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 ▪ OrderingBy
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
LongestCommonSubsequence ▪ SequenceAlignment ▪ ...