论文标题
关于算术进程中的分区编号与ETA商相关的分区编号的计算：RADU算法的实现
On the Computation of Identities Relating Partition Numbers in Arithmetic Progressions with Eta Quotients: An Implementation of Radu's Algorithm
论文作者
论文摘要
2015年，Cristian-Silviu Radu设计了一种算法，以检测Ramanujan和Kolberg研究的类别的身份。该课程包括Ramanujan的著名身份，该身份为$ P（5n+4），$ P（7n+5）$的划分属性提供了见证。我们使用Mathematica提供了该算法的实现。首先描述了基本理论，并简要介绍了该算法的轮廓，以描述包装的功能和效用。此后，我们为分区理论中最近的工作提供了多个示例。在许多情况下，我们使用包裹来得出各种身份或一致性的替代证明；在其他情况下，我们改善了先前确定的身份，至少在一种情况下，我们已经确认了常规猜想。
In 2015 Cristian-Silviu Radu designed an algorithm to detect identities of a class studied by Ramanujan and Kolberg. This class includes the famous identities by Ramanujan which provide a witness to the divisibility properties of $p(5n+4),$ $p(7n+5)$. We give an implementation of this algorithm using Mathematica. The basic theory is first described, and an outline of the algorithm is briefly given, in order to describe the functionality and utility of our package. We thereafter give multiple examples of applications to recent work in partition theory. In many cases we have used our package to derive alternate proofs of various identities or congruences; in other cases we have improved previously established identities, and in at least one case we have confirmed a standing conjecture.
