Starting with polynomial:
P : 4*t^2 - 2
Extension levels are: 2 3 56
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Trying to find an order 3 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^5 - 14*t^3 + 6*t
Solvable: 1
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Ending with final polynomial:
P : 4*t^61 - 531599802575561949837609695594068504860910779049284228655925262175154/155305158738556770794039759038947868295261702838393123027590315211*t^59 + 212179687376320765652573318733372064975260704791327559930903425099918696/155305158738556770794039759038947868295261702838393123027590315211*t^57 - 17512015686543560271780997712410320886841157386735082574677947147616172015/51768386246185590264679919679649289431753900946131041009196771737*t^55 + 1341311773706832769894895112646708357221462581247143304776505661217299623395/23008171664971373450968853190955239747446178198280462670754120772*t^53 - 342241692772272476496952590768018421937418310177734806294397765457804109305565/46016343329942746901937706381910479494892356396560925341508241544*t^51 + 33564290476100833931882072803950715344476063035152827618158283122269152129868675/46016343329942746901937706381910479494892356396560925341508241544*t^49 - 2593944685139722361721947084212374966941940784820698922301301446745149712723786575/46016343329942746901937706381910479494892356396560925341508241544*t^47 + 1285384650236233089409638250858221941421933615931498304461631965597710479816673785625/368130746639541975215501651055283835959138851172487402732065932352*t^45 - 129135441594562647295929616746619721278328068704271431943225376833444874779556890864875/736261493279083950431003302110567671918277702344974805464131864704*t^43 + 2651487285725600837627607299692222179330677990047296558345839945262467676968810797549125/368130746639541975215501651055283835959138851172487402732065932352*t^41 - 380363311074296569628988056982229920079546203942370803055604596660525169951091035131125/1564849082421007333540920939661142767095170461944686090253202688*t^39 + 39824100866926819643654094713136725823738904725641442188607861980473020568170420156246499875/5890091946232671603448026416884541375346221618759798443713054917632*t^37 - 1828085976689548484175854532117484695669825028039610974042338305161496473584310908214683733125/11780183892465343206896052833769082750692443237519596887426109835264*t^35 + 34598648067095023794966659507210776752299331205969857052218636112604179121059203773288229598125/11780183892465343206896052833769082750692443237519596887426109835264*t^33 - 269369089138379618722924515685030523339168247133600661514174077005771647699863057575544886140625/5890091946232671603448026416884541375346221618759798443713054917632*t^31 + 54999045889710372226490209055186983179441375090035664943544193915020235755854967410403316816736875/94241471139722745655168422670152662005539545900156775099408878682112*t^29 - 1143989351046907472336554147515540938250013767293232561591424115475811305430035617642384394747335625/188482942279445491310336845340305324011079091800313550198817757364224*t^27 + 1203100832681531766984073925614648244417065927312938514997599787296930552070280406315483506041071875/23560367784930686413792105667538165501384886475039193774852219670528*t^25 - 129780332582422967896636629421329496990553160233150342922636003166632907299511842165439467302505515625/376965884558890982620673690680610648022158183600627100397635514728448*t^23 + 2771444309825952923763506594739671667890032993000982751365261369373219599031050503522754289936381890625/1507863538235563930482694762722442592088632734402508401590542058913792*t^21 - 23088626633363033443185874407886030979294427018563965226179356301232539289395409150259419587497077859375/3015727076471127860965389525444885184177265468805016803181084117827584*t^19 + 73673697318669602671812619065590824191010754036251271190641371878311717748394014513971827611833135578125/3015727076471127860965389525444885184177265468805016803181084117827584*t^17 - 176022727273423024629757482929225251777726059822095179432716285373762898136013610700975692280008544609375/3015727076471127860965389525444885184177265468805016803181084117827584*t^15 + 2448347587789908879688322577537015224311501253301530126985678617589552938782354886041929981650084399296875/24125816611769022887723116203559081473418123750440134425448672942620672*t^13 - 5976867364098877453437375450927436347772154766208075931272819338580885212160216521727194126571306273640625/48251633223538045775446232407118162946836247500880268850897345885241344*t^11 + 2445865643116913764584425074263797990339962008369775414656104264501482598305079843131071925458343710140625/24125816611769022887723116203559081473418123750440134425448672942620672*t^9 - 5052907990792581499684354565964866361423492955219999243677738216332917819482084190171861402817748341859375/96503266447076091550892464814236325893672495001760537701794691770482688*t^7 + 6031071511372815417376327340330515016459578511185159936830611708016826956808878764931116167234429364765625/386013065788304366203569859256945303574689980007042150807178767081930752*t^5 - 1771927982075684331685202334898220132528574230532615473298769037433890026199164417773882720985101860859375/772026131576608732407139718513890607149379960014084301614357534163861504*t^3 + 84515877519463442811358795544314993892329305257039201253863152174547225633262421122365918536098631171875/772026131576608732407139718513890607149379960014084301614357534163861504*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: 1
  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:   59 out of 61
Indefinite weights: 0 out of 61
Negative weights:   2 out of 61
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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