↦ (maps to)

Creates a function.

Syntax

• x1[, x2[, ...]] ↦ expr

  • x1, x2, ... are symbols

  • expr is an expression optionally containing any of the symbols x1, x2, ...

Description

The ↦ operator creates a function. Its left operand is a comma-separated list of function arguments; all these are symbols that must be valid variable names. The right-hand side is an expression that may contain zero or more of these symbols. These symbols take precedence over any other symbol already defined with the same name.

The ↦ operator is implemented by the CreateFunction function.

Examples

f ≔ n ↦ n^2 + 1

custom function

f(21)

442

SequenceVector(10) @ f

(2, 5, 10, 17, 26, 37, 50, 65, 82, 101)

SequenceVector(10) @ (n ↦ n^n)

(1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 10000000000)

a ≔ (m, n) ↦ m^2 + 3⋅m⋅n − 2⋅n

custom function

a(3, 2)

23

A function may construct and return a function:

adder ≔ n ↦ (x ↦ x+n)

custom function

AddFive ≔ adder(5)

custom function

AddFive(394)

399

A custom plotter:

p ≔ f ↦ (
  grph ≔ plot(y = f(x));
  AdjustVisual(
    grph,
    "point size": 4,
    "fill color": "steelblue",
    "line width": 0,
    "window width": 400,
    "window height": 300
  )
);
p(sin)

p(cos)

See also

• CreateFunction