Back from vacation and 4 new articles online ! :-)


Hi all:

    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.


excellent! i like the site improvements, especially the calculator image branding.

where neither Internet nor email access were possible in any way
unless you have satellite broadband that is.



Hi, Hugh !

Hugh posted:

    "excellent! i like the site improvements, especially the calculator image branding. "

      I'll pass you comments on to Laura, she'll be *very* happy ! She's a fledgling "web designer" and is very eager to get feedback for her very first "professional" work, so thank you very much for providing it.

      Also, I hope you'll enjoy the 26-pages worth of articles :-)

Best regards from V.

My friend, it appears you page must be broken. The main image in the center is 404 and it redirects to Lycos, and the items on the side, look like broken images.


Thanks for the warning, Vincze, but it works Ok to me.

¿ Perhaps some configuration problem in your browser and/or
your firewall, such as forbidding popups or adds to appear ?

The free, french Lycos server I'm using to host my pages
does include some adds and such, like most other free
services, but that should present no problems at all.

Anyway, should you still be unable to reach some of the
articles, just tell me which are you interested in and
I'll send them to some public e-mail account of yours or
else post the direct links.

Best regards from V.


I disable everything and nothing. Only thing I see on page is your counter, and the menu on left. I try and click on link for each menu item, but it just shows "Page non trouvée" and then go to main Lycos page. Very strange.


Strange indeed ... I've tried just now (IE 6.0) and this
is approximately what you should see:

Best regards from V.


I get the same "Page non trouvée".
It seems the main page references other pages with ....calc\main.htm (a backslash) instead of ....calc/ (a regular, forward slash). Typical of a web site prepared on a Windows machine ;-)


Thanks a lot, I'll have Laura look into it ASAP.

Best regards from V.


Gentlemen, it appears to work in Internet Explorer, but not Mozilla Firefox.


Ah, I think I see problem. I go into IE and try, and it work. I normally use for 99.999999% of all things Firefox browser, and it not work in there. I wonder why that they case. ActiveX?


Nothing that complicated. I think when Explorer sees a \ (backslash) in a URL, it automatically translates to a / (forward slash) when sending a request to the web server. Firefox does not.

-- alain.



That's it! (I couldn't get it to work either). The IE Windoze thing again :-(


I just add IE render to Firefox, and then turn on flux capacitor, and all is fine in Firefox. Anything to upset Mr Gates.


Valentin's page also shows up fine with Netscape 8.1 (I'm a real dinosaur when it comes to browsers, and I, too, will do almost anything to not use Micro$oft products!)

In fact, those of you who have never tried WordPerfect instead of Word should give it a try!


Anybody remember AmiPro (by Lotus) in the days of Windows 3.1?

I was cleaning out some old manuals and the like and I found literature for AmiPro. I liked it much better than Word or WordPerfect then... and I think that's a bit of high praise from me as I preferred the DOS command line WordStar, maybe WordPerfect, over any GUI based word processor.

Yeah, I found the old WordStar manuals, too. I even found some literature on using VMS (ugh!... what horrible memories... ) on some old mainframe.

But none of this is older than my HP-34C with its Cylonic red LED eyes, and its spiral bound manual that could double as a high school or college math text. Yeah, it's also got that laminated quick reference card!


I remember AmiPro. I hate to say this, but I really did not like it.

I have OpenOffice at home, and it very nice and free. I also have M$ Office too, but I wanted to see what OpenOffice like and it very nice. I can use documents from both system back and forth just fine. Again, to upset Mr Gates.


With Firefox, the page looked just fine the first time that I loaded it. However, if I use Tools > Options... > Content, and uncheck "Load images automatically", of course I get the "broken images". I suspect that any problems with viewing this page with Firefox is a matter of browser configuration. Something else to check would be the configuration of extensions, such as AdBlock.



Sorry for the inconvenience, thanks for bringing the problem to my attention, and

Best regards from V.


Yes, it work now, what did you have to do?


Simply changing all incorrect "\" to the correct "/", as
someone kindly suggested. Thanks for the feedback and

Best regards from V.


Hi Valentin, welcome back :-)

Now it works fine also on Opera 9.22, which is the browser I currently use.

Thank you and your daughter for this nice improvement and articles!

Best regards.



Hi, Giancarlo:

Giancarlo wrote:

    "Thank you and your daughter for this nice improvement and articles!"

