Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 23
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^25 - 117094862224969112525494618304870109673/405532251666071461982930222261307442*t^24 + 652290940440620718643376723313873290655037/8516177284987500701641534667487456282*t^23 - 105581275562171617436230163958409912024935757/8516177284987500701641534667487456282*t^22 + 5841842147649615081887364520413583598616237685/4258088642493750350820767333743728141*t^21 - 22349348264006310165893269449533678229032851603/202766125833035730991465111130653721*t^20 + 1351269056798772563763006670214789332671342388780/202766125833035730991465111130653721*t^19 - 62899264019462597865002425044241472756431603787420/202766125833035730991465111130653721*t^18 + 2287292295242932456769945023851695204888473613310120/202766125833035730991465111130653721*t^17 - 65568794310814330996874635945096780201782412146869400/202766125833035730991465111130653721*t^16 + 1489008247842601169371004355608227955733254291215522560/202766125833035730991465111130653721*t^15 - 26828125866456085173054842046899186666301694926401299200/202766125833035730991465111130653721*t^14 + 382977825301505843286109326582968498414652212677876108800/202766125833035730991465111130653721*t^13 - 4313652558978953529895032360968543221296913332030594316800/202766125833035730991465111130653721*t^12 + 38070801077029454947942060876746365429458596936279331584000/202766125833035730991465111130653721*t^11 - 260674465120050108119960083743041420770362085411235286374400/202766125833035730991465111130653721*t^10 + 1366374527970748939732867358333540567282647085601420913152000/202766125833035730991465111130653721*t^9 - 5388311782007936899503281293865833522191021754197788886528000/202766125833035730991465111130653721*t^8 + 15632175383537392262548574181860783486965683325987935172608000/202766125833035730991465111130653721*t^7 - 32415285867230021580699553100651608762369452044434515179520000/202766125833035730991465111130653721*t^6 + 46279436754289222799665812282253533733004757569421063450624000/202766125833035730991465111130653721*t^5 - 43288059764704478882077781629180292438128989414170127912960000/202766125833035730991465111130653721*t^4 + 24757675242598837427790275705581499149208479909461176893440000/202766125833035730991465111130653721*t^3 - 7785049417110866528782532319557004406864061140145223843840000/202766125833035730991465111130653721*t^2 + 1101820331748363279843103045643637781976410480948948992000000/202766125833035730991465111130653721*t - 41102691230887578034539829622396008697823199892172472320000/202766125833035730991465111130653721
-------------------------------------------------
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:
| (81.533920206509354018 - 4.3162060882473676718e-315j)  +/-  (3.4e-118, 3.4e-118j)
| (47.188952852981575563 - 4.0761478467700479832e-315j)  +/-  (2e-115, 2e-115j)
| (61.094266564845074245 - 5.742609430628630502e-319j)  +/-  (2.83e-116, 2.83e-116j)
| (53.64436202726523478 - 8.0083156962651047147e-321j)  +/-  (9.15e-116, 9.15e-116j)
| (69.997927322739111801 - 1.0285389500837446099e-324j)  +/-  (4.22e-117, 4.22e-117j)
| (14.679698186663804945 - 8.9947111174084092323e-323j)  +/-  (1.76e-116, 1.76e-116j)
| (20.527954805842415213 - 1.0624116257031092607e-326j)  +/-  (1.21e-115, 1.21e-115j)
| (23.923659539578174961 - 1.3973218052240486252e-343j)  +/-  (2.2e-115, 2.2e-115j)
| (31.812126382317859059 - 1.5548030687075007859e-355j)  +/-  (4.19e-115, 4.19e-115j)
| (12.183414925086710815 - 5.172828712051879248e-363j)  +/-  (5.73e-117, 5.73e-117j)
