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!
John PS sage-algebra? On 15 May 2010 13:37, Simon King <simon.k...@nuigalway.ie> wrote: > Hi! > > I just noticed the following: > > sage: P.<x> = ZZ[] > sage: R = P.completion(x) > sage: R > Power Series Ring in x over Integer Ring > sage: (1/R(x)).parent() > Laurent Series Ring in x over Integer Ring > sage: F = FractionField(R) > sage: F > Fraction Field of Power Series Ring in x over Integer Ring > sage: F(1/R(x)) > BOOOOM > > In other words, the multiplicative inverse of an element of R can not > be interpreted as an element of its fraction field. > > I don't think it would make much sense to tinker with the (generic) > fraction field that is returned by R.fraction_field(). > > Should perhaps the default fraction field method be overloaded for > power series rings, so that R.fraction_field() returns the Laurent > Series Ring over the fraction field of R.base()? Would this be > mathematically correct? > > 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
