実行例(4)

(%i1) (qvpeds ([],[a,b,c,d],0,h1,r11,0 ),
       qe( bfpcad(ext( '(  a^3+b^2-1=0 and b^3+c^2-1=0 and c^3+d^2-1=0 and d^3+a^2-1=0  ) )))  );
Evaluation took 14.3200 seconds (16.7700 elapsed) using 2101.559 MB.
(%o1) [[a = root(a,1),b = root(b^2+a^3-1,2),
        c = root(c^9-3*c^6+3*c^3+a^4-2*a^2,1),d = root(d^3+a^2-1,1)],
       [a = root(a^3+a^2-1,1),
        b = root(b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12
                     +a^4*(6*b^9-18*b^6+18*b^3-2)+33*b^9
                     +a^2*((-12*b^9)+36*b^6-36*b^3+12)-18*b^6+18*b^3+a^8-4*a^6
                     -7,1),c = root(c^9-3*c^6+3*c^3+a^4-2*a^2,1),
        d = root(d^2+c^3-1,2)],
       [a = root(a-1,1),b = root(b^2+a^3-1,1),c = root(c^2+b^3-1,2),
        d = root(d^3+a^2-1,1)]]

(%i2) (qvpeds ([],[a,b,c,d],1,h1,r11,0 ),
       qe( bfpcad(ext( '(  a^3+b^2-1=0 and b^3+c^2-1=0 and c^3+d^2-1=0 and d^3+a^2-1=0  ) )))  );

[fpprec,fpprintprec,%ez,ratepsilon]: [16,30,1.0b-3,1.0b-16] 
equal(b^2+a^3-1,0) and equal(c^2+b^3-1,0) and equal(d^2+c^3-1,0)
                   and equal(d^3+a^2-1,0)
  
["and",equal(d^3+a^2-1,0),equal(d^2+c^3-1,0),equal(c^2+b^3-1,0),
 equal(b^2+a^3-1,0)]
  
[[a-1,a,a+1,a^2-2,a^3+a^2-1,a^4-2*a^2-7,a^9-3*a^6+3*a^3-4,
  a^25+2*a^24+3*a^23-5*a^22-13*a^21-21*a^20+7*a^19+35*a^18+63*a^17-26*a^16
      -115*a^15-204*a^14+31*a^13+266*a^12+501*a^11+115*a^10-271*a^9-657*a^8
      -290*a^7+77*a^6+444*a^5+253*a^4+62*a^3-135*a^2-98*a-49,
  a^27-9*a^24+36*a^21-81*a^18+108*a^15-81*a^12+9*a^9+54*a^6-54*a^3+33],
 [b-1,b,a^3+b^2-1,b^2+b+1,b^6-3*b^3+3,b^9-3*b^6+3*b^3-4,
  a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7],
 [c-1,c^2+b^3-1,c^2+c+1,c^9-3*c^6+3*c^3+a^4-2*a^2],[d^2+c^3-1,d^3+a^2-1]]
  
1 multi-roots: 0.0b0 0.0b0 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+75*b^9-144*b^6+144*b^3] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+75*b^9-144*b^6+144*b^3] 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
1 multi-roots: (-8.660804423214204b-1*%i)-5.000441678406675b-1 
 (-8.659596311546991b-1*%i)-5.000255856711448b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.222318903917476b-4 
2 multi-roots: (-8.659596311546991b-1*%i)-5.000255856711448b-1 
 (-8.660361378779625b-1*%i)-4.999302464884673b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.222409033757573b-4 
3 multi-roots: 8.660599669975173b-1*%i-5.000356595414205b-1 
 8.659772383882947b-1*%i-5.000121050417724b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 8.601649398563011b-5 
4 multi-roots: 8.659772383882947b-1*%i-5.000121050417724b-1 
 8.660390059677586b-1*%i-4.999522354169911b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 8.602096165627294b-5 
5 multi-roots: 2.231315975623363b-5*%i+9.999456693238325b-1 
 1.000007845795338b0-5.8207805235442b-5*%i 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.017326860553025b-4 
6 multi-roots: 1.000007845795338b0-5.8207805235442b-5*%i 
 3.589464596707269b-5*%i+1.000046484881349b0 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.017263500284118b-4 
1 multi-roots: (-9.199710801626131b-1*%i)-7.71947399037216b-1 
 (-9.199710804360586b-1*%i)-7.719473929391142b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 6.104229478123359b-9 
2 multi-roots: (-9.199710804360586b-1*%i)-7.719473929391142b-1 
 (-9.199710825477433b-1*%i)-7.719473924291037b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 2.172400328519447b-9 
3 multi-roots: 9.199708723835111b-1*%i-7.719494718698244b-1 
 9.19972984231248b-1*%i-7.71946537008062b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.615703863455374b-6 
