}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_0(x) + F_6(x, k_0))
Eq(F_6(x, k_0), k_0*F_7(x, k_0))
Eq(F_7(x, k_0), F_14(x, k_0) + F_15(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_8(x), 0)
Eq(F_10(x, k_0), F_14(x, k_0) + F_8(x) + F_9(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_13(x))
Eq(F_12(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_13(x), x)
Eq(F_14(x, k_0), F_13(x)*F_5(x, k_0))
Eq(F_15(x, k_0), k_0*F_16(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0) + F_18(x, k_0) + F_8(x))
Eq(F_17(x, k_0), F_13(x)*F_7(x, k_0))
Eq(F_18(x, k_0), k_0*F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_13(x)*F_21(x, k_0))
Eq(F_21(x, k_0), F_17(x, k_0) + F_22(x, k_0) + F_23(x, k_0) + F_24(x, k_0) + F_8(x))
Eq(F_9(x, k_0), F_22(x, k_0) + F_23(x, k_0) + F_8(x))
Eq(F_23(x, k_0), F_13(x)*F_7(x, k_0))
Eq(F_24(x, k_0), k_0*F_19(x, k_0))
Pack JSON:
{"name": "partial_row_and_col_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": true, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": true}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
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1], [0, 1], [0, 1], [3, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [2, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [3, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [4, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [3, 1], [4, 1], [4, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], 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1], [4, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [2, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [3, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [3, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [4, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [2, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [3, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [3, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [4, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [3, 1], [4, 1], [4, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [4, 1], [4, 1], [4, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 1]]}], [{"patt": [0], "pos": [[3, 1]]}], [{"patt": [0], "pos": [[4, 0]]}]], "assumptions": [{"class_module": "tilings.assumptions", "assumption": "TrackingAssumption", "gps": [{"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 1]]}]}]}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}], "indices": [0, 0], "direction": 2, "own_col": true, "own_row": false, "include_empty": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25331/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[19,x]*F[8,x]
F[8,x] = F[109,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[14,x]+F[28,x]
F[14,x] = F[15,x]*F[20,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[19,x]
F[17,x] = 1/F[19,x]*F[18,x]
F[18,x] = F[5,x]
F[19,x] = x
F[20,x] = F[0,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[19,x]*F[23,x]
F[23,x] = 1/F[19,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[0,x]+F[26,x]
F[26,x] = 1/F[19,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = F[29,x]
F[29,x] = F[19,x]*F[30,x]
F[30,x] = F[103,x]+F[31,x]
F[31,x] = 1/F[19,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[23,x]*F[5,x]
F[35,x] = F[36,x]
F[36,x] = F[19,x]*F[37,x]*F[51,x]
F[37,x] = F[38,x]
F[38,x] = F[19,x]*F[39,x]
F[39,x] = F[100,x]+F[40,x]
F[40,x] = F[41,x]+F[96,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[0,x]*F[4,x]
F[43,x] = F[44,x]
F[44,x] = F[19,x]*F[45,x]
F[45,x] = F[46,x]+F[93,x]
F[46,x] = F[33,x]+F[47,x]
F[47,x] = F[48,x]+F[72,x]
F[48,x] = F[23,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[19,x]*F[51,x]
F[51,x] = 1/F[19,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = 1/F[19,x]/F[76,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[19,x]*F[57,x]
F[57,x] = -F[73,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[19,x]*F[60,x]
F[60,x] = 1/F[19,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = -F[66,x]+F[64,x]
F[64,x] = 1/F[19,x]*F[65,x]
F[65,x] = F[6,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[2,x]*F[20,x]
F[68,x] = F[69,x]
F[69,x] = F[19,x]*F[70,x]
F[70,x] = F[71,x]+F[77,x]
F[71,x] = F[33,x]+F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[2,x]*F[23,x]
F[74,x] = F[75,x]
F[75,x] = F[19,x]*F[51,x]*F[76,x]
F[76,x] = F[2,x]+F[5,x]
F[77,x] = F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[2,x]*F[49,x]
F[80,x] = F[81,x]
F[81,x] = F[19,x]*F[51,x]*F[82,x]
F[82,x] = F[5,x]+F[83,x]
F[83,x] = F[5,x]+F[84,x]
F[84,x] = -F[92,x]+F[85,x]
F[85,x] = -F[88,x]+F[86,x]
F[86,x] = 1/F[19,x]*F[87,x]
F[87,x] = F[6,x]
F[88,x] = F[89,x]
F[89,x] = F[19,x]*F[90,x]
F[90,x] = 1/F[19,x]*F[91,x]
F[91,x] = F[37,x]
F[92,x] = F[2,x]+F[6,x]
F[93,x] = F[94,x]
F[94,x] = F[80,x]+F[95,x]
F[95,x] = F[0,x]*F[49,x]
F[96,x] = F[97,x]
F[97,x] = F[19,x]*F[98,x]*F[99,x]
F[98,x] = F[37,x]+F[4,x]
F[99,x] = F[26,x]+F[53,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[19,x]*F[99,x]
F[102,x] = F[4,x]+F[83,x]
F[103,x] = F[104,x]
F[104,x] = -F[107,x]+F[105,x]
F[105,x] = 1/F[19,x]*F[106,x]
F[106,x] = F[80,x]
F[107,x] = F[108,x]
F[108,x] = F[17,x]*F[49,x]
F[109,x] = -F[126,x]+F[110,x]
F[110,x] = -F[125,x]+F[111,x]
