? tst12([],[a,b,c,x,y],f->f,"(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0");
[y,1]
[x,3]
[c,11]
[b,41]
[a,1]
time = 635 ms.
3 217(188,41) 5631(66,259) 64685(1784,2346) 89877(26166,0)
*** combined adjacent 14994 cells.
time = 36,295 ms.
? tst12([],[a,b,c,x,y],f->f,"(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0");
*** using the modified Lazard's projection.
[y,1]
[x,3]
[c,10]
[b,35]
[a,1]
[[a,b,c],[a,b,c],[a,b,c],[a,b],[a,b],[a,b],[a,b],[a,b],[a,b]]
time = 3532 ms.
3 185(159,35) 4399(66,216) 49277(1528,1962) 68437(19782,0)
*** combined adjacent 11542 cells.
time = 28,779 ms.
? tst12([],[a,b,c,x,y],f->f,"(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0",7);
*** using the sum of squares projection.
[y,1]
[x,3]
[c,11]
[b,41]
[a,1]
time = 1000 ms.
3 217(188,41) 5247(70,217) 45213(1362,800) 54149(23862,0)
*** combined adjacent 13762 cells.
time = 28,612 ms.
? tst12([ex,ex],[a,b,c,x,y],f->f,"(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0");
[y,1]
[x,3]
[c,11]
[b,41]
[a,1]
time = 414 ms.
3 217(188,41) 5631(66,259) 64683(1784,2346) 5631(3936,0)
*** combined adjacent 5630 cells.
time = 8,926 ms.
? tst12([ex,ex],[a,b,c,x,y],f->f,"(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0");
*** using the modified Lazard's projection.
[y,1]
[x,3]
[c,10]
[b,35]
[a,1]
[[a,b,c],[a,b,c],[a,b,c],[a,b],[a,b],[a,b],[a,b],[a,b],[a,b]]
time = 3440 ms.
3 185(159,35) 4399(66,216) 49275(1528,1962) 4399(2928,0)
*** combined adjacent 4398 cells.
time = 7,138 ms.
? tst12([ex,ex],[a,b,c,x,y],f->f,"(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0",7);
*** using the sum of squares projection.
[y,1]
[x,3]
[c,11]
[b,41]
[a,1]
time = 979 ms.
3 217(188,41) 5247(70,217) 45211(1362,800) 5247(3680,0)
*** combined adjacent 5246 cells.
time = 12,066 ms.
Wolfram Language 12.2.0 Engine for Linux x86 (64-bit)
Copyright 1988-2021 Wolfram Research, Inc.
In[1]:= SetSystemOptions["InequalitySolvingOptions"->{"BrownProjection" -> False, "LazardProjection" -> True}];
In[2]:= CylindricalDecomposition[(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0,{a,b,c,x,y}];//Timing
Out[2]= {181.187008, Null}
In[3]:= CylindricalDecomposition[Exists[{x,y},(a*x^2+b*x-c)*y^2+(b*x^2+c*x-a)*y+c*x^2+a*x-b==0],{a,b,c}]//Timing
Out[3]= {2.216417, True}
