0123
Counting sequence:
1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, 8026793118, 56963722223, 409687815151, 2981863943718, 21937062144834, 162958355218089, 1221225517285209, 9225729232653663, 70209849031116183, 537935616492552297, 4147342550996290153, 32159907636432567578, 250717538500344886206, 1964347085978431234383, 15462159345628498316319, 122238900487877503161969, 970325471182457981369049, 7731901754611459464735903, 61832653368034108376289951, 496160668446334564552850382, 3994086214472224958400684810, 32249846204112036294187913385, 261146030249297632826781254745, 2120413738704495091271491918311, 17261552758464209062384238420415, 140866009086566471537151898081209, 1152255093424086818438412857457849, 9446255505732220228130962386849138, 77605976120870974798789195993060854, 638871960207677801581346205579164367, 5269593719698274144801147501982966687, 43546074424949522295598762444859283222, 360492017501820666899243272287238710354, 2989408934090878413848558248661778270753, 24830657393826555485196765893826983205921, 206574286596189079647607151790696535083690, 1721167054958634098292078281770092101234190, 14361624678910184463742956388632940510913255, 120003624172906284684386496661015381966460215, 1004091144104774887710677660817469956693896745, 8412379116280362798084334420149045180372065745, 70568601965509583999700570913173211417995599895, 592696352915737141155158304414269811625180513815, 4983828752747613883243003848561875299086419040630, 41955319647630625419685121361617055093746095070610, 353580101123476925841479568326204003011381189787025, 2982977888197288460856334813286086329900346423097025, 25191788657287969133197221062365363552353299256901050, 212961320424268052901347977030889177855765566499772030, 1802029377181834115712796993284051588785701583307477375, 15262640410049981470128292795529417581977441334901620095, 129387398314734947707278520388031717793130651335477952670, 1097835224720034153995899322754387876471474783381867211290, 9322965836046640245087771386100481543888046670441363963945, 79237749083534595744697936642257664242352289961317821184985, 674001835186897558496422954604088602276698603404230666488335, 5737611940754101897559486756682025101031544701855196105472135, 48880207639106029109864037266555049485030895947642148950079945, 416732819924005168941303055847836337070209442410774562729371337, 3555466038668341332857350275274274127162098794151439103334721090, 30355769587728752808745623826992489781310960285711940894116027718, 259348585280769159504560646369419454809065606135992140143169755743, 2217260844644401237638320280695767380950809122710632793912902718511, 18968482943473256494836126285868491927854086095697960845148436589678, 162376893849878899318899310438284523510874621590336764367202718179914, 1390864613366259845262369524455394534769712512709990634859530377076609, 11920868873672887089895802144384040441724901153261718164686540398140289, 102232046258469669096254152818036014445731761404192294362275666119480858, 877235458758050882348997045255957967356358643882754929570110850354969406, 7531637198565680192062731516611219079181807754162590042062011400254364327, 64699512542681939389075983601070193856270415221569799713117236111940589815, 556090580635296504452987405926664240669895733567319894815158226296552678465, 4782089279722654653555564174798767779019085510079773058006411122399642636105, 41144549237488563265008153977719317147448681040429879974857801593735308506951, 354180358263311128614716061199670700715336234836856195961027864983928507747655, 