Position
Details and Options
- Position[expr,pattern] tests all the subparts of expr in turn to try and find ones that match pattern.
- Position returns a list of positions in a form suitable for use in Extract, ReplacePart, and MapAt. The form is different from the one used in Part.
- Position looks only for matches to values in Association objects that appear in expr. It returns any part specifications within Association objects in the form Key[k]. »
- The default level specification for Position is {0,Infinity}, with Heads->True.
- A part specification {} returned by Position represents the whole of expr.
- Position[list,pattern,{1},Heads->False] finds positions only of objects that appear as complete elements of list.
- Position uses standard level specifications:
-
n levels 1 through n Infinity levels 1 through Infinity {n} level n only {n1,n2} levels n1 through n2 - A positive level n consists of all parts of expr specified by n indices.
- A negative level -n consists of all parts of expr with depth n.
- Level 0 corresponds to the whole expression.
- With the default option setting Heads->True, Position includes heads of expressions and their parts.
- Position traverses expressions in depth‐first order, yielding lists of indices in lexicographic order.
- Position[pattern][expr] is equivalent to Position[expr,pattern]. »
Examples
open all close allBasic Examples (3)
Find the positions at which b occurs:
Position[{a, b, a, a, b, c, b}, b]Position[{{a, a, b}, {b, a, a}, {a, b, a}}, b]Find all positions at which x to any power appears:
Position[{1 + x ^ 2, 5, x ^ 4, a + (1 + x ^ 2) ^ 2}, x ^ _]Find only those down to level 2:
Position[{1 + x ^ 2, 5, x ^ 4, a + (1 + x ^ 2) ^ 2}, x ^ _, 2]Find positions with prime values in an association:
Position[<|"a" -> 1, "b" -> 2, "c" -> 3, "d" -> 4|>, _Integer ? PrimeQ]Scope (5)
Find the positions of the first 2 b's that appear on level 1:
Position[{a, b, a, a, b, c, b, a, b}, b, 1, 2]op = Position[_Integer]op[{1, 1, f[a], 2, 3, y, f[8], 9, f[10]}]Get the positions of entries in a matrix that are symbols:
Position[{{a, 2}, {3, d}}, _Symbol, {2}, Heads -> False]Without HeadsFalse, the positions of the head List in each row would also be returned:
Position[{{a, 2}, {3, d}}, _Symbol, {2}]Extract[{{a, 2}, {3, d}}, %]Find positions inside an Association:
Position[<|{1 -> 1 + x ^ 2, 2 -> <|"a" -> x ^ 2|>, 3 -> x ^ 4, 4 -> a + (1 + x ^ 2) ^ 2}|>, x ^ _]Position works with any head:
Position[f[a, b, b, a], b]Options (1)
Properties & Relations (6)
Use Extract to extract parts based on results from Position:
u = {1 + x^2, 5, x^4, a + (1 + x^2)^2};Position[u, x ^ _]Extract[u, %]Position[expr,expr] returns {{}}, a list containing position {}, that means the whole expression:
Position[x, x]This returns an empty list of positions, because y was found nowhere in x:
Position[x, y]Depth-first traversal gives longer lists of indices first:
Position[f[g[h[x]]], _, Infinity]The keys of an association are not matched by Position:
Position[<|"a" -> {1, b}|>, "a"]However, keys are used to return positions inside of associations:
Position[<|"a" -> {1, b}|>, _]Position[p][e] is equivalent to Position[e,p]:
Position[_][{a, b}] === Position[{a, b}, _]Count returns the length of the result given by Position:
Length[Position[{1, "f", g, "h", "7"}, _ ? StringQ]]Count[{1, "f", g, "h", "7"}, _ ? StringQ]Possible Issues (1)
An Elementary Introduction to the Wolfram Language
NKS|OnlineText
Wolfram Research (1988), Position, Wolfram Language function, https://reference.wolfram.com/language/ref/Position.html (updated 2014).
CMS
Wolfram Language. 1988. "Position." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/Position.html.
APA
Wolfram Language. (1988). Position. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Position.html