模組:沙盒/a2569875/NumberTest2维基百科,自由的 encyclopedia 更多信息 代數, 維度 ... 凯莱-迪克森代數特性 代數 維度 有序 乘法性質 非平凡零因子 交換 結合 交錯 冪結合 實數 1 是 是 是 是 是 無 複數 2 否 是 是 是 是 無 四元數 4 否 否 是 是 是 無 八元數 8 否 否 否 是 是 無 十六元數 16 否 否 否 否 是 有 ≥ 32 关闭更多信息 , ... × {\displaystyle \times } e 0 {\displaystyle e_{0}} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 8 {\displaystyle e_{8}} e 9 {\displaystyle e_{9}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} e 0 {\displaystyle e_{0}} 1 {\displaystyle 1} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 8 {\displaystyle e_{8}} e 9 {\displaystyle e_{9}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} e 1 {\displaystyle e_{1}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} e 3 {\displaystyle e_{3}} − e 2 {\displaystyle -e_{2}} e 5 {\displaystyle e_{5}} − e 4 {\displaystyle -e_{4}} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} e 9 {\displaystyle e_{9}} − e 8 {\displaystyle -e_{8}} − e 11 {\displaystyle -e_{11}} e 10 {\displaystyle e_{10}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} e 2 {\displaystyle e_{2}} e 2 {\displaystyle e_{2}} − e 3 {\displaystyle -e_{3}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} − e 4 {\displaystyle -e_{4}} − e 5 {\displaystyle -e_{5}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} − e 8 {\displaystyle -e_{8}} − e 9 {\displaystyle -e_{9}} − e 14 {\displaystyle -e_{14}} − e 15 {\displaystyle -e_{15}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 3 {\displaystyle e_{3}} e 3 {\displaystyle e_{3}} e 2 {\displaystyle e_{2}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 5 {\displaystyle e_{5}} − e 4 {\displaystyle -e_{4}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} e 9 {\displaystyle e_{9}} − e 8 {\displaystyle -e_{8}} − e 15 {\displaystyle -e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} e 4 {\displaystyle e_{4}} e 4 {\displaystyle e_{4}} − e 5 {\displaystyle -e_{5}} − e 6 {\displaystyle -e_{6}} − e 7 {\displaystyle -e_{7}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} − e 8 {\displaystyle -e_{8}} − e 9 {\displaystyle -e_{9}} − e 10 {\displaystyle -e_{10}} − e 11 {\displaystyle -e_{11}} e 5 {\displaystyle e_{5}} e 5 {\displaystyle e_{5}} e 4 {\displaystyle e_{4}} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} − e 3 {\displaystyle -e_{3}} e 2 {\displaystyle e_{2}} e 13 {\displaystyle e_{13}} − e 12 {\displaystyle -e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} e 9 {\displaystyle e_{9}} − e 8 {\displaystyle -e_{8}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} e 6 {\displaystyle e_{6}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 4 {\displaystyle e_{4}} − e 5 {\displaystyle -e_{5}} − e 2 {\displaystyle -e_{2}} e 3 {\displaystyle e_{3}} − 1 {\displaystyle -1} − e 1 {\displaystyle -e_{1}} e 14 {\displaystyle e_{14}} − e 15 {\displaystyle -e_{15}} − e 12 {\displaystyle -e_{12}} e 13 {\displaystyle e_{13}} e 10 {\displaystyle e_{10}} − e 11 {\displaystyle -e_{11}} − e 8 {\displaystyle -e_{8}} e 9 {\displaystyle e_{9}} e 7 {\displaystyle e_{7}} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 5 {\displaystyle e_{5}} e 4 {\displaystyle e_{4}} − e 3 {\displaystyle -e_{3}} − e 2 {\displaystyle -e_{2}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} e 15 {\displaystyle e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} − e 12 {\displaystyle -e_{12}} e 11 {\displaystyle e_{11}} e 10 {\displaystyle e_{10}} − e 9 {\displaystyle -e_{9}} − e 8 {\displaystyle -e_{8}} e 8 {\displaystyle e_{8}} e 8 {\displaystyle e_{8}} − e 9 {\displaystyle -e_{9}} − e 10 {\displaystyle -e_{10}} − e 11 {\displaystyle -e_{11}} − e 12 {\displaystyle -e_{12}} − e 13 {\displaystyle -e_{13}} − e 14 {\displaystyle -e_{14}} − e 15 {\displaystyle -e_{15}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 9 {\displaystyle e_{9}} e 9 {\displaystyle e_{9}} e 8 {\displaystyle e_{8}} − e 11 {\displaystyle -e_{11}} e 10 {\displaystyle e_{10}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} − e 3 {\displaystyle -e_{3}} e 2 {\displaystyle e_{2}} − e 5 {\displaystyle -e_{5}} e 4 {\displaystyle e_{4}} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 10 {\displaystyle e_{10}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} e 8 {\displaystyle e_{8}} − e 9 {\displaystyle -e_{9}} − e 14 {\displaystyle -e_{14}} − e 15 {\displaystyle -e_{15}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} − e 2 {\displaystyle -e_{2}} e 3 {\displaystyle e_{3}} − 1 {\displaystyle -1} − e 1 {\displaystyle -e_{1}} − e 6 {\displaystyle -e_{6}} − e 7 {\displaystyle -e_{7}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 11 {\displaystyle e_{11}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} e 9 {\displaystyle e_{9}} e 8 {\displaystyle e_{8}} − e 15 {\displaystyle -e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} − e 3 {\displaystyle -e_{3}} − e 2 {\displaystyle -e_{2}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} − e 5 {\displaystyle -e_{5}} e 4 {\displaystyle e_{4}} e 12 {\displaystyle e_{12}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} e 8 {\displaystyle e_{8}} − e 9 {\displaystyle -e_{9}} − e 10 {\displaystyle -e_{10}} − e 11 {\displaystyle -e_{11}} − e 4 {\displaystyle -e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} − 1 {\displaystyle -1} − e 1 {\displaystyle -e_{1}} − e 2 {\displaystyle -e_{2}} − e 3 {\displaystyle -e_{3}} e 13 {\displaystyle e_{13}} e 13 {\displaystyle e_{13}} − e 12 {\displaystyle -e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} e 9 {\displaystyle e_{9}} e 8 {\displaystyle e_{8}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} − e 5 {\displaystyle -e_{5}} − e 4 {\displaystyle -e_{4}} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} e 3 {\displaystyle e_{3}} − e 2 {\displaystyle -e_{2}} e 14 {\displaystyle e_{14}} e 14 {\displaystyle e_{14}} − e 15 {\displaystyle -e_{15}} − e 12 {\displaystyle -e_{12}} e 13 {\displaystyle e_{13}} e 10 {\displaystyle e_{10}} − e 11 {\displaystyle -e_{11}} e 8 {\displaystyle e_{8}} e 9 {\displaystyle e_{9}} − e 6 {\displaystyle -e_{6}} − e 7 {\displaystyle -e_{7}} − e 4 {\displaystyle -e_{4}} e 5 {\displaystyle e_{5}} e 2 {\displaystyle e_{2}} − e 3 {\displaystyle -e_{3}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 15 {\displaystyle e_{15}} e 15 {\displaystyle e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} − e 12 {\displaystyle -e_{12}} e 11 {\displaystyle e_{11}} e 10 {\displaystyle e_{10}} − e 9 {\displaystyle -e_{9}} e 8 {\displaystyle e_{8}} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} − e 5 {\displaystyle -e_{5}} − e 4 {\displaystyle -e_{4}} e 3 {\displaystyle e_{3}} e 2 {\displaystyle