Reduced Gröbner bases under composition (Q1269748)

In this paper, the authors study how the reduced Gröbner bases computation behaves with respect to composition. Their main result is to give an equivalent condition to the fact that reduced Gröbner bases computation commutes with composition under the same term ordering: The composition must be given by a list of permuted univariate polynomials and must be compatible with the term ordering. This equivalence answers a question stated by \textit{H. Hong} [ibid. 25, No. 5, 643-663 (1998)]. In the last section, the authors show examples of compositions which satisfy the equivalence. They also state an equivalent condition to the fact that minimal Gröbner bases computation commutes with composition under the same term ordering and study the behaviour of reduced Gröbner bases with respect to composition under different term orderings.