Non-structural zeros and singular uncer- tainty in index reduction of dae — exam- ples and discussions

When massaging differential-algebraic equations during an index reduction process, one usually keeps track of structural zeros in order to be able to detect when non-differential equations appear. However, in a numerical setting structural zeros may turn out as small numbers, impossible to distinguish from zero when numerical precision is taken into account. Such coefficients are referred to as non-structural zeros. This note aims to provide a better understanding of the ad hoc procedure of replacing those and other small numbers by structural zeros, at critical stages in the index reduction process.