Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 7 40
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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 40 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^51 - 3748164888323388940709113950537899378550142119016790958881879731182326663/3452008873983076440048795220156472902343624860042187456485826643003883*t^49 + 1867662153975143239126747310170663868771959483410615928428973830356217307794/3452008873983076440048795220156472902343624860042187456485826643003883*t^47 - 9645462820748284348900674079458197937323782590077354798784549939181641230476050/58684150857712299480829518742660039339841622620717186760259052931066011*t^45 + 2001898753310817709785174891898277834109774058030504081096443704561401313265247080/58684150857712299480829518742660039339841622620717186760259052931066011*t^43 - 301495864114617411182657266311208860481891245837484999425344668122234940927438190520/58684150857712299480829518742660039339841622620717186760259052931066011*t^41 + 34162742987448473160452058187537035434975171414210965748253950046688939464560673180870/58684150857712299480829518742660039339841622620717186760259052931066011*t^39 - 2980479209522555112568047762601975998496108535260758513214115053577363160228980307999510/58684150857712299480829518742660039339841622620717186760259052931066011*t^37 + 203243452789597030050691503467992173492402919793280337313954326655047117550344679666447475/58684150857712299480829518742660039339841622620717186760259052931066011*t^35 - 643377652424242744387387388894962754374675047510034930117480234163207897415365701165043775/3452008873983076440048795220156472902343624860042187456485826643003883*t^33 + 27476852496223251337374246741554493458490364589651131042332274942030700952491573994309494100/3452008873983076440048795220156472902343624860042187456485826643003883*t^31 - 933531118257148004783066320539544069549443692392686586932870741415613564624324868613343318100/3452008873983076440048795220156472902343624860042187456485826643003883*t^29 + 25224924891544866827046731464469060076270604108124767856977137480111782132819024041339399069800/3452008873983076440048795220156472902343624860042187456485826643003883*t^27 - 540572664481302913661416719888677065320999199904967076593093965964937508243355635919048838521000/3452008873983076440048795220156472902343624860042187456485826643003883*t^25 + 9138695881946375161619832694992698888634200976142435902867608043803253288338973769910923142347500/3452008873983076440048795220156472902343624860042187456485826643003883*t^23 - 120894310319415214830795787647419658936386667341183294392092337107478965468164646101075288430727500/3452008873983076440048795220156472902343624860042187456485826643003883*t^21 + 1237392422315911944795478818802237878077863954693368415553287163649238015212293309914139623933430625/3452008873983076440048795220156472902343624860042187456485826643003883*t^19 - 9650442168240241803482983592206329602512174607906942710175573206008188295616586249862587671322923125/3452008873983076440048795220156472902343624860042187456485826643003883*t^17 + 56186933988559690605858199031965034289830650681546059114007122991848499684817384020794127988923256250/3452008873983076440048795220156472902343624860042187456485826643003883*t^15 - 237599316110131742693749828729981458340494888994263260839926796436216323799769522661436735149756556250/3452008873983076440048795220156472902343624860042187456485826643003883*t^13 + 703070499574945141615546249627729890048730702161076632050583047324635659820693002469622830900063350000/3452008873983076440048795220156472902343624860042187456485826643003883*t^11 - 1382674183315719054388050695773791533962867847426065313660270927979230644844785148711961983089613100000/3452008873983076440048795220156472902343624860042187456485826643003883*t^9 + 1679000703533775438654389550798169606460619949155161151061918041426243802967269835825038315438997268750/3452008873983076440048795220156472902343624860042187456485826643003883*t^7 - 1126401850311081012239995453983557825750585052570062168168090712179077916770482599613086059692053718750/3452008873983076440048795220156472902343624860042187456485826643003883*t^5 + 345717572934617183295563704991174356691094770989938268138052910489820546883088943143102889450063640625/3452008873983076440048795220156472902343624860042187456485826643003883*t^3 - 31800727012789693990202343057044898831806179800030850595352023832416349573784452196817352698884453125/3452008873983076440048795220156472902343624860042187456485826643003883*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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