02341_02431_03142_03241_03421_04132_04231_04321
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3034, 16804, 95612, 555492, 3281540, 19651112, 119018910, 727787376, 4487009062, 27861031928, 174075973624, 1093613391100, 6904102948136, 43777015956520, 278670507264640, 1780243538278168, 11409619073142716, 73340564797472456, 472707007354933214, 3054362834015095400, 19780941212654175178, 128379945643447396240, 834844153061932738914, 5438918034359620454692, 35494846453209702822230, 232014817000595702299080, 1518868658236297561127784, 9957245318507752548539492, 65363692387445564404593156, 429614886065543037722873296, 2827073998671356824855558220, 18624401809746407109879813184, 122825679080911533671750297672, 810837922902837937872541442760, 5357906033119850305622025430064, 35436597713443881870963583498160, 234577309208622110159096964198784, 1554102008207035098259484254774496, 10304246964848545066808374397661148, 68372423836758859514705173577701888, 454003739016769769403442221052972468, 3016742795234805222547059229845870720, 20058804129382143689552434397168175750, 133459026325991403281008956462372818952, 888497056890735824956265276276721096362, 5918597093542007146247006930366836714944, 39448138473325907242374037122132731954990, 263069180883301812394218073348822107843524, 1755255858087038022723776787528688283353226, 11717356516953219599813018044931450266587720, 78258191457460925919199413232550932864987562, 522917921456082544709742393019844533749208780, 3495697061919783483078037657087909680364079330, 23378892895343077199996497839804260212788062832, 156421936665732439788053333757816324566928296958, 1047005417442832561729181652959516381645498108556, 7010871872931817423666042671709003375218224074334, 46963614373137194906684113683246501382365458674688, 314711188992455822584420241095109489647394055674512, 2109692149235743000217977905012246176653219504388132, 14147428006151097648753972715590832398471712548130564, 94903642856020936070621560833861216040593960699559104, 636840887953573661797925069686972721591601363043668632, 4274817018709648746065500365230550384117590553698794528, 28703754049594161873848422671519711284792800150131720188, 192792734326187100051500011135685855584791022224529795496, 1295298278106715016898977594348346580977025975855905564676, 8705076566613250482545818819566275268796264584736496769656, 58518844840569305475100241878697391876704396174968909166636, 393492110854802772175956446111968047351078883237954619988656, 2646612568349061244270551780439254903298616316164827576489096, 17805566987865870227210052610764351439952153566336709134197832, 119820049460749290953853330472380988441100484306308989611014416, 806508025163420838701449893119515701552501388237911899110601920, 5429886704361896854964974395192796726978470742960130553286771672, 36565640157424356330025628490314531191425604317157304012991861104, 246293804302030046676718602727187708035349036037724624534210898976, 1659316871196050305696592157834720252647912926206957593421827169424, 11181457928712192557833196103026767543727786009535993786348437939488, 75363074880611227463244307896939298867440601491506554410895011353568, 508051502139799975521406927149363429247997401327499960753462464643760, 3425656246876307349777244084780882705177340564789222529520661514168096, 23102807487895443577758256386215338091104864381739324515698414935109564, 155836350051731524280952139119749644378687655277509446134987133785719328, 1051366083335782579632324820613346205684862780515872826758058964355861892, 7094447206346073628088713693300590481238380697170687038254149816111238176, 47880738297749236989723306119838025794387730851735760704809200901981063900, 323205784593648134430713062154774940594605056108561000718044479108150435144, 2182085708855401178216771174102931154303545749813259640099945107637702707620, 14734564811359814363651432517635770774627796078797907000514497719676560131440, 99511697372192107277313494478013233897311958313671868793061204789383208592342, 672172588447312619834506391304607236413945045761322662750625688275154974382584, 4541045778490245505091947046723288446414503959978466858941956991260047994967154, 30683012702284183432823346801422390046004707655788537638865206757863750551722256
Implicit equation for the generating function in Maple syntax:
F(x)^4+(-2*x-2)*F(x)^3+(x^2+6*x-1)*F(x)^2+(-6*x+4)*F(x)+2*x-2 = 0
Implicit equation for the generating function in latex syntax:
F \! \left(x \right)^{4}+\left(-2 x -2\right) F \! \left(x \right)^{3}+\left(x^{2}+6 x -1\right) F \! \left(x \right)^{2}+\left(-6 x +4\right) F \! \left(x \right)+2 x -2 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3034
a(8) = 16804
a(9) = 95612
a(10) = 555492
a(11) = 3281540
a(12) = 19651112
a(n+13) = -48/43*(n-1)*(2*n+1)*(2*n-1)/(n+13)/(n+12)/(n+11)*a(n)-12/43*(2*n+1)*(54*n^2-75*n-4)/(n+13)/(n+12)/(n+11)*a(n+1)+12/43*(970*n^3+2735*n^2+1988*n+242)/(n+13)/(n+12)/(n+11)*a(n+2)-6/43*(7240*n^3+45110*n^2+93311*n+65802)/(n+13)/(n+12)/(n+11)*a(n+3)+10/43*(12752*n^3+129726*n^2+442825*n+509838)/(n+13)/(n+12)/(n+11)*a(n+4)-6/43*(46435*n^3+641175*n^2+2953697*n+4543646)/(n+13)/(n+12)/(n+11)*a(n+5)+1/43*(392560*n^3+6617835*n^2+37135823*n+69383538)/(n+13)/(n+12)/(n+11)*a(n+6)-5/43*(66857*n^3+1306128*n^2+8483965*n+18324186)/(n+13)/(n+12)/(n+11)*a(n+7)+1/43*(153211*n^3+3370986*n^2+24602993*n+59545710)/(n+13)/(n+12)/(n+11)*a(n+8)-1/43*(19333*n^3+450900*n^2+3424580*n+8400570)/(n+13)/(n+12)/(n+11)*a(n+9)-1/86*(20750*n^3+611295*n^2+6019213*n+19810314)/(n+13)/(n+12)/(n+11)*a(n+10)+1/86*(5951*n^2+125222*n+660732)/(n+12)/(n+13)*a(n+11)+1/86*(182*n+1853)/(n+13)*a(n+12), n >= 13
