Gather

Group identical elements into sublists, in order of first appearance.

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

Gather(list)elements grouped by equality, in first-appearance order.

Gather(list, test)elements grouped by a custom two-argument equivalence test.

Typed signatures

Type	Package	Applies
(indexed_collection<T>, ((T, T) any -> boolean)?) -> list<list<T>> where T	combinatorics	always

Domain: Collections

Details

• Groups, not runs: every occurrence of a value lands in the same group wherever it appears — unlike Split, which only joins ADJACENT equal elements. See GatherBy to group by a function's value instead of the elements themselves.

Examples

Basic #

live ↗

In$\mathrm{Gather}(\bigl\lbrack1, 7, 3, 7, 2, 3, 9\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack7, 7\bigr\rbrack, \bigl\lbrack3, 3\bigr\rbrack, \bigl\lbrack2\bigr\rbrack, \bigl\lbrack9\bigr\rbrack\bigr\rbrack$

Symbolic elements

live ↗

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

Equal elements are grouped, with groups ordered by first appearance

live ↗

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

A custom equivalence groups pairs sharing a first component

live ↗

In$\mathrm{Gather}(\bigl\lbrack\bigl\lbrack a, 1\bigr\rbrack, \bigl\lbrack b, 1\bigr\rbrack, \bigl\lbrack a, 2\bigr\rbrack, \bigl\lbrack d, 1\bigr\rbrack, \bigl\lbrack b, 3\bigr\rbrack\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\mathrm{First}(\operatorname{\_1})=\mathrm{First}(\operatorname{\_2}))$Out$\bigl\lbrack\bigl\lbrack\bigl\lbrack a, 1\bigr\rbrack, \bigl\lbrack a, 2\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack b, 1\bigr\rbrack, \bigl\lbrack b, 3\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack d, 1\bigr\rbrack\bigr\rbrack\bigr\rbrack$

Scope #

A test decides which elements belong together: here, same parity

live ↗

In$\mathrm{Gather}(\bigl\lbrack1, 2, 3, 4, 5, 6\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_1}\bmod2=\operatorname{\_2}\bmod2)$Out$\bigl\lbrack\bigl\lbrack1, 3, 5\bigr\rbrack, \bigl\lbrack2, 4, 6\bigr\rbrack\bigr\rbrack$

Applications #

Groups the integers $1..10$ into residue classes mod $3$

live ↗

In$\mathrm{Gather}(1..10, (\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_1}\bmod3=\operatorname{\_2}\bmod3)$Out$\bigl\lbrack\bigl\lbrack1, 4, 7, 10\bigr\rbrack, \bigl\lbrack2, 5, 8\bigr\rbrack, \bigl\lbrack3, 6, 9\bigr\rbrack\bigr\rbrack$

Exact rationals are grouped by integer part, giving thirds in each unit interval

live ↗

In$\mathrm{Gather}(0..(0+\frac{1}{3})..3, (\operatorname{\_1}, \operatorname{\_2})↦\lfloor\operatorname{\_1}\rfloor=\lfloor\operatorname{\_2}\rfloor)$Out$\bigl\lbrack\bigl\lbrack0, \frac{1}{3}, \frac{2}{3}\bigr\rbrack, \bigl\lbrack1, \frac{4}{3}, \frac{5}{3}\bigr\rbrack, \bigl\lbrack2, \frac{7}{3}, \frac{8}{3}\bigr\rbrack, \bigl\lbrack3\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{Gather}(\mathrm{data}, \mathrm{test})$Out$\mathrm{Gather}(\mathrm{data}, \mathrm{test})$

Properties #

The group sizes are the multiplicities of the distinct elements

live ↗

In$\mathrm{Map}(\mathrm{Length}, \mathrm{Gather}(\bigl\lbrack1, 7, 3, 7, 2, 3, 9\bigr\rbrack))=\bigl\lbrack1, 2, 2, 1, 1\bigr\rbrack$Out$\mathrm{True}$

About

Examples	9
Checked against	Wolfram Language 9 agree
Crosswalk	Wolfram Language

See also: GatherBy, Split, Union