Let $p(x)$ be an n-degree polynomial with real coefficients. Let k be the discrete number of points which is intended to be plotted.
A straightforward approximated evaluation at such points has got time complexity $O(k*n^2)$.
The approximation is due to the impossibility of representing real numbers.
Let's initially consider a restriction of the problem.
Let $p(x)$ be an $n$-degree polynomial with integer coefficients.
One may want to plot the polynomial for $k$ consecutive integer positive values of $x$, or to plot it for some integer positive values such that the largest one is $k$.
This algorithm seems to be working, through a phase of initialization with time complexity $O(n^2)$ and a phase of actual evaluation with time complexity $O(k*n)$.
As $k$ is reasonably much larger than $n$ in - kind of - every realistic context, it just works better.
It is required to install "numpy" and "matplotlib" packages.
Since the "now it actually plots" commit, a scatter plot of the polynomial is displayed.
Completely aware that it's still pretty useless, I'm working on a formal proof that it actually works, to then finally generalize its features.
Next features hopefully available soon in this repository:
1. Formal proof;
2. Extension of the domain;
3. Extension of the domain of the polynomial coefficients;