### Can sage do symbolic optimization?

I know sage has many functions to do numerical optimization.

Now, I am wondering if sage can do symbolic optimization as well.

For example, if I wanted to maximize a function using numerical methods, I could do this:

```
f(x,y) = -(x * log(x) + y * log(y))
minimize(-f,[0.1, 0.1])
```

Which gives the answer:

```
(0.367880005621,0.367880005621)
```

Is there a function that can give the solution as $(\frac{1}{e}, \frac{1}{e})$ or do I have to compute the stationary points and perform the necessary substitutions myself?