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I have a system of polynomial equations with the unknowns being real numbers. The set of solutions is infinite. What software can I use to compute the real dimension of the solution set?

The CAD-based approach, which is implemented in various computer algebra systems, is too slow for my problems. I found several recent papers on other algorithms for finding the dimension but they were not accompanied with an open-source implementation.

I am looking for the implementation of some (preferably) non-randomized and exact method for computing the exact value of the dimension.

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  • $\begingroup$ What are the typical degrees, # of variables and # of equations you are studying? $\endgroup$
    – Alon Amit
    Jul 14, 2023 at 17:40
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    $\begingroup$ @AlonAmit The simplest problem includes about 30 equations, 30 variables with solution dimension around 15. But I would like to approach say 70 eqs. with 80 vars. and dim. 40. $\endgroup$
    – bcp
    Jul 14, 2023 at 19:11
  • $\begingroup$ According to Wikipedia, an abstract algorithm to compute the complex dimension of a variety is implemented at least in Maple and Macaulay2. You may need to consult the documentation for details. $\endgroup$ Jul 15, 2023 at 7:22
  • $\begingroup$ @IgorKhavkine I am interested in computing not complex but real dimension. If I am not mistaken, Maple has only the CAD method implemented for computing the real dimension. $\endgroup$
    – bcp
    Jul 15, 2023 at 9:14

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