in some of my Maple worksheets I'm using Maples fit-function to obtain a rational function fit to some data, as I'm interested in the zeros of enumerator and denominator, I chose my fit function accordingly. Afterwards I need to extract the results (mainly the zeros) and do some more calculation steps with them. When evaluating rational functions of high degree, I noticed that my way of extracting the results (I'm using patmatch) becomes increasingly slow up to the point where it takes a couple of minutes to extract 10 numbers.
E.g. the following minimal example (download link at the bottom) takes more than 20 minutes on my machine (Maple 18.01 Build ID 935137; Red Hat Version 6.6 running on system with an i5-3570, 8 GB of RAM). Additionally, the calculation requires an unreasonable amount of RAM.
I can work around the problem to some degree by extracting the leading coefficient beforehand, resulting in a substantial speed up, still I think that there might be some error in the code or my usage of patmatch.
Is there another way to extract these numbers in a similarly simple fashion?