| (0.5857864376269049512 - 8.907673233356361553e-377j)  +/-  (6.17e-124, 6.17e-124j)
| (1.4869148477335134858 - 4.8376406427601171206e-375j)  +/-  (1.79e-122, 1.79e-122j)
| (6.2209247797937094114 + 2.3963637542741526167e-371j)  +/-  (7e-119, 7e-119j)
| (17.454694144185131767 - 2.6776788205676546253e-367j)  +/-  (5.05e-116, 5.05e-116j)
| (0.88160272540341206572 - 3.6147626237070518713e-383j)  +/-  (2.81e-123, 2.81e-123j)
| (3.4142135623730950488 - 3.0711545431240989039e-381j)  +/-  (1.36e-120, 1.36e-120j)
| (0.28416107802396190096 + 6.6465655192154393646e-386j)  +/-  (2.6e-125, 2.6e-125j)
| (7.9659716426413273719 - 1.0776939985975451578e-375j)  +/-  (3.27e-118, 3.27e-118j)
| (36.394398262423198701 - 2.3049362591394880107e-384j)  +/-  (4.42e-115, 4.42e-115j)
| (0.055697237950505475958 - 2.8492500982726628069e-407j)  +/-  (5.03e-127, 5.03e-127j)
| (9.9498772636320483931 + 2.155747431427675206e-395j)  +/-  (1.56e-117, 1.56e-117j)
| (2.3410384928178377129 - 9.5890993352452873306e-410j)  +/-  (1.63e-121, 1.63e-121j)
| (4.7059679357036321564 + 8.6114473962621389591e-404j)  +/-  (1.04e-119, 1.04e-119j)
| (27.672132810563031407 + 2.0526212279872802348e-405j)  +/-  (3.53e-115, 3.53e-115j)
| (41.487634417649631584 - 3.7946842579862448736e-422j)  +/-  (3.54e-115, 3.54e-115j)
-------------------------------------------------
The weights are:
| (5.3801159462742186185e-35 - 9.5966155327887707657e-344j)  +/-  (2.12e-47, 5.37e-103j)
| (1.9397039002134867794e-20 + 4.0173475378799955628e-335j)  +/-  (3.35e-42, 8.47e-98j)
| (2.3657352335979426292e-26 - 5.6505717891720501014e-339j)  +/-  (6.42e-45, 1.63e-100j)
| (3.4789784230746532095e-23 + 4.9296738097499378914e-337j)  +/-  (9.03e-44, 2.29e-99j)
| (3.9449554262913039744e-30 + 4.1915058914053348569e-341j)  +/-  (1.69e-46, 4.27e-102j)
| (1.1094068364001634261e-06 + 8.7593913375997623625e-329j)  +/-  (2.2e-35, 5.57e-91j)
| (3.9266772817195447301e-09 + 1.2116653367870686355e-330j)  +/-  (4.29e-38, 1.09e-93j)
| (1.453181326262481066e-10 - 3.2350201032489670212e-331j)  +/-  (1.91e-39, 4.82e-95j)
| (6.6496853023377984126e-14 - 1.0725744877977222592e-332j)  +/-  (5.96e-42, 1.51e-97j)
| (1.2083237036996540822e-05 - 2.6158451887080675018e-328j)  +/-  (4.77e-36, 1.21e-91j)
| (0.13813212622733941325 + 1.4402543725456844583e-325j)  +/-  (9.46e-26, 2.39e-81j)
| (0.16746017044699523006 + 6.2716383165249169415e-326j)  +/-  (9.05e-26, 2.29e-81j)
| (0.0032368822230358113405 + 3.4250454916102268188e-327j)  +/-  (1.71e-33, 4.33e-89j)
| (7.6733252575716019969e-08 - 2.8976001476266589567e-331j)  +/-  (7.4e-38, 1.87e-93j)
| (0.18325389523701417745 - 1.3436290210580571196e-325j)  +/-  (3.77e-27, 9.55e-83j)
| (0.038888485764308315363 + 1.550835713127351042e-326j)  +/-  (8.78e-32, 2.22e-87j)
| (0.22825225309575162699 - 6.6802838036764195947e-326j)  +/-  (3.3e-28, 8.34e-84j)
| (0.00064654947898488485344 - 1.4656906680837394613e-327j)  +/-  (5.45e-35, 1.38e-90j)
| (7.5432185437955939452e-16 + 1.5772478976436109953e-333j)  +/-  (7.75e-44, 1.96e-99j)
| (0.13452242311716072239 + 1.4896074131291575496e-326j)  +/-  (9.16e-31, 2.32e-86j)
| (0.00010056230158502184266 + 5.9994956337059516531e-328j)  +/-  (2.36e-36, 5.98e-92j)
| (0.092814338851399926833 - 3.0857132147864435543e-326j)  +/-  (4.92e-33, 1.24e-88j)
| (0.012679039803457875674 - 7.5093466677215029036e-327j)  +/-  (1.4e-34, 3.53e-90j)
| (3.7783508281003895434e-12 + 6.4435964742321078351e-332j)  +/-  (6.35e-42, 1.61e-97j)
| (5.161382260013707316e-18 - 2.3706942369963108986e-334j)  +/-  (4.01e-45, 1.02e-100j)
Starting with polynomial:
P : 1/2*t^2 - 2*t + 1
Extension levels are: 2 23