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 112
a(6) = 568
a(7) = 3034
a(8) = 16804
a(9) = 95612
a(10) = 555492
a(11) = 3281540
a(12) = 19651112
a{\left(n + 13 \right)} = - \frac{48 \left(n - 1\right) \left(2 n - 1\right) \left(2 n + 1\right) a{\left(n \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} + \frac{\left(182 n + 1853\right) a{\left(n + 12 \right)}}{86 \left(n + 13\right)} + \frac{\left(5951 n^{2} + 125222 n + 660732\right) a{\left(n + 11 \right)}}{86 \left(n + 12\right) \left(n + 13\right)} - \frac{12 \left(2 n + 1\right) \left(54 n^{2} - 75 n - 4\right) a{\left(n + 1 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} + \frac{12 \left(970 n^{3} + 2735 n^{2} + 1988 n + 242\right) a{\left(n + 2 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} - \frac{6 \left(7240 n^{3} + 45110 n^{2} + 93311 n + 65802\right) a{\left(n + 3 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} + \frac{10 \left(12752 n^{3} + 129726 n^{2} + 442825 n + 509838\right) a{\left(n + 4 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} - \frac{\left(19333 n^{3} + 450900 n^{2} + 3424580 n + 8400570\right) a{\left(n + 9 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} - \frac{\left(20750 n^{3} + 611295 n^{2} + 6019213 n + 19810314\right) a{\left(n + 10 \right)}}{86 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} - \frac{6 \left(46435 n^{3} + 641175 n^{2} + 2953697 n + 4543646\right) a{\left(n + 5 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} - \frac{5 \left(66857 n^{3} + 1306128 n^{2} + 8483965 n + 18324186\right) a{\left(n + 7 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} + \frac{\left(153211 n^{3} + 3370986 n^{2} + 24602993 n + 59545710\right) a{\left(n + 8 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)} + \frac{\left(392560 n^{3} + 6617835 n^{2} + 37135823 n + 69383538\right) a{\left(n + 6 \right)}}{43 \left(n + 11\right) \left(n + 12\right) \left(n + 13\right)}, \quad n \geq 13
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24658/
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[22,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[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[22,x]
F[12,x] = F[110,x]+F[13,x]
F[13,x] = F[14,x]+F[88,x]
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[27,x]
F[16,x] = F[17,x]+F[23,x]
F[17,x] = F[0,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[22,x]
F[20,x] = 1/F[22,x]*F[21,x]
F[21,x] = F[5,x]
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = 1/F[22,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[32,x]+F[28,x]
F[28,x] = 1/F[22,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[0,x]+F[17,x]
F[32,x] = F[33,x]
F[33,x] = F[22,x]*F[34,x]
F[34,x] = F[35,x]+F[86,x]
F[35,x] = F[0,x]*F[36,x]
F[36,x] = 1/F[79,x]*F[37,x]
F[37,x] = -F[74,x]+F[38,x]
F[38,x] = 1/F[22,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[22,x]*F[42,x]
F[42,x] = F[18,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[0,x]^2
F[45,x] = F[46,x]
F[46,x] = F[22,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[0,x]*F[15,x]
F[49,x] = F[50,x]+F[63,x]
F[50,x] = F[51,x]
F[51,x] = F[22,x]*F[4,x]*F[52,x]
F[52,x] = 1/F[22,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[17,x]*F[22,x]
F[56,x] = F[57,x]
F[57,x] = F[17,x]*F[22,x]*F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[60,x]
F[60,x] = F[16,x]*F[22,x]
F[61,x] = F[62,x]
F[62,x] = F[22,x]*F[36,x]
F[63,x] = F[64,x]
F[64,x] = F[22,x]*F[65,x]
F[65,x] = -F[73,x]+F[66,x]
F[66,x] = 1/F[22,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = -F[72,x]+F[69,x]
F[69,x] = F[23,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[22,x]*F[36,x]*F[4,x]
F[72,x] = F[17,x]*F[2,x]
F[73,x] = F[0,x]*F[25,x]
F[74,x] = F[75,x]
F[75,x] = F[22,x]*F[36,x]*F[76,x]
F[76,x] = 1/F[22,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = -F[79,x]+F[43,x]
F[79,x] = F[0,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[22,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[0,x]*F[17,x]
F[84,x] = F[85,x]
F[85,x] = F[0,x]*F[17,x]*F[22,x]*F[4,x]
F[86,x] = F[87,x]
F[87,x] = F[20,x]*F[22,x]*F[36,x]
F[88,x] = F[89,x]
F[89,x] = F[108,x]*F[22,x]*F[90,x]
F[90,x] = F[4,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[22,x]*F[93,x]
F[93,x] = F[94,x]+F[98,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[17,x]*F[4,x]
F[96,x] = F[97,x]
F[97,x] = F[0,x]*F[17,x]*F[22,x]*F[90,x]
F[98,x] = F[99,x]
F[99,x] = F[0,x]*F[100,x]*F[17,x]*F[22,x]
F[100,x] = F[101,x]+F[4,x]
F[101,x] = -F[104,x]+F[102,x]
F[102,x] = 1/F[22,x]*F[103,x]
F[103,x] = F[6,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[22,x]
F[106,x] = 1/F[22,x]*F[107,x]
F[107,x] = F[91,x]
F[108,x] = 1/F[22,x]/F[4,x]*F[109,x]
F[109,x] = F[49,x]
F[110,x] = F[111,x]
F[111,x] = F[100,x]*F[108,x]*F[22,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_{22}\! \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_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{12}\! \left(x \right) = F_{110}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{88}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{22}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{86}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{79}\! \left(x \right)}
