QE on maxima

以下は，現在作成中の QE ツールの出力例です．
・有効桁数が fpprec の多倍長浮動小数点数を使用．
・２つの数値解間の距離が %ez より小ならばそれらは同じ値の根（重根や共通根）に対応し，%ez 以上ならばそれらは異なる値の根に対応する数値解と見做しています．

Maxima 5.39.0 http://maxima.sourceforge.net
using Lisp CMU Common Lisp 21b (21B Unicode)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.

(%i1) (qvpeds ([all], [c,b,a,x],0,h1,r11,0 ),qe( bfpcad(ext( '(   x^4+a*x^2+b*x+c>=0  ) )))  );

Evaluation took 11.3900 seconds (11.4100 elapsed) using 1307.972 MB.

(%o1) [[c = root(c,1),b = root(126976*c^3-135*b^4,1),
        root(8*a*c-9*b^2-2*a^3,1) <= a,true],
       [root(c,1) < c,b < root(b,1),
        root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
          <= a,true],
       [root(c,1) < c,b = root(b,1),
        root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,1)
          <= a,true],
       [root(c,1) < c,root(b,1) < b,
        root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
          <= a,true]]

(%i2) (qvpeds ([all], [c,b,a,x],1,h1,r11,0 ),qe( bfpcad(ext( '(   x^4+a*x^2+b*x+c>=0  ) )))  );

[fpprec,fpprintprec,%ez,ratepsilon]: [30,30,1.0b-5,1.0b-30] 
x^4+a*x^2+b*x+c >= 0 
x^4+a*x^2+b*x+c >= 0 
[[c],
 [b,256*c^3-27*b^4,1024*c^3-2187*b^4,1024*c^3+3*b^4,4096*c^3+27*b^4,
  126976*c^3-135*b^4],
 [a,8*a*c-9*b^2-2*a^3,
  256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2],
 [x^4+a*x^2+b*x+c]]
  
1 multi-roots: 0.0b0 0.0b0 [256*c^3-27*b^4,-27*b^4] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [256*c^3-27*b^4,-27*b^4] 
dist: 0.0b0 
3 multi-roots: 0.0b0 0.0b0 [256*c^3-27*b^4,-27*b^4] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [1024*c^3-2187*b^4,-2187*b^4] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [1024*c^3-2187*b^4,-2187*b^4] 
dist: 0.0b0 
3 multi-roots: 0.0b0 0.0b0 [1024*c^3-2187*b^4,-2187*b^4] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [1024*c^3+3*b^4,3*b^4] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [1024*c^3+3*b^4,3*b^4] 
dist: 0.0b0 
3 multi-roots: 0.0b0 0.0b0 [1024*c^3+3*b^4,3*b^4] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [4096*c^3+27*b^4,27*b^4] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [4096*c^3+27*b^4,27*b^4] 
dist: 0.0b0 
3 multi-roots: 0.0b0 0.0b0 [4096*c^3+27*b^4,27*b^4] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [126976*c^3-135*b^4,-135*b^4] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [126976*c^3-135*b^4,-135*b^4] 
dist: 0.0b0 
3 multi-roots: 0.0b0 0.0b0 [126976*c^3-135*b^4,-135*b^4] 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
1 multi-roots: 
 4.52295331325015833831979417428b-16*%i-2.44948974278317847258028706083b0 
 (-4.52295331325015213319900815541b-16*%i)-2.44948974278317772381428108859b0 
 [256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,
  (-5.0b-1*(16*a^4+6.27069374152493593138504723125b2*a))
   -1.74185937264581553649584645312b1*a^3-3.2b1*a^2-5.44b2] 
dist: 1.17428054512251951790867706837b-15 
common-roots: -2.44948974278317809819728407471b0 
             -2.44948974278317809819728407471b0 
dist: 1.57772181044202361082345713057b-30 
1 multi-roots: -1.41421356237309504880168872421b0*%i 
 (-1.41421356237309504880168872421b0*%i)-3.86941038573562221171322357299b-43 