4 multi-roots: 9.19972984231248b-1*%i-7.71946537008062b-1 
 9.199693865316476b-1*%i-7.719461755275532b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.61581395716781b-6 
5 multi-roots: (-1.128504487190754b0*%i)-4.107493297893198b-1 
 (-1.128519218977068b0*%i)-4.107484344965202b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.475896599372942b-5 
6 multi-roots: (-1.128519218977068b0*%i)-4.107484344965202b-1 
 (-1.128511078256128b0*%i)-4.107361243173334b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.475845008925132b-5 
7 multi-roots: 1.128511588695093b0*%i-4.107446393024692b-1 
 1.128511596096971b0*%i-4.107446267335344b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.458649779375334b-8 
8 multi-roots: 1.128511596096971b0*%i-4.107446267335344b-1 
 1.128511599631896b0*%i-4.107446225671621b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 5.463913988241733b-9 
9 multi-roots: 0.0b0 0.0b0 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
10 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
11 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
12 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
13 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
14 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
15 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
16 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
17 multi-roots: 1.182691836749522b0-2.085404757701443b-1*%i 
  1.182692087088606b0-2.085407026268325b-1*%i 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.378366674990088b-7 
18 multi-roots: 1.182692087088606b0-2.085407026268325b-1*%i 
  1.182692149170476b0-2.085403628805644b-1*%i 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.453718073079048b-7 
19 multi-roots: 2.085405167216828b-1*%i+1.182692020651834b0 
  2.085404528573458b-1*%i+1.182692021812494b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 6.387488296457688b-8 
20 multi-roots: 2.085404528573458b-1*%i+1.182692021812494b0 
  2.085405716985108b-1*%i+1.18269203054428b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.191615147068571b-7 
common-roots: 1.346676703722613b0 1.346676703722613b0 
dist: 1.665334536937735b-16 
1 multi-roots: (-8.660804423214204b-1*%i)-5.000441678406675b-1 
 (-8.659596311546991b-1*%i)-5.000255856711448b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.222318903917476b-4 
2 multi-roots: (-8.659596311546991b-1*%i)-5.000255856711448b-1 
 (-8.660361378779625b-1*%i)-4.999302464884673b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.222409033757573b-4 
3 multi-roots: 8.660599669975173b-1*%i-5.000356595414205b-1 
 8.659772383882947b-1*%i-5.000121050417724b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 8.601649398563011b-5 
4 multi-roots: 8.659772383882947b-1*%i-5.000121050417724b-1 
 8.660390059677586b-1*%i-4.999522354169911b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 8.602096165627294b-5 
5 multi-roots: 2.231315975623363b-5*%i+9.999456693238325b-1 
 1.000007845795338b0-5.8207805235442b-5*%i 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.017326860553025b-4 
6 multi-roots: 1.000007845795338b0-5.8207805235442b-5*%i 
 3.589464596707269b-5*%i+1.000046484881349b0 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7] 
dist: 1.017263500284118b-4 
common-roots: 1.0b0 1.0b0 
dist: 0.0b0 
common-roots: 7.548776662466926b-1 7.548776662466838b-1 
dist: 8.743006318923108b-15 
1 multi-roots: 0.0b0 0.0b0 [a^3+b^2-1,b^2] 
dist: 0.0b0 
1 multi-roots: (-9.199710801626131b-1*%i)-7.71947399037216b-1 
 (-9.199710804360586b-1*%i)-7.719473929391142b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 6.104229478123359b-9 
