? tst12([all,all],[b,a,c,x,y],(f1,f2,f3,f4)->f1*f2*imp(f3,f4),"0<a,0<b,a*(x-c)^2+b*(y-1)^2<1,x^2+y^2<2",17);
*** using Lazard's method (BM20) with realrad.
2
[y,2]
-6,-6,0
[x,4]
0,-6,-6,-6,0,0
[c,6]
-6,-6,-6,-6,-6,-6
[a,19]
[b,88]
time = 2,760 ms.
195 7267(66,222) 204071(1928,8123) 2944009(51650,175582) 74736(665464,86944)
*** combined adjacent 74625 cells.
time = 40min, 40,702 ms.
? tst12([all,all],[b,a,c,x,y],(f1,f2,f3,f4)->f1*f2*imp(f3,f4),"0<a,0<b,a*(x-c)^2+b*(y-1)^2<1,x^2+y^2<2",7);
*** using the sum of squares projection.
[y,2]
[x,4]
[c,7]
[a,24]
[b,133]
time = 5,272 ms.
141 5383(44,156) 161955(1406,6706) 1919543(38100,124228) 16266(512878,62332)
*** combined adjacent 16221 cells.
time = 21min, 12,041 ms.
Wolfram Language 12.2.0 Engine for Linux x86 (64-bit)
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In[1]:= CylindricalDecomposition[0<a&&0<b&&ForAll[{x,y},a*(x-c)^2+b*(y-1)^2<1,x^2+y^2<2],{b,a,c},"Function"]
;//Timing
Out[1]= {1039.502639, Null} (* The number of the top level cells is 1618. *)
