Question about CAS and Graphing

[Han]

(11-22-2014 10:30 AM)Gerald H Wrote:  I congratulate the previous posters on their ingenuity & knowledge of the machine to achieve better performance.

Exactly these efforts have convinced me to finally discontinue using the Prime.

Speaking only for myself, the only efforts involved were reading up on the CAS documentation and trying stuff out on my own -- which is what I imagined anyone would do for any CAS. In fact, I still do that now when I work with Maple and Mathematica -- and these are CAS that I've used for over a decade.

Specifically for the HP Prime, the separation of Home from CAS is a design choice that users must come to terms with before continuing to use the calculator. It's the same when switching from Maple to Mathematica and recognizing that functions in Mathematica are defined using square brackets -- which is often associated with vectors and matrices for users comfortable with Maple's design choices. One can simply choose to not use Mathematica since it would require relearning how to input expressions, or actually make an attempt to use it and take advantage of its capabilities.

The answers I gave when I posted a while back were simply what came to mind (namely because I was tinkering with plotfunc() for other reasons). In retrospect, the answer I should have given (which seems obvious, now) is below:

int(x,x);
f(x):=<copy the result from above>; (easy to do on the calc)
F1:=f;

then go into the Plot app and simply plot. The plot app can and will convert x to X on the fly provided you feed F0-F9 an actual CAS function. In fact, the function f itself doesn't even have to be in terms of x; it can be in terms of any dummy variable and the calculator is smart enough to convert to X. For example:

f(r):=1/2*r^2;
F1:=f;

F1 will correctly show 1/2*X^2. And even shorter is:

int(x,x);
F1:=(x)->copy result from above

The problem with trying to do everything in one step is that there are conflicts with priority -- something that no CAS will be able to resolve on its own.

For example, if one attempts to use:

f(x):=int(x,x);

then (from a programming point of view) how should f(3) be treated? Should f(3) be the result of evaluating int(x,x) first and then substituting in 3? Or should 3 be substituted first and then the integral evaluated (causing an error). Humans know the difference, but computers do not. Even Maple and Mathematica complain in this case.