      Thanks to you for your feedback and kind appreciation. I'll let her know and she'll be delighted: it is her first "professional" attempt, and as is my educational stand that children must be encouraged to attempt and solve real-world situations, I formally issued her a letter asking for her services in revamping my web page, with full specifications, and demanding to know cost and schedule. She complied, and all the process was treated with utmost "seriousness", conflicts and all, till the final result was delivered, accepted, put into production, and the payment fulfilled.

      That's a way for she to gain experience and training to deal with real professional demands well in advance. And after all the hard work, lots of googling for site creation tutorials, desperation when something didn't work as it should, excitement when finally the bulb did light up, and satisfaction with the final product being duly accepted by the "demanding customer" (i.e., me), she's more than happy with herself and convinced she can overcome non-trivial difficulties, learn a lot in the process, and enjoy her new Nintendo DS plus game cards of her choice.

      The bottom line is both her knowledge and her self-esteem have increased immensely with this "real world" little stratagem of mine.

      And she's asking for more work ... ! :-)

Best regards from V.


In the first paragraph of your new article, "Boldly Going...Matrix Square Root", you say "...nor can programmed solutions be found."

You must have missed my post in the thread:

which contains a programmed solution for the matrix square root problem. It requires the EGV function found on the HP48G and descendants.

The program gets the same solution you do for all your examples.


Hi, Rodger:

Rodger wrote:

    "You must have missed my post in the thread: [...]"

      First of all, thanks for the feedback, much appreciated. As for the thread you mention, it's from nearly three years ago. In that much time, there are tons of long, math-related threads posted here and the archives searching mechanism isn't particularly adequate to research them for a given topic.

      Besides, my last posted message in that thread was #21 while your first posted message was #32, so I had already stopped reading the thread by the time you first posted and thus your post went utterly unnoticed by me.

    "[...] which contains a programmed solution for the matrix square root problem. It requires the EGV function found on the HP48G and descendants."

      I'm not familiarized with the HP48G (and descendants) instruction set at all as I don't like RPL models, but I guess EGV stands for "EiGenValues" and so must be some built-in function that returns either the eigenvalues or eigenvectors (or both) of a given matrix, either general or of some special type.

      If that's correct, I think it might be the case that your approach only works for the special case of diagonalizable matrices. All the examples in my article deal with diagonalizable matrices, which explains why you get the same results. It might be the case that for some non-diagonalizable matrix my approach would still work but yours won't.

    Thanks again and
Best regards from V.


I think it might be the case that your approach only works for the special case of diagonalizable matrices. All the examples in my article deal with diagonalizable matrices, which explains why you get the same results. It might be the case that for some non-diagonalizable matrix my approach would still work but yours won't.

Yes, the HP48 program does require the matrix to be diagonalizable, but even though this is a "special" case, it isn't a rare case. Most matrices that arise from physical problems will be diagonalizable, for example.

There is a method which would be applicable to non-diagonalizable matrices. It uses the Schur decomposition, but it is more complicated. The HP48G program I've already given is very short and often will work.

While it is possible that your method may work with some non-diagonalizable matrices, it doesn't even work with some diagonalizable matrices that the HP48G program handles properly.

Your HP71 program doesn't seem to be able to find a square root of these matrices:

[[ 1 2 3 ]
[ 4 5 6 ]
[ 7 8 9 ]]


[[ -9  2 -6  3 ]
[ 5 1 5 7 ]
[ 6 0 3 1 ]
[ 3 -2 3 -1 ]]

Do you know why? I let it go for 900 iterations for both of them, and there was no sign of convergence.


Hi, Rodger:

    I'll have a look into it if I find the time. The first matrix is obviously singular, at first glance. Can you post your computed square roots for both of them so that I can compare ?

Best regards from V.


For the first one:

[[ (.449756,.762279) (.552622,.206796) (.655487,-.348687) ]
[ (1.01852,.0841513) (1.25147,.0228293) (1.48442,-.0384932) ]
[ (1.58729,-.593976) (1.95032,-.161138) (2.31335,.271701) ]]

and the second one:

[[ (.215101,2.95788) (-.183078,-.489361) (.215101,1.22583) (.343944,-1.07186) ]
[ (1.71776,-.117905) (1.29884,.0448131) (1.71776,-.117905) (2.49701,.0332699) ]
[ (.566935,-.973341) (.541642,-.264916) (.566935,.758709) (.813907,.511870) ]
[ (.457715,-1.30388) (-.478761,.495577) .457715,-1.30388) (.739943,.367923) ]]

I've only shown 6 digit results, although the calculator returned 12 digits. When the 12 digit results are squared, the error is out in the 11th or 12th place.


Best regards from V.

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