Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^29 - 616772358982709116157490999324063452976243194053/1550562711749803401852393689194704654275504354*t^28 + 5709543934014672309445511303114050627987805002029179/38764067793745085046309842229867616356887608850*t^27 - 1308612913412918501735958126973166180632587211378688691/38764067793745085046309842229867616356887608850*t^26 + 104134665727984303430941612219502988815537434382854442079/19382033896872542523154921114933808178443804425*t^25 - 489537720014341719843794289066518491130195195366159450325/775281355874901700926196844597352327137752177*t^24 + 44110284483860992804867295285104641837580048047663138406800/775281355874901700926196844597352327137752177*t^23 - 3123263582558882886695334894910720050801900455101525144053840/775281355874901700926196844597352327137752177*t^22 + 176713562646996747694200786181842405173064352781631852625721760/775281355874901700926196844597352327137752177*t^21 - 197127859413834169946004442548957691621209090137671045349299680/18909301362802480510395044990179325052140297*t^20 + 301149915571555572396774046430151683982819685087285101261214824000/775281355874901700926196844597352327137752177*t^19 - 9187097571673141616337962732238540974125931202580081931268472296000/775281355874901700926196844597352327137752177*t^18 + 230080350735618636456684690660087930344084662949039275306655406902400/775281355874901700926196844597352327137752177*t^17 - 4733649964911068659172971296971129338654960383213608176754313740937600/775281355874901700926196844597352327137752177*t^16 + 79922084424461846409966244542220861637382601624258175313914215297228800/775281355874901700926196844597352327137752177*t^15 - 1104310014964950646670603097106218179295868328939177590299699460469760000/775281355874901700926196844597352327137752177*t^14 + 12431407893078534126471955072577262689396668830740180775613238159216640000/775281355874901700926196844597352327137752177*t^13 - 113294753267257743309724841346895218149068637553857749760971581523329024000/775281355874901700926196844597352327137752177*t^12 + 828944199209655144915059646437238648360310976963673407478396103060924416000/775281355874901700926196844597352327137752177*t^11 - 4817207907335310162149031531838192344681233397654572324438570192841566208000/775281355874901700926196844597352327137752177*t^10 + 21932480938871936095300471600487869857983121100166178249200317498799001600000/775281355874901700926196844597352327137752177*t^9 - 76890803098258757482091184061716052181049715691018190978376626618315878400000/775281355874901700926196844597352327137752177*t^8 + 203012561664446319083509993747397653542806328968847308533980433294763950080000/775281355874901700926196844597352327137752177*t^7 - 392192170575090799472948546652096178735738686742614915368878376513090027520000/775281355874901700926196844597352327137752177*t^6 + 533403109761782315655244646016816780839488834971552250906878721383327989760000/775281355874901700926196844597352327137752177*t^5 - 484102095712082021191290892917483952790088726712466902136664419717824512000000/775281355874901700926196844597352327137752177*t^4 + 271006285362175578964653268110858943972558587899486970303184406014230528000000/775281355874901700926196844597352327137752177*t^3 - 82513325900747117853139825498420979350860670942389851225622449548559646720000/775281355874901700926196844597352327137752177*t^2 + 10833812333183961094235198792423543558394224856700937614164652455564410880000/775281355874901700926196844597352327137752177*t - 346332560338326875571777278403535917887764721494478454786462175332925440000/775281355874901700926196844597352327137752177
