论文标题
一种简单的方法，用于计算基本功能方面的某些伪椭圆形积分
A Simple Method for Computing Some Pseudo-Elliptic Integrals in Terms of Elementary Functions
论文作者
论文摘要
我们介绍了一种根据基本函数计算一些伪椭圆积分的方法。与Risch-Trager-Bronstein算法的代数情况相比，该方法简单而快速。该方法可以快速解决许多伪涡流积分，其他众所周知的计算机代数系统要么失败，要么在特殊功能方面返回答案，要么需要超过20秒的计算时间。随机测试表明，我们的方法解决了73.4％的积分，这些积分可以通过Risch-Trager-Bronstein算法的最佳实现来解决。与Risch，Davenport，Trager，Bronstein和Miller的象征性集成算法不同。我们的方法不是决策过程。该方法的实现少于200行Mathematica代码，并且可以轻松移植到可以求解多项式方程系统的其他CAS。
We introduce a method for computing some pseudo-elliptic integrals in terms of elementary functions. The method is simple and fast in comparison to the algebraic case of the Risch-Trager-Bronstein algorithm. This method can quickly solve many pseudo-elliptic integrals, which other well-known computer algebra systems either fail, return an answer in terms of special functions, or require more than 20 seconds of computing time. Randomised tests showed our method solved 73.4% of the integrals that could be solved with the best implementation of the Risch-Trager-Bronstein algorithm. Unlike the symbolic integration algorithms of Risch, Davenport, Trager, Bronstein and Miller; our method is not a decision process. The implementation of this method is less than 200 lines of Mathematica code and can be easily ported to other CAS that can solve systems of polynomial equations.