 [256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,
  (-8.0b0*a^4)-3.2b1*a^2-3.2b1] 
dist: 7.88860905221011805411728660181b-31 
2 multi-roots: 
 1.41421356237309504880261489839b0*%i-2.95418118567534149019656617711b-22 
 1.41421356237309504880076255003b0*%i+2.9541811856753414902004355875b-22 
 [256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,
  (-8.0b0*a^4)-3.2b1*a^2-3.2b1] 
dist: 1.94429469761416284867540568328b-21 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
1 multi-roots: 
 4.52295330147550776509999452971b-16*%i-2.44948974278317847258028887801b0 
 (-4.52295330147551542569579253843b-16*%i)-2.44948974278317772381427927141b0 
 [256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,
  (-5.0b-1*(16*a^4+6.27069374152493593138504723125b2*a))
   -1.74185937264581553649584645313b1*a^3-3.2b1*a^2
   -5.44000000000000000000000000001b2] 
dist: 1.17428054562583903487602624948b-15 
common-roots: -2.44948974278317809819728407471b0 
             -2.44948974278317809819728407471b0 
dist: 1.57772181044202361082345713057b-30 
1 multi-roots: 0.0b0 0.0b0 [8*a*c-9*b^2-2*a^3,-2*a^3] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [8*a*c-9*b^2-2*a^3,-2*a^3] 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
1 multi-roots: 
 8.16496580927726032731894282802b-1-1.6183536594179216924381257046b-22*%i 
 1.61835365941792169243742042834b-22*%i+8.16496580927726032732961767002b-1 
 [8*a*c-9*b^2-2*a^3,(-2*a^3)+4.0b0*a-2.17732421580726942061980806641b0] 
dist: 1.11547535241290012202233114443b-21 
1 multi-roots: 
 (-8.47286141428164487440940737737b-20*%i)-1.41421356237309504909493338483b0 
 8.47286141428164487616706655174b-20*%i-1.41421356237309504850844406359b0 
 [256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,
  8.0b0*a^4-3.2b1*a^2+3.2b1] 
dist: 6.10479709847422546500953724134b-19 
2 multi-roots: 
 1.41421356237309504879618188426b0-1.96859282073234240509586747592b-21*%i 
 1.96859282073234238751927573217b-21*%i+1.41421356237309504880719556416b0 
 [256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,
  8.0b0*a^4-3.2b1*a^2+3.2b1] 
dist: 1.16962633227785224686827731017b-20 
common-roots: 1.41421356237309504880168872421b0 
             1.41421356237309504880168872421b0 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: -1.41421356237309504880168872421b0 
             -1.41421356237309504880168872421b0 
dist: 0.0b0 
1 multi-roots: 
 8.1649658092772603273200008634b-1-1.30109252983440372998384918995b-22*%i 
 1.30109252983440372998339457472b-22*%i+8.16496580927726032732855963464b-1 
 [8*a*c-9*b^2-2*a^3,(-2*a^3)+4.0b0*a-2.17732421580726942061980806641b0] 
dist: 8.94560966410596198552565674457b-22 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
1 multi-roots: 
 (-1.16997742006955532323735088816b-17*%i)-3.35546475144558657978639517931b-1 
 1.16997742006955532102907767889b-17*%i-3.35546475144558652208708812765b-1 
 [x^4+a*x^2+b*x+c,
  x^4-4.77860936379455500840332276085b0*x^2
     -3.05577241698508990342139722064b0*x-5.0b-1] 
dist: 2.41004349697564216587243138313b-17 
1 multi-roots: 
 (-2.24047760152893241737421755167b-20*%i)-1.0109852688012821415609910299b0 
