Napier筹

Napier筹是一种计算工具, 可以用来计算乘法. 这里我倒不是为了专门说明或演示Napier筹, 而是为了测试SMathML的表达能力.

$$\begin{array}{ccccccccc}\cancel{\begin{array}{|cc|}\hline 0& \\ & 1\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 3\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 7\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 9\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 8\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 3\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 9\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 1\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 7\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 6\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 5\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 5& \\ & 4\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 7\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 1\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 9\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 5& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 6& \\ & 3\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 5& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 6& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 7& \\ & 2\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 0& \\ & 9\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 7\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 5& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 6& \\ & 3\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 7& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 8& \\ & 1\\ \hline\end{array}}\end{array}$$ 这是一个完整的Napier筹表.

$$\begin{array}{ccccc}\cancel{\begin{array}{|cc|}\hline 3& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 4\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 5& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 6\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 6& \\ & 3\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 1\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 7\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 7& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 4& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 8\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 4& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 0\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 5\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 5\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 2& \\ & 7\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 8\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 1& \\ & 2\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 9\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 3\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 8& \\ & 1\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 5& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 7\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 9\\ \hline\end{array}}\\ \cancel{\begin{array}{|cc|}\hline 8& \\ & 1\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 5& \\ & 4\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 3& \\ & 6\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 2& \\ & 7\\ \hline\end{array}}& \cancel{\begin{array}{|cc|}\hline 0& \\ & 9\\ \hline\end{array}}\end{array}$$ $$46785399\times 96431=4511562810969$$