Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 32
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 4 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Trying to find an order 32 Kronrod extension for:
P3 : t^9 - 71/3*t^7 + 1399/9*t^5 - 2965/9*t^3 + 590/3*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^41 - 20041075141830018175372523663011892468834990123001643323766876244686103/29244707524374122511034934906912935209344674454314263475326945859459*t^39 + 129415633377040605398195384614683189046207386183887171985235055291087635529/614138858011856572731733633045171639396238163540599532981865863048639*t^37 - 213044631207018688989069814934794267566016771400506562904122188009529271055555/5527249722106709154585602697406544754566143471865395796836792767437751*t^35 + 25910623366125810772157834210701115691101990579704017273868950153714689240278210/5527249722106709154585602697406544754566143471865395796836792767437751*t^33 - 739724802916301856502233695863932165648690275490621214795391493469231494364280740/1842416574035569718195200899135514918188714490621798598945597589145917*t^31 + 83679864012948300216343691595515228224973741061754889379014151034511559034358980/3343768736906660105617424499338502573845216861382574589737926659067*t^29 - 552816731313874482126716017179122259260378004358061820876979166914210636290915220/477681248129522872231060642762643224835030980197510655676846665581*t^27 + 40466278674053316653612035873785756249154896559828087143676555775513634545526555450/1008438190495659396932239134721135696873954291528078050873342960671*t^25 - 1056589312596232528953345919465447287464619506564242561348482654950353766825856404250/1008438190495659396932239134721135696873954291528078050873342960671*t^23 + 20759681238176470114494057095322975376588058015834805025023096945817954647980064270750/1008438190495659396932239134721135696873954291528078050873342960671*t^21 - 305339162869578934410894634417718977968185677282192964338645690796040988765088180960250/1008438190495659396932239134721135696873954291528078050873342960671*t^19 + 175252311723436412223198151228132609870700310563325984034596839983906042618315324908000/53075694236613652470117849195849247203892331133056739519649629509*t^17 - 1396716487033097854057589073481727546840447410934730750582098326217828743992968678632500/53075694236613652470117849195849247203892331133056739519649629509*t^15 + 7972786964268767995050370761006273199419069708860502876377641058791023827174942795707500/53075694236613652470117849195849247203892331133056739519649629509*t^13 - 31707827075173685152410304656819862598213467394946913382553357768940238210450421326122500/53075694236613652470117849195849247203892331133056739519649629509*t^11 + 84537444403092745956036447486519269725609452142091858430360661599485986246510141031923125/53075694236613652470117849195849247203892331133056739519649629509*t^9 - 142774270193978988620589571052160837132962420945333689703987839906329840007564777258925625/53075694236613652470117849195849247203892331133056739519649629509*t^7 + 139260873768401161875385398001801206071136765436129737916616693811246280820069296927246875/53075694236613652470117849195849247203892331133056739519649629509*t^5 - 65711645242755198784747544597407153585456180055463753625885990188387714297909981164690625/53075694236613652470117849195849247203892331133056739519649629509*t^3 + 9659132959185715036144239072041504598612480716467614111193838115790353720128539933781250/53075694236613652470117849195849247203892331133056739519649629509*t
-------------------------------------------------
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:   39 out of 41
Indefinite weights: 0 out of 41
Negative weights:   2 out of 41
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
