"If you're looking for a fast symbolic math library" you are doing it wrong
In none of the symbolic math Sw I used speed was an issue. But rather, capabilities. (Maple, Mathcad). Of course speed is good when evaluating a numeric problem
If you're talking about numeric math, which is what Theano does, then you're right about it.
But doesn't most of the sw we're talking about do both? For example, you mentioned Maple, which says right on its website it does both: http://www.maplesoft.com/products/maple/features/feature_det... Theano also does both. But maybe I'm using the terminology wrong? Or maybe it doesn't matter?
Either way, Theano is fast and is similar to (but not exactly!) SymPy.
Some are more geared towards Symbolic Math (like Maple), some others are focused on numeric computations and even if they do symbolic math are severely limited.
You're right, Theano does symbolic differentiations, but this looks like it's in support of its main purpose (multi-dimensional problems)
TL;DR: If you want to calculate a triple integral symbolically go for Maple (or maybe SymPy), if you want to calculate its value go for NumPy or Theano
"If you're looking for a fast symbolic math library" you are doing it wrong
In none of the symbolic math Sw I used speed was an issue. But rather, capabilities. (Maple, Mathcad). Of course speed is good when evaluating a numeric problem
If you're talking about numeric math, which is what Theano does, then you're right about it.