Starting with polynomial:
P : -t+1
Extension levels are: 1 6 15
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P2 : -t^7 + 8861/185*t^6 - 155826/185*t^5 + 253590/37*t^4 - 989880/37*t^3 + 1737720/37*t^2 - 1129104/37*t + 157104/37
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^22 + 26309879045129702626669592643112791313747716567049158559811415980412225996126674563/69995144603729783959229225352074787197119570786151681549278374033355742384460730*t^21 - 49316110814288874649259239170322160076414198144120369816373640196917878952789654001363/769946590641027623551521478872822659168315278647668497042062114366913166229068030*t^20 + 91944267510063070243324362502594431057073978485461543674207817905686265417768814671995/13999028920745956791845845070414957439423914157230336309855674806671148476892146*t^19 - 69862275215664165419706269605485690201035585313933278432575002158663545085184361070593365/153989318128205524710304295774564531833663055729533699408412422873382633245813606*t^18 + 1724265467965897961049954283658766101670295093389201042930486090914409760155758547776163855/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^17 - 5724219516583980251868158692685026511865192153575710213883877838501984354641220916627990871/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^16 + 1737511485579437478547883071539962971661115280350051566275975868766915269277328404482182783581/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^15 - 36690454004282948420515225667642512733607702682633813691613059487615970207552184587016264276925/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^14 + 596816355903627942986612833811720374293695591259939816619504385648827144273911385093162940117850/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^13 - 7491380797327609323512490551998077581654531084756804026309733529137723927781477449082494306604750/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^12 + 72387959267919960332042931072817013581760696548013049411648874548377939140767352903726250727285240/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^11 - 48636173831609507298053730100178062385507334449903723922070085809758393994509886356674504749455240/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^10 + 272008603587122568537947862855802154884502504227548514322626001508628616081001950892690049904382000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^9 - 1133439163078407595310561762390981740201205981491619169849185809737781071775936128038197806221874000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^8 + 93083970618805553337285697338875967049387553803389213285067378802590218454672803127257497473104000/189176066496566983673592500951553478911133975097707247430482091982042546985029*t^7 - 7411006557126954405129848509667653284267913091023352303590590512842135495364654529518742525316214400/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^6 + 293107686441663465549208985655875330340767261071807020916123671581998802887633819208195266011475200/189176066496566983673592500951553478911133975097707247430482091982042546985029*t^5 - 10190083097237255325945981586895360708514961326538368640763657865757448098605453857390180551622880000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^4 + 5641312603561335440023374310437556264333129153811724941084549309007809778846941000716718745452160000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^3 - 1599048544731343124687028430977081611672729738193794258008628889748374237786988039988967761124480000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^2 + 177754307755199367674031561363837651776978715489357541869219301290794619352224395904516827250432000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t - 3904052008840908854997022011723537224077101051251017268763737746561018357823073381273849614592000/6999514460372978395922922535207478719711957078615168154927837403335574238446073
-------------------------------------------------
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:   22 out of 22
Indefinite weights: 0 out of 22
