Starting with polynomial:
P : t^4 - 6*t^2 + 3
Extension levels are: 4 5 38
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : t^4 - 6*t^2 + 3
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : t^9 - 21*t^7 + 108*t^5 - 135*t^3 + 45*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^47 - 151302055808386406235788351169912012422458547913802523758603416/157281009354020553361820686714156147142188786633746890875247*t^45 + 161237173071669896791070725028756359330738100067290442957715631274/381968165574049915307278810591522071631029910396242449268457*t^43 - 299902668353958550999275199492552046942288160033885586653045150110877/2673777159018349407150951674140654501417209372773697144879199*t^41 + 270139225865718160195108344281932513837801800623180891113104471174502761/13368885795091747035754758370703272507086046863868485724395995*t^39 - 35008755808203192648067750921230584892357645302649940328094491780602897476/13368885795091747035754758370703272507086046863868485724395995*t^37 + 482834222616045503729186537214068664501590630207407698908267911128609138894/1909840827870249576536394052957610358155149551981212246342285*t^35 - 417461700998832535888013611098024544562877467942324143962594819500204690781/22468715622002936194545812387736592448884112376249555839321*t^33 + 23666249631424800271685782785191191967309629364316544874889496853646537981882/22468715622002936194545812387736592448884112376249555839321*t^31 - 1042653889854790203676510106194170067762851495452775831276269703554062447819536/22468715622002936194545812387736592448884112376249555839321*t^29 + 35803154648925375841810696892063197313962281073391324724139332459326229619940436/22468715622002936194545812387736592448884112376249555839321*t^27 - 957409209920702821559209778225683827550001651276444110103715275480065050049522398/22468715622002936194545812387736592448884112376249555839321*t^25 + 19850411508199807985106977280430617716662937231679988548613049238430671982014488550/22468715622002936194545812387736592448884112376249555839321*t^23 - 316593114687436976721746330872893622948209616030374771947114861902620362964507852600/22468715622002936194545812387736592448884112376249555839321*t^21 + 3838719757979088445200381966271117791885062337121351991037766099708940494583162795100/22468715622002936194545812387736592448884112376249555839321*t^19 - 34815519948742611021703154619546402302716736436366600158677422977752335456775933379850/22468715622002936194545812387736592448884112376249555839321*t^17 + 231107909475706326627691901134502903421125973185867597809021172619011327743453198028925/22468715622002936194545812387736592448884112376249555839321*t^15 - 1090856104398143010380091890394312090307213586894991134351714316832754693185361585313000/22468715622002936194545812387736592448884112376249555839321*t^13 + 3522836419189444667803658060389897833096920389065371186126743523944023074251290819197250/22468715622002936194545812387736592448884112376249555839321*t^11 - 7387857336351549913771532876087718967575365919608623360960897960220381728355933207166375/22468715622002936194545812387736592448884112376249555839321*t^9 + 9356886813252807854531678472081294769264238391312320572101476127424066279255908821256375/22468715622002936194545812387736592448884112376249555839321*t^7 - 6439301920336327724368002014162125131429763806088584504651433035180933074878515986773500/22468715622002936194545812387736592448884112376249555839321*t^5 + 2027407613257797915168760917658282956823359998225269574052157275022654109442503927088750/22468715622002936194545812387736592448884112376249555839321*t^3 - 198168884362339221527978734021707856831204359536056833247274128392041896735597582655625/22468715622002936194545812387736592448884112376249555839321*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:   47 out of 47
Indefinite weights: 0 out of 47
Negative weights:   0 out of 47
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (8.3879719478692855268 + 3.6837680035918443253e-911j)  +/-  (3.57e-244, 3.57e-244j)
| (-10.345187627170969024 + 6.0077507045288247964e-918j)  +/-  (3.28e-245, 3.28e-245j)
| (12.075964448234301428 - 8.7305503905546292756e-922j)  +/-  (4.35e-247, 4.35e-247j)
| (-7.2512325364809349188 - 4.8913437370188488912e-916j)  +/-  (4.39e-244, 4.39e-244j)
| (-7.8081124264065449526 - 1.9717417102066382484e-919j)  +/-  (4.83e-244, 4.83e-244j)
| (-8.3879719478692855268 + 3.6560345885788957278e-920j)  +/-  (3.8e-244, 3.8e-244j)
| (-9.6442128903123508674 + 3.8051998878284370312e-921j)  +/-  (1.09e-244, 1.09e-244j)
| (7.2512325364809349188 + 7.4720490571298467557e-918j)  +/-  (4.26e-244, 4.26e-244j)
| (7.8081124264065449526 - 2.7560439594375281436e-930j)  +/-  (4.41e-244, 4.41e-244j)
| (10.345187627170969024 - 2.3830135954296676752e-937j)  +/-  (3.47e-245, 3.47e-245j)
| (-8.996928534672914019 - 7.8606586905514962681e-939j)  +/-  (2.42e-244, 2.42e-244j)
| (-4.6903174458030172718 - 9.617736991622855025e-943j)  +/-  (1.4e-245, 1.4e-245j)
| (11.129686437959854323 - 1.198930861688633725e-940j)  +/-  (5.81e-246, 5.81e-246j)
| (5.1806548283792104012 + 8.7958376047804557174e-949j)  +/-  (4.12e-245, 4.12e-245j)
| (4.2075826795804653545 + 4.9257965914953126291e-964j)  +/-  (4.13e-246, 4.13e-246j)
| (6.7129823465334798671 + 2.0828118518905858569e-985j)  +/-  (3.08e-244, 3.08e-244j)
| (5.6800105651185864661 - 2.6038957898052034758e-1001j)  +/-  (9.62e-245, 9.62e-245j)
| (8.996928534672914019 - 6.876259076697606566e-1011j)  +/-  (2.47e-244, 2.47e-244j)
| (-11.129686437959854323 + 6.9050960996656485763e-1012j)  +/-  (5.41e-246, 5.41e-246j)
| (-12.075964448234301428 + 3.9241208738235238007e-1013j)  +/-  (4.55e-247, 4.55e-247j)
| (9.6442128903123508674 + 2.3600174892046575246e-1011j)  +/-  (1.13e-244, 1.13e-244j)
| (1.8803157728464403442 + 3.0624907114675565285e-1016j)  +/-  (6.54e-250, 6.54e-250j)
| (-2.7949624192159105732 - 2.6815737075079099413e-1014j)  +/-  (3.6e-248, 3.6e-248j)
| (2.7949624192159105732 - 2.0381174997326812325e-1014j)  +/-  (3.37e-248, 3.37e-248j)
| (-3.7313022243357029508 - 2.0231502580843255505e-1012j)  +/-  (9.81e-247, 9.81e-247j)
