Re: Re: Why can't Mathematica tell when something is algebraically zero?
- To: mathgroup at smc.vnet.net
- Subject: [mg108199] Re: [mg108127] Re: Why can't Mathematica tell when something is algebraically zero?
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Wed, 10 Mar 2010 01:46:33 -0500 (EST)
- References: <hn2ltj$3kt$1@smc.vnet.net> <201003091119.GAA06777@smc.vnet.net>
It seems better to use: Assuming[Element[r, Reals], PowerExpand[r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)]]] 0 PowerExpand with Assumptions ought to be as reliable as Simplify (which does not work in this case), whereas if you use it without assumptions it can return answers that will be false for some values of the variables (it makes use of the maximal assumptions that permit the expansion). The fact that Simplify works here with the assumption r>=0 but not r<0 appears to be a bug. Andrzej Kozlowski On 9 Mar 2010, at 12:19, dh wrote: > Hi, > Sqrt is a multivalued function. Therefore, your expression is not > necessarily zero. If you are sure that all your variables are real and= > that you only want the main branch of Power, then you can use = PowerExpand: > r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] // PowerExpand > Daniel > > On 08.03.2010 12:09, mmdanziger wrote: >> This isn't the first time that I've encountered something like this = in >> Mathematica but in my calculations I got a term like this: >> >> r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] >> >> Which is obviously identically zero. For some reason Simplify or = even >> FullSimplify can't figure this out. Once you get dependent on >> Mathematica these things are pretty disturbing...you forget about = your >> own knowledge because the program tells you that things are >> different. Then you sit there like an idiot checking an algebraic >> identity that any beginning precalc student should be able to solve = no >> problem. >> >> Is there any way to get Mathematica to "wake up" to these things? It >> has such a powerful algebraic engine for most things, why can't it = see >> something simple like the above? Do you really have to manually >> override and tell the program when things should be zero? >> >> For the time being I'll just sift through and test things by hand but >> I can't believe that there isn't a better way. >> >> Best, >> md >> > > > -- > > Daniel Huber > Metrohm Ltd. > Oberdorfstr. 68 > CH-9100 Herisau > Tel. +41 71 353 8585, Fax +41 71 353 8907 > E-Mail:<mailto:dh at metrohm.com> > Internet:<http://www.metrohm.com> > >
- References:
- Re: Why can't Mathematica tell when something is algebraically zero?
- From: dh <dh@metrohm.com>
- Re: Why can't Mathematica tell when something is algebraically zero?