F_{37}\! \left(x \right) = -F_{74}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{18}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{23}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{17}\! \left(x \right) F_{2}\! \left(x \right)
F_{73}\! \left(x \right) = F_{0}\! \left(x \right) F_{25}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{79}\! \left(x \right)+F_{43}\! \left(x \right)
F_{79}\! \left(x \right) = F_{0}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{22}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{36}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{108}\! \left(x \right) F_{22}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{22}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right) F_{90}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{100}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{22}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{91}\! \left(x \right)
F_{108}\! \left(x \right) = \frac{F_{109}\! \left(x \right)}{F_{22}\! \left(x \right) F_{4}\! \left(x \right)}
F_{109}\! \left(x \right) = F_{49}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{100}\! \left(x \right) F_{108}\! \left(x \right) F_{22}\! \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_22(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_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_22(x))
Eq(F_12(x), F_110(x) + F_13(x))
Eq(F_13(x), F_14(x) + F_88(x))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_27(x))
Eq(F_16(x), F_17(x) + F_23(x))
Eq(F_17(x), F_0(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_22(x))
Eq(F_20(x), F_21(x)/F_22(x))
Eq(F_21(x), F_5(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_26(x)/F_22(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x) - F_32(x))
Eq(F_28(x), F_29(x)/F_22(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), -F_0(x) + F_17(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_22(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_86(x))
Eq(F_35(x), F_0(x)*F_36(x))
Eq(F_36(x), F_37(x)/F_79(x))
Eq(F_37(x), F_38(x) - F_74(x))
Eq(F_38(x), F_39(x)/F_22(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_22(x))
Eq(F_42(x), F_18(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_0(x)**2)
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_22(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_0(x)*F_15(x))
Eq(F_49(x), F_50(x) + F_63(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_22(x)*F_4(x)*F_52(x))
Eq(F_52(x), F_53(x)/F_22(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_17(x)*F_22(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_17(x)*F_22(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_16(x)*F_22(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_22(x)*F_36(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_22(x)*F_65(x))
Eq(F_65(x), F_66(x) - F_73(x))
Eq(F_66(x), F_67(x)/F_22(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x) - F_72(x))
Eq(F_69(x), F_23(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_22(x)*F_36(x)*F_4(x))
Eq(F_72(x), F_17(x)*F_2(x))
Eq(F_73(x), F_0(x)*F_25(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_22(x)*F_36(x)*F_76(x))
Eq(F_76(x), F_77(x)/F_22(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_43(x) - F_79(x))
Eq(F_79(x), F_0(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_22(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_0(x)*F_17(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_0(x)*F_17(x)*F_22(x)*F_4(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_20(x)*F_22(x)*F_36(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_108(x)*F_22(x)*F_90(x))
Eq(F_90(x), F_4(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_22(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_98(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_17(x)*F_4(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_0(x)*F_17(x)*F_22(x)*F_90(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_0(x)*F_100(x)*F_17(x)*F_22(x))
Eq(F_100(x), F_101(x) + F_4(x))
Eq(F_101(x), F_102(x) - F_104(x))
Eq(F_102(x), F_103(x)/F_22(x))
Eq(F_103(x), F_6(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_22(x))
Eq(F_106(x), F_107(x)/F_22(x))
Eq(F_107(x), F_91(x))
Eq(F_108(x), F_109(x)/(F_22(x)*F_4(x)))
Eq(F_109(x), F_49(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_100(x)*F_108(x)*F_22(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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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, 1, 4, 2], "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, 1, 3, 2], "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, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"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, 1, 2], "pos": [[0, 0], [0, 0], [0, 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, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "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, 1, 4, 2], "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, 1, 3, 2], "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, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 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1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[5, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 3], [1, 1], [1, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 3], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 4], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 4], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [5, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[5, 0], [5, 0], [5, 0], [6, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[5, 0], [5, 0], [6, 0], [6, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[5, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 1], [1, 3], [1, 1], [1, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[4, 0], [4, 0], [4, 0], [5, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[5, 0], [5, 0], [5, 0], [6, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 4], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 4], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [6, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[5, 0], [5, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[5, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 3], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 3], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"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, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"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, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24813/
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[22,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[22,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[22,x]
F[12,x] = F[110,x]+F[13,x]
F[13,x] = F[14,x]+F[88,x]
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[27,x]
F[16,x] = F[17,x]+F[23,x]
F[17,x] = F[0,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[22,x]
F[20,x] = 1/F[22,x]*F[21,x]
F[21,x] = F[5,x]
F[22,x] = x
F[23,x] = F[24,x]
F[24,x] = F[22,x]*F[25,x]
F[25,x] = 1/F[22,x]*F[26,x]
F[26,x] = F[27,x]
F[27,x] = -F[32,x]+F[28,x]
F[28,x] = 1/F[22,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[0,x]+F[17,x]
F[32,x] = F[33,x]
F[33,x] = F[22,x]*F[34,x]
F[34,x] = F[35,x]+F[86,x]
F[35,x] = F[0,x]*F[36,x]
F[36,x] = 1/F[79,x]*F[37,x]
F[37,x] = -F[74,x]+F[38,x]
F[38,x] = 1/F[22,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[43,x]+F[41,x]
F[41,x] = 1/F[22,x]*F[42,x]
F[42,x] = F[18,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[0,x]^2
F[45,x] = F[46,x]
F[46,x] = F[22,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[0,x]*F[15,x]
F[49,x] = F[50,x]+F[63,x]
F[50,x] = F[51,x]
F[51,x] = F[22,x]*F[4,x]*F[52,x]
F[52,x] = 1/F[22,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[17,x]*F[22,x]
F[56,x] = F[57,x]
F[57,x] = F[17,x]*F[22,x]*F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[60,x]
F[60,x] = F[16,x]*F[22,x]
F[61,x] = F[62,x]
F[62,x] = F[22,x]*F[36,x]
F[63,x] = F[64,x]
F[64,x] = F[22,x]*F[65,x]
F[65,x] = -F[73,x]+F[66,x]
F[66,x] = 1/F[22,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = -F[72,x]+F[69,x]
F[69,x] = F[23,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[22,x]*F[36,x]*F[4,x]
F[72,x] = F[17,x]*F[2,x]
F[73,x] = F[0,x]*F[25,x]
F[74,x] = F[75,x]
F[75,x] = F[22,x]*F[36,x]*F[76,x]
F[76,x] = 1/F[22,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = -F[79,x]+F[43,x]
F[79,x] = F[0,x]+F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[22,x]*F[82,x]
F[82,x] = F[83,x]+F[84,x]
F[83,x] = F[0,x]*F[17,x]
F[84,x] = F[85,x]
F[85,x] = F[0,x]*F[17,x]*F[22,x]*F[4,x]
F[86,x] = F[87,x]
F[87,x] = F[20,x]*F[22,x]*F[36,x]
F[88,x] = F[89,x]
F[89,x] = F[108,x]*F[22,x]*F[90,x]
F[90,x] = F[4,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[22,x]*F[93,x]
F[93,x] = F[94,x]+F[98,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[17,x]*F[4,x]
F[96,x] = F[97,x]
F[97,x] = F[0,x]*F[17,x]*F[22,x]*F[90,x]
F[98,x] = F[99,x]
F[99,x] = F[0,x]*F[100,x]*F[17,x]*F[22,x]
F[100,x] = F[101,x]+F[4,x]
F[101,x] = -F[104,x]+F[102,x]
F[102,x] = 1/F[22,x]*F[103,x]
F[103,x] = F[6,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[22,x]
F[106,x] = 1/F[22,x]*F[107,x]
F[107,x] = F[91,x]
F[108,x] = 1/F[22,x]/F[4,x]*F[109,x]
F[109,x] = F[49,x]
F[110,x] = F[111,x]
F[111,x] = F[100,x]*F[108,x]*F[22,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_{22}\! \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_{22}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{12}\! \left(x \right) = F_{110}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{88}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{23}\! \left(x \right)
F_{17}\! \left(x \right) = F_{0}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = \frac{F_{21}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{21}\! \left(x \right) = F_{5}\! \left(x \right)
F_{22}\! \left(x \right) = x
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{32}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{22}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{86}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = \frac{F_{37}\! \left(x \right)}{F_{79}\! \left(x \right)}
F_{37}\! \left(x \right) = -F_{74}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = \frac{F_{42}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{42}\! \left(x \right) = F_{18}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{22}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = -F_{73}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = -F_{72}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{23}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{17}\! \left(x \right) F_{2}\! \left(x \right)
