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以波利亚计数定理作为算法的基础,运用数学软件MATLAB及Maple快速、准确实现一元取代烷烃的平面与立体同分异构体数目的计算。同时对波利亚论文中的一些推论进行数值模拟验证,试验模拟表明波利亚的推论:(1)c_1=(B_n)/(B_(n+1))≈0.355、c_2=(D_n)/(D_(n+1))≈0.305;(2)正确。最后通过MATLAB直线拟合给出可以快速推算B_n以及D_n的相对准确的简单公式。
Taking Polygon counting theorem as the basis of the algorithm, mathematical and software MATLAB and Maple are used to calculate the number of planar and stereoisomers of monosubstituted alkanes quickly and accurately. At the same time, some inferences of Boloniae papers are verified by numerical simulation. The experimental simulation shows that Bolonia’s deduction: (1) c_1 = (B_n) / (B_ (n + 1)) ≈0.355 and c_2 = (D_n) (D_ (n + 1)) ≈0.305; (2) Correct. Finally, a simple and straightforward formula that can calculate B_n and D_n quickly is given by MATLAB linear fitting.