imported>A2569875：A2569875已移動頁面Module:沙盒/a2569875/CayleyDickson/doc至Module:沙盒/a2569875/NumberTest2/doc，不留重新導向

2022-05-02T08:54:50Z

A2569875已移動頁面Module:沙盒/a2569875/CayleyDickson/doc至Module:沙盒/a2569875/NumberTest2/doc，不留重新導向

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{{NoteTA/MediaWiki}}
{{Documentation subpage}}
{| class="wikitable"
|+ [[凯莱-迪克森结构|凯莱-迪克森]]代數特性
|-
! rowspan=2|[[域上的代数|代數]]
! rowspan=2|[[向量空间的维数|維度]] !! rowspan=2|[[有序域|有序]] !! colspan=4|[[乘法]]性質 !! rowspan=2|非平凡<br>[[零因子]]
|-
! [[交換律|交換]] !! [[结合律|結合]] !! [[交错代数|交錯]] !! [[冪結合性|冪結合]]
|-
! [[實數]]
| style="text-align:center" | 1 || {{Yes}} || {{Yes}} || {{Yes}} || {{Yes}} || {{Yes}} || {{No|無}}
|-
! [[複數 (數學)|複數]]
| style="text-align:center" | 2 || {{No}} || {{Yes}} || {{Yes}} || {{Yes}} || {{Yes}} || {{No|無}}
|-
! [[四元數]]
| style="text-align:center" | 4 || {{No}} || {{No}} || {{Yes}} || {{Yes}} || {{Yes}} || {{No|無}}
|-
! [[八元數]]
| style="text-align:center" | 8 || {{No}} || {{No}} || {{No}} || {{Yes}} || {{Yes}} || {{No|無}}
|-
! [[十六元數]]
| style="text-align:center" | 16 || rowspan=2 {{No}} || rowspan=2 {{No}} || rowspan=2 {{No}} || rowspan=2 {{No}} || rowspan=2 {{Yes}} || rowspan=2 {{Yes|有}}
|-
!
| style="text-align:center" | ≥ 32
|}
*八元數代[[凯莱-迪克森结构]]構成
:{{計算結果|mathform((ele(3)+ele(10))+(ele(6)-ele(15)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform((ele(3)+ele(10))-(ele(6)-ele(15)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform((ele(3)+ele(10))*(ele(6)-ele(15)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform(div((ele(3)+ele(10)),(ele(6)-ele(15))))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform((ele(3)+ele(10))^(ele(6)-ele(15)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform(inverse(ele(6)-ele(15)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform((ele(3)+ele(10))*inverse(ele(6)-ele(15)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform(inverse(ele(6)-ele(15))*(ele(3)+ele(10)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
:{{計算結果|mathform((ele(3)+ele(10))*(ele(6)+ele(15)))|number class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath}}
{{乘法表
|table class = class="wikitable" style="text-align: center; margin:0.5em auto;"
|calculate = mathform({{{left}}} * {{{right}}})
|calculate title = <math>\times</math>
|first number list = ele(0),ele(1),ele(2),ele(3),ele(4),ele(5),ele(6),ele(7),ele(8),ele(9),ele(10),ele(11),ele(12),ele(13),ele(14),ele(15)
|second number list = ele(0),ele(1),ele(2),ele(3),ele(4),ele(5),ele(6),ele(7),ele(8),ele(9),ele(10),ele(11),ele(12),ele(13),ele(14),ele(15)
|first number show = e_{0}, e_{1}, e_{2}, e_{3}, e_{4}, e_{5}, e_{6}, e_{7}, e_{8}, e_{9}, e_{10}, e_{11}, e_{12}, e_{13}, e_{14}, e_{15}
|second number show = e_{0}, e_{1}, e_{2}, e_{3}, e_{4}, e_{5}, e_{6}, e_{7}, e_{8}, e_{9}, e_{10}, e_{11}, e_{12}, e_{13}, e_{14}, e_{15}
|class=Module:Complex_Number/CayleyDickson.cdmath=Module:Complex_Number/Octonion.omath
|number css = css
|use math=yes
}}

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Module:沙盒/a2569875/NumberTest2/doc - 版本历史

imported>A2569875：​A2569875已移動頁面Module:沙盒/a2569875/CayleyDickson/doc至Module:沙盒/a2569875/NumberTest2/doc，不留重新導向

imported>A2569875：A2569875已移動頁面Module:沙盒/a2569875/CayleyDickson/doc至Module:沙盒/a2569875/NumberTest2/doc，不留重新導向