Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 4 22
-------------------------------------------------
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 22 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^31 - 24747738563437975468285027669966887760383013/67113240439461787943559573994801479684474*t^29 + 17725417157318966622701995809882101681630819078/302009581977578045746018082976606658580133*t^27 - 38563209336510252181855187499909817888828268266835/7248229967461873097904433991438559805923192*t^25 + 6640251448466817785130490905029652852531582609451525/21744689902385619293713301974315679417769576*t^23 - 253961358105313632491565957461907925890836179010183575/21744689902385619293713301974315679417769576*t^21 + 116458771764497610811399109415608112648408076504397825/381485787761151215679180736391503147680168*t^19 - 175144226296048893742324036140191647073942952514072925/31790482313429267973265061365958595640014*t^17 + 4361975814607064495233822396398462498771985286596135375/63580964626858535946530122731917191280028*t^15 - 12366749513046126558299303385104007030854306247171723625/21193654875619511982176707577305730426676*t^13 + 70363915337526784742963560241662641666019914636387081625/21193654875619511982176707577305730426676*t^11 - 516905761537828875556797479328819236449994876601158794625/42387309751239023964353415154611460853352*t^9 + 42762151387960858368773252338570284822158787898373742875/1569900361157000887568645005726350401976*t^7 - 471257905744955351842683326880370425812594563493359800625/14129103250413007988117805051537153617784*t^5 + 260227047861899491324338498760047735475599167584956454375/14129103250413007988117805051537153617784*t^3 - 6847833317295372070523864713987475840910366583407053125/2354850541735501331352967508589525602964*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: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   29 out of 31
Indefinite weights: 0 out of 31
Negative weights:   2 out of 31
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