| (-6.1900953457259161156 + 4.0626958021507016116e-1009j)  +/-  (2.21e-244, 2.21e-244j)
| (-1.0379709584894152952 - 1.168670127698986761e-1019j)  +/-  (1.16e-251, 1.16e-251j)
| (-4.2075826795804653545 - 3.3119220650442997358e-1013j)  +/-  (4.28e-246, 4.28e-246j)
| (2.3344142183389772393 + 5.3132354739980096598e-1018j)  +/-  (5.72e-249, 5.72e-249j)
| (-3.2606044536978902265 - 6.548751909052408084e-1015j)  +/-  (1.97e-247, 1.97e-247j)
| (-6.7129823465334798671 + 9.1628084304653283914e-1013j)  +/-  (3.01e-244, 3.01e-244j)
| (1.0379709584894152952 - 4.1021041541135507067e-1022j)  +/-  (1.18e-251, 1.18e-251j)
| (0.74196378430272585765 + 1.0715077957819108445e-1022j)  +/-  (1.92e-252, 1.92e-252j)
| (4.6903174458030172718 + 1.0882208977935779782e-1016j)  +/-  (1.43e-245, 1.43e-245j)
| (1.43859344100724669 - 1.9224263351822209149e-1026j)  +/-  (8.93e-251, 8.93e-251j)
| (-0.74196378430272585765 - 8.7262057203035463086e-1029j)  +/-  (1.93e-252, 1.93e-252j)
| (-5.1806548283792104012 - 6.2560701824543284392e-1021j)  +/-  (4.33e-245, 4.33e-245j)
| (3.7313022243357029508 + 2.8267170710438458297e-1021j)  +/-  (9.21e-247, 9.21e-247j)
| (3.2606044536978902265 - 8.8516397142660589291e-1026j)  +/-  (2.12e-247, 2.12e-247j)
| (-1.8803157728464403442 - 2.519318083485280169e-1031j)  +/-  (7.62e-250, 7.62e-250j)
| (-0.41075117092504722344 - 3.763198954161545998e-1035j)  +/-  (1.74e-253, 1.74e-253j)
| (6.1900953457259161156 - 8.7456039534367670966e-1031j)  +/-  (2.07e-244, 2.07e-244j)
| (-2.3344142183389772393 + 8.832105631955736075e-1038j)  +/-  (5.55e-249, 5.55e-249j)
| (-1.6362670476688476717e-1056 - 2.936410261269903435e-1057j)  +/-  (7.81e-1055, 7.81e-1055j)
| (-5.6800105651185864661 + 1.0976942833473895243e-1039j)  +/-  (9.37e-245, 9.37e-245j)
| (0.41075117092504722344 - 7.5315992207736149739e-1050j)  +/-  (1.74e-253, 1.74e-253j)
| (-1.43859344100724669 + 1.1184206250992767366e-1047j)  +/-  (8.6e-251, 8.6e-251j)
-------------------------------------------------
The weights are:
| (1.2475064379081781241e-16 - 2.1100147650172803391e-926j)  +/-  (4.25e-75, 5.09e-197j)
| (1.6900836567097555006e-24 + 1.3704522658132407685e-932j)  +/-  (1.05e-79, 1.26e-201j)
| (9.39614761588446441e-33 - 2.9470220713444285732e-936j)  +/-  (7.32e-83, 8.76e-205j)
| (8.3401137562291704819e-13 - 4.0030605639190195856e-926j)  +/-  (3.38e-73, 4.04e-195j)
| (1.3066634478431745126e-14 + 3.5996943538975067042e-927j)  +/-  (1.09e-74, 1.31e-196j)
| (1.2475064379081781241e-16 - 2.7119092378329831389e-928j)  +/-  (2.39e-76, 2.87e-198j)
| (1.7000240016462269709e-21 - 5.7952686808323582483e-931j)  +/-  (2.68e-79, 3.21e-201j)
| (8.3401137562291704819e-13 - 5.280438470154243726e-925j)  +/-  (5.33e-77, 6.38e-199j)
| (1.3066634478431745126e-14 + 1.025715794936975906e-925j)  +/-  (4.51e-78, 5.4e-200j)
| (1.6900836567097555006e-24 - 1.3170197567242932605e-931j)  +/-  (3.84e-84, 4.6e-206j)
| (6.6177683010230741702e-19 + 1.5082872864655384187e-929j)  +/-  (5.05e-80, 6.05e-202j)
| (3.2418701260421270076e-06 + 3.0032229401468642259e-922j)  +/-  (2.81e-72, 3.36e-194j)
