translate,
vb. 1. (Euclidean geometry) to move (a figure or body) laterally, without rotation, dilation, or angular displacement, as in the figure below.
- n. 2. the image of some figure or body under a translation; in the figure below, KLM is a translate of ABC.
ABC and KLM are translates.
3. (Topological groups) the function derived from a given function f on a group G when the argument is multiplied (on the left or right) by a given element a of G; that is, the left translate of f by a, denoted La f or af, and the right translate, Ra f or fa, are respectively defined by
La f(x) = f(ax) and Ra f(x) = f(xa)
for all x in G.
- n. 2. the image of some figure or body under a translation; in the figure below, KLM is a translate of ABC.
3. (Topological groups) the function derived from a given function f on a group G when the argument is multiplied (on the left or right) by a given element a of G; that is, the left translate of f by a, denoted La f or af, and the right translate, Ra f or fa, are respectively defined by
La f(x) = f(ax) and Ra f(x) = f(xa)
for all x in G.