Starting with polynomial:
P : -t+1
Extension levels are: 1 3 20
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 20 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^24 + 54782894377735845569395894066993400119198300043552139913917413780161777/108274031606943837114186276598942891675900278703290455144610192690692*t^23 - 12676151202859883934616802815498572315327890052366924773297013069372919369/108274031606943837114186276598942891675900278703290455144610192690692*t^22 + 15140901796343237210288974758666587503769167781595557840508919910617804081037/920329268659022615470583351091014579245152368977968868729186637870882*t^21 - 1447208360663143933773753701028260571268827154317445453590076727781305557829823/920329268659022615470583351091014579245152368977968868729186637870882*t^20 + 2937546591504330580309848744528781425530971756419160650957076552977832036877910/27068507901735959278546569149735722918975069675822613786152548172673*t^19 - 2578236967486286804326051146802668218870076368887002999471811829399775850397576670/460164634329511307735291675545507289622576184488984434364593318935441*t^18 + 101818546985335799465477481427865239749324631531303145682457378597813098907961342340/460164634329511307735291675545507289622576184488984434364593318935441*t^17 - 183477748235824394627606179453493246929927801047427350892216581787840034693456572860/27068507901735959278546569149735722918975069675822613786152548172673*t^16 + 4396606202789971742542793683250440697397611316526733468575645009294981794728785146240/27068507901735959278546569149735722918975069675822613786152548172673*t^15 - 82747751260141401120969308157981653769719962992890809853950261169697454595703421526400/27068507901735959278546569149735722918975069675822613786152548172673*t^14 + 174847689646127195253558412831692202870830675797330079656439657689404313134133054803200/3866929700247994182649509878533674702710724239403230540878935453239*t^13 - 2027379926895947152196030676619019281971925526896751470168463955446256582596855696582400/3866929700247994182649509878533674702710724239403230540878935453239*t^12 + 18327370890772000047201697270156334628134819250309577629710331659852386964781630776755200/3866929700247994182649509878533674702710724239403230540878935453239*t^11 - 128067388929099517917864508004988329657868916743458323782936617806512439480080636078412800/3866929700247994182649509878533674702710724239403230540878935453239*t^10 + 683555506398611500029075583085452640762230184518778606953249784572432045609080842226432000/3866929700247994182649509878533674702710724239403230540878935453239*t^9 - 2743097733791552257819388501020280781173334486543776572800365276071740679756640700579072000/3866929700247994182649509878533674702710724239403230540878935453239*t^8 + 8108260914039856840203295284680942630407918895087959713521479229287104475572963516785664000/3866929700247994182649509878533674702710724239403230540878935453239*t^7 - 17191233810064106404872771235146949722069455264721747746141197964217321933123487404475392000/3866929700247994182649509878533674702710724239403230540878935453239*t^6 + 25252851972032608234654324472466380485121274043228397091136902118776042151376466072987648000/3866929700247994182649509878533674702710724239403230540878935453239*t^5 - 24525314832081964406499450576051328788267350900578943219930113942997418737670683105064960000/3866929700247994182649509878533674702710724239403230540878935453239*t^4 + 14722811096463254887910768138871263673259495584659385207523555781443126500814225123368960000/3866929700247994182649509878533674702710724239403230540878935453239*t^3 - 4900517652350925509124984271363642424569655228240776690843433424644098149057957001912320000/3866929700247994182649509878533674702710724239403230540878935453239*t^2 + 732574785994769382417138749811775903356111348299610444942182708816985093537944206786560000/3866929700247994182649509878533674702710724239403230540878935453239*t - 28286477967511376458807702544522327891422378500654021951225926616395731208572371517440000/3866929700247994182649509878533674702710724239403230540878935453239
-------------------------------------------------
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:   24 out of 24
Indefinite weights: 0 out of 24
Negative weights:   0 out of 24
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (75.019636638640397339 + 1.8052624520905529206e-258j)  +/-  (1.04e-118, 1.04e-118j)
| (42.070247795707412276 + 1.7854855403713646703e-259j)  +/-  (5.77e-116, 5.77e-116j)
| (36.674945929324176259 + 2.4502684276817269693e-272j)  +/-  (8.91e-116, 8.91e-116j)
| (48.212230239983200016 - 5.8543665286988420236e-280j)  +/-  (2.51e-116, 2.51e-116j)
| (63.888245258184157688 + 1.6072031979090550619e-283j)  +/-  (1.47e-117, 1.47e-117j)
| (14.447155169757654788 + 2.0730764202971536271e-286j)  +/-  (1.04e-116, 1.04e-116j)
| (55.335527698685229339 + 4.1486111714940702398e-296j)  +/-  (7.78e-117, 7.78e-117j)
| (3.369839231310923141 - 1.1955578211987827908e-301j)  +/-  (1.4e-120, 1.4e-120j)
| (6.1158131608799815209 - 1.622290450852371747e-302j)  +/-  (5.25e-119, 5.25e-119j)
| (27.601887261010381699 - 6.0920505335434590419e-311j)  +/-  (1.06e-115, 1.06e-115j)
| (4.6343473114327381783 - 8.5492215421263181192e-322j)  +/-  (9.83e-120, 9.83e-120j)
| (9.7696542667192863744 - 9.8497265956567658824e-318j)  +/-  (1.1e-117, 1.1e-117j)
| (17.219499332403395474 - 6.0776163733148324376e-323j)  +/-  (2.51e-116, 2.51e-116j)
| (11.971239372737726043 - 1.8790893541436852408e-337j)  +/-  (3.61e-117, 3.61e-117j)
| (0.29641296470810507665 + 3.1530030688200930951e-350j)  +/-  (2.62e-125, 2.62e-125j)
| (2.3185408153641858682 - 5.4690306642511417613e-348j)  +/-  (2e-121, 2e-121j)
| (31.883785617723148324 - 1.8242453475385612023e-351j)  +/-  (1.16e-115, 1.16e-115j)
| (7.8232631436879996743 + 1.4159513738632240362e-360j)  +/-  (2.57e-118, 2.57e-118j)
| (23.761991395825147751 - 1.7131217893147049366e-362j)  +/-  (7.92e-116, 7.92e-116j)
| (20.31409220729188586 + 6.8370508967246499782e-369j)  +/-  (5.03e-116, 5.03e-116j)
| (0.68831339843437577744 - 1.8706206198779518261e-385j)  +/-  (9.88e-124, 9.88e-124j)
| (1 + 1.9149106191930205823e-384j)  +/-  (6.32e-123, 6.32e-123j)
| (1.4916556008183887321 - 1.2034509123529571712e-383j)  +/-  (2.86e-122, 2.86e-122j)
| (0.056897625001077184683 + 3.8533190591127194962e-387j)  +/-  (4.32e-127, 4.32e-127j)
-------------------------------------------------
The weights are:
| (3.5102490163444012959e-32 + 7.5108062937405444326e-286j)  +/-  (3.53e-42, 2.43e-98j)
| (3.0759995402661462388e-18 - 2.9387273476318548557e-277j)  +/-  (9.52e-37, 6.55e-93j)
| (5.993140854921263515e-16 + 1.7383230037417178453e-276j)  +/-  (8.74e-36, 6.02e-92j)
| (7.5867750242903844139e-21 - 3.6292601742579907321e-279j)  +/-  (2.13e-38, 1.47e-94j)
| (1.7096787132010984665e-27 - 3.1856848630458675967e-283j)  +/-  (8.37e-42, 5.76e-98j)
