Thanks Travis, so there is coercion already. Now I think it natural to also have coercion from the polynomial fractions to power series, or at least have an expand() member function with a precision parameter and coercion in case of addition with some bigoh, see http://trac.sagemath.org/ticket/15698
And thanks to Peter for completely clarifying power series precision. On Wed, Jan 22, 2014 at 5:36 PM, Peter Bruin <pjbr...@gmail.com> wrote: > Hi Ralf, > > > I understand precision as being independent from element properties (as it >> is in Pari). >> > > In Sage, there are two kinds of precision: the precision of an individual > element and the default precision of the power series ring. The same power > series ring can contain elements that are represented using different > precisions; for example, you can have a power series ring R with default > precision 20, an element f in R with precision 10, and another element g in > R with infinite precision. > > An operation on power series (addition, inversion etc.) return the result > in the highest precision to which it is defined; this depends on the > precision of the elements, not on the default precision. The exception is > when the input has infinite precision and the output cannot be represented > with infinite precision. This is where the default precision comes in. > For example, 1 - x has infinite precision, but 1/(1 - x) = 1 + x + x^2 + > x^3 + ... cannot be represented exactly as a power series, so it is > truncated to the default precision. > > In PARI the situation is similar, except for two things: (1) there is no > distinction between polynomials and "power series of infinite precision > that happen to be polynomials", and (2) the default precision is a global > setting, not tied to any specific ring. Both of these are simply because > PARI has no (explicit) concept of polynomial rings and power series rings. > > Peter > > -- > 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.