2 multi-roots: (-9.199710804360586b-1*%i)-7.719473929391142b-1 
 (-9.199710825477433b-1*%i)-7.719473924291037b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 2.172400328519447b-9 
3 multi-roots: 9.199708723835111b-1*%i-7.719494718698244b-1 
 9.19972984231248b-1*%i-7.71946537008062b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.615703863455374b-6 
4 multi-roots: 9.19972984231248b-1*%i-7.71946537008062b-1 
 9.199693865316476b-1*%i-7.719461755275532b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.61581395716781b-6 
5 multi-roots: (-1.128504487190754b0*%i)-4.107493297893198b-1 
 (-1.128519218977068b0*%i)-4.107484344965202b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.475896599372942b-5 
6 multi-roots: (-1.128519218977068b0*%i)-4.107484344965202b-1 
 (-1.128511078256128b0*%i)-4.107361243173334b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.475845008925132b-5 
7 multi-roots: 1.128511588695093b0*%i-4.107446393024692b-1 
 1.128511596096971b0*%i-4.107446267335344b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.458649779375334b-8 
8 multi-roots: 1.128511596096971b0*%i-4.107446267335344b-1 
 1.128511599631896b0*%i-4.107446225671621b-1 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 5.463913988241733b-9 
9 multi-roots: 0.0b0 0.0b0 
 [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
     -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
  b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
10 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
11 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
12 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
13 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
14 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
15 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
16 multi-roots: 0.0b0 0.0b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 0.0b0 
17 multi-roots: 1.182691836749522b0-2.085404757701443b-1*%i 
  1.182692087088606b0-2.085407026268325b-1*%i 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.378366674990088b-7 
18 multi-roots: 1.182692087088606b0-2.085407026268325b-1*%i 
  1.182692149170476b0-2.085403628805644b-1*%i 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 3.453718073079048b-7 
19 multi-roots: 2.085405167216828b-1*%i+1.182692020651834b0 
  2.085404528573458b-1*%i+1.182692021812494b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 6.387488296457688b-8 
20 multi-roots: 2.085404528573458b-1*%i+1.182692021812494b0 
  2.085405716985108b-1*%i+1.18269203054428b0 
  [a^8-4*a^6+(6*b^9-18*b^6+18*b^3-2)*a^4+((-12*b^9)+36*b^6-36*b^3+12)*a^2+b^27
      -9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+33*b^9-18*b^6+18*b^3-7,
   b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12+27*b^9] 
dist: 1.191615147068571b-7 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
1 multi-roots: 9.802492832500017b-24*%i-3.332445010132976b-6 
 1.666222505066488b-6-2.885982035489848b-6*%i 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3+1.110223024625157b-16] 
dist: 5.771964070979697b-6 
2 multi-roots: 1.666222505066488b-6-2.885982035489848b-6*%i 
 2.885982035489848b-6*%i+1.666222505066488b-6 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3+1.110223024625157b-16] 
dist: 5.771964070979697b-6 
1 multi-roots: (-8.660255628474419b-1*%i)-5.00000111173379b-1 
 (-8.660252247378837b-1*%i)-5.000000835080218b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1.0b0] 
dist: 3.392395102543312b-7 
2 multi-roots: (-8.660252247378837b-1*%i)-5.000000835080218b-1 
