thread repost: Discussion on Parser/UI Options

[parisse]

A few remarks
1/ giac is indeed a CAS system designed to work with exact data. That does not mean that it is not suited to work with approx data, and you can check that it is fast for example for approx linear algebra. Being able to deal with exact data has sometimes a small efficiency price, but I'm convinced this is not as important as it was 10 or 20 years ago, since the CPU speed is now fast, even on calcs (and embedded toolchains limitations will most probably be a past inconvenience in a few years). I did not see any speed comparisons between the TI nspire and the HP Prime for example...
2/ I don't think that graphing with giac would be too slow on the Prime (and by the way the number of colors is not limited to 8 on giac, there are 2^16 colors available). But there is an important difference between giac and a calc when graphing: giac does a complete separation between the UI and computation kernel, if you plot something with giac, all data is computed once, then if you zoomout or do any UI change, the display is updated using the already computed data. This could be a problem for calc users used to have the data recomputed. This is not a limitation if you assume that there is a commandline just above the graph, that you can modify easily.
3/ programming in giac is fast enough for a scripting language, if one really needs speed, then a compiled language should be used anyway. It's more important to have an easy to teach language with an easy path from defining an algebraic function to a more complex function with local variables/tests and loops.
4/ giac was not designed to hide the maths. I strongly believe that using a CAS requires that you learn some notions, like what you can solve exactly and numerically (starting with what a floating point number is, and the difference with machine and arbitrary precision integers), or the difference between an expression and a function, etc.. Many math teachers are not comfortable with these notions today, and that's perhaps one reason why calc manufacturers or geogebra want to hide this (for example the expression/functions difference). Of course you can hide some notions for common school tasks, but at some point you must really understand what you do, that's why I think we must teach it.
5/ I don't believe that having dedicated typed and always affected variables like A-Z, Z1-Z0, L1-L0 etc is good, nor implicit multiplication, ... I don't believe that Apps are really a good thing to teach. It's much better to teach how to write a commandline to do a plot, with a good dialog box to help you enter the arguments. This is useful for all computational tasks, and in addition you can mix graphs of different kinds on the same graph, something impossible with distincts Apps but sometimes really useful like for example
n:=1000; p:=0.5; m:=mean(binomial,n,p); s:=stddev(binomial,n,p);
N:=100000; histogram( (ranm(N,binomial,n,p).-m)./s,-3,2/s); plot(normald(x),x)
All this vision is probably not shared by HP, I have no problem with that, perhaps I'm wrong after all, but of course I implement Xcas following my vision. And I don't think it's a problem for HP or geogebra (4.4 by the way, not 5.0) because it means I concentrate on improving the computing kernel, which is a plus whatever your vision is.