CylindricalDecomposition doesn't finish the process

Questions
,
1

hello,

I know CAD can take a while because its computational cost, but sometimes wolfram mathematica just quits after an hour or less and leaves me with these dots where it should show the number completed. By the way, the “failed” result is from a previous run using different parameters

Screenshot2025-03-13174738.png
Screenshot2025-03-13174738.png775×715 29.8 KB

Here is the command typed out

N@CylindricalDecomposition[
  {
   b^2 - (c^2 - a^2) == 0,
   a >= 0,
   c > 0,
   t > 0,
   c > a,
   b > 0,
   pl - (pn + t*b/c + a + 2*a/b*t + t*c/b) == 0,
   d - (4 t + b + t*a/c) == 0,
   lb^2 + t^2 - ((pn + c)^2 + (d - 2 t)^2) == 0,
   lb - (2 a + 2*a/b*t + t*c/b) == 0,
   lb > 0,
   t - 13 == 0
   },
  {t, a, c, lb, pn, b, pl, d}
  ]
2

Possibly you need to add either explicit times operators or spaces between some letters so that they are not regarded as new variables. For example, t*c instead of tc.

3

Thanks, Ill give that a shot