| (1.3931902620642152504e-06 + 5.823339792006246434e-272j)  +/-  (1.07e-31, 7.37e-88j)
| (7.1858134495868822891e-24 + 4.2117564194909202813e-281j)  +/-  (3.2e-40, 2.2e-96j)
| (0.03982511693875043963 + 2.9070138627148387469e-269j)  +/-  (1.27e-22, 8.73e-79j)
| (0.0035159562695344797527 + 5.4640853001179991215e-270j)  +/-  (1.01e-26, 6.98e-83j)
| (4.1711431889698697524e-12 + 8.1468836341041942125e-275j)  +/-  (2.97e-36, 2.05e-92j)
| (0.0133240028827746762 - 1.3044771589343152796e-269j)  +/-  (1.45e-25, 9.96e-82j)
| (0.00011838037995891330144 + 7.1284686823389098901e-271j)  +/-  (2.21e-30, 1.52e-86j)
| (9.7354276067142611874e-08 - 1.374643381800794943e-272j)  +/-  (6.66e-34, 4.58e-90j)
| (1.4767418908649068614e-05 - 2.1679927342398113568e-271j)  +/-  (7.76e-32, 5.34e-88j)
| (0.24521455947983486535 - 7.3347891141879015592e-269j)  +/-  (7.32e-27, 5.03e-83j)
| (0.092873771710030672376 - 6.3640273166910329923e-269j)  +/-  (7.51e-27, 5.17e-83j)
| (6.4345699339063945945e-14 - 1.169214343957965013e-275j)  +/-  (8.74e-38, 6.02e-94j)
| (0.0007303585359578107074 - 2.0835482917318921006e-270j)  +/-  (5.5e-31, 3.79e-87j)
| (1.7418091889575065824e-10 - 5.1323202841443594645e-274j)  +/-  (1.69e-36, 1.16e-92j)
| (4.9164951710763752478e-09 + 2.8409567594694359802e-273j)  +/-  (1.25e-35, 8.63e-92j)
| (0.20572841429233194651 + 2.1167340255295642812e-268j)  +/-  (1.18e-30, 8.15e-87j)
| (0.10429910269376440946 - 2.658556198650508778e-268j)  +/-  (6.44e-31, 4.43e-87j)
| (0.15668606103692920817 + 1.5338049825880519876e-268j)  +/-  (2.94e-31, 2.02e-87j)
| (0.13766801272177361686 + 1.7841045814688525371e-269j)  +/-  (7.41e-32, 4.97e-88j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 3 20
-------------------------------------------------
Trying to find an order 3 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 20 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^24 + 54782894377735845569395894066993400119198300043552139913917413780161777/108274031606943837114186276598942891675900278703290455144610192690692*t^23 - 12676151202859883934616802815498572315327890052366924773297013069372919369/108274031606943837114186276598942891675900278703290455144610192690692*t^22 + 15140901796343237210288974758666587503769167781595557840508919910617804081037/920329268659022615470583351091014579245152368977968868729186637870882*t^21 - 1447208360663143933773753701028260571268827154317445453590076727781305557829823/920329268659022615470583351091014579245152368977968868729186637870882*t^20 + 2937546591504330580309848744528781425530971756419160650957076552977832036877910/27068507901735959278546569149735722918975069675822613786152548172673*t^19 - 2578236967486286804326051146802668218870076368887002999471811829399775850397576670/460164634329511307735291675545507289622576184488984434364593318935441*t^18 + 101818546985335799465477481427865239749324631531303145682457378597813098907961342340/460164634329511307735291675545507289622576184488984434364593318935441*t^17 - 183477748235824394627606179453493246929927801047427350892216581787840034693456572860/27068507901735959278546569149735722918975069675822613786152548172673*t^16 + 4396606202789971742542793683250440697397611316526733468575645009294981794728785146240/27068507901735959278546569149735722918975069675822613786152548172673*t^15 - 