also do we have THETA notation in sympy ? http://en.wikibooks.org/wiki/Data_Structures/Asymptotic_Notation#Theta_Notation
On Tue, Feb 28, 2012 at 10:59 PM, Sergiu Ivanov <unlimitedscol...@gmail.com>wrote: > On Tue, Feb 28, 2012 at 7:21 PM, Aaron Meurer <asmeu...@gmail.com> wrote: > > On Tue, Feb 28, 2012 at 9:17 AM, Sergiu Ivanov > > <unlimitedscol...@gmail.com> wrote: > >> On Tue, Feb 28, 2012 at 5:29 PM, Ronan Lamy <ronan.l...@gmail.com> > wrote: > >>> Le mardi 28 février 2012 à 20:00 +0530, prateek papriwal a écrit : > >>> > >>> O() with multiple symbols is tricky, full of bugs and not very useful. > >>> > >>> "h(x, y) in O(f(x, y), x, y)" means that |h(x, y)| < C*|f(x, y)| for > >>> some real constant C over some open region of the (x, y) plane > >>> containing (0, 0). > >> > >> Wow, thank you for explanation! Can you point out some works where > >> big-O notations with multiple arguments is actually used? > > > > At zero, I imagine it comes in when doing some kind of series > > expansion in multiple variables. I don't think we really have > > anything like that implemented (though I could be wrong). > > Yes, that's what I vaguely thought of, at the first glance. > > > As another example, I think you could expression O(z**n) as O(f(x, y)) > > for some f, where z = x + I*y is a complex variable. > > Hm, indeed, I'm too used to natural numbers in complexity theory. > > > At infinity (which O() does not implement by the way), O notation is > > useful in algorithmic analysis, when looking at the asymptotic > > behavior of an algorithm. For example, you may see sometimes that a > > graph theory algorithm is something like O(|V| + |E|), which means > > that it is linear in the number of vertices plus the number of edges > > in the graph. |V| + |E| is of course a function of two variables. > > Yes, this sounds relevant; however, I've seen quite a number of > examples when either one of the variables is fixed and the complexity > of the algorithm is measured with respect to the other variable, or > both variables are parametrised with a single parameter. > > Thank you for your explanations! :-) > > Sergiu > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To post to this group, send email to sympy@googlegroups.com. > To unsubscribe from this group, send email to > sympy+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/sympy?hl=en. > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
