@Ronan ... the result i mentioned is shown by sympy On Tue, Feb 28, 2012 at 8:59 PM, Ronan Lamy <ronan.l...@gmail.com> wrote:
> Le mardi 28 février 2012 à 20:00 +0530, prateek papriwal a écrit : > > one more thing ;; > > O(x**2+y,x,y) + O(x+y,x,y) > > gives O(y+x**2,x,y) > > > > why so? > > 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). > > In particular, it implies h(x, g(x)) in O(f(x, g(x)), x) for any > continuous function g such that g(0) = 0. This can be used to show that > x+y isn't in O(x**2 + y, x, y) (take g(x) = 0) and that y+x**2 isn't in > O(x+y, x, y) (take g(x) = -x). Therefore, there is no inclusion > relationship between O(x+y, x, y) and O(y+x**2, x, y) and the result you > mention is wrong. > > -- > 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.
