Starting with polynomial:
P : -t+1
Extension levels are: 1 3 21
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^25 + 153017369601578761787736776779247597348907940012457474030335047284332052239/273434064559078089777878564374650933851057879499729097485061779728549636*t^24 - 45556795638842989400661455487811565788965413491449478620587663972279835724345/316607864226300946058596232433806344459119649947054744456387323896215368*t^23 + 135848276910169885325756520103135459265883250248532868581242570898710045585118889/6015549420299717975113328416242320544723273348994040144671359154028091992*t^22 - 7291119661429743974753341754749883663749393952074545479551742679864173750928270267/3007774710149858987556664208121160272361636674497020072335679577014045996*t^21 + 568483555771405471256016858378967307530474451080065896952824837183321230334334483987/3007774710149858987556664208121160272361636674497020072335679577014045996*t^20 - 8344070772096184932410717706545936069822408380651240488052809378421145084309013690945/751943677537464746889166052030290068090409168624255018083919894253511499*t^19 + 19864256289474111745612716306370433447948309897485507292397616284885552451301957010525/39575983028287618257324529054225793057389956243381843057048415487026921*t^18 - 702502892109623653759744671461776098737292158861062558169675576040913865530254726807690/39575983028287618257324529054225793057389956243381843057048415487026921*t^17 + 19603881924039445713877754614344986912073458150540414431894005795445226668831481777292690/39575983028287618257324529054225793057389956243381843057048415487026921*t^16 - 433864066139538936496966961604160875190723551486831516801569119793322218891073590279797440/39575983028287618257324529054225793057389956243381843057048415487026921*t^15 + 7628537569595419639293130715845921391793075332659564691899115450875524533210160055269595200/39575983028287618257324529054225793057389956243381843057048415487026921*t^14 - 106441514896651449774398984290205452274631450410840344859381130741854624402058320467212720000/39575983028287618257324529054225793057389956243381843057048415487026921*t^13 + 1174080971744547798581746279502646181206476883349031015443000877156159307527719118020085577600/39575983028287618257324529054225793057389956243381843057048415487026921*t^12 - 10171027879683504015475437170893288132711247917278216852513530669096853837383915696463086169600/39575983028287618257324529054225793057389956243381843057048415487026921*t^11 + 6232084722940353659254886886348757881336657866846137415129607659597646288059816749476122457600/3597816638935238023393139004929617550671814203943803914277128680638811*t^10 - 32270299257637621397306370379096667034905489601604376819198939863876649258824284549995962752000/3597816638935238023393139004929617550671814203943803914277128680638811*t^9 + 126284228464349020717159178687555457694023969395974708484858682603525810059270466027564935040000/3597816638935238023393139004929617550671814203943803914277128680638811*t^8 - 365696728374240721832568040826519437060849251097035247738027947644167761316471854827078355456000/3597816638935238023393139004929617550671814203943803914277128680638811*t^7 + 762743064589964349406485264710207781144941758679295174337805434162313633541407534124030660096000/3597816638935238023393139004929617550671814203943803914277128680638811*t^6 - 1106259238114574308218377546498815651868449713900595389888399365011885947471026533448384050176000/3597816638935238023393139004929617550671814203943803914277128680638811*t^5 + 1064285997897207986621413988830367442662468415089185553928667162825522828424667711166317941760000/3597816638935238023393139004929617550671814203943803914277128680638811*t^4 - 634740137324018265511673521836487993166598879932009891848830106088738466802367228699042918400000/3597816638935238023393139004929617550671814203943803914277128680638811*t^3 + 210433456143898885502201420602284623541782731837818581716356847983922495503699035619308359680000/3597816638935238023393139004929617550671814203943803914277128680638811*t^2 - 31397075787139551703547338904761707873892774535705138434600181460846231866818733889671700480000/3597816638935238023393139004929617550671814203943803914277128680638811*t + 1211572023660840046702216222537753000832413289963053308408879605124278259011585144191918080000/3597816638935238023393139004929617550671814203943803914277128680638811
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   25 out of 25
Indefinite weights: 0 out of 25
Negative weights:   0 out of 25
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (67.769307202450476166 - 1.4307109888374283111e-267j)  +/-  (4.45e-117, 4.45e-117j)
| (45.538863507424217346 - 6.7821771121346191491e-271j)  +/-  (1.85e-115, 1.85e-115j)
| (59.067522672463917384 + 7.3096825552084156132e-272j)  +/-  (2.7e-116, 2.7e-116j)
| (51.808566406395723183 - 1.9737624305190279253e-276j)  +/-  (9e-116, 9e-116j)
| (79.076768200541831028 - 5.3930897920932851758e-284j)  +/-  (2.98e-118, 2.98e-118j)
| (26.735222367430319898 + 5.7934484761937576049e-286j)  +/-  (3.73e-115, 3.73e-115j)
| (23.150355716673947967 + 7.81388334246439598e-292j)  +/-  (2.28e-115, 2.28e-115j)
| (40.020409689608362903 + 1.8026951241865884089e-299j)  +/-  (3.28e-115, 3.28e-115j)
| (16.967103209494998639 + 5.6523940740144828425e-306j)  +/-  (6.91e-116, 6.91e-116j)
| (3.369839231310923141 - 5.2410902681450979283e-318j)  +/-  (1.45e-120, 1.45e-120j)
| (11.906689190515888285 + 5.0623432086612601997e-312j)  +/-  (6.99e-117, 6.99e-117j)
| (6.1217103932917273099 + 3.6453079647117643093e-321j)  +/-  (6.93e-119, 6.93e-119j)
| (4.6385182731651540386 + 4.1070560461484436873e-326j)  +/-  (1.19e-119, 1.19e-119j)
| (2.31471326135905925 - 6.6447327917586188853e-327j)  +/-  (1.95e-121, 1.95e-121j)
| (19.905693712494289404 - 3.4943932811896805199e-320j)  +/-  (1.39e-115, 1.39e-115j)
| (1.4850338526973446574 + 3.1275654281320464426e-339j)  +/-  (2.96e-122, 2.96e-122j)
| (0.69270410740843515923 - 7.2258943049575614066e-341j)  +/-  (1.11e-123, 1.11e-123j)
| (14.307648105106831417 - 3.8817952959262210854e-333j)  +/-  (2.34e-116, 2.34e-116j)
| (0.29686759583904432319 + 2.3333571925473293445e-350j)  +/-  (2.8e-125, 2.8e-125j)
| (0.056897625001077184683 + 5.6422947821613701792e-358j)  +/-  (4.34e-127, 4.34e-127j)
| (7.8232631436879996743 - 9.3686178848313900247e-340j)  +/-  (3.77e-118, 3.77e-118j)
| (1 + 1.6589671261248477809e-352j)  +/-  (6.94e-123, 6.94e-123j)
| (9.748924797036712768 + 6.6650663406847198982e-348j)  +/-  (1.81e-117, 1.81e-117j)
| (35.107781443115741712 - 1.6889509207160822963e-361j)  +/-  (4.51e-115, 4.51e-115j)
| (30.703007478633826837 + 1.4045784069176903686e-379j)  +/-  (4.11e-115, 4.11e-115j)
-------------------------------------------------
The weights are:
| (3.5856685925829964344e-29 + 5.7917243839909645836e-296j)  +/-  (7.53e-43, 5.08e-99j)
| (9.7935197519197829975e-20 + 3.5149446343686558563e-290j)  +/-  (3.12e-39, 2.1e-95j)
| (1.7520432010467530735e-25 - 4.9408681607050652421e-294j)  +/-  (8.01e-42, 5.4e-98j)
| (2.1220182287676756841e-22 + 4.1817062494429141855e-292j)  +/-  (1.17e-40, 7.93e-97j)
| (6.1634898825646495582e-34 - 5.2310202289645683398e-299j)  +/-  (1.07e-45, 7.19e-102j)
| (9.2298768859581913674e-12 + 6.7530317863729327323e-287j)  +/-  (4.68e-37, 3.15e-93j)
