Starting with polynomial:
P : -t+1
Extension levels are: 1 5 14
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : -t^6 + 1831/56*t^5 - 20575/56*t^4 + 12175/7*t^3 - 23925/7*t^2 + 16365/7*t - 2265/7
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^20 + 17239261096906571440164201121282246570910097682008727604217823239013/56264940340587715043400028903977632338247906466191932088638723880*t^19 - 7091923313098679990129670003575803778097626388992824980001053597527299/168794821021763145130200086711932897014743719398575796265916171640*t^18 + 288511186924991866591632944678951931976769463617908956176036813228903479/84397410510881572565100043355966448507371859699287898132958085820*t^17 - 15570682450106490784756502781683489748242120685115939273406845254534904297/84397410510881572565100043355966448507371859699287898132958085820*t^16 + 295195638355380666235315908609788568832940785460942902570723120654708129259/42198705255440786282550021677983224253685929849643949066479042910*t^15 - 1625329055863301282026419618985182831482294846387192045116221178233137645095/8439741051088157256510004335596644850737185969928789813295808582*t^14 + 215026956987734252730945078948535824397729751844829008735538919043111182155/54803513318754267899415612568809382147644064739797336449972783*t^13 - 36027687991463861699890713493990816511981745452179455530364037240299880992835/602838646506296946893571738256903203624084712137770700949700613*t^12 + 137229971717328560949666895693304001437555161816475056664387988906676431113860/200946215502098982297857246085634401208028237379256900316566871*t^11 - 106712381909429091998240908235217816595636461896326000265239674878362725709340/18267837772918089299805204189603127382548021579932445483324261*t^10 + 678078714962247921812240405192306802037248050158246374093248186157850269848680/18267837772918089299805204189603127382548021579932445483324261*t^9 - 3158042683580151374470609239280583376395852074493536875025631553188203104886680/18267837772918089299805204189603127382548021579932445483324261*t^8 + 10564633939831315131198143038482394970254586002574043686329742261254593462087360/18267837772918089299805204189603127382548021579932445483324261*t^7 - 24665626132593713399284652150003838701222337824494844914731828225816873275878080/18267837772918089299805204189603127382548021579932445483324261*t^6 + 38595681144210070661961637013663991324959020437008470731569691198429435443560320/18267837772918089299805204189603127382548021579932445483324261*t^5 - 38200880038691311460875975443929319978067724646717855185619554787174118220918400/18267837772918089299805204189603127382548021579932445483324261*t^4 + 21960405241889805623352404797119764362228628838107275399947388540803514643750400/18267837772918089299805204189603127382548021579932445483324261*t^3 - 6431428996526799651048867740064713249773072143720675079119693080544226376332800/18267837772918089299805204189603127382548021579932445483324261*t^2 + 778294538200691437819120387378087702708265620090142987014089756123853466342400/18267837772918089299805204189603127382548021579932445483324261*t - 25855331751873156282252075685402362298884220770692273487826318868685814041600/18267837772918089299805204189603127382548021579932445483324261
-------------------------------------------------
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: 1
  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:   20 out of 20
Indefinite weights: 0 out of 20
Negative weights:   0 out of 20
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (45.69929265555645281 + 2.52139527493636614e-362j)  +/-  (2.97e-119, 2.97e-119j)
| (38.124801396034761753 - 5.2788469726555757496e-367j)  +/-  (1.26e-118, 1.26e-118j)
| (31.917041135685048132 - 1.7792619276952468594e-382j)  +/-  (3.16e-118, 3.16e-118j)
| (55.708994927955262875 - 7.004301675560267012e-397j)  +/-  (3.43e-120, 3.43e-120j)
| (22.135504700595737912 + 2.4809164531229880587e-406j)  +/-  (6.02e-118, 6.02e-118j)
| (5.1384848875831238418 + 1.3236974768593559796e-418j)  +/-  (3.97e-120, 3.97e-120j)
| (18.216897259461968595 - 1.7043221844876536342e-424j)  +/-  (5.66e-118, 5.66e-118j)
| (26.659505480519525506 - 3.9171497884019523976e-434j)  +/-  (4.54e-118, 4.54e-118j)
| (14.829781217182764814 + 2.7054801902644962291e-442j)  +/-  (5.69e-118, 5.69e-118j)
| (0.46071029871566730844 + 1.1160212966400348368e-457j)  +/-  (6.25e-125, 6.25e-125j)
| (0.18296039898248679851 + 2.1682925589344042537e-458j)  +/-  (6.27e-126, 6.27e-126j)
| (1.7268826167451200642 - 2.6969333632419469936e-456j)  +/-  (1.38e-122, 1.38e-122j)
| (2.5922508199253002476 + 8.9491840804862986757e-455j)  +/-  (1.09e-121, 1.09e-121j)
| (10.383881387273430402 - 5.5203170902607328883e-452j)  +/-  (4.2e-118, 4.2e-118j)
| (0.051820591636727342511 - 1.9115421901192107297e-465j)  +/-  (5.37e-127, 5.37e-127j)
| (8.9529512477548957267 - 7.3459678413149076026e-461j)  +/-  (1.76e-118, 1.76e-118j)
| (3.6952040745051673289 + 9.9255525231147583536e-471j)  +/-  (6.39e-121, 6.39e-121j)
| (6.9210206542003799166 - 9.1565236123803329785e-471j)  +/-  (2.86e-119, 2.86e-119j)
| (11.996386883024313579 - 7.211016497836441754e-478j)  +/-  (6.26e-118, 6.26e-118j)
| (1 + 3.8051008122170808464e-489j)  +/-  (9.45e-124, 9.45e-124j)
-------------------------------------------------
The weights are:
| (1.2098053219726933763e-19 - 1.7146159557841115388e-381j)  +/-  (1.46e-47, 3.43e-106j)
| (1.8825381063108377e-16 + 2.6844622999850801e-380j)  +/-  (2.93e-46, 6.88e-105j)
| (7.8233366316409455253e-14 - 5.1076826248034025131e-379j)  +/-  (2.69e-45, 6.31e-104j)
| (7.7412290335038208873e-24 - 1.3997724981098449829e-384j)  +/-  (4.78e-50, 1.12e-108j)
| (1.0243002826010025116e-09 - 1.1151662962707077472e-376j)  +/-  (7.59e-44, 1.78e-102j)
| (0.0094893871184571648362 + 5.4790097585146016857e-372j)  +/-  (1.16e-36, 2.74e-95j)
| (4.4686453047764291996e-08 + 1.2919503522045305841e-375j)  +/-  (3.26e-43, 7.66e-102j)
| (1.285025778691900265e-11 + 8.3162149215957675765e-378j)  +/-  (4.83e-45, 1.14e-103j)
| (1.135528898317400762e-06 - 1.4124614947419063234e-374j)  +/-  (9.04e-43, 2.12e-101j)
| (0.26371966563762811426 - 9.1639374743332021861e-371j)  +/-  (2.31e-34, 5.43e-93j)
| (0.12973860122835567933 + 9.5747408726194726597e-371j)  +/-  (1.86e-34, 4.36e-93j)
| (0.14128034009763489694 - 4.7998814658052946077e-371j)  +/-  (3.63e-35, 8.52e-94j)
| (0.071651695260231293473 + 2.9652685663815961959e-371j)  +/-  (1.07e-36, 2.5e-95j)
| (2.8637205349187389291e-05 - 6.6929780706136042824e-373j)  +/-  (3.2e-42, 7.52e-101j)
| (0.11235842152835689347 - 4.160229975389570364e-371j)  +/-  (8.2e-36, 1.93e-94j)
| (0.00026100878735252889896 + 1.2086102558967019248e-372j)  +/-  (5.87e-42, 1.38e-100j)
| (0.031481824038065833577 - 1.3899990263127809554e-371j)  +/-  (5.08e-40, 1.19e-98j)
| (0.0019132552267360547874 - 2.2260560061254271939e-372j)  +/-  (1.1e-41, 2.57e-100j)
| (1.5101272114971107826e-05 + 1.68299248640708077e-373j)  +/-  (4.33e-43, 1.02e-101j)
| (0.23806088134713705464 + 6.5792755929182143727e-371j)  +/-  (1.54e-39, 3.47e-98j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 5 14
