## Complex roots of unity and the map() function

Here’s a little application from Complex Variables class that uses map() to repeatedly apply Maxima functions to each element in a list.

We want to find the complex 6th roots of 1 — there should be six such complex numbers $z$ that solve the equation

$z^6=1$

Notice the solutions are returned as equations…this is sometimes really handy, but for now we want to isolate the right hand side of each equation. The command rhs(), when applied to an equation, returns just the right side. We can apply the rhs command to all the equations contained in our solution using the Maxima command map():

Finally, with the real and imaginary parts extracted, we can plot the six roots

## An odd gnuplot error and a work-around using maxima_tempdir

***Update***********************

I also have this problem in the latest windows installation—on the same machine that long filenames were never a problem before in Maxima.  To fix it choose the sbcl version of maxima, as described at My Windows Installation.

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I have a student running wxMaxima on his windows laptop.  He has partitioned his hard drive so he can run Windows 10 as well as other operating systems.

When he attempts any plotting command, he gets an error:

The part of the error message with directory name TANUSH~1 says to me that there is some problem with the long directory name, possibly also a problem caused by a space in that directory name, possibly due to the way those new partitions are formatted.

As a workaround, we set the maxima option maxima_tempdir to point to another directory and all worked as expected:

Of course, that new directory will now fill up with files with names like maxout_xxxx.dat and maxout_xxxx.gnuplot, but that was already happening in the default directory.  A natural feature for wxMaxima to include in future releases would be to clean up the directory by deleting all those files when the program is stopped…