In RPN/RPL, you work from the "inside out" or from the "bottom up". In algebraic notation, you take a "top down" approach.

Whether you write

Algebraic: total(squared(divs(x)))or

RPL+: x divs squared total (RPL: x DIVIS SQcomes arguably down to preference.SIGMALIST)

Algebraic has in its favor, that it matches natural language:

English: "Sum of squares of the divisors of a number."

RPN has in its favor, that it matches recipe-style step-by-step processing:

English: "Compute divisors for x. Square them. Sum them up."

Let's suggest, that no one is better or worse than the other.

When it comes to algebraic expressions involving operators, RPL doesn't look so good, though, I'd say.

Can you comprehend

1 3 a * 4 b * + 5 c * +or

1 3 a * 4 b * 5 c * + +at a glance?

How about the algebraic equivalent of

3*a+4*b+5*c?

The situation becomes worse when expressions are consumed by a function or construct that takes multiple arguments.

Consider

1 b 4 + x - FOR i ...

You can't glance where start and end value computations begin and end, without backtracking.

Consider these variations of using a comparison operator:

IF x SQ y == THEN

x SQ y == IF THEN

x SQ y IF == THEN

x SQ IF y == THEN

It's not hard to argue that, in these cases, the RP notation comes at the expense of readability.

Now. RPL calcs support algebraic expressions via a data type.

You could write

IF 'SQ(x)==y' EVAL THEN ...to increase readability.

What if you could type

IF SQ(x)==y THEN ...?

I'm working on supporting "immediate algebraic expressions" in RPL+, which permit just that.

You may write

instead ofexpr

'expr' EVAL

This pulls all of algebraic notation into RPL, and (gasp!) merges them.

An example:

1: 1 size(arr)-n FOR i

2: arr[i-n/2] divs squared total =x

3: IF SQ(x)==y THEN BREAK END

4: NEXT

This is not a particularly instructive example, but here're some notes:

Line 1: The algebraic expression *size(arr)-n* segments what comes before *FOR* into two blocks, and makes the calculation more readable

Line 2: pure RPL+ with an algebraic in the array-access operator (*=x* is equivalent to *'x' STO*)

You could write this line also entirely in algebraic notation:

x=total(squared(divs(arr[i-n/2])))Line 3: Algebraic makes the comparison more readable

As with every other RPL+ feature, you may use it, or not.

Am I instigating a forbidden love here, that should better remain unconsummated? Your opinions are welcome.