Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 5 36
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Trying to find an order 5 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
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Trying to find an order 36 Kronrod extension for:
P2 : t^7 - 53/3*t^5 + 215/3*t^3 - 55*t
Solvable: 1
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Ending with final polynomial:
P : t^43 - 4963877418916849657201242303771838011767550672355/5704955889151219891120510691412034070932977681*t^41 + 15582483346496486490146577962603997837003716930886671/45639647113209759128964085531296272567463821448*t^39 - 6098197867015311851302895372023274867119083006213349151/76066078522016265214940142552160454279106369080*t^37 + 958755324443548580784883270884038062551581739582485706261/76066078522016265214940142552160454279106369080*t^35 - 21400844444821631737887886127101785992104982501566278597507/15213215704403253042988028510432090855821273816*t^33 + 438560054185789614916890757605792370210730449806796730511453/3803303926100813260747007127608022713955318454*t^31 - 26950647391760341575932409362302311285899659501015124873979315/3803303926100813260747007127608022713955318454*t^29 + 1256614490418651424966435124563143819375658223621237949384904401/3803303926100813260747007127608022713955318454*t^27 - 3440163093652938825686381758241429672005321207156749649437778407/292561840469293327749769779046770977996562958*t^25 + 187142943638192877313609691564139295689213261169766167431961767975/585123680938586655499539558093541955993125916*t^23 - 3879670590354472266801737459360912055340512656067517936562270346225/585123680938586655499539558093541955993125916*t^21 + 60904767454619854786240470099389781386333450509724287913924324839875/585123680938586655499539558093541955993125916*t^19 - 716540752497881027313646401673761843524131047574813903695488220518025/585123680938586655499539558093541955993125916*t^17 + 3112645351439508528769245877520381132248487586482380458714351206243325/292561840469293327749769779046770977996562958*t^15 - 19569309231432629396867756692871929381723400628749110895560383104479875/292561840469293327749769779046770977996562958*t^13 + 86566293968857084684664941464214117504673857996615502967439242030349875/292561840469293327749769779046770977996562958*t^11 - 258734046356154026641315762276189376618199346518697208461050830465840625/292561840469293327749769779046770977996562958*t^9 + 1963800493752519211236203222740846003672776216396516615593185675763966625/1170247361877173310999079116187083911986251832*t^7 - 2131985069593241770535663888532769843616952462237571678837582175321160375/1170247361877173310999079116187083911986251832*t^5 + 1089735668106867422489501006172284041531174632245315294887706724318658125/1170247361877173310999079116187083911986251832*t^3 - 165734756789443697915182301854446094650607802136733150841421471262164375/1170247361877173310999079116187083911986251832*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:   41 out of 43
Indefinite weights: 0 out of 43
Negative weights:   2 out of 43
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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