-------------------------------------------------
Trying to find an order 5 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 14 Kronrod extension for:
P2 : -t^6 + 1831/56*t^5 - 20575/56*t^4 + 12175/7*t^3 - 23925/7*t^2 + 16365/7*t - 2265/7
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^20 + 17239261096906571440164201121282246570910097682008727604217823239013/56264940340587715043400028903977632338247906466191932088638723880*t^19 - 7091923313098679990129670003575803778097626388992824980001053597527299/168794821021763145130200086711932897014743719398575796265916171640*t^18 + 288511186924991866591632944678951931976769463617908956176036813228903479/84397410510881572565100043355966448507371859699287898132958085820*t^17 - 15570682450106490784756502781683489748242120685115939273406845254534904297/84397410510881572565100043355966448507371859699287898132958085820*t^16 + 295195638355380666235315908609788568832940785460942902570723120654708129259/42198705255440786282550021677983224253685929849643949066479042910*t^15 - 1625329055863301282026419618985182831482294846387192045116221178233137645095/8439741051088157256510004335596644850737185969928789813295808582*t^14 + 215026956987734252730945078948535824397729751844829008735538919043111182155/54803513318754267899415612568809382147644064739797336449972783*t^13 - 36027687991463861699890713493990816511981745452179455530364037240299880992835/602838646506296946893571738256903203624084712137770700949700613*t^12 + 137229971717328560949666895693304001437555161816475056664387988906676431113860/200946215502098982297857246085634401208028237379256900316566871*t^11 - 106712381909429091998240908235217816595636461896326000265239674878362725709340/18267837772918089299805204189603127382548021579932445483324261*t^10 + 678078714962247921812240405192306802037248050158246374093248186157850269848680/18267837772918089299805204189603127382548021579932445483324261*t^9 - 3158042683580151374470609239280583376395852074493536875025631553188203104886680/18267837772918089299805204189603127382548021579932445483324261*t^8 + 10564633939831315131198143038482394970254586002574043686329742261254593462087360/18267837772918089299805204189603127382548021579932445483324261*t^7 - 24665626132593713399284652150003838701222337824494844914731828225816873275878080/18267837772918089299805204189603127382548021579932445483324261*t^6 + 38595681144210070661961637013663991324959020437008470731569691198429435443560320/18267837772918089299805204189603127382548021579932445483324261*t^5 - 38200880038691311460875975443929319978067724646717855185619554787174118220918400/18267837772918089299805204189603127382548021579932445483324261*t^4 + 21960405241889805623352404797119764362228628838107275399947388540803514643750400/18267837772918089299805204189603127382548021579932445483324261*t^3 - 6431428996526799651048867740064713249773072143720675079119693080544226376332800/18267837772918089299805204189603127382548021579932445483324261*t^2 + 778294538200691437819120387378087702708265620090142987014089756123853466342400/18267837772918089299805204189603127382548021579932445483324261*t - 25855331751873156282252075685402362298884220770692273487826318868685814041600/18267837772918089299805204189603127382548021579932445483324261
-------------------------------------------------
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: 1
  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:   20 out of 20
Indefinite weights: 0 out of 20
Negative weights:   0 out of 20
