Power


给出关于 次幂.

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  • 数学函数,同时适合符号和数值运算.
  • 对形如 的可能的根给出精确的有理数结果.
  • 对于复数 Power 给出 的主值. »
  • 仅当 是一个整数时, 自动转换为 .
  • 仅当 是一个整数时, 自动转换为 .
  • 对某些特定参数,Power 自动运算出精确值.
  • Power 可求任意数值精度的值.
  • Power 自动线性作用于列表.
  • Power[x,y] 在复平面 上,对于定义域从 到0的非整数 有一个分支线间断.
  • Power[x,y,z,] 被视为 Power[x,Power[y,z,]].

背景
背景

  • Power is a mathematical function that raises an expression to a given power. The expression Power[x,y] is commonly represented using the shorthand syntax or written in 2D typeset form as . A number to the first power is equal to itself (), and 1 to any complex power is equal to 1 (). The inverse of a power function is given by Log, so solving the equation for b gives a principal solution of b=.
  • The operation of taking an expression to the second power is known as squaring and the operation of taking an expression to the third power is known as cubing. The rules for combining quantities containing powers are called the exponent laws, and the process of raising a base to a given power is known as exponentiation. Many expressions involving Power, Exp, Log, and related functions are automatically simplified, or else may be simplified using Simplify or FullSimplify. PowerExpand can be used to do formal expansion and associated simplification, and ExpToTrig can be used to get trigonometric forms of Power expressions.
  • The function Sqrt[x] is represented using Power[x,1/2]. Exponentiation using the base of the natural logarithm E can be input as Exp[x] but is represented using Power[E,x].
  • Power[x,y] has a branch cut discontinuity for y running from to 0 in the complex x plane for noninteger y. Because of this branch cut, Power[x,1/n] returns a complex root by default instead of the real one for negative real x and odd positive n. To obtain a real-valued n^(th) root, Surd[x,n] can be used. The special case CubeRoot[x] corresponds to Surd[x,3].
1988年引入
(1.0)