quo, rem, quorem -> poly divide

[Han]

(03-22-2018 04:31 PM)DrD Wrote:  

(03-22-2018 02:47 PM)Han Wrote:  Is there that much of a difference between typing a slash versus a comma?

Moreover the commands are more useful this way from a programming perspective because fractions are generally represented as numerator and denominator pairs and not as a single atomic object due to constraints on exact representations.

In programming, one has the luxury, when creating the program, with ample time to make the details fit the paradigm. A comma is only convenient for command syntax, and isn't a universal division symbol. Not to mention that it is more than just a comma at issue, the command name and syntax must also be considered.

Far more often, at the command entry, a student is interactively working with problems and solution steps as part of a lesson, or homework session. Often problems can be copy/pasted from some source to the command entry line. So, after copy and paste, a student must then "know" that a special command is required, and deal with it's entry syntax, and then configure numerator and denominator accordingly. When time is important, this is quite inefficient.

This is not an issue particular to the HP Prime (or any calculator or CAS); it is a an issue with any complex tool. Even a power drill might be difficult to use to a beginner who wishes to drill a hole and has no idea how to insert proper drill bits. To address your issue directly, a quotient is "merely" a numerator and denominator. However, it is quite a difficult problem for even simple cases. Consider the fraction

\[ \frac{\frac{x^2+1}{x}}{2x} \]

Some see \( \frac{x^2+1}{x} \) as the numerator, and \( 2x \) as the denominator. Some might simplify this a bit a see \( x^2+1 \) divided by \( 2x^2 \). What exactly is meant by the division in each case? If you really think about it from a programmer's perspective (in terms of object types -- rational divided by polynomial vs polynomial divided by polynomial), these are two very different division operations. How would a calculator know which is which? From a pedagogical point of view, the commands you mentioned forces the user to be more clear as to what they want to do (and also reinforces the notions of division in terms of numerator and denominator).

In case you were thinking parentheses would help:

Suppose the \( \frac{x^2+1}{x} \) were surrounded by a set of parentheses. Would the calculator then compute the quotient and remainder as \( [q(x), r(x) ]\) and then proceed to divide \( [q(x),r(x)] \) by \( 2x \) ? If so, how would it know that \( [ q(x), r(x) ] \) is not a vector or list as opposed to a quotient + remainder? What if it returned \( [q(x)/2x, r(x)/2x ] \)? That seems like a reasonable result (even if undesired).

Quote:The idea of textbook representation is more fluid than a special comma configured obscure command representation, at times when intermediate processing is quickly desired. I say 'obscure' command, because the same command has various names depending on the software encountered. From my experience, I think that IS a big difference.

However, there may be better reasons for not simply honoring the divide symbol as the operator ... I don't think comma, slash, or programming, is the underlying reason, is it?

I am of the opinion that it is. Said differently, I find that textbook representation can often be very ambiguous and relies too much on context. By forcing the user to specify what their arguments are (and as a side-effect requiring them to know what operation/command name is relevant), we reduce the possibility of ambiguity -- which is always desirable in mathematics.