1 | initial version |

The problem is really how to do partial_fractions and then extract the answer, but I added more of the story to make it clear this is a numeric question. For a first answer, I do not need 100 digits precision :)

2 | No.2 Revision |

~~The problem is really~~in competitive risks models, there are more interesting things to do OK, I'm dealing with a risk expert :) which University are you based in?

I am just trying now to program in Sage a pedagogic exercise: compute the ruin probability for the Cramer-Lundberg model with
a) hyperexponential claims; this should be easy,
except that I am novice enough to Sage to have forgotten how these 1.33456? numbers are called, and how to ~~do partial_fractions and then extract ~~convert
an expression involving many of these numbers to a type which will be accepted by the ~~answer, but I added more of the story to make it clear this is a numeric question. For a first answer, I do not need 100 digits precision :)~~command inverse_laplace

b) uniform claims (so the LT is not rational); after rationalizing the LT by Pade, this reduces to previous; it's a one liner in Mathematica, but takes hours in sage due to the crude help system.

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