Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 11 26
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Trying to find an order 11 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 26 Kronrod extension for:
P2 : t^15 - 641/6*t^13 + 29116/7*t^11 - 1045605/14*t^9 + 4515555/7*t^7 - 5082165/2*t^5 + 3863970*t^3 - 2916045/2*t
Solvable: 1
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Ending with final polynomial:
P : t^41 - 81565308699484619085528345650708918680856936140982019584978741/132950653289254862646262641431500852295769369208005485227806*t^39 + 497747372175492561609692039078534135554268311327998301331875625404/2947072814578482788658821885064935559222887684110788255883033*t^37 - 23295922296700774368241548116711123022534294088252858783462690584585/842020804165280796759663395732838731206539338317368073109438*t^35 + 151060574776309772365769233588648365756616585625514070934173478559894240/50100237847834207407199972046103904506789090629883400350011561*t^33 - 11602098522581959730682495029168914211170751182098587575278402893503734345/50100237847834207407199972046103904506789090629883400350011561*t^31 + 649020848436876815797981410118453660251848738536211294904084324046383237420/50100237847834207407199972046103904506789090629883400350011561*t^29 - 26954513112757326021841275322456041263574699799636818690186467780707524110685/50100237847834207407199972046103904506789090629883400350011561*t^27 + 839624448001761946773006189607509238889920852423886236146994059238944153522000/50100237847834207407199972046103904506789090629883400350011561*t^25 - 19687673082608000965419295934364353763431493815385658862927201566348699766457000/50100237847834207407199972046103904506789090629883400350011561*t^23 + 346876660444093575128692815286789057802425852753475193880181230578743990736927000/50100237847834207407199972046103904506789090629883400350011561*t^21 - 34293294593487554547463919419052390018252690000688468766779867957443624853294000/376693517652888777497744150722585748171346546089348874812117*t^19 + 19558618085196545375044633009072886995538087797984549540837670439644290239602250/22158442214875810441043773571916808715961561534667580871301*t^17 - 137352796435956291832111593775508664966284005869180708309440798223134602955431875/22158442214875810441043773571916808715961561534667580871301*t^15 + 35854038060978187509385183771036224143425696584013151089207195845965586097342500/1166233800782937391633882819574568879787450607087767414279*t^13 - 2303331797050782858212793939778490233867467902210925633544315678188313305524199375/22158442214875810441043773571916808715961561534667580871301*t^11 + 5046687050932010287900564880071772352558612029946329759747119438006998984060511875/22158442214875810441043773571916808715961561534667580871301*t^9 - 13253860512262349030574541077921420945120111259887550351661271735986697871392605625/44316884429751620882087547143833617431923123069335161742602*t^7 + 4537117322486721691444338985561930770425471857358764301492064010898198992079212500/22158442214875810441043773571916808715961561534667580871301*t^5 - 2329284645744138046761340249564982729481691704347195340502901540001631536171928125/44316884429751620882087547143833617431923123069335161742602*t^3 + 7677806118320347904471325094494563560600144434642240891761869697798015728218750/22158442214875810441043773571916808715961561534667580871301*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:   40 out of 41
Indefinite weights: 0 out of 41
Negative weights:   1 out of 41
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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