论文标题
在合理的双档代数中通过Gröbner基地减少IBP
IBP reduction via Gröbner bases in a rational double-shift algebra
论文作者
论文摘要
我们报告了基于Gröbner基础的逐件减少集成方法的方法。我们建立了基本的非交通性有理双换档代数，其中逐个组成的关系构成了左派理想。我们详细描述了单循环的无质量盒子作为一个例子，在其中我们通过Gröbner基础方法将全部减少到主积分，并报告实施的性能。我们还在更复杂的例子中确定了潜在的瓶颈，并在有趣的进一步方向上详细说明。
We report on an approach to integration-by-parts reduction based on Gröbner bases. We establish the underlying noncommutative rational double-shift algebra wherein the integration-by-parts relations form a left ideal. We describe in detail the one-loop massless box as an example where we achieved the full reduction to master integrals by means of the Gröbner basis approach, and report on the performance of the implementation. We also identify potential bottlenecks in more complicated examples and elaborate on interesting further directions.
