Am 2015-03-02 um 20:52 schrieb Raymond: > 1. From Meta-Ticket 17716, I couldn't understand the example 2, (4 * n^2 > * t + 3 * n * t^2 + O(n)) + (O(n^2 * t^3/2 )) evaluates to (3 * n * > t^2 + O(n^2 * t^3/2 )). > Highly likely that this is something basic, but despite reading the > explanation below, I couldn't quite get a hang of it.
Whenever something is asyptotically smaller, then it gets "eaten up" by O-terms: n^2 + O(n) = O(n). In the multivariate case, the powers (in the examples above) of each variable has to be smaller in the one expression than in the other. Thus, n^2 t^2 + O(n t) = O(n t), but n^2 t + O(n t^2) cannot be simplified. > So, are there > pointers to any mathematical primers - courses, lectures, etc, online > which would be most relevant to this project that you could point me to? For the asymptotic expressions this is difficult...you can look in Flajolet and Sedgewick, Analytic Combinatorics or Pemantle and Wilson, Analytic Combinatorics in Several Variables Both books work with asymptotics, but they present tools to solve combinatorial problems. Daniel -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-gsoc. For more options, visit https://groups.google.com/d/optout.