e_{2}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} 关闭 模块文档[查看] [编辑] [历史] [清除缓存] 八元數代凯莱-迪克森结构構成 e 3 + e 10 + e 6 − e 15 = e 3 + e 6 + e 10 − e 15 {\displaystyle {{{\,e_{3}}+{\,e_{10}}}+{{\,e_{6}}-{\,e_{15}}}}=e_{3}+e_{6}+e_{10}-e_{15}} e 3 + e 10 − e 6 − e 15 = e 3 − e 6 + e 10 + e 15 {\displaystyle {{{\,e_{3}}+{\,e_{10}}}-{{\,e_{6}}-{\,e_{15}}}}=e_{3}-e_{6}+e_{10}+e_{15}} ( e 3 + e 10 ) × ( e 6 − e 15 ) = 0 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}\times {\left({{\,e_{6}}-{\,e_{15}}}\right)}}=0} e 3 + e 10 e 6 − e 15 = 0 {\displaystyle {\frac {{\,e_{3}}+{\,e_{10}}}{{\,e_{6}}-{\,e_{15}}}}=0} ( e 3 + e 10 ) e 6 − e 15 = 0.88227210676109 + 0.33286328246845 e 6 − 0.33286328246845 e 15 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}^{{\,e_{6}}-{\,e_{15}}}}=0.88227210676109+0.33286328246845e_{6}-0.33286328246845e_{15}} ( e 6 − e 15 ) − 1 = − 0.5 e 6 + 0.5 e 15 {\displaystyle \left({{\,e_{6}}-{\,e_{15}}}\right)^{-1}=-0.5e_{6}+0.5e_{15}} ( e 3 + e 10 ) × ( e 6 − e 15 ) − 1 = 0 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}\times {\left({{\,e_{6}}-{\,e_{15}}}\right)^{-1}}}=0} ( e 6 − e 15 ) − 1 × ( e 3 + e 10 ) = 0 {\displaystyle {{\left({{\,e_{6}}-{\,e_{15}}}\right)^{-1}}\times {\left({{\,e_{3}}+{\,e_{10}}}\right)}}=0} ( e 3 + e 10 ) × ( e 6 + e 15 ) = 2 e 5 + 2 e 12 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}\times {\left({{\,e_{6}}+{\,e_{15}}}\right)}}=2e_{5}+2e_{12}} 上述文档嵌入自Module:沙盒/a2569875/NumberTest2/doc。 (编辑 | 历史)编者可以在本模块的沙盒 (创建 | 镜像)和测试样例 (创建)页面进行实验。本模块的子页面。 local p={} return p
更多信息 代數, 維度 ... 凯莱-迪克森代數特性 代數 維度 有序 乘法性質 非平凡零因子 交換 結合 交錯 冪結合 實數 1 是 是 是 是 是 無 複數 2 否 是 是 是 是 無 四元數 4 否 否 是 是 是 無 八元數 8 否 否 否 是 是 無 十六元數 16 否 否 否 否 是 有 ≥ 32 关闭更多信息 , ... × {\displaystyle \times } e 0 {\displaystyle e_{0}} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 8 {\displaystyle e_{8}} e 9 {\displaystyle e_{9}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} e 0 {\displaystyle e_{0}} 1 {\displaystyle 1} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 8 {\displaystyle e_{8}} e 9 {\displaystyle e_{9}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} e 1 {\displaystyle e_{1}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} e 3 {\displaystyle e_{3}} − e 2 {\displaystyle -e_{2}} e 5 {\displaystyle e_{5}} − e 4 {\displaystyle -e_{4}} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} e 9 {\displaystyle e_{9}} − e 8 {\displaystyle -e_{8}} − e 11 {\displaystyle -e_{11}} e 10 {\displaystyle e_{10}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} e 2 {\displaystyle e_{2}} e 2 {\displaystyle e_{2}} − e 3 {\displaystyle -e_{3}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} − e 4 {\displaystyle -e_{4}} − e 5 {\displaystyle -e_{5}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} − e 8 {\displaystyle -e_{8}} − e 9 {\displaystyle -e_{9}} − e 14 {\displaystyle -e_{14}} − e 15 {\displaystyle -e_{15}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 3 {\displaystyle e_{3}} e 3 {\displaystyle e_{3}} e 2 {\displaystyle e_{2}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 5 {\displaystyle e_{5}} − e 4 {\displaystyle -e_{4}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} e 9 {\displaystyle e_{9}} − e 8 {\displaystyle -e_{8}} − e 15 {\displaystyle -e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} e 4 {\displaystyle