Invariants for the computation of intransitive and transitive Galois groups
An important step in algorithms based on Stauduhar's approach for computing the Galois group of a polynomial over \(\mathbb{Z}\) is the computation of relative invariant polynomials. Most results on this step deal with the computation of invariants for transitive groups. The case of intransitive groups is reduced to the transitive case, often resulting in invariants that are too large to handle in practice. In this paper, the author describes a method using subdirect products to compute invariants in the intransitive case directly, as opposed to reducing to the transitive case. Numerical results demonstrate that the new method can be applied successfully in the majority of cases.
scientific article; zbMATH DE number 6017592
scientific article