 (-8.660254237679908b-1*%i)-4.999998053185997b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1.0b0] 
dist: 3.420560452027647b-7 
3 multi-roots: 8.660254036658418b-1*%i-5.000000000446686b-1 
 8.660254038379494b-1*%i-4.999999999906503b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1.0b0] 
dist: 1.803856285841607b-10 
4 multi-roots: 8.660254038379494b-1*%i-4.999999999906503b-1 
 8.660254038495248b-1*%i-4.999999999646812b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1.0b0] 
dist: 2.843207457168711b-11 
5 multi-roots: 1.632012483901229b-10*%i+9.999999990929849b-1 
 1.000000000452425b0-8.155697400955311b-11*%i 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1.0b0] 
dist: 1.381297987296357b-9 
6 multi-roots: 1.000000000452425b0-8.155697400955311b-11*%i 
 1.000000000454591b0-8.164377541315077b-11*%i 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1.0b0] 
dist: 2.167145783155763b-12 
1 multi-roots: 0.0b0 0.0b0 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [c^2+b^3-1,c^2] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3] 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: 7.548776662466963b-1 7.548776662466864b-1 
dist: 9.867107131356079b-15 
1 multi-roots: (-8.660255628474419b-1*%i)-5.00000111173379b-1 
 (-8.660252247378837b-1*%i)-5.000000835080218b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1] 
dist: 3.392395102543312b-7 
2 multi-roots: (-8.660252247378837b-1*%i)-5.000000835080218b-1 
 (-8.660254237679908b-1*%i)-4.999998053185997b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1] 
dist: 3.420560452027647b-7 
3 multi-roots: 8.660254036658418b-1*%i-5.000000000446686b-1 
 8.660254038379494b-1*%i-4.999999999906503b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1] 
dist: 1.803856285841607b-10 
4 multi-roots: 8.660254038379494b-1*%i-4.999999999906503b-1 
 8.660254038495248b-1*%i-4.999999999646812b-1 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1] 
dist: 2.843207457168711b-11 
5 multi-roots: 1.632012483901229b-10*%i+9.999999990929849b-1 
 1.000000000452425b0-8.155697400955311b-11*%i 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1] 
dist: 1.381297987296357b-9 
6 multi-roots: 1.000000000452425b0-8.155697400955311b-11*%i 
 1.000000000454591b0-8.164377541315077b-11*%i 
 [c^9-3*c^6+3*c^3+a^4-2*a^2,c^9-3*c^6+3*c^3-1] 
dist: 2.167145783155763b-12 
common-roots: 1.0b0 1.0b0 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [d^3+a^2-1,d^3] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [d^3+a^2-1,d^3] 
dist: 0.0b0 
common-roots: 1.0b0 1.0b0 
dist: 0.0b0 
common-roots: 7.548776662466929b-1 7.548776662466925b-1 
dist: 4.440892098500626b-16 
1 multi-roots: 0.0b0 0.0b0 [d^3+a^2-1,d^3] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [d^3+a^2-1,d^3] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [d^2+c^3-1,d^2] 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [d^3+a^2-1,d^3] 
dist: 0.0b0 
2 multi-roots: 0.0b0 0.0b0 [d^3+a^2-1,d^3] 
dist: 0.0b0 
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
[T,F]: [3,440] 
Evaluation took 14.8600 seconds (17.4500 elapsed) using 2063.632 MB.
(%o2) [[a = root(a,1),b = root(b^2+a^3-1,2),
        c = root(c^9-3*c^6+3*c^3+a^4-2*a^2,1),d = root(d^3+a^2-1,1)],
       [a = root(a^3+a^2-1,1),
        b = root(b^27-9*b^24+36*b^21-81*b^18+108*b^15-81*b^12
                     +a^4*(6*b^9-18*b^6+18*b^3-2)+33*b^9
                     +a^2*((-12*b^9)+36*b^6-36*b^3+12)-18*b^6+18*b^3+a^8-4*a^6
                     -7,1),c = root(c^9-3*c^6+3*c^3+a^4-2*a^2,1),
        d = root(d^2+c^3-1,2)],
       [a = root(a-1,1),b = root(b^2+a^3-1,1),c = root(c^2+b^3-1,2),
        d = root(d^3+a^2-1,1)]]