Applying Functions Video Version

It's very common to want to "map" a function over multiple expressions:

In[1]:=1

Map[f, {a, b, c, d}]

Out[1]=1

Notes for Python programmers:

Map in the Wolfram Language is like map in Python, except that it can operate on arbitrary expression trees of any depth.

/@ ("slash at") is a short notation for Map:

In[2]:=2

f /@ {a, b, c, d}

Out[2]=2

Notes for Java programmers:

Map in the Wolfram Language works similarly to the Stream.map method in Java, except that Map can be applied to any kind of expression.

This uses a pure function:

In[3]:=3

{#, #} & /@ {a, b, c, d}

Out[3]=3

Apply applies a function to multiple arguments:

In[1]:=1

Apply[f, {a, b, c, d}]

Out[1]=1

Notes for Python programmers:

Apply in the Wolfram Language is similar to the unpacking operator * in Python.

Expressions have "levels"—corresponding to the number of indices needed to extract a part. Functions like Map can operate at specific levels.

Notes for Java programmers:

"Levels" are another name for dimensions of an array, but generalized for all symbolic expressions. Multi-dimensional operations like this are not built into Java and would normally require loops.

Notes for Python programmers:

"Levels" are like dimensions of an array, but generalized for all symbolic expressions. Python's array functions are typically set up only for one-dimensional arrays.

Map defaults to operate at level 1:

In[1]:=1