Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 5 56
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Trying to find an order 5 Kronrod extension for:
P1 : 4*t^2 - 2
Solvable: 1
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Trying to find an order 56 Kronrod extension for:
P2 : 4*t^7 - 106/3*t^5 + 215/3*t^3 - 55/2*t
Solvable: 1
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Ending with final polynomial:
P : 4*t^63 - 264483516654345827142961299492409244134930684133619218827982976981121170483176607306962607374/74391046964816111147005084077851189236366973338259764854688931549778227355550752630201141*t^61 + 404070259569620935274153163216248911211572318711889796530648327963689068303502205677905376143773/273702908644134748559735686701527960397953958508691587672912106645410459138347108733758915*t^59 - 55262629917905635529343805359215355025157302246821197978583826817495182178693334492992720518117033547/145062541581391416736659913951809819010915598009606541466643416522067543343323967628892224950*t^57 + 6629764094453821937192375744349477513429847285509574368767796886796525466176212883951193842754162213409/96708361054260944491106609301206546007277065339737694311095611014711695562215978419261483300*t^55 - 742186474078914706232685825905724761171659585359104310496770185250977500572779258366651533423853280067/81097158116780666239921684948600877154949321039612322273455439006047543448399143328521160*t^53 + 11745110244392451724687493733746797026124481279246955575275355578857378879708411004657253536018414284139/12476485864120102498449489992092442639222972467632664965146990616315006684369098973618640*t^51 - 381798868116702784717215365034726418260218261245245716113146532391177105002990259451517255059157456065465/4990594345648040999379795996836977055689188987053065986058796246526002673747639589447456*t^49 + 49880297024474190390023052570197715024491143531003755980667344676649593586456189943133848479280706423890061/9981188691296081998759591993673954111378377974106131972117592493052005347495279178894912*t^47 - 5301740054219816749189332576857918306529609262961856629029117821353383682592987253851003782713931122588601631/19962377382592163997519183987347908222756755948212263944235184986104010694990558357789824*t^45 + 462346728158472683479989959595983554684750846412505421823392428131054355129896153625397355516281900776807584595/39924754765184327995038367974695816445513511896424527888470369972208021389981116715579648*t^43 - 33270142508078028578280967694624883650153258267869322462216770240874126230924333725445106439207482285570159868045/79849509530368655990076735949391632891027023792849055776940739944416042779962233431159296*t^41 + 1982517659804181371111357952838511668434471650714614231782643567954286825443185038565234727867592118151694821790325/159699019060737311980153471898783265782054047585698111553881479888832085559924466862318592*t^39 - 97996527807453414725829139763081852466192308020823456645730266660649645294504004246186331400002209472986932867411135/319398038121474623960306943797566531564108095171396223107762959777664171119848933724637184*t^37 + 4018894110249669903001997883860923893023020952107333437275599951309408027498412986775311923692675174098896334252474635/638796076242949247920613887595133063128216190342792446215525919555328342239697867449274368*t^35 - 136567256242003586615438632747562976448663013860479806791247022571822359846495337981544912255115106060147281399130807725/1277592152485898495841227775190266126256432380685584892431051839110656684479395734898548736*t^33 + 3835009254396320213481537439953300049120026025577092214068913838453077590592247603507448030305632285939007791693362286475/2555184304971796991682455550380532252512864761371169784862103678221313368958791469797097472*t^31 - 88631955754389911083822328857627418987933134731602376293226194670960982906700202674805947842241012514199378357458861305625/5110368609943593983364911100761064505025729522742339569724207356442626737917582939594194944*t^29 + 1676481202800241810885987343099128999424484726020062336261100192416345135678698214537534942530392751298689016529551363581525/10220737219887187966729822201522129010051459045484679139448414712885253475835165879188389888*t^27 - 25767074390494222576591549154267605093672335595050421890626569392109219300013201461678501899041790708941287862904772146517275/20441474439774375933459644403044258020102918090969358278896829425770506951670331758376779776*t^25 + 318901068937789226542403265558404839921034521612001565754705731016005027602486555759595630726272536599079286596494800766181875/40882948879548751866919288806088516040205836181938716557793658851541013903340663516753559552*t^23 - 3142520137825831960428370910871635976380963429941011160009404726352160787343045635705645654397387504581874593736362380906675625/81765897759097503733838577612177032080411672363877433115587317703082027806681327033507119104*t^21 + 24313605301162835154703219740454593262682469791998885140368066688022540304862669755062585363871153602660552679019604129794178125/163531795518195007467677155224354064160823344727754866231174635406164055613362654067014238208*t^19 - 145127036740661796107855582318037283894901476141521636933476474461898162938389735281915511056846658092737042028634729981555316875/327063591036390014935354310448708128321646689455509732462349270812328111226725308134028476416*t^17 + 653523974318826132254880252514494938679655551035473371367876111801266654334613506518287106441998668422497851743074775131463579375/654127182072780029870708620897416256643293378911019464924698541624656222453450616268056952832*t^15 - 2156154766371653354822487331555961702786615915231439180343195244457476679945175081930737359358716419338436333794179370473834503125/1308254364145560059741417241794832513286586757822038929849397083249312444906901232536113905664*t^13 + 5009007623958397126159520802993853480884973489712706786785621578034580618232459586577016077835839650765934491948215082292216440625/2616508728291120119482834483589665026573173515644077859698794166498624889813802465072227811328*t^11 - 7742334892374730065770789134277527266691537122972126731372737846516403808218886205634192536879220391127381435471275309705213759375/5233017456582240238965668967179330053146347031288155719397588332997249779627604930144455622656*t^9 + 7303318289168785714324427873732906068800474517188726667503394406476991646707449556913865748075070335027418177818777220874198674375/10466034913164480477931337934358660106292694062576311438795176665994499559255209860288911245312*t^7 - 3635745673965389433026492020431681979659082318826777169796935546225309145246669586082669127364438577838997501482703736458378743125/20932069826328960955862675868717320212585388125152622877590353331988999118510419720577822490624*t^5 + 715001641419277924030652236977470670409266978907096612713371595148328628141717939783901657687363612247124341845673649667977965625/41864139652657921911725351737434640425170776250305245755180706663977998237020839441155644981248*t^3 - 22954970122348436533368188744291437619925408573321481649396816859331442516032447491718434990386186985403263496503707599655559375/83728279305315843823450703474869280850341552500610491510361413327955996474041678882311289962496*t
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Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 0
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   62 out of 63
Indefinite weights: 0 out of 63
Negative weights:   1 out of 63
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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