论文标题
在计算扭曲共生的交点号码
On the computation of intersection numbers for twisted cocycles
论文作者
论文摘要
在代数几何学领域的数学中，扭曲的共生的交点数量出现。最近，它们出现在物理学中：扭曲共生的交点数量在Feynman积分的矢量空间上定义了标量产品。通过此应用，扭曲的共生的交点数量的实际有效计算成为一个有趣的话题。用于计算扭曲共生相交数量的现有算法需要在中间步骤中引入代数扩展（例如方形根），尽管最终结果可以在没有代数扩展的情况下表达。在本文中，我介绍了该算法的改进，该算法避免了代数扩展。
Intersection numbers of twisted cocycles arise in mathematics in the field of algebraic geometry. Quite recently, they appeared in physics: Intersection numbers of twisted cocycles define a scalar product on the vector space of Feynman integrals. With this application, the practical and efficient computation of intersection numbers of twisted cocycles becomes a topic of interest. An existing algorithm for the computation of intersection numbers of twisted cocycles requires in intermediate steps the introduction of algebraic extensions (for example square roots), although the final result may be expressed without algebraic extensions. In this article I present an improvement of this algorithm, which avoids algebraic extensions.
