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Full Version: November 2010 Issue of HP Solve is out!!!
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Hi All,

The wait is over! HP has posted online the November 2010 issue of HP Solve. I was happy to see my article on the PROOT function for the HP-50G appear!!! Hopefully future articles will bring you more on the subject.

Enjoy!!!

Namir

Good work to Richard for creating and editing the journal. Many, many thanks!

Namir,

Got to get out my advanced calculus and math dictionary and then purchase a 50g and then try to understand. But really, good article.

And the next time I see Mark, I can put two and two together! By the way Mark, when does 50 calculators not equal a collection? Also thanks again to Jake for more HP input from a veteran.

Cheers and Merry Christmas

how exciting ;(

Sorry Reth,

just don't don't get the negativism!

Merry Christmas

Yeah, why the face. Many people have been waiting for the new issue of HP Solve. With Richard as editor, my hope is that more folks from this website can contribute meaningful articles. Think of what the PP Journal would have been if it was published on the Internet?

Namir

I dunno, but maybe Reth wanted to indicate his limited excitement about a bimonthly newsletter appearing 1.5 months delayed? Just speculating, of course - and I perfectly know it's not Richard's fault, and it's showing the same quality as previous issues.

This article, and subsequent ones in the HP Solve newsletter, came as a fruit of studying the various algorithms AND approaches for solving the roots of polynomials. The duplication (or multiplicity) of roots is the worst enemy of many algorithms. The best approach to handle duplicate roots (and you can have several ones too, to make things worse) is to reduce the original polynomial to a simpler form where the duplicate roots are removed. Once you do this then you are pretty much set.

Calculating the roots of polynomials fall into two approaches: sequential and parallel (i.e. simultaneous). The latter work well because you avoid the deflation of polynomial required by the sequential methods (which typically causes round-off errors). The enemy of methods that calculate roots simultaneously is duplicate roots!!

Regarding duplicate roots, I have not seem many polynomials in real-life applications that have (a high number of) duplicate roots. So when solving polynomials in engineering and scientific applications, you should be fine with using most root-seeking algorithms.

Namir

Edited: 11 Dec 2010, 8:53 a.m.

Perhaps Reth's sad "smiley" is in line with his recent announcement that HP is no longer his favourite?

The "November 2010" issue is a 5+ MB, 46-page PDF.

Regarding "The PROOT Gem":

Quote:

The advent of the HP-48GX/G+/G family of calculators introduced a
new function PROOT that replaced the Solver when dealing with polynomials.

It should be mentioned that the PROOT function debuted ten years earlier on the HP-71B Math Pac, not on the HP-48G series. However, HP-71B's and their accessories are in very limited supply nowadays.

-- Karl

Edited: 11 Dec 2010, 6:50 p.m.

Quote:

It should be mentioned that the PROOT function debuted ten years earlier on the HP-71B Math Pac, not on the HP-48G series. However, HP-71B's and their accessories are in very limited supply nowadays.

Lucky for us who have them :)

There is going to be an upcoming article about the PROOT in the HP71B. It was limited to real-coefficient polynomials. You can use the EMU71 to test the Math ROM PROOT function because the emulator also supports the Math ROW software (available in a link from the emu71 web site)

So stay tuned!

Namir

Edited: 12 Dec 2010, 8:27 a.m. after one or more responses were posted

Quote:
.. PROOT in the HP71B .. was limited to real-coefficient polynomials ..

The HP-71B Math Pac routines for the Saturn microprocessor were an initial effort whose complex-number support hadn't reached full development. A more curious limitation is that the inverse functions of trigonometrics and hyperbolics -- ASIN, ACOS, ATAN, ASINH, ACOSH, and ATANH -- did not include complex numbers in their domains or ranges.

Trigonometrics and their inverses were built into the HP-71B for real-valued numbers only. Hyperbolics with domain and range both real and complex, as well as extension of trigonometrics to the complex domain and range, were added by the HP-71B Math Pac. In this way, its functionality went somewhat beyond the keystroke routines of the HP-41 Math ROM, which did not offer complex-number support for the hyperbolic functions.

Didn't the HP-48S series have PROOT in some form -- either the HP-71B Math Pac version or the HP-48G version?

-- Karl

Edited: 12 Dec 2010, 7:54 a.m.

Quote:
Didn't the HP-48S series have PROOT in some form...

My HP48SX, ROM version E, does not have a PROOT function. I suspect no HP48S did.

The HP-71B PROOT function was made available as an HP 48S/SX object by Bill Wickes in 1992:

"The HP 48 object listed below in ->ASC form is a high-performance polynomial root finder. Those of you who remember the HP 71B Math Pac will recognize this as the same as the PROOT command from that Pac; it is in fact the same assembly-language code, given an RPL front end to operate in the HP 48."

I see Wickes offered the PROOT object as a software object and not built-in as is the case with the HP-48G/G+/GX/GII/GII+ and the HP-50G.