Math & Counting Operations on Lists

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

MaximalBy, MinimalBy maximal, minimal elements based on a criterion

TakeLargest  ▪  TakeSmallest  ▪  TakeLargestBy  ▪  TakeSmallestBy

Multidimensional Arrays

CoordinateBounds  ▪  CoordinateBoundingBox

Statistical Analysis »

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

Vector-Oriented Operations »

Dot  ▪  Norm  ▪  Normalize  ▪  Projection  ▪  ...

Set-Oriented Operations

Union  ▪  Intersection  ▪  Complement  ▪  Subsets

Sequence-Related Operations »

SequencePosition find positions of sublists

SequenceCount  ▪  SequenceCases

LongestCommonSubsequence  ▪  SequenceAlignment  ▪  ...