82747751260141401120969308157981653769719962992890809853950261169697454595703421526400/27068507901735959278546569149735722918975069675822613786152548172673*t^14 + 174847689646127195253558412831692202870830675797330079656439657689404313134133054803200/3866929700247994182649509878533674702710724239403230540878935453239*t^13 - 2027379926895947152196030676619019281971925526896751470168463955446256582596855696582400/3866929700247994182649509878533674702710724239403230540878935453239*t^12 + 18327370890772000047201697270156334628134819250309577629710331659852386964781630776755200/3866929700247994182649509878533674702710724239403230540878935453239*t^11 - 128067388929099517917864508004988329657868916743458323782936617806512439480080636078412800/3866929700247994182649509878533674702710724239403230540878935453239*t^10 + 683555506398611500029075583085452640762230184518778606953249784572432045609080842226432000/3866929700247994182649509878533674702710724239403230540878935453239*t^9 - 2743097733791552257819388501020280781173334486543776572800365276071740679756640700579072000/3866929700247994182649509878533674702710724239403230540878935453239*t^8 + 8108260914039856840203295284680942630407918895087959713521479229287104475572963516785664000/3866929700247994182649509878533674702710724239403230540878935453239*t^7 - 17191233810064106404872771235146949722069455264721747746141197964217321933123487404475392000/3866929700247994182649509878533674702710724239403230540878935453239*t^6 + 25252851972032608234654324472466380485121274043228397091136902118776042151376466072987648000/3866929700247994182649509878533674702710724239403230540878935453239*t^5 - 24525314832081964406499450576051328788267350900578943219930113942997418737670683105064960000/3866929700247994182649509878533674702710724239403230540878935453239*t^4 + 14722811096463254887910768138871263673259495584659385207523555781443126500814225123368960000/3866929700247994182649509878533674702710724239403230540878935453239*t^3 - 4900517652350925509124984271363642424569655228240776690843433424644098149057957001912320000/3866929700247994182649509878533674702710724239403230540878935453239*t^2 + 732574785994769382417138749811775903356111348299610444942182708816985093537944206786560000/3866929700247994182649509878533674702710724239403230540878935453239*t - 28286477967511376458807702544522327891422378500654021951225926616395731208572371517440000/3866929700247994182649509878533674702710724239403230540878935453239
-------------------------------------------------
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:   24 out of 24
Indefinite weights: 0 out of 24
Negative weights:   0 out of 24
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (75.019636638640397339 + 1.8052624520905529206e-258j)  +/-  (1.04e-118, 1.04e-118j)
| (42.070247795707412276 + 1.7854855403713646703e-259j)  +/-  (5.77e-116, 5.77e-116j)
| (36.674945929324176259 + 2.4502684276817269693e-272j)  +/-  (8.91e-116, 8.91e-116j)
| (48.212230239983200016 - 5.8543665286988420236e-280j)  +/-  (2.51e-116, 2.51e-116j)
| (63.888245258184157688 + 1.6072031979090550619e-283j)  +/-  (1.47e-117, 1.47e-117j)
| (14.447155169757654788 + 2.0730764202971536271e-286j)  +/-  (1.04e-116, 1.04e-116j)
| (55.335527698685229339 + 4.1486111714940702398e-296j)  +/-  (7.78e-117, 7.78e-117j)
| (3.369839231310923141 - 1.1955578211987827908e-301j)  +/-  (1.4e-120, 1.4e-120j)
| (6.1158131608799815209 - 1.622290450852371747e-302j)  +/-  (5.25e-119, 5.25e-119j)
