本日のC.A.D.

? tst12([],[a,b,c,x],f1->f1,"a*x^2+(a+b)*x+b*c<1",17);
 *** using Lazard's method (BM20).
-5
[x,1]
0
[c,1]
[b,1]
[a,1]
[[[a],[b],[],[]],[[a+4],[b],[],[]]]
time = 264 ms.
5 15(0,0) [[a,b],[-4,0]]:-a^2+((4*c-2)*b-4)*a-b^2>>(4*c-2)*a-2*b 
33(0,0) 45(22,0) 
 *** combined adjacent 0 cells.
time = 10 ms.
? pp
%2 = [[a,a+4],[b],[-a^2+((4*c-2)*b-4)*a-b^2],[a*x^2+(a+b)*x+(c*b-1)]]

QEPCAD B による結果の検証．

? qepcad3("[a x^2+(a+b) x+b c<1].","","");
 *** simplifing by QEPCAD B. < gp2qe.i1 > gp2qe.o1 (with sol T)
0.05user 0.01system 0:00.07elapsed 93%CPU (0avgtext+0avgdata 8772maxresident)k
0inputs+0outputs (0major+1373minor)pagefaults 0swaps
[ a = 0 /\ b^2 + 2 a b + a^2 + 4 a = 0 ] \/ [ b^2 + 2 a b + a^2 + 4 a < 0 /\ b = 0 ] \/ [ a < 0 /\ 4 a b c - b^2 - 2 a b - a^2 - 4 a > 0 ] \/ [ a < 0 /\ a x^2 + b x + a x + b c - 1 < 0 ] \/ [ 4 a b c - b^2 - 2 a b - a^2 - 4 a < 0 /\ a x^2 + b x + a x + b c - 1 < 0 ]
 *** simplifing by QEPCAD B. < gp2qe.i2 > gp2qe.o2 (with sol E)
0.05user 0.00system 0:00.05elapsed 89%CPU (0avgtext+0avgdata 8796maxresident)k
0inputs+0outputs (0major+1372minor)pagefaults 0swaps
[ b = 0 /\ b >= _root_-1 b^2 + 2 a b + a^2 + 4 a ] \/ [ b = 0 /\ b^2 + 2 a b + a^2 + 4 a < 0 ] \/ [ b >= _root_-1 b^2 + 2 a b + a^2 + 4 a /\ 4 a b c - b^2 - 2 a b - a^2 - 4 a > 0 ] \/ [ b < _root_-1 b^2 + 2 a b + a^2 + 4 a /\ 4 a b c - b^2 - 2 a b - a^2 - 4 a > 0 ] \/ [ b >= _root_-1 b^2 + 2 a b + a^2 + 4 a /\ a x^2 + b x + a x + b c - 1 < 0 ] \/ [ b < _root_-1 b^2 + 2 a b + a^2 + 4 a /\ a x^2 + b x + a x + b c - 1 < 0 ] \/ [ 4 a b c - b^2 - 2 a b - a^2 - 4 a < 0 /\ a x^2 + b x + a x + b c - 1 < 0 ]
 *** simplifing by QEPCAD B. < gp2qe.i3 > gp2qe.o3 (with sol N)
0.04user 0.01system 0:00.06elapsed 88%CPU (0avgtext+0avgdata 8712maxresident)k
0inputs+0outputs (0major+1372minor)pagefaults 0swaps
[ b = 0 /\ b >= _root_-1 b^2 + 2 a b + a^2 + 4 a ] \/ [ b = 0 /\ b^2 + 2 a b + a^2 + 4 a < 0 ] \/ [ b >= _root_-1 b^2 + 2 a b + a^2 + 4 a /\ 4 a b c - b^2 - 2 a b - a^2 - 4 a > 0 ] \/ [ b < _root_-1 b^2 + 2 a b + a^2 + 4 a /\ 4 a b c - b^2 - 2 a b - a^2 - 4 a > 0 ] \/ [ b >= _root_-1 b^2 + 2 a b + a^2 + 4 a /\ a x^2 + b x + a x + b c - 1 < 0 ] \/ [ b < _root_-1 b^2 + 2 a b + a^2 + 4 a /\ a x^2 + b x + a x + b c - 1 < 0 ] \/ [ 4 a b c - b^2 - 2 a b - a^2 - 4 a < 0 /\ a x^2 + b x + a x + b c - 1 < 0 ]
 *** processing QEPCAD B's results. < gp2qe.i4 > gp2qe.o4 (with sol E)
0.00user 0.00system 0:00.01elapsed 93%CPU (0avgtext+0avgdata 8600maxresident)k
0inputs+0outputs (0major+1368minor)pagefaults 0swaps
a x^2 + b x + a x + b c - 1 < 0
 *** processing QEPCAD B's results. < gp2qe.i5 > gp2qe.o5 (with sol N)
0.00user 0.00system 0:00.02elapsed 75%CPU (0avgtext+0avgdata 8596maxresident)k
0inputs+0outputs (0major+1369minor)pagefaults 0swaps
a x^2 + b x + a x + b c - 1 < 0
 *** verifying the equivalence. < gp2qe.e6 (with sol E)
TRUE
0.01user 0.00system 0:00.02elapsed 72%CPU (0avgtext+0avgdata 8672maxresident)k
0inputs+0outputs (0major+1372minor)pagefaults 0swaps
 *** verifying the equivalence. < gp2qe.e7 (with sol N)
TRUE
0.01user 0.00system 0:00.03elapsed 53%CPU (0avgtext+0avgdata 8828maxresident)k
0inputs+0outputs (0major+1370minor)pagefaults 0swaps
time = 5 ms.