| (3.009411973620166612e-10 - 3.7724852401603202456e-286j)  +/-  (2.98e-36, 2.01e-92j)
| (2.1629256086480554245e-17 - 2.1268848963009687407e-289j)  +/-  (8.72e-40, 5.88e-96j)
| (1.1958480948658173921e-07 - 7.7331163995111003519e-285j)  +/-  (4.47e-35, 3.02e-91j)
| (0.039971903377629081166 + 8.6332902659542552321e-282j)  +/-  (1.82e-26, 1.22e-82j)
| (1.5360028596246490787e-05 - 9.4416567476317865539e-284j)  +/-  (9.71e-34, 6.55e-90j)
| (0.0034930228489410049335 + 1.793205331620356885e-282j)  +/-  (1.46e-30, 9.82e-87j)
| (0.013303493949480519353 - 4.0376713220113059679e-282j)  +/-  (4.05e-29, 2.73e-85j)
| (0.093555929041566365843 - 1.8438387743826667939e-281j)  +/-  (1.26e-26, 8.49e-83j)
| (6.9910621859471736706e-09 + 1.8294389100703768913e-285j)  +/-  (1.49e-36, 1.01e-92j)
| (0.15818085382756920473 + 4.4481756650422155443e-281j)  +/-  (4.05e-27, 2.73e-83j)
| (0.20841998680655675719 + 6.0193268052459719471e-281j)  +/-  (6.99e-27, 4.72e-83j)
| (1.5449525113647223026e-06 + 2.8706221175629034474e-284j)  +/-  (4.79e-35, 3.23e-91j)
| (0.24605095288242050837 - 2.0125063973138877311e-281j)  +/-  (2.29e-27, 1.55e-83j)
| (0.13770932411275023359 + 4.8655507787065529182e-282j)  +/-  (1.11e-27, 7.5e-84j)
| (0.00072556141569581385397 - 7.3836805743156212638e-283j)  +/-  (4.08e-33, 2.75e-89j)
| (0.098452881667116510382 - 7.6833426887854043583e-281j)  +/-  (1.37e-28, 9.26e-85j)
| (0.00011905820292751621662 + 2.7777988615317563381e-283j)  +/-  (5.36e-34, 3.61e-90j)
| (2.6295304203178861223e-15 + 1.4752186998689002523e-288j)  +/-  (6.8e-42, 4.59e-98j)
| (1.9347512209299742753e-13 - 1.0537150421003222132e-287j)  +/-  (7.91e-41, 5.34e-97j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 3 21
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 21 Kronrod extension for:
P2 : -t^4 + 49/4*t^3 - 153/4*t^2 + 57/2*t - 3/2
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^25 + 153017369601578761787736776779247597348907940012457474030335047284332052239/273434064559078089777878564374650933851057879499729097485061779728549636*t^24 - 45556795638842989400661455487811565788965413491449478620587663972279835724345/316607864226300946058596232433806344459119649947054744456387323896215368*t^23 + 135848276910169885325756520103135459265883250248532868581242570898710045585118889/6015549420299717975113328416242320544723273348994040144671359154028091992*t^22 - 7291119661429743974753341754749883663749393952074545479551742679864173750928270267/3007774710149858987556664208121160272361636674497020072335679577014045996*t^21 + 568483555771405471256016858378967307530474451080065896952824837183321230334334483987/3007774710149858987556664208121160272361636674497020072335679577014045996*t^20 - 8344070772096184932410717706545936069822408380651240488052809378421145084309013690945/751943677537464746889166052030290068090409168624255018083919894253511499*t^19 + 19864256289474111745612716306370433447948309897485507292397616284885552451301957010525/39575983028287618257324529054225793057389956243381843057048415487026921*t^18 - 702502892109623653759744671461776098737292158861062558169675576040913865530254726807690/39575983028287618257324529054225793057389956243381843057048415487026921*t^17 + 19603881924039445713877754614344986912073458150540414431894005795445226668831481777292690/39575983028287618257324529054225793057389956243381843057048415487026921*t^16 - 433864066139538936496966961604160875190723551486831516801569119793322218891073590279797440/39575983028287618257324529054225793057389956243381843057048415487026921*t^15 + 