[tikej]

Sure, but that's numerics. What I meant by high performance symbolic computing was things integrating hundred term expression or expanding, manipulating and simplifying expressions of similar lengths or solving (diagonalising) 9x9 matrix with symbolic expressions. Unfortunately in these applications SymPy is (painfully) slow, although I haven't tried using PyPy backend for this.

Yeah, SymEngine is a great idea and it is a lot faster, but its functionality is very limited compared to SymPy. The development is slower than SymPy and I suppose its due to the fact that its in C++, which is more difficult to write after all. Therefore I don't believe it will ever catch up with SymPy features and it boils down to the two-language problem. I think Julia (with multiple dispatch, parametric type system and JIT) is a great candidate for CAS, but it's still very far behind SymPy (although the nice thing is that functionalities can be "borrowed" via PyCall until they are rewritten).

[ChrisRackauckas]

Julia's ModelingToolkit.jl is already pretty far along and has a lot of SymPy, plus extra features like parallel simplification and generation of parallel sparse functions via its form of lambify. See the first tutorial on that: https://mtk.sciml.ai/dev/tutorials/symbolic_functions/ . The equation solver is in progress right now and is moving along quite fast. The nice thing is that this will all use Julia's multithreading, since separate tree cases are mostly independent so there's a lot of parallelism that the symbolic pieces can use here.