-------------------------------------------------
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:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (84.69461047364169805 - 9.1554860835986715057e-590j)  +/-  (2.68e-243, 2.68e-243j)
| (67.136123680443678173 - 2.3255374085888530699e-587j)  +/-  (8.41e-242, 8.41e-242j)
| (60.129278829378114457 - 1.1349221785037615168e-594j)  +/-  (2.44e-241, 2.44e-241j)
| (75.164701176918306872 + 2.2103915397600493304e-605j)  +/-  (1.9e-242, 1.9e-242j)
| (53.893264213788961834 + 2.0688247740225579499e-632j)  +/-  (5.01e-241, 5.01e-241j)
| (5.7737169591834981623 - 1.8102007814517594164e-659j)  +/-  (1.1e-245, 1.1e-245j)
| (48.275704626295250035 + 1.7213090573954486011e-696j)  +/-  (1.02e-240, 1.02e-240j)
| (30.345081551898866835 + 1.9001909338653262949e-731j)  +/-  (8.73e-241, 8.73e-241j)
| (38.519945575324838348 + 1.2276472780272884884e-755j)  +/-  (1.3e-240, 1.3e-240j)
| (12.83565314353618842 - 6.8365263342048360627e-767j)  +/-  (5.85e-243, 5.85e-243j)
| (20.429316540669066451 + 7.7447619403756987531e-777j)  +/-  (1.42e-241, 1.42e-241j)
| (96.958048557053312862 + 1.2319760081611026582e-787j)  +/-  (1.57e-244, 1.57e-244j)
| (10.758799469341025187 - 1.1952389002143596785e-790j)  +/-  (1.45e-243, 1.45e-243j)
| (4.5038959251329760802 - 4.6183700652862169166e-803j)  +/-  (1.67e-246, 1.67e-246j)
| (34.256800551599302158 - 2.0319096235713620033e-806j)  +/-  (1.28e-240, 1.28e-240j)
| (1.7137074822604837192 - 3.4283149129621303306e-832j)  +/-  (2.17e-249, 2.17e-249j)
| (0.23971225194117201998 - 1.3364025423391386481e-837j)  +/-  (3.91e-253, 3.91e-253j)
| (7.234591275098890658 + 6.0317309726172406211e-827j)  +/-  (6.01e-245, 6.01e-245j)
| (43.175196931390707469 - 3.6728545477939161419e-823j)  +/-  (1.29e-240, 1.29e-240j)
| (17.660137615195634717 + 9.105136585463802251e-829j)  +/-  (5.79e-242, 5.79e-242j)
| (3.4142135623730950488 + 7.9799446354735474015e-835j)  +/-  (2.31e-247, 2.31e-247j)
| (0.5857864376269049512 - 2.6660790693375601063e-839j)  +/-  (1.07e-251, 1.07e-251j)
| (26.752848151803946374 - 1.3589124021337514919e-827j)  +/-  (5.6e-241, 5.6e-241j)
| (0.0456374197855743167 - 5.4458483916187737479e-845j)  +/-  (1.08e-254, 1.08e-254j)
| (23.454523618031069879 - 2.740555172681939849e-831j)  +/-  (2.97e-241, 2.97e-241j)
| (8.894105489286762625 - 5.2449630985224660389e-836j)  +/-  (2.87e-244, 2.87e-244j)
| (1.0788922354753778824 + 9.7370720819704144973e-842j)  +/-  (1.58e-250, 1.58e-250j)
| (2.489356261202614551 - 1.0233184293998620451e-840j)  +/-  (2.53e-248, 2.53e-248j)
| (15.132836839326379458 + 1.0564965900463476558e-833j)  +/-  (1.89e-242, 1.89e-242j)
-------------------------------------------------
The weights are:
| (1.7436857949936847121e-36 - 1.1183769663224522361e-620j)  +/-  (5.43e-99, 7.53e-218j)
| (5.2011800271493299166e-29 + 6.1413770090753687995e-616j)  +/-  (1.82e-96, 2.52e-215j)
| (5.0708292221311981572e-26 - 5.7083091219911382526e-615j)  +/-  (1.49e-95, 2.06e-214j)
| (1.969174760443023858e-32 + 2.7646248250642773641e-618j)  +/-  (4.3e-98, 5.96e-217j)
| (2.321620723808094549e-23 + 6.8431554157277862513e-614j)  +/-  (4.88e-95, 6.76e-214j)
| (0.0042392136456407938265 - 6.3671558220353258005e-604j)  +/-  (6.16e-76, 8.54e-195j)
| (5.7820536456665651735e-21 - 8.0338433001862547347e-613j)  +/-  (1.31e-94, 1.82e-213j)
| (2.4831946243701501686e-13 - 3.4542906349305447808e-609j)  +/-  (3.98e-92, 5.52e-211j)
| (8.3082554100380501404e-17 - 7.1515452570376358213e-611j)  +/-  (7.84e-94, 1.09e-212j)
| (5.8224296806495040128e-06 - 1.8109200700377334017e-605j)  +/-  (1.07e-86, 1.48e-205j)
