Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 10 31
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Trying to find an order 10 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
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Trying to find an order 31 Kronrod extension for:
P2 : 16*t^14 - 3816/7*t^12 + 44964/7*t^10 - 225630/7*t^8 + 68715*t^6 - 108945/2*t^4 + 46845/4*t^2 - 2835/8
Solvable: 1
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Ending with final polynomial:
P : 16*t^45 - 2505479092273124086995121620335165330886523528336031926935851768/424635023160733130132146032946621864188665857294391564658621*t^43 + 1253177924028265265417554967432945036394010948222647082195793938136/1273905069482199390396438098839865592565997571883174693975863*t^41 - 961230571120433883668425147770083465572314551632350093385278610549600/9766605532696861993039358757772302876339314717771005987148283*t^39 + 236877677394598710426074641479182910651299567649414112816575642063504705/35810886953221827307810982111831777213244153965160355286210371*t^37 - 3241841520623864261306128105406329193646018733030809745752829830091677265/10231681986634807802231709174809079203784043990045815796060106*t^35 + 114605850882864024849534616807480908522484259593164191309147118346605442905/10231681986634807802231709174809079203784043990045815796060106*t^33 - 1527836729523441151200454231952612768749140146647841380934865349017655438635/5115840993317403901115854587404539601892021995022907898030053*t^31 + 249087371000921859782255436221415679739708635325503701373296515906781742764525/40926727946539231208926836699236316815136175960183263184240424*t^29 - 7818631233771551266424841183980512731613623375401358585315969942225303869101575/81853455893078462417853673398472633630272351920366526368480848*t^27 + 94791734165076819333069287340224612016512629874701239732139184306949503253781275/81853455893078462417853673398472633630272351920366526368480848*t^25 - 887048881492523561772411401338511146292124771037694322368541475867585466814973875/81853455893078462417853673398472633630272351920366526368480848*t^23 + 201685984853301712046667259451398038075340607951038024990032406104920985787272375/2588251569741611459853080581769885648388058558746767632204928*t^21 - 2210061844859151326654239306316508033436803002083796002241733860401886447208875625/5176503139483222919706161163539771296776117117493535264409856*t^19 + 9108897208154768031351292511115116035421378740542451926112001567293472705516746875/5176503139483222919706161163539771296776117117493535264409856*t^17 - 27727997517870741945466340780601048965929374452760503105188514301123607128601873125/5176503139483222919706161163539771296776117117493535264409856*t^15 + 972212950534848376270502734013187587599321534235013118485072060479794177363876093125/82824050231731566715298578616636340748417873879896564230557696*t^13 - 2959942725129121966875276497069053095650609325055580570317341308848043335539961854375/165648100463463133430597157233272681496835747759793128461115392*t^11 + 2975384059992633464178155941151492068541280273017082542982119952887684603852844628125/165648100463463133430597157233272681496835747759793128461115392*t^9 - 915824887927451128648838712207475550721426892271937938516483266596290682249207721875/82824050231731566715298578616636340748417873879896564230557696*t^7 + 4878625787542456685702186341444310132053474219547688215438546771329583504494029009375/1325184803707705067444777257866181451974685982078345027688923136*t^5 - 59454488797338681920246858457230338256375180838530176898692189401749096866357359375/115233461191974353690850196336189691476059650615508263277297664*t^3 + 37893565474375108784742165150937934602836629031782066675464863997108218075773578125/2650369607415410134889554515732362903949371964156690055377846272*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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