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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
>
> \!\(TraditionalForm
> \`\(-\(1\/6\)\)\ \[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,
>
> \!\(TraditionalForm
> \`\(-\(1\/6\)\)\ \[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
>
> \!\(TraditionalForm
> \`\((\(-2.34710341268466837`\) + 0.`\ \[ImaginaryI])\)\
>
> \[ExponentialE]\^\(\(\(-3\)\ \[Tau]\)/2\)\)
>
> \!\(TraditionalForm
> \`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.
>
> Thanks in advance, Bill
>
>
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