Is there some setting that allows partfrac to compute the partial
fraction representation for 1/(120+20*x^2+x^4)?
,----
| (%i1) partfrac(1/(120+20*x^2+x^4), x);
| 1
| (%o1) ----------------
| 4 2
| x + 20 x + 120
`----
As the denominator is a quadratic function of x^2, it is clear that
this can be handled. And indeed, solve has no problem obtaining the
zeros, and I could do a "manual" high school-like partial fraction
decomposition to obtain the desired result:
,----
| 1
| ---------------- =
| 4 2
| x + 20 x + 120
| (sqrt(sqrt(30) - 5) sqrt(30) + 6 sqrt(sqrt(30) - 5)) x sqrt(30)
| ------------------------------------------------------ + --------
| 240 120
| -----------------------------------------------------------------
| 2
| x + 2 sqrt(sqrt(30) - 5) x + 2 sqrt(30)
| sqrt(30) (sqrt(sqrt(30) - 5) sqrt(30) + 6 sqrt(sqrt(30) - 5)) x
| -------- - ------------------------------------------------------
| 120 240
| + -----------------------------------------------------------------
| 2
| x - 2 sqrt(sqrt(30) - 5) x + 2 sqrt(30)
`----
I suppose that enhancing partfrac to handle this type of problems
might also benefit ilt as that knows how to compute the inverse
Laplace transform of the "manual" result but not of the original
expression.
Best regards,
Albert.