Re: The Future of Graphing Calculators Message #18 Posted by Crawl on 13 Apr 2010, 9:41 a.m., in response to message #16 by Crawl
I guess I have a couple of other things to add.
First, since the Equation Editor was the thing that kicked this off:
I do not think the equation editor is intended to be used as a general purpose entry method. 90% of the time, good ol' RPN is what I'll use. What I'll use the equation editor for is symbolic work that involves cutting and pasting.
For example, consider the Fresnel Equations. The numerator and the denominator is identical except for one sign change. So the easiest way to enter them is to enter the numerator, select all and copy, hit divide, paste in the numerator as the denominator, and then use the cursor to change the one sign.
This is an example of what the Equation Editor is for, in my opinion. It is probably more efficient than another other method. (At least it is both efficient and easy to understand)
I also don't think Mathematica has anything like an equation editor, nor RPN.
Another thing is that I think people tend to underestimate how powerful CAS calculators are, and over estimate the advantages Mathematica has over them.
When someone says something like, "I don't need a CAS because I'm not in school", I imagine they think a CAS calculator can do something like the integral of sin(x)  something you can easily do in your head.
Of course it can do that, but they can do quite a bit more. They can definitely do things that, yes, you know how to do from school but would be far too tedious for you to ever want to do by hand, if you could avoid it. That was the point of some of the examples I gave earlier.
Much like, yes, if you went to school you could do, by hand, long division of two 8 digit numbers, but it would be rather tedious and is something that's better suited for a calculator.
I think these calculators are actually astoundingly powerful, certainly for something that can fit in your hand. I showed that the HP50 can solve the general quartic equation, which I think is a pretty impressive feat.
What advantage does Mathematica have over a calculator? Well, yes, it has a more powerful CAS, but not by as much as you might guess. It can evaluate integrals that require things like hypergeometric series or other special functions. For functions that have elementary solutions, the difference between them isn't that large. And there are expressions that Mathematica still can't simplify.
The main advantage, of course, is that it runs faster and has more memory. So, an HP50 could get you maybe 50 coefficients from this series, but eventually it will run out of memory.
That could even be fixed. It could be possible for a calculator emulator to use more memory than the calculator itself. You could write a program on a calculator, bug check it, test it, and then load it onto a computer and push it to the limit.
Something like that in the future of graphing calculators would be exciting.
