On 15 May 2010 15:40, Simon King <simon.k...@nuigalway.ie> wrote: > Hi John! > > On 15 Mai, 16:03, John Cremona <john.crem...@gmail.com> wrote: >> The fraction field of Z[[x]] would have to contain Q, so cannot by the >> Laurent Poly ring over Z. That's just Z[[x]] with x inverted, but you >> would need to invert all the integer primes too! > > That's why I wrote: "... so that R.fraction_field() returns the > Laurent > Series Ring over the **fraction field** of R.base()", where R=Z[[x]]. > So, would that be fine?
Certainly -- apologies for not reading what you wrote! > > I guess that in addition to R.fraction_field, the __div__ method of > elements of R needs to be adapted as well (because currently 1/R(x) > returns a Laurent polynomial over Z, not over Q). > There's a more general issue here, perhaps. In your R = Z[[x]], you ask for the inverse of x, which is not invertible as an element of R. The conservative response is to return 1/x in the smallest ring containing R in which x has in inverse, which is Laurent series over Z. The simpler response is to say "since R is an integral domain, let's form its field of fractions and do the inversion there". I think we should go for the simpler solution. Otherwise, for consistency every time someone entered 1/2 the result would not lie in Q but in Z[1/2]! If the user wants the ring of Laurent polys over Z, they should create it explicitly. In your example, 1/R(x) qould then return 1/x as a Laurent poly over Q. >> PS sage-algebra? > > Didn't know it exists. Sorry. It was created for discussions like this -- but not much used. There must be many readers of sage-devel for whom the current thread seems a little esoteric! John > > Best regards, > Simon > > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
