Starting with polynomial:
P : t^2 - 1
Extension levels are: 2 3 38
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : t^2 - 1
Solvable: 1
-------------------------------------------------
Trying to find an order 38 Kronrod extension for:
P2 : t^5 - 7*t^3 + 6*t
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : t^43 - 13538790826894975698918133043106201220877/16490431217411995115346353257132075356*t^41 + 5023791792361870677802820803790254245787457/16490431217411995115346353257132075356*t^39 - 372469002459309004732526088760107147733226209/5496810405803998371782117752377358452*t^37 + 18512296044115847598350252455393392225511764629/1832270135267999457260705917459119484*t^35 - 980382441175174613373656618407243249627195433575/916135067633999728630352958729559742*t^33 + 38134282692972321006511099015851214870110432777225/458067533816999864315176479364779871*t^31 - 2222537707512782775144512388699729710751150702543015/458067533816999864315176479364779871*t^29 + 98125793794491892210931737999407051502733339600862315/458067533816999864315176479364779871*t^27 - 6595384843580320032199012139318305705821375425569350015/916135067633999728630352958729559742*t^25 + 168679028940576238039456860502846413774988645983683796375/916135067633999728630352958729559742*t^23 - 3267536592708051596862914385435597251301077779264037212125/916135067633999728630352958729559742*t^21 + 47505015657659265791461917760450352457800901649813670944875/916135067633999728630352958729559742*t^19 - 255596889836545429378610268543177616592094915940519831456500/458067533816999864315176479364779871*t^17 + 1996878894183585434068273480712932241394511529114593522525125/458067533816999864315176479364779871*t^15 - 11038395946094716623086447532106293222163105582003240115401875/458067533816999864315176479364779871*t^13 + 41736432900405481638909101591131480061651765977973198947072500/458067533816999864315176479364779871*t^11 - 413033826811243223127466192473359835332333449423217476712923125/1832270135267999457260705917459119484*t^9 + 630277541799102361891880440491596969650443660214147650712910625/1832270135267999457260705917459119484*t^7 - 544747462033753238361273889135041681063248387186664572957881875/1832270135267999457260705917459119484*t^5 + 228698445490860556809413789831786310962768746103255596990228125/1832270135267999457260705917459119484*t^3 - 15520386894389696408665506786559774420695104982384131697853125/916135067633999728630352958729559742*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
-------------------------------------------------
The nodes are:
| (8.4552498233092936008 - 2.0169977638166347167e-825j)  +/-  (3.19e-245, 3.19e-245j)
| (-8.4552498233092936008 - 8.3881341154942620318e-830j)  +/-  (3.8e-245, 3.8e-245j)
| (9.8427072099169912637 + 2.5803238860047107536e-833j)  +/-  (6.19e-246, 6.19e-246j)
| (-9.1222847858849557952 - 3.2739348316086465309e-841j)  +/-  (1.97e-245, 1.97e-245j)
| (-9.8427072099169912637 - 2.9888697750653899611e-840j)  +/-  (6.83e-246, 6.83e-246j)
| (9.1222847858849557952 - 1.4597428990655968619e-840j)  +/-  (1.86e-245, 1.86e-245j)
| (-11.614324301063743987 - 9.1145634421778527688e-845j)  +/-  (1.19e-247, 1.19e-247j)
| (-1.4536321165021567392 + 5.132985003860715486e-849j)  +/-  (1.07e-250, 1.07e-250j)
| (-7.8259616172220058056 + 1.9613195036717271904e-841j)  +/-  (4.99e-245, 4.99e-245j)
