Comment #3 on issue 1180 by [email protected]: Strange behaviour of O notation http://code.google.com/p/sympy/issues/detail?id=1180
Solving O(expr1, x, y).contains(O(expr2, x, y)) is actually a difficult problem that requires determining whether expr2/expr1 is bounded when (x, y) -> (0, 0). Some of the issues are: * xy/(x**2 + y**2) is unbounded in the complex case but bounded in the real one * x**2*y/(x**4 + y**2) is bounded on the reals despite having no limit * The same expression goes to 0 along any line passing through the origin, but is identically 1/2 on the parabola y=x**2 The only simple cases I can see is when expr2/expr1 depends on a single variable or when it is a rational fraction with nonzero denominator. Implementing these and returning None in all other cases would be a rudimentary solution but it would solve the original issue and avoid returning wrong results. -- You received this message because you are listed in the owner or CC fields of this issue, or because you starred this issue. You may adjust your issue notification preferences at: http://code.google.com/hosting/settings --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "sympy-issues" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sympy-issues?hl=en -~----------~----~----~----~------~----~------~--~---