F_{73}\! \left(x \right) = F_{0}\! \left(x \right) F_{25}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{22}\! \left(x \right) F_{36}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = \frac{F_{77}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = -F_{79}\! \left(x \right)+F_{43}\! \left(x \right)
F_{79}\! \left(x \right) = F_{0}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{22}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{84}\! \left(x \right)
F_{83}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right) F_{36}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{108}\! \left(x \right) F_{22}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{22}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{98}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{0}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right) F_{90}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{0}\! \left(x \right) F_{100}\! \left(x \right) F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{104}\! \left(x \right)+F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = \frac{F_{103}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{103}\! \left(x \right) = F_{6}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{22}\! \left(x \right)
F_{106}\! \left(x \right) = \frac{F_{107}\! \left(x \right)}{F_{22}\! \left(x \right)}
F_{107}\! \left(x \right) = F_{91}\! \left(x \right)
F_{108}\! \left(x \right) = \frac{F_{109}\! \left(x \right)}{F_{22}\! \left(x \right) F_{4}\! \left(x \right)}
F_{109}\! \left(x \right) = F_{49}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{100}\! \left(x \right) F_{108}\! \left(x \right) F_{22}\! \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_22(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_22(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_22(x))
Eq(F_12(x), F_110(x) + F_13(x))
Eq(F_13(x), F_14(x) + F_88(x))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_27(x))
Eq(F_16(x), F_17(x) + F_23(x))
Eq(F_17(x), F_0(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_22(x))
Eq(F_20(x), F_21(x)/F_22(x))
Eq(F_21(x), F_5(x))
Eq(F_22(x), x)
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_22(x)*F_25(x))
Eq(F_25(x), F_26(x)/F_22(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x) - F_32(x))
Eq(F_28(x), F_29(x)/F_22(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), -F_0(x) + F_17(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_22(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_86(x))
Eq(F_35(x), F_0(x)*F_36(x))
Eq(F_36(x), F_37(x)/F_79(x))
Eq(F_37(x), F_38(x) - F_74(x))
Eq(F_38(x), F_39(x)/F_22(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_41(x) - F_43(x))
Eq(F_41(x), F_42(x)/F_22(x))
Eq(F_42(x), F_18(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_0(x)**2)
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_22(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_0(x)*F_15(x))
Eq(F_49(x), F_50(x) + F_63(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_22(x)*F_4(x)*F_52(x))
Eq(F_52(x), F_53(x)/F_22(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_17(x)*F_22(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_17(x)*F_22(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_16(x)*F_22(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_22(x)*F_36(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_22(x)*F_65(x))
Eq(F_65(x), F_66(x) - F_73(x))
Eq(F_66(x), F_67(x)/F_22(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x) - F_72(x))
Eq(F_69(x), F_23(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_22(x)*F_36(x)*F_4(x))
Eq(F_72(x), F_17(x)*F_2(x))
Eq(F_73(x), F_0(x)*F_25(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_22(x)*F_36(x)*F_76(x))
Eq(F_76(x), F_77(x)/F_22(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_43(x) - F_79(x))
Eq(F_79(x), F_0(x) + F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_22(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_84(x))
Eq(F_83(x), F_0(x)*F_17(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_0(x)*F_17(x)*F_22(x)*F_4(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_20(x)*F_22(x)*F_36(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_108(x)*F_22(x)*F_90(x))
Eq(F_90(x), F_4(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_22(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_98(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_17(x)*F_4(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_0(x)*F_17(x)*F_22(x)*F_90(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_0(x)*F_100(x)*F_17(x)*F_22(x))
Eq(F_100(x), F_101(x) + F_4(x))
Eq(F_101(x), F_102(x) - F_104(x))
Eq(F_102(x), F_103(x)/F_22(x))
Eq(F_103(x), F_6(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_22(x))
Eq(F_106(x), F_107(x)/F_22(x))
Eq(F_107(x), F_91(x))
Eq(F_108(x), F_109(x)/(F_22(x)*F_4(x)))
Eq(F_109(x), F_49(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_100(x)*F_108(x)*F_22(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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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:
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1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25277/
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[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[21,x]*F[7,x]
F[7,x] = F[68,x]+F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[0,x]^2
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[21,x]
F[12,x] = F[13,x]+F[64,x]
