HP Article VA042b - Boldly Going - Outsmarting PROOT (71B).pdf
15-page article belonging to my "Boldly Going" series, this is the original version for the HP-71B of my article "HP Article VA042a - Boldly Going - Outsmarting PROOT (42S)".
Though this article appears at first sight quite similar to the version for the HP-42S published in Update #24, it was actually written earlier and includes additional sections discussing the internal workings of PROOT and their differences, as well as more examples specific to the 12-digit precision available in the HP-71B, which aren't featured in the HP-42S version. Also, it can be very useful for HP-42S users to better understand the RPN version innards, as the BASIC code is much clearer and the algorithm is exactly the same.
The article includes a small 11-line BASIC subprogram PZER (plus an optional driver) for the HP-71B and emulators (Emu71/DOS, Emu71/Win, go71b, etc.) dealing with a glaring limitation of the HP-71B Math ROM’s keyword PROOT, the polynomial root finder which finds at once all real/complex roots of an Nth-degree polynomial but only works for polynomials having real coefficients. On the other hand, PZER works efficiently and accurately for polynomials whose coefficients are real and/or complex, and can work globally (no user inputs or initial guesses required whatsoever, just the coefficients) while also providing the user with extra control if desired. It can be called from your own programs or manually from the command line.
Tue Mar 31 08:41:52 2026 - permalink -
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https://www.hpmuseum.org/forum/thread-14855-post-143746.html#pid143746