01342_01432_10342_10432_13042_13402_14032_14302
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3024, 16612, 93276, 532320, 3076440, 17960372, 105730364, 626798512, 3738195608, 22410901332, 134972816236, 816207671136, 4953805377400, 30165298629812, 184236971206108, 1128327546064976, 6927662771933464, 42633172943886356, 262932544069921740, 1624844032283594112, 10059853795971239800, 62392495829113437172, 387602847698145984956, 2411643590507017314416, 15027002649528267321880, 93762577620375225247700, 585804175015592142139692, 3664473192545393695980704, 22949832227871798151698040, 143890172458190005721257780, 903114914788869484596461468, 5674053471566432078850084240, 35683062317504275545249374744, 224610577886291746799475336596, 1415076832614936140075866997388, 8922673908381772304870490900160, 56306649685926426074520318988920, 355598104379134980593178576602740, 2247400919876018947572498063771516, 14213797259386916288654050027060144, 89957201557566446993886589303416088, 569700377757212657075535972873776468, 3610197422520908548203800992249752556, 22891749157723822204954743399127496672, 145238194133169301471151619139718528888, 921992309370998225762457333914737530292, 5856114872629077235339537522977982829916, 37215116538596438258504046234822784743120, 236618544033594230959691941125976305678104, 1505186273033360558589606593708677109771028, 9579363189901278121408922777408894523066700, 60993159691658057575076345184383657962699776, 388523445601351970539128481069021320577923448, 2475932173888325615980987529144483654674731252, 15784824477353343159808259046172204588411462972, 100673375301629718007740335270562557517544131312, 642329650815469579632882001255933623728752514072, 4099818452041367793455938063905491630610589616852, 26177590409663244783097069166253032336889135740588, 167204661698770896879821366975392980727063719591712, 1068356632215997048535015223274631466412659495328888, 6828557168134573806978557591944578928238986385065012, 43659859497570598887539733759627537303522817202107164, 279236655516210472944791849778078829842308543649448976, 1786468726479316858193975465929479265776913161068361752, 11432669372834507901584675076600586686726993398415407252, 73185592168002438314527391524379394796412522966172798988, 468625462834034909336255648391128006759523819972446940480, 3001547854540994327726610612392752984982464676034125251704, 19230059967451469135825153449259512194672420294698336861044, 123233555854898152628718538730716878082751006339578226375420, 789927815332559252898780119684561400903740584394968351075888, 5064693126080748903714049214784957077367032849528727911358232, 32480558537366642016261670891380129821095844182758836710187092, 208351140420908019977648164058912246754429367490708221398675820, 1336804276551692557415747274568115753377759956772780408155730528, 8579004999086802818960402079232070704295302396802870259791990136, 55068196030819430635523899579279617727691735783909172018719900340, 353555320679793542067846719383797633523220482887659062730136746204, 2270410285068147730574637152386129131665776603605365999014937843024, 14582758028013781630570141053832404469189914575639834848937209939224, 93683117767444961381948702699812622192423294074860243099641152499220, 601959671881024594121804948801297751913903699018065448973857889744588, 3868619093962830992778613836465442335980763733378968461910072071010944, 24867105545578622169466434324604916543162772938433912873662993541485432, 159872378210002791289822668615423154861523645855143664712448905815680500, 1028013598363524434883622696429031029366939648800864480370744843229341884, 6611497821665414128561620427877208583535223039212942195165955829832566128, 42527987932324394473575797881555037080076563208708924255086747256081638936, 273603873343444384508451150864596532628726382936254302937185277788843658708, 1760518422989920881265488205253834926609046592879017855250261277713030298668, 11329960076872367917603957991339033229340005833757775912174629087301103530400, 72926311259735658566063158325049644296205991103988308804562823838012471292536, 469468877829671136144815867813435357078241687112339792467599888023416282083636
