Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 72
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Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 72 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^81 - 1643474764953179419581547059896946164917830058591818862458328040785604421331047614807889061500409031534537597120438475550646876667578144049824902016534001/553792915369863196119239423742795418009821556636420218289162139755845968706506479948136329988989529295775035494757967103534457016362022077168563479649*t^79 + 1063322693596533983832790002887066820985227148995379125793622101131677848106604615378343793100097107673920049382671379654320270239007046335276376734569737874/254445393548315522541272167665608705572080174670787667862588010158091391027313788084278854319265459406166908200294201101623939710220388521942312950109*t^77 - 35002048332008921814024867549361300550367658351877975803974544731906017155958675089920608244688440168325703164365764033062998629532790088827285435345705716313557/9414479561287674334027070203627522106166966462819143710915756375849381468010610159118317609812821998028175603410885440760085769278154375311865579154033*t^75 + 22100662254189839200580730921144310893613741819526204128939828476004533652858069557317385212471395193388757453863085201759663078031756359915292734720310081399940750/9414479561287674334027070203627522106166966462819143710915756375849381468010610159118317609812821998028175603410885440760085769278154375311865579154033*t^73 - 10547658685457251935544350693369057346973388208986391089553087087172621035158334532445302300824321708951857987524756313545390695067786841874737980608199282230203681375/9414479561287674334027070203627522106166966462819143710915756375849381468010610159118317609812821998028175603410885440760085769278154375311865579154033*t^71 + 172041380909188212767028204258367837413296691737658320895925024871968914046516087802372387319349527655064111637837822134866909047491145606141497508652291060920858309150/409325198316855405827263921896848787224650715774745378735467668515190498609156963439926852600557478175138069713516758293916772577311059796168068658871*t^69 - 3064226976705560820568654849756882434223738107065107020259342434512331021592348478515182196958177821656289614932705660024613738672425286462559430567647922669500432268925/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^67 + 763031857919891230662207588107463593926920048870486650867424577722260921725428708755260124580264434122058060686729163598119239040052207514277033450360397824678745437971575/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^65 - 158429429309758197662504484028479940117030085478758266109153134142577627368897572037931894783072030649915496822796697698923799717241407678134777009208079375614865716198817500/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^63 + 27713242678885350381677625447162048850360625508657353382644005582241845033763927766979517950492093098752562357973763253828578135362807997035863967593486873600974180384280003000/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^61 - 4116165368075263814215397394634824465983568221630683058542654125815392028007525415974860946651049903118856281432454485762780914881335197803546564832539362985059498036742570703500/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^59 + 522179737310239444200414967273056015645226874748122083267097377032380226432335318259827912477620780166286687537667968880846965152537276865195606735325415493910694805911605718739000/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^57 - 56830904635853647618460148731799618995887312673752053480949918250359911012892203173806792253389695171791335330152086225058048443483228437842525870549369999470686301345642517837568500/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^55 + 5323170041280105512286512254011163665106393266610860149664246524274640977192183121854080362552228004516481960458677767214451411912617640662028666591288843993492594116473765384234075000/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^53 - 430044076187929661490594296140752496761228517428188807406814312567999744937009380023138299298813575188194600356923771734736218300843026480327350436147105993065753191327917958907550602500/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^51 + 30002527520203563732240222074934702474653170257529853642054171248019430725015722780358703307368628143584083660464444599441970276695446266546360610516455046997383350035679281887959415668750/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^49 - 1808420645444794249843700117799558706617013222126618534555007567483055596499273942955050212734864486352049091853713321612176223871547423812636777252695550652833341436867190384854853829331250/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^47 + 94147030185459884829990880968034245158395454779695329524524021379312150101194330233001507136129429634750517991651988326565130066997019906931262351365878580607369731416261082304752057975512500/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^45 - 4228986008246915857081614294249104448241012994561891273483150183017753025439943822351745166382955959110757828911004231682560773619340330544902313838104630968039132219437589287872831703415156250/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^43 + 163620326037840363220896801166077931337871632568555753391386747746314778353674922494844596823496748708382416050651587618152788471220796901979024901716740023273670689784750700141193044658083187500/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^41 - 5439330854943089859491418916246547603966019025702941180999382855498759992005510900145442380336788000350628979054232888546763777699559838089986648960939846776795202987462217261536033201814677718750/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^39 + 154870800618534066445355913367658240539509507787000952066239755469051862662121729428697010987535741685084805630544393072958298986245732637280567504860057260206981212365582646335783445291969205562500/24077952842167965048662583640991105130861806810279139925615745206775911682891586084701579564738675186772827630206868134936280739841827046833415803463*t^37 - 101663594260217779559181733322635449557771716566716381377408459264066370663483668177229188722438061192238277980917480943410243269728451014835123120698736803324320644416440763654026531435393447218750/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^35 + 2096085273353462490605956237354270369618755512278259211714380852300051278845712678648703980056069004541880159634720897674327069520993314372045350671781860219406591242275236601412552505822453917968750/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^33 - 36470149736852039844198380387849756066886904243415082448167929572551687246158113329942543523973041330418057607835963746602427026242808344124164263174829531190875942377028378883157560986425184016437500/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^31 + 531733127251782756235413990068403792810681355137109073893882009224077833212404709997061492111388658772690757998197870482338829814846892950819364498388973606953373016785829772069535564778662468843875000/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^29 - 6442259683124804280378856653945941407050368458674240384342106877454264313970703516717534086069030980932458788148815672223243639617976846980732638722538917548781923489119834560048108869911682735575187500/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^27 + 64215074318845731349689423776630579320894451822582643020137170732772830342088858872758171296719420144141567473600969351782110656682719826983503857829898167115214446874718016210036949177809913023271375000/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^25 - 520365888338526233607700571616569141226160976034673246146640905976089053739892201984334075970173545051418198996916027285487540461783667383219514732102228905727359992531441329050755294607241941369820312500/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^23 + 3379227081253531242023208461026545850201469489469186496743204231789166465301086560233391042051771725496858719722992567650875303350716380422706800264954078464655751873498028784660790213293469869616921875000/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^21 - 17281470722065201720368008534880366028389465760568961057027239254027038779979204795581534203014368948675322098494058657918191963005938082586233810078407923212199561376312330067230780887631185989384126562500/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^19 + 68116777143532790448198886579332141465158799147636776000721655350423689338148955939046702648395022421175226803768229955864761901091422844560819878485380828324287913775797217743684834305516809971693105859375/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^17 - 201422942713709874047402191389785195669409333024234924724220201854459116966966344829233628643886795614017588428478335069109806102207580988550295386170443407376109993747458307430640064033158699984561976171875/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^15 + 431581215486878889661395308724819020942044141568692901121251561936619944666308003132344009603174134731925835709939293620422478380168378299779557010895346006733923816595123778369879864725124642304232167968750/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^13 - 639828334826805846190709143956556915162759841111062584538343214084120101383865333658202788717497888753310805755714769362010347135856616346171832538372649672868127743176021146870806877150148154593454974609375/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^11 + 615400266938760888035169729385515415643098597740140072691931314295016649015413796468008594758457477850544985396679721919981063976955227046669953317475438361300231151491342323060548714065101039956190222656250/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^9 - 348685335126071149448109155327286065688953280824047452267506552589389094983611159586544330505007964740640812442560651674703199369710286397138421513699095547553611931457283902149685358440136335075495705078125/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^7 + 98803841599786595052510731168504146391915945821864991759393171260852649621079624290264991224172856746647596938625935121849959124945974115588605807720412833820806081844883233658719293150133427411398933593750/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^5 - 9777398258814192980689294175992255869298436010823620249877498541713695416951863489402704987960342979516500944099228001345132919809650133883622858790059559619603118556973348214730045292721262309556494140625/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t^3 + 13112577893186197920903808945167375854291099706285243716973238895464293371112040177116846053876776470781020275541081733593283966426039565229626683763052214540755127634401820927117697804209574276240234375/650755482220755812126015774080840679212481265142679457449074194777727342780853677964907555803747978020887233248834273917196776752481812076578805499*t
-------------------------------------------------
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:   80 out of 81
Indefinite weights: 0 out of 81
Negative weights:   1 out of 81
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
