Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 7 40
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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 40 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^51 - 29985319106587111525672911604303195028401136952134327671055037849458613304/3452008873983076440048795220156472902343624860042187456485826643003883*t^49 + 7470648615900572956506989240682655475087837933642463713715895321424869231176/3452008873983076440048795220156472902343624860042187456485826643003883*t^47 - 19290925641496568697801348158916395874647565180154709597569099878363282460952100/58684150857712299480829518742660039339841622620717186760259052931066011*t^45 + 2001898753310817709785174891898277834109774058030504081096443704561401313265247080/58684150857712299480829518742660039339841622620717186760259052931066011*t^43 - 150747932057308705591328633155604430240945622918742499712672334061117470463719095260/58684150857712299480829518742660039339841622620717186760259052931066011*t^41 + 17081371493724236580226029093768517717487585707105482874126975023344469732280336590435/117368301715424598961659037485320078679683245241434373520518105862132022*t^39 - 1490239604761277556284023881300987999248054267630379256607057526788681580114490153999755/234736603430849197923318074970640157359366490482868747041036211724264044*t^37 + 203243452789597030050691503467992173492402919793280337313954326655047117550344679666447475/938946413723396791693272299882560629437465961931474988164144846897056176*t^35 - 643377652424242744387387388894962754374675047510034930117480234163207897415365701165043775/110464283967458446081561447045007132874995995521349998607546452576124256*t^33 + 6869213124055812834343561685388623364622591147412782760583068735507675238122893498577373525/55232141983729223040780723522503566437497997760674999303773226288062128*t^31 - 233382779564287001195766580134886017387360923098171646733217685353903391156081217153335829525/110464283967458446081561447045007132874995995521349998607546452576124256*t^29 + 3153115611443108353380841433058632509533825513515595982122142185013972766602378005167424883725/110464283967458446081561447045007132874995995521349998607546452576124256*t^27 - 67571583060162864207677089986084633165124899988120884574136745745617188530419454489881104815125/220928567934916892163122894090014265749991991042699997215092905152248512*t^25 + 2284673970486593790404958173748174722158550244035608975716902010950813322084743442477730785586875/883714271739667568652491576360057062999967964170799988860371620608994048*t^23 - 30223577579853803707698946911854914734096666835295823598023084276869741367041161525268822107681875/1767428543479335137304983152720114125999935928341599977720743241217988096*t^21 + 1237392422315911944795478818802237878077863954693368415553287163649238015212293309914139623933430625/14139428347834681098439865221760913007999487426732799821765945929743904768*t^19 - 9650442168240241803482983592206329602512174607906942710175573206008188295616586249862587671322923125/28278856695669362196879730443521826015998974853465599643531891859487809536*t^17 + 28093466994279845302929099515982517144915325340773029557003561495924249842408692010397063994461628125/28278856695669362196879730443521826015998974853465599643531891859487809536*t^15 - 118799658055065871346874914364990729170247444497131630419963398218108161899884761330718367574878278125/56557713391338724393759460887043652031997949706931199287063783718975619072*t^13 + 43941906223434071350971640601733118128045668885067289503161440457789728738793312654351426931253959375/14139428347834681098439865221760913007999487426732799821765945929743904768*t^11 - 43208568228616220449626584242930985436339620232064541051883466499350957651399535897248811971550409375/14139428347834681098439865221760913007999487426732799821765945929743904768*t^9 + 839500351766887719327194775399084803230309974577580575530959020713121901483634917912519157719498634375/452461707130709795150075687096349216255983597655449594296510269751804952576*t^7 - 563200925155540506119997726991778912875292526285031084084045356089538958385241299806543029846026859375/904923414261419590300151374192698432511967195310899188593020539503609905152*t^5 + 345717572934617183295563704991174356691094770989938268138052910489820546883088943143102889450063640625/3619693657045678361200605496770793730047868781243596754372082158014439620608*t^3 - 31800727012789693990202343057044898831806179800030850595352023832416349573784452196817352698884453125/7239387314091356722401210993541587460095737562487193508744164316028879241216*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:   49 out of 51
Indefinite weights: 0 out of 51
Negative weights:   2 out of 51
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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