Starting with polynomial:
P : t^6 - 15*t^4 + 45*t^2 - 15
Extension levels are: 6 72
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Trying to find an order 72 Kronrod extension for:
P1 : t^6 - 15*t^4 + 45*t^2 - 15
Solvable: 1
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Ending with final polynomial:
P : t^78 - 14894341737202044846756846383762638543745661560934306789131079400671395636820882418275105676840299/5342573332200329534681543360146324787536839884632186940033418877203503559205936278644583689761*t^76 + 1317662229414984575222179829267846390473557849873127699674661028556222255889974439837676615119996184625/357952413257422078823663405129803760764968272270356524982239064772634738466797730669187107213987*t^74 - 12067791773938842237847752314535333608015835676384327608763244714364039494699106268209996212617025450259525/3937476545831642867060297456427841368414650994973921774804629712498982123134775037361058179353857*t^72 + 7116139064804872651079693842781318987218720980883944883476212041038341974622994473708146007824657136892135675/3937476545831642867060297456427841368414650994973921774804629712498982123134775037361058179353857*t^70 - 3164790842482141466916543587591356364829561929440602739410155532305163877251359214730261514255733110067500133825/3937476545831642867060297456427841368414650994973921774804629712498982123134775037361058179353857*t^68 + 969081386103221407238079013768031107162017134443151202152936007610231499364553786691201597373939921354559464075/3456959214953154404793939821271151333112072866526709196492212214661090538309723474417083563963*t^66 - 24737562588288267672323928119047515056750609606547676566313019303085046972903340271143553140683058789740291674375/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^64 + 5697394698135969103470187888957218172610809613203918798838430226320755619965882933680117276888251693577741050934500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^62 - 1091018524190833002043599815248081995822700706071756268572667801524806143049569487196976984609132944687617499292191500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^60 + 175477925104332703419496829311234423645417539026437990081281369055728656795925412498913392990792467750774816143535031500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^58 - 23886071859715077801920617806772355505877892458728152874099607843410322824320644432338710650508667755149692481630212688500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^56 + 2767306095478694184554072607990009673971530024269721781918931991037458558179341954071511900176230842892604321605358784037500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^54 - 274001767007506868022378123759410080075655552664852175179084996250526830466084939524768044003085485409816930340619893476432500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^52 + 23253064367675904180888298026184648104005860136746181068342551084077307325584634389798669494183904962089405666728531833256952500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^50 - 1694412962142123633596619483397109721757715029671666093455498830884021335334627406661866280771879804032502554699139971993423987500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^48 + 106106450901406858473914383220565906176162785908014622487719436919053426896935638109290544129586048244776686506150427919448011918750/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^46 - 5710109272465470682100536816513334188885418845678764874022462448763342927759130349776584963535015346407068274701393763798498618906250/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^44 + 263857888611793914210033194778815904974905245784828261813890764712916471923612361040838442776738146796027332571444754089955616332406250/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^42 - 10452407413895271732801225825800309215655846632632432706447342021533744719014371330268846848209216044742826063035842849972663417825593750/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^40 + 354105383328632805891202479118150404991217925323513926061898584619744417503654422487597933125246747892878158031431557419358042098304156250/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^38 - 10226011314299593690138961481719064804303503928767688862457141797560171966514218930994444567332657755332891606039908503662154304296698968750/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^36 + 250690841243629806601163821978950754451517012716882823873244336799480981188497096487264823581441957464406917813240972372089815889748855468750/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^34 - 5190460448399098730322717123947078705247208864701669914693969885963185764124444477079270822319775316403351308718991996078618872942454803281250/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^32 + 90200450253512982912508183292088019385741163503887982733791339349369292302886952111695324777672365177253074205798754677991733172737599387812500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^30 - 1305868987428131663722020326760881247855832854138243886699845907742938566932951595306122737700299629037549993375349570337373889854155503436937500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^28 + 15609503380791049895390984385548583014951805089153914877306879872847074970164974315891455348234424739228449523178487771785503724237205401619937500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^26 - 152412052567841448682141211204019248112842191735786029097676334654946888581896559249343592532401416745177400337123176192734234152751520501539062500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^24 + 1200039212387607896263850290898850201861456560240866191576006426913635514882594379783484915059932504970585222841890875543703930772622414806642187500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^22 - 7501672848721856198233930336235429244903416306543302291257437461525805668372133736139098750943104020122358101644464087257919169422396878903776562500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^20 + 36532021790758895857432180898462064227699107447667445364732437537735773839580198988466453648503716573348852351394564257067432353813641599381801562500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^18 - 135396713364785204420893207048199257729125884712849748852897971726778903637251870360660412603268616376542069877058178808223945269220286060769385937500/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^16 + 370968665624107465776370298593577233455734459768672426301863676437655311404963621162144149568116382808988530341824739638637897209808615479062197265625/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^14 - 724325598014881984526471796682813525940973824190024099456743123033617979166733030084659920957597080355538425233793631115306326290557219895635294921875/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^12 + 961772516188576164488081630627910502045939678250928545166298797526287201970376730912244311613702442927971140430598460348069650079209540645287201171875/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^10 - 817754259729986681060958422699870340552167606393079006809253169614030429390784166297777154105112856421348382074024558629938754201205829967760111328125/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^8 + 411891052718277936807571844442870299622807428731758926744618900448662040461575543719487417607796673140538338429664544504982915329466260855836294921875/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^6 - 110442130666042051698604900161141521628395158252011564411823424788729915131995727087607137594331072293296618884978048932289137843543014342085791015625/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^4 + 12847162041962782308259862690892930000121797837919631292481501198205785803731915239365254466396990494322076216084401425489731718608242963383759765625/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633*t^2 - 295099793455003545529607819407369798614392204557360136845428807102478333026631048686372568020144228516899649377492602342401727074021758995693359375/314269019541195854981267256479195575737461169684246290590201110423735503482702134037916687633
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Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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:   76 out of 78
Indefinite weights: 0 out of 78
Negative weights:   2 out of 78
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
