O in Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg95893] O in Mathematica
- From: Francois Fayard <fayard.prof at gmail.com>
- Date: Thu, 29 Jan 2009 05:55:59 -0500 (EST)
Hello, At first, thanks for your help, but I've found what I was asking for. To input a O(1) in mathematica, you juste have to write n O[n,Infinity] which gives you O[1/n]^0 which is not simplified to 0. Now, I've got another question around O. Let's first explain what I call a O, or big O (in France). A O(f(x)) around zero is a function that can be written B(x)f(x) where B(x) is bounded around 0. I just want to make sure everyone speaks about the same thing. With that definition x = O(x) (around 0), but x Log[x] is not a O(x) (around 0) as x Log[x]/x=Log[x] is not bounded around 0. But when I write in Mathematica Log[x] O[x,0]^1 It is simplified to O[x,0]^1 which is obviously wrong. I've seen that if you multiply O[x,0]^1 by a fonction g(x) that is negligeable compared to x^epislon around 0 for a epsilon>0, the result is simplified to O[x,0]^1 which is wrong form a mathematical point of view. Do I have to understand that O[x,0]^n (in Mathematica) should be considered as a O[x,0]^(n-epsilon) (in mathematics) for whatever epsilon>0 you want ? If we consider this definition, are the results from Mathematica "certified" ? Another question should be : Why does Mathematica behave like that ? Thanks, Francois Fayard