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)((1))), {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)((1)))), {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