<p>Given a polynomial equation of degree <code>n</code> with <code>m</code> variables, that is guaranteed to have at least one solution, what is would be the Big O notation of the least complex algorithm to find a solution? </p>

CC BY-SA 4.0
2018-09-26T12:44:40.437Z
You may find this useful: http://mate.dm.uba.ar/~visita16/cimpa/notes/Sabia.pdf
Avi Tal
CC BY-SA 4.0
2020-04-13T01:36:43.460Z
I believe the efficiency of the algorithm would be O(n^m) if you are recursively looking at the algorithm m times, and most efficiently O(m). I'm unsure of your experience in Big O notation however, khan academy and other similar sites have some sites that may be able to help with what you are looking for.
[https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-o-notation](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-o-notation)
Lain
CC BY-SA 4.0
2020-04-14T02:18:49.960Z
There's an entire book on this subject: https://link.springer.com/book/10.1007/978-3-319-16721-3
Mahdi Cheraghchi
CC BY-SA 4.0
2020-04-14T08:03:06.223Z
This question is actually tricky, mostly because there is no defined nth degree polynomial solving formulas and because there are multiple ways of solving algorithmically polynomials. I asked this question mostly because I am not able to answer it as my training in calculus is clearly lacking and I'd miss any shortcut that would lead to a lower complexity
Ludovic Zenohate Lagouardette
<time-complexity><polynomials>
Complexity of solving a polynomial equation
Ludovic Zenohate Lagouardette
# Complexity of solving a polynomial equation

(Asked by: username_0 on 2018-09-26)

Given a polynomial equation of degree `n` with `m` variables, that is guaranteed to have at least one solution, what is would be the Big O notation of the least complex algorithm to find a solution?

**Tags:** time-complexity, polynomials
> **Comments:**
> **username_1**: You may find this useful: http://mate.dm.uba.ar/~visita16/cimpa/notes/Sabia.pdf  
> **username_2**: I believe the efficiency of the algorithm would be O(n^m) if you are recursively looking at the algorithm m times, and most efficiently O(m). I'm unsure of your experience in Big O notation however, khan academy and other similar sites have some sites that may be able to help with what you are looking for. [https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-o-notation](https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-o-notation)  
> **username_3**: There's an entire book on this subject: https://link.springer.com/book/10.1007/978-3-319-16721-3  
> **username_0**: This question is actually tricky, mostly because there is no defined nth degree polynomial solving formulas and because there are multiple ways of solving algorithmically polynomials. I asked this question mostly because I am not able to answer it as my training in calculus is clearly lacking and I'd miss any shortcut that would lead to a lower complexity  

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## 0 answers

