Ratios - Wolfram Mathematica 7 Documentation

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Built-in Mathematica Symbol

Ratios[list]
gives the successive ratios of elements in list.

Ratios[list, n]
gives the n

iterated ratios of list.

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

ratios at level k in a nested list.

Ratios divides successive elements by preceding ones, so that Ratios[{x₁, x₂}] gives {x₂/x₁}.

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

First ratios:

Second ratios:

First ratios:

Second ratios:

Ratios of rows, within each column:

Ratios of columns, within each row:

First ratios are constant for a geometric sequence:

FoldList with Times acts as an inverse of Ratios: