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Mathematica > Core Language > List Manipulation > Math & Counting Operations on Lists >

Built-in Mathematica Symbol

Differences

Differences[list]
gives the successive differences of elements in list.

Differences[list, n]
gives the n

differences of list.

Differences[list, {n₁, n₂, ...}]
gives the successive n_k

differences at level k in a nested list.

Differences[m, {1, 0}] or Differences[m, 1] finds the successive differences of rows in a 2D array or matrix m. Differences[m, {0, 1}] finds the differences of columns.

Differences[list, {n₁, n₂}] is equivalent to Differences[Differences[list, n₁], {0, n₂}].

First differences:

Second differences:

First differences:

Second differences:

Differences of rows, within each column:

Differences of columns, within each row:

Deduce the degree of a sequence by seeing when successive differences become constant:

Finite difference approximation to the Laplacian of a Gaussian:

First differences are constant for a linear function:

Second differences are constant for a quadratic function:

Successive differences are progressively shorter:

FoldList acts as an inverse of Differences:

Successive differences mod 2 of a sequence based on the primes:

Pascal-triangle-like pattern: