Starting with polynomial:
P : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Extension levels are: 3 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/6*t^31 + 17694833258112594148144259583071558749770837774895662089592190790891/121237738599720803700319730735352471616669226031815139541047685842*t^30 - 1206349592142792952576026375543821429833322052369666526717108110827565/20206289766620133950053288455892078602778204338635856590174614307*t^29 + 450911501735356992693217834038914593635328109190306174140190946332694519/29715132009735491103019541846900115592320888733288024397315609275*t^28 - 1358604173472146501958421363242341745956060314950331352869074309374165414732/505157244165503348751332211397301965069455108465896414754365357675*t^27 + 178627750273779836895355267646927605716593256339236222004232173499632857121564/505157244165503348751332211397301965069455108465896414754365357675*t^26 - 1392064643375242404726970037075671763546382477006581072786725207538542695724776/38858249551192565288564016261330920389958085266607416519566565975*t^25 + 4457374800181555200305382805247943473565523711284963425828514732953985337488600/1554329982047702611542560650453236815598323410664296660782662639*t^24 - 286860435045475908465736259123348591254349168671360182566298421630101694062198720/1554329982047702611542560650453236815598323410664296660782662639*t^23 + 883772448992192879192922021097514836928471762204695764043131558190419228176149440/91431175414570741855444744144308047976371965333193921222509567*t^22 - 645887882956517499243893615612022896806320118151517456363938142881882025839259941760/1554329982047702611542560650453236815598323410664296660782662639*t^21 + 22925514656010104702532680962254745646553543591325403716164627711156723892758358139520/1554329982047702611542560650453236815598323410664296660782662639*t^20 - 674361441084853628322151701918474238002221101019468167017468575074401878073562379712000/1554329982047702611542560650453236815598323410664296660782662639*t^19 + 16471217010216607929730921493983925122372510005990842251633073087121853841066992050163200/1554329982047702611542560650453236815598323410664296660782662639*t^18 - 334189821460761330797078808913448605741081146963790254586314957399587085783439145210188800/1554329982047702611542560650453236815598323410664296660782662639*t^17 + 330980930721580466794450972590738121220946677893787703229612704092097600100567328461900800/91431175414570741855444744144308047976371965333193921222509567*t^16 - 4613273623234903402010365681278998455396288501839321540168368151125709719083018180751769600/91431175414570741855444744144308047976371965333193921222509567*t^15 + 53028039578836387448467647024763360599724839324627870286088262512870439160720028223805440000/91431175414570741855444744144308047976371965333193921222509567*t^14 - 500003834122951046438184586300051539445251153645027445921923859084669566108661888069103616000/91431175414570741855444744144308047976371965333193921222509567*t^13 + 3840126717167618191579152250573370920962889933704823653209078336615931344731333766893522944000/91431175414570741855444744144308047976371965333193921222509567*t^12 - 23805056997491735552721886440974192602871925764628614818706661819167151401754750734513553408000/91431175414570741855444744144308047976371965333193921222509567*t^11 + 117732900106059605408257254246391889587484603048404959359086804973823144433103579020373016576000/91431175414570741855444744144308047976371965333193921222509567*t^10 - 457703189028720719908800388993037040816056122033452099057716381933623470480065763926578790400000/91431175414570741855444744144308047976371965333193921222509567*t^9 + 1372211891255621989276454665655116947826922269755109603524514054102658964543703979157076869120000/91431175414570741855444744144308047976371965333193921222509567*t^8 - 3094199298790022424041451799000372271077116615466049525487680166254498761166776283253622702080000/91431175414570741855444744144308047976371965333193921222509567*t^7 + 5075173969305435627352275568714228163317564039610998896686517538920313250316462077499884175360000/91431175414570741855444744144308047976371965333193921222509567*t^6 - 5782660656446225062753959604403356191780212678218365275174332136920358545104045608661111275520000/91431175414570741855444744144308047976371965333193921222509567*t^5 + 4283139299582315045495794938599502334552706027448383974655022775521476004474093020943286272000000/91431175414570741855444744144308047976371965333193921222509567*t^4 - 1861731639821596748449996584736571517496431349565260311569071181534471453885669877387551047680000/91431175414570741855444744144308047976371965333193921222509567*t^3 + 397935501484882796210241731873267489070155662970556164769194802710265526218265677917973381120000/91431175414570741855444744144308047976371965333193921222509567*t^2 - 28509537785313929327781102306876166805187472495924460556533868609821121529009124166850314240000/91431175414570741855444744144308047976371965333193921222509567*t + 82652741226836650112039942608612585864619801988375052242960071203366479070701431637934080000/91431175414570741855444744144308047976371965333193921222509567
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   30 out of 31
Indefinite weights: 0 out of 31
Negative weights:   1 out of 31
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
Starting with polynomial:
P : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Extension levels are: 3 28
-------------------------------------------------
Trying to find an order 28 Kronrod extension for:
P1 : -1/6*t^3 + 3/2*t^2 - 3*t + 1
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : -1/6*t^31 + 17694833258112594148144259583071558749770837774895662089592190790891/121237738599720803700319730735352471616669226031815139541047685842*t^30 - 1206349592142792952576026375543821429833322052369666526717108110827565/20206289766620133950053288455892078602778204338635856590174614307*t^29 + 450911501735356992693217834038914593635328109190306174140190946332694519/29715132009735491103019541846900115592320888733288024397315609275*t^28 - 1358604173472146501958421363242341745956060314950331352869074309374165414732/505157244165503348751332211397301965069455108465896414754365357675*t^27 + 178627750273779836895355267646927605716593256339236222004232173499632857121564/505157244165503348751332211397301965069455108465896414754365357675*t^26 - 1392064643375242404726970037075671763546382477006581072786725207538542695724776/38858249551192565288564016261330920389958085266607416519566565975*t^25 + 4457374800181555200305382805247943473565523711284963425828514732953985337488600/1554329982047702611542560650453236815598323410664296660782662639*t^24 - 286860435045475908465736259123348591254349168671360182566298421630101694062198720/1554329982047702611542560650453236815598323410664296660782662639*t^23 + 883772448992192879192922021097514836928471762204695764043131558190419228176149440/91431175414570741855444744144308047976371965333193921222509567*t^22 - 645887882956517499243893615612022896806320118151517456363938142881882025839259941760/1554329982047702611542560650453236815598323410664296660782662639*t^21 + 22925514656010104702532680962254745646553543591325403716164627711156723892758358139520/1554329982047702611542560650453236815598323410664296660782662639*t^20 - 674361441084853628322151701918474238002221101019468167017468575074401878073562379712000/1554329982047702611542560650453236815598323410664296660782662639*t^19 + 16471217010216607929730921493983925122372510005990842251633073087121853841066992050163200/1554329982047702611542560650453236815598323410664296660782662639*t^18 - 334189821460761330797078808913448605741081146963790254586314957399587085783439145210188800/1554329982047702611542560650453236815598323410664296660782662639*t^17 + 330980930721580466794450972590738121220946677893787703229612704092097600100567328461900800/91431175414570741855444744144308047976371965333193921222509567*t^16 - 4613273623234903402010365681278998455396288501839321540168368151125709719083018180751769600/91431175414570741855444744144308047976371965333193921222509567*t^15 + 53028039578836387448467647024763360599724839324627870286088262512870439160720028223805440000/91431175414570741855444744144308047976371965333193921222509567*t^14 - 500003834122951046438184586300051539445251153645027445921923859084669566108661888069103616000/91431175414570741855444744144308047976371965333193921222509567*t^13 + 3840126717167618191579152250573370920962889933704823653209078336615931344731333766893522944000/91431175414570741855444744144308047976371965333193921222509567*t^12 - 23805056997491735552721886440974192602871925764628614818706661819167151401754750734513553408000/91431175414570741855444744144308047976371965333193921222509567*t^11 + 117732900106059605408257254246391889587484603048404959359086804973823144433103579020373016576000/91431175414570741855444744144308047976371965333193921222509567*t^10 - 457703189028720719908800388993037040816056122033452099057716381933623470480065763926578790400000/91431175414570741855444744144308047976371965333193921222509567*t^9 + 1372211891255621989276454665655116947826922269755109603524514054102658964543703979157076869120000/91431175414570741855444744144308047976371965333193921222509567*t^8 - 3094199298790022424041451799000372271077116615466049525487680166254498761166776283253622702080000/91431175414570741855444744144308047976371965333193921222509567*t^7 + 5075173969305435627352275568714228163317564039610998896686517538920313250316462077499884175360000/91431175414570741855444744144308047976371965333193921222509567*t^6 - 5782660656446225062753959604403356191780212678218365275174332136920358545104045608661111275520000/91431175414570741855444744144308047976371965333193921222509567*t^5 + 4283139299582315045495794938599502334552706027448383974655022775521476004474093020943286272000000/91431175414570741855444744144308047976371965333193921222509567*t^4 - 1861731639821596748449996584736571517496431349565260311569071181534471453885669877387551047680000/91431175414570741855444744144308047976371965333193921222509567*t^3 + 397935501484882796210241731873267489070155662970556164769194802710265526218265677917973381120000/91431175414570741855444744144308047976371965333193921222509567*t^2 - 28509537785313929327781102306876166805187472495924460556533868609821121529009124166850314240000/91431175414570741855444744144308047976371965333193921222509567*t + 82652741226836650112039942608612585864619801988375052242960071203366479070701431637934080000/91431175414570741855444744144308047976371965333193921222509567
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
  current precision for roots: 212
 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
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   30 out of 31
Indefinite weights: 0 out of 31
Negative weights:   1 out of 31
Extension rule has valid weights: 0
**************************************
*** EXTENSION WITH INVALID WEIGHTS ***
**************************************
