Starting with polynomial:
P : -t+1
Extension levels are: 1 3 22
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 22 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^26 + 4228545905547300430408415524262927563568099536244204310844036343177796052106093/7105898277675986435604029008709067944869761621809490869676745675890861128580*t^25 - 580128246694719964621520173186871296490698222337701175696911026953073773971736501/3552949138837993217802014504354533972434880810904745434838372837945430564290*t^24 + 1482729696303718353689678970826524038228344690753282591445583704436127004030269947313/54004826910337496910590620466188916381010188325752130609543267136770544577208*t^23 - 856437320433505507643670185195313831537126024138139717000303870059908833348063673600863/270024134551687484552953102330944581905050941628760653047716335683852722886040*t^22 + 12038102925918772977415612406519160887817495971221378436105856215626516331053255650230363/45004022425281247425492183721824096984175156938126775507952722613975453814340*t^21 - 40466556792487009966025498545118542975409892602584501398583088825613203026416500354924777/2368632759225328811868009669569689314956587207269830289892248558630287042860*t^20 + 1903909040723666071255190319397880008121218097048378948387442559812000289345490216691508361/2250201121264062371274609186091204849208757846906338775397636130698772690717*t^19 - 3908621379877195496609933928985855151914942236768348395105860977191525965041632581256068365/118431637961266440593400483478484465747829360363491514494612427931514352143*t^18 + 121302881583919491406241222893135420921157030824545874728683734387610763128449409272801071282/118431637961266440593400483478484465747829360363491514494612427931514352143*t^17 - 3013805131867242998668653206971270829267819408248013753659776347925232701641936754318210239082/118431637961266440593400483478484465747829360363491514494612427931514352143*t^16 + 60126105304257393283371109272003249946327878903507386349120181740306114274128942136693597509312/118431637961266440593400483478484465747829360363491514494612427931514352143*t^15 - 963497463969523232004907341902028955635561774642230795831078048445041153933047859815630799760960/118431637961266440593400483478484465747829360363491514494612427931514352143*t^14 + 12374834829728847951866069420160054680628811333598504168747414676037792232537196911607311941564800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^13 - 126805622504593474236965092321569077037334272419921437506005190325210410527726111314751386572113280/118431637961266440593400483478484465747829360363491514494612427931514352143*t^12 + 1029344657451145492881500604893132858272231914095106900486091900758763988100202658043900067106618880/118431637961266440593400483478484465747829360363491514494612427931514352143*t^11 - 6554166354989082679399111572551312813449456433172404664587181431458754011507264797688463793642017280/118431637961266440593400483478484465747829360363491514494612427931514352143*t^10 + 32310390455066132344040279809300484753411569343498355681930593774922617550773873882098780383703065600/118431637961266440593400483478484465747829360363491514494612427931514352143*t^9 - 121262970412336351301208582295451055453479645035905161542934151376551191647568151321954122423329920000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^8 + 339110713987723482495164503477959032664715838263439779041951136065728305616301599610315532639337164800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^7 - 687446584359557873605377084009301174572950411517516247358364994332741069877828335170078295517722316800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^6 + 974825323228963933610564278388415840729345826939231456227514122477957817297154030571933410114541772800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^5 - 921818082405741626712593343990725797347408139454032788590925990198067333043497427062048690834787328000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^4 + 542902643343043252814517497822624590167411783227026325732733037210106156087980645247083516863221760000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^3 - 178452281769309534216899622041969023860035748940507935892426589784083747116018518619410262150508544000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^2 + 26491497967462269783446298348328655519136418334466197165019190719488907305614166600211828891869184000/118431637961266440593400483478484465747829360363491514494612427931514352143*t - 1020491282429560187778078345313434045209365593788776139837814677915478872919165487781240093466624000/118431637961266440593400483478484465747829360363491514494612427931514352143
-------------------------------------------------
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:   26 out of 26
Indefinite weights: 0 out of 26
Negative weights:   0 out of 26
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (81.687241197223027695 - 2.9962544906406045656e-301j)  +/-  (4.61e-118, 4.61e-118j)
| (70.157646397516836761 + 9.3247283114778467201e-300j)  +/-  (7.17e-117, 7.17e-117j)
| (61.26110702070883542 - 2.6122703216045034448e-307j)  +/-  (4.25e-116, 4.25e-116j)
| (53.819671066180005274 + 1.8544611164406560753e-325j)  +/-  (1.46e-115, 1.46e-115j)
| (27.952381100179126257 - 8.0451355324313436284e-345j)  +/-  (1.24e-114, 1.24e-114j)
| (9.7234697748382721264 + 2.0918884329506936889e-354j)  +/-  (6.1e-117, 6.1e-117j)
| (20.983792782064995893 - 9.9100863063387010063e-364j)  +/-  (7.34e-115, 7.34e-115j)
| (47.374747594439548081 + 2.9633561725273319339e-379j)  +/-  (4.15e-115, 4.15e-115j)
| (41.686894049480028444 - 3.3567130085421389764e-392j)  +/-  (7.3e-115, 7.3e-115j)
| (4.6409433704689130742 + 4.1168211362542145177e-399j)  +/-  (2e-119, 2e-119j)
| (2.312940187234474178 - 1.6634238424160525491e-401j)  +/-  (2.93e-121, 2.93e-121j)
| (18.154132935269028747 + 2.4508471935123726528e-394j)  +/-  (5.99e-115, 5.99e-115j)
| (11.78614021710795139 - 2.2468680851234667692e-398j)  +/-  (3.11e-116, 3.11e-116j)
| (15.873438609084622312 - 2.7875003924943371225e-397j)  +/-  (3.13e-115, 3.13e-115j)
| (32.054625231277264376 - 1.6441655922199477891e-401j)  +/-  (1.18e-114, 1.18e-114j)
| (0.69452680100404148137 + 7.8306306145410533317e-417j)  +/-  (1.13e-123, 1.13e-123j)
| (1 - 2.5247764363063565704e-416j)  +/-  (8.01e-123, 8.01e-123j)
| (13.879606471455716248 + 2.3954425936588980394e-409j)  +/-  (1.29e-115, 1.29e-115j)
| (6.125827168912950631 - 5.2791169840133411361e-412j)  +/-  (1.49e-118, 1.49e-118j)
| (1.4821091803842755336 + 1.0354670089351450694e-415j)  +/-  (3.84e-122, 3.84e-122j)
| (7.8232631436879996743 - 1.6552348242423066785e-411j)  +/-  (9.55e-118, 9.55e-118j)
| (3.369839231310923141 + 8.9657609910057707583e-415j)  +/-  (2.29e-120, 2.29e-120j)
| (0.29704659583194884071 - 1.2304495945474503761e-418j)  +/-  (3.3e-125, 3.3e-125j)
| (24.265551213156460982 - 1.7363910896261470547e-407j)  +/-  (1.03e-114, 1.03e-114j)
| (36.611651890275909503 - 2.5566287497734248606e-415j)  +/-  (1.01e-114, 1.01e-114j)
| (0.056897625001077184683 + 4.8181165616812211645e-430j)  +/-  (3.98e-127, 3.98e-127j)
-------------------------------------------------
The weights are:
| (4.6132389952737873769e-35 - 7.6928660193574642532e-333j)  +/-  (2.4e-40, 1.13e-97j)
| (3.3603584965612088858e-30 - 1.6466603020781025783e-329j)  +/-  (7.49e-39, 3.52e-96j)
| (2.0002939907643505133e-26 + 3.4760022264676990731e-328j)  +/-  (7.66e-38, 3.6e-95j)
| (2.9155953511230743144e-23 - 9.2115953044954158647e-327j)  +/-  (4.78e-37, 2.25e-94j)