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (45.69929265555645281 + 2.52139527493636614e-362j)  +/-  (2.97e-119, 2.97e-119j)
| (38.124801396034761753 - 5.2788469726555757496e-367j)  +/-  (1.26e-118, 1.26e-118j)
| (31.917041135685048132 - 1.7792619276952468594e-382j)  +/-  (3.16e-118, 3.16e-118j)
| (55.708994927955262875 - 7.004301675560267012e-397j)  +/-  (3.43e-120, 3.43e-120j)
| (22.135504700595737912 + 2.4809164531229880587e-406j)  +/-  (6.02e-118, 6.02e-118j)
| (5.1384848875831238418 + 1.3236974768593559796e-418j)  +/-  (3.97e-120, 3.97e-120j)
| (18.216897259461968595 - 1.7043221844876536342e-424j)  +/-  (5.66e-118, 5.66e-118j)
| (26.659505480519525506 - 3.9171497884019523976e-434j)  +/-  (4.54e-118, 4.54e-118j)
| (14.829781217182764814 + 2.7054801902644962291e-442j)  +/-  (5.69e-118, 5.69e-118j)
| (0.46071029871566730844 + 1.1160212966400348368e-457j)  +/-  (6.25e-125, 6.25e-125j)
| (0.18296039898248679851 + 2.1682925589344042537e-458j)  +/-  (6.27e-126, 6.27e-126j)
| (1.7268826167451200642 - 2.6969333632419469936e-456j)  +/-  (1.38e-122, 1.38e-122j)
| (2.5922508199253002476 + 8.9491840804862986757e-455j)  +/-  (1.09e-121, 1.09e-121j)
| (10.383881387273430402 - 5.5203170902607328883e-452j)  +/-  (4.2e-118, 4.2e-118j)
| (0.051820591636727342511 - 1.9115421901192107297e-465j)  +/-  (5.37e-127, 5.37e-127j)
| (8.9529512477548957267 - 7.3459678413149076026e-461j)  +/-  (1.76e-118, 1.76e-118j)
| (3.6952040745051673289 + 9.9255525231147583536e-471j)  +/-  (6.39e-121, 6.39e-121j)
| (6.9210206542003799166 - 9.1565236123803329785e-471j)  +/-  (2.86e-119, 2.86e-119j)
| (11.996386883024313579 - 7.211016497836441754e-478j)  +/-  (6.26e-118, 6.26e-118j)
| (1 + 3.8051008122170808464e-489j)  +/-  (9.45e-124, 9.45e-124j)
-------------------------------------------------
The weights are:
| (1.2098053219726933763e-19 - 1.7146159557841115388e-381j)  +/-  (1.46e-47, 3.43e-106j)
| (1.8825381063108377e-16 + 2.6844622999850801e-380j)  +/-  (2.93e-46, 6.88e-105j)
| (7.8233366316409455253e-14 - 5.1076826248034025131e-379j)  +/-  (2.69e-45, 6.31e-104j)
| (7.7412290335038208873e-24 - 1.3997724981098449829e-384j)  +/-  (4.78e-50, 1.12e-108j)
| (1.0243002826010025116e-09 - 1.1151662962707077472e-376j)  +/-  (7.59e-44, 1.78e-102j)
| (0.0094893871184571648362 + 5.4790097585146016857e-372j)  +/-  (1.16e-36, 2.74e-95j)
| (4.4686453047764291996e-08 + 1.2919503522045305841e-375j)  +/-  (3.26e-43, 7.66e-102j)
| (1.285025778691900265e-11 + 8.3162149215957675765e-378j)  +/-  (4.83e-45, 1.14e-103j)
| (1.135528898317400762e-06 - 1.4124614947419063234e-374j)  +/-  (9.04e-43, 2.12e-101j)
| (0.26371966563762811426 - 9.1639374743332021861e-371j)  +/-  (2.31e-34, 5.43e-93j)
| (0.12973860122835567933 + 9.5747408726194726597e-371j)  +/-  (1.86e-34, 4.36e-93j)
| (0.14128034009763489694 - 4.7998814658052946077e-371j)  +/-  (3.63e-35, 8.52e-94j)
| (0.071651695260231293473 + 2.9652685663815961959e-371j)  +/-  (1.07e-36, 2.5e-95j)
| (2.8637205349187389291e-05 - 6.6929780706136042824e-373j)  +/-  (3.2e-42, 7.52e-101j)
| (0.11235842152835689347 - 4.160229975389570364e-371j)  +/-  (8.2e-36, 1.93e-94j)
| (0.00026100878735252889896 + 1.2086102558967019248e-372j)  +/-  (5.87e-42, 1.38e-100j)
| (0.031481824038065833577 - 1.3899990263127809554e-371j)  +/-  (5.08e-40, 1.19e-98j)
| (0.0019132552267360547874 - 2.2260560061254271939e-372j)  +/-  (1.1e-41, 2.57e-100j)
| (1.5101272114971107826e-05 + 1.68299248640708077e-373j)  +/-  (4.33e-43, 1.02e-101j)
| (0.23806088134713705464 + 6.5792755929182143727e-371j)  +/-  (1.54e-39, 3.47e-98j)
