Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 7 50
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Trying to find an order 7 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 50 Kronrod extension for:
P2 : t^11 - 41*t^9 + 528*t^7 - 2520*t^5 + 4095*t^3 - 1575*t
Solvable: 1
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Ending with final polynomial:
P : t^61 - 159780808144946850849720776913993034898630070509315114892399548236809303183552022919486788037287/100371175104610794176270587397583032050826432384911432142286510164079626087515255181457820082*t^59 + 16920872504903924219997027400238389018654191869090700529397517223501415952918326013961477470525003/14338739300658684882324369628226147435832347483558776020326644309154232298216465025922545726*t^57 - 2093600716791832125925342625322359603721497240126883928791982580491329339905329298486982427488820675590/3864290241527515575786417614806946733956817646819090137478030641317065604369337324486126073157*t^55 + 667871905674191422322863550857891194654301058903291637280162276441507526401459045441546735476009828546315/3864290241527515575786417614806946733956817646819090137478030641317065604369337324486126073157*t^53 - 28627075379380359541565710940045635397828854479955867115186947807498032407436045623173727424543101022138825/702598225732275559233894111783081224355785026694380024996005571148557382612606786270204740574*t^51 + 56967521442231230933736363665681892900373349583112222123144510072101301641687628101512295517078974701931602025/7728580483055031151572835229613893467913635293638180274956061282634131208738674648972252146314*t^49 - 82724225890473480051623940317632977237508693303252070045991350323989372021090702176347223237066714206217822400/78863066153622766852784032955243810897077911159573268111796543700348277640190557642574001493*t^47 + 409518761565027971451951619385282387877725576972404418737068891675014947187814427063182369196226432138228499375/3428828963200989863164523171967122212916430919981446439643327986971664245225676419242347891*t^45 - 6863287206773352659221944723911884862094451688670495298600320503945434678636242815098472382151148357211492532875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^43 + 516327969467520883350800159317927691247669367382949087029806823853024947118871288352265915658183810319906464637625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^41 - 15936118585274951401972355308513498079650972602666867566836438748918575478646648021221558943375494233174855851834750/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^39 + 809714338457269421062330249411447523797033880381290110396192980476660439859102028350988344474412997607166841796694875/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^37 - 67818338497390518085729472641532272570863036777524860771469105805170867187811695413879850542054000336443496598444181875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^35 + 2340152978353774612886293491772624917167116549480248454438471417398294145578977980012267179996126805553389951607219345625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^33 - 33209040528286985412165288509882572289126686451407684975188887340150559047921168543941385010538740277954330174455258590000/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^31 + 772781589551746179614393733869947633571187692273581920907845017098874111533973979212856669463074516638557722256072912786875/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^29 - 29351705821549109945130204832188445620551177113720889836275291919487656822974525638057637712540236785163949600043021118193125/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^27 + 452119767326125705215553912363776054402515741773757581795471423254466867005331716671499050427906840929897106069517195250784375/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^25 - 2802304948338281798772379582349043271609327954873932778184413845648151567906232922254667376898546070074395441169401296276656250/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^23 + 27684275245083867525152899473931061589996571329917085988949202208337612114017526527813168726053692562358036812341463671018953125/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^21 - 430659646488430189711865624051208912312658952708388453302982847923401240983636462900423442312850835991624236367252446226160328125/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^19 + 2597587219698270978352310555292548320324132965764685092579536249681553965794764649569804318126344523810624873329283683687185984375/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^17 - 5959035681127417363221114155333294806103510376983194431170828005656551296221434468152505799122819832006245033987102749909736250000/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^15 + 20282628310618264616260192516998968006283198590280859540938420932034999832354366282421162762872700516658636388860755387947344609375/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^13 - 99031694638442722576733108535488769125703640039515760609322609337074044874343407437706952754854627166842850596400590795598934015625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^11 + 165411921160853798955631429309157981130339679849914337920417516469335835787531409780824743540613107172873002252329133018919389171875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^9 - 88163620056482861324495796113300036236002567439004925546999855016289482266728841514717837973421670349596512994219007479414093406250/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^7 + 53715951728280908639906399173428096683880089826235484661751897627190437405315563344903103650338456678878038272959463275378783515625/311711723927362714833138470178829292083311901816495130876666180633787658656879674476577081*t^5 - 30705653516209711921362997898995933601514035403032128828846563247689347693802819923755101415679317940194753343983125275883297890625/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*t^3 + 2611712053686638207598833125877332311503732718409969748444503409908438723489136389598145915786783089688252659346461790427988671875/623423447854725429666276940357658584166623803632990261753332361267575317313759348953154162*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:   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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