Wikipedia:Reference desk/Archives/Mathematics/2007 September 19

= September 19 =

Plotting software
Can someone reccomend the most user-friendly, down to earth peice of free software for plotting simple complex functions such as $$f(z) = z \times (2 + 3i) \,$$? The less command line syntax crap the better!


 * It may not exist. Plotting complex functions is awkward, because we cannot directly show input-output pairs. Common options are projecting a surface from 4D, plotting the mapped distortion of a cartesian grid, plotting the mapped distortion of a radial grid, and "domain coloring". That's the bad news. The good news is that gnuplot can assist you with the grid distortions, and already understands complex functions; and Hans Lundmark's complex analysis page can help with the coloring approach. --KSmrqT 17:35, 19 September 2007 (UTC)


 * Lundmark's paper on the colouring approach seems nice. In that he quotes Lucas' theorem
 * if f is a polynomial, then the zeros of f ′ all lie in the convex hull of the set of zeros of f.
 * Our page on Lucas' theorem seems to be something completely different. Any idea what the correct page should be? --Salix alba (talk) 18:57, 19 September 2007 (UTC)


 * Note that this function is just a rotation combined with a dilation, so you can probably picture it in your head (and it will be more helpful than a plot). For more complicated functions, though, even higher-degree polynomials, the plot could well be useful. Tesseran 19:44, 19 September 2007 (UTC)

Salix alba: you want the Gauss-Lucas theorem Algebraist 20:26, 19 September 2007 (UTC)


 * I was hoping there would be a peice of software that could simply flip between the inputs and outputs?


 * I'm not sure I understand you. What do you mean, exactly? Algebraist 11:46, 20 September 2007 (UTC)


 * I'm pretty sure Axiom computer algebra system will plot complex functions, although only on linux. Foxjwill 21:17, 21 September 2007 (UTC)