Re: Complexes, Reals, FullSimplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg48803] Re: [mg48782] Complexes, Reals, FullSimplify*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 17 Jun 2004 04:07:15 -0400 (EDT)*References*: <200406160854.EAA12221@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 16 Jun 2004, at 17:54, Stergios J. Papadakis wrote: > Dear group, > I am trying to use expressions of the below form as boundary conditions > in NDSolve. I keep getting "non-numerical" errors. I have tried a lot > of things and reduced the problem to this: > > These give different outputs: > > FullSimplify[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[(1/2)* > x]],Element[x, > Reals]] > > FullSimplify[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[0.5*x]],Element[x, > Reals]] > > I get: > > \!\(Cos[x] - Sin[x\/2]\) > > Re[(1 - 6 \[ImaginaryI]) Cos[x] - (1 + 2 \[ImaginaryI]) Sin[0.5 x]] > > > I think I can get my NDSolve to work if I can make the second > FullSimplify above give me an output without an Re in it. Mathematica > assumes that 0.5 may have some tiny imaginary part and therefore keeps > everything for full generality. How do I eliminate > this? Note that I have simplified things a lot here, the actual > expression that I will be using has many terms that all have the > form above, with many significant digits, which depend on earlier > calculations. I have tried using Chop, > > FullSimplify[Chop[Re[(1 - > 6* I)* Cos[x] - (1 + 2*I)*Sin[0.5* x]]], Element[x, Reals]] > > And that does not work, I get the same result. > > > > > > > Thanks, > Stergios > > The simplest way is to use ComplexExpand; you do not even need FullSimplify: ComplexExpand[Re[(1 - 6* I)* Cos[x] - (1 + 2*I)*Sin[0.5*x]], Element[x, Reals]] Cos[x] - Sin[0.5*x] Andrzej Kozlowski Chiba, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**Complexes, Reals, FullSimplify***From:*"Stergios J. Papadakis" <stergios.papadakis@jhuapl.edu>