3050347964573426902287055696017017494310536449983491222353582369799689043629414, 26283452319873828641217211734917362787974227994921162720122848413686900893393154, 226578692368982015117262691557149539633917159537843857602167268544424580799665473, 1954137034878456446059296060300693298720640130402484895134023885406082917362248049, 16861105876803276581768394583965365757440900035905243198788177363554151272115179407, 145548627762651031332656907332418264333959240176111730297392738948316871152722400487, 1256947823866067675154664190458028681729348684465570470888416528819599000104665297297, 10859495194446627827609529641750158312948557096513726987862856383462036401181159280529, 93860220237437985893457574770236665813245551911957651617770425827272968606700333900274, 811576473070327289653930381942630632511690809167683626232744908735066885957113185678326, 7020204892858844304477014923740672378993974155860488639570398897417298681700926577508839
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/1/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[15,x]*F[3,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[5,x,k[0]]
F[5,x,k[0]] = F[10,x,k[0]]*F[6,x,k[0]]
F[6,x,k[0]] = F[7,x,1,k[0]]
F[7,x,k[0],k[1]] = F[8,x,k[0]*k[1],k[1]]
F[8,x,k[0],k[1]] = F[1,x]+F[11,x,k[0],k[1]]+F[13,x,k[0],k[1]]+F[9,x,k[0],k[1]]
F[9,x,k[0],k[1]] = F[10,x,k[0]]*F[8,x,k[0],k[1]]
F[10,x,k[0]] = k[0]*x
F[11,x,k[0],k[1]] = F[10,x,k[1]]*F[12,x,k[0],k[1]]
F[12,x,k[0],k[1]] = (-F[7,x,1,k[1]]*k[1]+F[7,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[15,x]
F[14,x,k[0],k[1]] = (F[8,x,k[0],k[1]]*k[1]-F[8,x,k[0],1])/(-1+k[1])
F[15,x] = x
F[16,x,k[0]] = F[15,x]*F[17,x,k[0]]
F[17,x,k[0]] = (F[4,x,k[0]]*k[0]-F[4,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{15}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{5}\! \left(x , y\right)
F_{5}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{7}\! \left(x , 1, y\right)
F_{7}\! \left(x , y , z\right) = F_{8}\! \left(x , y z , z\right)
F_{8}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{13}\! \left(x , y , z\right)+F_{9}\! \left(x , y , z\right)
F_{9}\! \left(x , y , z\right) = F_{10}\! \left(x , y\right) F_{8}\! \left(x , y , z\right)
F_{10}\! \left(x , y\right) = y x
F_{11}\! \left(x , y , z\right) = F_{10}\! \left(x , z\right) F_{12}\! \left(x , y , z\right)
F_{12}\! \left(x , y , z\right) = \frac{-z F_{7}\! \left(x , 1, z\right)+y F_{7}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{15}\! \left(x \right)
F_{14}\! \left(x , y , z\right) = \frac{z F_{8}\! \left(x , y , z\right)-F_{8}\! \left(x , y , 1\right)}{-1+z}
F_{15}\! \left(x \right) = x
F_{16}\! \left(x , y\right) = F_{15}\! \left(x \right) F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}
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_15(x)*F_3(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_16(x, k_0) + F_5(x, k_0))
Eq(F_5(x, k_0), F_10(x, k_0)*F_6(x, k_0))
Eq(F_6(x, k_0), F_7(x, 1, k_0))
Eq(F_7(x, k_0, k_1), F_8(x, k_0*k_1, k_1))
Eq(F_8(x, k_0, k_1), F_1(x) + F_11(x, k_0, k_1) + F_13(x, k_0, k_1) + F_9(x, k_0, k_1))
Eq(F_9(x, k_0, k_1), F_10(x, k_0)*F_8(x, k_0, k_1))
Eq(F_10(x, k_0), k_0*x)
Eq(F_11(x, k_0, k_1), F_10(x, k_1)*F_12(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), (-k_0*F_7(x, k_0/k_1, k_1) + k_1*F_7(x, 1, k_1))/(-k_0 + k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_15(x))
Eq(F_14(x, k_0, k_1), (-k_1*F_8(x, k_0, k_1) + F_8(x, k_0, 1))/(1 - k_1))
Eq(F_15(x), x)
Eq(F_16(x, k_0), F_15(x)*F_17(x, k_0))