F[13,x] = F[14,x]+F[51,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[22,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = 1/F[21,x]*F[20,x]
F[20,x] = F[5,x]
F[21,x] = x
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[24,x]
F[24,x] = F[25,x]+F[49,x]
F[25,x] = F[0,x]*F[26,x]
F[26,x] = 1/F[43,x]*F[27,x]
F[27,x] = -F[38,x]+F[28,x]
F[28,x] = 1/F[21,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[8,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[0,x]*F[16,x]
F[33,x] = -F[37,x]+F[34,x]
F[34,x] = 1/F[21,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[2,x]+F[17,x]
F[37,x] = F[16,x]*F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[21,x]*F[26,x]*F[40,x]
F[40,x] = 1/F[21,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = -F[43,x]+F[8,x]
F[43,x] = F[0,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[21,x]*F[46,x]
F[46,x] = F[32,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[0,x]*F[16,x]*F[21,x]*F[4,x]
F[49,x] = F[50,x]
F[50,x] = F[19,x]*F[21,x]*F[26,x]
F[51,x] = F[52,x]
F[52,x] = F[21,x]*F[4,x]*F[53,x]
F[53,x] = 1/F[21,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[16,x]*F[21,x]
F[57,x] = F[58,x]
F[58,x] = F[16,x]*F[21,x]*F[59,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = F[61,x]
F[61,x] = F[15,x]*F[21,x]
F[62,x] = F[63,x]
F[63,x] = F[21,x]*F[26,x]
F[64,x] = F[65,x]
F[65,x] = F[21,x]*F[66,x]
F[66,x] = 1/F[21,x]*F[67,x]
F[67,x] = F[33,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = -F[16,x]+F[8,x]
F[70,x] = F[71,x]
F[71,x] = F[21,x]*F[72,x]
F[72,x] = F[73,x]+F[95,x]
F[73,x] = F[74,x]*F[93,x]
F[74,x] = -F[78,x]+F[75,x]
F[75,x] = 1/F[21,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = -F[2,x]+F[5,x]
F[78,x] = F[79,x]
F[79,x] = F[21,x]*F[80,x]
F[80,x] = 1/F[21,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[21,x]*F[84,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[16,x]*F[4,x]
F[87,x] = F[88,x]
F[88,x] = F[0,x]*F[16,x]*F[21,x]*F[89,x]
F[89,x] = F[4,x]+F[82,x]
F[90,x] = F[91,x]
F[91,x] = F[0,x]*F[16,x]*F[21,x]*F[92,x]
F[92,x] = F[4,x]+F[74,x]
F[93,x] = 1/F[21,x]/F[4,x]*F[94,x]
F[94,x] = F[69,x]
F[95,x] = F[96,x]
F[96,x] = F[21,x]*F[80,x]*F[93,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_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{21}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{68}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{64}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{51}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{22}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{49}\! \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_{43}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{17}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{0}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{32}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{21}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{33}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{8}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{21}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{95}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right) F_{93}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{21}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{21}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right)+F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{21}\! \left(x \right) F_{4}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{69}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right) F_{80}\! \left(x \right) F_{93}\! \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_21(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_21(x)*F_7(x))
Eq(F_7(x), F_68(x) + F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_0(x)**2)
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_21(x))
Eq(F_12(x), F_13(x) + F_64(x))
Eq(F_13(x), F_14(x) + F_51(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_22(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x)/F_21(x))
Eq(F_20(x), F_5(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_49(x))
Eq(F_25(x), F_0(x)*F_26(x))
Eq(F_26(x), F_27(x)/F_43(x))
Eq(F_27(x), F_28(x) - F_38(x))
Eq(F_28(x), F_29(x)/F_21(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_8(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_0(x)*F_16(x))
Eq(F_33(x), F_34(x) - F_37(x))
Eq(F_34(x), F_35(x)/F_21(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_17(x) - F_2(x))
Eq(F_37(x), F_16(x)*F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_21(x)*F_26(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_21(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), -F_43(x) + F_8(x))
Eq(F_43(x), F_0(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_21(x)*F_46(x))
Eq(F_46(x), F_32(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_0(x)*F_16(x)*F_21(x)*F_4(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_19(x)*F_21(x)*F_26(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_21(x)*F_4(x)*F_53(x))
Eq(F_53(x), F_54(x)/F_21(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_16(x)*F_21(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_16(x)*F_21(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_15(x)*F_21(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_21(x)*F_26(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_21(x)*F_66(x))
Eq(F_66(x), F_67(x)/F_21(x))
Eq(F_67(x), F_33(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), -F_16(x) + F_8(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_21(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_95(x))
