In this paper, we provide first a new algorithm for testing whether a monomial ideal is in Nœther position or not, without using its dimension, within a complexity which is quadratic in input size. Using this algorithm, we provide also a new algorithm to put an ideal in this position within an incremental (one variable after the other) random linear change of the last variables without using its dimension. We describe a modular (probabilistic) version of these algorithms for any ideal using the modular method used in [2] with some modifications. These algorithms have been implemented in the distributed library noether.lib [17] of Singular, and we evaluate their performance via some examples.