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本模板可以计算任意複數算術平方根或第一個非1的n次单位根

找出數字的平方根,表達式為:
{{root|數字}}
找出數字的n次方根,表達式為:
{{root|number|n}}

本模板的輸入值可以是任一複數(包含實數負數虛數

Examples:

  • {{root|0.000001}} gives 0.001
  • {{root|0.0001}} gives 0.01
  • {{root|0.81}} gives 0.9
  • {{root|2}} gives 1.4142135623731
  • {{root|25}} gives 5
  • {{root|27|3}} gives 3
  • {{root|256|4}} gives 4
  • {{root|-1}} gives i (result if answer is not a real number)
  • {{root|-4}} gives 2i
  • {{root|-7}} gives 2.6457513110646i
  • {{root|i}} gives 0.70710678118655+0.70710678118655i[1]
  • {{root|pi}} gives 1.7724538509055(OEIS中的数列A002161
  • {{root|e}} gives 1.6487212707001(OEIS中的数列A019774
  • {{root|i|-i}} gives 0.20787957635076(OEIS中的数列A049006
  • {{root|-6|-3}} gives 0.27516060407455-0.47659214649847i[2]
  • {{root|5|7/5}} gives 3.1569251777946
  • {{root|2/7|7/3}} gives 0.58455850144128
  • {{root|-2|1/3}} gives -8
  • {{root|-2/9|1/3}} gives -0.010973936899863
  • {{root|{{root|2|1/3}}|2}} gives 2.8284271247462
  • {{root|3|{{root|3|2}}}} gives 1.8856717068806
  • {{root|{{root|3|2}}|{{root|3|2}}}} gives 1.3731976212041

本模板也可以透過指定number class來支援其他數字,如四元數

  • {{root| j+k |number class=四元數}} gives 0.84089641525371+0.59460355750136j+0.59460355750136k[3]
  • {{root|1+2i+3j+4k | 4+3i+2j+k|number class=四元數}} gives 1.4191927056231-0.20671979310212i+0.10820151725293j+0.054100758626467k[4]

See also[编辑]

  • {{Radic}}:不含求值的多次方根模板
  • {{Sqrt}}:專門用於表示平方根的模板,但不含求值功能

註釋[编辑]

  1. ^ 已由Mathematica驗算,代碼為N[Sqrt[I],14],結果為0.70710678118655 + 0.70710678118655 I
  2. ^ 已由Mathematica驗算,代碼為N[(-6)^(1/(-3)), 14],結果為0.27516060407455 - 0.47659214649847 I
  3. ^ 已由Mathematica驗算,代碼為<< Quaternions`;MyPow[p_, q_] := Exp[q ** Log[p]];N[MyPow[Quaternion[0, 0, 1, 1], Quaternion[1/2, 0, 0, 0]], 14],結果為Quaternion[0.84089641525371, 0, 0.59460355750136, 0.59460355750136]
  4. ^ 已由Mathematica驗算,代碼為<< Quaternions`;MyPow[p_, q_] := Exp[q ** Log[p]];N[MyPow[Quaternion[1, 2, 3, 4], Quaternion[4, 3, 2, 1]^-1], 14],結果為Quaternion[1.4191927056231, -0.20671979310212, 0.10820151725293, 0.054100758626467]