You are logged on to the database as a database user.
You have the ALTER privilege for the table to which the column belongs.
More information: SQL Reference Manual, Privilege Specification (priv_spec)
Columns have been created for the table already.
The database is in the ONLINE operational state.
A constraint for a column is an integrity condition that must be met by all column values.
SQL Reference Manual, Constraint Definition (constraint_definition)