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Math & Counting Operations on Lists—Wolfram Language Documentation

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• Functions
  • Accumulate
  • BinCounts
  • Commonest
  • Complement
  • CoordinateBoundingBox
  • CoordinateBounds
  • Count
  • CountDistinct
  • CountDistinctBy
  • Counts
  • Differences
  • Dot
  • Fold
  • Interpolation
  • Intersection
  • Length
  • Listable
  • LongestCommonSubsequence
  • Max
  • MaximalBy
  • Mean
  • Median
  • Min
  • MinimalBy
  • MinMax
  • Nearest
  • Norm
  • Normalize
  • Ordering
  • OrderingBy
  • Projection
  • Ratios
  • SequenceAlignment
  • SequenceCases
  • SequenceCount
  • SequencePosition
  • Sort
  • SortBy
  • Subsets
  • TakeLargest
  • TakeLargestBy
  • TakeSmallest
  • TakeSmallestBy
  • Total
  • Union
  • Variance
• Related Guides
  • Handling Numerical Data
  • Discrete Mathematics
• Tech Notes
  • Operations on Scalars, Vectors, and Matrices
  • Manipulating Expressions like Lists
  • Testing and Searching List Elements
  • Basic Statistics
  • Partitioning Data into Clusters

Ordinary mathematical functions in the Wolfram Language are always "listable", so that they are immediately applied in parallel across lists. The Wolfram Language provides a wide variety of tightly integrated functions for analyzing elements in lists of any size and structure.

{..}+{..}, etc. — automatically operate in parallel on list elements

Listable — attribute carried by math functions specifying automatic threading over lists

Length — number of elements in a list

Total — total from adding up elements in a list

Accumulate  ▪  Differences  ▪  Ratios  ▪  Fold

Count — count how many elements match a pattern

Counts — make an association giving the number of copies of each distinct element

BinCounts — count the number of elements in a sequence of bins

CountDistinct — count the number of distinct elements

CountDistinctBy — count distinct values from applying a function

Max  ▪  Min  ▪  MinMax  ▪  Commonest  ▪  Sort  ▪  SortBy  ▪  Ordering  ▪  OrderingBy

MaximalBy, MinimalBy — maximal, minimal elements based on a criterion

TakeLargest  ▪  TakeSmallest  ▪  TakeLargestBy  ▪  TakeSmallestBy

CoordinateBounds  ▪  CoordinateBoundingBox

Mean  ▪  Variance  ▪  Median  ▪  Interpolation  ▪  Nearest  ▪  ...

Dot  ▪  Norm  ▪  Normalize  ▪  Projection  ▪  ...

Union  ▪  Intersection  ▪  Complement  ▪  Subsets

SequencePosition — find positions of sublists

SequenceCount  ▪  SequenceCases

LongestCommonSubsequence  ▪  SequenceAlignment  ▪  ...

▪
• Operations on Scalars, Vectors, and Matrices
▪
• Manipulating Expressions like Lists
▪
• Testing and Searching List Elements
▪
• Basic Statistics
▪
• Partitioning Data into Clusters

▪
• Handling Numerical Data
▪
• Discrete Mathematics

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