e_{4}} e 4 {\displaystyle e_{4}} − e 5 {\displaystyle -e_{5}} − e 6 {\displaystyle -e_{6}} − e 7 {\displaystyle -e_{7}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} − e 8 {\displaystyle -e_{8}} − e 9 {\displaystyle -e_{9}} − e 10 {\displaystyle -e_{10}} − e 11 {\displaystyle -e_{11}} e 5 {\displaystyle e_{5}} e 5 {\displaystyle e_{5}} e 4 {\displaystyle e_{4}} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} − e 3 {\displaystyle -e_{3}} e 2 {\displaystyle e_{2}} e 13 {\displaystyle e_{13}} − e 12 {\displaystyle -e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} e 9 {\displaystyle e_{9}} − e 8 {\displaystyle -e_{8}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} e 6 {\displaystyle e_{6}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 4 {\displaystyle e_{4}} − e 5 {\displaystyle -e_{5}} − e 2 {\displaystyle -e_{2}} e 3 {\displaystyle e_{3}} − 1 {\displaystyle -1} − e 1 {\displaystyle -e_{1}} e 14 {\displaystyle e_{14}} − e 15 {\displaystyle -e_{15}} − e 12 {\displaystyle -e_{12}} e 13 {\displaystyle e_{13}} e 10 {\displaystyle e_{10}} − e 11 {\displaystyle -e_{11}} − e 8 {\displaystyle -e_{8}} e 9 {\displaystyle e_{9}} e 7 {\displaystyle e_{7}} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 5 {\displaystyle e_{5}} e 4 {\displaystyle e_{4}} − e 3 {\displaystyle -e_{3}} − e 2 {\displaystyle -e_{2}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} e 15 {\displaystyle e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} − e 12 {\displaystyle -e_{12}} e 11 {\displaystyle e_{11}} e 10 {\displaystyle e_{10}} − e 9 {\displaystyle -e_{9}} − e 8 {\displaystyle -e_{8}} e 8 {\displaystyle e_{8}} e 8 {\displaystyle e_{8}} − e 9 {\displaystyle -e_{9}} − e 10 {\displaystyle -e_{10}} − e 11 {\displaystyle -e_{11}} − e 12 {\displaystyle -e_{12}} − e 13 {\displaystyle -e_{13}} − e 14 {\displaystyle -e_{14}} − e 15 {\displaystyle -e_{15}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 2 {\displaystyle e_{2}} e 3 {\displaystyle e_{3}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} e 9 {\displaystyle e_{9}} e 9 {\displaystyle e_{9}} e 8 {\displaystyle e_{8}} − e 11 {\displaystyle -e_{11}} e 10 {\displaystyle e_{10}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} − e 3 {\displaystyle -e_{3}} e 2 {\displaystyle e_{2}} − e 5 {\displaystyle -e_{5}} e 4 {\displaystyle e_{4}} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 10 {\displaystyle e_{10}} e 10 {\displaystyle e_{10}} e 11 {\displaystyle e_{11}} e 8 {\displaystyle e_{8}} − e 9 {\displaystyle -e_{9}} − e 14 {\displaystyle -e_{14}} − e 15 {\displaystyle -e_{15}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} − e 2 {\displaystyle -e_{2}} e 3 {\displaystyle e_{3}} − 1 {\displaystyle -1} − e 1 {\displaystyle -e_{1}} − e 6 {\displaystyle -e_{6}} − e 7 {\displaystyle -e_{7}} e 4 {\displaystyle e_{4}} e 5 {\displaystyle e_{5}} e 11 {\displaystyle e_{11}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} e 9 {\displaystyle e_{9}} e 8 {\displaystyle e_{8}} − e 15 {\displaystyle -e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} e 12 {\displaystyle e_{12}} − e 3 {\displaystyle -e_{3}} − e 2 {\displaystyle -e_{2}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} − e 5 {\displaystyle -e_{5}} e 4 {\displaystyle e_{4}} e 12 {\displaystyle e_{12}} e 12 {\displaystyle e_{12}} e 