Eq(F_17(x, k_0), (-k_0*F_4(x, k_0) + F_4(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": 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"class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": 0, "row_idx": null, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 2
Strategy pack name: point_and_row_placements_tracked_fusion
Tree: http://permpal.com/tree/2/
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[16,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[6,x,k[0]]
F[6,x,k[0]] = F[11,x,k[0]]*F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = F[9,x,k[0]*k[1],k[1]]
F[9,x,k[0],k[1]] = F[1,x]+F[10,x,k[0],k[1]]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[0]]*F[9,x,k[0],k[1]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0],k[1]] = F[11,x,k[1]]*F[13,x,k[0],k[1]]
F[13,x,k[0],k[1]] = (-F[8,x,1,k[1]]*k[1]+F[8,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[16,x]
F[15,x,k[0],k[1]] = (F[9,x,k[0],k[1]]*k[1]-F[9,x,k[0],1])/(-1+k[1])
F[16,x] = x
F[17,x,k[0]] = F[16,x]*F[18,x,k[0]]
F[18,x,k[0]] = (F[5,x,k[0]]*k[0]-F[5,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , 1, y\right)
F_{8}\! \left(x , y , z\right) = F_{9}\! \left(x , y z , z\right)
F_{9}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y , z\right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{9}\! \left(x , y , z\right)
F_{11}\! \left(x , y\right) = y x
F_{12}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{13}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = -\frac{z F_{8}\! \left(x , 1, z\right)-y F_{8}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{16}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = -\frac{-z F_{9}\! \left(x , y , z\right)+F_{9}\! \left(x , y , 1\right)}{-1+z}
F_{16}\! \left(x \right) = x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
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_16(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_17(x, k_0) + F_6(x, k_0))
Eq(F_6(x, k_0), F_11(x, k_0)*F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), F_9(x, k_0*k_1, k_1))
Eq(F_9(x, k_0, k_1), F_1(x) + F_10(x, k_0, k_1) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0)*F_9(x, k_0, k_1))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0, k_1), F_11(x, k_1)*F_13(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), (-k_0*F_8(x, k_0/k_1, k_1) + k_1*F_8(x, 1, k_1))/(-k_0 + k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_16(x))
Eq(F_15(x, k_0, k_1), (-k_1*F_9(x, k_0, k_1) + F_9(x, k_0, 1))/(1 - k_1))
Eq(F_16(x), x)
Eq(F_17(x, k_0), F_16(x)*F_18(x, k_0))
Eq(F_18(x, k_0), (-k_0*F_5(x, k_0) + F_5(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], 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{"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}]}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}
Specification 3
Strategy pack name: point_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/3/
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[16,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[6,x,k[0]]
F[6,x,k[0]] = F[11,x,k[0]]*F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = F[9,x,k[0]*k[1],k[1]]
F[9,x,k[0],k[1]] = F[1,x]+F[10,x,k[0],k[1]]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[0]]*F[9,x,k[0],k[1]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0],k[1]] = F[11,x,k[1]]*F[13,x,k[0],k[1]]
F[13,x,k[0],k[1]] = (-F[8,x,1,k[1]]*k[1]+F[8,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[16,x]
F[15,x,k[0],k[1]] = (F[9,x,k[0],k[1]]*k[1]-F[9,x,k[0],1])/(-1+k[1])
F[16,x] = x
F[17,x,k[0]] = F[16,x]*F[18,x,k[0]]
