? 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 Lazard's method (MPP17).
[y,1]
[x,3]
[c,11]
[b,41]
[a,1]
time = 414 ms.
3 217(188,41) 5631(66,259) 64685(1784,2346) 89867(26164,0)
*** combined adjacent 14984 cells.
time = 35,899 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",17);
*** using Lazard's method (BM20).
1
[y,1]
0,0,0
[x,3]
0,0,0,0,0,0
[c,10]
[b,35]
[a,1]
[[[a],[b],[],[],[]],[[a],[b],[c],[],[]]]
time = 3342 ms.
3 185(159,35) 4399(66,216) 49277(1528,1962) 68427(19780,0)
*** combined adjacent 11532 cells.
time = 26,522 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 = 1010 ms.
3 217(188,41) 5247(70,217) 45213(1362,800) 54139(23860,0)
*** combined adjacent 13752 cells.
time = 26,332 ms.
Wolfram Language 12.2.0 Engine for Linux x86 (64-bit)
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In[1]:= 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[1]= {190.523487, Null} (* The number of the top level cells is 35789. *)
