3
$\begingroup$

I'd like to ask you about the way of excluding just one point from this example:

myArg[z_] := Mod[Arg@z, 2 Pi]
RegionPlot[y > x && myArg[x + I y] <= Pi, {x, -2, 2}, {y, -2, 2}]

I want to exclude the $z \neq i$ $\mapsto$ point $(0,1)$.

Something like this:

enter image description here

$\endgroup$
8
  • 1
    $\begingroup$ Excluding a point would look the same as not excluding it. Perhaps you want to exclude a small region around the point of interest? If so, would just placing a white Point be an acceptable solution to your needs? $\endgroup$
    – rm -rf
    Oct 18 '15 at 21:06
  • 1
    $\begingroup$ Hard to remove just one point, but here's a fake plot: RegionPlot[ y > x && myArg[x + I y] <= Pi && Abs[x + I y - I] > 0.05, {x, -2, 2}, {y, -2, 2}, PlotPoints -> 75] $\endgroup$ Oct 18 '15 at 21:09
  • $\begingroup$ @R.M., I got your point. It's just for "educational usage" to show that $z \neq i$ is outside of the domain of a function. $\endgroup$
    – belford
    Oct 18 '15 at 21:12
  • $\begingroup$ @J.M.isback., thank you so much. That's the most useful fake plot I've seen today ;). $\endgroup$
    – belford
    Oct 18 '15 at 21:15
  • $\begingroup$ But, did you understand what I added to your code? $\endgroup$ Oct 18 '15 at 21:18
8
$\begingroup$

Credits to J. M. and R. M.

J. M. suggested drawing a surface outside the circle: a hole

Using the && operator he made the intersection of two sets:

RegionPlot[ y > x && myArg[x + I y] <= Pi 
&& Abs[x + I y - I] > 0.05, {x, -2, 2}, {y, -2, 2}, PlotPoints -> 75]

another hole

$\endgroup$
2
  • 1
    $\begingroup$ RegionPlot[y > x && myArg[x + I y] <= Pi, {x, -2, 2}, {y, -2, 2}, Epilog -> {White, AbsolutePointSize[6], Point[{0, 1}]}] $\endgroup$
    – Bob Hanlon
    Oct 18 '15 at 22:24
  • $\begingroup$ @BobHanlon, thank you. Another useful example. $\endgroup$
    – belford
    Oct 18 '15 at 22:30

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.