There has been a growing need to devise processes that can create comprehensive datasets in the world of Computer Algebra, both for accurate benchmarking and for new intersections with machine learning technology. We present here a method to generate integrands that are guaranteed to be integrable, dubbed the LIOUVILLE method. It is based on Liouville's theorem and the Parallel Risch Algorithm for symbolic integration. We show that this data generation method retains the best qualities of previous data generation methods, while overcoming some of the issues built into that prior work. The LIOUVILLE generator is able to generate sufficiently complex and realistic integrands, and could be used for benchmarking or machine learning training tasks related to symbolic integration.

翻译：在计算机代数领域，为精确基准测试及与机器学习技术的新交叉应用，对能够生成综合性数据集的流程需求日益增长。本文提出一种保证可积的被积函数生成方法，称为LIOUVILLE方法。该方法基于刘维尔定理及符号积分的并行Risch算法。我们证明该数据生成方法保留了先前数据生成方法的优良特性，同时克服了早期工作中固有的一些问题。LIOUVILLE生成器能够生成足够复杂且真实的被积函数，可用于符号积分相关的基准测试或机器学习训练任务。