F[111,x] = 1/F[19,x]*F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]+F[120,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[19,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[0,x]*F[20,x]
F[118,x] = F[119,x]
F[119,x] = F[19,x]*F[23,x]*F[4,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[19,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[19,x]*F[26,x]
F[124,x] = F[0,x]+F[114,x]
F[125,x] = F[122,x]
F[126,x] = F[127,x]+F[128,x]
F[127,x] = F[0,x]^2
F[128,x] = F[129,x]
F[129,x] = F[130,x]+F[2,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[19,x]
F[132,x] = F[133,x]+F[135,x]
F[133,x] = F[134,x]
F[134,x] = F[19,x]*F[4,x]*F[99,x]
F[135,x] = F[128,x]+F[136,x]
F[136,x] = F[137,x]+F[55,x]
F[137,x] = F[138,x]
F[138,x] = F[19,x]*F[53,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_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{109}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{28}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{5}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{103}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{23}\! \left(x \right) F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right) F_{37}\! \left(x \right) F_{51}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{100}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{96}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{93}\! \left(x \right)
F_{46}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{72}\! \left(x \right)
F_{48}\! \left(x \right) = F_{23}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{19}\! \left(x \right) F_{76}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{65}\! \left(x \right) = F_{6}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{33}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{2}\! \left(x \right) F_{23}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{2}\! \left(x \right) F_{49}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{5}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{5}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{6}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{19}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{37}\! \left(x \right)
F_{92}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{80}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{0}\! \left(x \right) F_{49}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{19}\! \left(x \right) F_{98}\! \left(x \right) F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{99}\! \left(x \right) = F_{26}\! \left(x \right)+F_{53}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{19}\! \left(x \right) F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = F_{4}\! \left(x \right)+F_{83}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{80}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{17}\! \left(x \right) F_{49}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{125}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = \frac{F_{112}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{120}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{19}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{19}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{19}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{124}\! \left(x \right) = F_{0}\! \left(x \right)+F_{114}\! \left(x \right)
F_{125}\! \left(x \right) = F_{122}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{128}\! \left(x \right)
F_{127}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{2}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{19}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{135}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{135}\! \left(x \right) = F_{128}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{55}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{19}\! \left(x \right) F_{53}\! \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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_19(x)*F_8(x))
Eq(F_8(x), F_109(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_19(x))
Eq(F_13(x), F_14(x) + F_28(x))
Eq(F_14(x), F_15(x)*F_20(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_19(x))
Eq(F_17(x), F_18(x)/F_19(x))
Eq(F_18(x), F_5(x))
Eq(F_19(x), x)
Eq(F_20(x), F_0(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_19(x)*F_23(x))
Eq(F_23(x), F_24(x)/F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), -F_0(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_19(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_19(x)*F_30(x))
Eq(F_30(x), F_103(x) + F_31(x))
Eq(F_31(x), F_32(x)/F_19(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_23(x)*F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_19(x)*F_37(x)*F_51(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_19(x)*F_39(x))
Eq(F_39(x), F_100(x) + F_40(x))
Eq(F_40(x), F_41(x) + F_96(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_0(x)*F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_19(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_93(x))
Eq(F_46(x), F_33(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_72(x))
Eq(F_48(x), F_23(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_19(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_19(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x)/(F_19(x)*F_76(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_19(x)*F_57(x))
