If polynomials were a subring of power series then 1-x would have an inverse. Who says it has not?
(Do not misunderstand me please, I simply don't know) On Wed, Jan 22, 2014 at 4:57 PM, Nils Bruin <nbr...@sfu.ca> wrote: > On Wednesday, January 22, 2014 3:49:01 AM UTC-8, Ralf Stephan wrote: >> >> While the ring type hierarchy does not reflect that polynomials are power >> series, you can have a power series without bigoh which is pratically a >> polynomial but, being a power series, has much less member functions >> available. >> > As a power series, it has *different* methods available. For instance, the > (formal) power series 1-x has a multiplicative inverse (formal) power series > 1+x+x^2+x^3+... > but the polynomial 1-x does not have a multiplicative inverse polynomial. > > The big-Oh term is giving you useful information: it is telling you that > "1 - x + O(x^10)" is considered a power series. You also see why, even if > this is the power series representation of the polynomial 1-x and not of a > power series 1-x+x^11+x^13+..., it is still essential to have some > "precision" associated to the object: once you take the inverse of a power > series, you need a precision to represent it in a finite way (ignoring > "lazy" approaches for now). > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sage-devel" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sage-devel/APnWIGYcq3M/unsubscribe. > To unsubscribe from this group and all its topics, 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 http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/groups/opt_out. > -- 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 http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
