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 > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
