AtomQ
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`AtomQ`

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AtomQ[expr]

yields True if expr is an expression which cannot be divided into subexpressions, and yields False otherwise.

Details

You can use AtomQ in a recursive procedure to tell when you have reached the bottom of the tree corresponding to an expression.
AtomQ gives True for symbols, numbers, strings, and other raw objects, such as sparse arrays.
AtomQ gives True for any object whose subparts cannot be accessed using functions like Map.

Examples

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Basic Examples (1)Summary of the most common use cases

Test if an expression cannot be subdivided:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-k2be3

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0cqzylab-epzva5

Out[2]=2

Since it is not an atom, its parts can be extracted:

In[3]:=3

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https://wolfram.com/xid/0cqzylab-cabb5g

Out[3]=3

This is a number that is an atom:

In[4]:=4

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https://wolfram.com/xid/0cqzylab-kf3sxf

Out[4]=4

Scope (6)Survey of the scope of standard use cases

Strings are not subdividable:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-1nd8i

Out[1]=1

Symbols are not subdividable:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-8hmg3

Out[1]=1

Numbers are not subdividable:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-far6y8

Out[1]=1

Rational numbers appear to have a compound structure:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-bsk1pa

As numbers, they are not subdividable:

In[2]:=2

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https://wolfram.com/xid/0cqzylab-eg34nn

Out[2]=2

The parts can be accessed through Numerator and Denominator:

In[3]:=3

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https://wolfram.com/xid/0cqzylab-e2jodr

Out[3]=3

Complex numbers appear to have a compound structure:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-bsc4t3

As numbers, they are not subdividable:

In[2]:=2

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https://wolfram.com/xid/0cqzylab-cu8wf6

Out[2]=2

The parts can be accessed through Re and Im:

In[3]:=3

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https://wolfram.com/xid/0cqzylab-f8rh1

Out[3]=3

SparseArray objects are atomic raw objects:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-mbixji

Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0cqzylab-jdun89

Out[2]=2

Commands that work with SparseArray objects typically do so on the represented array:

In[3]:=3

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https://wolfram.com/xid/0cqzylab-lk00k

Out[3]=3

In[4]:=4

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https://wolfram.com/xid/0cqzylab-eu6q9

Out[4]=4

In[5]:=5

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https://wolfram.com/xid/0cqzylab-qxw9je

Out[5]=5

The FullForm of a SparseArray object is designed to be sufficient to reconstruct the raw object:

In[6]:=6

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https://wolfram.com/xid/0cqzylab-c81bjf

In[7]:=7

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https://wolfram.com/xid/0cqzylab-bgsy21

Out[7]=7

Applications (2)Sample problems that can be solved with this function

Find the number of unsubdividable leaves in an expression:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-2oo76

A deeply nested expression:

In[2]:=2

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https://wolfram.com/xid/0cqzylab-savvp

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0cqzylab-f9jdq0

Out[3]=3

This is equivalent to LeafCount:

In[4]:=4

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https://wolfram.com/xid/0cqzylab-dzln3i

Out[4]=4

With the option Heads->False, only atoms with no branches are counted:

In[5]:=5

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https://wolfram.com/xid/0cqzylab-ctagw2

Out[5]=5

This corresponds to the dangling leaves you see with TreeForm:

In[6]:=6

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https://wolfram.com/xid/0cqzylab-e49qrx

Find the minimum and maximum "depth" of an expression:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-dj93a7

In[2]:=2

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https://wolfram.com/xid/0cqzylab-fkc1k3

Out[2]=2

In[3]:=3

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https://wolfram.com/xid/0cqzylab-il22ls

Out[3]=3

Depth gives the maximum depth plus 1:

In[4]:=4

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https://wolfram.com/xid/0cqzylab-fsqem4

Out[4]=4

Properties & Relations (1)Properties of the function, and connections to other functions

Map[f,expr,{-1}] generally maps f on atoms in expr:

In[1]:=1

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https://wolfram.com/xid/0cqzylab-bkmmbb

Out[1]=1

This is equivalent to the following recursive function:

In[2]:=2

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https://wolfram.com/xid/0cqzylab-ear85r

In[4]:=4

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https://wolfram.com/xid/0cqzylab-fykpeo

Out[4]=4

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