| (2.8208575760195054071e-12 + 4.6623964168367972215e-321j)  +/-  (1.41e-32, 6.62e-90j)
| (0.00011929896154742214371 - 8.0299218316835162897e-317j)  +/-  (1.86e-24, 8.75e-82j)
| (2.3665562953453965604e-09 + 2.7700751869558777536e-319j)  +/-  (1.47e-30, 6.93e-88j)
| (1.6076785979669893321e-20 + 1.9879512126207703192e-325j)  +/-  (7.72e-37, 3.63e-94j)
| (4.2168020044938158629e-18 - 3.3415734930753883169e-324j)  +/-  (3.97e-36, 1.87e-93j)
| (0.013295210541242622682 + 7.2374400268745123002e-316j)  +/-  (1.78e-22, 8.36e-80j)
| (0.093860342840994439417 + 2.912967872086956952e-315j)  +/-  (2.11e-18, 9.95e-76j)
| (3.3482316910086979878e-08 - 1.6964982778880824175e-318j)  +/-  (8.51e-31, 4e-88j)
| (1.6069280983510328903e-05 + 3.7898898669368554204e-317j)  +/-  (9.02e-29, 4.25e-86j)
| (2.6033602832569102007e-07 + 6.8922740199449502546e-318j)  +/-  (1.64e-30, 7.74e-88j)
| (5.1814477850914887329e-14 - 4.9641488296283759183e-322j)  +/-  (7.5e-36, 3.53e-93j)
| (0.20961866369887114654 - 8.9220590135783662002e-315j)  +/-  (2.27e-22, 1.07e-79j)
| (0.095895672012139556401 + 1.1582247703229241811e-314j)  +/-  (2.26e-22, 1.06e-79j)
| (1.9095416284483244919e-06 - 1.7725517059062010537e-317j)  +/-  (4.45e-30, 2.09e-87j)
| (0.0034789989701563441398 - 3.5709790930388601989e-316j)  +/-  (2.9e-28, 1.36e-85j)
| (0.15883686049461011683 - 6.8262466353793831592e-315j)  +/-  (4.19e-25, 1.97e-82j)
| (0.00072128883316692111595 + 1.7099210120101005746e-316j)  +/-  (5.99e-29, 2.82e-86j)
| (0.040046539189872420978 - 1.4364658509563677277e-315j)  +/-  (2.5e-27, 1.17e-84j)
| (0.2463835298109611071 + 2.9009568404233314713e-315j)  +/-  (1.35e-26, 6.35e-84j)
| (1.0090494124156337018e-10 - 3.8179009998450446588e-320j)  +/-  (2.81e-34, 1.32e-91j)
| (6.0437733484465731977e-16 + 4.4865318031368261009e-323j)  +/-  (1.61e-37, 7.6e-95j)
| (0.13772531953514619097 - 6.9435208564940686484e-316j)  +/-  (1.97e-28, 9.23e-86j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 3 22
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 22 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^26 + 4228545905547300430408415524262927563568099536244204310844036343177796052106093/7105898277675986435604029008709067944869761621809490869676745675890861128580*t^25 - 580128246694719964621520173186871296490698222337701175696911026953073773971736501/3552949138837993217802014504354533972434880810904745434838372837945430564290*t^24 + 1482729696303718353689678970826524038228344690753282591445583704436127004030269947313/54004826910337496910590620466188916381010188325752130609543267136770544577208*t^23 - 856437320433505507643670185195313831537126024138139717000303870059908833348063673600863/270024134551687484552953102330944581905050941628760653047716335683852722886040*t^22 + 12038102925918772977415612406519160887817495971221378436105856215626516331053255650230363/45004022425281247425492183721824096984175156938126775507952722613975453814340*t^21 - 40466556792487009966025498545118542975409892602584501398583088825613203026416500354924777/2368632759225328811868009669569689314956587207269830289892248558630287042860*t^20 + 1903909040723666071255190319397880008121218097048378948387442559812000289345490216691508361/2250201121264062371274609186091204849208757846906338775397636130698772690717*t^19 - 3908621379877195496609933928985855151914942236768348395105860977191525965041632581256068365/118431637961266440593400483478484465747829360363491514494612427931514352143*t^18 + 121302881583919491406241222893135420921157030824545874728683734387610763128449409272801071282/118431637961266440593400483478484465747829360363491514494612427931514352143*t^17 - 3013805131867242998668653206971270829267819408248013753659776347925232701641936754318210239082/118431637961266440593400483478484465747829360363491514494612427931514352143*t^16 + 