-------------------------------------------------
Trying to find an order 23 Kronrod extension for:
P1 : 1/2*t^2 - 2*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 1/2*t^25 - 117094862224969112525494618304870109673/405532251666071461982930222261307442*t^24 + 652290940440620718643376723313873290655037/8516177284987500701641534667487456282*t^23 - 105581275562171617436230163958409912024935757/8516177284987500701641534667487456282*t^22 + 5841842147649615081887364520413583598616237685/4258088642493750350820767333743728141*t^21 - 22349348264006310165893269449533678229032851603/202766125833035730991465111130653721*t^20 + 1351269056798772563763006670214789332671342388780/202766125833035730991465111130653721*t^19 - 62899264019462597865002425044241472756431603787420/202766125833035730991465111130653721*t^18 + 2287292295242932456769945023851695204888473613310120/202766125833035730991465111130653721*t^17 - 65568794310814330996874635945096780201782412146869400/202766125833035730991465111130653721*t^16 + 1489008247842601169371004355608227955733254291215522560/202766125833035730991465111130653721*t^15 - 26828125866456085173054842046899186666301694926401299200/202766125833035730991465111130653721*t^14 + 382977825301505843286109326582968498414652212677876108800/202766125833035730991465111130653721*t^13 - 4313652558978953529895032360968543221296913332030594316800/202766125833035730991465111130653721*t^12 + 38070801077029454947942060876746365429458596936279331584000/202766125833035730991465111130653721*t^11 - 260674465120050108119960083743041420770362085411235286374400/202766125833035730991465111130653721*t^10 + 1366374527970748939732867358333540567282647085601420913152000/202766125833035730991465111130653721*t^9 - 5388311782007936899503281293865833522191021754197788886528000/202766125833035730991465111130653721*t^8 + 15632175383537392262548574181860783486965683325987935172608000/202766125833035730991465111130653721*t^7 - 32415285867230021580699553100651608762369452044434515179520000/202766125833035730991465111130653721*t^6 + 46279436754289222799665812282253533733004757569421063450624000/202766125833035730991465111130653721*t^5 - 43288059764704478882077781629180292438128989414170127912960000/202766125833035730991465111130653721*t^4 + 24757675242598837427790275705581499149208479909461176893440000/202766125833035730991465111130653721*t^3 - 7785049417110866528782532319557004406864061140145223843840000/202766125833035730991465111130653721*t^2 + 1101820331748363279843103045643637781976410480948948992000000/202766125833035730991465111130653721*t - 41102691230887578034539829622396008697823199892172472320000/202766125833035730991465111130653721
-------------------------------------------------
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:
| (81.533920206509354018 - 4.3162060882473676718e-315j)  +/-  (3.4e-118, 3.4e-118j)
| (47.188952852981575563 - 4.0761478467700479832e-315j)  +/-  (2e-115, 2e-115j)
| (61.094266564845074245 - 5.742609430628630502e-319j)  +/-  (2.83e-116, 2.83e-116j)
| (53.64436202726523478 - 8.0083156962651047147e-321j)  +/-  (9.15e-116, 9.15e-116j)
| (69.997927322739111801 - 1.0285389500837446099e-324j)  +/-  (4.22e-117, 4.22e-117j)
| (14.679698186663804945 - 8.9947111174084092323e-323j)  +/-  (1.76e-116, 1.76e-116j)
| (20.527954805842415213 - 1.0624116257031092607e-326j)  +/-  (1.21e-115, 1.21e-115j)
| (23.923659539578174961 - 1.3973218052240486252e-343j)  +/-  (2.2e-115, 2.2e-115j)
| (31.812126382317859059 - 1.5548030687075007859e-355j)  +/-  (4.19e-115, 4.19e-115j)