7628537569595419639293130715845921391793075332659564691899115450875524533210160055269595200/39575983028287618257324529054225793057389956243381843057048415487026921*t^14 - 106441514896651449774398984290205452274631450410840344859381130741854624402058320467212720000/39575983028287618257324529054225793057389956243381843057048415487026921*t^13 + 1174080971744547798581746279502646181206476883349031015443000877156159307527719118020085577600/39575983028287618257324529054225793057389956243381843057048415487026921*t^12 - 10171027879683504015475437170893288132711247917278216852513530669096853837383915696463086169600/39575983028287618257324529054225793057389956243381843057048415487026921*t^11 + 6232084722940353659254886886348757881336657866846137415129607659597646288059816749476122457600/3597816638935238023393139004929617550671814203943803914277128680638811*t^10 - 32270299257637621397306370379096667034905489601604376819198939863876649258824284549995962752000/3597816638935238023393139004929617550671814203943803914277128680638811*t^9 + 126284228464349020717159178687555457694023969395974708484858682603525810059270466027564935040000/3597816638935238023393139004929617550671814203943803914277128680638811*t^8 - 365696728374240721832568040826519437060849251097035247738027947644167761316471854827078355456000/3597816638935238023393139004929617550671814203943803914277128680638811*t^7 + 762743064589964349406485264710207781144941758679295174337805434162313633541407534124030660096000/3597816638935238023393139004929617550671814203943803914277128680638811*t^6 - 1106259238114574308218377546498815651868449713900595389888399365011885947471026533448384050176000/3597816638935238023393139004929617550671814203943803914277128680638811*t^5 + 1064285997897207986621413988830367442662468415089185553928667162825522828424667711166317941760000/3597816638935238023393139004929617550671814203943803914277128680638811*t^4 - 634740137324018265511673521836487993166598879932009891848830106088738466802367228699042918400000/3597816638935238023393139004929617550671814203943803914277128680638811*t^3 + 210433456143898885502201420602284623541782731837818581716356847983922495503699035619308359680000/3597816638935238023393139004929617550671814203943803914277128680638811*t^2 - 31397075787139551703547338904761707873892774535705138434600181460846231866818733889671700480000/3597816638935238023393139004929617550671814203943803914277128680638811*t + 1211572023660840046702216222537753000832413289963053308408879605124278259011585144191918080000/3597816638935238023393139004929617550671814203943803914277128680638811
-------------------------------------------------
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
Sufficient bits for target precision reached
Positive weights:   25 out of 25
Indefinite weights: 0 out of 25
Negative weights:   0 out of 25
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (67.769307202450476166 - 1.4307109888374283111e-267j)  +/-  (4.45e-117, 4.45e-117j)
| (45.538863507424217346 - 6.7821771121346191491e-271j)  +/-  (1.85e-115, 1.85e-115j)
| (59.067522672463917384 + 7.3096825552084156132e-272j)  +/-  (2.7e-116, 2.7e-116j)
| (51.808566406395723183 - 1.9737624305190279253e-276j)  +/-  (9e-116, 9e-116j)
| (79.076768200541831028 - 5.3930897920932851758e-284j)  +/-  (2.98e-118, 2.98e-118j)
| (26.735222367430319898 + 5.7934484761937576049e-286j)  +/-  (3.73e-115, 3.73e-115j)
| (23.150355716673947967 + 7.81388334246439598e-292j)  +/-  (2.28e-115, 2.28e-115j)
| (40.020409689608362903 + 1.8026951241865884089e-299j)  +/-  (3.28e-115, 3.28e-115j)
| (16.967103209494998639 + 5.6523940740144828425e-306j)  +/-  (6.91e-116, 6.91e-116j)
