We introduce a primitive computation problem in the free tridendriform algebra generated by one element which is a Hopf algebra based on Schroeder trees. We know a complex way to generate all of them. To understand it clearer, we want to implement this method on a computer. However, we need to create some tools to implement Schroeder trees and the multiplications over this algebra to be able to compute the primitive elements. We also checked numerically that they are all primitive elements. In this paper, we detail how we made the problem mathematically understandable for a computer and how we implement it.

翻译：我们在由一个元素生成的自由三叉衍生代数中引入了一个原始元计算问题，该代数是基于施罗德树的Hopf代数。我们已知一种生成所有原始元的复杂方法。为了更清晰地理解该方法，我们希望在计算机上实现这一算法。然而，我们需要创建一些工具来实现施罗德树以及该代数上的乘法运算，从而能够计算原始元。我们还通过数值验证确认它们均为原始元。本文详细阐述了如何将这一问题转化为计算机可理解的数学形式，以及具体的实现过程。