Consider a subfield of the field of rational functions in several indeterminates. We present an algorithm that, given a set of generators of such a subfield, finds a simple generating set. We provide an implementation of the algorithm and show that it improves upon the state of the art both in efficiency and the quality of the results. Furthermore, we demonstrate the utility of simplified generators through several case studies from different application domains, such as structural parameter identifiability. The main algorithmic novelties include performing only partial Gröbner basis computation via sparse interpolation and efficient search for polynomials of a fixed degree in a subfield of the rational function field.

翻译：考虑多元有理函数域的一个子域。我们提出一种算法，给定该子域的一组生成元，能够找到一个简单的生成集。我们提供了该算法的实现，并证明其在效率和结果质量方面均优于现有技术。此外，我们通过来自不同应用领域（如结构参数可辨识性）的多个案例研究，展示了简化生成元的实用性。该算法的主要创新点包括：通过稀疏插值进行部分Gröbner基计算，以及高效搜索有理函数子域中固定次数的多项式。