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 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.