 2.24047760152893269859199915596b-20*%i-1.01098526880128214151321562239b0 
 [x^4+a*x^2+b*x+c,
  x^4-3.55546677120777806279111679242b0*x^2
     -3.05577241698508990342139722064b0*x-5.0b-1] 
dist: 6.55010344684744407831148213933b-20 
1 multi-roots: 
 2.22935715805258081302014670225b-18*%i-4.14333797761439630281210468432b-1 
 (-2.22935715805258088784912140497b-18*%i)-4.14333797761439627962993519833b-1 
 [x^4+a*x^2+b*x+c,
  x^4-3.42753994633320075795235578053b0*x^2
     -2.55577241698508990342139722064b0*x-5.0b-1] 
dist: 5.02536199426577147169718392348b-18 
1 multi-roots: 
 (-7.63751536911083876261312227633b-19*%i)-8.96295167765296091409417104731b-1 
 7.63751536911083876548501856105b-19*%i-8.96295167765296090286367856344b-1 
 [x^4+a*x^2+b*x+c,
  x^4-3.03243266180629550631765220844b0*x^2
     -2.55577241698508990342139722064b0*x-5.0b-1] 
dist: 1.89591805066530344113644713169b-18 
1 multi-roots: 
 4.44329956060120776495651206012b-21*%i-4.7445898461131539492366468499b-1 
 (-4.44329956060120776491378978904b-21*%i)-4.74458984611315394915833267933b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.89645721365288302103527609247b0*x^2
     -2.32127592854140316276702227643b0*x-5.0b-1] 
dist: 1.18449456333131606287348159343b-20 
1 multi-roots: 
 (-5.13518395612155029572934523107b-18*%i)-8.19617912427072101369893178291b-1 
 5.13518395612155030519077584595b-18*%i-8.19617912427072096157128200993b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.75961902983845013509216731558b0*x^2
     -2.32127592854140316276702227643b0*x-5.0b-1] 
dist: 1.15175247237145207854523711501b-17 
1 multi-roots: 
 (-6.2414826969557199979633340867b-13*%i)-6.38943104254668599248510111018b-1 
 (-6.95918202422128079528203919324b-12*%i)-6.38943104241533885902022292701b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.44948974278317809819728407471b0*x^2
     -2.08677944009771642211264733221b0*x-5.0b-1] 
dist: 1.45826385597869537841530414623b-11 
2 multi-roots: 
 (-6.95918202422128079528203919324b-12*%i)-6.38943104241533885902022292701b-1 
 7.58333029391685279498189770221b-12*%i-6.38943104242614942415515511763b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.44948974278317809819728407471b0*x^2
     -2.08677944009771642211264733221b0*x-5.0b-1] 
dist: 1.4582638571553690760678343437b-11 
1 multi-roots: 
 6.38943104246144034405208996102b-1-4.422502465774425554602186706b-14*%i 
 1.33349305972666630723236835579b-13*%i+6.38943104246298402619456223129b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.44948974278317809819728407471b0*x^2
     +2.08677944009771642211264733221b0*x-5.0b-1] 
dist: 2.3529170930722626582908906827b-13 
2 multi-roots: 
 1.33349305972666630723236835579b-13*%i+6.38943104246298402619456223129b-1 
 6.38943104246374990541382696251b-1-8.91242813149223756054934246976b-14*%i 
 [x^4+a*x^2+b*x+c,
  x^4-2.44948974278317809819728407471b0*x^2
     +2.08677944009771642211264733221b0*x-5.0b-1] 
dist: 2.35287498234870156742355194154b-13 
1 multi-roots: 
 3.72610157565100454685245607331b-20*%i+4.74458984611315394913552119431b-1 
 4.74458984611315394925945833492b-1-3.72610157565100454690915365651b-20*%i 
 [x^4+a*x^2+b*x+c,