13 {\displaystyle e_{13}} e 14 {\displaystyle e_{14}} e 15 {\displaystyle e_{15}} e 8 {\displaystyle e_{8}} − e 9 {\displaystyle -e_{9}} − e 10 {\displaystyle -e_{10}} − e 11 {\displaystyle -e_{11}} − e 4 {\displaystyle -e_{4}} e 5 {\displaystyle e_{5}} e 6 {\displaystyle e_{6}} e 7 {\displaystyle e_{7}} − 1 {\displaystyle -1} − e 1 {\displaystyle -e_{1}} − e 2 {\displaystyle -e_{2}} − e 3 {\displaystyle -e_{3}} e 13 {\displaystyle e_{13}} e 13 {\displaystyle e_{13}} − e 12 {\displaystyle -e_{12}} e 15 {\displaystyle e_{15}} − e 14 {\displaystyle -e_{14}} e 9 {\displaystyle e_{9}} e 8 {\displaystyle e_{8}} e 11 {\displaystyle e_{11}} − e 10 {\displaystyle -e_{10}} − e 5 {\displaystyle -e_{5}} − e 4 {\displaystyle -e_{4}} e 7 {\displaystyle e_{7}} − e 6 {\displaystyle -e_{6}} e 1 {\displaystyle e_{1}} − 1 {\displaystyle -1} e 3 {\displaystyle e_{3}} − e 2 {\displaystyle -e_{2}} e 14 {\displaystyle e_{14}} e 14 {\displaystyle e_{14}} − e 15 {\displaystyle -e_{15}} − e 12 {\displaystyle -e_{12}} e 13 {\displaystyle e_{13}} e 10 {\displaystyle e_{10}} − e 11 {\displaystyle -e_{11}} e 8 {\displaystyle e_{8}} e 9 {\displaystyle e_{9}} − e 6 {\displaystyle -e_{6}} − e 7 {\displaystyle -e_{7}} − e 4 {\displaystyle -e_{4}} e 5 {\displaystyle e_{5}} e 2 {\displaystyle e_{2}} − e 3 {\displaystyle -e_{3}} − 1 {\displaystyle -1} e 1 {\displaystyle e_{1}} e 15 {\displaystyle e_{15}} e 15 {\displaystyle e_{15}} e 14 {\displaystyle e_{14}} − e 13 {\displaystyle -e_{13}} − e 12 {\displaystyle -e_{12}} e 11 {\displaystyle e_{11}} e 10 {\displaystyle e_{10}} − e 9 {\displaystyle -e_{9}} e 8 {\displaystyle e_{8}} − e 7 {\displaystyle -e_{7}} e 6 {\displaystyle e_{6}} − e 5 {\displaystyle -e_{5}} − e 4 {\displaystyle -e_{4}} e 3 {\displaystyle e_{3}} e 2 {\displaystyle e_{2}} − e 1 {\displaystyle -e_{1}} − 1 {\displaystyle -1} 关闭 模块文档[查看] [编辑] [历史] [清除缓存] 八元數代凯莱-迪克森结构構成 e 3 + e 10 + e 6 − e 15 = e 3 + e 6 + e 10 − e 15 {\displaystyle {{{\,e_{3}}+{\,e_{10}}}+{{\,e_{6}}-{\,e_{15}}}}=e_{3}+e_{6}+e_{10}-e_{15}} e 3 + e 10 − e 6 − e 15 = e 3 − e 6 + e 10 + e 15 {\displaystyle {{{\,e_{3}}+{\,e_{10}}}-{{\,e_{6}}-{\,e_{15}}}}=e_{3}-e_{6}+e_{10}+e_{15}} ( e 3 + e 10 ) × ( e 6 − e 15 ) = 0 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}\times {\left({{\,e_{6}}-{\,e_{15}}}\right)}}=0} e 3 + e 10 e 6 − e 15 = 0 {\displaystyle {\frac {{\,e_{3}}+{\,e_{10}}}{{\,e_{6}}-{\,e_{15}}}}=0} ( e 3 + e 10 ) e 6 − e 15 = 0.88227210676109 + 0.33286328246845 e 6 − 0.33286328246845 e 15 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}^{{\,e_{6}}-{\,e_{15}}}}=0.88227210676109+0.33286328246845e_{6}-0.33286328246845e_{15}} ( e 6 − e 15 ) − 1 = − 0.5 e 6 + 0.5 e 15 {\displaystyle \left({{\,e_{6}}-{\,e_{15}}}\right)^{-1}=-0.5e_{6}+0.5e_{15}} ( e 3 + e 10 ) × ( e 6 − e 15 ) − 1 = 0 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}\times {\left({{\,e_{6}}-{\,e_{15}}}\right)^{-1}}}=0} ( e 6 − e 15 ) − 1 × ( e 3 + e 10 ) = 0 {\displaystyle {{\left({{\,e_{6}}-{\,e_{15}}}\right)^{-1}}\times {\left({{\,e_{3}}+{\,e_{10}}}\right)}}=0} ( e 3 + e 10 ) × ( e 6 + e 15 ) = 2 e 5 + 2 e 12 {\displaystyle {{\left({{\,e_{3}}+{\,e_{10}}}\right)}\times {\left({{\,e_{6}}+{\,e_{15}}}\right)}}=2e_{5}+2e_{12}} 上述文档嵌入自Module:沙盒/a2569875/NumberTest2/doc。 (编辑 | 历史)编者可以在本模块的沙盒 (创建 | 镜像)和测试样例 (创建)页面进行实验。本模块的子页面。 local p={} return p