Implicit equation for the generating function in Maple syntax:
(2*x^4-4*x^3+5*x^2-4*x+2)*F(x)^4+(7*x^3-17*x^2+18*x-10)*F(x)^3+(12*x^2-24*x+18)*F(x)^2+(10*x-14)*F(x)+4 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{4}-4 x^{3}+5 x^{2}-4 x +2\right) F \! \left(x \right)^{4}+\left(7 x^{3}-17 x^{2}+18 x -10\right) F \! \left(x \right)^{3}+\left(12 x^{2}-24 x +18\right) F \! \left(x \right)^{2}+\left(10 x -14\right) F \! \left(x \right)+4 = 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) = 3024
a(8) = 16612
a(9) = 93276
a(10) = 532320
a(11) = 3076440
a(12) = 17960372
a(13) = 105730364
a(14) = 626798512
a(15) = 3738195608
a(16) = 22410901332
a(17) = 134972816236
a(n+18) = 2457/8*(n+1)*(n+2)*(n+3)/(n+18)/(n+17)/(n+16)*a(n)-27/8*(1335*n+4699)*(n+3)*(n+2)/(n+18)/(n+17)/(n+16)*a(n+1)+9/8*(n+3)*(19981*n^2+161975*n+331664)/(n+18)/(n+17)/(n+16)*a(n+2)-1/8*(353299*n^3+4893588*n^2+22930553*n+35994540)/(n+18)/(n+17)/(n+16)*a(n+3)+1/32*(478769*n^3+8273982*n^2+50887063*n+105084210)/(n+18)/(n+17)/(n+16)*a(n+4)+1/32*(4269907*n^3+77123406*n^2+471299549*n+979111590)/(n+18)/(n+17)/(n+16)*a(n+5)-1/16*(4180985*n^3+74144124*n^2+435083365*n+841327344)/(n+18)/(n+17)/(n+16)*a(n+6)+1/16*(4575514*n^3+79382985*n^2+438654482*n+744991554)/(n+18)/(n+17)/(n+16)*a(n+7)-1/32*(5971595*n^3+98990334*n^2+477395227*n+525021234)/(n+18)/(n+17)/(n+16)*a(n+8)+3/32*(630305*n^3+9754982*n^2+37491381*n-1217762)/(n+18)/(n+17)/(n+16)*a(n+9)+1/16*(96032*n^3-379494*n^2-35788415*n-223758570)/(n+18)/(n+17)/(n+16)*a(n+10)+1/16*(467305*n^3+18371355*n^2+230492282*n+936832956)/(n+18)/(n+17)/(n+16)*a(n+11)-3/8*(102243*n^3+3771475*n^2+46165095*n+187727336)/(n+18)/(n+17)/(n+16)*a(n+12)+1/8*(196559*n^3+7544622*n^2+96527989*n+411747864)/(n+18)/(n+17)/(n+16)*a(n+13)-1/4*(39043*n^3+1585665*n^2+21472097*n+96955884)/(n+18)/(n+17)/(n+16)*a(n+14)+1/4*(9623*n^3+414993*n^2+5964820*n+28576542)/(n+18)/(n+17)/(n+16)*a(n+15)-1/2*(712*n^2+21191*n+157722)/(n+17)/(n+18)*a(n+16)+(29*n+447)/(n+18)*a(n+17), n >= 18
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) = 3024
a(8) = 16612
a(9) = 93276
a(10) = 532320
a(11) = 3076440
a(12) = 17960372
a(13) = 105730364
a(14) = 626798512
a(15) = 3738195608
a(16) = 22410901332
a(17) = 134972816236
a{\left(n + 18 \right)} = \frac{2457 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) a{\left(n \right)}}{8 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} - \frac{27 \left(n + 2\right) \left(n + 3\right) \left(1335 n + 4699\right) a{\left(n + 1 \right)}}{8 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{9 \left(n + 3\right) \left(19981 n^{2} + 161975 n + 331664\right) a{\left(n + 2 \right)}}{8 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{\left(29 n + 447\right) a{\left(n + 17 \right)}}{n + 18} - \frac{\left(712 n^{2} + 21191 n + 157722\right) a{\left(n + 16 \right)}}{2 \left(n + 17\right) \left(n + 18\right)} + \frac{\left(9623 n^{3} + 414993 n^{2} + 5964820 n + 28576542\right) a{\left(n + 15 \right)}}{4 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} - \frac{\left(39043 n^{3} + 1585665 n^{2} + 21472097 n + 96955884\right) a{\left(n + 14 \right)}}{4 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{\left(96032 n^{3} - 379494 n^{2} - 35788415 n - 223758570\right) a{\left(n + 10 \right)}}{16 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} - \frac{3 \left(102243 n^{3} + 3771475 n^{2} + 46165095 n + 187727336\right) a{\left(n + 12 \right)}}{8 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{\left(196559 n^{3} + 7544622 n^{2} + 96527989 n + 411747864\right) a{\left(n + 13 \right)}}{8 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} - \frac{\left(353299 n^{3} + 4893588 n^{2} + 22930553 n + 35994540\right) a{\left(n + 3 \right)}}{8 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{\left(467305 n^{3} + 18371355 n^{2} + 230492282 n + 936832956\right) a{\left(n + 11 \right)}}{16 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{\left(478769 n^{3} + 8273982 n^{2} + 50887063 n + 105084210\right) a{\left(n + 4 \right)}}{32 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{3 \left(630305 