再谈不等式自动发现与判定程序agl2010的改进和应用

A Revisit of Automatically Finding of Inequalities and Its Applications

对不等式自动发现与判定程序agl2010的功能进行了若干改进,通过15个具体实例演示了程序的强大功能;利用agl算法得到了一类三角形几何不等式最佳系数的估算方法;结合Bottema软件的xprove命令,得到了一种带约束条件不等式自动发现的设计方案;通过建立数据限制函数,实现了一类变元取值范围受限制条件不等式的自动发现和自动加强,从而拓展了包括Fan Ky不等式在内的一大批不等式类型;最后提出2个有趣的不等式问题.

Improvements have been made to programs of automatic finding and discrimination of inequalities. The powerful functions have been demonstrated in 15 practical examples. The estimation methods for finding optimized coefficients of a class of triangular inequalities are achieved by using agl algorithms. An approach for automatically finding constrained inequalities is also achieved by incorporating xprove in Bottema. The automatic finding of a class of inequalities with constrained range of input variables is realized by constructing data-constrained functions. A number of inequalities including Fan Ky inequality have been built and 2 intriguing problems of inequalities have also been raised.