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 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.