| (4.2592175938471911794e-28 + 1.1431579609891135827e-933j)  +/-  (1.28e-85, 1.53e-207j)
| (2.9315572109669786154e-07 - 2.8606607622636296473e-922j)  +/-  (6.54e-75, 7.83e-197j)
| (2.736725773248018462e-05 - 3.5327837242623262516e-921j)  +/-  (9.9e-73, 1.18e-194j)
| (3.465050660947275382e-11 + 2.9174931322476101361e-924j)  +/-  (4.55e-78, 5.45e-200j)
| (1.9859796877259149877e-08 + 6.9248557006191133892e-923j)  +/-  (2.52e-76, 3.01e-198j)
| (6.6177683010230741702e-19 - 4.3351586064821420847e-928j)  +/-  (9.67e-83, 1.16e-204j)
| (4.2592175938471911794e-28 - 1.6005103786028058024e-934j)  +/-  (1.64e-89, 1.96e-211j)
| (9.39614761588446441e-33 + 5.2964901242219668892e-937j)  +/-  (7.25e-92, 8.68e-214j)
| (1.7000240016462269709e-21 + 8.3609274852607550558e-930j)  +/-  (7.95e-85, 9.52e-207j)
| (0.030623559958487136856 + 4.7350555111770321308e-919j)  +/-  (1.1e-69, 1.32e-191j)
| (0.0037182307918566135314 + 3.9023643302289719112e-920j)  +/-  (1.24e-74, 1.48e-196j)
| (0.0037182307918566135314 + 7.7922500637433033036e-920j)  +/-  (1.24e-73, 1.49e-195j)
| (0.00017899958985304406843 + 4.1274845426018503174e-921j)  +/-  (1.4e-77, 1.68e-199j)
| (9.8436576765782592013e-10 - 2.2799532162508421404e-924j)  +/-  (1.17e-82, 1.4e-204j)
| (0.082358491827898504725 + 2.4012282761759933655e-918j)  +/-  (2.05e-68, 2.46e-190j)
| (2.736725773248018462e-05 - 1.1755127758088397127e-921j)  +/-  (5.55e-79, 6.65e-201j)
| (0.011972510815218026062 - 1.9349432795327981758e-919j)  +/-  (5.85e-75, 7e-197j)
| (0.00091760359389756927408 - 1.3189868605005803794e-920j)  +/-  (2.66e-77, 3.18e-199j)
| (3.465050660947275382e-11 + 3.2974358009591271268e-925j)  +/-  (2.36e-83, 2.82e-205j)
| (0.082358491827898504725 + 3.0781171849657424884e-918j)  +/-  (8.67e-72, 1.04e-193j)
| (0.0830130629252693536 - 4.7095904521840230074e-918j)  +/-  (1.28e-71, 1.53e-193j)
| (3.2418701260421270076e-06 + 1.0587669281253349738e-921j)  +/-  (1.86e-80, 2.23e-202j)
| (0.06097149712321006287 - 1.2021422172651268629e-918j)  +/-  (4.1e-74, 4.9e-196j)
| (0.0830130629252693536 - 3.9453140953125087091e-918j)  +/-  (9.67e-74, 1.16e-195j)
| (2.9315572109669786154e-07 - 6.7908497727676762467e-923j)  +/-  (7.43e-82, 8.9e-204j)
| (0.00017899958985304406843 + 1.0720071117453387704e-920j)  +/-  (1.53e-79, 1.83e-201j)
| (0.00091760359389756927408 - 2.9915956150646487338e-920j)  +/-  (7.49e-79, 8.94e-201j)
| (0.030623559958487136856 + 3.0033427181530614663e-919j)  +/-  (1.04e-78, 1.24e-200j)
| (0.14231327070083257264 + 4.0106833250033872248e-918j)  +/-  (4.42e-76, 5.3e-198j)
| (9.8436576765782592013e-10 - 1.4984387533459320392e-923j)  +/-  (1.16e-83, 1.39e-205j)
| (0.011972510815218026062 - 1.0935630341309562164e-919j)  +/-  (1.9e-79, 2.27e-201j)
| (0.16780369902047428483 - 3.7613234118215175193e-918j)  +/-  (1.52e-77, 1.87e-199j)
| (1.9859796877259149877e-08 + 1.3408849137412554834e-923j)  +/-  (1e-83, 1.23e-205j)
| (0.14231327070083257264 + 4.4229720554704417573e-918j)  +/-  (4.67e-78, 7.37e-200j)
| (0.06097149712321006287 - 8.5067270620808342458e-919j)  +/-  (8.37e-79, 8.81e-201j)
