I gave a talk at the GaTO seminar based on the results of this paper. Here is the note of my talk.
Given a rational homology solid torus X whose longitude is null-homologous, program slope.c determines whether a taut foliation on X(p/q) that is transverse to the core of the filling solid torus can have zero Euler class. In the case that it is possible for the Euler class to vanish, the required values of the relative Euler class are also calculated. To run the program, type gcc slope.c -o slope; ./slope; in the terminal.