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Re: Questions about Abs[_]

  • To: mathgroup at
  • Subject: [mg55634] Re: Questions about Abs[_]
  • From: Maxim <ab_def at>
  • Date: Thu, 31 Mar 2005 01:25:49 -0500 (EST)
  • References: <d2dpgh$lt5$>
  • Sender: owner-wri-mathgroup at

On Wed, 30 Mar 2005 08:54:41 +0000 (UTC), Dan <dantopa at> wrote:

> Hi Andrzej:
> Mathematica is considering the most general case. I am thinking that
> you are dealing with all positive numbers since you have stated the
> answer you want.
> Let's tell Mathematica we have all positive numbers.
> x = Abs[(2 z0 - 2 d m)^2];     (* define the function *)
> lst={z0,d,m};                   (* assemble all variables in a list *)
> Simplify[x,lst\[Element]Reals && lst > 0]     (* apply criteria *)
> output =
> (2 z0 - 2 d m)^2
> Hope this helps,
> Dan

Element[{x, y}, Reals] is just a conventional notation which means that  
both x and y are in Reals; {x, y}>0 cannot be used in the same way.  
Mathematica seems to interpret the assumption {x, y}>0 as equivalent to  
Element[{x, y}, Reals] (most likely based on the rule that everything  
appearing algebraically in inequalities is real):

Refine[Element[x, Reals], {x, y} > 0]
Refine[x > 0, {x, y} > 0]


x > 0

Going slightly off topic, this is one of many cases where Mathematica's  
parsing of vector input is shoddy:

NSolve[{x, y} == {0}]

{{False -> 0.}}

Of course we have an invalid input here, but Mathematica's output (and  
absense of warning messages) leaves the user at a loss about what went  

Maxim Rytin
m.r at

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