| (3.8837455196979428421e-09 + 4.2165837803630792186e-607j)  +/-  (3.09e-90, 4.28e-209j)
| (1.1410360204485980004e-41 + 1.5711607025300606546e-623j)  +/-  (5.03e-105, 6.97e-224j)
| (4.1867305990609401636e-05 + 5.1438400884206709594e-605j)  +/-  (2.65e-86, 3.68e-205j)
| (0.013030444645929648351 + 1.1738544219126918226e-603j)  +/-  (1.63e-81, 2.26e-200j)
| (5.4110043809359110527e-15 + 5.3469451432038995771e-610j)  +/-  (1.72e-93, 2.39e-212j)
| (0.1269840128101909687 - 2.9780523751748856414e-603j)  +/-  (1.29e-78, 1.79e-197j)
| (0.2130263685314482983 + 1.3256038124409942467e-603j)  +/-  (1.29e-78, 1.79e-197j)
| (0.0011244138760338435832 + 3.0613039823475107711e-604j)  +/-  (4.98e-85, 6.9e-204j)
| (8.6412517746668465588e-19 + 8.1995010314232679695e-612j)  +/-  (3.82e-95, 5.3e-214j)
| (5.6611584536829328079e-08 - 1.6458391846312372444e-606j)  +/-  (1.37e-90, 1.9e-209j)
| (0.033048489485214117498 - 1.8834414737646628098e-603j)  +/-  (1.94e-84, 2.7e-203j)
| (0.23411089308844294662 - 2.2530845095673045529e-603j)  +/-  (1.74e-82, 2.41e-201j)
| (8.2818643567781739259e-12 + 1.945080804238882401e-608j)  +/-  (6.1e-93, 8.46e-212j)
| (0.11181439012967145001 - 4.0914265104092931099e-604j)  +/-  (2.37e-84, 3.28e-203j)
| (2.0574524039073340386e-10 - 9.6251348635340187014e-608j)  +/-  (2.39e-92, 3.31e-211j)
| (0.00024160239615158812788 - 1.320774874469009853e-604j)  +/-  (5.52e-89, 7.61e-208j)
| (0.19197623098662213748 + 2.8690221228513793685e-603j)  +/-  (1.79e-86, 2.45e-205j)
| (0.070355544316772400574 + 2.5801229098000060127e-603j)  +/-  (2.66e-87, 3.62e-206j)
| (6.4564259957232436503e-07 + 5.755178773868200805e-606j)  +/-  (9.65e-91, 1.34e-209j)
Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 27
-------------------------------------------------
Trying to find an order 27 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^29 - 616772358982709116157490999324063452976243194053/1550562711749803401852393689194704654275504354*t^28 + 5709543934014672309445511303114050627987805002029179/38764067793745085046309842229867616356887608850*t^27 - 1308612913412918501735958126973166180632587211378688691/38764067793745085046309842229867616356887608850*t^26 + 104134665727984303430941612219502988815537434382854442079/19382033896872542523154921114933808178443804425*t^25 - 489537720014341719843794289066518491130195195366159450325/775281355874901700926196844597352327137752177*t^24 + 44110284483860992804867295285104641837580048047663138406800/775281355874901700926196844597352327137752177*t^23 - 3123263582558882886695334894910720050801900455101525144053840/775281355874901700926196844597352327137752177*t^22 + 176713562646996747694200786181842405173064352781631852625721760/775281355874901700926196844597352327137752177*t^21 - 197127859413834169946004442548957691621209090137671045349299680/18909301362802480510395044990179325052140297*t^20 + 301149915571555572396774046430151683982819685087285101261214824000/775281355874901700926196844597352327137752177*t^19 - 9187097571673141616337962732238540974125931202580081931268472296000/775281355874901700926196844597352327137752177*t^18 + 230080350735618636456684690660087930344084662949039275306655406902400/775281355874901700926196844597352327137752177*t^17 - 4733649964911068659172971296971129338654960383213608176754313740937600/775281355874901700926196844597352327137752177*t^16 + 79922084424461846409966244542220861637382601624258175313914215297228800/775281355874901700926196844597352327137752177*t^15 - 1104310014964950646670603097106218179295868328939177590299699460469760000/775281355874901700926196844597352327137752177*t^14 + 12431407893078534126471955072577262689396668830740180775613238159216640000/775281355874901700926196844597352327137752177*t^13 - 113294753267257743309724841346895218149068637553857749760971581523329024000/775281355874901700926196844597352327137752177*t^12 + 828944199209655144915059646437238648360310976963673407478396103060924416000/775281355874901700926196844597352327137752177*t^11 - 4817207907335310162149031531838192344681233397654572324438570192841566208000/775281355874901700926196844597352327137752177*t^10 + 21932480938871936095300471600487869857983121100166178249200317498799001600000/775281355874901700926196844597352327137752177*t^9 - 76890803098258757482091184061716052181049715691018190978376626618315878400000/775281355874901700926196844597352327137752177*t^8 + 203012561664446319083509993747397653542806328968847308533980433294763950080000/775281355874901700926196844597352327137752177*t^7 - 392192170575090799472948546652096178735738686742614915368878376513090027520000/775281355874901700926196844597352327137752177*t^6 + 533403109761782315655244646016816780839488834971552250906878721383327989760000/775281355874901700926196844597352327137752177*t^5 - 484102095712082021191290892917483952790088726712466902136664419717824512000000/775281355874901700926196844597352327137752177*t^4 + 271006285362175578964653268110858943972558587899486970303184406014230528000000/775281355874901700926196844597352327137752177*t^3 - 82513325900747117853139825498420979350860670942389851225622449548559646720000/775281355874901700926196844597352327137752177*t^2 + 10833812333183961094235198792423543558394224856700937614164652455564410880000/775281355874901700926196844597352327137752177*t - 346332560338326875571777278403535917887764721494478454786462175332925440000/775281355874901700926196844597352327137752177
-------------------------------------------------
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:   29 out of 29
Indefinite weights: 0 out of 29
Negative weights:   0 out of 29
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (84.69461047364169805 - 9.1554860835986715057e-590j)  +/-  (2.68e-243, 2.68e-243j)
| (67.136123680443678173 - 2.3255374085888530699e-587j)  +/-  (8.41e-242, 8.41e-242j)
| (60.129278829378114457 - 1.1349221785037615168e-594j)  +/-  (2.44e-241, 2.44e-241j)
| (75.164701176918306872 + 2.2103915397600493304e-605j)  +/-  (1.9e-242, 1.9e-242j)
| (53.893264213788961834 + 2.0688247740225579499e-632j)  +/-  (5.01e-241, 5.01e-241j)
| (5.7737169591834981623 - 1.8102007814517594164e-659j)  +/-  (1.1e-245, 1.1e-245j)
| (48.275704626295250035 + 1.7213090573954486011e-696j)  +/-  (1.02e-240, 1.02e-240j)
| (30.345081551898866835 + 1.9001909338653262949e-731j)  +/-  (8.73e-241, 8.73e-241j)
| (38.519945575324838348 + 1.2276472780272884884e-755j)  +/-  (1.3e-240, 1.3e-240j)
| (12.83565314353618842 - 6.8365263342048360627e-767j)  +/-  (5.85e-243, 5.85e-243j)
| (20.429316540669066451 + 7.7447619403756987531e-777j)  +/-  (1.42e-241, 1.42e-241j)
| (96.958048557053312862 + 1.2319760081611026582e-787j)  +/-  (1.57e-244, 1.57e-244j)
| (10.758799469341025187 - 1.1952389002143596785e-790j)  +/-  (1.45e-243, 1.45e-243j)
| (4.5038959251329760802 - 4.6183700652862169166e-803j)  +/-  (1.67e-246, 1.67e-246j)
| (34.256800551599302158 - 2.0319096235713620033e-806j)  +/-  (1.28e-240, 1.28e-240j)
| (1.7137074822604837192 - 3.4283149129621303306e-832j)  +/-  (2.17e-249, 2.17e-249j)
| (0.23971225194117201998 - 1.3364025423391386481e-837j)  +/-  (3.91e-253, 3.91e-253j)
| (7.234591275098890658 + 6.0317309726172406211e-827j)  +/-  (6.01e-245, 6.01e-245j)
