I'm working with functions that look like $$P(z,w)=\sum_{|i|+|j|\leq n}c_{ij}\cdot z^i w^j.$$ Where the exponents $i,j\in\mathbb{Z}$ and $c_{ij}\in\mathbb{R}$. I'm interested in plotting the image of the set $$\{(z,w)\in\mathbb{R}^2:P(z,w)=0\}$$ under the map $(z,w)\mapsto (\log{|z|},\log{|w|})$. I tried something and it works but it seems very slow and just not the best way to do it. My try:

Ps[z_, w_] := 5 + 1/z + 1/w + z + w;
r = ImplicitRegion[Ps[z, w] == 0, {z, w}];
rt = TransformedRegion[r, {Log@Abs@Indexed[#, 1], Log@Abs@Indexed[#, 2]}&];
RegionPlot[rt, PlotRange -> {{-3, 3}, {-3, 3}}]

After some effort it results in

enter image description here

which seems to be correct. Is there a better and faster way to make plots like this?


You could just use ContourPlot with the different branches of the inverse functions of your map:

   Ps[sz Exp[z], sw Exp[w]] == 0, {z, -3, 3}, {w, -3, 3}], 
  {sz, {1, -1}}, {sw, {1, -1}}]



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.