  x^4-2.89645721365288302103527609247b0*x^2
     +2.32127592854140316276702227643b0*x-5.0b-1] 
dist: 7.55455976814101740503286439967b-20 
1 multi-roots: 
 8.19617912427072098761958869152b-1-3.13943116569295322775812726995b-21*%i 
 3.13943116569295322775468371035b-21*%i+8.19617912427072098765062510133b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.75961902983845013509216731558b0*x^2
     +2.32127592854140316276702227643b0*x-5.0b-1] 
dist: 7.00404879414403669951788837319b-21 
1 multi-roots: 
 2.46936845160507392345254636383b-17*%i+4.14333797761439612007308924107b-1 
 4.14333797761439646236895064158b-1-2.46936845160507398188288178659b-17*%i 
 [x^4+a*x^2+b*x+c,
  x^4-3.42753994633320075795235578053b0*x^2
     +2.55577241698508990342139722064b0*x-5.0b-1] 
dist: 6.00897394505265450935583153395b-17 
1 multi-roots: 
 8.96295167765296090779340009951b-1-8.69963119046618331638821004739b-20*%i 
 8.69963119046618331598771326227b-20*%i+8.96295167765296090916444951125b-1 
 [x^4+a*x^2+b*x+c,
  x^4-3.03243266180629550631765220844b0*x^2
     +2.55577241698508990342139722064b0*x-5.0b-1] 
dist: 2.21520197802208732404660033187b-19 
1 multi-roots: 
 3.35546475144558654573716194067b-1-3.2321873145433364152600510801b-19*%i 
 3.23218731454333641635946277158b-19*%i+3.35546475144558655613632136628b-1 
 [x^4+a*x^2+b*x+c,
  x^4-4.77860936379455500840332276085b0*x^2
     +3.05577241698508990342139722064b0*x-5.0b-1] 
dist: 1.2244617433979626836819761986b-18 
1 multi-roots: 
 1.01098526880128213782781893505b0-2.07015345747187669505738755424b-18*%i 
 2.07015345747187669030859350914b-18*%i+1.01098526880128214524638771724b0 
 [x^4+a*x^2+b*x+c,
  x^4-3.55546677120777806279111679242b0*x^2
     +3.05577241698508990342139722064b0*x-5.0b-1] 
dist: 8.49572269592501254899699170041b-18 
1 multi-roots: 
 1.09731695855008129432850901121b-16*%i-6.29960524947436974960114115801b-1 
 (-1.09731695855008175020983658478b-16*%i)-6.29960524947436189807096491478b-1 
 [x^4+a*x^2+b*x+c,x^4-1.19055078897614960606377922946b0*x^2-5.0b-1*x] 
dist: 8.15248085790726489126442096385b-16 
1 multi-roots: 0.0b0 0.0b0 [x^4+a*x^2+b*x+c,x^4-5.0b-1*x^2] 
dist: 0.0b0 
1 multi-roots: 
 6.29960524947436582381894689913b-1-5.1915207100556332839659272546b-22*%i 
 5.19152071005563328395652911378b-22*%i+6.29960524947436582385315917366b-1 
 [x^4+a*x^2+b*x+c,x^4-1.19055078897614960606377922946b0*x^2+5.0b-1*x] 
dist: 3.57531436008650390541071687971b-21 
1 multi-roots: 
 (-8.67770249132643708238919796611b-23*%i)-1.31549862931202979917891670099b0 
 8.67770249132643708239032323801b-23*%i-1.31549862931202979917841983362b0 
 [x^4+a*x^2+b*x+c,
  x^4-4.90268221512206394838567282523b0*x^2
     -3.79286913672985525962281904563b0*x+5.0b-1] 
dist: 5.26306169342786570228478616546b-22 
1 multi-roots: 
 2.61198261984724332021478496099b-1-3.73328701456410231125396194552b-23*%i 
 3.73328701456410231125394316086b-23*%i+2.61198261984724332021514776701b-1 
 [x^4+a*x^2+b*x+c,
  x^4+7.12406849810570318368614385351b0*x^2
     -3.79286913672985525962281904563b0*x+5.0b-1] 
dist: 8.30135823846948556696946435113b-23 
1 multi-roots: 
 (-8.35793034501348062623930605099b-22*%i)-1.26839633131681513709955065996b0 
