This must have worked at some point, because the documentation for ImplicitRegion has the right picture. But when I evaluate

R = ImplicitRegion[x^2 + y^2 == 1, {x, y}];

I get an empty plot in 10.4.1.

It is not related to this generating a 1-d set. The following for example works fine:

R = ImplicitRegion[x == y, {x, y}];

Restricting the variables to be reals (as suggested here) does not change anything.

R = Assuming[{x, y} \[Element] Reals, 
   ImplicitRegion[x^2 + y^2 == 1, {x, y}]];

Is this a recently introduced bug?

  • $\begingroup$ it does work fine in 10.1. Perhaps try setting PlotPoints $\endgroup$
    – george2079
    Commented Jul 22, 2016 at 16:01
  • $\begingroup$ How very odd. ImplicitRegion[x^2 - y^2 == 1, {x, y}] // RegionPlot works, so that certainly is a mystery. It seems to hate ellipses in general; try ImplicitRegion[2 x^2 + 3 y^2 == 1, {x, y}] // RegionPlot as well. $\endgroup$ Commented Jul 22, 2016 at 16:02
  • $\begingroup$ The documentation says "RegionPlot will only visualize two-dimensional regions" - use ContourPlot instead $\endgroup$
    – Jason B.
    Commented Jul 22, 2016 at 16:02


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