n^{3} + 9754982 n^{2} + 37491381 n - 1217762\right) a{\left(n + 9 \right)}}{32 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} - \frac{\left(4180985 n^{3} + 74144124 n^{2} + 435083365 n + 841327344\right) a{\left(n + 6 \right)}}{16 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{\left(4269907 n^{3} + 77123406 n^{2} + 471299549 n + 979111590\right) a{\left(n + 5 \right)}}{32 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} + \frac{\left(4575514 n^{3} + 79382985 n^{2} + 438654482 n + 744991554\right) a{\left(n + 7 \right)}}{16 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)} - \frac{\left(5971595 n^{3} + 98990334 n^{2} + 477395227 n + 525021234\right) a{\left(n + 8 \right)}}{32 \left(n + 16\right) \left(n + 17\right) \left(n + 18\right)}, \quad n \geq 18
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/24557/
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[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[26,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[26,x]
F[11,x] = 1/F[26,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[26,x]
F[17,x] = F[18,x]+F[27,x]
F[18,x] = F[19,x]*F[2,x]
F[19,x] = 1/F[26,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[13,x]+F[22,x]
F[22,x] = 1/F[26,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[0,x]+F[4,x]
F[26,x] = x
F[27,x] = F[0,x]*F[28,x]*F[35,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = (1+F[29,x])*x+F[29,x]^2
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[34,x]+F[32,x]
F[32,x] = 1/F[26,x]*F[33,x]
F[33,x] = F[2,x]
F[34,x] = 2+F[34,x]^2+(-2+x)*F[34,x]
F[35,x] = 1/F[26,x]/F[34,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[34,x]+F[38,x]
F[38,x] = 1/F[0,x]*F[39,x]
F[39,x] = -F[42,x]+F[40,x]
F[40,x] = 1/F[26,x]*F[41,x]
F[41,x] = F[28,x]
F[42,x] = -F[45,x]+F[43,x]
F[43,x] = 1/F[26,x]*F[44,x]
F[44,x] = F[30,x]
F[45,x] = F[2,x]*F[38,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_{26}\! \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_{26}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{26}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{0}\! \left(x \right) F_{28}\! \left(x \right) F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}+x
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)
F_{34}\! \left(x \right) = F_{34}\! \left(x \right) x +F_{34} \left(x \right)^{2}-2 F_{34}\! \left(x \right)+2
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{26}\! \left(x \right) F_{34}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{28}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{30}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right) F_{38}\! \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_26(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_26(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_26(x))
Eq(F_11(x), F_12(x)/F_26(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_26(x))
Eq(F_17(x), F_18(x) + F_27(x))
Eq(F_18(x), F_19(x)*F_2(x))
Eq(F_19(x), F_20(x)/F_26(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_13(x) + F_22(x))
Eq(F_22(x), F_23(x)/F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), -F_0(x) + F_4(x))
Eq(F_26(x), x)
Eq(F_27(x), F_0(x)*F_28(x)*F_35(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), (x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2 + F_29(x) + 2)
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_32(x) - F_34(x))
Eq(F_32(x), F_33(x)/F_26(x))
Eq(F_33(x), F_2(x))
Eq(F_34(x), (x - 2)*F_34(x) + F_34(x)**2 + 2)
Eq(F_35(x), F_36(x)/(F_26(x)*F_34(x)))
Eq(F_36(x), F_37(x))
Eq(F_37(x), -F_34(x) + F_38(x))
Eq(F_38(x), F_39(x)/F_0(x))
Eq(F_39(x), F_40(x) - F_42(x))
Eq(F_40(x), F_41(x)/F_26(x))
Eq(F_41(x), F_28(x))
Eq(F_42(x), F_43(x) - F_45(x))
Eq(F_43(x), F_44(x)/F_26(x))
Eq(F_44(x), F_30(x))
Eq(F_45(x), F_2(x)*F_38(x))
Pack JSON:
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Specification JSON:
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{"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 2], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25044/
