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Operate

  • Operate[ p , f [ x , y ]] gives p [ f ][ x , y ].
  • Operate[ p , expr , n ] applies p at level n in the head of expr.
  • Examples: Operate[p, f[x,y]]; Operate[p, f[x][y][z], 1]; Operate[p, f[x][y][z], 2].
  • Operate[ p , f [ x ]] effectively applies the functional operator p to the function f.
  • Operate is essentially a generalization of Apply, which allows you to apply an operator to the head of an expression, rather than simply to replace the head.
  • See the Mathematica book: Section 2.2.9.
  • See also: Through, Apply, Heads.