quo, rem, quorem -> poly divide

[DrD]

I need to clarify: I was specifically referring to a direct command entry. Not a programming task, which is almost a different topic, in that a programmer is looking for commands that facilitate certain operations.

More to your point: At the command entry line, if you enter an ambiguous problem such as your example, a default approach might be to perform divisions on a first in first out. Then it's on you for the garbage collection. However, if YOU know what YOU mean, and can parenthesize accordingly, then the divisions would follow the parenthetical path, innermost outwards.

By way of my example, it was just a step involving "integration by partial fractions," and the specific example I used in that post was seeking the quotient and remainder for further operations.

I used wxMaxima as a math/word processor. Wanting to verify results, I copied the polynomial division from wxMaxima, which uses "quotient()" and "remainder()" to the prime, which uses quo() and rem().

My first approach was to try a direct command entry of the basic poly division. Failing that, and to make things easier, I assigned the numerator and denominator to variables, then used the equivalent prime CAS commands to finally arrive at a result. That seemed like a lot of hubbub to get a simple division of two poly's, which set my mind to wondering ....

To your conclusion:

1. The division operator, with poly's as arguments, would, itself, need to be smart enough to know that since you are asking for a [quotient, remainder], the result would not be just any old "vector or list." Context sensitivity.

2. Your divisor 2*x should also be parenthesized: ( (x^2+1) / (x) ) / (2*x);

IF it worked that way, the divide technology would be transparent to the student, at the command line. P/Q => [quotient, remainder] in some form. It doesn't, and neither did the other products I tried. Maybe this can't be done, I really don't know.

Uhmm ...{RTFM} If a beginner has trouble with that drill / bits dilemma, maybe that hole is just not meant to be?