Extract
Extract[expr,pos]
extracts the part of expr at the position specified by pos.
Extract[expr,{pos1,pos2,…}]
extracts a list of parts of expr.
Extract[expr,pos,h]
extracts parts of expr, wrapping each of them with head h before evaluation.
Details
- For integers i, j, …, Extract[expr,{i,j,…}] is equivalent to Part[expr,i,j,…]. »
- The position specifications used by Extract have the same form as those returned by Position, and used in functions such as MapAt and ReplacePart. »
- An individual position specification pos can also be of the more general form {part1,part2,…}, where the parti are Part specifications such as an integer i, All or Span[…]. »
- Specifications that extract multiple parts at one level retain the head at that level. »
- You can use Extract[expr,…,Hold] to extract parts without evaluation. »
- If expr is a SparseArray object or structured array, Extract[expr,…] extracts parts in the corresponding ordinary array. »
- Extract works on Association objects, using the same specification for keys as in Part. »
- Extract[pos][expr] is equivalent to Extract[expr,pos].
Examples
open allclose allBasic Examples (5)
Extract the second part from an expression:
Do it using the operator form:
Extract a nested part in an expression:
Extract several nested parts from an expression:
Extract the second column of matrix:
Extract the parts given by Position:
Scope (25)
Single versus Multiple Positions (5)
Extract a single element from a list:
Extract several elements from a list:
Extract the part at position {1,3} in a matrix:
Extract the first and third parts (rows) of a matrix:
Extract a length-one list of positions from the matrix:
Extract several elements of the matrix:
Extract the right-hand side of a rule and wrap the result in Hold to prevent evaluation:
Extract several parts from a list and wrap each part in Hold:
Forms Involving All (5)
Extract the second row of a matrix:
Extract the second column of a matrix:
Extract the first and third columns as a 
submatrix:
Extract the first and third columns separately, effectively creating a 
matrix:
Extract the first rule from each list in a list of lists of rules:
Extract the right-hand sides from all the rules in the second list:
Extract the left-hand sides from all the rules in the list of lists:
Extracting using All preserves the head at that level:
Extract all the right-hand sides of a list of rules, preventing evaluation using Hold:
Without the Hold, the expression would evaluate and produce side effects:
Separately extract the two sides in a list of rules, wrapping the two results in HoldComplete:
Associations (6)
Extract a part from an association by key:
If the key is a string, the Key wrapper is optional:
Extract a part from an association by key:
Extract a part from an association by position:
Extract multiple parts from an association:
Extract a nested part from an association:
Extract multiple nested parts from an association:
Extract several values from an association without evaluation:
Without the Hold, the values in the association would evaluate and produce messages:
Special Array Types (3)
If expr is a sparse array, Extract[expr,…] extracts parts in the corresponding ordinary array:
Subarrays are returned as a SparseArray object:
Extract the first and third columns as a single sparse array:
Extracting as two separate columns returns a list of sparse arrays:
Converting to an ordinary array shows the result is the transpose of the first extraction:
Extracting from a structured array extracts parts in the corresponding ordinary array:
When possible, the result is returned as another structured array:
Spans and Sublists (6)
Extract the third through fifth elements of a list:
Extract the elements at odd positions:
Extract a span from a general expression, which keeps the head:
Extract the first two elements from each list:
Extract the first and last element from each list:
Extract the first element of the second through fourth rows:
Extract the second element of the first, third and fourth rows:
Extract the first, second and fifth elements of the last two rows:
Extract the first and fifth columns:
Extract the right-hand side of the first two rules in the list and prevent evaluation:
Properties & Relations (6)
If pos is not a list, pos and {pos} are equivalent specifications:
For a list of integers {i,j,…}, Extract[expr,{i,j,…}] is equivalent to Part[expr,i,j,…]:
Extract[expr,{{i1,i2,…},{j1,j2,…},…}] is equivalent to {Part[expr,i1,i2,…],Part[expr,j1,j2,…],…}:
This extends to the empty list:
Extract is the inverse of Position:
In Extract[expr,{pos1,pos2,…},h], h wraps the result of extracting each of the posi:
If only a single position spec is given, h will be the outermost head:
Specifications that extract multiple parts at one level retain the head at that level:
Possible Issues (2)
Extract[expr,{}] returns an empty list of subexpressions because the list of positions is empty:
Extract[expr,{{}}] extracts the subexpression at position {}, which is the whole expression:
A list of lists in the second argument is always interpreted as a list of position specifications:
As a result, specifications that are equivalent in Part may be treated differently by Extract:
Use a list of lists and remove the extra list at the end if consistency between Part and Extract is needed:
Text
Wolfram Research (1996), Extract, Wolfram Language function, https://reference.wolfram.com/language/ref/Extract.html (updated 2021).
CMS
Wolfram Language. 1996. "Extract." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/Extract.html.
APA
Wolfram Language. (1996). Extract. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Extract.html