? tst12([all,all],[a,b,c,x,y],(f1,f2)->imp(f1,f2),"x^8+y^8<1,a*x+b*y+c<0");
*** using Lazard's method (MPP17).
[y,2]
[x,4]
[c,10]
[b,12]
[a,1]
time = 14144 ms.
3 65(206,12) 963(196,62) 9219(384,432) 4385(8672,876)
*** combined adjacent 4376 cells.
time = 6,522 ms.
? tst12([all,all],[a,b,c,x,y],(f1,f2)->imp(f1,f2),"x^8+y^8<1,a*x+b*y+c<0",17);
*** using Lazard's method (BM20).
2
[y,2]
0,0
[x,4]
[c,5]
[b,11]
[a,1]
[[[a],[],[c],[],[]],[[a],[b],[c],[],[]]]
time = 15104 ms.
3 65(158,11) 615(178,21) 5439(352,392) 4385(5952,540)
*** combined adjacent 4376 cells.
time = 4,781 ms.
? tst12([all,all],[a,b,c,x,y],(f1,f2)->imp(f1,f2),"x^8+y^8<1,a*x+b*y+c<0",7);
*** using the sum of squares projection.
[y,2]
[x,4]
[c,10]
[b,12]
[a,1]
time = 14724 ms.
3 65(174,12) 615(190,22) 4503(372,272) 3665(5952,540)
*** combined adjacent 3656 cells.
time = 4,693 ms.
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In[1]:= CylindricalDecomposition[ForAll[{x,y},x^8+y^8<1,a*x+b*y+c<0],{a,b,c},"Function"];//Timing
Out[1]= {11094.458733, Null} (* The number of the top level cells is 129. *)
In[2]:= CylindricalDecomposition[ForAll[{x,y},x^8+y^8<1,a*x+b*y+c<0],{a,b,c},"Function",WorkingPrecision->30];//Timing
Out[2]= {3.261566, Null}
