quo, rem, quorem -> poly divide

[Han]

First: Perhaps the partfrac() command may be helpful in what you are trying to achieve.

Quote: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.

Let's just say -- for the sake of academic discussion -- that the division operator could in fact discern through parsing parentheses that the numerator should return a [quotient, remainder] pair and not be treated as a vector or list. I.e. it behaves just how you imagined it should. How, then, would one quickly take this [quotient, remainder] pair and divide both components by a single polynomial (or ratio of polynomials) if one desired the output [quotient/(2x), remainder/(2x)] as a list/vector? Would we then have to apply some sort of quorem2list() command first? (If so, we're pretty much back to square one for a different set of users).

My hunch is that / behaves the way it does for ratios of polynomials for the same reason that 13/7 stays exactly as 13/7.