| (5.5385553550273007612 - 4.8738165685055378431e-841j)  +/-  (1.24e-245, 1.24e-245j)
| (11.614324301063743987 - 2.8514166853741705284e-847j)  +/-  (1.13e-247, 1.13e-247j)
| (6.0851485338123196603 - 1.2227532441765712901e-843j)  +/-  (2.41e-245, 2.41e-245j)
| (-10.646866902853343831 - 1.2605673639556163834e-853j)  +/-  (1.37e-246, 1.37e-246j)
| (6.6462155938569140026 - 9.1350356339862255066e-853j)  +/-  (3.93e-245, 3.93e-245j)
| (-5.0039108648545928963 + 3.6391587814744258677e-856j)  +/-  (4.99e-246, 4.99e-246j)
| (10.646866902853343831 - 4.881064431785410546e-858j)  +/-  (1.32e-246, 1.32e-246j)
| (2.4494897427831780982 - 3.2424240687774762568e-860j)  +/-  (3.37e-249, 3.37e-249j)
| (-5.5385553550273007612 + 6.7376967091928099045e-856j)  +/-  (1.27e-245, 1.27e-245j)
| (-2.9491284863764277952 + 3.256427497542135676e-865j)  +/-  (2.13e-248, 2.13e-248j)
| (-6.6462155938569140026 + 1.1293547731535964115e-862j)  +/-  (4.37e-245, 4.37e-245j)
| (1.9527064670283988894 - 1.0990299968790369673e-870j)  +/-  (5.52e-250, 5.52e-250j)
| (0.49105520599650593361 + 7.1369220468483932501e-875j)  +/-  (1.51e-253, 1.51e-253j)
| (3.9627450258545238853 - 2.5592421481958383623e-866j)  +/-  (4.71e-247, 4.71e-247j)
| (3.4531419002475825609 + 1.4131700989055938972e-869j)  +/-  (1.05e-247, 1.05e-247j)
| (-6.0851485338123196603 + 8.8184220997975087876e-869j)  +/-  (2.34e-245, 2.34e-245j)
| (1.120936058367399685 - 4.5263338194036597801e-885j)  +/-  (5.06e-251, 5.06e-251j)
| (7.2250219823996450916 + 1.7018324839479394387e-877j)  +/-  (5.14e-245, 5.14e-245j)
| (5.0039108648545928963 - 2.3157394563448944518e-889j)  +/-  (5.05e-246, 5.05e-246j)
| (-7.2250219823996450916 + 1.5132015323465003715e-902j)  +/-  (4.95e-245, 4.95e-245j)
| (-1.120936058367399685 - 5.0132747489901265542e-925j)  +/-  (4.86e-251, 4.86e-251j)
| (7.8259616172220058056 - 2.3921424625579933884e-926j)  +/-  (4.46e-245, 4.46e-245j)
| (2.9491284863764277952 + 7.1330404470555233393e-941j)  +/-  (1.95e-248, 1.95e-248j)
| (-5.6210833496281124389e-966 + 2.0424183914571919293e-967j)  +/-  (2.42e-964, 2.42e-964j)
| (1.4536321165021567392 - 1.079243946258856818e-942j)  +/-  (1.12e-250, 1.12e-250j)
| (-2.4494897427831780982 + 4.7339652514275366726e-941j)  +/-  (3.66e-249, 3.66e-249j)
| (-1 + 1.5540733514602345572e-943j)  +/-  (2.26e-251, 2.26e-251j)
| (-1.9527064670283988894 - 5.0479889202885215205e-942j)  +/-  (5.76e-250, 5.76e-250j)
| (1 - 1.5904600202913036817e-943j)  +/-  (2.15e-251, 2.15e-251j)
| (-3.4531419002475825609 + 1.4929687142836135103e-939j)  +/-  (1.08e-247, 1.08e-247j)
| (-4.4791957217248377852 + 2.5227624714598303715e-939j)  +/-  (1.59e-246, 1.59e-246j)
| (-0.49105520599650593361 - 3.6393575414140649701e-949j)  +/-  (1.51e-253, 1.51e-253j)
| (-3.9627450258545238853 - 4.0843940997118861896e-946j)  +/-  (4.77e-247, 4.77e-247j)
| (4.4791957217248377852 + 2.0830090951592856608e-954j)  +/-  (1.73e-246, 1.73e-246j)
-------------------------------------------------
The weights are:
| (7.7119614325224268536e-17 + 6.9508071422812989313e-841j)  +/-  (5.75e-84, 1.69e-205j)
| (7.7119614325224268536e-17 + 9.1695260111650684961e-843j)  +/-  (2.07e-84, 6.08e-206j)
| (2.7668016910326341335e-22 - 1.5594961491420686908e-844j)  +/-  (2.58e-87, 7.57e-209j)
| (2.3433145409096327762e-19 - 4.1844385985180061896e-844j)  +/-  (5.51e-86, 1.62e-207j)
| (2.7668016910326341335e-22 + 1.1831453841333689612e-845j)  +/-  (9.48e-88, 2.78e-209j)