F[18,x,k[0]] = (F[5,x,k[0]]*k[0]-F[5,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , 1, y\right)
F_{8}\! \left(x , y , z\right) = F_{9}\! \left(x , y z , z\right)
F_{9}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y , z\right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{9}\! \left(x , y , z\right)
F_{11}\! \left(x , y\right) = y x
F_{12}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{13}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = -\frac{z F_{8}\! \left(x , 1, z\right)-y F_{8}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{16}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = -\frac{-z F_{9}\! \left(x , y , z\right)+F_{9}\! \left(x , y , 1\right)}{-1+z}
F_{16}\! \left(x \right) = x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
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_16(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_17(x, k_0) + F_6(x, k_0))
Eq(F_6(x, k_0), F_11(x, k_0)*F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), F_9(x, k_0*k_1, k_1))
Eq(F_9(x, k_0, k_1), F_1(x) + F_10(x, k_0, k_1) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0)*F_9(x, k_0, k_1))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0, k_1), F_11(x, k_1)*F_13(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), (-k_0*F_8(x, k_0/k_1, k_1) + k_1*F_8(x, 1, k_1))/(-k_0 + k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_16(x))
Eq(F_15(x, k_0, k_1), (-k_1*F_9(x, k_0, k_1) + F_9(x, k_0, 1))/(1 - k_1))
Eq(F_16(x), x)
Eq(F_17(x, k_0), F_16(x)*F_18(x, k_0))
Eq(F_18(x, k_0), (-k_0*F_5(x, k_0) + F_5(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", 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0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 0, "strategy_class": "FusionStrategy", "tracked": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "ReverseRule"}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}]}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}]}, "class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionStrategy", "sub_assumption": {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}}}]}
Specification 4
Strategy pack name: insertion_col_placements_tracked_fusion
Tree: http://permpal.com/tree/4/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[14,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[9,x,k[0]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0]] = F[13,x,k[0]]*F[4,x]
F[13,x,k[0]] = (F[9,x,k[0]]*k[0]-F[9,x,1])/(-1+k[0])
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x,1]
F[16,x,k[0]] = F[17,x]+F[18,x,k[0]]+F[29,x,k[0]]
F[17,x] = 0
F[18,x,k[0]] = -k[0]*(F[19,x,1]-F[19,x,k[0]])/(-1+k[0])
F[19,x,k[0]] = F[20,x,k[0]]*F[4,x]
F[20,x,k[0]] = F[16,x,k[0]]+F[21,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]
F[22,x,k[0]] = F[11,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,1,k[0]]
F[24,x,k[0],k[1]] = F[1,x]+F[25,x,k[0],k[1]]+F[26,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[11,x,k[1]]*F[24,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[11,x,k[1]]*F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0]*k[1],k[1]]
F[28,x,k[0],k[1]] = (-F[24,x,1,k[1]]*k[1]+F[24,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[29,x,k[0]] = F[11,x,k[0]]*F[30,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]+F[61,x,k[0]]
F[31,x,k[0]] = F[2,x]+F[32,x,k[0]]
F[32,x,k[0]] = F[17,x]+F[33,x,k[0]]+F[60,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]*F[4,x]
F[34,x,k[0]] = F[35,x,k[0]]+F[46,x,k[0]]
F[35,x,k[0]] = F[36,x,1,k[0]]
F[36,x,k[0],k[1]] = F[37,x,k[1]]+F[40,x,k[0],k[1]]
