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I have about 20 polynomial equations in about 20 variables, 15 equations are linear function and the rest of like degree 5.

I would like to find all real solutions to those (Because it's polynomials I expect this to be possible). I only want numeric approximations; I know symbolically is hard but that's okay since i don't care.

Sage solve tries to solve symbolically and is unable. Sympy nsolve requires a starting vector, and while it finds a solution I don't know how to make it find all solutions (I tried random vectors but that didn't help).

What program should I use? Is this possible? Is 20 too much?

Andy
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  • Linear equations are easy. Degree-5 equations are, in general, impossible to solve exactly. But you can resort to approximation numerical methods. – Stef Sep 08 '21 at 11:01
  • @Stef I want numerical, do you have a recommended program that finds ALL of them? – Andy Sep 08 '21 at 11:34
  • No I don't. I guess a method might be to first guess the number of solutions, then repeatedly use random starting vectors until you've found the correct number of solutions. But guessing the number of solutions might not be so easy. – Stef Sep 08 '21 at 11:40
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    There are sophisticated tools and algorithms for this. E.g. PHCpack. – Erwin Kalvelagen Sep 08 '21 at 18:06

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