Length

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Length[expr]

gives the number of top-level elements in expr (the arity of its head). Length of any atom is 0.

Examples (5)

Every input below was run against the current Mathilda build and its output recorded.

Basic examples (1)

In[1]:= Length[{a, b, c}]
Out[1]= 3

Applications (4)

The number of elements of a list

In[2]:= Length[{a, b, c}]
Out[2]= 3

The argument count of any function

In[3]:= Length[f[x, y]]
Out[3]= 2

Plus[a, b, c] has three arguments

In[4]:= Length[a + b + c]
Out[4]= 3

An atom has no parts

In[5]:= Length[x]
Out[5]= 0

Performance

Against other systems, from the benchmark suite (same input, results cross-checked for agreement):

case	Mathilda	Wolfram	Python
GroebnerBasis cyclic-5	43.5 s	18 s	8.78e+03 s
NSolve degree 40	9.27 s	0.779 s	341 s
Factor x^120 - 1	7.01 s	0.044 s	3.85 s
Graph construction, 40000 edges	5.81 s	3.98 s	14.7 s
Characters of 200k chars	4.38 s	2.54 s	0.419 s
StringSplit on space, 200k chars	3.12 s	4.13 s	0.723 s

Implementation notes

builtin_length (in src/core.c) returns an EXPR_INTEGER equal to the argument's arg_count when it is an EXPR_FUNCTION, and 0 for atoms (which have no parts).

• Returns the count of top-level arguments for functions.
• Returns 0 for all atomic expressions.

Attributes: none registered.

References

• Source: src/core.c
• Specification: docs/spec/builtins/structural-manipulation.md
• Tests: tests/test_assoc_atomicity.c
• Tests: tests/test_association.c
• Tests: tests/test_autocompile.c
• Tests: tests/test_basin_hopping.c

Notes & additional examples

Notes

Length[expr] returns the number of top-level arguments (arg_count) when expr is a function, and 0 for every atom — a symbol, number, or string has no parts. Because a sum is Plus[...] and a list is List[...] internally, the same count works on both; Length makes no distinction between a List and any other head.