60126105304257393283371109272003249946327878903507386349120181740306114274128942136693597509312/118431637961266440593400483478484465747829360363491514494612427931514352143*t^15 - 963497463969523232004907341902028955635561774642230795831078048445041153933047859815630799760960/118431637961266440593400483478484465747829360363491514494612427931514352143*t^14 + 12374834829728847951866069420160054680628811333598504168747414676037792232537196911607311941564800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^13 - 126805622504593474236965092321569077037334272419921437506005190325210410527726111314751386572113280/118431637961266440593400483478484465747829360363491514494612427931514352143*t^12 + 1029344657451145492881500604893132858272231914095106900486091900758763988100202658043900067106618880/118431637961266440593400483478484465747829360363491514494612427931514352143*t^11 - 6554166354989082679399111572551312813449456433172404664587181431458754011507264797688463793642017280/118431637961266440593400483478484465747829360363491514494612427931514352143*t^10 + 32310390455066132344040279809300484753411569343498355681930593774922617550773873882098780383703065600/118431637961266440593400483478484465747829360363491514494612427931514352143*t^9 - 121262970412336351301208582295451055453479645035905161542934151376551191647568151321954122423329920000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^8 + 339110713987723482495164503477959032664715838263439779041951136065728305616301599610315532639337164800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^7 - 687446584359557873605377084009301174572950411517516247358364994332741069877828335170078295517722316800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^6 + 974825323228963933610564278388415840729345826939231456227514122477957817297154030571933410114541772800/118431637961266440593400483478484465747829360363491514494612427931514352143*t^5 - 921818082405741626712593343990725797347408139454032788590925990198067333043497427062048690834787328000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^4 + 542902643343043252814517497822624590167411783227026325732733037210106156087980645247083516863221760000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^3 - 178452281769309534216899622041969023860035748940507935892426589784083747116018518619410262150508544000/118431637961266440593400483478484465747829360363491514494612427931514352143*t^2 + 26491497967462269783446298348328655519136418334466197165019190719488907305614166600211828891869184000/118431637961266440593400483478484465747829360363491514494612427931514352143*t - 1020491282429560187778078345313434045209365593788776139837814677915478872919165487781240093466624000/118431637961266440593400483478484465747829360363491514494612427931514352143
-------------------------------------------------
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:   26 out of 26
Indefinite weights: 0 out of 26
Negative weights:   0 out of 26
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (81.687241197223027695 - 2.9962544906406045656e-301j)  +/-  (4.61e-118, 4.61e-118j)
| (70.157646397516836761 + 9.3247283114778467201e-300j)  +/-  (7.17e-117, 7.17e-117j)
| (61.26110702070883542 - 2.6122703216045034448e-307j)  +/-  (4.25e-116, 4.25e-116j)
| (53.819671066180005274 + 1.8544611164406560753e-325j)  +/-  (1.46e-115, 1.46e-115j)
| (27.952381100179126257 - 8.0451355324313436284e-345j)  +/-  (1.24e-114, 1.24e-114j)
| (9.7234697748382721264 + 2.0918884329506936889e-354j)  +/-  (6.1e-117, 6.1e-117j)
| (20.983792782064995893 - 9.9100863063387010063e-364j)  +/-  (7.34e-115, 7.34e-115j)
| (47.374747594439548081 + 2.9633561725273319339e-379j)  +/-  (4.15e-115, 4.15e-115j)
| (41.686894049480028444 - 3.3567130085421389764e-392j)  +/-  (7.3e-115, 7.3e-115j)
