本日のC.A.D.

Mathematica による結果の検証.

? tst12([],[a,b,c,d,e,f,x],(f1,f2,f3,f4,f5,f6,f7)->f1*f2*f3*f4*f5*f6*f7,"a==0,b<0,c<0,d==0,e<0,a*x^2+b*x+c>0,d*x^2+e*x+f<0",11);Ans(1)
 *** roots will be displayed in [pol,[zero,root,multi,deg]] for mma.
 *** using Lazard's method (MPP17).
[x,2]
[f,3]
[e,4]
[d,1]
[c,3]
[b,1]
[a,1]
time = 156 ms.
1 1(0,0) 1(0,0) 1(0,0) 
[[a,b,c,d],[0,-1,-1,0]]:e^2*a+(-e*d*b+d^2*c)>>(-e*b+2*d*c) 
[[a,b,c,d],[0,-1,-1,0]]:e^2*a+(-2*e*d*b+4*d^2*c)>>(-2*e*b+8*d*c) 
1(0,3) 
[[a,b,c,d,e],[0,-1,-1,0,-1]]:f^2*a^2+(-f*e*b+(-2*f*d+e^2)*c)*a+(f*d*b^2-e*d*c*b+d^2*c^2)>>-2*f*c*a+(f*b^2-e*c*b+2*d*c^2) 
5(0,0) 1(0,2) 
 *** combined adjacent 0 cells.
time = 87 ms.
 *** "Reduce"ing the conjunctions.
{0.239348, Null}
 *** verifying the equivalence.
{0.009403, True}
1[a = [a,[1,1,1,1]],b < [b,[1,1,1,1]],c < [c,[1,1,1,1]],d = [d,[1,1,1,1]],e < [e,[1,1,1,1]],f < [f*b^2-e*c*b,[1,1,1,1]],[e*x+f,[1,1,1,1]] < x < [b*x+c,[1,1,1,1]]]
time = 7 ms.