| (27.601887261010381699 - 6.0920505335434590419e-311j)  +/-  (1.06e-115, 1.06e-115j)
| (4.6343473114327381783 - 8.5492215421263181192e-322j)  +/-  (9.83e-120, 9.83e-120j)
| (9.7696542667192863744 - 9.8497265956567658824e-318j)  +/-  (1.1e-117, 1.1e-117j)
| (17.219499332403395474 - 6.0776163733148324376e-323j)  +/-  (2.51e-116, 2.51e-116j)
| (11.971239372737726043 - 1.8790893541436852408e-337j)  +/-  (3.61e-117, 3.61e-117j)
| (0.29641296470810507665 + 3.1530030688200930951e-350j)  +/-  (2.62e-125, 2.62e-125j)
| (2.3185408153641858682 - 5.4690306642511417613e-348j)  +/-  (2e-121, 2e-121j)
| (31.883785617723148324 - 1.8242453475385612023e-351j)  +/-  (1.16e-115, 1.16e-115j)
| (7.8232631436879996743 + 1.4159513738632240362e-360j)  +/-  (2.57e-118, 2.57e-118j)
| (23.761991395825147751 - 1.7131217893147049366e-362j)  +/-  (7.92e-116, 7.92e-116j)
| (20.31409220729188586 + 6.8370508967246499782e-369j)  +/-  (5.03e-116, 5.03e-116j)
| (0.68831339843437577744 - 1.8706206198779518261e-385j)  +/-  (9.88e-124, 9.88e-124j)
| (1 + 1.9149106191930205823e-384j)  +/-  (6.32e-123, 6.32e-123j)
| (1.4916556008183887321 - 1.2034509123529571712e-383j)  +/-  (2.86e-122, 2.86e-122j)
| (0.056897625001077184683 + 3.8533190591127194962e-387j)  +/-  (4.32e-127, 4.32e-127j)
-------------------------------------------------
The weights are:
| (3.5102490163444012959e-32 + 7.5108062937405444326e-286j)  +/-  (3.53e-42, 2.43e-98j)
| (3.0759995402661462388e-18 - 2.9387273476318548557e-277j)  +/-  (9.52e-37, 6.55e-93j)
| (5.993140854921263515e-16 + 1.7383230037417178453e-276j)  +/-  (8.74e-36, 6.02e-92j)
| (7.5867750242903844139e-21 - 3.6292601742579907321e-279j)  +/-  (2.13e-38, 1.47e-94j)
| (1.7096787132010984665e-27 - 3.1856848630458675967e-283j)  +/-  (8.37e-42, 5.76e-98j)
| (1.3931902620642152504e-06 + 5.823339792006246434e-272j)  +/-  (1.07e-31, 7.37e-88j)
| (7.1858134495868822891e-24 + 4.2117564194909202813e-281j)  +/-  (3.2e-40, 2.2e-96j)
| (0.03982511693875043963 + 2.9070138627148387469e-269j)  +/-  (1.27e-22, 8.73e-79j)
| (0.0035159562695344797527 + 5.4640853001179991215e-270j)  +/-  (1.01e-26, 6.98e-83j)
| (4.1711431889698697524e-12 + 8.1468836341041942125e-275j)  +/-  (2.97e-36, 2.05e-92j)
| (0.0133240028827746762 - 1.3044771589343152796e-269j)  +/-  (1.45e-25, 9.96e-82j)
| (0.00011838037995891330144 + 7.1284686823389098901e-271j)  +/-  (2.21e-30, 1.52e-86j)
| (9.7354276067142611874e-08 - 1.374643381800794943e-272j)  +/-  (6.66e-34, 4.58e-90j)
| (1.4767418908649068614e-05 - 2.1679927342398113568e-271j)  +/-  (7.76e-32, 5.34e-88j)
| (0.24521455947983486535 - 7.3347891141879015592e-269j)  +/-  (7.32e-27, 5.03e-83j)
| (0.092873771710030672376 - 6.3640273166910329923e-269j)  +/-  (7.51e-27, 5.17e-83j)
| (6.4345699339063945945e-14 - 1.169214343957965013e-275j)  +/-  (8.74e-38, 6.02e-94j)
| (0.0007303585359578107074 - 2.0835482917318921006e-270j)  +/-  (5.5e-31, 3.79e-87j)
| (1.7418091889575065824e-10 - 5.1323202841443594645e-274j)  +/-  (1.69e-36, 1.16e-92j)
| (4.9164951710763752478e-09 + 2.8409567594694359802e-273j)  +/-  (1.25e-35, 8.63e-92j)
| (0.20572841429233194651 + 2.1167340255295642812e-268j)  +/-  (1.18e-30, 8.15e-87j)
| (0.10429910269376440946 - 2.658556198650508778e-268j)  +/-  (6.44e-31, 4.43e-87j)
| (0.15668606103692920817 + 1.5338049825880519876e-268j)  +/-  (2.94e-31, 2.02e-87j)
| (0.13766801272177361686 + 1.7841045814688525371e-269j)  +/-  (7.41e-32, 4.97e-88j)
