       Re: Partial Fraction Decomposition with imaginary coeff.

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: Partial Fraction Decomposition with imaginary coeff.
• From: roger at isy.liu.se (Roger Germundsson)
• Date: Tue, 10 Mar 92 08:54:59 +0100

```>      You just don't know how difficult Apart has made my life.
>         It is crucial to the implementation of inverse linear
>         transforms.  Under 1.2, it would not handle polynomials
>         with rational coefficients expressed in decimal form.
>         Under 1.2 and 2.0, Apart does not break up terms like
>         1 / (x^2 + 1).  About two years ago, I had to write a general
>         purpose routine to work around Apart's drawbacks.  I call it
>         MyApart.  It is embedded in the signal processing packages
>         for Mathematica and is used by the inverse z- and Laplace
>         transforms when Apart doesn't complete the decomposition.
>         MyApart is, of course, darn slow.

I don't know if you want to do full (numeric) factorization
... which of one would want in a straight forward implementation
of Z and Laplace transforms. But using apart on pieces that
that can be separated by Gaussian integers is quite simple:

In:= GApart[ r_ ] :=
Apart[ Numerator[ r ]/Factor[ Denominator[ r ], GaussianIntegers->True ] ]

In:= GApart[ 17/((1 + x)(1 + x^2)) ]

17    17 I     17    17 I
-(--) - ----   -(--) + ----
4      4       4      4        17
Out= ------------ + ------------ + ---------
-I + x         I + x       2 (1 + x)

//Roger

```

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