Eq(F_57(x), F_58(x) - F_73(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_19(x)*F_60(x))
Eq(F_60(x), F_61(x)/F_19(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_64(x) - F_66(x))
Eq(F_64(x), F_65(x)/F_19(x))
Eq(F_65(x), F_6(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_2(x)*F_20(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_19(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_77(x))
Eq(F_71(x), F_33(x) + F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_2(x)*F_23(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_19(x)*F_51(x)*F_76(x))
Eq(F_76(x), F_2(x) + F_5(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_2(x)*F_49(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_19(x)*F_51(x)*F_82(x))
Eq(F_82(x), F_5(x) + F_83(x))
Eq(F_83(x), F_5(x) + F_84(x))
Eq(F_84(x), F_85(x) - F_92(x))
Eq(F_85(x), F_86(x) - F_88(x))
Eq(F_86(x), F_87(x)/F_19(x))
Eq(F_87(x), F_6(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_19(x)*F_90(x))
Eq(F_90(x), F_91(x)/F_19(x))
Eq(F_91(x), F_37(x))
Eq(F_92(x), F_2(x) + F_6(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_80(x) + F_95(x))
Eq(F_95(x), F_0(x)*F_49(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_19(x)*F_98(x)*F_99(x))
Eq(F_98(x), F_37(x) + F_4(x))
Eq(F_99(x), F_26(x) + F_53(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_19(x)*F_99(x))
Eq(F_102(x), F_4(x) + F_83(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x) - F_107(x))
Eq(F_105(x), F_106(x)/F_19(x))
Eq(F_106(x), F_80(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_17(x)*F_49(x))
Eq(F_109(x), F_110(x) - F_126(x))
Eq(F_110(x), F_111(x) - F_125(x))
Eq(F_111(x), F_112(x)/F_19(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x) + F_120(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_19(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_0(x)*F_20(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_19(x)*F_23(x)*F_4(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_19(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_19(x)*F_26(x))
Eq(F_124(x), F_0(x) + F_114(x))
Eq(F_125(x), F_122(x))
Eq(F_126(x), F_127(x) + F_128(x))
Eq(F_127(x), F_0(x)**2)
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x) + F_2(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_19(x))
Eq(F_132(x), F_133(x) + F_135(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_19(x)*F_4(x)*F_99(x))
Eq(F_135(x), F_128(x) + F_136(x))
Eq(F_136(x), F_137(x) + F_55(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_19(x)*F_53(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": 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[0, 4], [3, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 1], [3, 2], [3, 1], [3, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[3, 0], [3, 1], [3, 4], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 4], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 2], [3, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 4], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 2], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 0], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[3, 0], [3, 1], [3, 4], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 4], [0, 2]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 1], [3, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[3, 0], [3, 4], [3, 1], [3, 1], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 2], [0, 4], [0, 4], [0, 2], [0, 2]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [3, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 1], [2, 1], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 1], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 1], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 4], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[3, 0], [3, 4], [3, 1], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 2]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25337/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[19,x]*F[8,x]
F[8,x] = F[109,x]+F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[0,x]*F[2,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[14,x]+F[28,x]
F[14,x] = F[15,x]*F[20,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[19,x]
F[17,x] = 1/F[19,x]*F[18,x]
F[18,x] = F[5,x]
F[19,x] = x
F[20,x] = F[0,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[19,x]*F[23,x]
F[23,x] = 1/F[19,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[0,x]+F[26,x]
F[26,x] = 1/F[19,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = F[29,x]
F[29,x] = F[19,x]*F[30,x]
F[30,x] = F[103,x]+F[31,x]
F[31,x] = 1/F[19,x]*F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[23,x]*F[5,x]
F[35,x] = F[36,x]
F[36,x] = F[19,x]*F[37,x]*F[51,x]
F[37,x] = F[38,x]
F[38,x] = F[19,x]*F[39,x]
F[39,x] = F[100,x]+F[40,x]
F[40,x] = F[41,x]+F[96,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[0,x]*F[4,x]
F[43,x] = F[44,x]
F[44,x] = F[19,x]*F[45,x]
F[45,x] = F[46,x]+F[93,x]
F[46,x] = F[33,x]+F[47,x]
F[47,x] = F[48,x]+F[72,x]
F[48,x] = F[23,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[19,x]*F[51,x]
F[51,x] = 1/F[19,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = 1/F[19,x]/F[76,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[19,x]*F[57,x]
F[57,x] = -F[73,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[19,x]*F[60,x]
