If I do a region plot of the following inequality,

RegionPlot[(4 - y^2)^2 ((8 + y^2) - 18 x y + 9 x^2) > 
36 (1 - y^2) ((4 + y^2) - 8 x y + (4 + y^2) x^2) && x >= y, {x, 0, 
1}, {y, 0, 1}]

Mathematica plots a region where it is valid:


However, if I change x >=y to x>y inside the RegionPlot command, the region vanishes altogether. I know that the diagonal line is x=y, but there clearly is a finite region where x>y is true and Mathematica does not displays that. Am I missing something?


You need to increase the number of plot points RegionPlot uses:

inequalities = (4-y^2)^2 ((8+y^2)-18 x y+9 x^2)>36 (1-y^2) ((4+y^2)-8 x y+(4+y^2) x^2) && x> y;

enter image description here

You could also use region functionality:

reg = ImplicitRegion[inequalities, {x, y}];
DiscretizeRegion[reg, {{0, 1}, {0, 1}}, Axes->True]

enter image description here

  • $\begingroup$ Thank you! But why the option plot points matter for showing the existence of the region? this seems to be quite dangerous, to be honest! Or, is this a standard feature. Sorry, I am a newbie. $\endgroup$ – anotherone Jul 19 '19 at 15:09
  • $\begingroup$ Also, is there any other important matter that I should be aware of before plotting regions? Anyway to crosscheck? This time I got suspicious because I randomly checked x=0.9 and y=0.89 and found it to be consistent! $\endgroup$ – anotherone Jul 19 '19 at 15:11

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.