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Wolfram Language & System Documentation Center
MaximalBy
  • See Also
    • MinimalBy
    • Max
    • TakeLargest
    • TakeLargestBy
    • FindMaximum
    • Maximize
    • RankedMax
    • ReverseSortBy
    • Ordering
  • Related Guides
    • Math & Counting Operations on Lists
    • Functional Programming
    • Elements of Lists
    • Function Composition & Operator Forms
    • Tabular Objects
    • See Also
      • MinimalBy
      • Max
      • TakeLargest
      • TakeLargestBy
      • FindMaximum
      • Maximize
      • RankedMax
      • ReverseSortBy
      • Ordering
    • Related Guides
      • Math & Counting Operations on Lists
      • Functional Programming
      • Elements of Lists
      • Function Composition & Operator Forms
      • Tabular Objects

MaximalBy[data,f]

returns a list of the elements ei of data for which the value of f[ei] is maximal.

MaximalBy[data,f,n]

returns a list of the elements ei of data corresponding to the n largest f[ei].

MaximalBy[data,f,n,p]

uses the ordering function p for sorting.

MaximalBy[f]

represents an operator form of MaximalBy that can be applied to an expression.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page
BUILT-IN SYMBOL
  • See Also
    • MinimalBy
    • Max
    • TakeLargest
    • TakeLargestBy
    • FindMaximum
    • Maximize
    • RankedMax
    • ReverseSortBy
    • Ordering
  • Related Guides
    • Math & Counting Operations on Lists
    • Functional Programming
    • Elements of Lists
    • Function Composition & Operator Forms
    • Tabular Objects
    • See Also
      • MinimalBy
      • Max
      • TakeLargest
      • TakeLargestBy
      • FindMaximum
      • Maximize
      • RankedMax
      • ReverseSortBy
      • Ordering
    • Related Guides
      • Math & Counting Operations on Lists
      • Functional Programming
      • Elements of Lists
      • Function Composition & Operator Forms
      • Tabular Objects

MaximalBy

MaximalBy[data,f]

returns a list of the elements ei of data for which the value of f[ei] is maximal.

MaximalBy[data,f,n]

returns a list of the elements ei of data corresponding to the n largest f[ei].

MaximalBy[data,f,n,p]

uses the ordering function p for sorting.

MaximalBy[f]

represents an operator form of MaximalBy that can be applied to an expression.

Details

  • By default, values of f[ei] are compared using Order, the same canonical order as in Sort.
  • MaximalBy[data,f] returns the list of maximal elements ei of data in the order they appear in the input.
  • MaximalBy[data,f,n] returns the ei sorted in the order of decreasing f[ei], with those having the same value of f[ei] being taken in the order they appear in data.
  • The data can have the following forms:
  • {e1,e2,…}list of values, including numbers, quantities, dates, ...
    Association[…]association of values »
    QuantityArray[…]quantity array or other structured array »
    Tabular[…]type-consistent tabular data »
    TabularColumn[…]type-consistent column data »
    Dataset[…]general hierarchical data »
  • For tabular data tab, MaximalBy[tab,f,…] applies the function f to individual rows of tab, with the row being an association <|col1val1,…|> if tab has column keys or a list {val1,…} if tab does not have column keys.
  • MaximalBy[data,f, UpTo[n]] gives n elements, or as many as are available. »
  • MaximalBy[f][data] is equivalent to MaximalBy[data,f]. »

Examples

open all close all

Basic Examples  (4)

Find the maximal element by its last part:

Do the same using the operator form of MaximalBy:

All maximal elements are returned, in order of appearance:

Obtain the first three maximal elements:

Prune an association to its maximal values:

Scope  (10)

Obtain the first four maximal elements or as many as are available:

MaximalBy works with symbolic expressions, using canonical Order by default:

Find maximal element in a list of comparable quantities with various units:

Comparing by QuantityMagnitude loses the unit information:

Find numerically largest element:

MaximalBy works on QuantityArray:

MaximalBy will order dates according to canonical order by default:

Convert the dates to absolute times to sort them numerically:

Equivalently, convert the dates to DateObject form and use NumericalOrder instead of Order:

Take the letters of the Polish alphabet:

Transliterate them to the Hiragana script:

These are the five largest Polish letters according to canonical order:

These are the five largest Polish letters according to the rules of the Polish alphabet:

These are the five largest Polish letters according to canonical order of their Hiragana transliteration:

These are the five largest Polish letters according to alphabetic order in Japanese of their transliteration:

Construct a TabularColumn object with 100 words:

Select the five longest words:

Normalize the result to a list:

Find the four rows in a Tabular object with largest values in a given column:

Use general functional notation instead of the column name:

Use function of both columns:

Take a dataset of the solar system planets:

Find the three planets with the maximal number of moons:

When there are common values of f[ei] for different elements ei, the original order will be kept:

Applications  (3)

Find the four longest texts available in ExampleData["Text"]:

Find the five constellations with maximal number of bright stars:

Take a dataset of the solar system planets:

Find the two planets with the maximal mass:

Properties & Relations  (3)

MaximalBy[{e1,e2,…},f,n] compares values f[ei] using canonical Order:

TakeLargestBy[{e1,e2,…},f,n] compares values f[ei] using NumericalOrder:

For a specific ordering function p, MaximalBy[data,f,n,p] is equivalent to TakeLargestBy[data,f,n,p]:

For association, the function f is applied to values:

Possible Issues  (1)

By default, the maximal element is determined using canonical Order, not numerical ordering:

Compare numerical values of the elements of the list:

See Also

MinimalBy  Max  TakeLargest  TakeLargestBy  FindMaximum  Maximize  RankedMax  ReverseSortBy  Ordering

Function Repository: Maximal

Related Guides

    ▪
  • Math & Counting Operations on Lists
  • ▪
  • Functional Programming
  • ▪
  • Elements of Lists
  • ▪
  • Function Composition & Operator Forms
  • ▪
  • Tabular Objects

History

Introduced in 2014 (10.0) | Updated in 2015 (10.3) ▪ 2025 (14.2)

Wolfram Research (2014), MaximalBy, Wolfram Language function, https://reference.wolfram.com/language/ref/MaximalBy.html (updated 2025).

Text

Wolfram Research (2014), MaximalBy, Wolfram Language function, https://reference.wolfram.com/language/ref/MaximalBy.html (updated 2025).

CMS

Wolfram Language. 2014. "MaximalBy." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/MaximalBy.html.

APA

Wolfram Language. (2014). MaximalBy. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MaximalBy.html

BibTeX

@misc{reference.wolfram_2025_maximalby, author="Wolfram Research", title="{MaximalBy}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/MaximalBy.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_maximalby, organization={Wolfram Research}, title={MaximalBy}, year={2025}, url={https://reference.wolfram.com/language/ref/MaximalBy.html}, note=[Accessed: 01-December-2025]}

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