Negative weights:   0 out of 22
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (51.359534756119901976 + 3.8672286780637625251e-359j)  +/-  (1.97e-118, 1.97e-118j)
| (26.66981914785292782 + 4.8822652898089531943e-360j)  +/-  (9.26e-117, 9.26e-117j)
| (36.983861465946604198 - 4.523805950561496623e-368j)  +/-  (2.68e-117, 2.68e-117j)
| (43.477548916216631191 + 6.0441426811224935956e-377j)  +/-  (8.87e-118, 8.87e-118j)
| (61.722809882347021376 + 1.4677877849760618015e-383j)  +/-  (1.73e-119, 1.73e-119j)
| (2.5026000900489822054 + 6.3935118732797313779e-390j)  +/-  (1.91e-121, 1.91e-121j)
| (18.989963815544515587 + 5.9817045721770165056e-388j)  +/-  (1.9e-116, 1.9e-116j)
| (6.2405562445845701221 + 2.074572308534538697e-399j)  +/-  (4.1e-119, 4.1e-119j)
| (22.513854438283054221 + 4.1549241145482085659e-403j)  +/-  (1.25e-116, 1.25e-116j)
| (7.9886543552868417152 + 1.4540995047613967779e-406j)  +/-  (1.61e-118, 1.61e-118j)
| (12.448513062956781353 + 2.8021957441822113286e-409j)  +/-  (2.68e-117, 2.68e-117j)
| (10.058786281531488491 - 3.7110749476808497615e-418j)  +/-  (6.85e-118, 6.85e-118j)
| (31.453884329869046294 + 4.3489662009337872124e-434j)  +/-  (5.9e-117, 5.9e-117j)
| (0.18796958875044643007 - 4.8398131087518919027e-454j)  +/-  (4.93e-126, 4.93e-126j)
| (16.747795959967403197 - 2.6961706372237484282e-453j)  +/-  (2.01e-116, 2.01e-116j)
| (1.6541959590375844653 + 3.3140610469498825928e-476j)  +/-  (1.94e-122, 1.94e-122j)
| (0.514875726733407578 - 9.2838466848772238441e-477j)  +/-  (1.05e-124, 1.05e-124j)
| (4.779596384709730006 + 2.8598273193627943495e-469j)  +/-  (9.15e-120, 9.15e-120j)
| (0.028629036838637826372 - 5.8450275108669742557e-481j)  +/-  (1.38e-127, 1.38e-127j)
| (15.012327971044918406 + 1.1649842891927630192e-469j)  +/-  (1.12e-116, 1.12e-116j)
| (3.5457097106199221859 + 1.6963929510996332655e-482j)  +/-  (1.45e-120, 1.45e-120j)
| (1 + 2.3312821721234455653e-485j)  +/-  (1.71e-123, 1.71e-123j)
-------------------------------------------------
The weights are:
| (4.3724954197808845773e-22 + 1.0194872891797069893e-378j)  +/-  (6.68e-45, 7.16e-102j)
| (1.1654591231410906652e-11 - 3.861738939846166496e-371j)  +/-  (1.43e-39, 1.53e-96j)
| (5.1720899573089944319e-16 + 9.0838211817509536133e-375j)  +/-  (2.11e-42, 2.26e-99j)
| (9.3006055115398986157e-19 - 1.274952082548032936e-376j)  +/-  (8.15e-44, 8.73e-101j)
| (1.9547040020587408072e-26 - 2.5554534845650202542e-381j)  +/-  (1.15e-47, 1.24e-104j)
| (0.07759504614180601374 + 9.1310151510363967799e-366j)  +/-  (4.78e-26, 5.12e-83j)
| (1.7591888251813527864e-08 - 2.2977262939172958022e-369j)  +/-  (4.02e-39, 4.31e-96j)
| (0.0031095189937765831899 - 1.0832817808558624804e-366j)  +/-  (3.38e-33, 3.62e-90j)
| (6.4395630658350829568e-10 + 2.4685175645045311349e-370j)  +/-  (4.87e-40, 5.22e-97j)
| (0.00064679260053752160235 + 3.9363838900342611618e-367j)  +/-  (3.65e-35, 3.91e-92j)
| (9.9357143823789377621e-06 + 4.797256681462334632e-368j)  +/-  (6.46e-38, 6.92e-95j)
| (9.5636673880753032923e-05 - 1.3362689822011928495e-367j)  +/-  (6.3e-37, 6.74e-94j)
| (1.1218055062113998029e-13 - 5.5753215896464582439e-373j)  +/-  (1.9e-43, 2.04e-100j)
| (0.20185815884884053729 + 1.3753074276389618353e-365j)  +/-  (8.45e-34, 9.05e-91j)
| (7.3203424433606836473e-08 + 1.1322113774902169656e-368j)  +/-  (1.23e-39, 1.32e-96j)
| (0.14317511321009582144 - 1.3992512090924946273e-365j)  +/-  (9.54e-35, 1.02e-91j)
| (0.24339358257489662448 - 1.8150335131865531826e-365j)  +/-  (3.74e-34, 4.01e-91j)
| (0.011233536623740156727 + 2.5790865610619071929e-366j)  +/-  (8.81e-37, 9.46e-94j)
| (0.078257067523096930185 - 5.2232087984553653699e-366j)  +/-  (1.64e-34, 1.75e-91j)
| (7.2995178380774323972e-07 - 2.317211924896971126e-368j)  +/-  (2.28e-39, 2.44e-96j)
| (0.032793594213054785883 - 5.2066422576922155952e-366j)  +/-  (1.78e-36, 1.92e-93j)
| (0.20783119547907180383 + 1.7898760059683817946e-365j)  +/-  (1.74e-35, 1.83e-92j)
Starting with polynomial:
P : -t+1
Extension levels are: 1 6 15
-------------------------------------------------
Trying to find an order 6 Kronrod extension for:
P1 : -t+1
Solvable: 1
-------------------------------------------------
Trying to find an order 15 Kronrod extension for:
P2 : -t^7 + 8861/185*t^6 - 155826/185*t^5 + 253590/37*t^4 - 989880/37*t^3 + 1737720/37*t^2 - 1129104/37*t + 157104/37
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -t^22 + 26309879045129702626669592643112791313747716567049158559811415980412225996126674563/69995144603729783959229225352074787197119570786151681549278374033355742384460730*t^21 - 49316110814288874649259239170322160076414198144120369816373640196917878952789654001363/769946590641027623551521478872822659168315278647668497042062114366913166229068030*t^20 + 91944267510063070243324362502594431057073978485461543674207817905686265417768814671995/13999028920745956791845845070414957439423914157230336309855674806671148476892146*t^19 - 69862275215664165419706269605485690201035585313933278432575002158663545085184361070593365/153989318128205524710304295774564531833663055729533699408412422873382633245813606*t^18 + 1724265467965897961049954283658766101670295093389201042930486090914409760155758547776163855/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^17 - 5724219516583980251868158692685026511865192153575710213883877838501984354641220916627990871/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^16 + 1737511485579437478547883071539962971661115280350051566275975868766915269277328404482182783581/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^15 - 36690454004282948420515225667642512733607702682633813691613059487615970207552184587016264276925/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^14 + 596816355903627942986612833811720374293695591259939816619504385648827144273911385093162940117850/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^13 - 7491380797327609323512490551998077581654531084756804026309733529137723927781477449082494306604750/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^12 + 72387959267919960332042931072817013581760696548013049411648874548377939140767352903726250727285240/76994659064102762355152147887282265916831527864766849704206211436691316622906803*t^11 - 48636173831609507298053730100178062385507334449903723922070085809758393994509886356674504749455240/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^10 + 272008603587122568537947862855802154884502504227548514322626001508628616081001950892690049904382000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^9 - 1133439163078407595310561762390981740201205981491619169849185809737781071775936128038197806221874000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^8 + 93083970618805553337285697338875967049387553803389213285067378802590218454672803127257497473104000/189176066496566983673592500951553478911133975097707247430482091982042546985029*t^7 - 7411006557126954405129848509667653284267913091023352303590590512842135495364654529518742525316214400/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^6 + 293107686441663465549208985655875330340767261071807020916123671581998802887633819208195266011475200/189176066496566983673592500951553478911133975097707247430482091982042546985029*t^5 - 10190083097237255325945981586895360708514961326538368640763657865757448098605453857390180551622880000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^4 + 5641312603561335440023374310437556264333129153811724941084549309007809778846941000716718745452160000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^3 - 1599048544731343124687028430977081611672729738193794258008628889748374237786988039988967761124480000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t^2 + 177754307755199367674031561363837651776978715489357541869219301290794619352224395904516827250432000/6999514460372978395922922535207478719711957078615168154927837403335574238446073*t - 3904052008840908854997022011723537224077101051251017268763737746561018357823073381273849614592000/6999514460372978395922922535207478719711957078615168154927837403335574238446073
-------------------------------------------------
