Vertica provides CREATE statements for each type of user-defined extension. Each CREATE statement adds a user-defined function to the Vertica catalog:

CREATE statement Extension
CREATE FUNCTION (Scalar) User-defined scalar functions (UDSFs)
CREATE AGGREGATE FUNCTION User-defined aggregate functions (UDAFs)
CREATE ANALYTIC FUNCTION User-defined analytic functions (UDAnF)
CREATE TRANSFORM FUNCTION User-defined transform functions (UDTFs)
CREATE statements for user-defined load:
CREATE SOURCE Load source functions
CREATE FILTER Load filter functions
CREATE PARSER Load parser functions

Vertica also provides CREATE FUNCTION (SQL), which stores SQL expressions as functions that you can invoke in a query.