Well, as I already said, talk is cheap. I think many people greatly underestimate the work required to build a standard full-featured CAS. This is probably not a coincidence that all calculators CAS were outsourced (well, except for the HP28/48 symbolic engine, but it's symbolic capabilities were very limited). Another thing to keep in mind is that most components of the CAS are highly interdependant, a small change in one component may have side-effects in other components (that's why regression tests based on integration are very effective), that's why I'm very conservative with any change people ask.
Probably someone can build a toy-CAS that would return answers more similar to what some teachers expect from highschools students for problems that can be solved by mental computation. But this is in my opinion a bad usage of CAS, a CAS should not be used to replace your brain. It should be used where it is more efficient than our brain, i.e. for real computations.
I would propose the result to be (2^10)! instead of "undef"
After all, what better name is there for it?
Then you have the TI cas, which basically hasn't been touched since they purchased Derive in 1993 or whenever it was...
Basically, there are essentially no CAS systems still under active development which aren't either a) way too big and b) proprietary.
The calculators development group of Texas Instruments bought the Derive symbolic calculation kernel. They did it for the purpose of incorporating it into their mobile devices, in the first part they had to rewrite it to adapt it to the famous Motorola68K processor, then to the processor of the TI-NSPIRE CAS, the changes have been minimal since it is very stable and is "finished", it has some new commands, it needs simplification control commands, as GIAC has, but they have not been incorporated in the HP-prime, I mean the autosimplify() command.
The symbolic calculation kernel GIAC was designed to make scientific calculations, not to teach mathematics, that is, to perform calculations where it is impractical to do them by hand or impossible by hand, for this reason he has not invented a graphing calculator to teach mathematics. The current CAS kernel perform calculations (real computations/technical computation) or throw answers (black box), the true focus should be for example show intermediate steps, promote algebraic reasoning, not as a electronic calculator machine.
The origin of Derive goes back to the 70s, based on the development of expert systems (AI) and the success of REDUCE CAS. Its development lasted 36 years, unfortunately its development was not continued.
https://en.wikipedia.org/wiki/MuMATH
The only legendary CAS that is still being developed (more than 50 years) is Maxima as the evolution of Macsyma
http://maxima.sourceforge.net/
The CAS that uses the notation closest to the notation of the mathematics textbooks is Scientific WorkPlace 6 due to its real mathematical text editor. Scientific WorkPlace use the MuPAD kernel (with commands renamed to the standard mathematical notation), MuPAD now owned by MatLab who uses it inside Symbolic Toolbox library
https://www.mackichan.com/index.html?pro...~mainFrame
A good book on MuPAD and Scientific WorkPlace
Doing Mathematics with Scientific WorkPlace Version 6
https://www.mackichan.com/index.html?pro...~mainFrame