Eq(F_73(x), F_74(x)*F_93(x))
Eq(F_74(x), F_75(x) - F_78(x))
Eq(F_75(x), F_76(x)/F_21(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), -F_2(x) + F_5(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_21(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_21(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_21(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_16(x)*F_4(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_0(x)*F_16(x)*F_21(x)*F_89(x))
Eq(F_89(x), F_4(x) + F_82(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_0(x)*F_16(x)*F_21(x)*F_92(x))
Eq(F_92(x), F_4(x) + F_74(x))
Eq(F_93(x), F_94(x)/(F_21(x)*F_4(x)))
Eq(F_94(x), F_69(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_21(x)*F_80(x)*F_93(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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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, 1, 4, 2], "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, 1, 3, 2], "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, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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, 1, 4, 2], "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, 1, 3, 2], "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": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]], "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, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 0], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 1], [2, 1], [2, 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], [0, 1], [2, 0]]}, {"patt": [0, 2, 3, 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3]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [4, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [6, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[5, 0], [5, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[5, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 3], [1, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 3], [1, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 3], [1, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 1], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 1], [1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"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, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 1], [1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"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, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 3], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 1], [1, 3], [1, 3], [1, 1], [1, 1]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[1, 3], [1, 3], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25477/
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[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[21,x]*F[7,x]
F[7,x] = F[68,x]+F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[0,x]^2
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[21,x]
F[12,x] = F[13,x]+F[64,x]
F[13,x] = F[14,x]+F[51,x]
F[14,x] = F[0,x]*F[15,x]
F[15,x] = F[16,x]+F[22,x]
F[16,x] = F[0,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = 1/F[21,x]*F[20,x]
F[20,x] = F[5,x]
F[21,x] = x
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[24,x]
F[24,x] = F[25,x]+F[49,x]
F[25,x] = F[0,x]*F[26,x]
F[26,x] = 1/F[43,x]*F[27,x]
F[27,x] = -F[38,x]+F[28,x]
F[28,x] = 1/F[21,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = -F[8,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[0,x]*F[16,x]
F[33,x] = -F[37,x]+F[34,x]
F[34,x] = 1/F[21,x]*F[35,x]
F[35,x] = F[36,x]
F[36,x] = -F[2,x]+F[17,x]
F[37,x] = F[16,x]*F[2,x]
F[38,x] = F[39,x]
F[39,x] = F[21,x]*F[26,x]*F[40,x]
F[40,x] = 1/F[21,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = -F[43,x]+F[8,x]
F[43,x] = F[0,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[21,x]*F[46,x]
F[46,x] = F[32,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[0,x]*F[16,x]*F[21,x]*F[4,x]
F[49,x] = F[50,x]
F[50,x] = F[19,x]*F[21,x]*F[26,x]
F[51,x] = F[52,x]
F[52,x] = F[21,x]*F[4,x]*F[53,x]
F[53,x] = 1/F[21,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[16,x]*F[21,x]
F[57,x] = F[58,x]
F[58,x] = F[16,x]*F[21,x]*F[59,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = F[61,x]
F[61,x] = F[15,x]*F[21,x]
F[62,x] = F[63,x]
F[63,x] = F[21,x]*F[26,x]
F[64,x] = F[65,x]
F[65,x] = F[21,x]*F[66,x]
F[66,x] = 1/F[21,x]*F[67,x]
F[67,x] = F[33,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = -F[16,x]+F[8,x]
F[70,x] = F[71,x]
F[71,x] = F[21,x]*F[72,x]
F[72,x] = F[73,x]+F[95,x]
F[73,x] = F[74,x]*F[93,x]
F[74,x] = -F[78,x]+F[75,x]
F[75,x] = 1/F[21,x]*F[76,x]
F[76,x] = F[77,x]
F[77,x] = -F[2,x]+F[5,x]
F[78,x] = F[79,x]
F[79,x] = F[21,x]*F[80,x]
F[80,x] = 1/F[21,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[21,x]*F[84,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[16,x]*F[4,x]
F[87,x] = F[88,x]
F[88,x] = F[0,x]*F[16,x]*F[21,x]*F[89,x]
F[89,x] = F[4,x]+F[82,x]
F[90,x] = F[91,x]
F[91,x] = F[0,x]*F[16,x]*F[21,x]*F[92,x]
F[92,x] = F[4,x]+F[74,x]
F[93,x] = 1/F[21,x]/F[4,x]*F[94,x]
F[94,x] = F[69,x]
F[95,x] = F[96,x]
F[96,x] = F[21,x]*F[80,x]*F[93,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_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{21}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{68}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{64}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{51}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{22}\! \left(x \right)
