Re: Re: Integrate Bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg13248] Re: [mg13218] Re: Integrate Bug?*From*: David Withoff <withoff>*Date*: Fri, 17 Jul 1998 03:17:44 -0400*Sender*: owner-wri-mathgroup at wolfram.com

> Examining the difference in the terms produced, the "bug" is much easier > to reproduce > > In[1]:= awm = Log[1-W] > > Out[1]= Log[1 - W] > > In[2]:= Integrate[D[awm,W],W] > > Out[2]= Log[-1 + W] > > But if you do the integration normally, the answer is "Log[Abs[-1 + > W]]." Since Mathematica > can't know what the value of W (or b Nt W in your case) is, it seems to > assume > 1. I would > just use /. Log[a_] :> Log[Abs[a_]] before making your numerical > substitutions. > > Alan The assumption made by Mathematica is that Log refers to the general complex logarithm function. With that, an assumption about the value of W isn't needed. The result is correct for all values of W except when W is 1, where it is undefined. For general complex functions, Log[Abs[-1 + W]] is an incorrect result. Abs is not a differentiable as a function of a complex argument, and so couldn't be part of an indefinite integral (antiderivative). Presumably "do the integration normally" means doing the calculation with the assumption that everything is real, that differentiation refers to directional differentiation along the real axis, and so forth. Dave Withoff Wolfram Research

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