A  few comments.
1. Giving someone a surprising or undesirable result because
a GCD computation is considered expensive sounds like a really
bad idea.  (I believe I'm overstating the situation here, but that's
sort of what it sounds like.
2. (Judging from Macsyma/Maxima)  it is ok, workable, and
only occasionally surprising, to allow almost anything in the
"general representation" used in the top-level command language.
Maybe not division by an explicit zero,  or wrong-number-of-args
to a famous function.  but unreduced fractions is ok if the
reduction is not obvious.

3. On the other hand, a select set of canonical representations
is available in Maxima. NOT everything that might be made canonical, but
ones that seemed useful.

Thus canonical rational expressions are ratios of polynomials with
INTEGER coeficients. The nice thing about this is GCD is well defined.
If you have ratio of polynomials with RATIONAL coefficients, you
could canonicalize by making the denominator monic, but frankly,
you can continue down that route and have any number of peculiar
edge cases -- puzzling even to someone who knows some
modern algebra, and just outright mysterious to someone who
is a physicist (etc) who thinks a field is where you play baseball,
and a ring is worn on a finger.

It's your design decision, so you live with the consequences.
Or change your design.  I recall that Axiom had a mathematical
category called  "integration result"  to use as a container for
results from Risch or other procedures.

RJF



>

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