| (3.369839231310923141 - 5.2410902681450979283e-318j)  +/-  (1.45e-120, 1.45e-120j)
| (11.906689190515888285 + 5.0623432086612601997e-312j)  +/-  (6.99e-117, 6.99e-117j)
| (6.1217103932917273099 + 3.6453079647117643093e-321j)  +/-  (6.93e-119, 6.93e-119j)
| (4.6385182731651540386 + 4.1070560461484436873e-326j)  +/-  (1.19e-119, 1.19e-119j)
| (2.31471326135905925 - 6.6447327917586188853e-327j)  +/-  (1.95e-121, 1.95e-121j)
| (19.905693712494289404 - 3.4943932811896805199e-320j)  +/-  (1.39e-115, 1.39e-115j)
| (1.4850338526973446574 + 3.1275654281320464426e-339j)  +/-  (2.96e-122, 2.96e-122j)
| (0.69270410740843515923 - 7.2258943049575614066e-341j)  +/-  (1.11e-123, 1.11e-123j)
| (14.307648105106831417 - 3.8817952959262210854e-333j)  +/-  (2.34e-116, 2.34e-116j)
| (0.29686759583904432319 + 2.3333571925473293445e-350j)  +/-  (2.8e-125, 2.8e-125j)
| (0.056897625001077184683 + 5.6422947821613701792e-358j)  +/-  (4.34e-127, 4.34e-127j)
| (7.8232631436879996743 - 9.3686178848313900247e-340j)  +/-  (3.77e-118, 3.77e-118j)
| (1 + 1.6589671261248477809e-352j)  +/-  (6.94e-123, 6.94e-123j)
| (9.748924797036712768 + 6.6650663406847198982e-348j)  +/-  (1.81e-117, 1.81e-117j)
| (35.107781443115741712 - 1.6889509207160822963e-361j)  +/-  (4.51e-115, 4.51e-115j)
| (30.703007478633826837 + 1.4045784069176903686e-379j)  +/-  (4.11e-115, 4.11e-115j)
-------------------------------------------------
The weights are:
| (3.5856685925829964344e-29 + 5.7917243839909645836e-296j)  +/-  (7.53e-43, 5.08e-99j)
| (9.7935197519197829975e-20 + 3.5149446343686558563e-290j)  +/-  (3.12e-39, 2.1e-95j)
| (1.7520432010467530735e-25 - 4.9408681607050652421e-294j)  +/-  (8.01e-42, 5.4e-98j)
| (2.1220182287676756841e-22 + 4.1817062494429141855e-292j)  +/-  (1.17e-40, 7.93e-97j)
| (6.1634898825646495582e-34 - 5.2310202289645683398e-299j)  +/-  (1.07e-45, 7.19e-102j)
| (9.2298768859581913674e-12 + 6.7530317863729327323e-287j)  +/-  (4.68e-37, 3.15e-93j)
| (3.009411973620166612e-10 - 3.7724852401603202456e-286j)  +/-  (2.98e-36, 2.01e-92j)
| (2.1629256086480554245e-17 - 2.1268848963009687407e-289j)  +/-  (8.72e-40, 5.88e-96j)
| (1.1958480948658173921e-07 - 7.7331163995111003519e-285j)  +/-  (4.47e-35, 3.02e-91j)
| (0.039971903377629081166 + 8.6332902659542552321e-282j)  +/-  (1.82e-26, 1.22e-82j)
| (1.5360028596246490787e-05 - 9.4416567476317865539e-284j)  +/-  (9.71e-34, 6.55e-90j)
| (0.0034930228489410049335 + 1.793205331620356885e-282j)  +/-  (1.46e-30, 9.82e-87j)
| (0.013303493949480519353 - 4.0376713220113059679e-282j)  +/-  (4.05e-29, 2.73e-85j)
| (0.093555929041566365843 - 1.8438387743826667939e-281j)  +/-  (1.26e-26, 8.49e-83j)
| (6.9910621859471736706e-09 + 1.8294389100703768913e-285j)  +/-  (1.49e-36, 1.01e-92j)
| (0.15818085382756920473 + 4.4481756650422155443e-281j)  +/-  (4.05e-27, 2.73e-83j)
| (0.20841998680655675719 + 6.0193268052459719471e-281j)  +/-  (6.99e-27, 4.72e-83j)
| (1.5449525113647223026e-06 + 2.8706221175629034474e-284j)  +/-  (4.79e-35, 3.23e-91j)
| (0.24605095288242050837 - 2.0125063973138877311e-281j)  +/-  (2.29e-27, 1.55e-83j)
| (0.13770932411275023359 + 4.8655507787065529182e-282j)  +/-  (1.11e-27, 7.5e-84j)
| (0.00072556141569581385397 - 7.3836805743156212638e-283j)  +/-  (4.08e-33, 2.75e-89j)
| (0.098452881667116510382 - 7.6833426887854043583e-281j)  +/-  (1.37e-28, 9.26e-85j)
| (0.00011905820292751621662 + 2.7777988615317563381e-283j)  +/-  (5.36e-34, 3.61e-90j)
| (2.6295304203178861223e-15 + 1.4752186998689002523e-288j)  +/-  (6.8e-42, 4.59e-98j)
| (1.9347512209299742753e-13 - 1.0537150421003222132e-287j)  +/-  (7.91e-41, 5.34e-97j)