| (12.183414925086710815 - 5.172828712051879248e-363j)  +/-  (5.73e-117, 5.73e-117j)
| (0.5857864376269049512 - 8.907673233356361553e-377j)  +/-  (6.17e-124, 6.17e-124j)
| (1.4869148477335134858 - 4.8376406427601171206e-375j)  +/-  (1.79e-122, 1.79e-122j)
| (6.2209247797937094114 + 2.3963637542741526167e-371j)  +/-  (7e-119, 7e-119j)
| (17.454694144185131767 - 2.6776788205676546253e-367j)  +/-  (5.05e-116, 5.05e-116j)
| (0.88160272540341206572 - 3.6147626237070518713e-383j)  +/-  (2.81e-123, 2.81e-123j)
| (3.4142135623730950488 - 3.0711545431240989039e-381j)  +/-  (1.36e-120, 1.36e-120j)
| (0.28416107802396190096 + 6.6465655192154393646e-386j)  +/-  (2.6e-125, 2.6e-125j)
| (7.9659716426413273719 - 1.0776939985975451578e-375j)  +/-  (3.27e-118, 3.27e-118j)
| (36.394398262423198701 - 2.3049362591394880107e-384j)  +/-  (4.42e-115, 4.42e-115j)
| (0.055697237950505475958 - 2.8492500982726628069e-407j)  +/-  (5.03e-127, 5.03e-127j)
| (9.9498772636320483931 + 2.155747431427675206e-395j)  +/-  (1.56e-117, 1.56e-117j)
| (2.3410384928178377129 - 9.5890993352452873306e-410j)  +/-  (1.63e-121, 1.63e-121j)
| (4.7059679357036321564 + 8.6114473962621389591e-404j)  +/-  (1.04e-119, 1.04e-119j)
| (27.672132810563031407 + 2.0526212279872802348e-405j)  +/-  (3.53e-115, 3.53e-115j)
| (41.487634417649631584 - 3.7946842579862448736e-422j)  +/-  (3.54e-115, 3.54e-115j)
-------------------------------------------------
The weights are:
| (5.3801159462742186185e-35 - 9.5966155327887707657e-344j)  +/-  (2.12e-47, 5.37e-103j)
| (1.9397039002134867794e-20 + 4.0173475378799955628e-335j)  +/-  (3.35e-42, 8.47e-98j)
| (2.3657352335979426292e-26 - 5.6505717891720501014e-339j)  +/-  (6.42e-45, 1.63e-100j)
| (3.4789784230746532095e-23 + 4.9296738097499378914e-337j)  +/-  (9.03e-44, 2.29e-99j)
| (3.9449554262913039744e-30 + 4.1915058914053348569e-341j)  +/-  (1.69e-46, 4.27e-102j)
| (1.1094068364001634261e-06 + 8.7593913375997623625e-329j)  +/-  (2.2e-35, 5.57e-91j)
| (3.9266772817195447301e-09 + 1.2116653367870686355e-330j)  +/-  (4.29e-38, 1.09e-93j)
| (1.453181326262481066e-10 - 3.2350201032489670212e-331j)  +/-  (1.91e-39, 4.82e-95j)
| (6.6496853023377984126e-14 - 1.0725744877977222592e-332j)  +/-  (5.96e-42, 1.51e-97j)
| (1.2083237036996540822e-05 - 2.6158451887080675018e-328j)  +/-  (4.77e-36, 1.21e-91j)
| (0.13813212622733941325 + 1.4402543725456844583e-325j)  +/-  (9.46e-26, 2.39e-81j)
| (0.16746017044699523006 + 6.2716383165249169415e-326j)  +/-  (9.05e-26, 2.29e-81j)
| (0.0032368822230358113405 + 3.4250454916102268188e-327j)  +/-  (1.71e-33, 4.33e-89j)
| (7.6733252575716019969e-08 - 2.8976001476266589567e-331j)  +/-  (7.4e-38, 1.87e-93j)
| (0.18325389523701417745 - 1.3436290210580571196e-325j)  +/-  (3.77e-27, 9.55e-83j)
| (0.038888485764308315363 + 1.550835713127351042e-326j)  +/-  (8.78e-32, 2.22e-87j)
| (0.22825225309575162699 - 6.6802838036764195947e-326j)  +/-  (3.3e-28, 8.34e-84j)
| (0.00064654947898488485344 - 1.4656906680837394613e-327j)  +/-  (5.45e-35, 1.38e-90j)
| (7.5432185437955939452e-16 + 1.5772478976436109953e-333j)  +/-  (7.75e-44, 1.96e-99j)
| (0.13452242311716072239 + 1.4896074131291575496e-326j)  +/-  (9.16e-31, 2.32e-86j)
| (0.00010056230158502184266 + 5.9994956337059516531e-328j)  +/-  (2.36e-36, 5.98e-92j)
| (0.092814338851399926833 - 3.0857132147864435543e-326j)  +/-  (4.92e-33, 1.24e-88j)
| (0.012679039803457875674 - 7.5093466677215029036e-327j)  +/-  (1.4e-34, 3.53e-90j)
| (3.7783508281003895434e-12 + 6.4435964742321078351e-332j)  +/-  (6.35e-42, 1.61e-97j)
| (5.161382260013707316e-18 - 2.3706942369963108986e-334j)  +/-  (4.01e-45, 1.02e-100j)
