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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:


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?