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[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[26,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[26,x]
F[11,x] = 1/F[26,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[26,x]
F[17,x] = F[18,x]+F[27,x]
F[18,x] = F[19,x]*F[2,x]
F[19,x] = 1/F[26,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[13,x]+F[22,x]
F[22,x] = 1/F[26,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[0,x]+F[4,x]
F[26,x] = x
F[27,x] = F[0,x]*F[28,x]*F[35,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = (1+F[29,x])*x+F[29,x]^2
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[34,x]+F[32,x]
F[32,x] = 1/F[26,x]*F[33,x]
F[33,x] = F[2,x]
F[34,x] = 2+F[34,x]^2+(-2+x)*F[34,x]
F[35,x] = 1/F[26,x]/F[34,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[34,x]+F[38,x]
F[38,x] = 1/F[0,x]*F[39,x]
F[39,x] = -F[42,x]+F[40,x]
F[40,x] = 1/F[26,x]*F[41,x]
F[41,x] = F[28,x]
F[42,x] = -F[45,x]+F[43,x]
F[43,x] = 1/F[26,x]*F[44,x]
F[44,x] = F[30,x]
F[45,x] = F[2,x]*F[38,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_{26}\! \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_{26}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{26}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{0}\! \left(x \right) F_{28}\! \left(x \right) F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}+x
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)
F_{34}\! \left(x \right) = F_{34}\! \left(x \right) x +F_{34} \left(x \right)^{2}-2 F_{34}\! \left(x \right)+2
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{26}\! \left(x \right) F_{34}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{28}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{30}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right) F_{38}\! \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_26(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_26(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_26(x))
Eq(F_11(x), F_12(x)/F_26(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_26(x))
Eq(F_17(x), F_18(x) + F_27(x))
Eq(F_18(x), F_19(x)*F_2(x))
Eq(F_19(x), F_20(x)/F_26(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_13(x) + F_22(x))
Eq(F_22(x), F_23(x)/F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), -F_0(x) + F_4(x))
Eq(F_26(x), x)
Eq(F_27(x), F_0(x)*F_28(x)*F_35(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), (x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2 + F_29(x) + 2)
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_32(x) - F_34(x))
Eq(F_32(x), F_33(x)/F_26(x))
Eq(F_33(x), F_2(x))
Eq(F_34(x), (x - 2)*F_34(x) + F_34(x)**2 + 2)
Eq(F_35(x), F_36(x)/(F_26(x)*F_34(x)))
Eq(F_36(x), F_37(x))
Eq(F_37(x), -F_34(x) + F_38(x))
Eq(F_38(x), F_39(x)/F_0(x))
Eq(F_39(x), F_40(x) - F_42(x))
Eq(F_40(x), F_41(x)/F_26(x))
Eq(F_41(x), F_28(x))
Eq(F_42(x), F_43(x) - F_45(x))
Eq(F_43(x), F_44(x)/F_26(x))
Eq(F_44(x), F_30(x))
Eq(F_45(x), F_2(x)*F_38(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 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[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], 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0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, "idx": 1}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 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, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 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2], "pos": [[3, 0], [3, 0], [3, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [6, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [6, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 2], [4, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 2], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 2], [3, 0], [3, 2], [3, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 2], [3, 2], [3, 0], [3, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[3, 2], [3, 0], [3, 2], [3, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[3, 2], [3, 2], [3, 0], [3, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 2], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": true}}]}
Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://www.permpal.com/tree/25381/
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[26,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[26,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[26,x]
F[11,x] = 1/F[26,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[26,x]
F[17,x] = F[18,x]+F[27,x]
F[18,x] = F[19,x]*F[2,x]
F[19,x] = 1/F[26,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[13,x]+F[22,x]
F[22,x] = 1/F[26,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = -F[2,x]+F[25,x]
F[25,x] = -F[0,x]+F[4,x]
F[26,x] = x
F[27,x] = F[0,x]*F[28,x]*F[35,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = (1+F[29,x])*x+F[29,x]^2
F[30,x] = -F[2,x]+F[31,x]
F[31,x] = -F[34,x]+F[32,x]
F[32,x] = 1/F[26,x]*F[33,x]
F[33,x] = F[2,x]
F[34,x] = 2+F[34,x]^2+(-2+x)*F[34,x]
F[35,x] = 1/F[26,x]/F[34,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = -F[34,x]+F[38,x]
F[38,x] = 1/F[0,x]*F[39,x]
F[39,x] = -F[42,x]+F[40,x]
F[40,x] = 1/F[26,x]*F[41,x]
F[41,x] = F[28,x]
F[42,x] = -F[45,x]+F[43,x]
F[43,x] = 1/F[26,x]*F[44,x]
F[44,x] = F[30,x]
F[45,x] = F[2,x]*F[38,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_{26}\! \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_{26}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{26}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{27}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = x
F_{27}\! \left(x \right) = F_{0}\! \left(x \right) F_{28}\! \left(x \right) F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}+x
F_{30}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = \frac{F_{33}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)
F_{34}\! \left(x \right) = F_{34}\! \left(x \right) x +F_{34} \left(x \right)^{2}-2 F_{34}\! \left(x \right)+2
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{26}\! \left(x \right) F_{34}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{39}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{28}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{45}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = \frac{F_{44}\! \left(x \right)}{F_{26}\! \left(x \right)}
F_{44}\! \left(x \right) = F_{30}\! \left(x \right)
F_{45}\! \left(x \right) = F_{2}\! \left(x \right) F_{38}\! \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_26(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_26(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_26(x))
Eq(F_11(x), F_12(x)/F_26(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_26(x))
Eq(F_17(x), F_18(x) + F_27(x))
Eq(F_18(x), F_19(x)*F_2(x))
Eq(F_19(x), F_20(x)/F_26(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_13(x) + F_22(x))
Eq(F_22(x), F_23(x)/F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), -F_2(x) + F_25(x))
Eq(F_25(x), -F_0(x) + F_4(x))
Eq(F_26(x), x)
Eq(F_27(x), F_0(x)*F_28(x)*F_35(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), (x - 3)*(F_29(x) + 1) + (F_29(x) + 1)**2 + F_29(x) + 2)
Eq(F_30(x), -F_2(x) + F_31(x))
Eq(F_31(x), F_32(x) - F_34(x))
Eq(F_32(x), F_33(x)/F_26(x))
Eq(F_33(x), F_2(x))
Eq(F_34(x), (x - 2)*F_34(x) + F_34(x)**2 + 2)
Eq(F_35(x), F_36(x)/(F_26(x)*F_34(x)))
Eq(F_36(x), F_37(x))
Eq(F_37(x), -F_34(x) + F_38(x))
Eq(F_38(x), F_39(x)/F_0(x))
Eq(F_39(x), F_40(x) - F_42(x))
Eq(F_40(x), F_41(x)/F_26(x))
Eq(F_41(x), F_28(x))
Eq(F_42(x), F_43(x) - F_45(x))
Eq(F_43(x), F_44(x)/F_26(x))
Eq(F_44(x), F_30(x))
Eq(F_45(x), F_2(x)*F_38(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 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[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], 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3]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 3], [2, 3], [2, 3], [2, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 2], [4, 2], [4, 2], [4, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[5, 2], [5, 2], [5, 2], [5, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [6, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [6, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 2], [4, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [4, 2], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[3, 2], [3, 0], [3, 2], [3, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 2], [3, 2], [3, 0], [3, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[3, 2], [3, 0], [3, 2], [3, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[3, 2], [3, 2], [3, 0], [3, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[3, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[3, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 2], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": true}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25392/
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[25,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[25,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[25,x]
F[11,x] = 1/F[25,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[25,x]
F[17,x] = F[18,x]+F[26,x]
F[18,x] = F[19,x]*F[2,x]
F[19,x] = 1/F[25,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[13,x]+F[22,x]
F[22,x] = 1/F[25,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = -F[2,x]+F[5,x]
F[25,x] = x
F[26,x] = F[0,x]*F[27,x]*F[30,x]
F[27,x] = -F[0,x]+F[28,x]
F[28,x] = 1/F[25,x]*F[29,x]
F[29,x] = F[2,x]
F[30,x] = 1/F[25,x]/F[43,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = -F[43,x]+F[33,x]
F[33,x] = 1/F[0,x]*F[34,x]
F[34,x] = -F[37,x]+F[35,x]
F[35,x] = 1/F[25,x]*F[36,x]
F[36,x] = F[27,x]
F[37,x] = -F[42,x]+F[38,x]
F[38,x] = 1/F[25,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[41,x]+F[27,x]
F[41,x] = (1+F[41,x])*x+F[41,x]^2
F[42,x] = F[2,x]*F[33,x]
F[43,x] = 2+F[43,x]^2+(-2+x)*F[43,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_{25}\! \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_{25}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{25}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = x
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{25}\! \left(x \right) F_{43}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{34}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{27}\! \left(x \right)
F_{41}\! \left(x \right) = F_{41}\! \left(x \right) x +F_{41} \left(x \right)^{2}+x
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{33}\! \left(x \right)
F_{43}\! \left(x \right) = F_{43}\! \left(x \right) x +F_{43} \left(x \right)^{2}-2 F_{43}\! \left(x \right)+2
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_25(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_25(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_25(x))
Eq(F_11(x), F_12(x)/F_25(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_25(x))
Eq(F_17(x), F_18(x) + F_26(x))
Eq(F_18(x), F_19(x)*F_2(x))
Eq(F_19(x), F_20(x)/F_25(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_13(x) + F_22(x))
Eq(F_22(x), F_23(x)/F_25(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), -F_2(x) + F_5(x))
Eq(F_25(x), x)
Eq(F_26(x), F_0(x)*F_27(x)*F_30(x))
Eq(F_27(x), -F_0(x) + F_28(x))
Eq(F_28(x), F_29(x)/F_25(x))
Eq(F_29(x), F_2(x))
Eq(F_30(x), F_31(x)/(F_25(x)*F_43(x)))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x) - F_43(x))
Eq(F_33(x), F_34(x)/F_0(x))
Eq(F_34(x), F_35(x) - F_37(x))
Eq(F_35(x), F_36(x)/F_25(x))
Eq(F_36(x), F_27(x))
Eq(F_37(x), F_38(x) - F_42(x))
Eq(F_38(x), F_39(x)/F_25(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_27(x) - F_41(x))
Eq(F_41(x), (x - 3)*(F_41(x) + 1) + (F_41(x) + 1)**2 + F_41(x) + 2)
Eq(F_42(x), F_2(x)*F_33(x))
Eq(F_43(x), (x - 2)*F_43(x) + F_43(x)**2 + 2)
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 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": 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"pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 2], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 2], [3, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 2], [4, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 0], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 0], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[4, 0], [4, 2], [4, 2], [4, 0], [4, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 2], [3, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[3, 0], [3, 2], [3, 2], [3, 0], [3, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[4, 0], [4, 2], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[6, 0], [6, 0], [6, 0], [6, 0], [6, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[2, 3]]}], [{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://www.permpal.com/tree/25696/
