I of a given ideal I⊴ K [x1,..., xn] in a polynomial ring is one of the basic tasks in computational commutative algebra. For example, radical computation is an ingredient in de Jong’s normalization algorithm (see de Jong, 1998; Decker et al., 1999; Matsumoto, 2000). Moreover, algorithms for primary decomposition often start by forming the radical ideal (see Becker and Weispfenning, 1993, Algorithm 8.6).

A very common approach for computing the radical of I is by reducing to the case where I is zero-dimensional (see Gianni et al., 1988; Alonso et al., 1991; Krick and Logar, 1991; Becker and Weispfenning, 1993). A nice presentation of this method can be found in Becker and Weispfenning (1993, Section 8.7). The main idea is to choose a subset of the indeterminates which is maximally independent modulo I. After renumbering, let this subset be {x1,..., xd}. Then the main step is to pass to the ideal I:= IK (x1,..., xd)[xd+ 1,..., xn] generated by I in the polynomial ring over the rational func-