I am trying to implement the kind of solution Bob Hanlon provided here, but on another equation. There are two problems. First, this time, the gap at the top-right is not fully closed by the method, and second, I would like to add a standard blue fill to the regions below zero in the contour plot, while the above zero region should remain white.
Can these things be achieved?
Here is my code:
Clear["Global`*"]
expr2 = 1/(32 (p1 - p2)^2 (-(-1 + p2) p2)^(3/2) (-1 + p1 + p2)^2) (-1 + p1)^2 p1^2 (-64 Sqrt[-(-1 + p1) p1] (-1 + p2)^2 p2^2 - 32 (-1 + p1) p1 (-(-1 + p2) p2)^(3/2) - 32 (-(-1 + p2) p2)^(5/2) + (32 (-(-1 + p2) p2)^(7/2))/((-1 + p1) p1) - (192 (p1 - p2)^2 (-1 + p1 + p2)^2)/Sqrt[1/(p2 - p2^2)] + (64 (-1 + p2)^3 p2^3 (-3 + 2 Sqrt[((-1 + p2) p2)/((-1 + p1) p1)]))/Sqrt[-(-1 + p1) p1] + 32 (1/(p1 - p1^2))^(3/2) (6 (-1 + p1) p1 (-1 + p2)^3 p2^3 - 2 (-1 + p2)^4 p2^4 + Sqrt[1/(p1 - p1^2)] (-(-1 + p2) p2)^(9/2) + (2 (-1 + p2)^4 p2^4)/(((-1 + p2) p2)/((-1 + p1) p1))^(3/2) + 6 (-1 + p1)^4 p1^4 Sqrt[((-1 + p2) p2)/((-1 + p1) p1)] - 12 (-1 + p1)^4 p1^4 (((-1 + p2) p2)/((-1 + p1) p1))^(3/2))) // Simplify;
fd = FunctionDomain[expr2, {p1, p2}]; expr3 = expr2 // FullSimplify[#, fd] &; ContourPlot[Numerator@expr3 == 0, {p1, 0.5, 1}, {p2, 0.5, 1}, MaxRecursion -> 5, FrameLabel -> {p1, p2}, WorkingPrecision -> 50] // Quiet
PlotPoints ->50
? $\endgroup$