变量间依赖关系的计算机自动推理机器证明方法及其应用

给出机器证明原理在微分情形和一些力学问题中的应用．引进保持性质的导数的形式记号，建立了微分方程变量间依赖关系的自动推理的机械化证明原理，从而方程间的变换（如Ｂａｃｋｌｕｎｄ变换等）均可机械地验证．并具体给出该方法在：弹性力学控制方程的自动推理；（ＰＫＰ）方程的Ｂａｃｋｌｕｎｄ变换的正确性的机械化验证及各向异性弹力中的不变量的自动推理中的应用并用计算机代数系统实现了其运算．给出了计算机判断和推导方程变量间内在关系的计算机代数方法．

Mechanic Proving Method in Computer Automatic Reasoning of Relations Among Variables and Its Applications

New applications of mechanic proving principle in differential field and some mechanic problems are given.Introduced formal notations of derivative which keep the properties of derivative and their operations are easily realized on computer,A mechanization proving principle of automatic reasoning of transformations between differential equations is built.And following topics:Automatically reasoning control equations of elasticity;Mechanization verifying of correctness of Transformations between differential equations,such as Backlund transformation and Stiffness (flexibility) Invariance of Aeolotropy material are studied by using the principle.This technique may provide a new computer algebra way for studying the inherent link among variables in Mechanics problems.