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

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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. --KSmrq^T 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)