I want to find (and plot) the positive region (within a certain domain say
y<3) of a function
f[x,y] of two variables for a high order polynomial with high precision coefficients. What is an effective way to do this (as automated as possible).
For the one dimensional case I was able to do this by finding the roots using the method proposed in https://mathematica.stackexchange.com/a/16444/45020 and testing positivity in between. For a multivariable function the problem becomes a lot more complicated. However, I am hoping that Mathematica can still determine the intersections between the function and 0. A 3D plot of
0 suggest that mathematica determines the intersect but how to extract this data and whether there is any accuracy to this I don't know.
I can give as an example function
-2 y^2 Sin[x] + y^3 but I am really looking for a solution that would also work for much more complicated functions (too big to include an example here).
I managed to make the desired plot using the option
RegionFunction -> (#3 >= 0 &) however I still not know how to determine the intersection (if possible to high precision).