Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 52
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Trying to find an order 7 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
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Trying to find an order 52 Kronrod extension for:
P2 : 16*t^11 - 328*t^9 + 2112*t^7 - 5040*t^5 + 4095*t^3 - 1575/2*t
Solvable: 1
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Ending with final polynomial:
P : 16*t^63 - 234671598234143765633661789270223013302353924635939486545100389690767199270999544833856297210419221356/16497646471044866892978592775626964551478161310849288120924829533477545433268323305220391248855399*t^61 + 4574667135287898190214941695862048755339967304762765718180526352181988199987801715260886377876746450060445/775389384139108743969993860454467333919473581609916541683466988073444635363611195345358388696203753*t^59 - 536296205051839814721396949100727466692630301364785409426203490105792640467434527933319514882533078889574901/353147640300980220025937797830747498616789948059961989281579024271073794324020940454321642376488838*t^57 + 4854884773237187882696127795885902349352258911715673381726188654988580920930022119413894532326338168163844905290/17833955835199501111309858790452748680147892377028080458719740725689226613363057492943242940012686319*t^55 - 18053306741074739255031695565910896520222911412311985955590165221616488333553908888419515770324888881847348709293615/499350763385586031116676046132676963044140986556786252844152740319298345174165609802410802320355216932*t^53 + 7379868445984555547756610904636527230611480649593084075347681621813056276317248419994478616295776764616427287953971525/1997403053542344124466704184530707852176563946227145011376610961277193380696662439209643209281420867728*t^51 - 1190162027183663618838766206594063675304210595453796372684963030796342800487535116270621120497832712888544422271788523375/3994806107084688248933408369061415704353127892454290022753221922554386761393324878419286418562841735456*t^49 + 117084461164805971766159624687674731845704643101895350449307425810521177952604717361742915868641353761653292449382115325/6071133901344511016616122141430722954943963362392538028500337268319736719442742976321103979578786832*t^47 - 1071031886163076370654113792919518202907950968013861010647488468979733837375698774139936527320104750876406060289873118375/1055849374146871481150629937640125731294602323894354439739189090142562907729172691534105039926745536*t^45 + 184657442462855434676963858419712603769063651260725821597003076577408859902255521772439087027087951944412017748811554786375/4223397496587485924602519750560502925178409295577417758956756360570251630916690766136420159706982144*t^43 - 13120040120656522259400624963525120473997285431557390253659589064422242992807884611374438440301850250059371583831805606686125/8446794993174971849205039501121005850356818591154835517913512721140503261833381532272840319413964288*t^41 + 96386758896902156194808617869441129238079423590319078924769183714444670631021521654219909719032528538329290750511717272794375/2111698748293742962301259875280251462589204647788708879478378180285125815458345383068210079853491072*t^39 - 18778179868026802511597923676537027121870049943036272850744631905100743949041080300729707142083023142519131213045921339064736125/16893589986349943698410079002242011700713637182309671035827025442281006523666763064545680638827928576*t^37 + 1516338289580052273594195492251714062225207393187060183802734039449690290258140988601943363072736644155918984935592841259152409375/67574359945399774793640316008968046802854548729238684143308101769124026094667052258182722555311714304*t^35 - 50695803677344274507970732414815115488428324273925173295529533717301921966886206967869460013047319085405904130488917437999404048125/135148719890799549587280632017936093605709097458477368286616203538248052189334104516365445110623428608*t^33 + 350028618836774656728541178178256275766633991653589450996174087758495981224695582351068520667610903513340898433942003730932442008125/67574359945399774793640316008968046802854548729238684143308101769124026094667052258182722555311714304*t^31 - 15911988731236101878439240350261709550252957996177656666886458615904159331678636164915386959925999407999075811078563040840737981690625/270297439781599099174561264035872187211418194916954736573232407076496104378668209032730890221246857216*t^29 + 592300460375891718982852082248787020687580894377484465901076276020416139924067374362581524685382101442883113600235827355978580962755625/1081189759126396396698245056143488748845672779667818946292929628305984417514672836130923560884987428864*t^27 - 8967959840084428790486347584160871246692619488195101394137552211334794647028072873633054345504825071365197886671201849996662859606471875/2162379518252792793396490112286977497691345559335637892585859256611968835029345672261847121769974857728*t^25 + 13695593591010606476395072011680291835540722262311165723010533633552672716865293939573579827620438877114418182425083530327801681690234375/540594879563198198349122528071744374422836389833909473146464814152992208757336418065461780442493714432*t^23 - 534662287879981179593999847236373894475537953477398898867767260507100496564189187725495150670483740972911498888235204512373724116094171875/4324759036505585586792980224573954995382691118671275785171718513223937670058691344523694243539949715456*t^21 + 8234415687080176403258234748847438177711032005514337950246584000737268513917735759663690708297168934408726681016608233889354867814144140625/17299036146022342347171920898295819981530764474685103140686874052895750680234765378094776974159798861824*t^19 - 46434654191827294809407220014255533187200153778962453229082453404441761871111699770213587492609023637292196092478010390477999101288484375/32608927702209881898533309893111819003828019744929506391492693784911876871319067630715884965428461568*t^17 + 56152581006122021217435979201437889291309960204524069859684892642015248935526268609309652840098179602933093937024959008204790506585364140625/17299036146022342347171920898295819981530764474685103140686874052895750680234765378094776974159798861824*t^15 - 380402275679775498306617296478544055651993414664021899564657847166221808531487969162292068244508173541615190509319061987028515819969328328125/69196144584089369388687683593183279926123057898740412562747496211583002720939061512379107896639195447296*t^13 + 1850778233272863631662084339099328762996213262780884586456581426293256159339710054250371689472652772288889846366341738231900834368080040828125/276784578336357477554750734372733119704492231594961650250989984846332010883756246049516431586556781789184*t^11 - 3083716811583990434953242603970440917079125755115167303884995092050052915035676362746098185532779703321796314778455317156028012292368764609375/553569156672714955109501468745466239408984463189923300501979969692664021767512492099032863173113563578368*t^9 + 410229609701060994664964233293945964360239344361474346273271327931411151657299562717553442461476225994513636862248815155793117718507594953125/138392289168178738777375367186366559852246115797480825125494992423166005441878123024758215793278390894592*t^7 - 998767035297252618256928099005450864397940237261339353779707537266480069324184565461056192757588275707244949341243084727500382102374507109375/1107138313345429910219002937490932478817968926379846601003959939385328043535024984198065726346227127156736*t^5 + 570676999298825140041405168061796982172043357377171750171128328530162246614863611665301079320197274120118448517678998610128697063045161953125/4428553253381719640876011749963729915271875705519386404015839757541312174140099936792262905384908508626944*t^3 - 48560977569682808836047547183542374777029412953274914215891947443935936781656424066790158221483019252767155733087933479024742062843668359375/8857106506763439281752023499927459830543751411038772808031679515082624348280199873584525810769817017253888*t
-------------------------------------------------
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:   61 out of 63
Indefinite weights: 0 out of 63
Negative weights:   2 out of 63
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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