F[37,x,k[0]] = F[38,x,k[0]]
F[38,x,k[0]] = F[11,x,k[0]]*F[39,x,k[0]]
F[39,x,k[0]] = F[1,x]+F[37,x,k[0]]
F[40,x,k[0],k[1]] = F[17,x]+F[41,x,k[0],k[1]]+F[44,x,k[1],k[0]]
F[41,x,k[0],k[1]] = k[1]*(F[42,x,k[0],1]-F[42,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[42,x,k[0],k[1]] = F[43,x,k[0],k[0]*k[1]]
F[43,x,k[0],k[1]] = F[11,x,k[0]]*F[36,x,k[0],k[1]]
F[44,x,k[0],k[1]] = F[11,x,k[0]]*F[45,x,k[1],k[0]]
F[45,x,k[0],k[1]] = F[21,x,k[0]]+F[40,x,k[0],k[1]]
F[46,x,k[0]] = F[47,x,1,k[0]]
F[47,x,k[0],k[1]] = F[32,x,k[1]]+F[48,x,k[0],k[1]]
F[48,x,k[0],k[1]] = F[17,x]+F[49,x,k[0],k[1]]+F[55,x,k[0],k[1]]+F[58,x,k[1],k[0]]
F[49,x,k[0],k[1]] = -k[0]*(F[50,x,1,k[1]]-F[50,x,k[0],k[1]])/(-1+k[0])
F[51,x,k[0],k[1]] = F[50,x,k[0]*k[1],k[1]]
F[51,x,k[0],k[1]] = F[4,x]*F[52,x,k[0],k[1]]
F[52,x,k[0],k[1]] = F[53,x,k[0],k[1]]+F[54,x,k[0],k[1]]
F[53,x,k[0],k[1]] = F[40,x,k[0]*k[1],k[1]]
F[54,x,k[0],k[1]] = F[48,x,k[0]*k[1],k[1]]
F[55,x,k[0],k[1]] = k[1]*(F[56,x,k[0],1]-F[56,x,k[0],k[1]/k[0]])/(-k[1]+k[0])
F[56,x,k[0],k[1]] = F[57,x,k[0],k[0]*k[1]]
F[57,x,k[0],k[1]] = F[11,x,k[0]]*F[47,x,k[0],k[1]]
F[58,x,k[0],k[1]] = F[11,x,k[0]]*F[59,x,k[1],k[0]]
F[59,x,k[0],k[1]] = F[16,x,k[0]]+F[48,x,k[0],k[1]]
F[60,x,k[0]] = F[11,x,k[0]]*F[31,x,k[0]]
F[61,x,k[0]] = F[62,x,1,k[0]]
F[62,x,k[0],k[1]] = F[59,x,k[0]*k[1],k[1]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = y x
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x , 1\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x , y\right) = -\frac{y \left(F_{19}\! \left(x , 1\right)-F_{19}\! \left(x , y\right)\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{16}\! \left(x , y\right)+F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , 1, y\right)
F_{24}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{24}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{27}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{28}\! \left(x , y z , z\right)
F_{28}\! \left(x , y , z\right) = -\frac{z F_{24}\! \left(x , 1, z\right)-y F_{24}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{29}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x , 1, y\right)
F_{36}\! \left(x , y , z\right) = F_{37}\! \left(x , z\right)+F_{40}\! \left(x , y , z\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{40}\! \left(x , y , z\right) = F_{17}\! \left(x \right)+F_{41}\! \left(x , y , z\right)+F_{44}\! \left(x , z , y\right)
F_{41}\! \left(x , y , z\right) = \frac{z \left(F_{42}\! \left(x , y , 1\right)-F_{42}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{42}\! \left(x , y , z\right) = F_{43}\! \left(x , y , y z \right)
F_{43}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{36}\! \left(x , y , z\right)
F_{44}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{45}\! \left(x , z , y\right)
F_{45}\! \left(x , y , z\right) = F_{21}\! \left(x , y\right)+F_{40}\! \left(x , y , z\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , 1, y\right)
F_{47}\! \left(x , y , z\right) = F_{32}\! \left(x , z\right)+F_{48}\! \left(x , y , z\right)
F_{48}\! \left(x , y , z\right) = F_{17}\! \left(x \right)+F_{49}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)+F_{58}\! \left(x , z , y\right)
F_{49}\! \left(x , y , z\right) = -\frac{y \left(F_{50}\! \left(x , 1, z\right)-F_{50}\! \left(x , y , z\right)\right)}{-1+y}
F_{51}\! \left(x , y , z\right) = F_{50}\! \left(x , y z , z\right)
F_{51}\! \left(x , y , z\right) = F_{4}\! \left(x \right) F_{52}\! \left(x , y , z\right)
F_{52}\! \left(x , y , z\right) = F_{53}\! \left(x , y , z\right)+F_{54}\! \left(x , y , z\right)
