Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 10 31
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Trying to find an order 10 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
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Trying to find an order 31 Kronrod extension for:
P2 : t^14 - 477/7*t^12 + 11241/7*t^10 - 112815/7*t^8 + 68715*t^6 - 108945*t^4 + 46845*t^2 - 2835
Solvable: 1
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Ending with final polynomial:
P : t^45 - 313184886534140510874390202541895666360815441042003990866981471/424635023160733130132146032946621864188665857294391564658621*t^43 + 313294481007066316354388741858236259098502737055661770548948484534/1273905069482199390396438098839865592565997571883174693975863*t^41 - 480615285560216941834212573885041732786157275816175046692639305274800/9766605532696861993039358757772302876339314717771005987148283*t^39 + 236877677394598710426074641479182910651299567649414112816575642063504705/35810886953221827307810982111831777213244153965160355286210371*t^37 - 3241841520623864261306128105406329193646018733030809745752829830091677265/5115840993317403901115854587404539601892021995022907898030053*t^35 + 229211701765728049699069233614961817044968519186328382618294236693210885810/5115840993317403901115854587404539601892021995022907898030053*t^33 - 12222693836187529209603633855620902149993121173182731047478922792141243509080/5115840993317403901115854587404539601892021995022907898030053*t^31 + 498174742001843719564510872442831359479417270651007402746593031813563485529050/5115840993317403901115854587404539601892021995022907898030053*t^29 - 15637262467543102532849682367961025463227246750802717170631939884450607738203150/5115840993317403901115854587404539601892021995022907898030053*t^27 + 379166936660307277332277149360898448066050519498804958928556737227798013015125100/5115840993317403901115854587404539601892021995022907898030053*t^25 - 7096391051940188494179291210708089170336998168301554578948331806940683734519791000/5115840993317403901115854587404539601892021995022907898030053*t^23 + 403371969706603424093334518902796076150681215902076049980064812209841971574544750/20220715388606339530102192045077231628031707490209122126601*t^21 - 4420123689718302653308478612633016066873606004167592004483467720803772894417751250/20220715388606339530102192045077231628031707490209122126601*t^19 + 36435588832619072125405170044460464141685514962169807704448006269173890822066987500/20220715388606339530102192045077231628031707490209122126601*t^17 - 221823980142965935563730726244808391727434995622084024841508114408988857028814985000/20220715388606339530102192045077231628031707490209122126601*t^15 + 972212950534848376270502734013187587599321534235013118485072060479794177363876093125/20220715388606339530102192045077231628031707490209122126601*t^13 - 2959942725129121966875276497069053095650609325055580570317341308848043335539961854375/20220715388606339530102192045077231628031707490209122126601*t^11 + 5950768119985266928356311882302984137082560546034165085964239905775369207705689256250/20220715388606339530102192045077231628031707490209122126601*t^9 - 7326599103419609029190709697659804405771415138175503508131866132770325457993661775000/20220715388606339530102192045077231628031707490209122126601*t^7 + 4878625787542456685702186341444310132053474219547688215438546771329583504494029009375/20220715388606339530102192045077231628031707490209122126601*t^5 - 59454488797338681920246858457230338256375180838530176898692189401749096866357359375/879161538635058240439225741090314418610074238704744440287*t^3 + 75787130948750217569484330301875869205673258063564133350929727994216436151547156250/20220715388606339530102192045077231628031707490209122126601*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:   43 out of 45
Indefinite weights: 0 out of 45
Negative weights:   2 out of 45
Extension rule has valid weights: 0
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*** EXTENSION WITH INVALID WEIGHTS ***
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