For the thoroughly modern calculus student, an introduction to Complex Variables is all the more daunting because we don’t have the kind of geometric intuition-building machinery available to us for functions as we did for real-valued functions in calculus. Not that attempts haven’t been made…. In the coming weeks, I want to work on several techniques in Maxima. Here’s a first approach: conformal maps. The code **drawgridC** below is limited in its versatility, but couldn’t be simpler to call. Here are some examples,

/* plot the traces of complex valued function _f
along grid lines in the square
-1 <= Real(z) <= 1, -1<=Ima(z)<=1
blue - images of _f along horizontal lines
red - images of _f along vertical lines */
drawgridC(_f):=block(
[fx,fy,fxt,fyt,pl,j,ngrid],
fx:realpart(rectform(subst(z=x+%i*y,_f))),
fy:imagpart(rectform(subst(z=x+%i*y,_f))),
pl:[],
ngrid:19,
for j:0 thru ngrid do(
fxt:subst([x=-1+j*2/ngrid,y=t],fx),
fyt:subst([x=-1+j*2/ngrid,y=t],fy),
pl:cons([parametric(fxt,fyt,t,-1,1)] , pl)
),
pl:cons([color=red],pl),
for j:0 thru ngrid do(
fxt:subst([y=-1+j*2/ngrid,x=t],fx),
fyt:subst([y=-1+j*2/ngrid,x=t],fy),
pl:cons([parametric(fxt,fyt,t,-1,1)] , pl)
),
pl:cons([color=blue],pl),
pl:cons([xlabel="",ylabel=""],pl),
pl:cons([nticks=200],pl),
apply(wxdraw2d,pl)
);

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I just want to get drawgridC() running without further ado! Is there some flag I need to reset or some package I need to load to get this to run? And how do I copy Maxima code without painstaking copying line by line?

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Hi William,

several ways to get going with that right away:

1. Copy all the code from the post, paste the whole thing to an input cell in wxMaxima, hit shift-return.

Now you can use drawgridC until you end that maxima session

2. Copy all the code from the post and paste into your favorite text editor. Save the result into a file named drawgridC.mac, in a directory on your computer where you can find it easily.

Then in wxMaxima choose File —> Load Package… and navigate to drawgridC.mac

after that, you can use drawgridC until the end of that maxima session.

Please let me know if that helps!

eb

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Thank you very much for these functions. I was wondering if you knew of a way to animate the mapping for a range of inputs? (e.g. 1/z^n for n=1,2,3)

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