F_{53}\! \left(x , y , z\right) = F_{40}\! \left(x , y z , z\right)
F_{54}\! \left(x , y , z\right) = F_{48}\! \left(x , y z , z\right)
F_{55}\! \left(x , y , z\right) = \frac{z \left(F_{56}\! \left(x , y , 1\right)-F_{56}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}
F_{56}\! \left(x , y , z\right) = F_{57}\! \left(x , y , y z \right)
F_{57}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{47}\! \left(x , y , z\right)
F_{58}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{59}\! \left(x , z , y\right)
F_{59}\! \left(x , y , z\right) = F_{16}\! \left(x , y\right)+F_{48}\! \left(x , y , z\right)
F_{60}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , 1, y\right)
F_{62}\! \left(x , y , z\right) = F_{59}\! \left(x , y z , z\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_14(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_9(x, k_0))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0), F_13(x, k_0)*F_4(x))
Eq(F_13(x, k_0), (-k_0*F_9(x, k_0) + F_9(x, 1))/(1 - k_0))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x, 1))
Eq(F_16(x, k_0), F_17(x) + F_18(x, k_0) + F_29(x, k_0))
Eq(F_17(x), 0)
Eq(F_18(x, k_0), -F_19(x, 1) + (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_20(x, k_0)*F_4(x))
Eq(F_20(x, k_0), F_16(x, k_0) + F_21(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0))
Eq(F_22(x, k_0), F_11(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, 1, k_0))
Eq(F_24(x, k_0, k_1), F_1(x) + F_25(x, k_0, k_1) + F_26(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_11(x, k_1)*F_24(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_11(x, k_1)*F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0*k_1, k_1))
Eq(F_28(x, k_0, k_1), (-k_0*F_24(x, k_0/k_1, k_1) + k_1*F_24(x, 1, k_1))/(-k_0 + k_1))
Eq(F_29(x, k_0), F_11(x, k_0)*F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0) + F_61(x, k_0))
Eq(F_31(x, k_0), F_2(x) + F_32(x, k_0))
Eq(F_32(x, k_0), F_17(x) + F_33(x, k_0) + F_60(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0)*F_4(x))
Eq(F_34(x, k_0), F_35(x, k_0) + F_46(x, k_0))
Eq(F_35(x, k_0), F_36(x, 1, k_0))
Eq(F_36(x, k_0, k_1), F_37(x, k_1) + F_40(x, k_0, k_1))
Eq(F_37(x, k_0), F_38(x, k_0))
Eq(F_38(x, k_0), F_11(x, k_0)*F_39(x, k_0))
Eq(F_39(x, k_0), F_1(x) + F_37(x, k_0))
Eq(F_40(x, k_0, k_1), F_17(x) + F_41(x, k_0, k_1) + F_44(x, k_1, k_0))
Eq(F_41(x, k_0, k_1), -F_42(x, k_0, 1) + (-k_0*F_42(x, k_0, 1) + k_1*F_42(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_42(x, k_0, k_1), F_43(x, k_0, k_0*k_1))
Eq(F_43(x, k_0, k_1), F_11(x, k_0)*F_36(x, k_0, k_1))
Eq(F_44(x, k_0, k_1), F_11(x, k_0)*F_45(x, k_1, k_0))
Eq(F_45(x, k_0, k_1), F_21(x, k_0) + F_40(x, k_0, k_1))
Eq(F_46(x, k_0), F_47(x, 1, k_0))
Eq(F_47(x, k_0, k_1), F_32(x, k_1) + F_48(x, k_0, k_1))
Eq(F_48(x, k_0, k_1), F_17(x) + F_49(x, k_0, k_1) + F_55(x, k_0, k_1) + F_58(x, k_1, k_0))
Eq(F_49(x, k_0, k_1), -F_50(x, 1, k_1) + (k_0*F_50(x, k_0, k_1) - F_50(x, 1, k_1))/(k_0 - 1))
Eq(F_51(x, k_0, k_1), F_50(x, k_0*k_1, k_1))
Eq(F_51(x, k_0, k_1), F_4(x)*F_52(x, k_0, k_1))
Eq(F_52(x, k_0, k_1), F_53(x, k_0, k_1) + F_54(x, k_0, k_1))
Eq(F_53(x, k_0, k_1), F_40(x, k_0*k_1, k_1))
Eq(F_54(x, k_0, k_1), F_48(x, k_0*k_1, k_1))
Eq(F_55(x, k_0, k_1), -F_56(x, k_0, 1) + (-k_0*F_56(x, k_0, 1) + k_1*F_56(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_56(x, k_0, k_1), F_57(x, k_0, k_0*k_1))
Eq(F_57(x, k_0, k_1), F_11(x, k_0)*F_47(x, k_0, k_1))
Eq(F_58(x, k_0, k_1), F_11(x, k_0)*F_59(x, k_1, k_0))
Eq(F_59(x, k_0, k_1), F_16(x, k_0) + F_48(x, k_0, k_1))