F[60,x] = 1/F[19,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = -F[66,x]+F[64,x]
F[64,x] = 1/F[19,x]*F[65,x]
F[65,x] = F[6,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[2,x]*F[20,x]
F[68,x] = F[69,x]
F[69,x] = F[19,x]*F[70,x]
F[70,x] = F[71,x]+F[77,x]
F[71,x] = F[33,x]+F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[2,x]*F[23,x]
F[74,x] = F[75,x]
F[75,x] = F[19,x]*F[51,x]*F[76,x]
F[76,x] = F[2,x]+F[5,x]
F[77,x] = F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[2,x]*F[49,x]
F[80,x] = F[81,x]
F[81,x] = F[19,x]*F[51,x]*F[82,x]
F[82,x] = F[5,x]+F[83,x]
F[83,x] = F[5,x]+F[84,x]
F[84,x] = -F[92,x]+F[85,x]
F[85,x] = -F[88,x]+F[86,x]
F[86,x] = 1/F[19,x]*F[87,x]
F[87,x] = F[6,x]
F[88,x] = F[89,x]
F[89,x] = F[19,x]*F[90,x]
F[90,x] = 1/F[19,x]*F[91,x]
F[91,x] = F[37,x]
F[92,x] = F[2,x]+F[6,x]
F[93,x] = F[94,x]
F[94,x] = F[80,x]+F[95,x]
F[95,x] = F[0,x]*F[49,x]
F[96,x] = F[97,x]
F[97,x] = F[19,x]*F[98,x]*F[99,x]
F[98,x] = F[37,x]+F[4,x]
F[99,x] = F[26,x]+F[53,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[19,x]*F[99,x]
F[102,x] = F[4,x]+F[83,x]
F[103,x] = F[104,x]
F[104,x] = -F[107,x]+F[105,x]
F[105,x] = 1/F[19,x]*F[106,x]
F[106,x] = F[80,x]
F[107,x] = F[108,x]
F[108,x] = F[17,x]*F[49,x]
F[109,x] = -F[126,x]+F[110,x]
F[110,x] = -F[125,x]+F[111,x]
F[111,x] = 1/F[19,x]*F[112,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]+F[120,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[19,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[0,x]*F[20,x]
F[118,x] = F[119,x]
F[119,x] = F[19,x]*F[23,x]*F[4,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[19,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[19,x]*F[26,x]
F[124,x] = F[0,x]+F[114,x]
F[125,x] = F[122,x]
F[126,x] = F[127,x]+F[128,x]
F[127,x] = F[0,x]^2
F[128,x] = F[129,x]
F[129,x] = F[130,x]+F[2,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[19,x]
F[132,x] = F[133,x]+F[135,x]
F[133,x] = F[134,x]
F[134,x] = F[19,x]*F[4,x]*F[99,x]
F[135,x] = F[128,x]+F[136,x]
F[136,x] = F[137,x]+F[55,x]
F[137,x] = F[138,x]
F[138,x] = F[19,x]*F[53,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_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{109}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{0}\! \left(x \right) F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{28}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{5}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{0}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{103}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{23}\! \left(x \right) F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{19}\! \left(x \right) F_{37}\! \left(x \right) F_{51}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{100}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{96}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{93}\! \left(x \right)
F_{46}\! \left(x \right) = F_{33}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{72}\! \left(x \right)
F_{48}\! \left(x \right) = F_{23}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = \frac{F_{52}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{19}\! \left(x \right) F_{76}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = \frac{F_{61}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = -F_{66}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = \frac{F_{65}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{65}\! \left(x \right) = F_{6}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right) F_{20}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{71}\! \left(x \right) = F_{33}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{2}\! \left(x \right) F_{23}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{2}\! \left(x \right) F_{49}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{5}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{5}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = -F_{92}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = \frac{F_{87}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{87}\! \left(x \right) = F_{6}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{19}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = \frac{F_{91}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{91}\! \left(x \right) = F_{37}\! \left(x \right)
F_{92}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{80}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{0}\! \left(x \right) F_{49}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{19}\! \left(x \right) F_{98}\! \left(x \right) F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{99}\! \left(x \right) = F_{26}\! \left(x \right)+F_{53}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{19}\! \left(x \right) F_{99}\! \left(x \right)
F_{102}\! \left(x \right) = F_{4}\! \left(x \right)+F_{83}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = \frac{F_{106}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{106}\! \left(x \right) = F_{80}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{17}\! \left(x \right) F_{49}\! \left(x \right)
F_{109}\! \left(x \right) = -F_{126}\! \left(x \right)+F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = -F_{125}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = \frac{F_{112}\! \left(x \right)}{F_{19}\! \left(x \right)}
