  We consider several notions of genericity appearing in algebraic geometry and
commutative algebra. Special emphasis is put on various stability notions which
are defined in a combinatorial manner and for which a number of equivalent
algebraic characterisations are provided. It is shown that in characteristic
zero the corresponding generic positions can be obtained with a simple
deterministic algorithm. In positive characteristic, only adapted stable
positions are reachable except for quasi-stability which is obtainable in any
characteristic.