 8.35793034501348062625014797815b-22*%i-1.26839633131681513709478200116b0 
 [x^4+a*x^2+b*x+c,
  x^4-4.51570275957450820467053128978b0*x^2
     -3.29286913672985525962281904563b0*x+5.0b-1] 
dist: 5.05314820570176695705561472995b-21 
1 multi-roots: 
 3.49188104507532910404015377995b-23*%i+2.98842309414307218065285325202b-1 
 2.98842309414307218065613316054b-1-3.49188104507532910403992032144b-23*%i 
 [x^4+a*x^2+b*x+c,
  x^4+5.33076228416614959738464811917b0*x^2
     -3.29286913672985525962281904563b0*x+5.0b-1] 
dist: 3.35343542885119089772093274405b-22 
1 multi-roots: 
 (-5.10955124220135577792387388171b-22*%i)-1.1495332358829680004419098722b0 
 5.10955124220135577792837906846b-22*%i-1.14953323588296800043902649925b0 
 [x^4+a*x^2+b*x+c,
  x^4-3.58590105561473348013717487389b0*x^2
     -2.16812942838935673533957135587b0*x+5.0b-1] 
dist: 3.05910773620696643491835445611b-21 
1 multi-roots: 
 4.29760429000264513227806165013b-1-4.9825698827127380563723750383b-17*%i 
 4.9825698827127377393878597465b-17*%i+4.29760429000264633921325792835b-1 
 [x^4+a*x^2+b*x+c,
  x^4+2.15309806062091933677807113863b0*x^2
     -2.16812942838935673533957135587b0*x+5.0b-1] 
dist: 1.56516218758945019086233255227b-16 
1 multi-roots: 
 (-1.09877730976256428518192469349b-21*%i)-1.00617122801969079931775349078b0 
 1.09877730976254185519229728272b-21*%i-1.00617122801969079931174334307b0 
 [x^4+a*x^2+b*x+c,
  x^4-2.54325618867219212419273854599b0*x^2
     -1.04338972004885821105632366611b0*x+5.0b-1] 
dist: 6.39930635240535273049586094033b-21 
1 multi-roots: 
 6.38943104246272475524586123887b-1-7.84439082707517235056253391037b-20*%i 
 7.84439082708190432497441062349b-20*%i+6.38943104246272476186112486434b-1 
 [x^4+a*x^2+b*x+c,x^4-1.04338972004885821105632366611b0*x+5.0b-1] 
dist: 6.79875661664383746823339492112b-19 
1 multi-roots: 
 (-4.8300774831537619911512151596b-22*%i)-9.65994523816328465899519279333b-1 
 4.8300774707834158989233615011b-22*%i-9.65994523816328465899094849168b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.26361409430139643717899746966b0*x^2
     -7.67624175513389459396781893817b-1*x+5.0b-1] 
dist: 1.05514307182643029247458493579b-21 
1 multi-roots: 
 1.119137819361247989040796719b-15*%i+6.94963770046457076218883279372b-1 
 6.94963770046457864444214852857b-1-1.11913781936124711403020335568b-15*%i 
 [x^4+a*x^2+b*x+c,
  x^4-4.13672885217763849890412496005b-1*x^2
     -7.67624175513389459396781893817b-1*x+5.0b-1] 
dist: 2.37301011549313127333803802423b-15 
1 multi-roots: 
 6.33988972265475161381443097681b-22*%i-9.23416931585132456001273979169b-1 
 (-6.33988972265475161353799507713b-22*%i)-9.23416931585132455992195460933b-1 
 [x^4+a*x^2+b*x+c,
  x^4-1.9717229852393250817227538327b0*x^2
     -4.91858630977920707737240121529b-1*x+5.0b-1] 
dist: 9.16663850192252560176095861665b-21 
1 multi-roots: 
 7.49558352273654755133389531399b-1-9.2980021082756567072476690926b-18*%i 
 9.29800210827546330169426966815b-18*%i+7.49558352273654772974086850138b-1 
 [x^4+a*x^2+b*x+c,
  x^4-7.95576487395121227355033572426b-1*x^2
     -4.91858630977920707737240121529b-1*x+5.0b-1] 
dist: 2.57701737215882295851533416416b-17 
