主观几何中一组余弦定律方程的解

Solution of Simultaneous Equations of Cosine Law Arising from Subjectivity Geometry

本文讨论在主观几何应用例子中出现的由余弦定理建立的一组六元二次带根式的代数方程的解.应用隐函数存在定理,本文证明这组方程存在有唯一的实解.把求解问题转化为无约束非线性优化问题,可以用已知的诸法来求解.文中给出了用下降法求解的数值例子.

This paper discusses the solution of a group of two-order, six-element rooted algebraic simultaneous equations Setup by cosine law arising from the application example of subjectivity geometry[1]. By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations. Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods. A numerical example by descent method is given.