Re: confused about asserting variable is element of Reals
- To: mathgroup at smc.vnet.net
- Subject: [mg103126] Re: [mg103084] confused about asserting variable is element of Reals
- From: Leonid Shifrin <lshifr at gmail.com>
- Date: Tue, 8 Sep 2009 06:01:32 -0400 (EDT)
- References: <200909070636.CAA04019@smc.vnet.net>
Dushan,
you got confused due to your probably procedural programming background.
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 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 information
that <a> should be considered real (in that particular
computation):
In[1] =
ClearAll[a];
Simplify[Im[a], Assumptions -> Element[a, Reals]]
Out[1] = 0
Regards,
Leonid
On Mon, Sep 7, 2009 at 10:36 AM, dushan <dushanm at spinn.net> wrote:
> I'm still learning Mathematica (using 7.0.1) and don't understand
> Mathematica's response. After finally finding out how to assert that a
> variable is real, I tried to verify this by asking Mathematica to show me
> that
> it knew the imaginary part of the variable is zero. But I couldn't
> find a way to do that.. Here're my instructions:
>
> In[1]:= a (ESC)el(ESC) Reals
> Out[1]:= a (the element-of symbol) Reals
>
> In[2]:= ##Im[a]
> Out[2]:= Im[a]
>
> where '##' is any of {null, Refine[, Simplify[, FullSimplify[}. I
> also tried some other combinations, such as 'a^2 - Re[a]^2', but these
> didn't help either.
>
> What am I doing wrong? How do I verify such things?
>
> Thanks.
>
> - Dushan Mitrovich
>
>
- References:
- confused about asserting variable is element of Reals
- From: dushan <dushanm@spinn.net>
- confused about asserting variable is element of Reals