论文标题
代数函数的严格数值集成
Rigorous numerical integration of algebraic functions
论文作者
论文摘要
我们提出了一种算法，该算法使用富士的不等式来绑定某种类型椭圆的代数函数，从而使我们能够在线段上具体实施严格的高斯 - leguss-legendre集成方法，以实现代数函数。我们考虑了路径分裂策略以改善该方法的收敛性，并表明这些策略具有显着的实用和渐近益处。我们实施了这些方法来计算代数riemann表面的周期矩阵，这些方法在Sagemath中可用。
We present an algorithm which uses Fujiwara's inequality to bound algebraic functions over ellipses of a certain type, allowing us to concretely implement a rigorous Gauss-Legendre integration method for algebraic functions over a line segment. We consider path splitting strategies to improve convergence of the method and show that these yield significant practical and asymptotic benefits. We implemented these methods to compute period matrices of algebraic Riemann surfaces and these are available in SageMath.
