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Apply

  • Apply[ f , expr ] or f @@ expr replaces the head of expr by f.
  • Apply[ f , expr , levelspec ] replaces heads in parts of expr specified by levelspec.
  • Examples: Apply[f, a, b, c ]; Apply[Plus, g[a, b]].
  • Level specifications are described in Section A.3.6.
  • The default value for levelspec in Apply is {0}.
  • Examples: Apply[f, a,b , c,d ].
  • Apply[f, a,b , c,d , 1 ].
  • Apply[f, a , -2].
  • See the Mathematica book: Section 1.8.11Section 2.2.3.
  • See also: Map, Scan, Level, Operate, MapThread.

    Further Examples

    This substitutes New for Old at the head of the expression using the shorthand notation for Apply. (Neither New nor Old has a built-in meaning in Mathematica.)

    In[1]:=

    Out[1]=

    The head of a product is Times; the head of a list is List. (You can see heads explicitly using FullForm[].)

    In[2]:=

    Out[2]=

    This changes a line into a polygon.

    In[3]:=

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    This constructs a list of circles from a list of pairs of centers and radii.

    In[4]:=

    Out[4]=