F_{16}\! \left(x \right) = F_{0}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{49}\! \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_{43}\! \left(x \right)}
F_{27}\! \left(x \right) = -F_{38}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = -F_{8}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right)
F_{33}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = \frac{F_{35}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{17}\! \left(x \right)
F_{37}\! \left(x \right) = F_{16}\! \left(x \right) F_{2}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{8}\! \left(x \right)
F_{43}\! \left(x \right) = F_{0}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{32}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = \frac{F_{54}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{21}\! \left(x \right) F_{26}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{21}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = \frac{F_{67}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{67}\! \left(x \right) = F_{33}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{8}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{21}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{95}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right) F_{93}\! \left(x \right)
F_{74}\! \left(x \right) = -F_{78}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = \frac{F_{76}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{21}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = \frac{F_{81}\! \left(x \right)}{F_{21}\! \left(x \right)}
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{21}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right)+F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{93}\! \left(x \right) = \frac{F_{94}\! \left(x \right)}{F_{21}\! \left(x \right) F_{4}\! \left(x \right)}
F_{94}\! \left(x \right) = F_{69}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right) F_{80}\! \left(x \right) F_{93}\! \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_21(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_21(x)*F_7(x))
Eq(F_7(x), F_68(x) + F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_0(x)**2)
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_21(x))
Eq(F_12(x), F_13(x) + F_64(x))
Eq(F_13(x), F_14(x) + F_51(x))
Eq(F_14(x), F_0(x)*F_15(x))
Eq(F_15(x), F_16(x) + F_22(x))
Eq(F_16(x), F_0(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x)/F_21(x))
Eq(F_20(x), F_5(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_49(x))
Eq(F_25(x), F_0(x)*F_26(x))
Eq(F_26(x), F_27(x)/F_43(x))
Eq(F_27(x), F_28(x) - F_38(x))
Eq(F_28(x), F_29(x)/F_21(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) - F_8(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_0(x)*F_16(x))
Eq(F_33(x), F_34(x) - F_37(x))
Eq(F_34(x), F_35(x)/F_21(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_17(x) - F_2(x))
Eq(F_37(x), F_16(x)*F_2(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_21(x)*F_26(x)*F_40(x))
Eq(F_40(x), F_41(x)/F_21(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), -F_43(x) + F_8(x))
Eq(F_43(x), F_0(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_21(x)*F_46(x))
Eq(F_46(x), F_32(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_0(x)*F_16(x)*F_21(x)*F_4(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_19(x)*F_21(x)*F_26(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_21(x)*F_4(x)*F_53(x))
Eq(F_53(x), F_54(x)/F_21(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_16(x)*F_21(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_16(x)*F_21(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_15(x)*F_21(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_21(x)*F_26(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_21(x)*F_66(x))
Eq(F_66(x), F_67(x)/F_21(x))
Eq(F_67(x), F_33(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), -F_16(x) + F_8(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_21(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_95(x))
Eq(F_73(x), F_74(x)*F_93(x))
Eq(F_74(x), F_75(x) - F_78(x))
Eq(F_75(x), F_76(x)/F_21(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), -F_2(x) + F_5(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_21(x)*F_80(x))
Eq(F_80(x), F_81(x)/F_21(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_21(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_16(x)*F_4(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_0(x)*F_16(x)*F_21(x)*F_89(x))
Eq(F_89(x), F_4(x) + F_82(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_0(x)*F_16(x)*F_21(x)*F_92(x))
Eq(F_92(x), F_4(x) + F_74(x))
Eq(F_93(x), F_94(x)/(F_21(x)*F_4(x)))
Eq(F_94(x), F_69(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_21(x)*F_80(x)*F_93(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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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, 1, 4, 2], [0, 3, 2, 4, 1], [0, 3, 4, 2, 1], [0, 4, 1, 3, 2], [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, 1, 4, 2], "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, 1, 3, 2], "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, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 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