On Friday, June 8, 2018 at 9:56:56 AM UTC-7, vdelecroix wrote: > > > 2) Laurent polynomials should conform to the rule (R0) and a / b > should always be a rational fraction > > +1 to this. That seems to be the only consistent choice. There is a bit of an issue, with the partial "division" operation one would often like to do in rings in which one has explicitly inverted some elements (such as laurent polynomials, power series, and p-adic numbers):
We have this: sage: R=Zp(7) sage: a,b=R(1),R(2) sage: parent(a/b) 7-adic Field with capped relative precision 20 and often it is suggested that "//" works to stay in the ring, and it does: sage: parent(a//b) 7-adic Ring with capped relative precision 20 but it is not quite equivalent to the much safer explicit back-conversion (which is possibly unduly expensive): sage: parent(R(a/b)) as you can see in this example: sage: parent(a//7) 7-adic Ring with capped relative precision 20 sage: parent(R(a/7)) ValueError: negative valuation The latter is probably the error you'd be hoping for. Instead, "//" does some euclidean division and will let you silently continue with the wrong result (wrong at least if you get taught "//" is the alternative for "/" you should use to stay in the ring) Incidentally, sage: parent(a^(-1)) 7-adic Field with capped relative precision 20 so at least for p-adics, there is no distinction for 1/a and a^(-1). If laurent polynomials were consistent with that, one would need 1//x to get the inverse of x ... or use an explicit conversion. Given how laurent polynomials are printed, this might be a tad inconvenient. So no rule R0 for exponentiation in this case? One technical way around that would be to have "x" a monomial rather than an element of the ring, but I don't think we need *more* parents. -- 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.