| (2.3433145409096327762e-19 + 1.1014671964473451145e-842j)  +/-  (3.86e-87, 1.13e-208j)
| (2.2741178968319067287e-30 + 6.9948789508069246165e-850j)  +/-  (1.15e-91, 3.37e-213j)
| (0.070592696122256454101 - 4.1335134125038836881e-833j)  +/-  (7.58e-61, 2.22e-182j)
| (1.2293079070645965307e-14 - 1.4108669432527181419e-841j)  +/-  (2.09e-84, 6.15e-206j)
| (4.7030639462551040684e-08 - 3.1467103566115485958e-837j)  +/-  (1.39e-81, 4.07e-203j)
| (2.2741178968319067287e-30 - 4.4426961478706750922e-849j)  +/-  (2.28e-93, 6.68e-215j)
| (2.0098488468246290991e-09 + 6.5818060724999257147e-838j)  +/-  (3.87e-83, 1.14e-204j)
| (8.3685693050790483142e-26 - 1.6809110979893141609e-847j)  +/-  (4.22e-91, 1.24e-212j)
| (5.8129323103963033009e-11 - 1.2221738527186124383e-838j)  +/-  (1.53e-84, 4.48e-206j)
| (7.7178860480090892783e-07 + 3.4177092479382437346e-837j)  +/-  (9.09e-83, 2.67e-204j)
| (8.3685693050790483142e-26 + 1.4645568791457680643e-846j)  +/-  (7.41e-92, 2.17e-213j)
| (0.0098892130188462243777 - 4.3788933164811401829e-834j)  +/-  (1.63e-75, 4.8e-197j)
| (4.7030639462551040684e-08 - 6.5573593757083201354e-838j)  +/-  (4.59e-84, 1.35e-205j)
| (0.0025862816694361694241 + 7.4924403320231368078e-835j)  +/-  (1.37e-78, 4.03e-200j)
| (5.8129323103963033009e-11 - 1.4635651071927869714e-839j)  +/-  (3.99e-86, 1.17e-207j)
| (0.02941484458537991661 + 1.3049121677476166824e-833j)  +/-  (3.17e-75, 9.31e-197j)
| (0.17427167871350475071 + 6.2162043764197497504e-833j)  +/-  (4.75e-73, 1.39e-194j)
| (7.9602234868012884237e-05 + 1.7140248293233552603e-835j)  +/-  (2.51e-82, 7.36e-204j)
| (0.00052032744767408467761 - 5.3355079941268169749e-835j)  +/-  (4.17e-81, 1.23e-202j)
| (2.0098488468246290991e-09 + 1.0725753457060555041e-838j)  +/-  (2.88e-86, 8.45e-208j)
| (-0.029891536805174519972 + 2.4792218177837794948e-832j)  +/-  (4.91e-74, 1.44e-195j)
| (1.0857977726372399784e-12 + 2.0688353527162811092e-839j)  +/-  (2.57e-88, 7.54e-210j)
| (7.7178860480090892783e-07 + 1.3330034855086907406e-836j)  +/-  (4.1e-85, 1.2e-206j)
| (1.0857977726372399784e-12 + 1.6222920719121953844e-840j)  +/-  (4.98e-89, 1.46e-210j)
| (-0.029891536805174519972 + 1.8987708402648410842e-832j)  +/-  (7.23e-78, 2.12e-199j)
| (1.2293079070645965307e-14 - 3.6541807044922514739e-840j)  +/-  (1.92e-89, 5.64e-211j)
| (0.0025862816694361694241 + 1.5519503415193967231e-834j)  +/-  (6.41e-82, 1.88e-203j)
| (0.19561051776700420173 - 5.0378712488501137586e-833j)  +/-  (5.94e-78, 1.75e-199j)
| (0.070592696122256454101 - 5.8500342674953852823e-833j)  +/-  (3.78e-79, 1.11e-200j)
| (0.0098892130188462243777 - 2.4115384885323300834e-834j)  +/-  (2.33e-83, 6.85e-205j)
| (0.14472168218664816689 - 1.8569927976441820703e-832j)  +/-  (1.86e-79, 5.45e-201j)
| (0.02941484458537991661 + 8.152324387225972971e-834j)  +/-  (1.73e-82, 5.09e-204j)
| (0.14472168218664816689 - 2.3552103014943726891e-832j)  +/-  (4.13e-80, 1.21e-201j)
| (0.00052032744767408467761 - 2.2409920054092465587e-835j)  +/-  (7.04e-86, 2.07e-207j)
| (9.131054738037835216e-06 - 1.5476576667010177751e-836j)  +/-  (1.09e-87, 3.19e-209j)
| (0.17427167871350475071 + 5.5337462054467871024e-833j)  +/-  (2.74e-83, 8.3e-205j)
| (7.9602234868012884237e-05 + 6.200272691882353122e-836j)  +/-  (4.71e-87, 1.38e-208j)
| (9.131054738037835216e-06 - 5.0352801815208399665e-836j)  +/-  (7.03e-88, 2.09e-209j)
