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Re: confused about asserting variable is element of

• To: mathgroup at smc.vnet.net
• Subject: [mg103196] Re: [mg103084] confused about asserting variable is element of
• From: dushanm at spinn.net (Dushan Mitrovich)
• Date: Thu, 10 Sep 2009 07:21:12 -0400 (EDT)

Many thanks to all who replied.  Bob Hanlon's several alternative usages
were particularly informative.  The one I was most interested in, also
suggested by Dan Litchblau:

    $Assumptions = Element[a, Reals];
or
    $Assumptions = $Assumptions && Element[a, Reals];


Leonid Shifrin notes that

  In some hypothetical procedural language the statement Element[a, Reals]
  would only make sense if it globally assigns <a> a property of being
  real.

In fact, this is precisely what I want: an instruction telling Mathematica
that, within the scope of that particular Notebook and absent user instruc-
tions to the contrary, it is to assume in all procedures that the specified
variable is real.  In particular, I don't want to have to re-specify that
property every time I perform an operation, as suggested below:

  In Mathematica, everything is an expression, and most expressions don't
  introduce side effects (global changes).  When you enter Element[a,
  Reals], this by itself does nothing.  It does not, in particular, change
  any global property of symbol <a>.  However, this expression can be used
  in commands like Simplify, FullSimplify, etc., to give them the informa-
  tion that <a> should be considered real (in that particular computation)


I did initially refer to the UsingAssociations.html article, where I found
this description,

  x \[Element\ dom  or  Element[x,dom]       assert that x is an element
                                               of the domain dom

This seemed like a straightforward statement of what I wanted to do, so
that's what I tried.  The problem is that I thought it was an instruction
that applied globally to that Notebook.  Now I've learned better.

Thanks for all the help and education.

- Dushan

• Follow-Ups:
  • Re: Re: confused about asserting variable is
    • From: Leonid Shifrin <lshifr@gmail.com>