Skip to content

Tally

Status: Stable

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

Description

Tally[list] counts the number of occurrences of each distinct element in list.

Examples

All examples below are verified against the current Mathilda build.

In[1]:= Tally[{a, a, b, a, c, b, a}]
Out[1]= {{a, 4}, {b, 2}, {c, 1}}

Implementation notes

Algorithm. builtin_tally counts distinct elements, returning {element, multiplicity} pairs in first-occurrence order. With the default sameness test it uses a chained hash table (expr_hash for bucketing, expr_eq for equality) for O(n) expected counting; with a custom two-argument test it falls back to an O(n²) linear scan, evaluating test[a, b] per comparison. Multiplicities are tracked in a parallel int64_t array.

  • Protected.
  • Returns a list of {element, count} pairs.
  • Elements appear in the order of their first occurrence.

Attributes: Protected.

Implementation status

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

References

Notes & additional examples

Worked examples

In[1]:= Tally[{a, b, a, c, b, a}]
Out[1]= {{a, 3}, {b, 2}, {c, 1}}

In[1]:= Tally[Table[Mod[n^2, 5], {n, 0, 20}]]
Out[1]= {{0, 5}, {1, 8}, {4, 8}}

In[1]:= Tally[Table[GCD[n, 12], {n, 1, 12}]]
Out[1]= {{1, 4}, {2, 2}, {3, 2}, {4, 2}, {6, 1}, {12, 1}}

Notes

Tally[list] returns {element, count} pairs for each distinct element, in the order of first appearance. It is a compact way to read off the distribution of a computed sequence — for example, the multiplicities of the quadratic residues mod 5 ({0, 1, 4} appearing 5, 8, and 8 times among n = 0 .. 20), or the divisor structure of GCD[n, 12].