论文标题
计算平面多项式矢量场的Liouvillian第一积分的有效方法
An Efficient Method for Computing Liouvillian First Integrals of Planar Polynomial Vector Fields
论文作者
论文摘要
在这里，我们提出了一种计算平面中多项式矢量场的Darboux多项式的有效方法。这种方法是列出的多项式向量字段，呈现出Liouvillian第一积分（或等效地，与呈现Liouvillian通用解决方案的理性一阶微分方程（合理1odes）相同）。获得此方法的关键是将求解由方程式导致的（非线性）代数系统的过程将其转化为Darboux多项式存在的条件为可行的Steos（需要较少的存储器消耗的过程）。我们还对开发的算法进行了简短的性能分析。
Here we present an efficient method to compute Darboux polynomials for polynomial vector fields in the plane. This approach is restricetd to polynomial vector fields presenting a Liouvillian first integral (or, equivalently, to rational first order differential equations (rational 1ODEs) presenting a Liouvillian general solution). The key to obtaining this method was to separate the procedure of solving the (nonlinear) algebraic systems resulting from the equation that translates the condition of existence of a Darboux polynomial into feasible steos (procedures that requires less memory consumption). We also present a brief performance analysis of the algorithms developed.