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[25,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[25,x]*F[7,x]
F[7,x] = F[13,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[25,x]
F[11,x] = 1/F[25,x]*F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[2,x]*F[4,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[25,x]
F[17,x] = F[18,x]+F[26,x]
F[18,x] = F[19,x]*F[2,x]
F[19,x] = 1/F[25,x]*F[20,x]
F[20,x] = F[21,x]
F[21,x] = -F[13,x]+F[22,x]
F[22,x] = 1/F[25,x]*F[23,x]
F[23,x] = F[24,x]
F[24,x] = -F[2,x]+F[5,x]
F[25,x] = x
F[26,x] = F[0,x]*F[27,x]*F[30,x]
F[27,x] = -F[0,x]+F[28,x]
F[28,x] = 1/F[25,x]*F[29,x]
F[29,x] = F[2,x]
F[30,x] = 1/F[25,x]/F[43,x]*F[31,x]
F[31,x] = F[32,x]
F[32,x] = -F[43,x]+F[33,x]
F[33,x] = 1/F[0,x]*F[34,x]
F[34,x] = -F[37,x]+F[35,x]
F[35,x] = 1/F[25,x]*F[36,x]
F[36,x] = F[27,x]
F[37,x] = -F[42,x]+F[38,x]
F[38,x] = 1/F[25,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[41,x]+F[27,x]
F[41,x] = (1+F[41,x])*x+F[41,x]^2
F[42,x] = F[2,x]*F[33,x]
F[43,x] = 2+F[43,x]^2+(-2+x)*F[43,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_{25}\! \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_{25}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{11}\! \left(x \right) = \frac{F_{12}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{25}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = \frac{F_{20}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = \frac{F_{23}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)
F_{25}\! \left(x \right) = x
F_{26}\! \left(x \right) = F_{0}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)
F_{30}\! \left(x \right) = \frac{F_{31}\! \left(x \right)}{F_{25}\! \left(x \right) F_{43}\! \left(x \right)}
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = -F_{43}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{34}\! \left(x \right) = -F_{37}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = \frac{F_{36}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{42}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{25}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{27}\! \left(x \right)
F_{41}\! \left(x \right) = F_{41}\! \left(x \right) x +F_{41} \left(x \right)^{2}+x
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{33}\! \left(x \right)
F_{43}\! \left(x \right) = F_{43}\! \left(x \right) x +F_{43} \left(x \right)^{2}-2 F_{43}\! \left(x \right)+2
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_25(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_25(x)*F_7(x))
Eq(F_7(x), F_13(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_25(x))
Eq(F_11(x), F_12(x)/F_25(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_2(x)*F_4(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_25(x))
Eq(F_17(x), F_18(x) + F_26(x))
Eq(F_18(x), F_19(x)*F_2(x))
Eq(F_19(x), F_20(x)/F_25(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), -F_13(x) + F_22(x))
Eq(F_22(x), F_23(x)/F_25(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), -F_2(x) + F_5(x))
Eq(F_25(x), x)
Eq(F_26(x), F_0(x)*F_27(x)*F_30(x))
Eq(F_27(x), -F_0(x) + F_28(x))
Eq(F_28(x), F_29(x)/F_25(x))
Eq(F_29(x), F_2(x))
Eq(F_30(x), F_31(x)/(F_25(x)*F_43(x)))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x) - F_43(x))
Eq(F_33(x), F_34(x)/F_0(x))
Eq(F_34(x), F_35(x) - F_37(x))
Eq(F_35(x), F_36(x)/F_25(x))
Eq(F_36(x), F_27(x))
Eq(F_37(x), F_38(x) - F_42(x))
Eq(F_38(x), F_39(x)/F_25(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_27(x) - F_41(x))
Eq(F_41(x), (x - 3)*(F_41(x) + 1) + (F_41(x) + 1)**2 + F_41(x) + 2)
Eq(F_42(x), F_2(x)*F_33(x))
Eq(F_43(x), (x - 2)*F_43(x) + F_43(x)**2 + 2)
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
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