Algebraic HP calculators, hierarchy of operations.

[Vtile]

Hello! For resent topic of mine I actually found new thing to me that the hierarchy of operations is so much depated subject. What is the hierarchy of operation in HP algebraic (or RPN+ALG). Is it PEMDAS or PEJMDAS or do not allow at all.

Test expression used and PEMDAS/PEJMDAS as seen on video. (Note that video is somewhat opinionated for PEJMDAS, but informative.)
https://youtu.be/4x-BcYCiKCk

Video do use expression:

\begin{equation}
\frac{1}{2\sqrt{3}}
\end{equation}
Typed in as key sequence: [1] [/] [2] [Sqrt] [3] [=]

Ie. HP50g do give invalid syntax when the algebraic expression shown in video is entered as algebraic expression (as is written on video without user added parenthesis or operators) through the stack (which is actually nice), with EQW it is giving the correct formatting and added parentheses at right position (as is logical).

I do not want to start flame war here, there seems to be two interpretations differing for variety of reasons.

Edit. Added LaTeX for test equation.

[Joe Horn]

(04-04-2021 11:17 PM)Vtile Wrote:  What is the hierarchy of operation in HP algebraic (or RPN+ALG). Is it PEMDAS or PEJMDAS or do not allow at all.

There is no single answer to that question. Different HP models use different rules. For example, the HP 300S returns sqrt(3)/2 whereas the HP 300S+ returns sqrt(3)/6. Also, as you noticed, some HP models don't allow implied multiplication at all.

[Steve Simpkin]

Both TI and Casio have changed how they handle the priority of implied multiplication over the years. TI issued the following guidance regarding which TI graphing models treat implied multiplication with a higher priority.
https://education.ti.com/en/customer-sup...sage/11773

Edit: Fixed the above link from TI.

[Vtile]

I do understand. Thank you for information. Is there any kind of time window when and how HP did use logic or another to parse algebraic entry.

I would assume from my current understanding ie. that early pioneer series would have used higher priority implicid multiplication. Then with same or other models at some point removed this extra layer used for grouping at paper (at some branches of mathematic). Etc.

[Steve Simpkin]

(04-05-2021 08:23 AM)Vtile Wrote:  I do understand. Thank you for information. Is there any kind of time window when and how HP did use logic or another to parse algebraic entry.

I would assume from my current understanding ie. that early pioneer series would have used higher priority implicid multiplication. Then with same or other models at some point removed this extra layer used for grouping at paper (at some branches of mathematic). Etc.

I can't confirm for all of the Pioneer models that use algebraic entry but the HP-20S and HP-22S do not support implied multiplication. The HP 35S does support implied multiplication but does not give it priority.

[Rick314]

The HP 10bII+ allows setting "Chain" mode (the default, 2 + 3 * 4 = 20) or "Algebraic" mode (2 + 3 * 4 = 14). It is a non-RPN calculator except for specific 2-input functions. 100 INPUT 125 %CH = 25, but 2 INPUT 3 y^x = <pending input, no answer yet>. Also functions + - * / do not work with INPUT, but dDAYS, DATE, nCr, nPr, df,t<>P, INV df,t<>P do work with INPUT. Clear as mud!

[Vtile]

(04-05-2021 05:50 PM)Rick314 Wrote:  The HP 10bII+ allows setting "Chain" mode (the default, 2 + 3 * 4 = 20) or "Algebraic" mode (2 + 3 * 4 = 14). It is a non-RPN calculator except for specific 2-input functions. 100 INPUT 125 %CH = 25, but 2 INPUT 3 y^x = <pending input, no answer yet>. Also functions + - * / do not work with INPUT, but dDAYS, DATE, nCr, nPr, df,t<>P, INV df,t<>P do work with INPUT. Clear as mud!

I can see where the "chain" mode comes as an some accounting etc, it's a "rolling sum". Input accumulator is lifted to answer accumulator for every operator so actually the expression follows rule "Do bending operation to previous answer" kind of two level rpn stack with obviously infix operator...

That HP11bII+ must be like close to classic semi algebraic (there was real word for this input scheme I have sometimes seen here relating old TIs from 70s) 4-function calculators with a twist? I would assume it do not allow entry as one chunk ie.. '1+2+3' [ENTER or =] resulting answer.

I was more interested from machines which do take input as whole expression until input confirmation. As with that "whole expression as once" -scheme the machine do part of the interpretation of expression, while machine with partial results usually do left the interpretting job to user (user is the master, calc is rather dumb slave and some try to be smart and confuse master)... Fair enough I was not particularly clear of my original wording. I do try to have time tomorrow to use some LATEX and proper editing the first post.