|Re: Derivation of (HP) Derivatives...|
Message #4 Posted by Valentin Albillo on 25 May 2012, 9:43 a.m.,
in response to message #1 by Matt Agajanian
Two side comments:
On the 28C, only symbolic integration of polynomials was possible.
Yes, but it also had a Taylor Series Expansion capability which, coupled with the symbolic polynomial integration, did allow you to obtain an approximation to the corresponding TSE of the integral of an arbitrary function (as long as it admitted a TSE, of course) to any given degree of accuracy (subject to available memory and time, of course). In practice it was of little use.
Although (and correct me if I'm wrong, please), the 28C/S was able to produce symbolic derivatives for any and all functions.
Sure, that's actually very easy on any machine or language as long as you've got recursion, slightly more involved without.
Later, on the 50G, the symbolic integration is capable of producing symbolic derivatives and antiderivatives/integrals of not only polynomials but any function even those including logarithmic and trigonometric functions.
No, not "any function" but just the ones that admit symbolic integration in terms of elementary functions. This includes polynomials, rational functions of polynomials, some trigonometrics and their inverses, and some exponentials and their inverses, but it won't work on functions as simple as Sin(x2), ex2, xx, or 1/Ln(x) for instance.
Have a nice weekend.