実行例(2)

http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/2019-13.pdf
https://github.com/hiwane/qe_problems/blob/master/problems/exam/manual-fof/tsukuba2010-Ri-1-m.mpl

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 ([ex],[a,b,x],0,0,r11,0 ),
       qe( bfpcad(ext( '(     -1 <= x and x <= 3 and b = x^3/3 - a*x^2/2 and a > 0   ) )))  );
Evaluation took 1.7400 seconds (1.7400 elapsed) using 188.173 MB.
(%o1) [[root(a,1) < a and a < root(a-2,1),
        root(6*b+3*a+2,1) <= b and b <= root(2*b+9*a-18,1),true],
       [a = root(a-2,1),root(6*b+a^3,1) <= b and b <= root(2*b+9*a-18,1),
        true],
       [root(a-2,1) < a and a <= root(a-3,1),
        root(6*b+a^3,1) <= b and b <= root(b,1),true],
       [root(a-3,1) < a,root(2*b+9*a-18,1) <= b and b <= root(b,1),true]]

(%i2) (qvpeds ([ex],[a,b,x],1,0,r11,0 ),
       qe( bfpcad(ext( '(     -1 <= x and x <= 3 and b = x^3/3 - a*x^2/2 and a > 0   ) )))  );

[fpprec,fpprintprec,%ez,ratepsilon]: [16,30,1.0b-3,1.0b-16] 
x+1 >= 0 and x-3 <= 0 and equal((2*x^3-3*a*x^2-6*b)/6,0) and a > 0 
["and",equal((2*x^3-3*a*x^2-6*b)/6,0),x-3 <= 0,x+1 >= 0,a > 0] 
[[x-3],[x+1],[2*x^3-3*a*x^2-6*b]] 
[[b],[2*b+9*a-18],[6*b+3*a+2],[6*b+a^3]] 
[[a-3,a-2,a,a+1,a+6,3*a-7,3*a+2],[b,2*b+9*a-18,6*b+3*a+2,6*b+a^3],
 [x-3,x+1,2*x^3-3*a*x^2-6*b]]
  
common-roots: 0.0b0 0.0b0 
dist: 0.0b0 
common-roots: -1.333333333333333b0 -1.333333333333333b0 
dist: 0.0b0 
common-roots: -1.5b0 -1.5b0 
dist: 0.0b0 
common-roots: -4.5b0 -4.5b0 
dist: 0.0b0 
common-roots: -1.0b0 -1.0b0 
dist: 0.0b0 
1 multi-roots: 9.999999999999999b-1-3.469517903370656b-17*%i 
 3.469446951953614b-17*%i+1.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-3.0b0*x^2+1.0b0] 
dist: 1.309231643767475b-16 
1 multi-roots: 0.0b0 0.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-3.0b0*x^2] 
dist: 0.0b0 
common-roots: 3.0b0 3.0b0 
dist: 0.0b0 
1 multi-roots: 6.938893903907228b-17*%i+2.0b0 2.0b0-6.939035806741312b-17*%i 
 [2*x^3-3*a*x^2-6*b,2*x^3-6*x^2+8] 
dist: 2.61846328753495b-16 
common-roots: -1.0b0 -1.0b0 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-6*x^2] 
dist: 0.0b0 
common-roots: 3.0b0 3.0b0 
dist: 0.0b0 
1 multi-roots: 2.166666666666667b0-4.163490115220211b-17*%i 
 4.163336342344337b-17*%i+2.166666666666667b0 
 [2*x^3-3*a*x^2-6*b,2*x^3-6.5b0*x^2+1.01712962962963b1] 
dist: 1.861907491918325b-16 
common-roots: -1.0b0 -1.0b0 
dist: 0.0b0 
common-roots: 3.0b0 3.0b0 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-6.5b0*x^2] 
dist: 0.0b0 
1 multi-roots: 2.333333333333333b0-5.551280766043446b-17*%i 
 5.551115123125783b-17*%i+2.333333333333334b0 
 [2*x^3-3*a*x^2-6*b,2*x^3-7*x^2+1.27037037037037b1] 
dist: 1.171009175116753b-15 
common-roots: 3.0b0 3.0b0 
dist: 0.0b0 
common-roots: -1.0b0 -1.0b0 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-7*x^2] 
dist: 0.0b0 
1 multi-roots: 1.387778780781446b-17*%i+2.666666666666667b0 
 2.666666666666667b0-1.387968122423659b-17*%i 
 [2*x^3-3*a*x^2-6*b,2*x^3-8.0b0*x^2+1.896296296296296b1] 
dist: 1.144396291987333b-16 
common-roots: 3.0b0 3.0b0 
dist: 0.0b0 
common-roots: -1.0b0 -1.0b0 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-8.0b0*x^2] 
dist: 0.0b0 
1 multi-roots: 3.0b0-4.163336342344337b-17*%i 4.163123343336605b-17*%i+3.0b0 
 [2*x^3-3*a*x^2-6*b,2*x^3-9*x^2+27] 
dist: 2.371429941323172b-16 
common-roots: 3.0b0 3.0b0 
dist: 0.0b0 
common-roots: -1.0b0 -1.0b0 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-9*x^2] 
dist: 0.0b0 
1 multi-roots: 5.550866638069772b-17*%i+3.5b0 3.5b0-5.551115123125783b-17*%i 
 [2*x^3-3*a*x^2-6*b,2*x^3-1.05b1*x^2+4.2875b1] 
dist: 5.661043993863231b-16 
common-roots: 3.0b0 3.0b0 
dist: 5.551115123125783b-17 
common-roots: -1.0b0 -1.0b0 
dist: 0.0b0 
1 multi-roots: 0.0b0 0.0b0 [2*x^3-3*a*x^2-6*b,2*x^3-1.05b1*x^2] 
dist: 0.0b0 
[T,F]: [39,253] 
Evaluation took 2.5500 seconds (2.5600 elapsed) using 169.662 MB.
(%o2) [[root(a,1) < a and a < root(a-2,1),
        root(6*b+3*a+2,1) <= b and b <= root(2*b+9*a-18,1),true],
       [a = root(a-2,1),root(6*b+a^3,1) <= b and b <= root(2*b+9*a-18,1),
        true],
       [root(a-2,1) < a and a <= root(a-3,1),
        root(6*b+a^3,1) <= b and b <= root(b,1),true],
       [root(a-3,1) < a,root(2*b+9*a-18,1) <= b and b <= root(b,1),true]]