Level

Every subexpression of expr at the given level(s) — level 0 is expr itself.

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

Level(expr, n)levels 1 through n

Level(expr, {n})level n alone

Level(expr, {n1, n2})levels n1 through n2

Level(expr, PositiveInfinity)every level, all the way to the leaves

Level(expr, {-1})every leaf, regardless of depth — Wolfram's own "leaves" shorthand

Typed signatures

Type	Package	Applies
(any, any) -> list<any>	combinatorics	always

Domain: Collections

Details

• Wolfram's own POST-ORDER: a node's children (recursively) come before the node itself, so Level({1, {2, 3}, 4}, 2) is {1, 2, 3, {2, 3}, 4} — {2, 3} printed AFTER its own parts, not before them. Siblings keep their original order; only each node's position relative to its OWN descendants moves.
• A negative level counts depth from the leaves (an atom has depth 1, any other expression 1 more than its deepest part): {-1} is the leaves, {-2} the expressions one step above them, and bare -1 every proper subexpression.
• No 4th-argument predicate form, and no Heads option.

Examples

Basic #

live ↗

In$\mathrm{Level}(\bigl\lbrack1, \bigl\lbrack2, 3\bigr\rbrack, 4\bigr\rbrack, 1)$Out$\bigl\lbrack1, \bigl\lbrack2, 3\bigr\rbrack, 4\bigr\rbrack$

Scope #

live ↗

In$\mathrm{Level}(\bigl\lbrack1, \bigl\lbrack2, 3\bigr\rbrack\bigr\rbrack, \bigl\lbrack0\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack1, \bigl\lbrack2, 3\bigr\rbrack\bigr\rbrack\bigr\rbrack$

post-order: {2, 3} prints after its own parts 2 and 3

live ↗

In$\mathrm{Level}(\bigl\lbrack1, \bigl\lbrack2, 3\bigr\rbrack, 4\bigr\rbrack, 2)$Out$\bigl\lbrack1, 2, 3, \bigl\lbrack2, 3\bigr\rbrack, 4\bigr\rbrack$

{-1} is Wolfram's own leaves shorthand

live ↗

In$\mathrm{Level}(\bigl\lbrack1, \bigl\lbrack2, 3\bigr\rbrack, 4\bigr\rbrack, \bigl\lbrack-1\bigr\rbrack)$Out$\bigl\lbrack1, 2, 3, 4\bigr\rbrack$

live ↗

In$\mathrm{Level}(\bigl\lbrack1, \bigl\lbrack2, \bigl\lbrack3\bigr\rbrack\bigr\rbrack\bigr\rbrack, ∞)$Out$\bigl\lbrack1, 2, 3, \bigl\lbrack3\bigr\rbrack, \bigl\lbrack2, \bigl\lbrack3\bigr\rbrack\bigr\rbrack\bigr\rbrack$

Level $1$ is the single top-level element

live ↗

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

Level $2$ collects the parts one deeper along with the earlier ones

live ↗

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

Each added level contributes a more deeply nested piece

live ↗

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

Down to the innermost atom $a$

live ↗

In$\mathrm{Level}(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 4)$Out$\bigl\lbrack a, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack$

Asking for more levels than exist changes nothing

live ↗

In$\mathrm{Level}(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 5)$Out$\bigl\lbrack a, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack$

A list of levels selects just those

live ↗

In$\mathrm{Level}(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack2, 3\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack a\bigr\rbrack, \bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack$

live ↗

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

About

Examples	12
Checked against	Wolfram Language 12 agree
Crosswalk	Wolfram Language

See also: MapIndexed, Pick