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A combination of commands partial_fraction(x) and coefficient(x,n)

I have asked this question over here but I got no answer.

I am trying to do some iterative calculations where each time SAGE constructs a fraction and lists the coefficients in the partial fraction decomposition of that fraction. I realized that doing everything symbolically, SAGE wants to keep everything as integer as possible. So what it does is to simplify fractions like 1/(x-3/2) as 2/(2x-3) and then when I ask for


it returns 0, while I expect it to return 1.

I have tried to solve things numerically, but there are two problems:

  1. The errors get really big after each iteration
  2. It takes much much longer to calculate it

Any suggestions to get SAGE to solve this is greatly appreciated.