| (43.175196931390707469 - 3.6728545477939161419e-823j)  +/-  (1.29e-240, 1.29e-240j)
| (17.660137615195634717 + 9.105136585463802251e-829j)  +/-  (5.79e-242, 5.79e-242j)
| (3.4142135623730950488 + 7.9799446354735474015e-835j)  +/-  (2.31e-247, 2.31e-247j)
| (0.5857864376269049512 - 2.6660790693375601063e-839j)  +/-  (1.07e-251, 1.07e-251j)
| (26.752848151803946374 - 1.3589124021337514919e-827j)  +/-  (5.6e-241, 5.6e-241j)
| (0.0456374197855743167 - 5.4458483916187737479e-845j)  +/-  (1.08e-254, 1.08e-254j)
| (23.454523618031069879 - 2.740555172681939849e-831j)  +/-  (2.97e-241, 2.97e-241j)
| (8.894105489286762625 - 5.2449630985224660389e-836j)  +/-  (2.87e-244, 2.87e-244j)
| (1.0788922354753778824 + 9.7370720819704144973e-842j)  +/-  (1.58e-250, 1.58e-250j)
| (2.489356261202614551 - 1.0233184293998620451e-840j)  +/-  (2.53e-248, 2.53e-248j)
| (15.132836839326379458 + 1.0564965900463476558e-833j)  +/-  (1.89e-242, 1.89e-242j)
-------------------------------------------------
The weights are:
| (1.7436857949936847121e-36 - 1.1183769663224522361e-620j)  +/-  (5.43e-99, 7.53e-218j)
| (5.2011800271493299166e-29 + 6.1413770090753687995e-616j)  +/-  (1.82e-96, 2.52e-215j)
| (5.0708292221311981572e-26 - 5.7083091219911382526e-615j)  +/-  (1.49e-95, 2.06e-214j)
| (1.969174760443023858e-32 + 2.7646248250642773641e-618j)  +/-  (4.3e-98, 5.96e-217j)
| (2.321620723808094549e-23 + 6.8431554157277862513e-614j)  +/-  (4.88e-95, 6.76e-214j)
| (0.0042392136456407938265 - 6.3671558220353258005e-604j)  +/-  (6.16e-76, 8.54e-195j)
| (5.7820536456665651735e-21 - 8.0338433001862547347e-613j)  +/-  (1.31e-94, 1.82e-213j)
| (2.4831946243701501686e-13 - 3.4542906349305447808e-609j)  +/-  (3.98e-92, 5.52e-211j)
| (8.3082554100380501404e-17 - 7.1515452570376358213e-611j)  +/-  (7.84e-94, 1.09e-212j)
| (5.8224296806495040128e-06 - 1.8109200700377334017e-605j)  +/-  (1.07e-86, 1.48e-205j)
| (3.8837455196979428421e-09 + 4.2165837803630792186e-607j)  +/-  (3.09e-90, 4.28e-209j)
| (1.1410360204485980004e-41 + 1.5711607025300606546e-623j)  +/-  (5.03e-105, 6.97e-224j)
| (4.1867305990609401636e-05 + 5.1438400884206709594e-605j)  +/-  (2.65e-86, 3.68e-205j)
| (0.013030444645929648351 + 1.1738544219126918226e-603j)  +/-  (1.63e-81, 2.26e-200j)
| (5.4110043809359110527e-15 + 5.3469451432038995771e-610j)  +/-  (1.72e-93, 2.39e-212j)
| (0.1269840128101909687 - 2.9780523751748856414e-603j)  +/-  (1.29e-78, 1.79e-197j)
| (0.2130263685314482983 + 1.3256038124409942467e-603j)  +/-  (1.29e-78, 1.79e-197j)
| (0.0011244138760338435832 + 3.0613039823475107711e-604j)  +/-  (4.98e-85, 6.9e-204j)
| (8.6412517746668465588e-19 + 8.1995010314232679695e-612j)  +/-  (3.82e-95, 5.3e-214j)
| (5.6611584536829328079e-08 - 1.6458391846312372444e-606j)  +/-  (1.37e-90, 1.9e-209j)
| (0.033048489485214117498 - 1.8834414737646628098e-603j)  +/-  (1.94e-84, 2.7e-203j)
| (0.23411089308844294662 - 2.2530845095673045529e-603j)  +/-  (1.74e-82, 2.41e-201j)
| (8.2818643567781739259e-12 + 1.945080804238882401e-608j)  +/-  (6.1e-93, 8.46e-212j)
| (0.11181439012967145001 - 4.0914265104092931099e-604j)  +/-  (2.37e-84, 3.28e-203j)
| (2.0574524039073340386e-10 - 9.6251348635340187014e-608j)  +/-  (2.39e-92, 3.31e-211j)
| (0.00024160239615158812788 - 1.320774874469009853e-604j)  +/-  (5.52e-89, 7.61e-208j)
| (0.19197623098662213748 + 2.8690221228513793685e-603j)  +/-  (1.79e-86, 2.45e-205j)
| (0.070355544316772400574 + 2.5801229098000060127e-603j)  +/-  (2.66e-87, 3.62e-206j)
| (6.4564259957232436503e-07 + 5.755178773868200805e-606j)  +/-  (9.65e-91, 1.34e-209j)
