Count

The number of elements equal to value in the collection.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageCount✓↗

Count(collection, value)the number of elements equal to value.

Count(QuotientRing(Integers, m))$m$ exactly, past $2^{53}$ too (the quotient-ring-collection patch).

Count(collection, value, level)matches counted down to level (levels 1 through level), or — with level written as $\{level\}$ — at that level only.

Typed signatures

Type	Package	Applies
(collection<any>, any?) -> infinity | integer	combinatoricsreplaces compute-engine	always
(collection<any>, any?) -> infinity | integer	compute-engine	always
(collection<any>, any?) -> infinity | integer	residuesreplaces compute-engine	always

Domain: Collections

Details

• A value absent from the collection counts as 0.
• A lazy family's count past $2^{53}$ comes back as the exact integer, when its kernel counts in bigint.
• Tests exact equality against a fixed value — not a Wolfram-style typed pattern like _Integer.
• See Length for the total element count, and IndexOf for a single matching position.
• A bare integer level spec counts matches at every level from 1 through it; $\{level\}$ counts that level only.

Examples

6 more kept as data, checked against the oracles

Basic #

live ↗

In$\mathrm{Count}(\bigl\lbrack1, 2, 2, 3, 2\bigr\rbrack, 2)$Out$3$

live ↗

In$\mathrm{Count}(\bigl\lbrack1, 2, 2, 3, 2, 4\bigr\rbrack, 2)$Out$3$

A value absent from the collection counts as 0

live ↗

In$\mathrm{Count}(\bigl\lbrack1, 2, 3\bigr\rbrack, 9)$Out$0$

live ↗

In$\mathrm{Count}(\bigl\lbrack a, b, a, a, b, c, b\bigr\rbrack, b)$Out$3$

Scope #

The value can itself be a list

live ↗

In$\mathrm{Count}(\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack1, 2\bigr\rbrack, 3\bigr\rbrack, \bigl\lbrack1, 2\bigr\rbrack)$Out$2$

A predicate counts the elements satisfying it, like Wolfram's pattern test $\_?(\# > 2 \&)$

live ↗

In$\mathrm{Count}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, ()↦\operatorname{\_1}\gt2)$Out$2$

Only top-level elements are compared by default

live ↗

In$\mathrm{Count}(\bigl\lbrack\bigl\lbrack a, a, b\bigr\rbrack, b, \bigl\lbrack a, b, a\bigr\rbrack\bigr\rbrack, b)$Out$1$

A bare level spec counts matches down through level 2

live ↗

In$\mathrm{Count}(\bigl\lbrack\bigl\lbrack a, a, b\bigr\rbrack, b, \bigl\lbrack a, b, a\bigr\rbrack\bigr\rbrack, b, 2)$Out$3$

$\{2\}$ counts matches at level 2 only

live ↗

In$\mathrm{Count}(\bigl\lbrack\bigl\lbrack a, a, b\bigr\rbrack, b, \bigl\lbrack a, b, a\bigr\rbrack\bigr\rbrack, b, \bigl\lbrack2\bigr\rbrack)$Out$2$

Without a value to match, Count gives the cardinality of the collection itself

live ↗

In$\mathrm{Count}(\mathrm{FactorialNumbers})$Out$∞$

Properties #

The counts of the distinct values add up to the Length

live ↗

In$\mathrm{Count}(\bigl\lbrack1, 2, 2, 3, 3, 3\bigr\rbrack, 1)+\mathrm{Count}(\bigl\lbrack1, 2, 2, 3, 3, 3\bigr\rbrack, 2)+\mathrm{Count}(\bigl\lbrack1, 2, 2, 3, 3, 3\bigr\rbrack, 3)=\mathrm{Length}(\bigl\lbrack1, 2, 2, 3, 3, 3\bigr\rbrack)$Out$\mathrm{True}$

Possible issues #

Count tests exact equality; a typed pattern like _Integer matches nothing

live ↗

In$\mathrm{Count}(\bigl\lbrack1, a, 2, b\bigr\rbrack, \operatorname{\_Integer})$Out$0$

Wolfram's _Integer pattern counts every integer element, here 2 (1 and 2).

Count tests exact equality, so a pattern like $\_Integer$ matches nothing

live ↗

In$\mathrm{Count}(\bigl\lbrack a, 2, a, a, 1, c, b, 3, 3\bigr\rbrack, \operatorname{\_Integer})$Out$0$

Wolfram's _Integer pattern counts every integer element, here 4 (2, 1, 3, 3).

About

Examples	19
Checked against	Wolfram Language 10 agree
Crosswalk	Wolfram Language

See also: Length, IndexOf