WolframLang: Get Parts of List

By Xah Lee. Date: 2022-07-04. Last updated: 2023-12-22.

There are many functions that extract sub-expression:

Part → get top-level elements by index, or index range, or get a column of matrix, or get value from Association (Hashtable, Map, Dictionary) This is the most versatile and most frequently used function to get part of a expression.
Extract → get any arbitrarily nested element by its Position. This is the most simple and logical.

Select → get elements by a filtering function.
Cases → get elements by Pattern.

Get Parts by Index

Part[expr, i]

🔸 SHORT SYNTAX: expr[[i]]

ith part of expr. If i is negative, count from right.

Part

x = {a, b, c, {d1, d2}, e};
Part[x, 2] === b

(* short syntax *)
x[[2]] === b

(* count from right *)
x[[-2]] === {d1, d2}

Part[expr, {a, b, c}]

🔸 SHORT SYNTAX: expr[[{a, b, c}]]

Same as { Part[expr, a], Part[expr, b], Part[expr, c] }

x = {a, b, c, {d1, d2}, e};
x[[{2,-1}]] === {b, e}

Part[expr, a, b, c]

🔸 SHORT SYNTAX: expr[[a, b, c]]

same as Part[Part[Part[expr, a], b], c]

x = {a, b, c, {d1, d2}, e};
x[[4,1]] === d1

Part[expr, m;;n]

🔸 SHORT SYNTAX: expr[[m;;n]]

(note: a;;b is short for Span[a, b])

parts m through n. If m is omitted, default to beginning. If n is omitted, default to end.

x = {a, b, c, {d1, d2}, e};
x[[2;;4]] === {b, c, {d1, d2}}

expr[[m;;]] → part m to end
expr[[;;n]] → beginning to n
expr[[;;,j]] → column j
expr[[m1;;n1, m2;;n2]] → submatrix

(* column 1 *)
{{a,b}, {c,d}}[[;;,1]] === {a, c}

Get Element by Position Spec: Extract

Extract

Extract[expr, position]
Extract[expr, {pos1, pos2, etc}]

return the part of expr at a given Position, or a list of them. .

Extract

💡 TIP: this is the most logical way to get a subexpression, or a list of them. But is not convenient if you want a range of adjacent expressions.

xx = {a, {{b,c}, d}, e};

Extract[ xx, {1} ] === a
Extract[ xx, {2} ] === {{b, c}, d}
Extract[ xx, {3} ] === e
Extract[ xx, {2, 1} ] === {b, c}
Extract[ xx, {2, 1, 1} ] === b

(* extract multiple items *)
Extract[ xx, { {3}, {2, 1, 1} } ] === {e, b}

Get Parts by Filter Function

Select

Get elements by a filter function

Select

Select[ {3,4,5,6}, EvenQ ] === {4, 6}

Select[ Range[20], PrimeQ ] === {2, 3, 5, 7, 11, 13, 17, 19}

Select[
 {{3}, {0, 23}, {9}, {4,5,6}},
 Function[ Length[#] === 2 ]
] === {{0, 23}}

Get Parts by Pattern

Cases

Get elements by Pattern

Cases

Cases[ {a, f[3], f[9]}, f[_] ] === {f[3], f[9]}

Cases[ {a, f[3], g[4], f[5]}, _[_] ] === {f[3], g[4], f[5]}

Cases[ {{2}, {4, 8}, {c}}, {_ , _} ] === {{4, 8}}