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{120}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{19}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{19}\! \left(x \right) F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{19}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{124}\! \left(x \right) = F_{0}\! \left(x \right)+F_{114}\! \left(x \right)
F_{125}\! \left(x \right) = F_{122}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{128}\! \left(x \right)
F_{127}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{2}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{19}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{135}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{135}\! \left(x \right) = F_{128}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{55}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{19}\! \left(x \right) F_{53}\! \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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_19(x)*F_8(x))
Eq(F_8(x), F_109(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_0(x)*F_2(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_19(x))
Eq(F_13(x), F_14(x) + F_28(x))
Eq(F_14(x), F_15(x)*F_20(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_19(x))
Eq(F_17(x), F_18(x)/F_19(x))
Eq(F_18(x), F_5(x))
Eq(F_19(x), x)
Eq(F_20(x), F_0(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_19(x)*F_23(x))
Eq(F_23(x), F_24(x)/F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), -F_0(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_19(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_19(x)*F_30(x))
Eq(F_30(x), F_103(x) + F_31(x))
Eq(F_31(x), F_32(x)/F_19(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_23(x)*F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_19(x)*F_37(x)*F_51(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_19(x)*F_39(x))
Eq(F_39(x), F_100(x) + F_40(x))
Eq(F_40(x), F_41(x) + F_96(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_0(x)*F_4(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_19(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_93(x))
Eq(F_46(x), F_33(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_72(x))
Eq(F_48(x), F_23(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_19(x)*F_51(x))
Eq(F_51(x), F_52(x)/F_19(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x)/(F_19(x)*F_76(x)))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_19(x)*F_57(x))
Eq(F_57(x), F_58(x) - F_73(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_19(x)*F_60(x))
Eq(F_60(x), F_61(x)/F_19(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_64(x) - F_66(x))
Eq(F_64(x), F_65(x)/F_19(x))
Eq(F_65(x), F_6(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_2(x)*F_20(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_19(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_77(x))
Eq(F_71(x), F_33(x) + F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_2(x)*F_23(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_19(x)*F_51(x)*F_76(x))
Eq(F_76(x), F_2(x) + F_5(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_2(x)*F_49(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_19(x)*F_51(x)*F_82(x))
Eq(F_82(x), F_5(x) + F_83(x))
Eq(F_83(x), F_5(x) + F_84(x))
Eq(F_84(x), F_85(x) - F_92(x))
Eq(F_85(x), F_86(x) - F_88(x))
Eq(F_86(x), F_87(x)/F_19(x))
Eq(F_87(x), F_6(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_19(x)*F_90(x))
Eq(F_90(x), F_91(x)/F_19(x))
Eq(F_91(x), F_37(x))
Eq(F_92(x), F_2(x) + F_6(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_80(x) + F_95(x))
Eq(F_95(x), F_0(x)*F_49(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_19(x)*F_98(x)*F_99(x))
Eq(F_98(x), F_37(x) + F_4(x))
Eq(F_99(x), F_26(x) + F_53(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_19(x)*F_99(x))
Eq(F_102(x), F_4(x) + F_83(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x) - F_107(x))
Eq(F_105(x), F_106(x)/F_19(x))
Eq(F_106(x), F_80(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_17(x)*F_49(x))
Eq(F_109(x), F_110(x) - F_126(x))
Eq(F_110(x), F_111(x) - F_125(x))
Eq(F_111(x), F_112(x)/F_19(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x) + F_120(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_19(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_0(x)*F_20(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_19(x)*F_23(x)*F_4(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_19(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_19(x)*F_26(x))
Eq(F_124(x), F_0(x) + F_114(x))
Eq(F_125(x), F_122(x))
Eq(F_126(x), F_127(x) + F_128(x))
Eq(F_127(x), F_0(x)**2)
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x) + F_2(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_19(x))
Eq(F_132(x), F_133(x) + F_135(x))
Eq(F_133(x), F_134(x))
Eq(F_134(x), F_19(x)*F_4(x)*F_99(x))
Eq(F_135(x), F_128(x) + F_136(x))
Eq(F_136(x), F_137(x) + F_55(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_19(x)*F_53(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 2, 3, 4, 1], [0, 2, 4, 3, 1], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 2, 3, 1], [0, 4, 3, 2, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 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, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], 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