1 multi-roots: 
 1.03401156272799309188393045594b-19*%i-8.83251837810700396804617510575b-1 
 (-1.03401156272799304752829508618b-19*%i)-8.83251837810700395251773718947b-1 
 [x^4+a*x^2+b*x+c,
  x^4-1.69948573504594766924564690096b0*x^2
     -2.45929315488960353868620060764b-1*x+5.0b-1] 
dist: 1.56655387320991285239749179312b-18 
1 multi-roots: 
 7.96303936790265302555727618361b-1-3.40419552049028707429902475843b-21*%i 
 3.40419552049944803968351960399b-21*%i+7.96303936790265302568553128937b-1 
 [x^4+a*x^2+b*x+c,
  x^4-1.1137806681726386454165880796b0*x^2
     -2.45929315488960353868620060764b-1*x+5.0b-1] 
dist: 1.45206029523254927419705052618b-20 
1 multi-roots: 
 (-5.70609945371498130990553057283b-21*%i)-8.40896415253714543050874201664b-1 
 5.70609945371498131018153821252b-21*%i-8.40896415253714543011376750803b-1 
 [x^4+a*x^2+b*x+c,x^4-1.41421356237309504880168872421b0*x^2+5.0b-1] 
dist: 4.11130989883287052898186383085b-20 
2 multi-roots: 
 8.40896415253714543012849282445b-1-6.53339775168399828589095914175b-21*%i 
 6.53339775168399828561495150206b-21*%i+8.40896415253714543049401670022b-1 
 [x^4+a*x^2+b*x+c,x^4-1.41421356237309504880168872421b0*x^2+5.0b-1] 
dist: 3.88177560186052570543478329165b-20 
1 multi-roots: 
 2.15893555484106906165912452485b-16*%i+8.83251837810700183846822208909b-1 
 8.83251837810700608209569020613b-1-2.15893555484106797595047500567b-16*%i 
 [x^4+a*x^2+b*x+c,
  x^4-1.69948573504594766924564690097b0*x^2
     +2.45929315488960353868620060765b-1*x+5.0b-1] 
dist: 6.05412132418777109501344790091b-16 
1 multi-roots: 
 6.37787066397529175282449379547b-20*%i-7.96303936790265302727748521798b-1 
 (-6.37787066396800919273345251121b-20*%i)-7.963039367902653023965322255b-1 
 [x^4+a*x^2+b*x+c,
  x^4-1.1137806681726386454165880796b0*x^2
     +2.45929315488960353868620060765b-1*x+5.0b-1] 
dist: 3.54929751662912295409283425277b-19 
1 multi-roots: 
 9.23416931585132422243653899598b-1-6.27472747421841058511382108183b-18*%i 
 6.2747274742183885879114162131b-18*%i+9.23416931585132489749815540504b-1 
 [x^4+a*x^2+b*x+c,
  x^4-1.9717229852393250817227538327b0*x^2
     +4.91858630977920707737240121529b-1*x+5.0b-1] 
dist: 6.86627313685598614587092899877b-17 
1 multi-roots: 
 (-1.99636848170413194768633600558b-15*%i)-7.49558352273655235457557488862b-1 
 1.99636848170413258293302923552b-15*%i-7.49558352273654292649918892678b-1 
 [x^4+a*x^2+b*x+c,
  x^4-7.95576487395121227355033572426b-1*x^2
     +4.91858630977920707737240121529b-1*x+5.0b-1] 
dist: 4.10254003056179335802065997111b-15 
1 multi-roots: 
 9.65994523816328465899290503781b-1-2.66934379792368063978571497834b-22*%i 
 2.66934379792368063978568047301b-22*%i+9.65994523816328465899323624718b-1 
 [x^4+a*x^2+b*x+c,
  x^4-2.26361409430139643717899746966b0*x^2
     +7.67624175513389459396781893818b-1*x+5.0b-1] 
dist: 5.34895175649003922093343053329b-22 
1 multi-roots: 
 (-4.29381502396318990315032909949b-19*%i)-6.9496377004645747104791949945b-1 
 4.29381502396139055973603979073b-19*%i-6.94963770046457469615178632778b-1 
 [x^4+a*x^2+b*x+c,
  x^4-4.13672885217763849890412496004b-1*x^2
     +7.67624175513389459396781893818b-1*x+5.0b-1] 
