↦ (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.

If the left-hand side contains multiple symbols, it must be surrounded by parentheses.

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