|Back from vacation and 4 new articles online ! :-)|
Message #1 Posted by Valentin Albillo on 20 Aug 2007, 6:58 a.m.
Just came back from my summer vacations I've spent in a little, rural village where neither Internet nor email access were possible in any way. Quite refreshing, if a little isolated. It will now take me quite a long time to read the tons of threads newly posted here, I see you all have been pretty busy, vacations or not.
Speaking of vacations, among many other things I've taken advantage of the free time and quiet environment I've enjoyed to write *three* new articles, all of them focused in the new HP35s (which I carried with me as my sole computing device in order to familiarize myself with its pros and cons), which will be promptly submitted to Datafile for their eventual publication in the very next issue, so you'll be able
to have a look at them there come October (subject to Mr. Editor's kind approval of course).
Meanwhile, thanks to the invaluable help of my 15-year old daughter Laura (who got a Nintendo DS plus assorted game cards for her considerable efforts), my humble HP calculator site boasts a brand-new aspect and layout, and to commemorate the occasion I've just uploaded there and made freely available for download the following four articles of mine which were previously featured in Datafile, all of them in PDF format:
Long Live the HP-35 !
This 5-page article, belonging to my ongoing "Long Live ..." series, is intended as a commemorative article for the HP-35's 35th anniversary, and I think you'll agree it's quite an original approach to it. It does include three sample applications featuring four small programs, addressing such topics as root finding and numerical integration, as well as providing the appropriate historical context
and a few personal anecdotes to spice it all.
Boldly Going - Matrix Square Root
This 6-page article is the first of a new series of articles, the "Boldly Going" series which, as its name implies, is intended to effectively go "... where no HP calc has gone before ...", and so they will be dealing with unusually difficult programming tasks in a straightforward manner, thus expanding the limits of what you can do with your HP model and how simply can you do it.
To provide a taste for the series, this first article deals with this task of finding the matrix square root of square matrices. Two full programs are featured: a 7-line subprogram for the HP-71B which can deal with real- or complex-valued NxN matrices, and a 45-step routine for the HP-15C which will find the square root of real-valued matrices up to 4x4. Full examples are provided, with comments and notes, as well as the underlying algorithm.
Boldly Going - Identifying Constants
This is a 14-page article which includes a truly awesome (if simple) program which allows ye goode olde HP-71B to perform some rather impressive 'symbolic' feats. The program does not require any additional ROMs or files, just a bare bones HP-71B, and can be converted to any other suitably fast HP model or emulator with minimum effort.
It's a relatively simple program which provides basic functionality for an advanced, very useful and most impressive feature which is nevertheless absent in our beloved machines’ built-in instruction sets, namely identifying numeric constants, i.e., the capability of, given some real, numeric value, to try and identify its exact symbolic form if possible, and that failing, to provide an approximate symbolic expression of user-specified relative accuracy.
This will allow us to perform some pretty nifty feats, such as give exact, symbolic
results for definite integrals (even if they can’t be expressed in terms of elementary functions), finite or infinite summations, and specific values of transcendental functions, among other uses.
The full 14-page article boasts more than 40 worked out examples, as well as three detailed extensions, the last being an 'exercise' for the reader, solution included ! :-)
Small Fry - Primes A'counting
This 1-page article belongs to the new series "Small Fry", which is intended to feature very *small* articles (maximum 1 page), while still keeping all the flavour and bite of the usual longer ones.
This first article deals with the topic of prime counting, i.e., finding out how many prime numbers there are up to a given limit N. For large N, generating all primes up to N and returning the count is prohibitively expensive in terms of running time and/or memory usage. What can we do about it when N goes sky-high (say 1010, 1015, or more) ? The article features an 8-line user-defined function for the HP-71B to accomplish the feat very quickly, as well as several comparative examples against other well-known prime counting procedures.
That's all for now, you can download them for free at my site, and I sincerely hope you'll enjoy them and will consider them good read for these quiet summer evenings (26 pages in all, nearly a full regular Datafile issue !). Any and all comments are really welcome, thanks in advance for them and
Best regards from V.
Edited for typos
Edited: 20 Aug 2007, 7:03 a.m.