Calculator site update - 2005/05/16



#5

Hi, all:

I've just updated my still fledgling (time, time!) calculator-related site, which you can access using
this link, to include a couple of my HP-related articles featured in past Datafile issues, and now made publicly available online on my site.

All of them do include a program, full documentation and examples, and as of now you can find the following articles there:

  • HP-11C: Long Live the HP-11C !

    5-page article, includes an 84-step program which will quickly and accurately find the limit sum of any user-defined
    infinite alternating series, no matter how slowly it does converge (if at all).

  • HP-12C: Long Live the HP-12C !

    6-page article, includes a 72-step program which will play a challenging game of Bridge-It! against the user.

  • HP-12C: Tried & Tricky Trigonometrics

    10-page article, includes a 99-step program which evaluates all six trigonometric functions (sin, cos, tan and their
    inverses) very quickly and with full accuracy over an extended range of arguments.

  • Time Voyager

    An HP-related short story, in memoriam of Sir Isaac Newton.

  • HP-12C: Serendipitous Solver

    8-page article, includes a 37-step program which makes use of the built-in machine code solver and a number of
    financial functions to find a real root of polynomials up to 14th-degree (up to 1480th-degree or more if there are
    groups of repeated coefficients). The program can also evaluate the polynomial for given arguments. Both root
    finding and evaluation are implemented using built-in financial functions. without user-code loops or branching.

  • HP-15C: Long Live the HP-15C !

    6-page article, includes a 64-step program which will compute and store the value of Euler's constant e
    (=2.71828+) up to 208 decimal digits, using matrix operations.

  • HP-15C: Nth-degree Polynomial Fitting

    7-page article, includes a 42-step program which will compute explicitly the coefficients of a polynomial of degree
    N (for 2 <= N <= 6), which exactly fits (passes through) a given set of data points (x,y).

  • HP-41C: Long Live the Advantage ROM !

    8-page article, includes the 62-step HP-41C/Advantage ROM version of the HP-15C program featured in "HP-15C: Nth-degree Polynomial Fitting", extended to handle degrees much higher than 6.

  • HP-71B: Modest Mater

    12-page article, includes a relatively short BASIC program for the HP-71B that, given a typical 'Mate-in-N-moves'
    problem chess position, will recursively search for the solution. Full explanation of its inner workings is provided, as
    well as two complete, amazing examples.

  • HP-42S: Long Live the HP-42S !

    14-page article, includes a long and "professional-looking" program to solve the classic '8-Queen Puzzle',
    incorporating a number of important techniques such as menus, error control, alphanumeric and graphic outputs,
    user ergonomy, and other advanced techniques, all from a didactic viewpoint. Full explanation of its inner workings
    is provided, as well as a complete run including all 92 solutions and the filtered subset of the 12 primary ones.

  • HP-71B: Math ROM Baker's Dozen (Vol. 1)

    10-page article, first part of a two-part article featuring 13 assorted mini-topics discussing novel, unusual, or
    otherwise interesting aspects of using the extremely powerful and versatile Math plug-in ROM for the HP-71B.

Hope they make interesting reading. I'll keep updating my site with new articles in the near future, as time permits.

Best regards from V.


#6

Cool articles Valentin. I really like the one for the HP41C and how to use the Advantage ROM to perform polynomial curve fitting. I agree with your comments on that ROM --- wish HP had introduced it earlier.

How about a multiple regression program using the Advatnate ROM?

Regards,

Namir


#7

Hi, Namir:

Namir wrote:

"Cool articles Valentin [...] How about a multiple regression program using the Advantage ROM?"

Thanks for your interest and kind comments, Namir. As for your question, if by "multiple regression" you mean a *linear* regression in several variables, i.e., to fit:

     y = a1.x1+a2.x2+ ... + an.xn
to a set of data, in such a way as to minimize the error by some criterium (say, least squares) then the mathematical treatment is nearly identical to the polynomial regression case, and so an extremely simple modification to
a polynomial regression program would do.

However, the program featured in my article does not compute a polynomial regression but a polynomial *fit*, i.e., there's no error to minimize, the resulting polynomial is an exact fit and actually passes through all the points given.

That said, it's a very simple affair to modify the program to make it compute a least squares polynomial regression instead, and then to further modify it to compute a multi-variable linear regression. But the article was just a commemorative one for the Advantage ROM and I wanted to keep things simple. Should I actually need to perform that kind of computation using one of my handhelds, it would be preferable to write a program for the 42S, which is faster, has more RAM and a larger display, plus it's got convenient menus for data entry and results output.

And in the case of multiple linear regression, my beloved bare-bones HP-71B includes statistic statements that can do it off-the-shelf with no programming involved. :-)

Best regards from V .

#8

I read a short story some years back (Omni Magazine, January 1979) with the same basis as your "Time Traveller", but a different ending.

In Newton's last 34 years, he turned from the scientific brilliance of his youth toward persuits of religion and alchemy. In an effort to prevent Newton's "collapse" (actually caused by a temporary mental disorder), it was decided to travel back in time to give Newton the tools to continue his masterworks - a calculator.

Upon presenting the calculator to Sir Isaac, the traveller demonstrated a calculation sequence that gave a result of 666, causing Sir Isaac to become nearly deranged, and to eject the traveller from his home as a servant of Satan - after which Newton abandoned science in favor of religion and alchemy.


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