Re: confused about asserting variable is element of Reals
- To: mathgroup at smc.vnet.net
- Subject: [mg103099] Re: confused about asserting variable is element of Reals
- From: Szabolcs Horvát <szhorvat at gmail.com>
- Date: Tue, 8 Sep 2009 05:56:37 -0400 (EDT)
- References: <h829lj$3tg$1@smc.vnet.net>
On 2009.09.07. 8:36, dushan 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? > I recommend reading through this introductory tutorial: http://reference.wolfram.com/mathematica/tutorial/UsingAssumptions.html x \[Element] Reals does not tell Mathematica to treat x as a real number in the future, just like x == 2 doesn't assign the value 2 to x. However, these expressions can be used in assumptions. Simplify[Im[x], x \[Element] Reals] Assuming[x \[Element] Reals, Simplify[Im[x]]] Assuming[x == 2, Refine[x]] I hope this helps, Szabolcs