       Re: Real integrand->complex result.

• To: mathgroup at smc.vnet.net
• Subject: [mg20304] Re: [mg20293] Real integrand->complex result.
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Fri, 15 Oct 1999 20:20:38 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```The tiny imaginary parts that you often get in Mathematica computations
involving non-exact numbers can be got rid of using the function Chop. (I
would also recommend that if you want people to seriously look at examples
you send by e-mail you should either use InputForm or paste in a complete
notebook as a NotebookExpression).
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

----------
>From: William Golz <wgolz at attglobal.net>
>To: mathgroup at smc.vnet.net
>Subject: [mg20304] [mg20293] Real integrand->complex result.
>Date: Tue, 12 Oct 1999 03:39:30 -0400
>

> Synopsis of the problem:
> I get a complex result of the form f(t)=(a+bi)g(t) when evaluating a
> real integrand F(x,t)*phi(x) over the interval {x:0<x<L). All of the
> variables have been properly declared as real and the functions have
> been declared as real for real arguments (using the package "ReIm").
>
> To see the problem more clearly, the code can be copied into Mathematica
> (3 or 4) and executed. (The Traditional or Standard Forms will not paste
> into a text document such as this)
>
>  When evaluating the integral
>
>                  \!\(\[Integral]\_0\%\[ScriptL]\( simpF\[CurlyPhi]\_n\)
> \[DifferentialD]x\)
>
>                  over the interval (0,ScriptL) where ScriptL=1. The
> integrand
>                  \!\(simpF\[CurlyPhi]\_n\ is, for n=1, given by
>
>                  \`\(-\(1\/6\)\)\ \[ExponentialE]\^\(\(\(-3\)\
> \[Tau]\)/2\)\
>                  \((\((3 + 2\ \[Pi]\^2)\)\ \(cos(\[Pi]\ x)\) -
>                  6\ \[ExponentialE]\^\(x/2\) + 3)\)\
>                  \((cos(3.66558239083868908`\ x) +
> sin(3.66558239083868908`\ x))\)\)
>
>  and for n=2,
>
>                  \`\(-\(1\/6\)\)\ \[ExponentialE]\^\(\(\(-3\)\
> \[Tau]\)/2\)\
>                  \((\((3 + 2\ \[Pi]\^2)\)\ \(cos(\[Pi]\ x)\) -
>                  6\ \[ExponentialE]\^\(x/2\) + 3)\)\
>                  \((cos(6.58302641111680308`\ x) +
> sin(6.58302641111680308`\ x))\)\)
>
> I get the result for n=1,2, respectively
>
>                  \`\((\(-2.34710341268466837`\) + 0.`\ \[ImaginaryI])\)\
>
>                  \[ExponentialE]\^\(\(\(-3\)\ \[Tau]\)/2\)\)
>
>                  \`2\[InvisibleSpace]'' ''\[InvisibleSpace]\(\((
>                  \(-1.26446964467229783`\) + 0.`\ \[ImaginaryI])\)\
>                  \[ExponentialE]\^\(\(\(-3\)\ \[Tau]\)/2\)\)\)
>
> For simple functions F, the product F*phi can be integrated by parts,
> where the result contains no potential for complex coefficients when the
> variables are real valued. However, evaluating an identical integrand in
> Mathematica will give the result f(t)=(a+0.i)g(t). There does not seem
> to be any way to avert this, either by defining the variables to be real
> and the functions to be real valued (for real arguments).
>
> The evaluation of the integral is also quite slow, even for n=2, even
> when the expression is simplified as much as possible, and the final
> program will need to evaluate a larger number of terms.
>