# Changes When Using Solve with Plot3D and Evaluate

I’m solving the following equation, which should be straightforward:

``func1[A1_, A2_] := -((    4 I + 4 I A2^2 - 12 I A1 (1 + A2 ((2 - I) + A2 - 2 I eig)) +      A2 ((1 + 2 I) + 2 eig) ((5 + 4 I) + 4 eig ((1 + 2 I) + eig)))/(    8 A2)); sol1[A1_, A2_] := Solve[func1[A1, A2] == 0, eig]; ``

I want to extract the analytic solution to this, but I’m not sure that what Mathematica is producing is correct. Here are the plots to explain what I mean: This is a smooth plot and something that I expect. I’m plotting this with the line:

``Plot3D[Re[eig /. sol1[A1, A2][]], {A1, 0, 1}, {A2, 0, 1}] ``

Now if I try to get the analytic expression for this solution and I plot it, I get something different. I can demonstrate this just by changing my Plot3D command:

``Plot3D[Evaluate[Re[eig /. sol1[A1, A2][]]], {A1, 0, 1}, {A2, 0, 1}] ``

produces: As you can see, the plot is different; it’s jagged with a discontinuity. With this, I can’t be sure that the analytic solution I extract from Mathematica is right. I’d like to either replicate the first plot with an explicit expression that I can acquire somehow or find out what function exactly Mathematica is plotting in the first instance. Am I missing something in regard to rule solutions here?

Thanks