| (4.6409433704689130742 + 4.1168211362542145177e-399j)  +/-  (2e-119, 2e-119j)
| (2.312940187234474178 - 1.6634238424160525491e-401j)  +/-  (2.93e-121, 2.93e-121j)
| (18.154132935269028747 + 2.4508471935123726528e-394j)  +/-  (5.99e-115, 5.99e-115j)
| (11.78614021710795139 - 2.2468680851234667692e-398j)  +/-  (3.11e-116, 3.11e-116j)
| (15.873438609084622312 - 2.7875003924943371225e-397j)  +/-  (3.13e-115, 3.13e-115j)
| (32.054625231277264376 - 1.6441655922199477891e-401j)  +/-  (1.18e-114, 1.18e-114j)
| (0.69452680100404148137 + 7.8306306145410533317e-417j)  +/-  (1.13e-123, 1.13e-123j)
| (1 - 2.5247764363063565704e-416j)  +/-  (8.01e-123, 8.01e-123j)
| (13.879606471455716248 + 2.3954425936588980394e-409j)  +/-  (1.29e-115, 1.29e-115j)
| (6.125827168912950631 - 5.2791169840133411361e-412j)  +/-  (1.49e-118, 1.49e-118j)
| (1.4821091803842755336 + 1.0354670089351450694e-415j)  +/-  (3.84e-122, 3.84e-122j)
| (7.8232631436879996743 - 1.6552348242423066785e-411j)  +/-  (9.55e-118, 9.55e-118j)
| (3.369839231310923141 + 8.9657609910057707583e-415j)  +/-  (2.29e-120, 2.29e-120j)
| (0.29704659583194884071 - 1.2304495945474503761e-418j)  +/-  (3.3e-125, 3.3e-125j)
| (24.265551213156460982 - 1.7363910896261470547e-407j)  +/-  (1.03e-114, 1.03e-114j)
| (36.611651890275909503 - 2.5566287497734248606e-415j)  +/-  (1.01e-114, 1.01e-114j)
| (0.056897625001077184683 + 4.8181165616812211645e-430j)  +/-  (3.98e-127, 3.98e-127j)
-------------------------------------------------
The weights are:
| (4.6132389952737873769e-35 - 7.6928660193574642532e-333j)  +/-  (2.4e-40, 1.13e-97j)
| (3.3603584965612088858e-30 - 1.6466603020781025783e-329j)  +/-  (7.49e-39, 3.52e-96j)
| (2.0002939907643505133e-26 + 3.4760022264676990731e-328j)  +/-  (7.66e-38, 3.6e-95j)
| (2.9155953511230743144e-23 - 9.2115953044954158647e-327j)  +/-  (4.78e-37, 2.25e-94j)
| (2.8208575760195054071e-12 + 4.6623964168367972215e-321j)  +/-  (1.41e-32, 6.62e-90j)
| (0.00011929896154742214371 - 8.0299218316835162897e-317j)  +/-  (1.86e-24, 8.75e-82j)
| (2.3665562953453965604e-09 + 2.7700751869558777536e-319j)  +/-  (1.47e-30, 6.93e-88j)
| (1.6076785979669893321e-20 + 1.9879512126207703192e-325j)  +/-  (7.72e-37, 3.63e-94j)
| (4.2168020044938158629e-18 - 3.3415734930753883169e-324j)  +/-  (3.97e-36, 1.87e-93j)
| (0.013295210541242622682 + 7.2374400268745123002e-316j)  +/-  (1.78e-22, 8.36e-80j)
| (0.093860342840994439417 + 2.912967872086956952e-315j)  +/-  (2.11e-18, 9.95e-76j)
| (3.3482316910086979878e-08 - 1.6964982778880824175e-318j)  +/-  (8.51e-31, 4e-88j)
| (1.6069280983510328903e-05 + 3.7898898669368554204e-317j)  +/-  (9.02e-29, 4.25e-86j)
| (2.6033602832569102007e-07 + 6.8922740199449502546e-318j)  +/-  (1.64e-30, 7.74e-88j)
| (5.1814477850914887329e-14 - 4.9641488296283759183e-322j)  +/-  (7.5e-36, 3.53e-93j)
| (0.20961866369887114654 - 8.9220590135783662002e-315j)  +/-  (2.27e-22, 1.07e-79j)
| (0.095895672012139556401 + 1.1582247703229241811e-314j)  +/-  (2.26e-22, 1.06e-79j)
| (1.9095416284483244919e-06 - 1.7725517059062010537e-317j)  +/-  (4.45e-30, 2.09e-87j)
| (0.0034789989701563441398 - 3.5709790930388601989e-316j)  +/-  (2.9e-28, 1.36e-85j)
| (0.15883686049461011683 - 6.8262466353793831592e-315j)  +/-  (4.19e-25, 1.97e-82j)
| (0.00072128883316692111595 + 1.7099210120101005746e-316j)  +/-  (5.99e-29, 2.82e-86j)
| (0.040046539189872420978 - 1.4364658509563677277e-315j)  +/-  (2.5e-27, 1.17e-84j)
| (0.2463835298109611071 + 2.9009568404233314713e-315j)  +/-  (1.35e-26, 6.35e-84j)
| (1.0090494124156337018e-10 - 3.8179009998450446588e-320j)  +/-  (2.81e-34, 1.32e-91j)
| (6.0437733484465731977e-16 + 4.4865318031368261009e-323j)  +/-  (1.61e-37, 7.6e-95j)
| (0.13772531953514619097 - 6.9435208564940686484e-316j)  +/-  (1.97e-28, 9.23e-86j)