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:   22 out of 22
Indefinite weights: 0 out of 22
Negative weights:   0 out of 22
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (51.359534756119901976 + 3.8672286780637625251e-359j)  +/-  (1.97e-118, 1.97e-118j)
| (26.66981914785292782 + 4.8822652898089531943e-360j)  +/-  (9.26e-117, 9.26e-117j)
| (36.983861465946604198 - 4.523805950561496623e-368j)  +/-  (2.68e-117, 2.68e-117j)
| (43.477548916216631191 + 6.0441426811224935956e-377j)  +/-  (8.87e-118, 8.87e-118j)
| (61.722809882347021376 + 1.4677877849760618015e-383j)  +/-  (1.73e-119, 1.73e-119j)
| (2.5026000900489822054 + 6.3935118732797313779e-390j)  +/-  (1.91e-121, 1.91e-121j)
| (18.989963815544515587 + 5.9817045721770165056e-388j)  +/-  (1.9e-116, 1.9e-116j)
| (6.2405562445845701221 + 2.074572308534538697e-399j)  +/-  (4.1e-119, 4.1e-119j)
| (22.513854438283054221 + 4.1549241145482085659e-403j)  +/-  (1.25e-116, 1.25e-116j)
| (7.9886543552868417152 + 1.4540995047613967779e-406j)  +/-  (1.61e-118, 1.61e-118j)
| (12.448513062956781353 + 2.8021957441822113286e-409j)  +/-  (2.68e-117, 2.68e-117j)
| (10.058786281531488491 - 3.7110749476808497615e-418j)  +/-  (6.85e-118, 6.85e-118j)
| (31.453884329869046294 + 4.3489662009337872124e-434j)  +/-  (5.9e-117, 5.9e-117j)
| (0.18796958875044643007 - 4.8398131087518919027e-454j)  +/-  (4.93e-126, 4.93e-126j)
| (16.747795959967403197 - 2.6961706372237484282e-453j)  +/-  (2.01e-116, 2.01e-116j)
| (1.6541959590375844653 + 3.3140610469498825928e-476j)  +/-  (1.94e-122, 1.94e-122j)
| (0.514875726733407578 - 9.2838466848772238441e-477j)  +/-  (1.05e-124, 1.05e-124j)
| (4.779596384709730006 + 2.8598273193627943495e-469j)  +/-  (9.15e-120, 9.15e-120j)
| (0.028629036838637826372 - 5.8450275108669742557e-481j)  +/-  (1.38e-127, 1.38e-127j)
| (15.012327971044918406 + 1.1649842891927630192e-469j)  +/-  (1.12e-116, 1.12e-116j)
| (3.5457097106199221859 + 1.6963929510996332655e-482j)  +/-  (1.45e-120, 1.45e-120j)
| (1 + 2.3312821721234455653e-485j)  +/-  (1.71e-123, 1.71e-123j)
-------------------------------------------------
The weights are:
| (4.3724954197808845773e-22 + 1.0194872891797069893e-378j)  +/-  (6.68e-45, 7.16e-102j)
| (1.1654591231410906652e-11 - 3.861738939846166496e-371j)  +/-  (1.43e-39, 1.53e-96j)
| (5.1720899573089944319e-16 + 9.0838211817509536133e-375j)  +/-  (2.11e-42, 2.26e-99j)
| (9.3006055115398986157e-19 - 1.274952082548032936e-376j)  +/-  (8.15e-44, 8.73e-101j)
| (1.9547040020587408072e-26 - 2.5554534845650202542e-381j)  +/-  (1.15e-47, 1.24e-104j)
| (0.07759504614180601374 + 9.1310151510363967799e-366j)  +/-  (4.78e-26, 5.12e-83j)
| (1.7591888251813527864e-08 - 2.2977262939172958022e-369j)  +/-  (4.02e-39, 4.31e-96j)
| (0.0031095189937765831899 - 1.0832817808558624804e-366j)  +/-  (3.38e-33, 3.62e-90j)
| (6.4395630658350829568e-10 + 2.4685175645045311349e-370j)  +/-  (4.87e-40, 5.22e-97j)
| (0.00064679260053752160235 + 3.9363838900342611618e-367j)  +/-  (3.65e-35, 3.91e-92j)
| (9.9357143823789377621e-06 + 4.797256681462334632e-368j)  +/-  (6.46e-38, 6.92e-95j)
| (9.5636673880753032923e-05 - 1.3362689822011928495e-367j)  +/-  (6.3e-37, 6.74e-94j)
| (1.1218055062113998029e-13 - 5.5753215896464582439e-373j)  +/-  (1.9e-43, 2.04e-100j)
| (0.20185815884884053729 + 1.3753074276389618353e-365j)  +/-  (8.45e-34, 9.05e-91j)
| (7.3203424433606836473e-08 + 1.1322113774902169656e-368j)  +/-  (1.23e-39, 1.32e-96j)
| (0.14317511321009582144 - 1.3992512090924946273e-365j)  +/-  (9.54e-35, 1.02e-91j)
| (0.24339358257489662448 - 1.8150335131865531826e-365j)  +/-  (3.74e-34, 4.01e-91j)
| (0.011233536623740156727 + 2.5790865610619071929e-366j)  +/-  (8.81e-37, 9.46e-94j)
| (0.078257067523096930185 - 5.2232087984553653699e-366j)  +/-  (1.64e-34, 1.75e-91j)
| (7.2995178380774323972e-07 - 2.317211924896971126e-368j)  +/-  (2.28e-39, 2.44e-96j)
| (0.032793594213054785883 - 5.2066422576922155952e-366j)  +/-  (1.78e-36, 1.92e-93j)
| (0.20783119547907180383 + 1.7898760059683817946e-365j)  +/-  (1.74e-35, 1.83e-92j)