dist: 1.67039524946424430892380307845b-18 
1 multi-roots: 
 1.00617122801969079926553973356b0-1.60075239406241646868279412713b-19*%i 
 1.60075239406241646862513736191b-19*%i+1.00617122801969079936395710029b0 
 [x^4+a*x^2+b*x+c,
  x^4-2.54325618867219212419273854599b0*x^2
     +1.04338972004885821105632366611b0*x+5.0b-1] 
dist: 3.34936273279166823298162816124b-19 
1 multi-roots: 
 (-3.77185753862812953984534199095b-24*%i)-6.38943104246272475855369706517b-1 
 3.77185746499376146262928840184b-24*%i-6.38943104246272475855328903805b-1 
 [x^4+a*x^2+b*x+c,x^4+1.04338972004885821105632366611b0*x+5.0b-1] 
dist: 4.14942038334135943047182928317b-23 
1 multi-roots: 
 1.14953323588296799935017434052b0-1.25168566885221419821833160929b-18*%i 
 1.25168566885221419738370885239b-18*%i+1.14953323588296800153076203092b0 
 [x^4+a*x^2+b*x+c,
  x^4-3.58590105561473348013717487389b0*x^2
     +2.16812942838935673533957135587b0*x+5.0b-1] 
dist: 3.31991426545575543023864496728b-18 
1 multi-roots: 
 (-2.58295399767902797007565021885b-19*%i)-4.29760429000264573649957309613b-1 
 2.58295399767902797030577470367b-19*%i-4.29760429000264573499174648236b-1 
 [x^4+a*x^2+b*x+c,
  x^4+2.15309806062091933677807113863b0*x^2
     +2.16812942838935673533957135587b0*x+5.0b-1] 
dist: 5.38146323165938018060210022577b-19 
1 multi-roots: 
 1.2683963313168151249994797521b0-1.02128852191271037829509986173b-17*%i 
 1.02128852191271037157319651058b-17*%i+1.26839633131681514919485290902b0 
 [x^4+a*x^2+b*x+c,
  x^4-4.51570275957450820467053128978b0*x^2
     +3.29286913672985525962281904563b0*x+5.0b-1] 
dist: 3.16643045115257576716717302982b-17 
1 multi-roots: 
 8.98733613243950412511068357208b-21*%i-2.98842309414307218067753665713b-1 
 (-8.98733613243950412511912321165b-21*%i)-2.98842309414307218063144975543b-1 
 [x^4+a*x^2+b*x+c,
  x^4+5.33076228416614959738464811916b0*x^2
     +3.29286913672985525962281904563b0*x+5.0b-1] 
dist: 1.85561005632311052538934339445b-20 
1 multi-roots: 
 1.315498629312029794561387534b0-3.5935851244110502148689984252b-18*%i 
 3.5935851244110502062082304748b-18*%i+1.31549862931202980379594900061b0 
 [x^4+a*x^2+b*x+c,
  x^4-4.90268221512206394838567282523b0*x^2
     +3.79286913672985525962281904563b0*x+5.0b-1] 
dist: 1.1701817878693290753327731022b-17 
1 multi-roots: 
 2.54178527994425949722680256301b-23*%i-2.61198261984724332021510649724b-1 
 (-2.54178527994425949722681244282b-23*%i)-2.61198261984724332021482623075b-1 
 [x^4+a*x^2+b*x+c,
  x^4+7.12406849810570318368614385351b0*x^2
     +3.79286913672985525962281904563b0*x+5.0b-1] 
dist: 5.80496512960753920779203206589b-23 
[T,F]: [92,175] 

Evaluation took 13.7400 seconds (13.7800 elapsed) using 1299.854 MB.

(%o2) [[c = root(c,1),b = root(126976*c^3-135*b^4,1),
        root(8*a*c-9*b^2-2*a^3,1) <= a,true],
       [root(c,1) < c,b < root(b,1),
        root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
          <= a,true],
       [root(c,1) < c,b = root(b,1),
        root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,1)
          <= a,true],
       [root(c,1) < c,root(b,1) < b,
        root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
          <= a,true]]