quo, rem, quorem > poly divide

03222018, 06:00 PM
(This post was last modified: 03222018 08:37 PM by Han.)
Post: #6




RE: quo, rem, quorem > poly divide
(03222018 04:31 PM)DrD Wrote:(03222018 02:47 PM)Han Wrote: Is there that much of a difference between typing a slash versus a comma? 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. 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 sideeffect requiring them to know what operation/command name is relevant), we reduce the possibility of ambiguity  which is always desirable in mathematics. Graph 3D  QPI  SolveSys 

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Messages In This Thread 
quo, rem, quorem > poly divide  DrD  03222018, 02:38 PM
RE: quo, rem, quorem > poly divide  Han  03222018, 02:47 PM
RE: quo, rem, quorem > poly divide  DrD  03222018, 04:31 PM
RE: quo, rem, quorem > poly divide  Han  03222018 06:00 PM
RE: quo, rem, quorem > poly divide  Tim Wessman  03222018, 04:43 PM
RE: quo, rem, quorem > poly divide  DrD  03222018, 04:57 PM
RE: quo, rem, quorem > poly divide  DrD  03222018, 08:23 PM
RE: quo, rem, quorem > poly divide  Han  03222018, 09:24 PM
RE: quo, rem, quorem > poly divide  DrD  03232018, 11:55 AM
RE: quo, rem, quorem > poly divide  Han  03232018, 12:51 PM
RE: quo, rem, quorem > poly divide  DrD  03232018, 01:21 PM

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