Eq(F_60(x, k_0), F_11(x, k_0)*F_31(x, k_0))
Eq(F_61(x, k_0), F_62(x, 1, k_0))
Eq(F_62(x, k_0, k_1), F_59(x, k_0*k_1, k_1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionsStrategy", "workable": false}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 3], [1, 3], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 3], [1, 3]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 3]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 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"class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "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": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 5
Strategy pack name: point_and_row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/5/
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[16,x]*F[4,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[6,x,k[0]]
F[6,x,k[0]] = F[11,x,k[0]]*F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,1,k[0]]
F[8,x,k[0],k[1]] = F[9,x,k[0]*k[1],k[1]]
F[9,x,k[0],k[1]] = F[1,x]+F[10,x,k[0],k[1]]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]
F[10,x,k[0],k[1]] = F[11,x,k[0]]*F[9,x,k[0],k[1]]
F[11,x,k[0]] = k[0]*x
F[12,x,k[0],k[1]] = F[11,x,k[1]]*F[13,x,k[0],k[1]]
F[13,x,k[0],k[1]] = (-F[8,x,1,k[1]]*k[1]+F[8,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]*F[16,x]
F[15,x,k[0],k[1]] = (F[9,x,k[0],k[1]]*k[1]-F[9,x,k[0],1])/(-1+k[1])
F[16,x] = x
F[17,x,k[0]] = F[16,x]*F[18,x,k[0]]
F[18,x,k[0]] = (F[5,x,k[0]]*k[0]-F[5,x,1])/(-1+k[0])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , 1, y\right)
F_{8}\! \left(x , y , z\right) = F_{9}\! \left(x , y z , z\right)
F_{9}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y , z\right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{9}\! \left(x , y , z\right)
F_{11}\! \left(x , y\right) = y x
F_{12}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{13}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = -\frac{z F_{8}\! \left(x , 1, z\right)-y F_{8}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right) F_{16}\! \left(x \right)
F_{15}\! \left(x , y , z\right) = -\frac{-z F_{9}\! \left(x , y , z\right)+F_{9}\! \left(x , y , 1\right)}{-1+z}
F_{16}\! \left(x \right) = x
F_{17}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = -\frac{-y F_{5}\! \left(x , y\right)+F_{5}\! \left(x , 1\right)}{-1+y}
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_16(x)*F_4(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_17(x, k_0) + F_6(x, k_0))
Eq(F_6(x, k_0), F_11(x, k_0)*F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, 1, k_0))
Eq(F_8(x, k_0, k_1), F_9(x, k_0*k_1, k_1))
Eq(F_9(x, k_0, k_1), F_1(x) + F_10(x, k_0, k_1) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1))
Eq(F_10(x, k_0, k_1), F_11(x, k_0)*F_9(x, k_0, k_1))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x, k_0, k_1), F_11(x, k_1)*F_13(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), (-k_0*F_8(x, k_0/k_1, k_1) + k_1*F_8(x, 1, k_1))/(-k_0 + k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1)*F_16(x))
Eq(F_15(x, k_0, k_1), (-k_1*F_9(x, k_0, k_1) + F_9(x, k_0, 1))/(1 - k_1))
Eq(F_16(x), x)
Eq(F_17(x, k_0), F_16(x)*F_18(x, k_0))
Eq(F_18(x, k_0), (-k_0*F_5(x, k_0) + F_5(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "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", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "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, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": 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