Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 5 56
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Trying to find an order 5 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
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Trying to find an order 56 Kronrod extension for:
P2 : t^7 - 53/3*t^5 + 215/3*t^3 - 55*t
Solvable: 1
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Ending with final polynomial:
P : t^63 - 132241758327172913571480649746204622067465342066809609413991488490560585241588303653481303687/74391046964816111147005084077851189236366973338259764854688931549778227355550752630201141*t^61 + 404070259569620935274153163216248911211572318711889796530648327963689068303502205677905376143773/273702908644134748559735686701527960397953958508691587672912106645410459138347108733758915*t^59 - 55262629917905635529343805359215355025157302246821197978583826817495182178693334492992720518117033547/72531270790695708368329956975904909505457799004803270733321708261033771671661983814446112475*t^57 + 6629764094453821937192375744349477513429847285509574368767796886796525466176212883951193842754162213409/24177090263565236122776652325301636501819266334934423577773902753677923890553994604815370825*t^55 - 742186474078914706232685825905724761171659585359104310496770185250977500572779258366651533423853280067/10137144764597583279990210618575109644368665129951540284181929875755942931049892916065145*t^53 + 11745110244392451724687493733746797026124481279246955575275355578857378879708411004657253536018414284139/779780366507506406153093124505777664951435779227041560321686913519687917773068685851165*t^51 - 381798868116702784717215365034726418260218261245245716113146532391177105002990259451517255059157456065465/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^49 + 49880297024474190390023052570197715024491143531003755980667344676649593586456189943133848479280706423890061/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^47 - 5301740054219816749189332576857918306529609262961856629029117821353383682592987253851003782713931122588601631/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^45 + 462346728158472683479989959595983554684750846412505421823392428131054355129896153625397355516281900776807584595/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^43 - 33270142508078028578280967694624883650153258267869322462216770240874126230924333725445106439207482285570159868045/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^41 + 1982517659804181371111357952838511668434471650714614231782643567954286825443185038565234727867592118151694821790325/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^39 - 97996527807453414725829139763081852466192308020823456645730266660649645294504004246186331400002209472986932867411135/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^37 + 4018894110249669903001997883860923893023020952107333437275599951309408027498412986775311923692675174098896334252474635/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^35 - 136567256242003586615438632747562976448663013860479806791247022571822359846495337981544912255115106060147281399130807725/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^33 + 3835009254396320213481537439953300049120026025577092214068913838453077590592247603507448030305632285939007791693362286475/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^31 - 88631955754389911083822328857627418987933134731602376293226194670960982906700202674805947842241012514199378357458861305625/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^29 + 1676481202800241810885987343099128999424484726020062336261100192416345135678698214537534942530392751298689016529551363581525/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^27 - 25767074390494222576591549154267605093672335595050421890626569392109219300013201461678501899041790708941287862904772146517275/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^25 + 318901068937789226542403265558404839921034521612001565754705731016005027602486555759595630726272536599079286596494800766181875/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^23 - 3142520137825831960428370910871635976380963429941011160009404726352160787343045635705645654397387504581874593736362380906675625/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^21 + 24313605301162835154703219740454593262682469791998885140368066688022540304862669755062585363871153602660552679019604129794178125/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^19 - 145127036740661796107855582318037283894901476141521636933476474461898162938389735281915511056846658092737042028634729981555316875/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^17 + 653523974318826132254880252514494938679655551035473371367876111801266654334613506518287106441998668422497851743074775131463579375/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^15 - 2156154766371653354822487331555961702786615915231439180343195244457476679945175081930737359358716419338436333794179370473834503125/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^13 + 5009007623958397126159520802993853480884973489712706786785621578034580618232459586577016077835839650765934491948215082292216440625/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^11 - 7742334892374730065770789134277527266691537122972126731372737846516403808218886205634192536879220391127381435471275309705213759375/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^9 + 7303318289168785714324427873732906068800474517188726667503394406476991646707449556913865748075070335027418177818777220874198674375/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^7 - 3635745673965389433026492020431681979659082318826777169796935546225309145246669586082669127364438577838997501482703736458378743125/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^5 + 715001641419277924030652236977470670409266978907096612713371595148328628141717939783901657687363612247124341845673649667977965625/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*t^3 - 22954970122348436533368188744291437619925408573321481649396816859331442516032447491718434990386186985403263496503707599655559375/155956073301501281230618624901155532990287155845408312064337382703937583554613737170233*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
  current precision for roots: 848
  current precision for roots: 1696
 current precision for weights: 848
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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