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.